Sketch Subjects Michael Thomas De Vlieger

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Subject List

I am an artist at the “triple point of creativity, analytics & spirituality”. This page has become a running tally of themes that at one point and another have influenced me. Oddly, you’ll find work on both sides of the brain, right and left, in this list.

An artist’s portfolio of drawings is often a very deep section of that person’s history; it can’t help but become very personal. (Click here for a chronology of work.) In my case it is a section that cuts right through the development of my latter-day maturity and professional poise to the years when I was insecure, brooding, and vulnerable. The work slices through my formation, through mistaken notions and failure, through discoveries and success. Some prominent characteristics of by-gone days have entirely faded away currently, washed away by time and experience. Other characteristics, like my business methodology, productivity, Catholic spirituality, fatherhood, and husbandhood, rarely show if ever. The fact is that many of the drawings produced in my twenties were attempts at figuring out the world and who I was. Looking at the early sketches is like reading the interior rings of an oak tree, vestiges of winters long gone by, stored in a strong tree trunk. Travelling through my sketchbooks is like visiting the center of a large city; you encounter examples of what the city had been long ago in a different era, now entirely enveloped in what the city is today. I have attempted not to hide anything and allow the viewer to trace through a mind that was complex even in chilhood. I hope you enjoy the portfolio.

My childhood differs from most on the surface because I am a mixed race man, the mestizo son of a Filipina mother and a Navy father, brought up on the outskirts of a rust belt town. More significantly, my history is shaped by early curiosity and precocious skills in literacy, numeracy, and artistic expression. Science, math, language, and art converge to form me into who I am today, a man at the triple-point of reason, creativity, and spirituality. Unlike many, I was a true geek, having adopted nondecimal numbers, invented and evolved a language, and unabashedly expressed these in my sketches. The result is that some aid must be provided to decode what appears in the art. This subject list attempts to do that. Not everything will be rendered comprehensible, but this list does provide some guidance behind the work. The subjects appear alphabetically, with ð following d, þ following t.

In recent years this list has included latter day work in number theory and professional practice as well as drawings, as I am a multipotentiate.

Click on the letters below to jump to a section in the site map:

a# a b c d ð e f g h i j k l m n o p q r s t þ u v w x y z

3-Smooth Arrangement: numeral names for the 3-smooth composites s7836a13.

A numbers.

The items in this section consist of integer sequences listed in the OEIS that I had contributed starting at 11 June 2014 (táyyâ 9357) with A243822. I have written more than a hundred integer sequences, several dozen in collaboration, including a few with Dr. Neil Sloane. This section has become so large that only the favorites are listed here. For a full list and description of each, see this page.

A243822, (V0051), Semidivisor Counting Function ξ_d(n). “Number of ‘semidivisors’ of n, numbers m < n that do not divide n but divide n^ε for some integer ε > 1.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 4, 0, 2, …}. Number of necessarily composite integers 1 < k < n such that k | n^ε with ε > 1, and 1 < GCD(k, n) < k. Semidivisors must be composite since a prime p must either divide or be coprime to n (if k is coprime to n, then GCD(k, n) = 1). ξ_d(n) = r(n) − τ(n) = ξ(n) − ξ_t(n), therefore, ξ_d(n) = n − (τ(n) + φ(n) + ξ_t(n) − 1). In terms of the OEIS, a(n) = A010846(n) − A000005(n) = A045763(n) − A243823(n), or a(n) = n − (A000005(n) + A000010(n) + A243823(n) − 1). 11 June 2014 (táyyâ 9357). See entry at the “OEIS” page on my math site.

A243823, (V0061), Semitotative Counting Function ξ_t(n). “Quantity of ‘semitotatives,’ numbers m < n that are products of at least one prime divisor p of n and one prime q coprime to n”, Reneyan sequence at the Online Encyclopedia of Integer Sequences {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 3, 3, 4, 0, 3, 0, 5, …}. Number of necessarily composite nondivisors ξ_t in the cototient of n such that ξ_t= rt, where r is a product of prime divisors p | n, and t is a product of nondivisor primes q coprime to n. ξ_t(n) = ξ(n) − ξ_d(n) = n − (τ(n) + φ(n) + ξ_d(n) − 1) = n − (r(n) + φ(n) − 1). In terms of the OEIS, a(n) = A045763(n) − A243822(n) = n − (A000005(n) + A000010(n) + A243822(n) − 1) = n − (A010846(n) + A000010(n) − 1). 11 June 2014 (táyyâ 9357). See entry at the “OEIS” page on my math site.

A244052, (V0032), “Highly regular numbers a(n) defined as positions of records in A010846: a(1) = 1 and a(n) is the least number k > a(n − 1) such that A010846(k) > A010846(a(n − 1)),” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 2, 4, 6, 10, 12, 18, 24, 30, 42, 60, 84, …}, 18 June 2014 (táyyâ 9362). Subject of a major study, “Turbulent Candidates”, w9374. See entry at the “OEIS” page on my math site.

A272618, (V0050), “Irregular array read by rows: n-th row contains (in ascending order) the nondivisors 1 ≤ k < n such that all the prime divisors p of k also divide n.” (List of semidivisors ξ_d < n). Reneyan sequence at the Online Encyclopedia of Integer Sequences {0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 8, 0, 8, 9, 0, 4, 8, 9, 0, 0, 4, 8, 12, 16, 0, 8, 16, …}, 3 May 2016 (táyyâ 9833). See the Sequence Page or the entry at the “OEIS” page on my math site.

A272619, (V0060), “Irregular array read by rows: n-th row contains (in ascending order) the numbers 1 ≤ k < n such that at least one prime divisor p of k also divides n and at least one prime divisor q of k is coprime to n.” (List of semitotatives ξ_t < n). Reneyan sequence at the Online Encyclopedia of Integer Sequences {0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 10, 0, 6, 10, 12, 6, 10, 12, 6, 10, 12, 14, 0, 10, 14, 15, 0, 6, 12, 14, 15, 18, …}, 3 May 2016 (táyyâ 9833). See the Sequence Page or the entry at the “OEIS” page on my math site.

A275055, (V1020), Dataset pertaining to divisor counting function τ(n). “Irregular triangle read by rows listing divisors d of n in order of appearance in a matrix of products that arranges the powers of prime divisors p of n along independent axes.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 4, 3, 6, 12, 1, 13, …}. The matrix of products that are divisors of n is arranged such that the powers of the prime divisors range across an axis, one axis per prime divisor. Thus a squarefree semiprime has a 2-dimensional matrix, a sphenic number has 3 dimensions, etc. Generally, the number of dimensions for the matrix of divisors = ω(n) = A001221(n). Because of this, τ(n) * (mod ω(n)) = 0 for n > 1. This follows from the formula for τ(n). Prime divisors p of n are considered in numerical order. Product matrix of tensors T = 1, p, p^2, …, p^e that include the powers 1 ≤ e of the prime divisor p that divide n. Crossrefs: Cf. A027750, A000005 (row length), A000203 (row sums), A056538. This sequence sets the stage for A275280. 14 July 2016 (táyyâ 9893). See the entry at the “OEIS” page on my math site.

A275280, (V3020), Dataset pertaining to the regular counting function r(n). “Irregular triangle listing numbers m of n that have prime divisors p that also divide n, in order of appearance in a matrix of products that arranges the powers of prime divisors p of n along independent axes.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 4, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 4, 8, 5, 10, 1, 11, 1, 2, 4, 8, 3, 6, 12, 9, 1, 13, …}. Product matrix of tensors T = 1, p, p^2,..., p^e that include the powers 1 ≤ e of prime divisors p such that p^e ≤ n. This sequence is analogous to A275055 but differs from it in that the tensors T include not only powers p^e that divide n but all powers p^e ≤ n. The matrix a(n) is bounded by n, thus all products m ≤ n. Let ω(n) = A001221(n). The matrix a(n) has ω(n) dimensions and is an ω(n)-dimensional simplex with (ω(n) − 1) right-angle sides and 1 irregular surface that is bounded by n. A027750(n) is a subset of A162306(n) and in a(n), the terms of A275055(n) appear in an contiguous ω(n)-dimensional parallelepiped (parallelotope) with 1 at the origin and n at the opposite corner. Thus the ω(n)-dimensional array described by A275055(n) is fully contained in the simplex-like matrix described by a(n). Divisors appear within the parallelepiped while nondivisors appear in the field outside the parallelepiped (see examples at A275280). Terms within the parallelepiped appear in A027750(n) while those outside appear in A272618(n). For a(2^x + 2) there is a term m = (n − 2); m ≠ (n − 1) except for n = 2, since GCD(n, n − 1) = 1. a(p^e) = A027750(p^e) = A162306(p^e) = A275055(p^e) for e ≥ 1. Crossrefs: Cf. A162306, A010846 (row length), A243103 (row product), A027750 (divisors of n), A000005 (number of divisors of n), A272618 (nondivisors m ≤ n that have prime divisors p that also divide n), A243822 (number of such nondivisors of n), A275055 (Product of tensor of prime divisor powers that are also divisors). This sequence describes the structure of the “regular matrix” of n, the significance of differences among the distinct primes p of n regarding the regular function r(n), and part of a proof regarding necessary-but-not-sufficient conditions for terms in A244052. 28 July 2016 (táyyâ 98a5). See the entry at the “OEIS” page on my math site.

A275881, Regular-Dominant or Parity Numbers. “Numbers n such that A010846(n) ≥ n/2.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 2, 3, 4, 6, 8, 10, 12, 18, 30}, 25 December 2016 (táyyâ 99ab). Consider integers 1 ≤ r ≤ n such that all prime divisors p | r also divide n: call such numbers r “regular” to n. Divisors d | n are regulars r that themselves divide n along with their prime divisors, while “semidivisors” are nondivisor regular numbers r. This sequence is the finite set of positive integers n that are at parity or dominated by regular numbers. The number 3 has divisors {1, 3} and the nonregular 2. The number 8 has divisors {1, 2, 4, 8} and nonregular {3, 5, 6, 7}. The number 12 has divisors {1, 2, 3, 4, 6, 12} and semidivisors {8, 9} and nonregular {5, 7, 10, 11}. As n increases, the totient dominates the ranges of prime p > 3. The totient counts numbers (“totatives”) 1 ≤ t ≤ n coprime to n; with the exception of t = 1 (the empty product, a divisor and thus regular to all n), all totatives are nonregular since gcd(t, n) = 1. Though there are more regular r than divisors d for n > 30, the ratio of the regular counting function ratio r(n)/n = A010846(n)/n < ½ and generally diminishes as highly divisible n increases. The sequence A244052 shows numbers that set records for the regular counting function. The numbers that arrange the sequence are the primorials A002110. The regular counting function ratio r(n)/n decreases as the primorial increases. This is evident, looking at the way the regular counting function behaves, as seen in A275280 and the Mertens function method for counting regulars. The sequence is provably finite. See the entry at the “OEIS” page on my math site.

A287352, (V0321), “π-code,” Pi-code, “Irregular triangle T(n,k) = A112798(n,1) followed by first differences of A112798(n).” Reneyan sequence at the Online Encyclopedia of Integer Sequences {0, 1, 2, 1, 0, 3, 1, 1, 4, 1, 0, 0, 2, 0, 1, 2, 5, 1, 0, 1, 6, 1, 3, 2, …}. This is a method of coding the indices of all the prime factors p of n with multiplicity, in order from least to greatest. Irregular triangle T(n,k) = first differences of prime divisors p of n. Row lengths = Ω(n) = A001222(n). Row sums = A061395(n). Row maxima = A286469(n). We can concatenate the rows 1 ≤ n ≤ 28 as none of the values of k in this range exceed 9: {0, 1, 2, 10, 3, 11, 4, 100, 20, 12, 5, 101, 6, 13, 21, 1000, 7, 110, 8, 102, 22, 14, 9, 1001, 30, 15, 200, 103}; a(29) = {10}, which would require a digit greater than 9. a(1) = 0 by convention. a(0) is not defined (i.e., null set). a(n) is defined for positive nonzero n. a(p) = A000720(p) for p prime. a(p^e) = A000720(p) followed by (e − 1) zeros. a(product(p^e)) is the concatenation of the a(p^e) of the unitary prime power divisors p^e of n, sorted by the prime p (i.e. the function a(n) mapped across the terms of row n of A141809). a(A002110(n)) = an array of n 1s. T(n,k) could be used to furnish A067255(n). We read data in row n of T(n,k). If T(n,1) = 0, then write 0. If T(n,1) > 0, then increment the k-th place from the right. For k > 1, increment the k-th place to the right of the last-incremented place. T(n,k) can be used to render n in decimal. If T(n,1) = 0, then write 1. If T(n,1) > 0, then multiply 1 by A000720(T(n,1)). For k > 1, multiply the previous product by π(x) = A000720(x) of the running total of T(n,k) for each k. Ignoring zeros in row n > 1 and decoding the remaining values of T(n,k) as immediately above yields the squarefree kernel of n = A007947(n). Leading zeros of a(n) are trimmed, but as in decimal notation numbers that include leading zeros symbolize the same n as without them. Zeros that precede nonzero values merely multiply implicit 1 by itself until we encounter nonzero values. Thus, {0,0,2} = 1 × 1 × π(2) = 3, as {2} = pi(2) = 3. Because of this no row n > 1 has 0 for k = 1 of T(n,k). 23 May 2017 (táyyâ 9aaa). See the Sequence Page or the entry at the “OEIS” page on my math site. I dedicate this sequence, an often-used tool and one I consider to be among my best, to my wife.

A288784, (V3200), Necessary but insufficient condition for highly regular numbers: “Irregular triangle read by rows: T(n,m) is the list of numbers k × p_n#≤ k × t < (k + 1) × p_n# such that ω(k × t) = n, with 1 ≤ k < prime(n + 1).” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 2, 3, 4, 6, 10, 12, 18, 24, 30, 42, 60, 84, 90, 120, 150, 180, 210, …}, 15 June 2017 (táyyâ 9b13). A060735 and A002110 are subsets. This sequence is a necessary but insufficient condition for A244052. Terms that are in A060735 and A002110 are also in A244052. The first terms of this sequence that are not in A244052 are {3, 4290, 881790, 903210, 1009470, 17160990, 363993630, 380570190, 406816410, 434444010, ...}. Primorial p_n# = A002110(n) is the smallest squarefree number with n prime factors. Consider the list of squarefree numbers t with n prime factors greater than and including p_n# but less than 2p_n#. Extend the list to include products k × t of this list with 1 ≤ k < prime(n+1) such that k × t < (k+1) × p_n#. This list contains squarefree numbers k × t with n distinct primes and presumes that the number (k+1) × p_n# serves as a "limit" beyond which k × t > (k+1)p_n# are not in the sequence. Charts: Relation of A288784 with A002110, A060735, and A244052; Tree Associated with Computation of terms of A288813 via Directed Iteration of A287352(A002110(n)). See the entry at the “OEIS” page on my math site.

A288813, (V3201), “Turbulent candidates” in A288784: “Irregular triangle read by rows: T(m, k) is the list of squarefree numbers A002110(m) < t < 2 × A002110(m) such that A001221(t) = m.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {3, 10, 42, 330, 390, 2730, 3570, 3990, 4290, 39270, 43890, 46410, 51870, 53130, 570570, …}, 24 June 2017 (táyyâ 9b20). A002110, A060735, and A244052 are subsets. a(n) = terms t of row m of A288784 such that p_m# < t < 2 × p_m#. The only odd term is 3; the only other term not ending in 10, 30, 70, or 90 in decimal is 42. All terms t in row m have ω(t) = m and at least one prime q coprime to t such that q < A006530(t). Consider "tier" m and primorial p_m#, let “distension” i = π(A006530(T(m, k))) − m and let “depth” j = m − π(A053669(T(m, k))) + 1. Distension is the difference in the index of gpf(T(m, k)) and pi(m), while depth is the difference between the index of the least prime totative of T(m, k) and pi(m) + 1. We can calculate the maximum distension i given m and j via i_max = A020900(m − j + 1) − m − j + 1. This enables us to use permutations of 0 and 1 values in the notation A067255 (multiplicity notation) and produce a(n) with some efficiency. See the entry at the “OEIS” page on my math site.

A301414, (V1241), “Numbers k in A301413 such that k × A002110(m) is in A002182.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 2, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 144, 216, 240, 288, 360, 480, 576, 720, 1080, …}, 9 April 2018 (táyyâ a121). This sequence along with was the focus of a major study wa111, replete with magnificent charts like na137. See the entry at the “OEIS” page on my math site.

A307540, (V2100), Graph of the totient ratio. “Irregular triangle T(n, k) such that squarefree m with gpf(m) = prime(n) in each row are arranged according to increasing values of φ(m)/m.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 2, 6, 3, 30, 10, 15, 5, 210, 42, 70, 14, 105, 21, 35, 7, 2310, 330, 462, 66, 770, 110, 154, 1155, 22, 165, 231, 33, 385, 55, 77, 11, 30030, …}, 13 April 2019 (táyyâ a387). See diagram. Let gpf(m) = A006530(m) and let φ(m) = A000010(m) for m in A005117. Row n contains m in A005117 such that A006530(m) = n, sorted such that φ(m)/m increases as k increases. Let m be the squarefree kernel A007947(m') of m. We only consider squarefree m since φ(m)/m = φ(m' )/m'. Let prime p | n and prime q be a nondivisor of n. Since m is squarefree, we might encode the multiplicities of its prime divisors in a positional notation M that is finite at n significant digits. For example, m = 42 can be encoded reverse(A067255(42)) = 1,0,1,1 = 7¹ × 5⁰ × 3¹ × 2¹. It is necessary to reverse row m of A067255 (hereinafter simply A067255(m)) so as to preserve zeros in M = A067255(m) pertaining to small nondivisor primes q < p. The code M is a series of 0s and 1s since m is squarefree. Then it is clear that row n contains all m such that A067255(m) has n terms, and there are 2^{(n − 1)} possible terms for n ≥ 1. We may use an approach that generates the binary expansion of the range 2^{(n − 1)} ≤ M ≤ 2ⁿ − 1, or we may append 1 to the reversed (n − 1)-tuples of {1, 0} to achieve codes M → m for each row n. Originally it was thought that the codes M were in order of the latter algorithm, and we could avoid sorting. Observation shows that the m still require sorting by the function φ(m)/m indeed to be in increasing order in row n. Still, the latter approach is slightly more efficient than the former in generating the sequence. For n > 0, row lengths = A000079(n − 1). T(n, 1) = A002110(n) = p_n#. T(n, 2) = A306237(n) = p_n#/prime(n − 1). T(n, 2ⁿ − 1) = A006094(n). T(n, ⁿ) = A000040(n) = prime(n). Last even term in row n = A077017(n). First odd term in row n = A070826(n). See the entry at the “OEIS” page on my math site.

A322156, “Irregular triangle where row n includes all decreasing sequences S = {k₀ = n, k₁, k₂, ..., k_m} in reverse lexical order such that the sum of subsequent terms k_j for all i < j ≤ m does not exceed any k_i.” Reneyan sequence at the Online Encyclopedia of Integer Sequences {1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 3, 3, 1, 3, 1, 1, 3, 2, 3, 2, 1, 3, 3, 4, 4, 1, 4, 1, 1, 4, 2, 4, 2, 1, 4, 2, 1, 1, 4, 2, 2, 4, 3, 4, 3, 1, 4, 4, …}, 11 December 2018 (táyyâ a2a7). A visually-appealing study: see diagram. Algorithm: Let S be a sequence starting with n. Let k be the index of a term in S, with n at position k = 0. Let S_r be the r-th sequence in row n. Starting with S₁ = {n}, we either (A) append a 1 to the left of S_r, or (B) we drop the most recently-appended term S_(k) and increment the rightmost term (k − 1). By default we execute (A) and test according to the following. Consider the reversed accumulation A_{(r + 1)} = Sum(reverse(S_{(r + 1)})) = Sum(k_m, k_{(m − 1)}, …, k₂, k₁). If S_r − A_{(r + 1)} contains nothing less than 0, then S_{(k + 1)} is retained, else we execute (B). We end after k₁ = n, since otherwise we would enter an endless loop that also increments k₀ ad infinitum.
The first sequence S in row n is {n} while the last is {n, n}. All rows n contain {{n}, {n, 1}, {n, n}}. Only one repeated term k may appear at the end of any S in row n. The longest possible sequence S in row n has 2 + floor(log2(n)) terms = 2 + A113473(n). The sequence S describes unique integer partitions L that are recursively symmetrical. The sequences S in row n, converted into integer partitions L, sum to n² ≤ N ≤ 3 × n². See the entry at the “OEIS” page on my math site.

Acrâ /Utch-rung/, “high, celebrated”, a title applied to women I feel are exceptional, much like the use of aði (aðebyn, meaning “fair”) applied to fair haired or skinned women. Acraðebna “highly regarded and fair” = aðilarsâ, /utch-ruh-LAWR-sung/ Acrataïrâ /utch-ruh-TAW-ee-rung/ “highly regarded and foremost” = Aðifani, Acraroetylâ /utch-ruh-SHOY-tü-lung/ “highly regarded and driven” = Aðimallâ.

Adevanâ /uh-DAY-va-nung/, “Deepa”, Lakepoint-era love interest, s5231b00. Old lrixe name Ativanâ, “heavenly”.

Aðiavlikâ /uh-thee-AV-li-kung/, “The Fair Amy”, early high school crush, portrait in pencil (naïve) j339a. Namesake of a fictional city “Avlicir” depicted in a map (naïve) k3160. Also Avlikâ, Ævlikâ, Avlica. The name Avlikâ derives from Amy’s surname.

Aðicínþî /uh-thee-CHEEN-thing/, “Fair Cynthia”, worldly companion in Paris during Káxa Maïréne, prone to laughter, represented by the character Tracy Svoboda in the novel Roam Away Home.

Aðiëvinzâ /uh-thee-AYV-in-zung/, “The Fair Evans girl”, my first true crush at age 11, a female classmate of my sister’s. Namesake of the two dozen fourth life phase of mid 1981. Representative work from the two dozen fourth life phase: s2485. The name Evinza predated lrixe; the given name of the rentikâ was not used as it was common.

Aðihaxhâ /uh-thee-HAWSH-hung/, “fair and quiet”, a name normally applied to Barbara, aðilarsâ. See aðilarsâ.

Aðifani /uh-THEE-faw-nee/, Aðiðifani /uh-thee-THEE-faw-nee/, “The Fair Stefani”, attractive and popular seventh-grade cheerleader in an unexpected crush on me, late Iuleine era (eighth grade). Also Taïrâ (foremost, first, best), Acrataïrâ (highly regarded and foremost). A main character “the prettiest girl in seventh grade” in _otherworld son_. Namesake of the two dozen eleventh life phase of early 1984.

Aðifanâ /uh-THEE-faw-nung/, “Stefani”, the last date before focusing on the woman that would be my wife (Aðilyrâ), late Nixaþine era (July 1998).

Aðijamyse /uh-thee-ZHAW-mü-suh/, “The Fair Jayme”, high school girlfriend, s3964a00. Namesake of the three dozen eighth xrgâ between 1987 and 1988, namesake of the argam-ajamyse numerals, a predecessor stage of the argam numerals.

Aðikarine /uh-thee-kuh-ZHEE-nuh/, “Blond Katie”, Aðikeslyne /uh-thee-kuss-LÜ-nuh/, “The Fair Kesly”, figure in the Kaxa Sarynal and the 4703 Acratayyâ (Heyday), March 1992.

Aðikylet /uh-thee-KÜl-et/, “The Fair Nicole”, figure in the Kaxyn Kajixaþal of late summer 1993.

Aðilarsâ /uh-thee-LAWR-sung/, “The Fair Larson girl”, a daughter of my father’s friend. Namesake of the three dozen second life phase of mid 1985. Also Aðilarsonâ, Aðivarwa, Aðihaxha (fair and serene), Acraðebna (highly regarded and fair).

Aðilyrâ /uh-THEE-lü-jung/, “The Fair Laura”, eventually my wife Laura Ann. Feature page. Engagement portrait in ballpoint s3964a13. Signature s5231a23. Memory portrait in ballpoint s5231a59. Passenger in Angelina as Icarus is driving s5231a66. Dedicatee of the Jeleyn Añikçine Xisaëna, s611ba01. Domestic picture with husband s611ba08. Namesake of the five dozen tenth xrgâ of early 1998, the last life stage named for a lady of interest. Representative work of the five dozen tenth life phase: t5a0b, s5231a66, s5231a70.

Aðilyra ke Reney /uh-THEE-lü-juh kuh she-NAY-ee/, “Laura and Mike”, title page and dedication of the Jeleyn Añikçine Xisaëna, s611ba01.

Aðimallâ /uh-thi-MAWL-lung/, “fair and unexpected” (diminutive), the lrixe name of a crush. The word “unanticipated” is ymalhynâ /üm-AWL-hü-nung/. Used as a particular name, also known as Aðimilâ /uh-thee-MEE-lung/, Acraroetylâ /utch-ruh-SHOY-tü-lung/, Acrali /uch-ruh-LEE/, Acramilâ /uch-ruh-MEE-lung/.

Aðimisâ /uh-thee-MEE-song/, “Fair Melissa”, ballerina and Ralysine era (high school) crush, namesake of a pencil portrait of a lady on a starship (naïve), j34b9. Also Aðibryne (a name based on her surname).

Aðinarâ /uh-thee-NAW-rung/, “Dinar”, Safrine era (university) girlfriend of Pakistani descent in the engineering program. Namesake of the four dozen fifth xrgâ of mid 1991, the final life-phase of cime, lifetime-spring or childhood, which ended at the Asmið Galmine “Turning of Adult Youth”, the coming of age or quarterlife turning point at tayya 4600 / 15 October 1991.

Aðitinâ /uh-thee-TEE-nung/, “Fair Christina”, Late Ralysine era (first year university) acquaintance, (naïve), dedicatee k3a06,

Aðitriçâ /uh-thee-TREE-khung/, “The Fair Tracy”, coworker at tavnemika and namesake of the aðitriçâ drawing style. This is distinguished from “Atriçâ” /TREE-kung/, another girl named Tracie.

(Jimalmyne) aðitriçal /uh-thee-TREE-khull/, a marker sketching style of August 1997. Examples: Aveacrixe s5231a43, Amagal s5231a44, Asmarâ s5231a46, author Beth Kobliner s4231a48, sister and niece s5231a49, Icarus and Amagal s5231a50, Asayme s5231a51, Aðilyra ke Reney s611ba01, Great Mosque of Cordoba s611ba09, portrait of the Blessed Mother and Christ child: s51a3a39. An early and deficient example: Arebinâ s5231a09. The palette is limited to three near-primaries, three muted colors, and two methods for black. The red trends orange, the blue toward violet, and the green a sunny chartreuse. Muted colors consist of apricot for heft, a peach for highlighted skin, and a light warm gray for general pale color. This is topped by absolute black, either by the hairline of a ballpoint pen or the pointed tip of a Sharpie. The subject could be laid out in ballpoint or technical pencil, avoiding graphite value. The drawings are to be rapid, energetic, and exuberant. Texture will be conveyed to some extent by the natural bleed of the marker, not any conscious manipulation of graphite. The style is named after a coworker from tavnemika, Aðitriçâ.

Aðiyose “fair Josephine”: one of the foremost moonstones of the sreda xisaën.

Ahilðiñâ /uh-HEEL-thee-nung/: “Hildy”, Mid Safrine era lover, rentika of the four dozen sixth xrga of late 1991-early 1992. The relationship was interrupted by the Semester in Italy. The latter third of the xrga proved to be a massive life change in Italy. Examples of work: portrait of Arebinâ, j4656; sketch of Castiglion Fiorentino, s45b0a07; “Camélia versus Ðebñinâ”, s45b0a12.

AIA Architectural Drawing Award: 1995 St. Louis AIA/CPC Merit Award for Architectural Drawing s45b0a20. 1997 St. Louis AIA/CPC Architectural Drawing Award s5810a02.

Aix-en-Provence, France: Place de la Université s5810a03, S. Jean de Malta s5810a04.

Ajinevrâ /uh-zhi-NAVE-rung/, “Jennifer”, wild Amherst-era girlfriend, namesake of the five-dozen-ninth xrgâ of late 1997-early 1998. Autograph at s5231a15. The “ten thousandth day”, 16 November 1997, tayya 5954, fell in the ajinevral xrga. Representative work from the five dozen ninth life phase: s5231a63, j5978.

Akaisone /uh-KAY-so-nuh/), Intong, Laotian Literacy Council student, s3964a04.

Akarine, Aðikarine /uh-kah-JEE-nuh/), Catherine, French lover, also Akeslyne /uh-CASE-lü-nuh/, Akætlyne /uh-CAT-lü-nuh/, Aðikaty /uh-thee-KAH-tü/.

Akimakinâ /uh-KEE-ma-kee-nung/, “Kimberly”, Texan classmate at the S. Chiara study center in Castiglion Fiorentino, Italy. s45b0a14.

Akimalâ /uh-ki-MAW-lung/, “Camélia”, see Camélia. Namesake of the three dozen seventh xrgâ of mid 1987. In 2003, the middle name Camélia was given to my daughter.

Akimvriwâ /uh-KEEM-vree-wung/, “Kimberly”, Lakepoint-era girlfriend and neighbor, a first grade teacher five years senior, namesake of the five-dozen-second xrgâ of early 1995. The Rykami Arysane sketchbook s5231 was started; representative work of the five dozen second life-phase: s5231a01, s5231a02.

Alargamal /ul-AR-ga-mull/, “(of) the numbers”, the name of the seven dozen eighth xrgâ of winter 2006-2007. Representative work: a782b, a7887. Vinci LLC’s worksite visualizations proceed toward a "total, immersive modeling" approach that would eventually become Vinci Digital Worksite™.

Aleys /ul-ACE/, “happiness, folly”, the name (aleysminal) of the nine dozen tenth xrgâ of spring 2017. Representative work: a9a00, a9a09, a9a64. The span featured my daughter’s appearance in the “follies” middle school play, as well as a trip to Rome and the Amalfi coast. Business started hot and profitable but chilled to near quiet by the end of the xrgâ.

Alikçâ /uh-LEEK-khung/, “(financial) economy”, Reneyan income chart s5231a22. The word for money is alik /uh-LEEK/ or ðanar /the-NAWR/.

Alim /uh-LEEM/, “peace, calm”, a term for the “bedroom eyes” a woman gets when she is in the mood. From the verb ĝálym /GHAUL-üm/, “to establish, to be at peace”, and is related to the word ’alíme /‘a-LEE-muh/, “peace, peacefulness”.

Alimxeleþnal /uh-ling-sheh-LAYTH-null/, “peaceful coding”, name of the nine-dozen-third xrgâ of mid-2014. Cool summer spent with kids at Disney. Long course swimming, some laid back projects. Most of all, the start of Reneyan contribution to the OEIS and expanded confidence in Wolfram language. Major projects were a9388, r9369, and a proof regarding anti-divisors, n93a9.

Alindði /uh-LEEND-thee/, “Lindsay”, undergrad and hostess at Cafe Danielle on Euclid Avenue, St. Louis five years junior. Namesake of the five-dozen-eighth xrgâ of mid-1997. Signature at s5231a22. Representative work of the five dozen eighth life phase: s3964a07, s5231a49, award winning ballpoint drawing s5810a02. the aðitriçâ marker drawing style was invented. The Kaxa Lecorbu, a journey to Paris, Aix-en-Provence, and Tuscany, took place in the five-dozen-eighth xrga recorded in the Rykami Samaðene sketchbook s5810. Also Alindðyne (plural genitive case of “Lindsay”: Lindsays’, akin to the nickname “Linds”)

Alpha (Totative): Let the integer r ≥ 2 be a number base; then α = (r + 1). Divisibility rules for omega, the alpha rules later realized s7836a26. A major indirect relationship shown in digit maps and spectra in the 2 Mb PDF “Digit Base Relationship” d87a9, expanded, 11Mb d87aa, and in the 2011 paper “Dozenal FAQs”, 5.6Mb PDF d8907. The notion is incorporated into a peer-reviewed article published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Alpha has a special intuitive relationship with the number base, inherited by the divisors of alpha. Together the alpha and omega relationships (r ± 1) comprise indirect relationships leverageable by human cognition.

Alphabet, lrixe: the 1996 alphabet of my constructed language a5231b05. After the 2002 cessation of the development of lrixe, the English transliteration became the sole conveyance of the language (See “Weird Letters”).

Amagal /uh-muh-GALL/, “Madeline”, Panamanian acquaintance met on a train between Florence and Paris during the Kaxa Lecorbu; her autograph s5810a06, in aðitriçâ marker style s5231a44, with Icarus s5231a50.

Amaryâ /uh-MAWR-yung/, “Mary”, acquaintance in Castiglion Fiorentino, Italy, commissioned j475a. Later I would learn that Amaryâ was a classmate of Aveacrixe and that the two were evidently rivals.

Amherst, an apartment at 6055-A Amherst Avenue in University City, Missouri where I resided with A. Barrett between late June 1996 and June 1998. Amherst often refers to this period, one of artistic experimentation and architect internship at a downtown St. Louis firm. Amherst is a major division of the Ñixaþine (Apprenticeship) era.

Ámma /‘AM-ma/ The lřixe word for mother.

Amyñikâ /uh-MU-nee-kung/, “Monique, Monica”, friend at university, s5231a07. Namesake of the three dozen eleventh xrgâ of early 1989. The character Iesha has a quality taken from amýñikâ (her middle name) in the novel Roam Away Home.

Amyqâ /uh-MÜNG-ung/, coworker Ming, s5810a06.

‘An /‘AWN/ The lřixe word for a regular (Gregorian) year, borrowed from the French. This is a year of 365.26 standard 24 hour days, divided into 12 months (lřixe més).

Ana /ON-na/ The lřixe first person singular pronoun, meaning “I”. Genitive suffix is -i.

“Analysis of Multiplication Tables”, a paper illustrating the effects of elementary number-theoretical digit-base relationships in the multiplication table of a number base, 1½ Mb PDF d872a. This paper summarizes description of digit maps, and the effect of the relationship of digit and base on multiplication tables. Octal, decimal, duodecimal, and hexadecimal tables serve to illustrate the effects.

Analytical sketches: Clay tile unit in Tuscany s45b0a08. Masonry vignettes s45b0a11. Sienese Gothic window s45b0a18. Section through an Etruscan tomb s45b0a20. Paris mansard s45b0a24. Columns at the Great Mosque of Cordoba s51a3a03, bays at the Great Mosque of Cordoba s51a3a03, Place de la Université s5810a03, Tuscan ceiling s5810a06, Italian hospital room section s5810a07. Joliet urbanistic close s5231a63. University City retail commons cross section s5231a72. Seattle transit, store, and suburban parking study s5231a77, downtown urbanism s5231a78, building studies s5231a79. Hotel floor plan, Écija, Spain s611ba0b. Masonry arches in Tuscany s6861a03, Roman arcade in Lucca s6861a04.

Angalydðan /ung-gul-LÜD-thon/, “(steel) factory”, emblematic of Joliet, IL, and industry in general. Camélia s5697a01.

Anglo-Saxon (Numeral) Names: alternative transdecimal numeral names s7836a13.

Añikçâ /uh-NEE-khung/, “oneness”; the name of the sixth xisaën, the Commitment Era, 19 October 1998 — 13 August 2003, encompassing engagement, wedding, the Nottingham, the Avindelor, ending shortly after the birth of Axalaïrâ.

Anityananðâ /u-nit-ya-NAWN-thull/, “everlasting” < Sanskrit, a love interest at university during second year, a Jain grad student from India seven years senior. Namesake of the four dozenth xrgâ of mid 1989.

Anrenâ /un-JAY-nung/, “Reneyan year”, a blue-calendar period of 432 days or 12 ekronyn.

Ansanþarðal /un-sun-THAWR-thull/, “(of a) return to earth”, name of the seven dozen seventh xrgâ of mid 2006. Representative work can be seen in the Vinci LLC portfolio, job numbers that begin with “77”.

Antarctic Nunatak, j5a1a.

Antidivisors, a set of proofs concerning the arithmetic relationship of antidivisors k of n with positive integers n. Using concepts in the set of proofs in Neutral Numbers, several Reneyan OEIS sequences were defined and submitted, including A241556 Number of prime anti-divisors m of n, A241557 Numbers k that do not have prime anti-divisors, A242028 Numbers k such that the least common multiple of the anti-divisors of k is less than k, A242029 Number of anti-divisors m ≤ n of n that are coprime to n. The proof page was started at tayya 93a9 / 12 August 2014 and has been continually edited.

Anviomiral /un-vee-O-mi-shull/, “(of an) aquarium”, name of the eight dozen third xrgâ of late 2009. The name derives from the large aquarium bought during that age which became a focus at the family dinner table. Exemplary work: a8306, a8337, a8373.

Anvio Vinci /un-VEE-oh VEEN-chee/, “showing Vinci”, name of the ten dozen third xrgâ of early 2019, deriving from penance rendered at that time.

Apacinâ /uh-PAW-chee-nung/, “Taylor” Safrine era (university) female friend and love interest. Namesake of the four dozen sixth xrgâ of late 1991 / early 1992, the first life-phase of gilme, lifetime-summer or adult youth. Gilme began at the Asmið Galmine “Turning of Adult Youth”, the coming of age or quarterlife turning point at tayya 4600 / 15 October 1991. (Gilme will end at Asmið Vivixe “Turning of Midlife”, at tayya 9000 / 28 January 2013.) The Apacinal xrga saw the commencement of the Kaxa Mairenal / Semester in Tuscany, which represents a sort of personal rebirth, the advent of “modern Mike”. Representative work of the four dozen sixth xrga: portrait of Arebinâ j4656, sketches in Italy s45b0a07, s45b0a12.

Arah /AWR-ahh/, the one true God, God the Father.

Arahilâ /uh-SHAW-hee-lung/, “Rachel”, late high school love interest, three years junior. Namesake of the three dozen ninth xrgâ of mid 1988.

Arahkaxa, “God-quest”, my personal quest for a relationship with God, atoning for sins and general lack of spirituality in late university years.

Archbishop Joseph Naumann, autograph, s3964a13.

Arebinâ /uh-JAY-bee-nung/, acquaintance Rachel at university, a precocious med student. Aðitriçâ-style and pencil sketch s5231a09, getting deleted s5231a22. Dedicatee (rentikâ) of the 1990-1991 Rykami Arebine (lost), the dedication drawing restored soon after loss at j4656. Rykami Arebine is the precursor to Rykami Yasmyne (s45b0). Namesake of the four dozen third xrgâ of late 1990. Also Axaðhanâ. Arebinâ is conveyed by Radha in Roam Away Home.

Arezzo, Tuscany: a5810a07, in the distance behind Aveacrixe s5568a00.

Argam /AHR-gam/, Arabic word meaning “numbers”, singular ragam, both spelt “arqam” or “raqam”. Reference at s7836b00. Used to signify a set of numerals devised for number bases larger than decimal (transdecimal number bases). Printable PDF with sexagesimal argam (with ismarragam 2009, with prime decomposition 2010). Duodecimal numerals grew into a hexadecimal solution, then a vigesimal solution by 1986 (argam ajamyse of 1986, remembered partially in 2008 at s7836a02). The first such set, argam aymane, appeared in a composition book s4547, dated 18 July 1991. The argam arimaxa of 1990-1992 reforms this set s45b0b80,s7836a02. The argam were reformed in 2006 s7836a02. Duodecimal argam s5231a25, construction measurements in argam s5231a87. Cyclical diagrams and sexagesimal symmetry s5231a90. Numerals and names for primes tied to chemical elements s7836a12. Numerals and names for prime powers s5231a91, numerals for composites s7836b14, s7836b00, numerals and names for superior highly composite numbers s5231a91, numerals generated via “Infinite Multiplication Table” s5231a92, s7836a11. Numerals for small composites s5231a93, s5231a94; numerals for factors of superior highly composite numbers s5231a92; sexagesimal argam for the divisors of cubes of primes, composites s5231a95, bases 60 and 120 s5231a96, of base 360 s5231a97. The argam aðilyre is the name of an expanded numeral set s7836b00; for superior highly composite numbers s7836a01. History of development in sketchbook introduction s7836a01, s7836a02. “Argam for Sexagesimal with Ismarragam” (sexagesimal numerals) s7836a52. The name of the seven dozen eighth xrgâ of winter 2006-2007 is Alargamal.

Arimaxâ /uh-JEE-ma-shah/, “Rima”, a girlfriend at university. Namesake of the four dozen eighth xrgâ between 1992 and 1993, namesake of the argam arimaxa numeral set. Representative work: argam arimaxa s45b0b80.

Arqam, see “Argam”.

Arycisaymal /uh-ji-chee-SIGH-mull/, the four dozen fourth xrgâ of early 1991, and namesake of the rucisaime drawing style. The life phase is the only one named for two girls, Aryciwâ and Asaime. The word has come to signify the drawing style more than the relationships. See rucisaime.

Aryciwâ /uh-JÜ-chee-wung/, acquaintance of the middle year of university. Namesake, with Asaime, of the four dozen fourth xrgâ of early 1991, and namesake of the rucisaime drawing style. Also Aryciô, Aryþiô.

Aryñâ /uh-JÜN-ung/, also aryñme /uh-JÜN-muh/, spirituality, religion. ~ Reneyâ /sheh-NEIGH-ung/, my personal belief system, in late ñixáþâ an attempt at a personal religion; ~ Ráctâ /JOCK-tung/, the Catholic church, literally, “orthodox”; ~ Alíme /uh-LEEM-eh/, Islam, literally, “of peace”. From aryñme, the words avnarýn /of-na-ROON/ “church, temple”, rinislám /sheen-ees-LAHM/, “Islam (religion), rináh /shee-NAH/, “creed”. This is a major component of one’s life.

Aryñluimy /uh-jün-LOO-i-mi/, St. Louis, literally, “Holy Louis City”. My adopted hometown since 2 January 1994. A major subject for Añikçine-era jimlyn veronal. Map drawn by memory showing potential places to live s5231a22. Heat map showing familiarity with s5231a45. Old North St. Louis s5231a74. Francis Park studies in spring j6146a, j6416b, j6417, autumn j624a. Typical vernacular masonry j6284, j6285. St. Louis Hills Christmas scene j628b. Chase Park Plaza from Forest Park j6374. The Palm House at Tower Grove Park j63aa. Lindell highrises from Washington Avenue j63b6. Home in the Central West End j6400, New Cathedral j6421. Downtown smokestack j652a. The Jewel Box j6580. Third Baptist Church and Grand Avenue j65a9. Central Paper Company warehouse j6692. McRee Town j6786. SLU Hospital j6787. Compton Heights Water Tower j6791. Civil Courts Building j6797. Southwestern Bell Building j6798. The arch, part of a montage j6924. St. Louis Union Station j6a96. The Climatron j6aaa. Crown Candy Kitchen j6b53.

“Arynluimy Reneyâ” /uh-jün-LOO-i-mi she-NAY-ung/, “Reneyan St. Louis”, my familiarity with my adopted hometown in mid 1997 s5231a45.

Arysani /uh-jee-SAW-nee/, “Red Anne”; close friend at university in the chemical engineering program; dedicatee of the Rykami Arysane s5231a18. Namesake of the three dozen tenth xrgâ of late 1988. Also Rixâ, Anirixâ.

Arys /uh-RÜSS/, “art”.

Arysiwâ /uh-RÜ-see-wung/, “(art) studio”; Arysiwa Reneyâ /uh-RÜ-see-wa she-NAY-ung/, “De Vlieger Studio”, s3964a02.

Aryskinþral /uh-jis-KEEN-thrull/, “Computer drawing”, name of the five dozen fifth xrgâ of mid 1996. Representative work: s5568a00.

Asayme /uh-SAW-ee-muh/, female friend since university. Also Nílâ /NEE-lung/ “little one”, Axinílâ /uh-shi-NEE-lung/, Anixíwlâ /uh-ni-SHEEW-lung/, “the little woman”. Pictured at dinner, rejecting an advance a5231a11. Portrait in marker studied through author Beth Kobliner s5231a48. Aðitriçâ style marker portrait s5231a51. Namesake, with Aryciwâ, of the four dozen fourth xrgâ of early 1991. Dedicatee (rentikâ) of the rather undeveloped 1996 Rykami Asaime (s5697, the dedication drawing with Camélia standing in for Asaime). Rykami Asayme was to be the successor to Rykami Arysani (s5231). Asayme is the younger, architecture student component of the character Rosalba in Roam Away Home.

“Asayme fi Xensley”, dinner in Chicago, rejection s5231a11.

Asmarâ /us-MAW-rung/, “Asma”, acquaintance from Euclid Avenue in St. Louis, a med student who amazingly described herself as “pretty shallow”. Namesake of the five-dozen-seventh xrgâ of early 1997. Signature at s5231a29. As Camélia s5231a31. Marker portrait from memory s5231a46. Representative work from the five dozen seventh life phase: s5231a27, s5231a28, s3964a06.

Asmið Galmine /us-MEETHE GAWL-mee-nuh/, “Turning of Adult Youth”, coming of age or quarterlife turning point. The beginning of Galminal Xiomðe, the lifetime-summer, at tayya 4600 / 15 October 1991.

Asmið Vivixe /us-MEETHE VEE-vee-shuh/, “Turning of Midlife”, the midlife turning point. The beginning of Vhonmal Xiomðe, the lifetime-autumn, at tayya 9000 / 28 January 2013.

Asresþ /as-RACE-TH/ A lrixe word meaning “simplification”, deriving from the verb sáryh /SAWR-üh/ “to simplify, to reduce, to make brief”. This is a term for lrixe grammar as well, a name for the reduction of verbs with three radicals in which the second or third are -h- or the lrixe letter hawtíl. The hawtíl is dropped when only one such radical exists. If the second and the third radicals are hawtlýn, the second radical vowel is lost. An initial hawtíl is never dropped, and may harden to a sahháwtl. The lrixe hawtíl is a weak letter and is sometimes elided grammatically.

Asyðanâ /uh-su-THON-ung/, “Susan”, wild but well-off neighbor at Lakepoint. Namesake of the five-dozen-first xrgâ of late 1994. Representative work: s51a3a03, s51a3a15.

Atélier Cezanne: s5810a03.

Atriçâ /uh-TREE-khung/, “Tracy”, a girl met on Amtrak in 1994.

Aþikolaðiwâ /uh-thi-ko-LAW-thee-wung/, Christina, middle school crush and classmate of my sister’s, namesake of the two-dozen-ninth xrgâ of late 1983. Representative work: j29b5. The name Þikolaðiô predates lrixe and is a melding of her first and last names.

Aþrimallâ, /uh-THREE-mawl-lung/, “taking things to the stars” but is interpreted as “endurance, longevity”. The name of the nine dozen sixth xrgâ of mid 2015. Representative work, a9633, g9638, a9640, a9659, a9663, c9680, h9681.

Augusta, Missouri: j6159.

Autobiography, The Reneyan. (L'Vixsaenyn Reneyor, l-vish-SAW-en-ün she-NAY-orr). The story of my life. The work began near the start of Eĝájñalékxiðanal Xrgâ (August 2018) as a transection of life taken every first day of the xrgyn (i.e., every 144th day after 1 July 1970), taken from the journals (jeleynyn reneyor), working from the latest to the earliest. Originally the aim was to fully cover all written entries, then by using entries near those dates or ephemera, photos, messages, etc. to reconstruct unrecorded days. This was sufficient to construct a record 29 years deep. After a month of work the product was extended into ralysa xisaen (i.e., high school), then into childhood such that by the end of 2018, an unbroken record existed called the Firsts Transection. Because the earliest "entries", which were fashioned from the nixaþine karmyn jimlal (i.e., of the mid nineties), painted a rather complete portrait of childhood experience, supplemental entries were admitted during the Semester Abroad and the Summer in Val di Chiana from a novelization of the journal entries called The Sugar Factory. The completed childhood entries generated two novelizations in the form of romans-a-clef called _otherworld son_ and The Official Troublemaker.

Avatar: I’ve used two principal avatars. See “Icarus” and “Reney”. Icarus is a questing but yet-to-mature and brooding Gen-X twentysomething, while Reney is neutral to positive in demeanor. Reney was adopted in 1998, while Icarus was then a cute notion. Icarus developed in the early 1990s and became a major theme between 1995 and 2000.

Aveacrixe /uh-vey-uh-CHREE-shuh/, “Beatrice”, girlfriend in Tuscany; s5231a43, dedicatee s5568a00. Also Ymalhynâ (“Unanticipated”), shortened to Imallâ, Ymallâ, though these names also generally refer to other “unanticipated” female relationships, i.e., mutual crushes / love interests.

Averenðe /uh-veh-JEN-thuh/, “Brenda”, friend at university. Depicted on a Post-It note s5231b00.

Avikari /uh-vee-KAW-shee/, “Victoria”, classmate at university, especially the semester in Italy. s45b0a14.

Avin /uh-VEEN/, “home”, one’s household.

Avindelor /uh-VEEN-deh-lor/, home on Delor Street, the name of my house, name of the six dozen fourth xrgâ of mid 2000. Expansion sketches s611bb05, s611bb06.

“Avlicir”, canonically “Iral Imelavlike”, map of a port on the home planet of an interstellar empire (naïve) k3160.

Ávnâ /AWV-nung/, “glory, splendor”, also a place where something reigns supreme, as in kimavna, a library, where information reigns supreme.

Ávnadéhinâ /AWV-na-duh-HEE-nung/, “daughter coming into her own”, name of the ten dozen second xrgâ of late 2017—early 2018. A busy period with lots of wet infrastructure work. See aa062, aa069, aa0b4.

Award winner: 1995 St. Louis AIA/CPC Merit Award for Architectural Drawing s45b0a20. 1997 St. Louis AIA/CPC Architectural Drawing Award s5810a02.

Axájnal /uh-SHAWZH-null/, “Seething”, name of the nine dozen first xrgâ of mid to late 2013. This period included intense work, several of Vinci LLC's best pieces (r9119, a9158, a9168, a9194) produced with the help of the architect John Guenther. Family went on its third trip to Pensacola Beach.

Axilbanâ /uh-SHEEL-baw-nung/, “Shelby”. Also Axelwâ, Xelbr. One of the foremost moonstones of the sreda xisaën.

Aximelâ /uh-SHEE-may-lung/, “Michele”, girlfriend in early high school, most significant female relationship during ralysa, namesake of the three-dozen-fifth xrgâ of late 1986.

Aymanî /ay-MAW-ning/, “Imani”, the most prominent and closest college girlfriend, relationship on and off over seven years, s3964a02, stylized s5231a10, memory study s5231a21. Namesake of the four dozen first xrgâ between 1989-90. Also Xibane /shee-BAWN-uh/, Alyðirâ /uh-lü-THEE-shung/ (beguiling). The character Iesha roughly corresponds to aymanî in the novel Roam Away Home.

Ayntô /AYN-tong/, Akaisone /uh-KAY-so-nuh/), Intong, Laotian Literacy Council student, s3964a04.

Ayuleyâ /uh-YU-lay-ung/, “Julie”, high school acquaintance, s3964a01. Namesake of the three dozen fourth xrgâ of mid 1986. (The life phase is actually named after two Julies.) The life phase saw a great deal of development and institutionalization of duodecimal numeration, the intensification of lrixe in class notes, and a profusion of self-motivated artwork encouraged by friendly competition with Dante. Representative work: Camélia Lorielal j3410, color drawing of the Challenger disaster j3461, portrait of a starship lady j34b9.

Azennâ /uh-ZAYN-nung/, “correction, compensation”, literally, a “coming to the light”.

Bae /bay/, the name I apply to myself seen as Aðimallâ’s (meaning Acramilâ’s) limerent object, the edifice of her imagination that she has erected upon my image. The name is used to disambiguate who I really am versus what I seem to be in the eyes of Acramilâ. This edifice is perhaps the personification of all things masculine in her eyes, mounted atop my image much like my imago Camélia is the more unmoored personification of the Goddess-Maiden. Also sometimes called “Adonis”. The construction and pursuit of Bae by Acramilâ helped precipitate the Krunþe Imallâ or “Reneyan mid life crisis” of the eight dozen tenth through nine dozen eighth xrgyn, named after Acramilâ, though her actions were only part of the crisis’ focus. See also Camélia for a similar construct I projected in my youth upon Arysani and others.

“Balance Study”, 2010 study that includes cyclic logarithmic, geometric, and scalar diagrams exploring the divisors and totatives of the smallest integers. Download the 1¾ Mb PDF d8483.

Balloon Race, s5231a80.

Banana: s5231a22.

Barcelona, Spain: ballpoint sketch of market on La Rambla from memory s5231a60. Setting of much of the second half of the 2021 novel Roam Away Home, a travelogue memoir of Káxa Maïrénal of 1992.

Bases, Comparison of Number: the DozensOnline “mashups” < Comparison of Bases 60 and 120 > Post at the DozensOnline Forum h8abb→. Comparison of bases {72, 96, 108}, {60, 84, 90, 120}, {32, 48, 80, 112}, {30, 42, 70}, < Midscale Mashups > Post at the DozensOnline Forum h8b09→. Comparison of bases 12k with 1 ≤ k ≤ 12 (figures expressed in duodecimal) < The Dozen Mashup > Post at the DozensOnline Forum h8b19→.

Base 5 (Quinary): < Quick Kid: Quinary >, Post at the DozensOnline Forum h8ab8→

Base 6 (Senary): divisors of the cube of 6 in base 6 s5231a95, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. < Hey Superior Senary, You Ready to Rumble? >, Post at the DozensOnline Forum h891b→

Base 7 (Septenary): < Lucky, Sacred Seven >, Post at the DozensOnline Forum h8ab4b→

Base 8 (Octal): divisors of the cube of 8 in base 8 s5231a95, fractions, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. < Octal, the Awkward Beauty > Post at the DozensOnline Forum h8898→.

Base 9 (Nonary): < Everything Done up to the Nines >, Post at the DozensOnline Forum h8ab4a→

Base 10 (Decimal): divisors of the cube of 10 in decimal s5231a95, fractions, irrational numbers s5231a98, s7836a41. Powers of primes p ≤ 7 s7836a34. Powers of 10 in bases 12, 16, 60, and 120 s7836a36. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. < Dare I admit good things about Decimal? > Post at the DozensOnline Forum h8752→. < Plain Ol’ Vanilla Decimal >, Post at the DozensOnline Forum h8a14a→

Base 11 (Undecimal): < Undecimal the Unbelievable > Post at the DozensOnline Forum h891a→.

Base 12 (Duodecimal, Dozenal): Set of duodecimal numerals s5231a25, fractions s5231a91, divisors of the cube of 12 s5231a95, fractions and irrational numbers s5231a98, s7836a41. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 16, and 60 s7836a36, powers of 12 in bases 16, 60, and 120 s7836a36. Factorials s5231a37. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. A 2011 paper on merits, “Dozenal FAQs”, 5.6Mb PDF d8907. < Delightful Darling Dozenal >, Post at the DozensOnline Forum h8a14b→. All tayya dates and Vinci LLC project numbers are duodecimal. Lrixe: ñiçme.

Base 13 (Tridecimal): < Tridecimal Phobia > Post at the DozensOnline Forum h8aa8→.

Base 14 (Tetradecimal): divisors of the cube of 14 in base 14 s5231a95, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. < Operation Base Fortnight > Post at the DozensOnline Forum h8913→.

Base 15 (Pentadecimal): divisors of the cube of 15 in base 15 s5231a95, irrational numbers s5231a98. Abbreviated multiplication table for use with complementary divisor method s7836b03. < La Quinceañera > Post at the DozensOnline Forum h8914→.

Base 16 (Hexadecimal): divisors of the cube of 16 in base 16 s5231a95, fractions, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Argam numerals for s7836a02, PDF here. Powers of primes p ≤ 7 s7836a34. Powers of 10, 12, and 60 s7836a36, powers of 16 in bases 12, 60, and 120 s7836a36. Abbreviated multiplication table for use with complementary divisor method s7836b03. < Sympathy for the Hexadecimal > Post at the DozensOnline Forum h8899→, Can Hexadecimal Be Civilizational?, h9681→.

Base 18 (Octodecimal): irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. < Octodecimal, Not Quite Semiprime, but … > Post at the DozensOnline Forum h8b25a→.

Base 20 (Vigesimal): divisors of the cube of 20 in base 20 s5231a95. Powers of primes p ≤ 7 s7836a34. Powers of 20 in sexagesimal and base 120 s7836a36. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. < Vigesimal, Super Decimal on Steroids? > Post at the DozensOnline Forum h8a05a→.

Base 21 (Unvigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. Writing and digit map exploring divisibility tests. DozensOnline post analyzing base 21 h89a0→. < Unvigesimal Light and Magic > Post at the DozensOnline Forum h8ab4→.

Base 22 (Duovigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 24 (Tetravigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. < Acrobatic Tetravigesimal (Base 24) > Post at the DozensOnline Forum h8b25b→.

Base 25 (Pentavigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. < Bingo Pentavigesimal (Base 25) > Post at the DozensOnline Forum h8b30a→.

Base 26 (Hexavigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 27 (Heptavigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 28 (Octovigesimal): divisors of the cube of 28 in base 28 s5231a95. Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 30 (Trigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. < Outpost Trigesimal > Post at the DozensOnline Forum h8b1a1→.

Base 32 (Duotrigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 33 (Tritrigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 34 (Tetratrigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. DozensOnline post analyzing divisibility tests in base 34 h8988→. DozensOnline post analyzing divisibility tests in base 36 h8989→.

Base 35 (Pentatrigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 36 (Hexatrigesimal): divisors of the cube of 36 in base 36 s5231a95. Powers of primes p ≤ 7 s7836a34. Powers of 36 in sexagesimal s7836a36. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. < 36: A Marriage of Squares! > Post at the DozensOnline Forum h8b28→.

Base 38 (Octotrigesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 40 (Quadragesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 42 (Duoquadragesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. < 42: The Answer to the Universe (Not) > Post at the DozensOnline Forum h8b1a2→.

Base 44 (Tetraquadragesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 45 (Pentaquadragesimal): divisors of the cube of 45 in base 45 s5231a95. Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 48 (Octoquadragesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03. < 48: You got your 3 in my hexadecimal! > Post at the DozensOnline Forum h8b11→.

Base 54 (Tetraquinquagesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 55 (Pentaquinquagesimal): DozensOnline post analyzing divisibility tests in base 55 h8987→.

Base 56 (Hexaquinquagesimal): Abbreviated multiplication table for use with complementary divisor method s7836b03.

Base 60 (Sexagesimal): “Argam for Sexagesimal with Ismarragam” (sexagesimal numerals and their names) s7836a52. Cyclical diagram s5231a90. Sexagesimal cyclical diagram and totatives s7836a51. Numerals for small multiples of sexagesimal prime divisors s5231a03; sexagesimal argam for the divisors of cubes of primes, composites s5231a95, bases 60 and 120, s5231a96. Fractions s5231a97. Multiplication through an abbreviated table and manipulation of complementary divisors s5231a99, s7836a52, 100+ page, 6½ megabyte PDF d7a60, abbreviated multiplication table for use with complementary divisor method s7836b02. Divisor counting function vs. totient function (in sexagesimal figures) s7836a07. Primorials and prime decomposition vs totient ratio (sexagesimal figures) s7836b09, s7836a08. Totatives of, paired with additive complements s7836b09. Argam numerals and names tied to chemical elements (sexagesimal arrangement) s7836a12. “The Optimized Sequence” s7836a19. Fractions expressed in sexagesimal s7836a31. Powers of primes p ≤ 7 s7836a34, p ≤ 11, and {10, 12} s7836a35. Powers of 10, 12, 16, 20, 36 s7836a36. Factorials s5231a37. Irrational numbers , s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. “The Irrational Page”, “The Reciprocals of the Simplest Primes for Selected Bases” s7836a41. “Primes in Sexagesimal Scale”, “Stanislaw Ulam’s Spiral in Sexagesimal”, “Values of Π − 1”, s7836a53. Argam kinoctove arranged in dozens and sixties s7836b00. “Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, s7836b01. In 2007-2008, sexagesimal became the lingua franca of many of my elementary number theory studies by dint of its 5-smoothness and the plethora of small regular numbers. < Sublime Sexagesimal > Post at the DozensOnline Forum h8b06d→. < Sexagesimal vs Centovigesimal > Post at the DozensOnline Forum h8abb→.

Bases {64, 66}: abbreviated multiplication table for use with complementary divisor method s7836b02.

Base 70 (Septuagesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < Sweet Sister 70 > Post at the DozensOnline Forum h8b06a→.

Base 72 (Duoseptuagesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < Silly 72, Sitting on a Post > Post at the DozensOnline Forum h8b06b→.

Base 80 (Octogesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < Base 80, Hexadecimal >3s Quinary > Post at the DozensOnline Forum h8b10a→.

Base 84 (Tetraoctogesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < 84, Alternative to Sexagesimal? > Post at the DozensOnline Forum h8b06c→.

Base 90 (Nonogesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < Base 90: Plenty Fine > Post at the DozensOnline Forum h8b09b→.

Base 96 (Hexanonogesimal): abbreviated multiplication table for use with complementary divisor method s7836b02. < Base 96: Middle Sister with all the Friends > Post at the DozensOnline Forum h8b09c→.

Base 99 (Enneanonogesimal): DozensOnline post analyzing divisibility tests in base 99 h8988a→.

Base 100 (Centesimal): divisors of the cube of 100 in base 100 s5231a95. < The Hundred as a Number Base > Post at the DozensOnline Forum h8b01b→.

Base 108 (Centoctal): < 108: Three cubed, two squared > Post at the DozensOnline Forum h8b09a→.

Base 109 (Centenneal):< 109: At least the neighbors are nice > Post at the DozensOnline Forum h8b0a→.

Base 112 (Centoduodecimal): < 112: Rarified Air at the Top of Mid Scale > Post at the DozensOnline Forum h8b10b→.

Base 120 (Centovigesimal): factors of 120 to the first through third power in base 120 s5231a96. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 12, 16, 20, 60 s7836a36. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b02. Totatives of, paired with additive complements s7836b09. DozensOnline post analyzing divisibility tests in base 120 h8988b→. < Sexagesimal vs Centovigesimal > Post at the DozensOnline Forum h8abb→.

Base 144 (Centotetraquadragesimal): < 144, Twelve’s Bigger Brother > Post at the DozensOnline Forum h8b01a→.

Base 173 (Centotriseptuagesimal): < 173: Cold Shoulders from the Neighbors > Post at the DozensOnline Forum h8b0b→.

Base 196 (Centohexanonogesimal): divisors of the cube of 196 in base 196 s5231a95.

Base 210 (Ducentodecimal): < Base 210: Diminishing Returns? > Post at the DozensOnline Forum h8b00b→.

Base 240 (Ducentoquadragesimal): < 240: Pounds, Shillings, & Pence > Post at the DozensOnline Forum h8b00c→.

Base 360 (Trecentosexagesimal): Argam numerals sufficient to represent base 360 s7836b00. divisors of the cube of 360 s5231a97, fractions s5231a98. “The Optimized Sequence” s7836a19. Factorials in pure and sexagesimal-coded base 360 s5231a37. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Prime powers / geometric progressions s7836b09. Totatives of, paired with additive complements s7836b09. < Superhero 360 > Post at the DozensOnline Forum h8b00a→.

Base Tour: a systematic exploration of integer number bases using number theory. See < Le Tour des Bases >.

Base 2520 (Dumillequinquacentovigesimal): Factorials in pure and sexagesimal-coded base 2520 s5231a37. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41.

Beach scenes: from photographs at Pensacola, FL j6305, j6308. On site at Pensacola NAS j637b. From photographs at Waikiki j630b.

“Big Me”, Icarus as a rich man s5231a56.

Bildungsroman, Reneyan. The Reneyan "coming-of-age" story. This includes events of the Ahilðiñal and Mairenal Xrgyn as recorded by the remastered Jeleyn Sarynal, and of the Kajixaþal and Samaðenal Xrgyn as recorded by the Jeleyn Kajixaþe. An extension may include the Jezrimel (Dynamic City) period of the Xiübanal, Asmaral, and Alindðal Xrgyn. These segments illustrate the transformation of Reney/Icarus from a brainy and introverted collegian naif to a young upwardly mobile professional having met the woman that would be his wife. The early bildungsroman takes place on a semester abrad, deals with an affair that leads to further relationships with women off limits and a desire for atonement. The next installment moves from commencement through a summer of work downtown, into a layoff and confusion, and finally to a move to a different city for the actual commencement of a career. The last installment has the protagonist ascend among the young professionals to have a crisis and then grow to move beyond casual affairs and petty idiosyncrasies, meeting the woman he would marry. Some of the themes include the fleeting nature of life, the definition of "home" for a graduate twenty-something, travel, relationships, issues having to do with high intelligence, psychological-emotional abuse, sexual relationships, faith, and personal growth.

Boss: My boss at a staff meeting s5231a13.

Camélia, an imago or personification of the ideal mate for Icarus, assembled around a girl of south Asian descent met in Ralysine (high school) era. Pencil study with skyscrapers and fighter jets in background (naïve) j3410. Cradling Icarus s3964a06, with Ðebñinâ s45b0a12, at a window in S. Chiara study center (Kim M. serving as model) s45b0a13, in the form of Asmarâ, dancing with Icarus s5231a31, depicted on a Post-It note s5231b00, in a sari at the Joliet riverside s5697a01. Camélia is usually depicted as exotic, often Indian descent, with long raven hair. The imago set the mold for university crushes. Ironically, when the perfect mate Aðilyrâ did materialize, she was nothing like this vision of Camélia. In 2003, the middle name Camélia was given to my daughter. Lrixe name of Camélia is Akimalâ /uh-kee-MAW-lung/, diminutive Kimxâ /KEENG-shung/. Namesake of the three dozen seventh xrgâ of mid 1987. Representative work: architectural plans produced on computer for a role-playing game k3711, postapocalyptic color drawing j374b.

“La Camélia alla Finestra”, drawing of Camélia at the east-facing window of S. Chiara study center s45b0a13. Actual model is classmate Akimakinâ.

“La Camélia fi Xereneye”, Camélia in a sari with Joliet riverfront industrial buildings in the background s5697a01.

“Camélia Lorielal”, Camélia stands in a city of skyscrapers, fighter jets in the sky above, pencil, (naïve) j3410.

“Camélia versus Ðebñinâ”, stylized and symbolic drawing of a sacred Camélia and a profane Debnina, s45b0a12.

Can Hexadecimal Be Civilizational?, insight into making hexadecimal a plausible civilizational number base through mediation/duplation, h9681.

Canaletto, Venice, Italy: s45b0a16.

Canon, argam: to the extent that there is a standard for argam transdecimal numerals: numerals s7836b00 (the document here is updated for argam below 60), numeral names s7836a16, prime powers s7836a13.

Canopy: constructability study k63a7c.

Carha Reneyâ /KAWR-huh she-NAY-ung/, my homestead s5231a29. Canonical spelling is karha reneyâ.

Cars: s5231a60; “Angelina” s5231a66.

Carymâ /cha-RÜ-mung/, “life-path”, the name of my personal logo, divised in 1985. In a 1988 self-portrait (age 17) j3b84. With a bird and sword s45b0a08, with wings and sword (the “battle crest”) s45b0a14, s45b0a24. In the Rykami Arysane dedication s5231a00, Mairenâ clutching the logo in the Val di Chiana s5231a24. Icarus logo study including past configurations of the Carymâ s5231a31. With other logos s5810a07. The Carymâ logo is the basis for Vinci LLC’s logo. Former spelling for the word karme /KAWR-muh/.

< The Case for Dozenal >, a thread I started 17 April 2006 (tayya 7696) at the DozensOnline Forum that endeavored to produce a strong, logical case for using duodecimal vs. decimal numeration, retrievable here. This thread is seminal in my interest in elementary number theory, an offshoot of my middle-school interest in number bases.

Castiglion Fiorentino, Tuscany: s45b0a06, s45b0a07, s45b0a08, s45b0a09, s45b0a0b, s45b0a11. Castello di Montecchio Vesponi s45b0a13. Classmates s45b0a14, Mairenâ, local friends s45b0a1a. Opening and closing setting for the 2021 novel Roam Away Home, a travelogue memoir of Káxa Maïrénal of 1992: the name is stylized as “Castiglion Aretino”.

Central West End, St. Louis (subject matter): Chase Park Plaza from Forest Park j6374, Lindell Highrises j63b6, a home j6400, the New Cathedral j6421, Third Baptist Church j65a9.

Cerveteri, Italy: s45b0a20, winner of the 1995 St. Louis AIA/CPC Architectural Drawing Award.

Cezanne’s Studio: s5810a03.

“Challenger [Disaster], The”, colored pencil drawing (naïve) j3461.

Charm Girl: a term posed by Aðitriçâ for lyðrelyn and .

Chart: Income vs. home affordability and housing expenses s5231a22, timeline of life sentiment s5231a45. “Ratio of Divisor and Totient Function and Superior Highly Composite Number”, “Ratio of Totient Function and Superior Highly Composite Number”, s7836a07. “Prime Factor Diversity vs. φ/r Ratio” s7836a08.

Chartres, France: cathedral s5810a02, wider scene including cathedral j6304.

Chase Park Plaza, St. Louis: j6374.

Chimera: marker picture s5231a52. Typographic element and logo s5231a41.

Christian, Amyñikâ s5231a07, depiction of a natural cross that is a scar on my chest s5231a12, God as an element in the list of what appeals to quarterlife boys s5231a19. “Truth vs. the World”, impromptu poster developed with J. Mank for a Christian retreat k8a18.

Churches: “St. Basil’s”, church on Red Square in Moscow in colored pencil (naïve), j2a28. Castiglion Fiorentino s45b0a06, s45b0a07. Siena Cathedral s45b0a18. Notre Dame de Paris s45b0a24. Stream-of-thought sketch s5231a17. As part of Reneyan home s5231a29. Chartres Cathedral s5810a02, j6304, S. Jean de Malta s5810a04. Great Mosque-Cathedral of Córdoba, Spain s51a3a03, s51a3a15, s611ba09, Granada Cathedral s611ba11, New Cathedral of St. Louis j6421. Third Baptist Church (Grand Avenue, St. Louis) j65a9.

Cime /CHEE-muh/, The lřixe word meaning “childhood”, more specifically, “boyhood”, name of the Cime Xiomðe, the lifetime-spring or childhood, between tayya 0 / 1 July 1970 and tayya 4600 / 15 October 1991. The gender impartation is not quite as strong as it might be in English, but is not neutral as in “childhood”. The word címe can be used for girls. The word derives from cílþ /CHEELTH/ “child” and the suffix –me /-muh/ conveying a state of being. Címe, along with the more feminine word jénme /ZHAYN-muh/ are names for one’s childhood, but can connote a span of time up to twenty one years old. The turning (asmíð) of one’s childhood to one’s ĝílme/míðre xiómðe is called “máðrine” /MAUTHE-ri-nuh/ for women, or “ĝálmine” /GHAUL-mi-nuh/ for men, and is one’s “coming of age”.

Cityscape: Arezzo in the distance behind Aveacrixe s5568a00. Heidelberg j6295. Lindell Boulevard highrises, St. Louis j63b6. McRee Town St. Louis j6786.

Claire Camélia, my daughter. Sketching at the Art Museum s5231a87. Also possessing the names Axalaïrâ /uh-shuh-LAW-ee-rung/, Xalyrâ /shuh-LÜ-rung/, Kimalâ /kee-MAW-lung/, Kimxâ /KING-shung/. Namesake of the six dozen tenth xrgâ of early 2003, common subject of Salcyrâ (Entrepreneurship) era drawings.

Climatron, The: j6aaa.

Coffee culture: fellow patrons s5231a08, s5231a10, s5231a17, s5231a18. Coffee cup and Coke s5231a09. Coffee cup with streams of thought s5231a21. Open mic night at Pony Expresso s5231a23. Biracial couple playing chess at Cafe Aesop s5231a41.

“Complementary Divisor Method”, new title of the Reciprocal Divisor Method, summarized s5231a99, retranscribed at s7836a52, 100+ page, 6½ megabyte PDF manual d7a60. Full sexagesimal multiplication table in argam, 111k PDF, abbreviated sexagesimal multiplication table 102k PDF.

Composite Number, a number with integer factors other than 1 and itself: numerals generated by “Infinite Multiplication Table” s5231a92, s7836a11. Numerals for small composites s5231a93, s5231a94; highly composite numerals and products of powers of the smallest primes s7836b14, superior highly composite numbers s5231a91, s5231a92, minimize totient ratio s5231a07, s5231a08, dn34, dn36. Summary of highly composite and superior highly composite argam numerals s7836b00.

Compton Heights Water Tower, St. Louis: j6791, j6aa0.

Concept, architectural (sketches): glass catwalk s5231a02, urban homestead s5231a29. Joliet close s5231a63. University City retail commons cross section s5231a72. Seattle transit, store, and suburban parking study s5231a77, downtown urbanism s5231a78, building studies s5231a79. Avindelor expansion s611bb05, s611bb06.

Concept, graphic: studies for a birthday card s5231a04, s5231a. For a drawing s5231a29. Icarus logo s5231a31. Jennifer drawing layout s5231a70. Studies for a poster commemorating the 1998 Great Forest Park Balloon Race s5231a80.

Constructability: steel for a running track k6331.

Coprime, numbers that have 1 as the sole common factor with a number base: s5231a90.

Córdoba (Spain): Great Mosque-Cathedral s51a3a03, s51a3a15; marker sketch s611ba09. Noted as a favorite destination s5231a14.

Constructability / Construction analyses: Section through an Etruscan tomb s45b0a20. Columns at the Great Mosque of Cordoba s51a3a03, bays at the Great Mosque of Cordoba s51a3a03, Tuscan ceiling s5810a06, University City retail commons cross section s5231a72. Masonry arches in Tuscany s6861a03, Roman arcade in Lucca s6861a04. The study of probable construction in hand-drawn sections has been a long-running activity since 1989. Many of the sketches were ephemeral, used to produce construction documents and carried out on onionskin. Several have been recorded in sketchbooks and project workbooks. This activity is most related to my current construction visualization modeling (see the portfolio).

Construction Trailers: s5231a87.

Coworkers: boss s5231a13, Icarus countercurrent s5810a06. Collaboration with s5231a63 and result of collaboration s5231a74. Sold to, j63b6, j6aa0. Commissioned by, j6924. Gift to, j6b53.

Crushes (lyðrelyñ), non-reciprocating limerent objects; love-interests that did not develop into relationships: freshman year high school Aðiavlikâ/Avlica (naïve) j339a, Akimalâ j3410 (see Camélia). Sophomore year Aðimisâ, Amisâ (naïve) j34b9. Junior year high school Ayuleyâ (naïve) s3964a01. First year at university Arysani s5231a18. Third year at university Arebinâ j4656. Shortly after commencement Asayme s5231a11, s5231a51. A common lrixe name for a crushee is Ymalhynâ /üm-AWL-hü-nung/, “Unanticipated”, shortened to Imallâ /ee-MAWL-lung/. This name normally applies to Aveacrixe; s5231a43, dedicatee s5568a00.

Curamiral /CHOO-jah-mi-shull/, “(of the) silence underwater”, name of the eight dozenth xrgâ of mid 2008. The name derives from Claire’s remark, having just learned to swim underwater, that she “loves the silence underwater.” Representative work: a80a4, a80b0, a80b6; the period was one of convergence of GIS and construction modeling, producing the Vinci Digital Worksite™ as it is now conceived.

“Cyclic Resonance”, 2009 paper illustrating the geometric relationship among divisors in clock-like diagrams that positioned the integers 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), equiangularly around a circle. Download the 800k PDF d818b.

Dalen, ell, ðalâ, name of the duodecimal digit eleven, resembling a backward 7.

< Dare I admit good things about Decimal? > Post at the DozensOnline Forum dated 11 April 2011 (tayya 8752) available here. This post recognizes the benefits of decimal, often downplayed by dozenalists. It is a summary of the saving graces of decimal, but not an apology for its use. The post was incorporated in the late 2011 paper “Dozenal FAQs”, a 5.6Mb PDF d8907.

Dancing, partying: s5231a31, s5231a59.

Dante, a close friend and talented artist during ralysine (high school), currently a professional fine artist in Chicago. Many of my early drawings were done alongside Dante or in a friendly competition with his skills. Dante’s early skills focused on nature and fantasy, especially horror. My skills were focused on the human figure (especially female figures), technical subjects, and architecture. Images influenced, produced in friendly competition with, or produced alongside Dante: maps of cities in an interstellar empire k3155, k3160. Drawings of conditions in the interstellar cities j3187, j3410. Challenger disaster j3461. Starship lady j34b9. Macintosh-produced plans for role playing games k3670, k3711. Sketchbook of starships s3730. Postapocalyptic Los Angeles j374b.

Decimal, the standard number system based on ten: divisors of the cube of 10 in decimal s5231a95, fractions, irrational numbers s5231a98, s7836a41. Powers of primes p ≤ 7 s7836a34. Powers of 10 in bases 12, 16, 60, and 120 s7836a36. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03.

Dedicatees, see also Rentikâ; Aðijamyse (naïve) s3964a00, Aðitinâ (naïve) k3a06, Arebinâ (reconstructed) j4656, Arysani dedication s5231a00, earlier life sketch on side B s5231b00; pictured s5231a18. Aveacrixe s5568a00, Camélia standing in for Asayme s5697a01, pictured s5231a11, s5231a51; Samaðenâ s5810a00, Aðilyrâ s611ba01, pictured s5231a59.

“Des Bâtiments de France”, winner of the 1997 AIA-CPC Architectural Drawing Award, s5810a02.

Desen, dess, dejâ, name of the duodecimal digit ten, resembling an upside down 2.

Des Plaines River, behind Xrine s5231a28, industrial vignettes s5231a57, Camélia in a sari at the Rockdale, IL riverside s5697a01.

Details, architectural: Clay tile unit in Tuscany s45b0a08. Masonry vignettes s45b0a11. Sienese Gothic window s45b0a18. Section through an Etruscan tomb s45b0a20. Paris mansard s45b0a24. Columns at the Great Mosque of Cordoba s51a3a03, bays at the Great Mosque of Cordoba s51a3a03, Place de la Université s5810a03, Tuscan ceiling s5810a06, Italian hospital room section s5810a07. Hotel floor plan, Écija, Spain s611ba0b. Masonry arches in Tuscany s6861a03, Roman arcade in Lucca s6861a04.

Diagram, Cyclical: sketched s5231a90, for twelve s7836a01, for sixty s5231a90, s7836a51. As a method to indicate totatives and their additive complements at s7836b01. These diagrams developed into the 2009 “Cyclic Resonance” paper (800k PDF), and was incorporated into the March 2010 “Balance Study” (1¾ Mb PDF).

Digit, of number bases, integers r ≥ 2; any integer 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r). For numerals, see “argam” or “numeral”. A predominant subject of the latter pages of Rykami Arysane s5231, and the entirety of Rykami Argam s7836. Relationships and their impact on multiplication tables described at “Analysis of Multiplication Tables”, 1½ Mb PDF d872a. Subject of “Digit Base Relationship”, exploring elementary number-theoretical relationships of digits to bases 2-120, 2 Mb PDF d87a9. I expanded this study to incorporate the effects of such relationships in the multiplication table, divisibility tests, and digital representation of fractions in the mid-2011 presentation “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5. “Neutral Digits”, 1.15 Mb PDF d8895, and material in the article “Exploring Number Bases as Tools”, published in the March 2012 edition of ACM-Inroads, a magazine of computer science education.

Digit, Neutral, of number bases, integers r ≥ 2; any integer 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), with n neither dividing r evenly nor coprime to r. The very subject of “Neutral Digits”, 1.15 Mb PDF d8895, wherein they are defined and certain aspects mathematically proven. Described, impact on the multiplication tables illustrated in the mid-2011 paper “Analysis of Multiplication Tables”, 1½ Mb PDF d872a. Predominant part of “Digit Base Relationship”, 2 Mb PDF d87a9, and material published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Generally, described in the Rykami Argam s7836. There are two flavors of neutral digit: the semidivisor, a regular nondivisor digit, and the semitotative, product of at least one prime divisor and at least one prime totative.

“Digit Base Relationship”, 2 Mb PDF d87a9, a presentation devised for late June 2011 that describes the number-theoretic relationship of digits, integers 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), to number bases, integers r ≥ 2. This work concentrates on digit maps that serve to describe elementary number theoretical relationships of digits to bases 2 through 120. This has become my principal method of evaluating number bases for use as tools for human computation.

“Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5, a presentation devised for late June 2011 that describes the number-theoretic relationship of digits, integers 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), to number bases, integers r ≥ 2. This work developed into the paper “Neutral Digits”, 1.15 Mb PDF d8895, attempting to mathematically define and prove the existence of the types of digits described in d87a9. The notion was published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Paper evolved from thoughts that also yielded “Analysis of Multiplication Tables”, a paper illustrating the effects of elementary number-theoretical digit-base relationships in the multiplication table of a number base, 1½ Mb PDF d872a. This paper summarizes description of digit maps, and the effect of the relationship of digit and base on multiplication tables. Octal, decimal, duodecimal, and hexadecimal tables serve to illustrate the effects.

Digit Map, a chart that plots the digits, integers n of a number base, integer r ≥ 2 in sequence from 0 through ω = (r − 1), with the digit “0” signifying congruence with base r. Examples of digit maps appear at “Digit Base Relationship”, 2 Mb PDF d87a9, and “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5. I invented digit maps in 2009.

Digit Spectrum, a bar chart that plots the digits, integers n of a number base, integer r ≥ 2 with the digit “0” signifying congruence with base r, aggregating the digits by type. The types include the unit (purple), divisors (red), semidivisors (orange), semitotatives (yellow), totatives (light gray), omega totatives (light blue), alpha totatives (light green), alpha-omega totatives (light purple), in that order. Digit spectra are effective in quantifying the ratio of digit types to the number base for grand bases, number bases beyond human ability to leverage them. Examples of digit spectra appear at “Digit Base Relationship”, 2 Mb PDF d87a9, and “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5. I invented digit maps in 2009; digit spectra summarize the types of digits for a grand base. I invented digit spectra in early 2011.

Divisibility Test, Intuitive, a method for determining whether an arbitrary integer x is an integer multiple of a second integer n: Let the integer r ≥ 2 be a number base; then α = (r + 1) and ω = (r − 1). Divisibility rules for omega, the alpha rules later realized s7836a26. A major indirect relationship shown in digit maps and spectra in the 2 Mb PDF “Digit Base Relationship” d87a9, expanded, 11Mb d87aa, and in the 2011 paper “Dozenal FAQs”, 5.6Mb PDF d8907. The notion is incorporated into a peer-reviewed article published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Alpha has a special intuitive relationship with the number base, inherited by the divisors of alpha. Together the alpha and omega relationships (r ± 1) comprise indirect relationships leverageable by human cognition.

Divisor, integers that divide a larger integer evenly: cyclical diagrams s5231a90. Of cubes of prime number bases s5231a95, s7836a20, of select composite bases s5231a95. Of cubes of 60 and 120 in respective bases s5231a96, of 360 in base 360 s5231a97. Importance in leverage s7836a06. Divisor counting function vs. totient function s7836a07. Distinct prime divisor vs. totient ratio s7836a20, refined at s7836a08.

Divisor, Distinct Prime, one of the primes p | r (integer r ≥ 2 being a number base), ignoring multiplicity of p in the prime decomposition of r. Effect on totient ratio s7836a08.

Dog Portraits: verone-style Jimla Alindðe j5916, Jimla Aðitriçe j5978.

Domesticity: considering an urban homestead s5231a29. With fiancée Laura s611ba01, s611ba08. Drawings for home improvement s611bb05, s611bb06.

Dozenal: Base 12 or duodecimal. Set of duodecimal numerals s5231a25, fractions s5231a91, divisors of the cube of 12 s5231a95, fractions and irrational numbers s5231a98, s7836a41. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 16, and 60 s7836a36, powers of 12 in bases 16, 60, and 120 s7836a36. Factorials s5231a37. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. A 2011 paper on merits, “Dozenal FAQs”, 5.6Mb PDF d8907. All tayya dates and Vinci LLC project numbers are duodecimal. Lrixe: ñiçme.

“Dozenal FAQs”, 2011 paper for the Dozenal Society of America, exploring the benefits and drawbacks of duodecimal numeration, compared to decimal. Download the 5.6Mb PDF d8907.

Dozenal Society, a non profit organization founded by F. Emerson Andrews shortly before World War II that advocates research and public education regarding base twelve or duodecimal numeration (The Dozenal Society of America or DSA) and founded in Britain in the early 1960s (the Dozenal Society of Great Britain or DSGB). My middle-school interest in base twelve, having become internalized in high school and solidly incorporated into some of my professional methods as a tool in my twenties led to contact with the DSGB in 2002, and membership in the DSA in 2006. I am the president of the DSA since 2008, having written for and edited the Duodecimal Bulletin, the official journal of the DSA, and the DozensOnline Forum.

DozensOnline, a web forum administered by the Dozenal Society of Great Britain that began in August 2005. My username is icarus, retrievable at user 50, having joined 13 April 2006 (tayya 7692). Much of my writing revolves around elementary number theory, spurred by < The Case for Dozenal >, a thread I started 17 April 2006 that endeavored to produce a strong, logical case for using duodecimal vs. decimal numeration, retrievable here.

Drive-By Series, The, a collection of verone-style drawings produced from the recent memory of having driven past the subject on commutes home from work downtown. McRee Town at Dusk j6786, SLU Hospital j6787.

Duodecimal, counting using a base of twelve rather than ten. Set of duodecimal numerals s5231a25, fractions s5231a91, divisors of the cube of 12 s5231a95, fractions and irrational numbers s5231a98, s7836a41. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 16, and 60 s7836a36, powers of 12 in bases 16, 60, and 120 s7836a36. Factorials s5231a37. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. A 2011 paper on merits, “Dozenal FAQs”, 5.6Mb PDF d8907. All tayya dates and Vinci LLC project numbers are duodecimal. Lrixe: ñiçme.

Duomo (Cathedrals): Siena Cathedral s45b0a18. Notre Dame de Paris s45b0a24. Chartres s5810a02, j6304, Granada s611ba11, St. Louis, Missouri j6421.

Duplation, see Mediation/Duplation.

Ðakát /the-COT/ A lřixe word meaning “direction”, deriving from the verb ðákyt (DTHAWK-üh), “to direct, to command”. The word can mean “a plan, an intent.”, and in the case of jeléynyn reñéyor (journals), this is the preferred meaning.

-ðan /-than/ The lřixe suffix signifying a region or nation. The suffix is related to the verb ványh /VAWN-üh/, “to inhabit, to dwell”, through transformation of /v/ to /ð/.

Ðebninâ /THEYB-nee-nung/, “Fair One”, a sister of a friend. With Camélia s45b0a12. Ðebninâ became emblematic of typical Joliet-area girls, carefree, shallow, but beautiful, prone to reject both Reney and Icarus. From the verb ðábyn /THAH-bün/, “to make fair, to lighten, to bleach”.

Ðel- /(THEYLL/ lrixe prefix meaning “great”, “optimum”, “superior”.

Ðélme /(THEYLL-muh/ lrixe word meaning “greatness”. The word is used to connote anything that is most beneficial or causing the most joy. The modern lrixe word is “ðélme” (THEY’LL-ma). The old lrixe word Ðeláima /(theyll-EYE-ma/ is more commonly seen in early work.

Ðeleĝajenâ /the-leh-GHAW-zheh-nung/, the “Great Teenage Depression” of 1984-1987. This is a depression centered around November 1985, arising from social misunderstanding, mostly due to the mismatched Reneyan social immaturity and intellectual prowess. This depression was the most severe in life, forming the backdrop for instability and lack of confidence in Safrine (university years), setting the stage for the Krunþe Galmine quarterlife crisis of 1993-1994, 1996, and 1998. The tension of high school years has served as a great well of energy, and has generally strengthened me.

Ðelsaënyñ Reneyan /thell-SAW-en-een she-NAY-an/, the “Reneyan Golden Age” of 2004-today. This is a sustained system of Salcyrine and Viðanine (Entrepreneurhsip and Balance-age) highs, wherein the years have been inordinately satisfactory and spiritually serene. The Saryña Xarikavincal (Business Establishment High) of 2004 merged into the Saryña Saxisorþal (Mountaintop High, a Catholic spiritual high) of 2006, then the Saryñ Argamal (Numeric High) of 2007-2008 and the Saryña Rynviðanal (Spiritual Balance High) of today. The system of highs follows relatively high times after marriage and the birth of my children. The Ðelsaënyñ Reneyan has endured the Egajñalikçavare (Global Financial Crisis) and has proven quite resilient. Most of the work during the Reneyan Golden Age appears in the Vinci LLC portfolio and the Rykami Argam.

Early Work: any work produced before Asmið Galmine, the coming of age or quarterlife turning point at tayya 4600 / 15 October 1991. This work includes technique development and schoolwork, but also naïve artwork produced for the purpose of expression rather than exercise of technique. Fourth grade map of South America j2050. “St. Basil’s”, church on Red Square in Moscow in colored pencil, j2a28. “Loril Ya”, canonically “Ðani Lorielal”, map of the capital city of an interstellar empire k3155, “Avlicir”, canonically “Iral Imelavlike”, map of a port on the home planet of an interstellar empire k3160. “Loriternal Yev”, urban, sci-fi perspective study j3187. Portrait of Aðiavlikâ, freshman year high school crush j339a. “Camélia Lorielal”, Camélia with skyscrapers j3410. Architectural, nocturnal perspective study j3439. “Challenger [Disaster], The”, colored pencil drawing j3461. “Misa Elyamî”, pencil drawing j34b9. “Attack on Temys”, raster plan view vignette k3670. Typical hardware j36b0. “Caqualis Base”, raster plan of base k3711. “Egalitarian Army”, starship sketchbook s3730.“Warday L.A.”, postapocalyptic Los Angeles, colored pencil j374a. Early self-portrait j3b84. Aðijamyse, high school girlfriend, s3964a00. Restored dedication drawing of Arebine j4656, originally drawn summer 1991.

Écija, Spain: floor plan of a hotel s611ba0b.

Eĝajen /eh-GHAW-zhen/, “troubles”. Rejection by Asayme s5231a11, lamenting past s5231a12, lamenting a running injury s5231a20, s5231a21, shamefully arguing with sister s5231a28, falling to earth outshone by rivals s5231a74.

Eĝájenimy /eh-GHAWZH-ni-mü/ The lřixe name for New Lenox, Illinois, setting of the nucleation of the Ðeleĝájena (Great Ralysine Depression). The town thus bears the name “City of Troubles”. A setting in The Official Troublemaker.

Eĝajñalikçavareal /eh-ghuhj-nuh-lik-khuh-VAW-je-ull/, “(of the) global financial crisis”, name of the eight dozen first xrgâ of late 2008. Representative work: a8187.

Eĝájñalékxiðanal /eh-ghuhj-nuh-LAKE-shee-thah-null/, “(of the) crisis for the enlightened”, name of the ten dozen first xrgâ of mid 2018. Representative work: aa254, aa286. Business projects dry up and some opportunities disappear.

‘Ekráne /‘ay-KRAWN-uh)/ A lřixe word meaning a cyclical period of 36 days, deriving from the French word “écran” (screen). Twelve such periods comprise an ‘anréna /‘on-RAIN-a)/, the Reneyan “year” of 432 days. Eighteen ‘anrényn comprise the xiómðe (she-AUM-the), or “life season”. The life season, a little longer than 21 years, is regarded as the lřixe definition of a generation, when one comes of age. Four life seasons comprise a lifetime, a little more than 85 years long. The ‘ekráne and ‘anréna are considered the trakaðsyne /tra-KAWTHE-sü-nuh/ or “Blue Calendar”.
The classical ‘ekrányn bear names for the nóvinyn and amores roughly at or before the Lakepoint Era as follows:

0. Axánthal /uh-SHAWNT-hull/.
1. Aðilýral /uh-thee-LÜSH-ull)/.
2. Arýsanal (uh-JÜS-un-ull).
3. Amýnikal (uh-MÜN-ik-ull).
4. Áymanal (EYE-mahn-ull).
5. Arahílal (uh-jah-HEEL-ull).
6. Asáimal (uh-SAW-eem-ull).
7. Aðináral (uh-thee-NAWR-ull).
8. Aveakríxal (uh-vay-uh-KREESH-ull).
9. Samáðenal (sa-MAUTHE-ayn-ull).
10. Ryxóxnal (jü-SHOWSH-null).
11. Akimvříwal (uh-keem-VREEW-ull).

The names of ‘ekrányn and thus the Blue Calendar are rarely used after the Xeĝříwa Reneya, táyyâ 6225.

Eiffel Tower: stylized s45b0a24, from a memory s5231a12.

Ekrinþal /eh-KREEN-thull/, “with challenge”, i.e., a proving or testing, name of the seven dozen first xrgâ of early 2004. Representative work: a7158, a71b9. Work in this era was predominently architectural, concerning a local university landmark and technical drawings for a corporate retrofit. Construction visualization work was ramping up.

Elements, Chemical: used to name the primes less than around 540 s7836a12.

Elevation, Architectural (sketch): vignette in red ink of my urban homestead s5231a31. Bay of the Great Mosque of Cordoba, Spain s51a3a15, Place de la Université, Aix-en-Provence, France s5810a03, Partial study of Euclid Avenue architecture, in ballpoint s5231a59. Seattle residential high rise building studies s5231a79. St. Louis masonry studies j6284, j6285.

Empire, Interstellar: theme of some ralysine (high school) era drawings. Maps of cities k3155, k3160. Drawings of conditions in cities, j3187, j3410. Starship, with female commander j34b9. Macintosh-produced plan views k3630, k3711. Lrixe: kxmere aþral.

Emily: character met in Paris hailing from Coventry in the novel Roam Away Home. Emily had just come from Bruges and had mentioned a place to stay in that town. She painted the town red with the protagonist, tagging along with Patrice and Guy. The protagonist was fixated on the pin in Emily’s long blond hair.

Emýlanþâ /eh-MÜLL-awn-thung/: “pageant, masquerade”; a sort of showy parade as in Mardi Gras celebrations done proper. Name of the ten-dozen-sixth life-phase. The name refers to the entire putting on of airs and the pretense associated with the time of covid.

Engineers returning from lunch, s5231a10.

Ennâ /ANE-nung/, light reflected or refracted from elsewhere. Examples: Francis Park j6146a, St. Louis masonry studies j6284, j6285, St. Louis Hills Christmas scene j628b. Heidelberg j6295. Beach light effects j6305, j6308. Ocean underwater light j630b. Oversaturated light from sand j637b. Light on brick massing and spring foliage j63aa. Light on vernacular j6400 and ornamental masonry j6421. Light through a glass building j6580 and a geodesic dome. Light dappling a street, reflected from midrise windows j65a9. Sunlight on masonry and asphalt j6726. Urban light vs. twilight j6786, j6787, j6789, j6791. I have been interested in drawing ennâ since late grade school. Also, suffixed to a female name, signifies she is socially off limits.

Enta /EN-ta/ The lřixe word meaning “dead”, something that ceases to live. The word derives from the verb nátyh (NAWT-üh), “to die, to pass away”. Sometimes the word is intensified via duplication, written “entent”. A corpse is said to be “entent”, “dead and gone”.

“Enter Ecbatana”, imagined rucisaime-style scene s4952a09.

Eprañikçâ /uh-PRAWN-ik-khung/, “before unity”, engagement, name of the six dozen first xrgâ of early 1999. Representative work: j6147, j6159; s611ba01, s611ba08, s6119a09, s611ba0b.

Epravin /uh-PRAW-veen/, “before home”, househunting, name of the six dozen third xrgâ of early 2000. Representative work: j6304, j6305, j6374, j637b, j63aa, j63b6; k6331, k635a, k63a8f.

Eprkatme /uh-purr-CAWT-muh/, “before fatherhood”, name of the six dozen ninth xrgâ of late 2002. Representative work: j6924.

Eprsalcyrunâ /uh-purr-sull-CHÜ-roo-nung/, “before success”, emergent entrepreneurship, name of the seven dozenth xrgâ of late 2003. Representative work: a7013, a7024, a70a0, a70a8, four projects that implied that construction visualization would prove more lucrative than a career in architecture. This period saw the development of construction visualization with a second client while at tavnemika. At this time it seemed that the work I do today represents God’s calling, that I ought to surrender dreams of designing skyscrapers or making fine art to producing illustrations of construction worksites.

Etruscan Tombs at Cerveteri, on site drawing s45b0a20, winner of the 1995 St. Louis AIA/CPC Architectural Drawing Award

Eureka Springs, Arkansas: The Flatiron building j6726.

“An Excursion, An Exploration”: subtitle for the Rykami Nixaþe s4952a00, subtitle in the Rykami Argam s7836a01.

“Exploring Number Bases as Tools”, a peer-reviewed article I wrote in January 2012, published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. The article examines the relationship of digits and number bases, using digit maps, examining the manifestations of the relationships on multiplication tables, divisibility tests, and fractions. The downloadable articles “Digit Base Relationship”, 2 Mb PDF d87a9, “Neutral Digits”, 1.15 Mb PDF d8895, and “Dozenal FAQs”, 5.6Mb PDF d8907 precede the article.

Factorials, integers n! that are products of all integers 1 ≤ n, with 0! defined as equal to 1: in bases 12, 60, 360, 2520 s7836a37.

Factory/Smokestacks: In Joliet vignettes s5231a14, s5231a18. Above Icarus’ head s5231a27. Camélia s5697a01. A page of vignettes of factories in Joliet, IL s5231a57. Ink study s5231a60. Downtown St. Louis metal stack j652a. McRee Town j6786.

Failure: with a date s5231a11, with a sport injury s5231a20, relating with sister s5231a28, in career s5231a74.

Female Subjects: Adevanâ s5231b00. Aðiavlikâ/Avlica (naïve) j339a. “Misa Elyamî” (naïve) j34b9. Aðijamyse (naïve) s3964a00. Aðilyrâ s3964a13, s5231a59, dedicatee s611ba01, s611ba08. Akaisone/Ayntô s3964a04. Akimakinâ s45b0a14. Amagal s5810a06, s5231a44, s5231a50. Amyñikâ s5231a07. Amyqâ s5810a06. Arebinâ s5231a09, getting deleted s5231a22. Dedicatee j4656. Arysani s5231a18. Asayme a5231a11, s5231a51. Asmarâ s5231a31, s5231a46. Aveacrixe/Ymalhyna s5231a43, dedicatee s5568a00. Avikari s45b0a14. Aymanî/Xibane s3964a02, s5231a10, s5231a21. Ayuleyâ s3964a01. Camélia/Akimalâ/Axanthi, (naïve) j3410, s3964a06, s45b0a12, s45b0a13, s5231a31, s5231b00, s5697a01. Ðebninâ s45b0a12. Mairenâ a45b0a1a, s5231a12, s5231a16, s5231a24. Ñimanþyñe s5231a49, s5231a67. Samaðenâ dedicatee s5810a00, s5231a41. Xrine s5231a28, s5231a49.

Fiancée: Aðilyrâ, recently engaged s3964a13, as dedicatee of the Jeleyn Añikçine Xisaëna, s611ba01. Domestic picture with husband s611ba08.

Firenze/Florence, Italy: In a vignette s5231a18. Palazzo Vecchio s5810a06, Palazzo Vecchio at the Piazza della Signoria s5810a09. Setting for the first two chapters of the 2021 novel Roam Away Home, a travelogue memoir of Káxa Maïrénal of 1992.

Fishing: “Fixin’ to Fish” j8584.

Fraction Map, a post at the DozensOnline Forum, h8aaa-1→. The post examines the digital expansions of unit fractions with integer denominators between 2 and 16 inclusive, and integer number bases between 2 and 30 inclusive. The expansions are classified according to < Icarus’ Standard Nomenclature for Number Bases >, h8910.

Fractions, digital: Octal s5231a98, Decimal s5231a98, Duodecimal s5231a91, s5231a98, Hexadecimal s5231a98, Sexagesimal s5231a97, s7836a31. Base 360 / Kintoval / Kinoctoval s5231a98. See also fraction map.

Francis Park, St. Louis Hills: verone-style Impressionist drawings on site in spring j6146a, j6416b, j6417, autumn j624a.

Forest Park, St. Louis: Chase Park Plaza j6374, the Jewel Box j6580.

Game, Role-Playing, drawings in service of (all naïve); “Loriternal Yev”, canonically “Imel Lorielal”, capital city of an interstellar empire j3187. “Camélia Lorielal”, Camélia in a near-future urban scene j3410. “Misa Elyamî”, female captain of a starship j34b9. “Loril Ya”, canonically “Ðani Lorielal”, map of the capital city of an interstellar empire k3155, “Avlicir”, canonically “Iral Imelavlike”, map of a port on the home planet of an interstellar empire k3160. “Attack on Temys”, raster plan view vignette k3670. Typical hardware j36b0. “Caqualis Base”, raster plan of base k3711. “Egalitarian Army”, starship sketchbook s3730.

Gilme /GHEEL-muh/, “youth”, name of the Gilme Xiomðe, the lifetime-summer or prime of life, between tayya 4600 / 15 October 1991 and tayya 9000 / 28 January 2013.

Girlfriend, Noviâ /NO-vee-ung/, “(romantic) girlfriend”. Aðijamyse, s3964a00. Mairenâ warming a45b0a1a, at the wheel of her Fiat s5231a12, nobly with Icarus in Siena s5231a16, things seen her way s5231a24. Her autograph and note s5810a07. Aveacrixe s5568a00, s5231a43. Xibane: stylized s5231a10, memory study s5231a21. Samaðenâ sketchbook dedicatee s5810a00. Ink memory portrait s5231a41. Ajiñevrâ: signature s5231a15. Aðilyrâ: signature s5231a23. Memory portrait in ballpoint s5231a59. Passenger on a date s5231a66.

Granada, Spain: cathedral s611ba11.

"A Graph of Highly Composite, Superior Highly Composite, Superabundant, and Colossally Abundant Numbers", graphic summary of a study wa111, involving a dozen OEIS sequences (especially the named ones), including A301413 et al., available at na137.

Great Hundred, i.e., the number 120: factors of 120 to the first through third power in base 120 s5231a96. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 12, 16, 20, 60 s7836a36. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b02. Totatives of, paired with additive complements s7836b09. DozensOnline post analyzing divisibility tests in base 120 h8988b→.

Great Mosque of Cordoba (Spain): s51a3a03, s51a3a15; marker sketch s611ba09.

Hán /HAWN/ The lřixe word for family, particularly the nuclear family. It derives from the verb hányh /HAWN-üh/, “to be related to, to be kindred”. The word hánme /HAWN-muh/ means “familyhood”.

Heidelberg, Germany: a snowbound study from a photograph not produced on site j6295.

Hexadecimal, number system based on 16 rather than 10, commonly used in computer science: divisors of the cube of 16 in base 16 s5231a95, fractions, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Argam numerals for s7836a02, PDF here. Powers of primes p ≤ 7 s7836a34. Powers of 10, 12, and 60 s7836a36, powers of 16 in bases 12, 60, and 120 s7836a36. Abbreviated multiplication table for use with complementary divisor method s7836b03. Can Hexadecimal Be Civilizational?, h9681→.

Highly regular number, indices of the record transform of OEIS A244052. Each term has more regular numbers than the last. See Turbulent Candidates for proof and associated information, A288813 (primary “turbulent” candidates for A244052), A288784, the necessary-but-insufficient condition for A244052. See also the text file highlyregular.txt. The sequence is akin to that of the highly composite numbers (OEIS A002182).

Hildy /HEEL-dee/ minor character in the novel Roam Away Home who was the girlfriend of Kristos (that mad Greek genius) who let the protagonist know that Iesha inexplicably admired him. The name pertains to ahilðiñâ, but in the 2021 novel, was also made to apply to ayalánþe. Subject of a sketch in the novel.

Hospital: hospital room in Italy s5810a07, SLU Hospital j6787.

Icarus, avatar in self-portraiture, and username at the DozensOnline Forum. Feature Page. At the threshold of starting a career s5231a01, admiring Arebinâ s5231a09, on the floor, in crisis s5231a12, sanding shutters s5231a12, color portrait in a mirror s5231a13, coming to draw s5231a15, nobly wed with Mairenâ in Siena s5231a16, losing his ability to run s5231a20, pondering where he’s been, what to draw, slaying the past s5231a22, effacing Arebinâ emblematic of dud relationships s5231a22, Picasso-style self-portrait s5231a27, arguing shamefully with his sister s5231a28. Icarus dancing with Asmarâ as Camélia s5231a31, embracing her s3964a06, coming to sketch s3964a07, countercurrent s5810a06. Icarus with Amagal s5231a50, as a rich man s5231a56, driving s5231a63, passing cars as he drives Angelina s5231a66, with Aðilyrâ as passenger s5231a66. Falling to the earth in Old North St. Louis in disgrace s5231a74. Early self-portrait j3b84. With fiancee Laura s611ba01, In comparison to a wedded Reney s611ba08. Icarus embodies my sentiments in the Apprenticeship Era, curious and prodigal, but fragile and lost. Icarus often is depicted wearing a backward Chicago Bulls cap. Icarus was the son of Daedalus in Greek mythology, an inventor who built wings that Icarus misused and crashed to the sea after venturing too close to the sun. The name De Vlieger means “son of the flyer”, hence Icarus. The other avatar in self portraiture is Reney, tending to be neutral or positive in outlook. See also Reney. The name Bae distinguishes me from how I am seen in the eyes of Acramilâ/Aðimallâ. It is an edifice of an imagination, the personification of all things masculine, mounted atop my image much like my imago Camélia is the more unmoored personification of the Goddess-Maiden. See also Bae. My neutral lrixe name is Mella or Mixa; see also Mella, Mixa. If you're around and I have just fumbled something you may hear me say maliyya Mixa, “dear Mike”.

“Icarus and Camélia”, Icarus is united with his ideal mate s3964a06, Asmarâ as Camélia, dancing with Icarus s5231a31.

“Icarus at the Park”, color self-portrait in a mirror s5231a13.

“Icarus Casca dal Cielo”, Icarus falling from the sky in disgrace in Old North St. Louis s5231a74.

“Icarus Countercurrent”, Icarus is walking against the current s5810a06.

“Icarus Ectefe Xrine”, Icarus is shamefully arguing with his sister, and the two are parted in their lifestyles, s5231a28.

“Icarus fi Krunþe Alanþe”, Icarus lies on the floor strewn with implements of his trade, alone and in crisis s5231a12.

“Icarus Guidando”, Icarus at the wheel s5231a63.

“Icarus k’Amagal”, a picture of me and Amagal s5231a50.

“Icarus Lasciando a Disegnare”, Icarus “breaking away” to draw s5231a15; see also “Icarus Viene a Disegnare”.

Icarus logo: Icarus and sun s5231a31, stylized s5231a41, s5231a43.

“Icarus Nixaþinal, Reney Añikçinal”, Icarus brooding at an office computer, celibate, compared to his later happy situation s611ba08.

< Icarus’ Standard Nomenclature for Number Bases >, a post placed 5 December 2011 (tayya 8910) at the DozensOnline Forum retrievable here. This post summarizes my nomenclature (terms) for the study of number bases. This nomenclature appears across the 2011-2012 body of papers and diagrams, notably “Analysis of Multiplication Tables”, 1½ Mb PDF d872a, “Digit Base Relationship”, 2 Mb PDF d87a9, “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5, “Neutral Digits”, 1.15 Mb PDF d8895, and “Exploring Number Bases as Tools”, published in the March 2012 edition of ACM-Inroads, a magazine of computer science education.

“Icarus Viene a Disegnare”, entering Cafe Philippe in office attire, with paintbox (Wydown at Forsythe, Clayton, MO) to sketch s3964a07. Perhaps modeled on the similar “Icarus Lasciando a Disegnare” s5231a15.

Ice, a major tahil theme in 1997. Ice and Flower t5998, Icicle and Spring Thunderhead t5a0b, Tahil Heatone / Prairie Snow and Snowbound t6032. Antarctic Nunatak j5a1a.

Iesha /eye-EE-shuh/, character principally representing aymánî in the novel Roam Away Home. The protagonist had seen the “ravishingly beautiful” Iesha late in freshman year of college and dreamed about her all summer. Hildy, the girlfriend of Kristos (that mad Greek genius), had suggested Iesha had a crush on the protagonist, who initially thought it a joke, but it was true. She was a puzzle he never figured out. Radha interposed in their relationship and Iesha didn’t talk to the protagonist for a whole year. Even then, Rosalba felt like she was walking in Iesha's shadow. The protagonist nicknamed Iesha “Number One”.

Ikaryne /ee-KAW-rü-nuh/, “Icarus”. See “Icarus”. Rarely, used in phrases pertaining to me. See also “Reney”.

Imallâ /ee-MAWL-nung/, a diminutive form of ymalhynâ, “Unanticipated”, usually a name for Beatrice in the nixaþine but applied to other crushes. The word also applies to a crisis or something unforeseen. See also ymalhynâ, aveacrixe. Beatrice understood the name as “Malina”, diminutive of Italian “Amalia” (Emily).

Imel /ee-MAIL/, “city”, St. Louis j628b, Heidelberg j6295, Chartres j6304.

Imoni, Imani, see aymani.

“Incontra la Laura”, ballpoint memory portrait of Laura s5231a59.

Industrial buildings: In Joliet vignettes s5231a14, s5231a18. Above Icarus’ head s5231a27. Camélia s5697a01, Gare de Marseilles, France s5810a02. A page of industrial buildings in Joliet, IL s5231a57. Ink study s5231a60. Downtown St. Louis smokestack j652a. Central Paper Company, classic brick warehouse j6692. McRee Town j6786.

“Infinite Multiplication Table” s5231a92, s7836a11.

Injury, running s5231a20, s5231a21.

Insecurity: Icarus embraced by Camélia s3964a06, at the threshold of a career s5231a01, getting rejected by Asayme s5231a11, on the floor in crisis reminiscing about better times in the past s5231a12. Getting beyond the past s5231a22.

Intaqa kyre: /EEN-tong-uh KÜ-zhuh/ literally, a slowing heart or power-center. Name of the ten dozen fourth xrgâ of mid 2019.

Introduction: Rykami Argam s7836a01, s7836a02, s7836a03.

Introspective: stage of life and maturity level at age 24 s5231a02. Feelings for erstwhile university girlfriends s5231a07, s5231a09, s5231a10. Recollections of travels s5231a12, s5231a14. Thoughts on Samaðenâ s5231a41. How to move on from the past, where to live, earning power vs. house affordability s5231a22. Imagining what Mairenâ is feeling s5231a24. Falling to earth in disgrace, outshone by rivals s5231a74.

Irrational numbers: bases {6, 8, 10, 12, 14, 16, 18, 20, 36, 60, 120, 360, 2520} s7836a41.

Irrational Page, the: s7836a41.

Ismarragam /is-muhr-RAH-gam/, Arabic word meaning “number name”. Used to signify names for numerals devised for number bases larger than decimal (transdecimal number bases). Numerals and names for prime powers s5231a91, numerals and names for superior highly composite numbers s5231a91, numerals for small composites s5231a92, numerals for factors of superior highly composite numbers s5231a92. Study for primes, using the chemical elements s7836a12. For prime powers and 3-smooth composites s7836a13. Alternative “Anglo-Saxon” s7836a13. “Canonical” s7836a16.

-iwá /ee-wung/ A lřixe suffix roughly corresponding to the “–ium” prefix in English. It often connotes a place where a given activity is practiced. Examples are arýsiwá (a-JÜS-ee-wung) “studio”, kímiwá /KEEM-ee-wung/, “study room, small library”.

Iya /EE-ya/ The lřixe third person feminine singular pronoun, meaning “she”. Masculine is Ywa /Ü-wa/. Accusative suffix is -ik, dative is -ha.

Jacobs, Allan: lecture notes and signature s5231a60.

Jalleilâ /shuh-LAY-lung/, /juh-LAY-lung/, “hurrah”, alleluia; exclamation of happiness, joy.

Jayme, see ajamyse.

Jennifer, see ajinevrâ.

Jeleyn /zhuh-LAYN/, “written (account)”, a journal or diary. The word appears in earliest jeleynyn as “chelene”.

Jeleyn Añikçine Xisaëna /zhuh-LAYN uh-NEEK-kheen-uh shi-SAW-en-uh/, Journal of the Commitment Era, s611b, a journal and sketchbook of the latter engagement and first days of marriage during the Añikçine (Commitment) era, 1999-2000.

Jeleyn Kajixaþe /zhuh-LAYN kah-jih-SHAW-thuh/, Journal of the False Apprenticeship, s4a03, firsthand account of the “Commuting” (postgraduation) summer, the Searching, and the loss of work that resulted in a move to Arynluimy (St. Louis) in early 1994. It is a work of the late, post-saryna Safrine (Enlightenment) era, 1993. The story arc includes lamentation of college days, then lamentation of work downtown in Chicago. Travel includes Minneapolis, Columbus, Kansas City, and Atlanta. The Safyra Confession and the relationships with Samaðenâ and Rysena figure prominently. The account is perhaps a finer bildungsroman than Jeleyn Sarynal of early-mid 1992.

Jeleyn Sarynal /zhuh-LAYN sa-RÜN-ull/, Journal of the Acme, s4666, firsthand account of the Nakry Saryna (the First Acme) which includes the Semester Abroad, the Kaxa Mairenal, and the Summer in Val di Chiana of mid Safrine (Enlightenment) era, early-mid 1992. The account describes the culture shock, acclimation, and final embracing of Italian culture. It describes an affair with Mairena and the psychological effect on the protagonist, as well as his shedding introversion. An effect of the affair is the commencement of the Arahkaxa (the Quest for God). The protagonist returns home a changed man. This work was remastered in 2013, originally as the Reneyan Bildungsroman.

Jeleyn Tiviç-Anrene /zhuh-LAYN TEE-vikh an-JAY-nuh/, Journal of the Two Dozenth Reneyan Year, s6000, a sketchbook of the latter engagement and first days of marriage during the Añikçine (Commitment) era, 1999-2000. The book is focused on career activities, with technical sketches in ballpoint.

Jeleyn Verakrexal /zhuh-LAYN vuh-xuh-KRAY-shull/, Journal of the Resurgence, s6563, a sparsely developed sketchbook of the first days of marriage during the Añikçine (Commitment) era, 2001-2002. The book is akin to Jeleyn Tiviç-Anrene.

Jeleyn Anviomiral /zhuh-LAYN un-vee-O-mi-shull/, Journal of the Aquarium, s8330, a sketchbook full of Vinci LLC trade secrets, code, and digital model objects that forms the basis of some active business methods. The work commenced during the Viðanine (Era of Balance), 2009-2010.

Jená /ZHAY-nung/, The lřixe word meaning “girl”, applicable to any female younger than asmíð máðrine “coming of age” (just over 21 years). See cime. The word jená derives from the verb jányh /JAWN-üh/, “to curl”. Lřixe feminine names commonly begin with the prefix “a-”, which is an archaic article meaning “the”. Feminine names that begin with the letter A traditionally drop that first letter, or have the letter L prefixed (the modern definite article is vocalic “l”.) Examples are Ann (Nínâ or Lánâ), Amy (Mýna or Lámyn), Heather (Açeþrýne, Æþrýne), Jennifer (Ajinévřâ), Melissa (Amísâ) and Michelle (Aximélâ). Traditionally the prefix is lost at marriage or childbirth, taking on the suffix -énâ, denoting a mature woman. The Reneyan use of the naming convention preserves the traditional name for significant women. Thus, though there may be plenty of Kimberlys, there shall be only one Akímvřiwâ, many Jennifers, only one Ajinévřâ.

Jennifer, a figure model at the St. Louis Artists Guild: s5231a70, s5231a71.

Jimlâ /JEEM-lung/, “drawing”, stylistically the term is a short version of jimla fiakral.

Jimla fiakral /JEEM-luh fee-AWK-rull/, “drawing on black”, see (Jimalmyne) Verone, “inversed” style.

Jody, a character in the 2021 novel Roam Away Home representing arysiúðyne, met on an intercity train (the Côte Vermeille) from Paris to Barcelona. The protagonist and Jody discussed art, and the latter showed her body art to wow Paul from England. The meeting of Jody triggered a dreamy sequence of rhyme, including a sonnet, describing artists, and the generally sleepy mood of the second class car that evening.

Joliet, IL, my hometown, see also Xereney. Camélia at an industrial riverfront s5697a01. Noted as a favorite destination s5231a14. Vignette showing a factory in Joliet s5231a18. A page of vignettes showing industrial buildings around town s5231a57. Joliet urbanistic close s5231a63. Joliet is often depicted wistfully, as a rustbelt industrial town overrun with smokestacks and factories. Setting of _otherworld son_ and The Official Troublemaker.

“Joliet Page, The”: vignettes of its industry, in ballpoint s5231a57.

Joreyrâ /jo-JAY-shung/, /juh-RAY-shung/, mania, a state of bliss; a climax.

Julie, see ayuleyâ.

“Juventus”, “Iuventus”, “youth” > Latin, the second life season or xiómðe, i.e., the Xiómðe Gílmal (Summertide/young adulthood life-season) starting at Asmíð Gálmiñe (coming of age, quarterlife turning) at táyyâ 4600 (about age 21¼), and lasting 4600 táyyin (7776 days) till Asmíð Vívixe (midlife turning).

Kaji Anta Vare /KAW-zhee AWN-tuh VAW ray/, “Near-end of the world, millennialist”. Name of the ten dozen sixth xrgâ of mid 2020.

Kaji Ñixaþa /KAW-zhee ni-SHAW-thung/, “False Apprenticeship”. Name of the four dozen tenth xrgâ of mid 1993. Representative work: s4952b02.

Kamleral /kuhm-LAY-jull/, “(of the) valuable time”. Name of the seven dozen fifth xrgâ of late 2005. Representative work: a7519, a7565, a75a5. The work associated with a7519 was intense; if the decision had gone against Vinci’s client, it is possible that Vinci LLC, then nearly a year old, may not have survived.

Karlmel /KARL-mull/, the lrixe name of my son Karl Michael. Namesake of the seven dozen ninth xrgâ of mid 2007. The life phase saw much business travel. Exemplary work: construction visualization at Vinci LLC: a7940, a7966, a7992; number theoretical musings: s7836a06.

Karmejimlal /kuhr-muh-JEEM-lull/, “drawn life-path”, a map of life events. Small study of mood throughout life s5231a45.

Kárnaþ kxáne /KAWR-nuth KSHAWN-uh/ “civil strife”, name of the ten dozen ninth life phase of late 2020-early 2021, translated as “the landslide”. In this life phase Roam Away Home was written. My son was culminating eighth grade while my daughter was finishing senior year.

Kárnaþ mólle /KAWR-nuth MOL-luh/ “wife in distress”, name of the nine dozen fifth life phase of early 2015. The wife broke form at muay thai and dislocated her kneecap. Exemplary work: a9530 · a9569; Vinci LLC experienced a return to the heyday years, income-wise. The period saw the inversion of politics which began in the previous þábirállysal life-phase of late 2014.

Katie, see aðikarine.

Katírâ /kah-TEE-jung/, “controller”. Also katíra señû (controller sign), katíriñe (controller-tide), ixtuvhónme (mid-virilitas). The seventh of a dozen Señunin Tivanal that in the case of vixsáën or the lifetime, represent periods of 1600 tayyin = 2592 days, or roughly 7 years 1 month, three such periods to the 4600 tayyin (7776 day) life-season or xiómðe. Katírâ pertains to the third of four life-seasons, namely the middle of xiómðe vhónmal (Autumntide/Adult life-season, “Virilitas”), tayyin a600–c000 (2020 0304-2027 0408). The zodiac equivalent of katírâ is Scorpio. This señû started with covid lockdowns. An excerpt from The Sugar Factory (káxa maïrénal) was written as the novel Roam Away Home during the final days of governmental abuse of the public.

Kaxâ /KAW-shung/, “journey”.

Kax Aðilyre /KAWSH uh-thee-LÜ-ruh/, late apprentice-era journey to Seattle, Washington s5231a77, s5231a78, s5231a79.

Kax Andaluse /KAWSH-AWN-da-loo-suh/, early apprentice-era journey to the Great Mosque of Cordoba and southern Spain, s51a3a03, s51a3a15.

Kaxa Lecorbu /KAW-shuh le-cor-BOO/, apprentice-era journey intended to visit the work of Charles Jeanneret “Le Corbusier”, conceptualized s5231a20, relished s5231a21. Drawings from the trip s5810a02, s5810a03, s5810a04, s5810a06, s5810a07, s5810a09. A verone-style drawing produced from a record photograph at Chartres was produced in 2000 j6304.

Káxa Maïréne /KAW-shuh ma-ee-SHAY-nuh/, the early 1992 premier section of foreign study by the Illinois Institute of Technology at the Centro Studi S. Chiara in Castiglion Fiorentino, Tuscany. Sketchbook Rykami Yasmyne s45b0; Castiglion Fiorentino s45b0a06, s45b0a07, s45b0a08, s45b0a09, s45b0a0b, s45b0a11. Cortona s45b0a13, Castello di Montecchio Vesponi s45b0a13. Venice s45b0a14, s45b0a16, Siena s45b0a17, s45b0a18. Campaniles / Bell Towers s45b0a81. Paris sketches on site s45b0a24. Cloud studies s45b0a17. Classmates s45b0a14, Mairenâ, local friends s45b0a1a. Camélia s45b0a12, s45b0a13. Argam Arimaxa 1992 s45b0b80. The Kaxa Mairene is named after Mairenâ. Subject of The Sugar Factory.

Kaxa Tivansal /KAW-shuh tee-VAWN-sull/, “journey to paradise”, commitment-era journey to Tuscany, Italy. Drawings from the Kaxa Tivansal: masonry arches in Lucca s6861a03, building wall in Lucca s6861a04, night view of the Piazza del Campo in Siena s6861b02. Namesake of the six dozen eighth xrgâ of early 2002. Representative work includes the travel drawings, but also the drawing j6870.

Kaxa Xegriwal /KAW-shuh sheh-GREE-wull/, “honeymoon” (literally, “nuptial travel”), commitment-era journey to Andalusia, Spain. Drawings from the Kaxa Xegriwal: Great Mosque of Córdoba s611ba09, Écija hostal s611ba0b, Granada cathedral s611ba11.

“Kentaro Open Mic”, s5231a23.

Kim, Kimberly, see akimvriwâ (nixaþine girlfriend). For “Blond Kim”, see ðebninâ.

Kimavna Reneya /ki-MAWV-nuh sheh-NAY-ung/, the “Reneyan Library”, the collection of books owned by Michael De Vlieger. Many of the books in the library bear dedicatees (rentikyn) such as k3a06.

Kinoctoval, Kintoval; base 360. Divisors of the cube of 360 s5231a97, fractions s5231a98. “The Optimized Sequence” s7836a19. Factorials in pure and sexagesimal-coded base 360 s5231a37.

Kinsevoctoval, Kinsoval; base 2520. Factorials in pure and sexagesimal-coded base 2520 s5231a37.

Kinþrâ /KEEN-thrung/, “Information Engine”, lrixe word for a computer. Older forms have cinþra, cynthra, synthra.

Kinþrehanal /kin-threh-HAW-null/, “(of the) social network”, name of the eight dozen second xrgâ of early 2009. Representative work: a8205, a8226, a8235, my personal favorite a82a4. The life phase saw one of the strongest spring demand seasons in the history of Vinci LLC, with many large projects.

Kinþriüleyâ /kin-three-OO-lay-ung/, “computer science”, name of the two dozen second xrga of late 1980 - early 1981. My father bought me an Apple II + in mid December 1980, contributing to the Talent Dynamic and the development of a good proportion of skills that lead to the establishment of Vinci LLC 24 years later.

Kobliner, Beth, author: marker portrait study s5231a48.

Karnaþmollal, /ker-nawth-MOLE-lull/, from karnaþe molle , “injured wife”, name of the nine dozen fifth xrgâ of early 2015. Representative work: a9530, a9569, r9589, r9591, a95a4. This is a period in the quieter, spring phase of the cyclical phase of Vinci LLC. Laura had a martial arts accident that incapacitated her ability to walk.

Krunþe /KROON-thuh/, “crisis, shock”. A disintegration of one’s character, often incorporating a review of one’s life and a reintegration within several months to a year. The krunþe is not quite a depression but may have some of the same effects as depression, as one is generally left unsure of oneself during self-analysis. Krunþe / karnaþ is also generally an injury or a setback.

Krunþe Galmine /KROON-thuh GAWL-mee-nuh/, “crisis of adult youth”, a quarterlife crisis. The Reneyan quarterlife crisis had three phases. The first phase was the Krunþyñ Kajixaþal ke Nekarhal, “apprenticeship-nomad crises” of 1993-94, followed by the Azenna Tavnal, “career frustration correction” in 1996 and Azennyñ Raþkyñe ke Noviñe, “arrogance and novia correction” of 1998. The latter two corrections are more or less documented in the Rykami Arysane, s5231. The Krunþe Galmine was the second largest system of crises after the Ðelegajenâ, the “Great Teenage Depression” of 1984-1987. Since the Krunþe Galmine, sentiments have ever been in positive territory.

Krunþimallal /kroonth-ee-MAWL-lull/, “midlife crisis”, a playful, tentative name of the eight dozen tenth xrgâ of early 2012. Representative work: a8a00, a8a25, a8a30, a8a58. This life phase continued a recovery in Vinci LLC production from the Great Recession, waning toward the middle of the xrga.

Kxán /KXHAWN/ The lřixe word for a state or kingdom. The word may appear as a suffix –kán (-KAWN). The suffix derives from the verb káxyn /KAWSH-ün)/, “to rule (by birthright)”.

Kxmere /KSHMEH-ruh/, “empire”, also “circle of friends”. Also ximere /SHEE-meh-ruh/, where it can connote “harem”.

Kýmâ /KÜ-mung/, “information, knowledge”.

Kyñiçme /KÜ-neekh-muh/, “sexagesimal”, the number system based on sixty: “Argam for Sexagesimal with Ismarragam” (sexagesimal numerals and their names) s7836a52. Cyclical diagram s5231a90. Sexagesimal cyclical diagram and totatives s7836a51. Numerals for small multiples of sexagesimal prime divisors s5231a03; sexagesimal argam for the divisors of cubes of primes, composites s5231a95, bases 60 and 120, s5231a96. Fractions s5231a97. Multiplication through an abbreviated table and manipulation of complementary divisors s5231a99, s7836a52, 100+ page, 6½ megabyte PDF d7a60, abbreviated multiplication table for use with complementary divisor method s7836b02. Divisor counting function vs. totient function (in sexagesimal figures) s7836a07. Primorials and prime decomposition vs totient ratio (sexagesimal figures) s7836b09, s7836a08. Totatives of, paired with additive complements s7836b09. Argam numerals and names tied to chemical elements (sexagesimal arrangement) s7836a12. “The Optimized Sequence” s7836a19. Fractions expressed in sexagesimal s7836a31. Powers of primes p ≤ 7 s7836a34, p ≤ 11, and {10, 12} s7836a35. Powers of 10, 12, 16, 20, 36 s7836a36. Factorials s5231a37. Irrational numbers , s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. “The Irrational Page”, “The Reciprocals of the Simplest Primes for Selected Bases” s7836a41. “Primes in Sexagesimal Scale”, “Stanislaw Ulam’s Spiral in Sexagesimal”, “Values of Π − 1”, s7836a53. Argam kinoctove arranged in dozens and sixties s7836b00. “Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, s7836b01. In 2007-2008, sexagesimal became the lingua franca of many of my elementary number theory studies by dint of its 5-smoothness and the plethora of small regular numbers.

Lakepoint, an apartment at Pheasant Run along Dorsett Road in Maryland Heights, Missouri where I resided between 2 January 1994 and late June 1996. Lakepoint often refers to the first years in St. Louis, the first career job in architecture, one of loneliness, confusion, and discovery. Lakepoint is the first major division of the Ñixaþine (Apprenticeship) era, containing over fifty days of the last part of the Safrine (Enlightenment) era.

“La Mia Bella Angelina”, celebration of the purchase of a used Honda Accord s5231a66.

“La Mia Donna Italiana”, Icarus and Mairenâ standing in the Piazza del Campo, Siena, married s5231a16.

“La Sorella e La Nipotina”, marker portrait of Xrine and daughter s5231a49.

Landmarks: Gran Mezquita-Catedral de Córdoba / Great Mosque of Cordoba s51a3a03, s51a3a15, s611ba09. Chartres Cathedral s5810a02, j6304, Palazzo Vecchio (Florence) s5810a09, Torre del Mangia (unfinished sketch) s45b0a18, (by night) s6861b02. Granada Cathedral s611ba11. Chase Park Plaza, St. Louis j6374, New Cathedral, St. Louis j6421, Compton Heights Water Tower, St. Louis j6791, j6aa0. Civil Courts Building, St. Louis j6797. St. Louis Union Station j6a96. The Climatron j6aaa.

Láxine /LAW-shee-nuh/ A lřixe word meaning “elder threshold”, deriving from the verb láxyh (LOSH-üh) “to be senior, to be an elder” and the suffix –ine (-ee-nuh), meaning “a span of time”. In the trakaða reneya, this is the name of the turning between the second and the third xiómðyn, roughly equivalent to the “senior citizenship” acquired at age 65.

Lectajinal /luhch-TAW-zhee-null/, “(of a) virtual solid”, name of the six dozen eleventh xrgâ of early 2008. The Life Phase of Virtual Solid Order was a time when I was codifying methodologies associated with construction visualization at Vinci LLC. Exemplary work: a7b33, a7b54; s7836a08.

Lecture Notes with doodles: at S. Chiara Study Center, Italy s45b0a11. Daniel Sullivan s5231a27. Architectural professional practice s5231a57. Urbanism s5231a59. Allan Jacobs, “Making Great Streets” s5231a60.

Leisure: Sugar Island suite of 2010, s6796: j8581, j8583, j8584.

Lekxâ /lake-shung/, “light, flash” name of the nine dozen seventh xrgâ of late 2015 and early 2016. Representative work: a9768, b9785, b9790, b97a1, a97a3, a97a8. The last quarters of 2015 were slow and a marketing push called “Blitz™” materialized and spurred vigorous demand in 2016.

Lérâ /LAY-shung/ The lřixe word for something valuable or cherished. The word also was transliterated lyra or lira, and derives from the verb láryh (LAWH-rüh), “to value, to treasure”. The seven dozen fifth xřĝa was called kamleral, meaning “valuable time”. Kamlera is also a motto for the Salcyra Xisaen, meaning “time is valuable.”

“Le Memorie secondo Lei”, imagining Mairenâ in the Val di Chiana s5231a24.

< Le Tour des Bases >, a tour of number bases incorporating a brief introductory summary, number theoretical analysis of digits, arithmetic tables, expansions of unit fractions, intuitive divisibility tests. Thread at the DozensOnline Forum, h8a08c→. Bases covered: Quinary (5), h8ab8→; Senary (6), h891b→; Septenary (7), h8ab4b→; Octal (8), h8898→; Nonary (9), h8ab4a→; Decimal (10), h8a14a→; Undecimal (11), h891a→; Duodecimal/Dozenal (12), h8a14b→; Tridecimal (13), h8aa8→; Tetradecimal (14), h8913→; Pentadecimal (15), h8914→; Hexadecimal (16), h8899→; Vigesimal (20), h8a05a→; Unvigesimal (21), h8ab4→; Sexagesimal (60), h8b06d→; Septuagesimal (70), h8b06a→; Base 72, h8b06b→; Base 84, h8b06c→; Base 100, h8b01b→; Base 120, h8abb→; Base 144, h8b01a→; Base 210, h8b00b→; Base 240, h8b00c→; Base 360, h8b00a→. See also individual bases on this page, under "Base __".

Leverage, the notion that the divisors and regular numbers of a number base are key to its utility for general human intuitive computation: s7836a06. Divisor counting function vs. totient function s7836a07. Broadly incorporated into the “Complementary Divisor Method”, summarized s5231a99; 100+ page, 6½ megabyte PDF manual RDM2007. Subsequently incorporated into “Balance Study”, 2010 study that includes cyclic logarithmic, geometric, and scalar diagrams exploring the divisors and totatives of the smallest integers, 1¾ Mb PDF, and “Cyclic Resonance”, 2009 paper illustrating the geometric relationship among divisors in clock-like diagrams that positioned the integers 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), equiangularly around a circle, 800k PDF. The notion of leverage exhibits itself in the color coding present in “Digit Base Relationship”, 2 Mb PDF d87a9. The notion within the digit range of a number base is shown at “Neutral Digits”, 1.15 Mb PDF d8895.

Líðe /LEE-thuh/ The lřixe word signifying a visceral or physical state. It is normally applied to the visceral, physical, or “animal” component of one’s existence. It is related to the word elúð /(ell-OOTHE/, meaning one’s body.

Life Stage Page, The: s5231a02.

Lindsay, see alindði.

Livenâ: wife of a nixaþine friend. Also Aðilivâ.

Logos: Paris Rush logo s45b0a24. Caryma logos (see also Carymâ): Mock logo for a trip to Greece s5231a25. Icarus logo s5231a31, s5231a41, s5231a43. Study for a Chimera logo s5231a52. “Rose logo” s5231a78.

Loneliness: Icarus with Camélia s3964a06, admiring Arebinâ s5231a10, on the floor reminiscing better times s5231a12. Thinking about erstwhile relationships s5231a41.

“Lorielâ”, a fictional interstellar nation devised for a role playing game shared among four high school friends. The country is named after Gelyrâ, canonically, Acralyrâ or Ðellyrâ, “Great Lori”, a classmate of my sister’s on whom I had a crush in seventh grade. Drawings in service of; “Loriternal Yev”, canonically “Imel Lorielal”, capital city of an interstellar empire j3187. “Camélia Lorielal”, Camélia in a near-future urban scene j3410. “Misa Elyamî”, female captain of a starship j34b9. “Loril Ya”, canonically “Ðani Lorielal”, map of the capital city of an interstellar empire k3155, “Avlicir”, canonically “Iral Imelavlike”, map of a port on the home planet of an interstellar empire k3160.

“Loril Ya”, canonically “Ðani Lorielal”, map of the capital city of an interstellar empire k3155.

“Loriternal Yev”, canonically, “Imel Lorielal”, an urban, sci-fi perspective study (naïve) j3187.

Lorus /LO-joos/, “alignment”, the examination of higher number bases as s7836a03.

Los Angeles, postapocalyptic, colored pencil (naïve) j374a

Lrixe /lur-EE-shuh/, a constructed language developed since 1983, revised several times and used intensively in sketches, journals, and introspectives. The original spelling in ralysine (high school) was lurysh. The language developed out of fascination with Greek and Cyrillic alphabets learned in fifth and eighth grades (iüleya xisaën), amplified by hazing in eighth grade. The idea was to mystify written thoughts in an exotic writing, opaque to prying eyes. The exotic, alien writing had the effect of intellectually intimidating bullies throughout latter iüleine and ralysine. The conlang was carried through safrine (university years) in class notes, then in sketchbooks. The language began influenced by Russian and Spanish, then affected by Italian and Arabic, with a pastiche of Asianness attempting to incorporate Filipino heritage. The language development ceased in 2002, but is still used to refer to life events, phases and stages, and concepts. The language had an alphabet that increasingly became cursive and nonmodular: the late-1996 manifestation of the alphabet can be seen at a5231b05. After the cessation of the development of lrixe, the English transliteration became the sole conveyance of the language. The language is named after Gelyrâ, canonically, Acralyrâ or Ðellyrâ, “Great Lori”, a classmate of my sister’s on whom I had a crush in seventh grade. Lrixe is also the namesake of the two dozen tenth xrgâ of late 1983-early 1984, a period wherein I taught myself Russian and also developed the constructed language lrixe. Representative work: j2a28.

Lrixe Name, the name of a significant person in the lrixe constructed language, intended to internalize that person. Depictions of significant people in sketches and drawings reflect a subjective representation of that person, thus the lrixe projection of the significant person ends up being entirely different from the actual person. The lrixe projection is often a highly reduced, idealized or caricatured version of that person. Given a lrixe name, the person’s projection becomes an actor on the stage of the drawing. Most of the significant female relationships resulted in a lrixe name, following the pattern using the definite article prefix a-, and a transliterated or lrixe-reformulated name for the girl. This name is inteneded to designate the girl as unique in the world, having the meaning “the one and only _”. Some received a lrixe descriptor for a name, e.g., Xibane and Ymalhynâ. The names “Icarus” and “Camélia” function as lrixe names (likaryne and akimalâ, respectively) but have been Anglicized in this portfolio. “Icarus” is an avatar used to represent myself in the nixasine (Apprenticeship era), often questing, confused, and vulnerable. “Camélia” is an imago, the sum total embodiment of qualities of the ideal mate for Icarus, extracted from relationships with girlfriends and female friends between 1987 and 1991.

Lucca, Tuscany: stone arches s6861a03, infilled Roman arcade s6861a04.

Luna di Miele / Luna de Miel, literally, “honeymoon”, commitment-era journey to Andalusia, Spain.

Lyðrelâ /LÜTHE-ray-lung/, a crush; a non-reciprocating limerent object; a love-interest that did not develop into a more serious mutual relationship. Freshman year high school Aðiavlikâ/Avlica j339a. Junior year high school Ayuleyâ s3964a01. First year at university Arysani s5231a18. Third year at university Arebinâ j4656. Shortly after commencement Asayme s5231a11, s5231a51. The word ymalhynâ /üm-AWL-hü-nung/, “Unanticipated”, is used for a crushee that reciprocates the attraction. The word is often shortened: Imallâ /ee-MAWL-lung/, Ymallâ /ü-MAWL-lung/. The diminutive often refers to Aveacrixe; s5231a43, dedicatee s5568a00 but is also used for several other crushes.

During and after ineh salcyrune, the term lyðrelâ came to apply to those attracted who had to be maintained off limits, i.e., a moonstone. The term applies to any woman or girl (normally younger) that showed affection around vivixe. The term comes from the song “Blinded by the Light”. The most notable moonstones were acramilâ (aðimallâ), axilvanâ, aðiyose, akitanâ, nannenâ. A more correct term would be ymlyðrelâ.

Maëlla /MA-ay-luh/, /MILE-luh/, the lrixe proper name “Michael”.

Mairenâ /MY-ray-nung/, Mara ‘in ashen light’, i.e., belonging to someone else; lover in Tuscany 17 years my senior. The relationship ultimately contributed to my conversion, but continued thereafter intermittently for a few years. Warming a45b0a1a, at the wheel of her Fiat s5231a12, nobly with Icarus in Siena s5231a16, things seen her way s5231a24. Her autograph and note s5810a07. Namesake of the four dozen seventh xrgâ of mid 1992 and the Kaxa Mairene, the 1992 semester in Italy. Examples of work from this period include: Paris Rush vignettes s45b0a20, sketch from an Italian fashion magazine j4741, portrait of Amarya j475a. A main character in The Sugar Factory. Maïrénâ appears as “Noemi” in Roam Away Home.

Maki, Fumihiko, autograph s3964a05.

Maliyya /MAH-lee-yuh/, “dear, close”.

Map, Digit, a type of chart that plots the digits, integers n of a number base, integer r ≥ 2 in sequence from 0 through ω = (r − 1), with the digit “0” signifying congruence with base r. Examples of digit maps appear at “Digit Base Relationship”, 2 Mb PDF d87a9, and “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5. I invented digit maps in 2009.

Map, geographic: Planning French travel a5231a08, St. Louis s5231a22, s5231a45, Greece s5231a25, World s5231a45. Naïve examples: fourth grade map of South America j2050. “Loril Ya”, canonically “Ðani Lorielal”, map of the capital city of an interstellar empire k3155, “Avlicir”, canonically “Iral Imelavlike”, map of a port on the home planet of an interstellar empire k3160.

Marilenâ /muh-REE-lay-nung/, Mary ‘in ashen light’; coworker at tavnemikâ. Autograph and note at s5231a27.

Marla /MAR-luh/, the name of a red maple tree planted in April 2003 and cut down July 2021. The tree was named after an ex-president's first wife, though long before he was president and not necessarily because I was fond of him, but rather, because her surname had been Maples.

Marseilles, France: gare (train station) s5810a02.

Mashup (Comparison of Number Bases): < Comparison of Bases 60 and 120 > Post at the DozensOnline Forum h8abb→. Comparison of bases {72, 96, 108}, {60, 84, 90, 120}, {32, 48, 80, 112}, {30, 42, 70}, < Midscale Mashups > Post at the DozensOnline Forum h8b09→. Comparison of bases 12k with 1 ≤ k ≤ 12 (figures expressed in duodecimal) < The Dozen Mashup > Post at the DozensOnline Forum h8b19→.

Masonry: Steel pan stair vs k635a. Load-bearing CMU vs. steel pan stair k635a, exterior masonry wall detail study k63a3, face brick and loand bearing CMU on the exterior and interior k63a7a, variable CMU wall thickness study k63a7b. Wall simplification study k63b8a, k63b8b.

Masonry studies: stone arches in Tuscany s6861a03, infilled Roman arcade in Lucca, Tuscany s6861a04. South St. Louis masonry in light j6284, j6285. Chartres reconstructed bridge j6304. Masonry massing at the Palm House j63aa. Central West End home j6400. Decorative stone j6421, masonry midrises along an urban street j65a9. Brick warehouse j6692. Flatiron building in Eureka Springs j6726.

Máðrine /MAUTHE-ree-nuh/ A lřixe word signifying the commencement of motherhood. It derives from the word ‘ámma /‘AM-ma/, “mother”, probably its predecessor maþír /ma-THEER/ and the verb yányh /YAWN-üh/ “to span”, which typically appears as the word inéh /ee-NEH/, “an age, a time”. This word can refer to a very specific time in one’s lifespan, around 21 years 4 months old, when one has lived one’s 7,776th day. This is the transition between the life season of childhood and womanhood. The more common application is to a time when a woman begins to expect a child. This applies to a woman, whether or not she intends to give birth.

McCausland, an apartment along McCausland Avenue in St. Louis, Missouri where I resided between June 1998 and October 1999 (marriage). McCausland often refers to the clearing of decks to make way for marriage to Laura, crises associated with career development and adjustment to life as a couple. McCausland is the last major division of the Ñixaþine (Apprenticeship) era, spilling over into the Añikçine (Commitment) era.

-me /-ma/ The lřixe suffix connoting a state of being. The suffix was formerly –ayma, belying the derivation from the verb yámyh, “to be, to exist”.

Mediation/Duplation, a method of multiplication that avoids memorization of the multiplication table by doubling (duplation) and halving (mediation) the multiplicands. A main variant is “Russian” multiplication. Can Hexadecimal Be Civilizational?, h9681.

Meeting of the Waters, Carl Milles’ fountain at Aloe Plaza in St. Louis, s3964a05.

Mella /MAYL-luh/ Maëlla /MA-ay-luh/, the lrixe proper name “Michael”.

Melodrama: Rejection by Asayme s5231a11, lamenting past s5231a12, lamenting a running injury s5231a20, s5231a21, shamefully arguing with sister s5231a28, falling to earth outshone by rivals s5231a74.

Mennexâ /mun-NAY-shung/, “complexity: a highly ordered system”.

“Meraviglie Passate”, an imagined rucisaime-style scene s4952b02.

Merralenâ /mur-RAW-lay-nung/, Margaret, a coworker who commissioned j6924 in summer 2002.

“La Mia Bella Angelina”, celebration of the purchase of a used Honda Accord s5231a66.

“La Mia Donna Italiana”, Icarus and Mairenâ standing in the Piazza del Campo, Siena, married s5231a16.

Micel /MICH-el/, “Mitchell”, the name of my ñixaþ-añikçine-era boss (1995-2004). He appears in the Rykami Arysani at s5231a13, and purchased Jimla Micele j6aa0.

Michele, see aximelâ.

“Misa Elyamî”, pencil portrait of a lady on a starship (naïve), based on Aðimisâ j34b9.

Missouri River: j6159.

Mixa /MEE-shuh/, the diminutive name “Mike”.

Modular Mathematics: used to identify the primes less than 120, 540 s7836a12.

Molla, /MOLE-luh/, a wife. Molli is the possessive, “my wife”, while molle is the genitive “wife’s” and mollyn is the plural.

Monteriggioni (SI), Tuscany: architectural analysis of the city gate s6861a03.

Monte San Savino, Tuscany: s5810a06.

Moonstone: also lyðrelâ. A term that applies to any woman or girl (normally younger) that showed affection around vivixe. The term comes from the song “Blinded by the Light”. The most notable moonstones were Acramilâ (Aðimallâ), Axilbanâ, Aðiyose, Akitanâ, Nannenâ.

Multiplication: sexagesimal, via complementary divisors, summarized s5231a99, s7836a52;100+ page, 6 megabyte PDF manuad7a60. Full-length "direct" sexagesimal multiplication table here, abbreviated here. Abbreviated tables for bases {60, 64, 66, 70, 72, 80, 84, 90, 96, 120} s7836b02.

“Multiplication Synopsis”, 44 page booklet featuring multiplication tables for each base between 2 and 60 inclusive, 30Mb PDF d9470. This is the unabridged version of “Multiplication Tables in Various Bases”, updated in mid November 2014 using Mathematica 10 to produce the tables, thus is error free unlike d86bb. Includes the Lamadrid Number Base Nomenclature leaflet and an explanation of argam transdecimal numerals.

“Multiplication Tables, Analysis of”, a paper illustrating the effects of elementary number-theoretical digit-base relationships in the multiplication table of a number base, 294k PDF d872a. This paper summarizes description of digit maps, and the effect of the relationship of digit and base on multiplication tables. Octal, decimal, duodecimal, and hexadecimal tables serve to illustrate the effects.

“Multiplication Tables in Various Bases”, paper showing direct multiplication tables for bases 2 through 30, 32, 36, 40, and 60, 294k PDF d86bb. Available at the DSA website, it is often the very most popular download since mid 2011.

“Multiplicity Notation” (MN), the concatenation of multiplicities of prime factors of a number, the prime communicated by little-endian position. Example, the number 84 has a standard form prime decomposition 2² × 3 × 7. This would be written “2101” in multiplicity notation. Trouble arises when any multiplicity exceeds 9; argam numerals may be used. Used in algorithms, the multiplicities may appear as a list, or as a Wolfram Mathematica association without the zeroes for concision. MN accentuates gaps in prime decomposition through the appearance of zeros and is most appropriate for studying sequences predominantly or strictly containing products of the smallest primes. These numbers tend to be highly composite. See OEIS A054841; MN is the reverse order of A054841 as it is bigendian as in traditional positional notation. An alternative to MN is “π-code” (pi-code, A287352) or “zerocode” (zerocode can be derived from pi-code). We can use π-code to abbreviate MN for numbers with widely separated distinct prime factors; π-code accentuates multiplicity via the appearance of zeros. It is most appropriate in representing squarefree numbers and is best as a list, since the terms tend to be larger than 9.

Myxdije /müsh-DEE-zheh/, “shadow of the moon”, usually translated as “moon-shadow” but with slightly different meaning, the name of the nine dozen eleventh xrgâ of mid 2017. Representative work: a9b20. The total eclipse of the sun transited the St. Louis area in the middle of this quiet demand period, and much of the time I felt I was in the shadow of the moon, or “moonstones”.

Nagel, Patrick, influence: s3964a00, s3964a01. Mr. Nagel was a serigraphist of the 1970s and 1980s famous for simple and clean, stylized depictions of female subjects.

“Nei Panni di una Bomba”, partially completed monochrome study of a girl in an Italian magazine j4741, the title of the article is also the title of the work.

“Neutral Digits”, 1.15 Mb PDF d8895, a paper that attempts to define and mathematically prove the existence of neutral digits. I’d first considered neutral digits as “nontotative nondivisors” in the 2007 work “The Reciprocal Divisor Method”, a 100+ page 6½ megabyte PDF manual d7a60. The notion of neutral digits emerged in a presentation “Digit Base Relationship”, 2 Mb PDF d87a9, Neutral digits played a role and were described in my paper published in the March 2012 edition of ACM-Inroads, a magazine of computer science education.

“Neutral Numbers”, d936b, a June 2014 paper that defines and mathematically proves the existence of two types of numbers m that are neither divisors of nor coprime to n. The paper establishes the term “semidivisor” and “semitotative”, and the “semicoprime” neutral relationship. It constructs the set of such numbers and gives algorithms that construct and quantify neutral 0 < m < n. An html version of the paper appears at the math site. This paper derives from the “Neutral Digits” paper above. Associated Reneyan OEIS Sequences: A243822 number of semidivisors m of n, A243823 number of semitotatives m of n. Sequence A045763 defines the value of the neutral function ξ(n) = n − (τ(n) + φ(n) − 1), easily derived from the divisor counting τ(n) and Euler totient φ(n) functions.

Ñiçme /NEEKH-muh/, “duodecimal, base twelve”, considered in 1982, adopted in 1985. Currently the basis for all internal mathematics. Ralysine spelling: niçymâ.

Ñimanþyñe /ni-MAWN-thü-nuh/, “little Sammy”, my niece. With her mother s5231a49, marker portrait from life, age 6 s5231a67.

Ñixaþ /ni-SHAWTH/, “apprentice (of a building professional)”.

Ñixaþâ /ni-SHAW-thung/, “apprenticeship (of a building professional)”; the name of the fifth xisaën, 25 February 1994 — 19 October 1998, containing the Lakepoint, Amherst, and some of the McCausland eras. The era begins shortly after moving to St. Louis from Joliet to work at my first career job. The era is one of loneliness, confusion, discovery, and struggling with where I am going and who I want to be. It is the flowering of the Arahkaxa, the Quest for God, and experimentation with non-Christian religions, though He doesn’t quite make it into my art.

Noemi /no-AY-mee/, major character in Roam Away Home representing the Tuscan “cougar” maïrénâ about whom the protagonist revolves and to whom he returns. Signora Noemi speaks in Tuscan drawl (dialetto toscano). In a subsequent movement, Noemi is the leading lady.

Novels, Reneyan. The Reneyan novels currently include four unpublished memoirs taken from the Reneyan Autobiography of Eĝájñalékxiðanal Xrgâ. Chronologically, these are Roam Away Home (2021), _otherworld son_ (2019), The Official Troublemaker (2019), and The Sugar Factory (2013). The novel otherworld_son describes the mestizo son of an immigrant from the third world growing up in Xereney (Joliet, Illinois) in the seventies and early eighties. The Official Troublemaker describes his teen crisis in Egajenimy (New Lenox, Illinois), high school life, and coming of age. The Sugar Factory describes his experience abroad in the early nineties. The works remain in the hands of Reneyan heirs and likely will not be published unless they undertake the process after my passing. The novelization of memoirs represents preparation for departure whenever it shall come, and a cessation of Reneyan art and research, including work on this website. Novelization of other segments may or may not materialize; instead perhaps creative novels may come forth, or no new writing at all.

Noviâ /NO-vee-ung/, “(romantic) girlfriend”. Xibane: stylized s5231a10, memory study s5231a21. Ajiñevrâ: signature s5231a15. Aðilyrâ: signature s5231a23. Memory portrait in ballpoint s5231a59. Passenger on a date s5231a66.

Number Base: a system of expressing quantities using a number of digits in a positional arrangement of places according to powers of the number of digits. Subject of much work throughout ralysine to the current era. A major thread of my intellectual life. Most of my work concerns duodecimal and sexagesimal, but large tracts have been developed that aim to organize a framework with which any integer number base can be examined. See the following examples of my musings on number bases. The set of transdecimal numerals called argam arimaxa in 1992, s45b0b80. Rykami Argam, the Book of Numbers s7836. Articles “Analysis of Multiplication Tables”, 1½ Mb PDF d872a, “Digit Base Relationship”, 2 Mb PDF d87a9, “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5, “Neutral Digits”, 1.15 Mb PDF d8895, and “Exploring Number Bases as Tools”, published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Posts at the DozensOnline Forum under my username icarus: < Number Base Theory 101 >, a thread summarizing what I knew about canonical number theory as it applies to number bases, h8884→, < Icarus’ Standard Nomenclature for Number Bases >, a post summarizing my thoughts regarding analysis of number bases, h8910→. View an online tour of number bases at DozensOnline Forum, < Le Tour des Bases >, based on h8884 and h8910, along with the aforementioned PDF resources.

Number Base Tour: a systematic exploration of integer number bases using number theory. See < Le Tour des Bases >.

Numbers: subject of the Rykami Argam, the Book of Numbers s7836. For instances outside of the Rykami Argam: argam arimaxa transdecimal numerals s45b0b80. Duodecimal argam s5231a25, construction measurements in argam s5231a87. Cyclical diagrams and sexagesimal symmetry s5231a90. Prime powers, digits and names for s5231a91, superior highly composite numbers, digits and names for s5231a91. Divisors of cubes of 60 and 120 in respective bases s5231a96, of 360 in base 360 s5231a97. Fractions, s5231a91, s5231a98. Irrational numbers in various bases s5231a98, s7836a41. Factorials in bases {12, 60, 360, 2520} s7836a37.

Numbers, Lrixe, lrixe-language numbers. The lrixe language uses a number system based on twelve (duodecimal numeration), thus there are twelve digits. 0 xarâ /SHAR-ung/, 1 anâ /ON-ung/, 2 tivâ /TEE-vung/, 3 tarâ /TAW-rung/, 4 þesâ /THAY-sung/, 5 kynâ /KÜ-nung/, 6 exhâ /AYSH-hung/, 7 rynâ /RÜ-nung/, 8 aþnâ /AWTH-nung/, 9 narâ /NAW-rung/, digit-ten dejâ /DAY-jung/, digit-eleven ðalâ /DHAW-lung/. The lrixe suffix for dozens is -içâ, thus one dozen niçâ /NEE-khung/, two dozen tiviçâ /TEE-vi-khung/, three dozen atriçâ, four dozen þesiçâ /THAY-si-khung/, etc. The decimal number 27, which is 2 dozen 3, is called tiviçtarâ, the decimal 128, which is ten dozen eight, is called dejiçaþnâ. The reneyan xrgyñ are assigned lrixe numbers before they are named for a significant event within the 144-day period. There are several nonduodecimal names for numbers; digit-twelve niçâ /NEE-khung/, digit-thirteen þizâ /THY-zung/, digit-fourteen ranâ /JAW-nung/, digit-fifteen lexâ /LAY-shung/, digit-sixteen ractâ /JAWCH-tung/. These names are used for trans-duodecimal bases and for xrgyñ that exceed the twelve-dozenth.

< Number Base Theory 101 >, a thread initiated 10 October 2011 (tayya 8884) on the DozensOnline Forum, retrievable here. This thread attempts to synthesize all the relevant elementary number theory I learned between 2006 and late 2011 so that other forum members can better understand the underpinnings of my observations and conjectures about number bases. Canonical mathematical references are given, terms are defined, and invented concepts are fleshed out in the post. Much of the material appears in the 2011 body of work, notably “Analysis of Multiplication Tables”, 1½ Mb PDF d872a, “Digit Base Relationship”, 2 Mb PDF d87a9, “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5, “Neutral Digits”, 1.15 Mb PDF d8895, and “Exploring Number Bases as Tools”, published in the March 2012 edition of ACM-Inroads, a magazine of computer science education.

Number Theory studies: argam arimaxa transdecimal numerals s45b0b80. Duodecimal argam s5231a25, cyclical diagrams and sexagesimal symmetry s5231a90. Divisors cubes of 60 and 120 in respective bases s5231a96, of 360 in base 360 s5231a97. Fractions in various bases s5231a91, s5231a98. Irrational numbers in various bases s5231a98. Divisor counting function vs. totient function s7836a07. Prime decomposition, primorials vs totient ratio s7836a08. Elementary number theory grew to become my foremost pasttime between 2007 and the present. The kernel of interest lay in my middle school years, by enrichment units given by my teacher Ms. Betty Svitek, and by hexadecimal in the Applesoft in 1981. I used duodecimal throughout high school and college, through the Reneyan calendar of days and in measurements in a metricized system of US customary length. This was spurred by interaction with the American and British Duodecimal Societies, discussions on a duodecimal web forum, mainly by my drive to rationally justify duodecimal. The fascination continues, and has led to the publication of digit maps, multiplication table studies and examination of the relationship of digits to bases in a computer science teaching magazine in March 2012.

Numerals: Printable PDF with sexagesimal argam (with ismarragam 2009, with prime decomposition 2010). Argam arimaxa transdecimal numerals s45b0b80, s7836a01, s7836a02, 2006 reform s7836a02. Sexagesimal argam s5231a09. Duodecimal argam s5231a25. “Canonical” argam numeral names s7836a16. Numerals and names for primes, taken from the chemical elements s7836a12. Numerals and names for prime powers s5231a91, “canonical” s7836a13. Numerals and names for superior highly composite numbers s5231a91. Composite numerals generated by “Infinite Multiplication Table” s5231a92, s7836a11. Numerals for small composites s5231a92, s5231a93, s5231a94; numerals for factors of superior highly composite numbers s5231a92, s7836a19; sexagesimal argam for the divisors of cubes of primes, composites, bases 60 and 120 s5231a95, s5231a96.

Nurokaxâ /noo-sho-KAW-shung/ “wanderlust” but more properly, a memoir-travelogue. One name of the ten dozen ninth life phase of late 2020-early 2021. In this life phase Roam Away Home was written. My son was culminating eighth grade while my daughter was finishing senior year.

Nurotevlâ /noo-sho-TAYV-lung/, “mind games” (literally “psychological warfare”). Name of the two dozen eighth xrgâ of early 1983. There was much psychological stress from peers and family during late seventh grade. This tended to focus energy on creative and intellectual strengths, especially coding and sketching.

Octal, number system based on 8 rather than 10, commonly used in computer science in the mid to late 20th century: divisors of the cube of 8 in base 8 s5231a95, fractions, irrational numbers s5231a98, s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41.

The Official Troublemaker: Working title of an unpublished autobiographical novelization of high school days, or rather most of the ralysâ era, between the summers of 1984 and 1988. In terms of the xrgyn or Reneyan life phases, this work runs from Axavynal through the end of the Arahilal xrgyn. The account was written using biographical ephemera such as class notes, photos, etc., and the nixaþine karmyn jimlal (i.e., of the mid nineties). The work was composed in Eĝájñalékxiðanal Xrgâ (i.e., the ten dozen second of late 2018) as an extension into childhood of the Reneyan Autobiography. The work was novelized in the ten dozen fifth xrgâ (i.e., late 2019) and cleffed, with GAN portraits used to convey the protagonist and characters. Chronologically, this work serves as a sort of "sequel" to _otherworld son_ that immediately precedes it. (Some of the action that occurs in the first chapter is continued from the experiences in the latter chapters of this preceding work.) It is unclear, in this misandrist age, if the work will be published any time soon. It is dedicated to my parents, left to my heirs, and it may be to the latter if they see fit in their time, to decide to publish it.

Old North St. Louis: imagined scene, with Icarus falling s5231a74. Crown Candy Kitchen j6b53.

Omega (Totative): Let the integer r ≥ 2 be a number base; then ω = (r − 1). Divisibility rules for s7836a26. A major indirect relationship shown in digit maps and spectra in the 2 Mb PDF “Digit Base Relationship” d87a9, expanded, 11Mb d87aa, and in the 2011 paper “Dozenal FAQs”, 5.6Mb PDF d8907. The notion is incorporated into a peer-reviewed article published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Omega has a special intuitive relationship with the number base, inherited by the divisors of omega. Together the alpha and omega relationships (r ± 1) comprise indirect relationships leverageable by human cognition.

_otherworld son_: Working title of an autobiographical novelization of the first 14 years of my life, in the form of a roman-a-clef. In terms of the xrgyn or Reneyan life phases, this work runs from Ðasþan-Aþral Xrgâ through Iüley-Aðifanal Xrgâ, (i.e., 1974-1984, age 4 through 13). The account was written using biographical ephemera and the nixaþine karmyn jimlal (i.e., of the mid nineties), and was composed in Eĝájñalékxiðanal Xrgâ (i.e., the ten dozen second of late 2018) as an extension into childhood of the Reneyan Autobiography. The work was novelized in the ten dozen fifth xrgâ (i.e., late 2019) and cleffed, with GAN portraits used to convey the protagonist and characters. Chronologically, the novelization of high school called The Official Troublemaker follows this work immediately as a sort of "sequel". It is unclear, in this bigoted age so tilted against boys and men, if the work will be published any time soon. It is dedicated to Karlmel ke Xalyrâ, and it may be to them, if they see fit in their time, to decide to publish it.

Options: steel pan stair vs CMU k635a.

Orrâ, /OR-rung/, “storm”; a lrixe word that also refers to a turbulent time in life.

Page, Irrational: s7836a53.

Page, Joliet: vignettes of its industry, in ballpoint s5231a57.

Page, Life Stage: s5231a02.

Page, Prime: argam numerals, Ulam’s spiral, and primes less than 2160 s7836a53, reference (primes less than 2520) s7836b01.

Page, Title, of a sketchbook: Rykami Jamyse s3964a00, Rykami Yasmyne s45b0a00, Rykami Nixaþkaxa s4952a00, Rykami Arysane s5231a00, s5231b00, Rykami Samaðene s5810a00, Jeleyn Añikçine Xisaëna s611ba01, Rykami Argam s7836a00. Restored rentikâ for the lost Rykami Arebine j4656. Original title page of the Rykami Arysane, as Rykami Rukamine s5231a01.

Page, Totative: s7836b01.

Palazzo Vecchio: a5810a06, a5810a09.

Parapet: constructability study k63a7c.

Paris, France: on site rucisaime sketches of the Notre Dame and 21 Quay Bellemonte s45b0a24. Eiffel Tower from memory s5231a12. Square René Viviani, s5810a02. Setting for much of the first half of the 2021 novel Roam Away Home, a travelogue memoir of Káxa Maïrénal of 1992.

Peer Numbers: appears in blue ink in the table “Highly Composite Integers and Peers” s7836b00, s7836b14. Let the integer x be an element of the highly composite number sequence, Sloane’s A005179. Then an integer n has a divisor counting function value σ₀ equivalent to the x that is immediately less than n. Example, {12, 18, 20} all have the same quantity of divisors σ₀ = 6, 12 is the smallest of these and is a HCN; 28 also has 6 divisors but exceeds the HCN 24. Thus {12, 18, 20} are peers with σ₀ = 6.

Pensacola, Florida: from photographs at Pensacola, FL j6305, j6308. On site at Pensacola NAS j637b.

Peregrinajes, “pilgrimages”: s5231a14.

Perspective Study: “Loriternal Yev”, urban, sci-fi (naïve) j3187. Architectural, nocturnal, (naïve) j3439.

Piazza S. Marco (Venice, Italy): stylized rucisaime s45b0a16.

“π-Code” (pi-code, PC) is the smallest prime index followed by first differences of the remaining prime indices of the prime decomposition of a positive integer n, with multiplicity. For example, the number 84 = 2 × 2 × 3 × 7; PC(84) is “1012”. We start with the prime that is 1 from the starting point of nothing, then multiply it with the prime that is 0 primes more than the first, then by the prime that is 1 prime more than the last, then the prime that is 2 primes more than the last. This way we arrive at n. The number 1 appears in π-code as “0”. We can use π-code to abbreviate multiplicity notation for numbers with widely separated distinct prime factors; π-code accentuates multiplicity via the appearance of zeros. It is most appropriate in representing squarefree numbers and is best as a list, since the terms tend to be larger than 9. We can derive “zero-code” from π-code by subtracting 1 from each term. Pi-code has an application in algorithms that generate squarefree numbers between primorials. The “sweep” algorithm, which had depended on permutations given A020900, was made far more efficient as “loop-sweep” in mid 2017. See A287352 here or at OEIS.

Plan, Architectural (sketch): bay of the Great Mosque of Cordoba, Spain s51a3a15, home of my Filipino uncle and aunt s5231a14, Place de la Université, Aix-en-Provence, France s5810a03, apartment in Foiano della Chiana, Tuscany s5810a07. Seattle coffeeshop and close s5231a77, downtown square s5231a78, high rise residential studies s5231a79. Hotel in Écija, Spain s611ba0b. Naïve (i.e., produced before university): “Attack on Temys”, raster plan view vignette k3670. “Caqualis Base”, raster plan of base k3711.

“Pleasure-Xibane”, Xibane/Aymani set next to the stylized word “pleasure”, along with wanderlust streams of thought s5231a21.

Portraiture, Self, Feature Page. Earliest, age 17 j3b84. At the threshold of starting my career s5231a01, admiring Arebinâ s5231a09, on the floor, in crisis s5231a12, sanding shutters s5231a12, color portrait in a mirror s5231a13, coming to draw s5231a15, nobly wed with Mairenâ in Siena s5231a16, losing my ability to run s5231a20, pondering where I’ve been, what to draw, slaying the past s5231a22, effacing Arebinâ emblematic of dud relationships s5231a22, Picasso-style self-portrait s5231a27, arguing shamefully with my sister s5231a28. Dancing with Asmarâ (she as Camélia) s5231a31, embracing her s3964a06, coming to sketch s3964a07, countercurrent s5810a06. With Amagal s5231a50, as a rich man s5231a56, driving s5231a63, passing cars as I drive Angelina s5231a66, with Aðilyrâ as passenger s5231a66. Falling to the earth in Old North St. Louis in disgrace s5231a74. With fiancee Laura s611ba01, Domesticated s611ba08.

Postapocalyptic: Los Angeles, colored pencil (naïve) j374a

Powers, exponents, multiplicity: of primes s5231a91, s7836a13, argam summary s7836b00. Specific: two s5231a91, s5231a95, s7836a13, s7836a20, s7836a34, s7836a35, in base 360 s7836b09, three s5231a91, s5231a95, s7836a13, s7836a20, s7836a34, s7836a35, in base 360 s7836b09, five s5231a91, s5231a95, s7836a13, s7836a20, s7836a34, s7836a35, in base 360 s7836b09, seven s5231a91, s5231a95, s7836a13, s7836a20, s7836a34, s7836a35, in base 360 s7836b09, eleven s5231a91, s7836a13, s7836a35, in base 360 s7836b09, thirteen s5231a91, s7836a13, in base 360 s7836b09, seventeen s5231a91, s7836a13, nineteen s5231a91. Three-smooth s7836a13, five smooth s7836a13. Squares s7836a11. “End Digit Cycles Exhibited in Geometric Progression of Prime Factors”, i.e., reduced residue systems for n (mod r) with select r ≥ 2 and primes n ≤ 7 s7836a35.

Prefixes: Aði- /uh-thee-/, “fair complected”, a short form of a ðebni /uh THEYB-nee/ meaning fair complected, from the verb ðábyn /THAH-bün/, “to make fair, to lighten, to bleach”. Epr- /uh-purr-/, a prefix signifying the imminent start of something. Ñi- /nee-/, diminutive prefix, from the verb yányr /YAWN-ür/ “to be small”; yá /YAWR/ via asrésþ. Sa- /suh-/, intensifier, similar to “super-”. Va- /vuh-/, prefix meaning “new”. Xa- /shuh-/, prefix meaning “out of”, Xi- /shee-/, feminine prefix, often used to intensify another word. Ym- /üm-/, lrixe negation, similar to English un- or im-/in-. The prefix can connote evil tendencies, e.g. ymánjâ (üm-AWN-zhung), “evil spirit, devil, demon”.

Prime Page, The: primes in sexagesimal to 2160 s7836a53 primes in sexagesimal to 2520 used as a reference s7836b01.

Primes, names for transdecimal digits that are prime powers s5231a91, “canonical” s7836a13, summary of canon s7836b00. As factors s7836a06. Divisor counting function vs. totient function s7836a07. Argam numerals and names tied to chemical elements s7836a12, s7836b01. Primes in sexagesimal to 2160 s7836a53, primes in sexagesimal to 2520 used as a reference s7836b01.

Primorials, integers #k that are the product of the set of primes 0 through k, with each prime having multiplicity of 1. Minimizing the totient ratio s7836a08.

“Pueritas”, “boyhood” > Latin, the first life season or xiómðe, i.e., the Xiómðe Címal (Springtide/Childhood life-season) starting at Xócin (Birth) and lasting 4600 táyyin (7776 days) till Asmíð Gálmiñe (coming of age, quarterlife turning).

Radha /ROD-huh/ a minor character representing arébinâ in Roam Away Home. The protagonist regrets giving Radha a pointillism of the Louvre. Radha came between Iesha and the protagonist and is detested by Iesha and Rosalba. She went by the nickname of “Little Trouble”; Rosalba asserted that the protagonist couldn’t help from staying out of trouble.

Radix, Mixed: a positional notation with multiple radixes coding different places: names and symbols for s7836a19.

Radix, Pure: a positional notation with one number base across all places: names and symbols for s7836a19.

Ralysâ /shuh-LÜ-sung/, “rebellion”; the name of the third xisaën, 9 October 1984 — 3 June 1989, roughly coterminous with high school. Sometimes ralysine /shuh-LÜS-in-eh/, “rebellion age”, “rebellion times”. Setting of The Official Troublemaker.

Ratio, Divisor-Totative, let the integer r ≥ 2 be a number base, the divisor counting function σ₀(r), and the Euler totient function φ(r). The divisor-totative ratio is then σ₀(r) / φ(r). Study of superior highly composite numbers vs divisor-totative ratio s7836a20, refined at s7836a07. This is a measure of balance between divisors and totatives of r.

Ratio, Totient, let the integer r ≥ 2 be a number base, and the Euler totient function φ(r). The totient ratio is then φ(r) / r. Study of superior highly composite numbers vs totient ratio s7836a07. Study of primorials vs totient ratio s7836b09, s7836a08, dn34, dn36. This is a measure of the number of totatives of r as a fraction of r.

“Reciprocal Divisor Method”, now called the Complementary Divisor Method, summarized s5231a99, retranscribed at s7836a52, 100+ page, 6 megabyte PDF manual d7a60.

“Red World Rising”, postapocalyptic Los Angeles in colored pencil (naïve) j374a.

Regime, totative/totient, given the standard form prime decomposition of the integer r ≥ 2, the number r′ having the prime decomposition equivalent to the product of the distinct prime divisors of r. Examination of the totient ratio s7836b09, s7836a12.

Regular Number, integers that are multiples solely of divisors of a number base: sexagesimal and base-120 s5231a96, of 360 s5231a97.

Relationship, Indirect (Number Theory): Let the integer r ≥ 2 be a number base; then α = (r + 1) and ω = (r − 1). Divisibility rules for omega, the alpha rules later realized s7836a26. A major indirect relationship shown in digit maps and spectra in the 2 Mb PDF “Digit Base Relationship” d87a9, expanded, 11Mb d87aa, and in the 2011 paper “Dozenal FAQs”, 5.6Mb PDF d8907. The notion is incorporated into a peer-reviewed article published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Alpha has a special intuitive relationship with the number base, inherited by the divisors of alpha. Together the alpha and omega relationships (r ± 1) comprise indirect relationships leverageable by human cognition.

Rella /SHELL-uh/, /RELL-uh/, focus.

Reney /she-NAY-ee/, a nickname adopted in 1988, having transcended from Ralysine (high school), meaning “born again”. Feature Page. Early self-portrait j3b84. With fiancee Laura s611ba01, Domesticated and in comparison to Icarus s611ba08. Reney tends to project a positive or neutral self-portrayal, in contrast to Icarus, the other avatar for self portraiture. Reneyâ /she-NAY-ung/, genitive of the name Reney; used in general phrases pertaining to me. See Icarus, Bae.

Rentikâ /SHANE-ti-kung/, “dedicatee”, someone for whom another thing is named; many sketchbooks of my twenties were dedicated to female friends and girlfriends, most featured their portraits. Aðijamyse (naïve) s3964a00, Aðitinâ (naïve) k3a06, Arebinâ (reconstructed) j4656, Arysani dedication s5231a00, earlier life sketch on side B s5231b00; pictured s5231a18. Aveacrixe s5568a00, Camélia standing in for Asayme s5697a01, pictured s5231a11, s5231a51; Samaðenâ s5810a00, Aðilyrâ s611ba01, pictured s5231a59. The human namesakes of xrgyñ are also called rentikâ. Rentikyn also appear in Reneyan novels.

Resistence, the notion that the totatives and to a degree, semitotatives of a number base are key to its utility for general human intuitive computation, illustrated by charts that compare prime decomposition vs totient ratio at dn34, dn36. Cyclical diagrams and description of the problem at s7836a06. Divisor counting function vs. totient function s7836a07. Primorials' effectiveness, fields of effectiveness vs. totient ratio s7836a08. Broadly incorporated into the “Complementary Divisor Method”, summarized s5231a99; 100+ page, 6½ megabyte PDF manual RDM2007. Subsequently incorporated into “Balance Study”, 2010 study that includes cyclic logarithmic, geometric, and scalar diagrams exploring the divisors and totatives of the smallest integers, 1¾ Mb PDF, and “Cyclic Resonance”, 2009 paper illustrating the geometric relationship among divisors in clock-like diagrams that positioned the integers 0 < n ≤ r, with the digit “0” signifying congruence with r (mod r), equiangularly around a circle, 800k PDF. The notion of resistence exhibits itself in the color coding present in “Digit Base Relationship”, 2 Mb PDF d87a9. The notion within the digit range of a number base is shown at “Neutral Digits”, 1.15 Mb PDF d8895.

Rivers: Des Plaines River: behind Xrine s5231a28, (Rockdale, IL) industrial vignettes s5231a57, Camélia in a sari at the riverside s5697a01, Missouri River (Augusta, MO) j6159.

Rockdale, IL, industrial suburb of Joliet, IL on the Des Plaines River s5231a57, Camélia in a sari at the riverside s5697a01. The factories in Rockdale, south of Joliet, are emblematic of my childhood in Joliet.

Roam Away Home, a 2021 novel, travelogue, and roman-a-clef based on Káxa Maïrénal, a 1992 backpack trip to Paris, Brussels, and Barcelona from Tuscany.

Roetylâ /SHOY-tü-lung/ “driven, motivated” = Aðimallâ.

Roof: constructability study k63a7c.

Robynaþâ /sho-BÜN-ath-ung/ a heist or coup. Namesake of the ten-dozen-eighth life phase of late 2020 that represented the middle of the covid age. In terms of my son, it was a time of togetherness in his eighth grade with aðiryþyne.

Rosalba /ro-SAL-bah/, major character in Roam Away Home who is the amalgamation principally of arysani and asaime. Rosalba represents wholesomeness and serves as a foil for Noemi.

Rocio /ro-THEE-oh/, character in the novel Roam Away Home. In memoir, Rocio is an actual person but in the novel came to represent the archetype of the sage or of wisdom. She appears as the angel of the Seu in Barcelona.

Roseann, see arysani.

Rslenþe /ur-SLAYN-thuh/, “exile”, name of the two dozen seventh xrgâ of late 1982-early 1983. I was the pariah of the seventh grade, receiving indignation from the entire middle school, with the lowest social status in the school. This tended to concentrate energy on creative and intellectual skills that eventually formed the background behind entrepreneurship. This period fortified my character, eventually winnowing away a “type-A” mentality. Liberation from peer indignation took place at Vianjegajñal Xrga (age 15), and rebirth at Mairenal Xrga at age 21. The name rslenþe served as the name of the entire xisaën (life-stage) in my late teens.

Rucisaime, (Jimalmyne) arycisaymal /uh-ru-chi-SIGH-mull/, a pencil drawing technique involving three weights of graphite in order to broaden the value gamut available to pencil drawing. Sketches are laid out with a hard (4H) lead, then developed as necessary. The hard lead would be used for highlight massing, a medium (HB) would be used generally, with a soft lead (2B or 6B) would deliver deeper black for deep shadows or dark colors. The rucisaime drawing was usually richly developed and endeavoring to be a realistic depiction of a scene e.g., s45b0a20, s5697a01. Less often, the technique was used in a stylized way, e.g., s45b0a16. The style dominated safrine (University) era drawings. The nixaþine (Apprenticeship) era drawings moved away from the labor-intensive rucisaime.

L’Rukaminâ /lshu-KAW-mee-nung/, “the threshold”, “the verge”. s5231a01. A drawing showing Icarus at the start of his career, leaving the safety of university and family. Icarus is entering a courtyard, perhaps a relatively protected outdoor anteroom or verdant patio, opening to whatever lies beyond. It is tiled in azulejos and steps have him descend from the good life of previous years. The decor is influenced by the recent Kax-Andalus, the November 1994 trip to the south of Spain. There is no telling how far he must descend. Name of the four dozen ninth xrgâ of early 1993.

Rykamî /shu-KAW-ming/, “carrying”; word used for a sketchbook, also used for a test or a gateway mechanism.

Rykami Argam /shu-KAW-mi AHR-gum/, The Book of Numbers, s7836, a sketchbook exploring higher number bases, developed during Salcyrine (the Entrepreneurship Era), 2006-2009.

Rykami Arebine /shu-KAW-mi uh-JAY-bee-nung/, The Rebine Sketchbook, is a lost sketchbook where rapid monochrome pencil drawings in the rucisaime style were studied. It primarily developed during Safrine (the Enlightenment), university years 1990-1991. This large horizontal format sketchbook served as the model behind the Rykami Yasmyne, which succeeded it, and became the receptacle of drawings during the spring 1992 semester in Italy. A single sketch was redrawn a couple months after the book was lost, the rentikâ (dedicatee) Arebinâ j4656.

Rykami Arysane /shu-KAW-mi uh-jee-SAW-nuh/, The Roseann Sketchbook, s5231, an experimental, stream-of-consciousness sketchbook primarily developed during Ñixaþine (the Apprenticeship), 1996-1998.

Rykami Asayme /shu-KAW-mi uh-SAW-ee-muh/, The Saaema Sketchbook, s5697, an undeveloped sketchbook with a single notable drawing, La Camélia fi Xereneye.

Rykami Aþriüleal /shu-KAW-mi uh-three-oo-LAY-ull/, The Book of Astronomy, s2485, an attempt at writing an astronomy book at age 11 (thus all work is naïve), with pictures, developed during Iuleine (the Era of Exploration), 1981.

Rykami Aveacrixe /shu-KAW-mi uh-vey-uh-CHREE-shuh/, The Beatrice Sketchbook, s5568, a rucisaime sketchbook that is the receptacle for some figure drawings at the St. Louis Artists Guild produced in the late 1990s.

Rykami Az-Zahra /shu-KAW-mi as-SAH-ruh/, The Az-Zahra Sketchbook, s51a3, a lightly developed sketchbook intended to receive sketches from the Kax Andaluse (travel to Andalucia, Spain), developed during Ñixaþine (the Apprenticeship), November 1994.

Rykami Jamyse /shu-KAW-mi ZHAW-mü-suh/, The Jayme Sketchbook, s3964, a sketchpad primarily of portraiture, begun during Ralysine (the Rebellion), 1988, rediscovered and developed in 1997.

Rykami Nixaþe /shu-KAW-mi ni-SHAW-thuh/, The Book of the Apprenticeship, also the Rykami Nixaþkaxe /shu-KAW-mi ni-shath-KAW-shuh/, The Book of Travels of the Apprentice s4592, a small sketchbook that received imagined trips after having visited Tuscany for a semester.

Rykami Peretivanal /shu-KAW-mi puh-shuh-tee-VAW-null/, The Book of the Demolition of the Zodiac, s6861, a black-paper sketchpad developed in 2002 during a trip to Tuscany.

Rykami Samaðene /shu-KAW-mi suh-MAW-they-nuh/, The Samath Sketchbook, s5810, a book of ballpoint ink sketches and travelogue recording the Kaxa Lecorbu (the Le Corbusier journey) of May 1997.

Rykami Xaðral /shu-KAW-mi SHAWTHE-rull/, the Architect Registration Examination or ARE, name of the six dozen fifth xrgâ of late 2000.

Rykami Xaþtivanal /shu-KAW-mi shuth-tee-VAW-null/, The Book of the Construction of the Zodiac, s6796, a black-paper sketchpad developed in 2010 at Sugar Island, Michigan, and still active.

Rykami Xillaþral /shu-KAW-mi shil-LAWTH-rull/, The Book of Starships, s3730, teenage drawings of spacecraft for a role-playing game.

Rykami Yasmyne /shu-KAW-mi YAS-mü-nuh/, The Jasmine Sketchbook, s45b0, a large sketchbook that received sketches from the semester in Tuscany, some award-winning. The work is mostly representational rucisaime. Begun during Safrine (the Enlightenment) or university years, 1991 through 1993. The sketchbook is modeled on the lost Rykami Arebine.

Ryñ /JÜN/, “holy, sacred; very dear, special”; Ryñvinxâ /jün-VEEN-shung/, a holy object, a relic, something very dear.

Rynhaxharal /shin-huh-SHAW-rull/, “(of the) sacred silence”, name of the eight dozen fifth xrgâ of mid 2010. The year saw three vacations, the final up north to Sugar Island, Michigan, during a year of quietude in the office. Representative work: a8517, a8583; jimlyñ: j8581, j8583, j8584.

Rýñmárâ /shin-MAW-jung/, St. Mary, Maryam, the blessed mother of Christ Jesus. Aðitríçâ-style portrait: s51a3a39.

Rynsariral /shin-SAW-ree-rull/, “(of the) sacred service”, name of the eight dozen fourth xrgâ of winter 2009-2010. The name derives from several callings: religious retreats, the sponsorship of my best friend through RCIA, mentorship in the office. Representative work: two major classified projects, a84a0, a84b2. Vinci LLC began to see reduced demand due to the poor construction economy.

Rynvínxa /shün-VEEN-sha/ A lrixe word meaning “holy marker” or “monument”. The word derives from the verb rányh (JAWN-ooh) “to be sacred”, and ványx /VAWN-oosh/) “to convey, to broadcast”. The rynvínxa is a form of Reneyan prayer, a crafted rodlike marker that is built into a home or a building as an homage to the Lord to bless and protect those living there. The rynvínxa has traditionally been a very ornate object, but simple rynvínxyn suffice, serving the purpose of directing the Lord’s blessing to the location, and distributing it there. (A rynvínxa is installed at avindelor).

Rysenâ /JÜ-say-nung/, “Rosa” ‘in ashen light’, i.e., belonging to someone else; first St. Louis girlfriend, a wild divorcée and mother of one, of Lakepoint era. Namesake of the five dozenth xrgâ of early 1994.

Sáën /SAW-ehn/ The lřixe word for “time”, deriving from the verb sáhyn /SAW-hün/, “to last”. The word vixsáen /vish-SAW-ehn/ means “lifetime”. Saenýn means “all time”. Saenýn is the name of the planet Saturn.

Safylâ /suh-FÜ-lung/, “desire, eros”.

Safylesþ /suh-FÜl-esth/, “admiration, adoration”. The reneyan “elixir”, feminine attention, affection, and adoration, that is to be resisted. A reneyan weakness.

Safylikâ /suh-FÜ-li-kung/, “love interest, limerent object”. Icarus is the safylika of Aðimilá, and this is the crux of the krunþimalle. The classic reneyan safylikyn were Aðiavlikâ, Acraximelâ, Akerysâ, Ayuleyâ, and Arysani. Acraximelâ was the asmiðâ that eventually precipitated the Vianje Egajen of 3310. The only apparent safylikâ of the Gold Regime was Aðilyrâ.

Safyrâ /suh-FÜ-rung/, “enlightenment”; the name of the fourth xisaën, 3 June 1989 — 25 February 1994, roughly coterminous with university. Sometimes safrine /suh-FREEN-eh/, “enlightenment age”, “enlightenment times”.

Saganal /sa-GAWN-ull/, “(relating to) Carl Sagan”, name of the two dozen first xrgâ of mid 1980. The life phase took in wonderment of the Voyager missions and Carl Sagan's Cosmos. I would pivot away from astronomy in the next phase, and toward computer science.

“St. Basil’s”, church on Red Square in Moscow in colored pencil (naïve), j2a28.

St. Louis Artists Guild: figure drawings; ink (Terry), s3964a12. Marker (Jennifer) s5231a70, s5231a71.

St. Louis, Missouri, (metropolitan) see also Arynluimy. A major subject for Añikçine-era jimlyn veronal. Map drawn by memory showing potential places to live s5231a22. Heat map showing familiarity with s5231a45. Backdrop to a portrait s5231a46. Icarus failing in Old North St. Louis s5231a74. Great Forest Park Balloon Race sketches s5231a80. Francis Park studies in spring j6146a, j6416b, j6417, autumn j624a. Typical vernacular masonry j6284, j6285. St. Louis Hills Christmas scene j628b. Chase Park Plaza from Forest Park j6374. The Palm House at Tower Grove Park j63aa. Lindell highrises from Washington Avenue j63b6. Home in the Central West End j6400, New Cathedral j6421. Downtown smokestack j652a. The Jewel Box j6580. Third Baptist Church and Grand Avenue j65a9. Central Paper Company warehouse j6692. McRee Town j6786. SLU Hospital j6787. Compton Heights Water Tower j6791. Civil Courts Building j6797. Southwestern Bell Building j6798. The arch, part of a montage j6924. St. Louis Union Station j6a96. The Climatron j6aaa. Crown Candy Kitchen j6b53.

St. Louis Hills: Francis Park spring studies j6146a, j6146b, j6147, Francis Park autumn studies j624a, typical masonry studies j6284, j6285, Christmas scene j628b.

“St. Louis Hills Christmas”, j628b, a major verone-style drawing of late 1999.

St. Louis Union Station: j6a96.

Sairenâ /SIGH-ray-nung/, “Sara”, a coworker and subject of my limerent adoration in the Ñixaþine (apprenticeship) who purchased Jimla Sairene j6147, a verone scene in Francis Park. Also Aðisaïrâ.

Salcyrâ /sull-CHÜ-rung/, “success, actualization, transcendence”, a word assigned to any exuberant liberation. The name of the seventh xisaën, 13 August 2003 — 6 May 2008, roughly coterminous with the establishment of Vinci LLC. Sometimes salcrine /sull-CHREEN-eh/, “entrepreneuship age”, “entrepreneuship times”.

Samaðenâ /suh-MAW-they-nung/, Samath ‘in ashen light’, i.e., belonging to someone else; girlfriend shortly after college. Samaðenâ was a widow and my best friend’s girlfriend, my relationship with her ultimately a reason for my conversion. Sketchbook dedicatee s5810a00. Ink memory portrait s5231a41. Namesake of the four dozen eleventh xrgâ of late 1993. I moved to St. Louis at tayya 4b76 (2 January 1994), precisely nine years before the birth of my daughter Claire, five-eighths of the way through Samaðenal xrga, quashing the relationship with Samaðena.

Saxisorþal /suh-shee-SAWR-thull/, “(of the) top of the mountain”. Name of the seven dozen sixth xrgâ of winter 2005-2006. The Mountaintop Life-Phase is named for a spiritual high in the wake of a Catholic spiritual retreat in January 2006. The period witnessed successful integration of GIS (DEMs and ortho aerials) into Vinci LLC’s worksite visualizations. Representative work: r7660, r7687, a76b6.

Scenes, Imagined: “Enter Ecbatana” s4952a09, “Meraviglie Passate” s4952b02. New Santa Chiara s45b0a11, “La Camélia alla Finestra” s45b0a13. Siena's Piazza del Campo as backdrop to “La Mia Donna Italiana” s5231a16. Foiano della Chiana as backdrop to “Le Memorie secondo Lei” s5231a24. Old North St. Louis as backdrop to “Icarus Casca dal Cielo” s5231a74.

Schemes: steel pan stair vs CMU k635a.

Seattle, Washington: mass transit, store, and suburban parking study s5231a77, downtown urbanism s5231a78, building studies s5231a79.

Section Detail, Architectural (sketch): column at the Great Mosque of Cordoba, Spain s51a3a03, bay of the Great Mosque of Cordoba, Spain s51a3a15, Gare de Marseilles, France s5810a02, Tuscan ceiling s5810a06, Italian hospital room s5810a07, Tuscan stone arches s6861a03, Roman arcade in Lucca, Tuscany s6861a04.

Semester in Italy: lrixe, Kaxa Mairene; the early 1992 premier section of foreign study by the Illinois Institute of Technology at the Centro Studi S. Chiara in Castiglion Fiorentino, Tuscany. Sketchbook Rykami Yasmyne s45b0; Castiglion Fiorentino s45b0a06, s45b0a07, s45b0a08, s45b0a09, s45b0a0b, s45b0a11. Cortona s45b0a13, Castello di Montecchio Vesponi s45b0a13. Venice s45b0a14, s45b0a16, Siena s45b0a17, s45b0a18. Campaniles / Bell Towers s45b0a81. Paris sketches on site s45b0a24. Cloud studies s45b0a17. Classmates s45b0a14, Mairenâ, local friends s45b0a1a. Camélia s45b0a12, s45b0a13. Argam Arimaxa 1992 s45b0b80.

Semicoprime, in elementary number theory, one of three arithmetic relationships between nonzero positive integers m and n such that m does not divide n^e for integer e ≥ 0 and gcd(m, n) > 1. The other relationships are more well-known; the regular relation has m | n^e for integer e ≥ 0, while the coprime relation has gcd(m, n) = 1. A semicoprime number m with respect to n is the product of at least one prime p that also divides n and at least one prime q that does not divide n. If all p | n are factors of m, then n is regular to m, therefore the relationship is assymetric. If m < n, then we call m a semitotative of n. Smallest number m > n such that m and n are semicoprime: A291989. This was a coinage of mine in 2008.

Semidivisor, in elementary number theory, a necessarily composite number 1 < m < n such that m | n^e with e > 1. All prime divisors p of m also divide n and no prime divisors q that do not divide n produce m. The semidivisor is regular, i.e., it divides some non-negative integer power of n. It is also “neutral”, i.e., a nondivisor in the cototient of n. A test for semidivisors is n^{floor(log2(n))} mod m ≡ 0. As a regular number with respect to n, the number m has a “richness” that is the smallest integer power e of n^e which m divides; for semidivisors m, the richness e > 1 while for divisors d, 0 ≤ e ≤ 1. Regarding number base n, simplified fractions with semidivisor m in the denominator expanded in base n terminates in A279907(n,m) digits, or that smallest power e of n which m divides. In the OEIS, row n of A272618 constructs all semidivisors of n. The semidivisor counting function ξ_d = A243822. The record transform is A293556, and numbers n where records occur is A293555. The difference between semidivisors and divisors, two species of regular number, appears at A299990, and the difference between semitotatives and semidivisors, two species of nondivisors in the cototient of n, appears at A300858. I coined the word in 2008 as one of two species of nondivisors in the cototient of n. The word is published at OEIS and in a 2011 article in the ACM Inroads magazine. The word also appears in Neutral Digits and its later manifestation as Neutral Numbers and has led to the proposal of over a dozen OEIS sequences, including my very first, A243822.

Semitotative, in elementary number theory, a necessarily composite number 1 < m < n such that m does not divide n^e with integer e ≥ 0. The semidivisor is the product of at least one prime divisor p that also divides n and at least one prime divisor q that does not divide n. The semitotative is “neutral”, i.e., a nondivisor in the cototient of n, and non-regular. The test for semitotatives involves the complement of the range 1 ≤ m ≤ n and the union of the regulars of n (see row n of A162306) and the reduced residue system of n (see row n of A038566). A semitotative m = g × t has a “regular factor” g and a “coprime factor” t vis-á-vis n g | n^e with integer e ≥ 0 while gcd(t,n) = 1. Simplified fractions 1/m with m a semitotative in base n, expanded in base n, are mixed recurrent (See Hardy & Wright, ed. 6). In the OEIS, row n of A272619 constructs all semitotatives of n. The semitotative counting function ξ_t = A243823. The record transform is A292868, and numbers n where records occur is A292867. The difference between semitotatives and semidivisors, two species of nondivisors in the cototient of n, appears at A300858. I coined the word in 2008 as one of two species of nondivisors in the cototient of n. The word is published at OEIS and in a 2011 article in the ACM Inroads magazine. The word also appears in Neutral Digits and its later manifestation as Neutral Numbers and has led to the proposal of over a dozen OEIS sequences.

“Senectus”, “elderhood” > Latin, the last life season or xiómðe, i.e., the Xiómðe Vhónmal (Wintertide/senior life-season) starting at Asmíð Aðéliñe (midlife turning) at táyyâ d600 (nearly age 64), and lasting 4600 táyyin (7776 days) till Asmíð Táyaráwe (personal judgment day).

Señû, /SAY-nyung/, a glyph, a sacred sign; a divine revelation.

Señunin Tivanal, /SAY-nyung tee-VAW-null/, signs of the zodiac. In the case of vixsáën or the lifetime, these represent periods of 1600 tayyin = 2592 days, or roughly 7 years 1 month, three such periods to the 4600 tayyin (7776 day) life-season or xiómðe. These have the following equation:

Xiómðe Címal (Springtide/Childhood life-season, “Pueritas”) Xócin (Birth)

0. Akmírâ /uk-MEE-jung/, “being”, (Aries), tayyin 0–1600 (1970 0701-1977 0804).
1. Avlírâ /of-LEE-jung/, “possessor”, (Taurus), tayyin 1600–3000 (1977 0805-1984 0908).
2. Aþrírâ /uth-REE-jung/, “thinker”, (Gemini), tayyin 3000–4600 (1984 0909-1991 1014).

Xiómðe Gálmal (Summertide/Young Adult life-season, “Iuventus”) Asmíð Gálmiñe (Coming of Age, quarterlife dawning, 1991 1015)

3. Asaþírâ /us-uh-THI-jung/, “empath”, (Cancer), tayyin 4600–6000 (1991 1015-1998 1118).
4. Aktírâ /uk-TEE-jung/, “ruler”, (Leo), tayyin 6000–7600 (1998 1119-2005 1223).
5. Srerírâ /sruh-JEE-jung/, “server”, (Virgo), tayyin 7600–9000 (2005 1224-2013 0127).

Xiómðe Vhónmal (Autumntide/Adult life-season, “Virilitas”) Asmíð Vívixe (Midlife turning, 2013 0128)

6. Viðnírâ /vidth-NEE-jung/, “balance”, (Libra), tayyin 9000–a600 (2013 0128-2020 0303).
7. Katírâ /kah-TEE-jung/, “controller”, (Scorpio), tayyin a600–c000 (2020 0304-2027 0408).
8. Safírâ /sah-FEE-jung/, “philosopher”, (Sagittarius), tayyin c000–d600 (2027 0409-2034 0513).

Xiómðe Aðélal (Wintertide/Senior life-season, “Senectus”) Asmíð Aðéliñe (Senior citizenship, 2034 0514)

9. Dysírâ /du-SEE-jung/, “master”, (Capricorn), tayyin d600–f000 (2034 0514-2041 0617).
10. Kalírâ /ka-LEE-jung/, “universalist”, (Aquarius), tayyin f000–g600 (2041 0618-2048 0722).
11. Ixtírâ /ish-TEE-jung/, “believer”, (Pisces), tayyin g600–i000 (2048 0723-2055 0827).

Antvixe (End of life) Asmíð Táyaráwe (Judgment day, 2055 0828).

“La Sevillana”, stream of consciousness drawing s5231a07.

Sexagesimal, the number system based on sixty: s5231a90. “Argam for Sexagesimal with Ismarragam” (sexagesimal numerals and their names) s7836a52. Cyclical diagram s5231a90. Sexagesimal cyclical diagram and totatives s7836a51. Numerals for small multiples of sexagesimal prime divisors s5231a03; sexagesimal argam for the divisors of cubes of primes, composites s5231a95, bases 60 and 120, s5231a96. Fractions s5231a97. Multiplication through an abbreviated table and manipulation of complementary divisors s5231a99, s7836a52, 100+ page, 6½ megabyte PDF d7a60, abbreviated multiplication table for use with complementary divisor method s7836b02. Divisor counting function vs. totient function (in sexagesimal figures) s7836a07. Primorials and prime decomposition vs totient ratio (sexagesimal figures) s7836b09, s7836a08. Totatives of, paired with additive complements s7836b09. Argam numerals and names tied to chemical elements (sexagesimal arrangement) s7836a12. “The Optimized Sequence” s7836a19. Fractions expressed in sexagesimal s7836a31. Powers of primes p ≤ 7 s7836a34, p ≤ 11, and {10, 12} s7836a35. Powers of 10, 12, 16, 20, 36 s7836a36. Factorials s5231a37. Irrational numbers , s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. “The Irrational Page”, “The Reciprocals of the Simplest Primes for Selected Bases” s7836a41. “Primes in Sexagesimal Scale”, “Stanislaw Ulam’s Spiral in Sexagesimal”, “Values of Π − 1”, s7836a53. Argam kinoctove arranged in dozens and sixties s7836b00. “Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, s7836b01. In 2007-2008, sexagesimal became the lingua franca of many of my elementary number theory studies by dint of its 5-smoothness and the plethora of small regular numbers. OEIS Sequences: a250073 powers of 2 in base 60; a250089 60-regular or 5-smooth numbers in base 60.

Shelbie, /SHELL-bee/, the common name of my vehicle (2007-2021). Other names used have been Nina (1993-1997) and Angelina (1997-9). The name also was lrixe: Xílwâ /SHEEL-wung/, Xelvâ /SHAYL-vung/.

Siena, Tuscany: s45b0a16, unfinished sketch of Piazza del Campo s45b0a17, unfinished sketch of Torre del Mangia s45b0a18, Torre del Mangia by night s6861b02. Noted as a favorite destination s5231a14. As the scene for the imagined “La Mia Donna Italiana” s5231a16.

Sister (Lisa): Icarus shamefully arguing with s5231a28, with her daughter s5231a49. Namesake of the eighth xrgâ of late 1973.

Snowbound study: drawings or sketches produced during inclement winter months that preclude most on-site drawings. St. Louis masonry studies j6284, j6285, Heidelberg cityscape j6295, Chartres Cathedral j6304, beach drawings j6305, j6308. Downtown industrial smokestack j652a.

“La Sorella e La Nipotina”, marker portrait of Xrine and daughter s5231a49.

Spectrum, Digit, a bar chart that plots the digits, integers n of a number base, integer r ≥ 2 with the digit “0” signifying congruence with base r, aggregating the digits by type. The types include the unit (purple), divisors (red), semidivisors (orange), semitotatives (yellow), totatives (light gray), omega totatives (light blue), alpha totatives (light green), alpha-omega totatives (light purple), in that order. Digit spectra are effective in quantifying the ratio of digit types to the number base for grand bases, number bases beyond human ability to leverage them. Examples of digit spectra appear at “Digit Base Relationship”, 2 Mb PDF d87a9, and “Digit Base Relationships (A Guide toward Measuring Radix Utility?)”, 11 Mb PDF d87b5. I invented digit maps in 2009; digit spectra summarize the types of digits for a grand base. I invented digit spectra in early 2011.

Spy, the (coworker): s5810a06.

Stefani / Stephanie, see aðifani or aðifanâ. Fair-haired Stefani(e) (aðifani) is “the prettiest girl in seventh grade”, a major character in the 2019 childhood memoir otherworld_son.

Stream of Consciousness drawings: on my maturity level in 1995 s5231a02, at Stacks Cafe in August 1996 s5231a08, sketch loosening exercises s5231a17, s5231a18, s5231a19, s5231a20, s5231a21. Pondering getting beyond the past s5231a22. Thinking about erstwhile relationships s5231a41.

Structure: Steel: structure for a running track k6331. Load-bearing CMU: vs. steel pan stair k635a, exterior masonry wall detail study k63a3, face brick and loand bearing CMU on the exterior and interior k63a7a, variable CMU wall thickness study k63a7b.

Success: pondering s5231a13, hypothetically married and happy s5231a16, hypothetically rich s5231a56, in control s5231a63. Happily engaged s611ba01, at home with my wife s611ba08.

Suffixes: -me /-muh/, suffix denoting a state of being. -or /-or/, old lrixe genitive (possessive) plural. -yñ /-üñ/, lrixe plural, -yñe /-üñe/, lrixe genitive (possessive) plural.

The Sugar Factory: Working title of an unpublished autobiographical novelization of the Semester Abroad and the Summer in Val di Chiana. In terms of the xrgyn or Reneyan life phases, this work runs from the middle of Ahilðiñal through the end of the Mairenal xrgyn of the safyrâ era (between late January through late July 1992, 180 days). A general record of all the time in Italy was kept in a daily planner. Using ephemera and photographs and the accounts, memory was jogged and a clear memoir produced of the entire time abroad. The work was composed largely during Sreda-Ymxavral Xrgâ (i.e., the nine dozenth of early 2013). It is unclear if the work will be published during my lifetime; it will be up to heirs whether to publish, however the current age is inclement and unfit for a traditional coming-of-age novel or bildungsroman. A segment of The Sugar Factory was expanded between late February and early May 2021 to stand as the travelogue and roman-a-clef Roam Away Home.

Sugar Island, Michigan, northern home of the Goodheart family (xihan goodheart). Suite of Verone-style drawings on site: j8581, j8583, j8584, and an unrecorded gift to Mr. Goodheart, j8585. See also Rykami Xaþtivanal, s6796.

Superior Highly Composite Numbers: integers particularly rich in divisors s5231a91. Numerals for factors of superior highly composite numbers s5231a92, s7836a01. Divisor counting function vs. totient function of SHCNs s7836a07, minimize totient ratio s5231a08, dn34, dn36. Examination of relationship between the divisor counting function and totient ratio of s7836a20. Summary of argam numerals s7836b00.

Table: “Infinite Multiplication Table” multiplicative exercise used to generate composite numerals s5231a92, s7836a11. “Divisor and Totient Functions for the Superabundant Numbers” s7836a07. “Sexagesimal φ/r for Totative Regimes”, “Prime Factor Diversity vs. φ/r Ratio”, “Sexagesimal φ/r for Totative Regimes” s7836a08. “Sexagesimal Totatives”, “Primes Pre 79ab”, “Prime Number Names Taken from the Chemical Elements”, s7836a12. “Alternative ‘Anglo Saxon’ Nomenclature for Transdecimal Integers”, “Standard Ismarragam / Nomenclature of Powers of Primes”, “Nomenclature of Compounds of Simple Primes Generated by ‘Power of Prime’ Nomenclature”, s7836a13. “2008 Nomenclature and Symbology for Argam” s7836a16. “The Optimized Sequence”, “My Reference for Mixed Radixes Which Represent Higher Integer Radixes in the Optimized Sequence”, s7836a19. “Survey of the Divisors of Cubes of Bases” s5231a95; “Survey of the Cubes of Powers of Prime Bases”, “Examination of Relationship between Divisors and Totatives” s7836a20. “Omega Divisibility Tests for Bases 2 ≤ r ≤ 93” s7836a26. “Sexagesimal Fractions to [Forty Five]” s7836a31. “Powers of the Primes in Selected Bases” s7836a34, “End Digit Cycles Exhibited in Geometric Progression of Prime Factors”, i.e., reduced residue systems for n (mod r) with select r ≥ 2 and primes n ≤ 7 s7836a35. “The Factorial Page” s7836a37. “Essential Multiplication Facts” (the abbreviated multiplication table), “Argam for Sexagesimal with Ismarragam” (sexagesimal numerals) s7836a52. “The Irrational Page”, “The Reciprocals of the Simplest Primes for Selected Bases” s7836a41. “Primes in Sexagesimal Scale”, “Stanislaw Ulam’s Spiral in Sexagesimal”, “Values of Π − 1”, s7836a53. “Geometric Progression of the Simplest Six Prime Numbers”, “Highly Composite Integers and Peers” s7836b00. “Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, s7836b01. Abbreviated multiplication tables for bases {10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 45, 48, 54, 56}: s7836b03, {60, 64, 66, 70, 72, 80, 84, 90, 96, 120}: s7836b02. “Sexagesimal Totative Pairs”, “Hundal (Base 120) Totative Pairs”, “Kinoctoval (Base 360) Totative Pairs”, s7836b09, “Relationships between Totatives and Totative Regimes of Highly Composite Numbers”, s7836b09.

Tahil /TAW-heel/, plural tahlyn, formerly tahli, “given, sent”. Rocket and Orbit t5738, Ice and Flower t5998, Icicle and Spring Thunderhead t5a0b, Tahil Heatone / Prairie Snow and Snowbound t6032. A hand-drawn greeting card. Tahlyn were produced in three Christmas seasons between November 1996 and late 1998. The very first tahlyn featured lit candles drawn in colored pencil on black paper torn or randomly cut from a tabloid-size sheet. Approximately five dozen tahlyn-1996 saw production. Tavnemika used the candle theme for their 1997 Christmas cards. The 1997 season featured moonlit icicles on more carefully-geometric cuts with slots and tabs; approximately three dozen were made. The final season in 1998 featured curvy cuts and elaborate tabs that sometimes folded several times to lock the card closed; only a handful were produced. This formula of “inversed drawing” or jimla veronal grew over the next seven years into a major method of expression.

Tajiney /TAWZH-i-nay/, “a gross / a dozen dozen days”, a red-calendar period of 144 days; see xrga, “life-phase”.

Talent Dynamic, a vicious cycle of focus and development of a set of skills and innate ability that has the side effect of less concentration and development of some common skills. In my case, the talent dynamic focused first on a profound early reading and arithmetic ability at ages 3-8, spreading to involve computer programming at 10-12, and linguistic and artistic ability between 11-18. These talents/skills form the foundation of capabilities now central in my career, allowing entry into a natural state of flow during production. The lrixe phrase ne hanme tiv savme, “suppress social in favor of intellectual development” or simply tivsavme /tif-SAWV-muh/, refers to the Reneyan “Great Talent Dynamic” (Ðeltivsavme Reneya). This is the name of the one dozen ninth xrga of late 1978, seeing severe punishment for acting out in third grade, resulting in further withdrawal from “fitting in” with other kids, and focusing on studies.

Tatvasafral /tut-vuh-SAWF-shull/, “everything known”, name of the eight dozen eleventh xrgâ of late 2012, which closes the Gilme Xiomðe or Summer of Life. The period ends Adult Youth according to the Reneyan Calendar. The name of the period refers to the summarization of things that I know about integers so that these can be presented at the website www.numberbases.com, and includes procurement of the domain, development of the Tour des Bases (h8b60). A visit to Brooklyn before Sandy and the waning of the Krunþaðimalla are main features of the period. Loss and gathering of recollection or built-up knowledge color the Tatvasafral Xrga. The period sees the paucity of business with the notable exception of a8b70, and the halted a8b30.

Taqgâ /TAWNG-gung/, “length, measure, metric”. Name for a method of dimensioning involving a mixed radix. The method uses argam numerals shown at s7836b00 to represent pure number bases. I use these in writing dimensions in the course of developing construction visualization. The dimension strings are a mixed radix system, using an “infinite base” for feet, dozenal for inches, and either octal or hexadecimal for fractions of an inch. This way, all strings have at most three places. The “infinite base” effectively never escalates higher than the middle 100s. This practice streamlines dealing with plan information so that projects can be assembled within the 1-3 week development window, and one of what I consider my most effective tools. At times, feet are expressed in sexagesimal. The system is also called taqga-reneya.

Taþkeluþþyñal /tuth-kuh-LOOTH-thü-null/, “(of) proofs and relationships”, name of the eight dozen seventh xrgâ of early 2011. This period saw development of digit maps and mathematical proofs. Representative work: a8723, a8743; work in the office remained slight but inquiries were on the rise. I revamp Vinci LLC’s website and that of the Dozenal Society of America. I write three major papers on digit-base relationships. The first outlines the relationships and their impact on multiplication tables, “Analysis of Multiplication Tables”, 1½ Mb PDF d872a. The study “Digit Base Relationship”, exploring elementary number-theoretical relationships of digits to bases 2-120, 2 Mb PDF d87a9, emerged in the summer. I expanded this study to incorporate the effects of such relationships in the multiplication table, divisibility tests, and digital representation of fractions in the mid-2011 presentation 11 Mb PDF d87b5.

Tavnai /TAWV-neh/, tavneðan /TAWV-neh/, “workplace”. The tavnekilû was a small architecture firm on Michigan Avenue downtown Chicago in 1993. The tavnelimâ was a large design-build firm in the St. Louis suburbs between 1994-1995 (Lakepoint phase of the Apprenticeship era). The tavnemikâ was a respected and professional mid-size architecture firm downtown in St. Louis, between late 1995 and late 2004 (Amherst phase of Apprenticeship through the beginning of the Entrepreneurship era.) Tavnenuwe was the notion of a new workplace in mid 2003 through early 2004, specifically a Clayton, Missouri firm or a branch of a large architecture firm downtown in St. Louis.

Tavnaimika, Tavnemika /TAWV-neh-mi-kung/, “workplace-M”. A respected and professional mid-size architecture firm downtown in St. Louis, where I worked late 1995 and late 2004. The dates of employment were tayyiñ 5454 through 7300 (Amherst phase of Apprenticeship through the beginning of the Entrepreneurship era.) Name of the five dozen fourth xrgâ of late 1995-early 1996.

Tayyâ /TIE-yung/, “day”, the basic unit of the Reneyan calendars. The tayya is the localized number of days elapsed since 19:04 GMT 1 July 1970, expressed duodecimally (by dozens). The duodecimal reckoning as described had its start in early 1985. Larger, dozenal groupings of days: tayyiniçâ/tajiniçâ, “one dozen days”; tayyiney/tajiney (more commonly, xrga) “one gross/dozen dozen days”, about five months; tayyinam/tajinam (more commonly, xisaen) “one great gross days”, 1728 days, about 4 years 10 months. The “blue calendar” groupings of days are not named for the numbers of days; the three-dozen day ekron is “atriç tayyor”, &lqduo;three dozens of days”, “tayyin atriçâ”, “days three dozen (in number)”.

Tayyiney /TAWY-yi-nay/, “a gross / a dozen dozen days”, a red-calendar period of 144 days, also written tajiney; see xrga, “life-phase”.

Terranuova (Tuscany): 1995 workplace location, an opportunity to work at an Arezzo, Italy architecture firm. Name of the five dozen third xrgâ of mid 1995. Representative work: s5231a04.

Terry, model at the St. Louis Artists Guild, s3964a12.

Test, Intuitive Divisibility (Number Theory): Let the integer r ≥ 2 be a number base; then α = (r + 1) and ω = (r − 1). Divisibility rules for omega, the alpha rules later realized s7836a26. A major indirect relationship shown in digit maps and spectra in the 2 Mb PDF “Digit Base Relationship” d87a9, expanded, 11Mb d87aa, and in the 2011 paper “Dozenal FAQs”, 5.6Mb PDF d8907. The notion is incorporated into a peer-reviewed article published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. Alpha has a special intuitive relationship with the number base, inherited by the divisors of alpha. Together the alpha and omega relationships (r ± 1) comprise indirect relationships leverageable by human cognition.

“The Threshold” (L'Rukaminâ), s5231a01. A drawing showing Icarus at the start of his career, leaving the safety of university and family. Icarus is entering a courtyard, perhaps a relatively protected outdoor anteroom or verdant patio, opening to whatever lies beyond. It is tiled in azulejos and steps have him descend from the good life of previous years. The decor is influenced by the recent Kax-Andalus, the November 1994 trip to the south of Spain. There is no telling how far he must descend.

Tikmírâ /tick-MEE-rung/ “duality”, twinning, coupling.

Tivánâ /tee-VAW-nung/ “heavens”, the connotation is a second, better existence. This word is used for the zodiac as well.

Tina, see aþikolaðiwâ or aðiëvinzâ.

Title Page: Rykami Jamyse s3964a00, Rykami Yasmyne s45b0a00, Rykami Nixaþkaxa s4952a00, Rykami Arysane s5231a00, s5231b00, Rykami Samaðene s5810a00, Jeleyn Añikçine Xisaëna s611ba01, Rykami Argam s7836a00. Restored rentikâ for the lost Rykami Arebine j4656. Original title page of the Rykami Arysane, as Rykami Rukamine s5231a01.

Torre del Mangia (Siena, Italy): constructed by unfinished sketch s45b0a18, by night s6861b02. In the background of “La Mia Donna Italiana” s5231a16.

Torre d’Orologio (Clock Tower) (Venice, Italy): s45b0a14.

Totative, digits coprime to the number base: Importance as resistance to human computation s7836a06. Divisor counting function vs. totient function s7836a07, s7836a20. Sexagesimal s5231a90, s7836a51, used to sieve primes s7836a12, s7836a53, “Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, s7836b01. Paired complementary totatives for bases 60, 120, 360 s7836b09. See “resistence”.

Totative Page, The: s7836b01.

Tour des Bases: a systematic exploration of integer number bases using number theory. See < Le Tour des Bases >.

Tour Eiffel: stylized s45b0a24, from a memory s5231a12.

Tracy (Svoboda), a main character in the 2021 novel Roam Away Home prone to laughter and companion to the protagonist in Paris. The character represents aðicínþi.

Trakaða /tra-KAW-the/, calendar, literally, “march” (of days).

Trakaðryse /tra-KAWTHE-ji-suh/, the red calendar, using twelve 144-day xrgyn to each 1728-day xisaën. The red calendar was prevalent between the inception of ñiçme in 1985 and 1990, then readopted in 1996, and is the currently dominant calendar. Gregorian calendar in argam, with blue and red calendar transitions marked 3310.

Trakaðsyne /tra-KAWTHE-su-nuh/, the blue calendar, using twelve 36-day ekronyn to each 432-day anrenâ. The blue calendar was prevalent between 1990 and 1996. Gregorian calendar in argam, with blue and red calendar transitions marked 3310.

Transcendence: coming of age, entering the world s5231a01, realization of stage of development in early 20s s5231a02. Pondering what success would be like s5231a13, s5231a56. Getting beyond past demons s5231a22.

Transdecimals, numerals for digits greater than 9 in bases greater than decimal s45b0b80. Generally the subject of Rykami Argam, s7836, with many pages of examples. Sexagesimal argam s5231a09. Duodecimal argam s5231a25. Numerals and names for prime powers s5231a91, numerals and names for superior highly composite numbers s5231a91, numerals for small composites s5231a92, numerals for factors of superior highly composite numbers s5231a92.

Truth, vs. the World, k8a18, “veritas” in Icarus' career s5231a74.

“Truth vs.the World”, on-the-fly drawing jointly developed by J. Mank (“truth” side), poster for reference for J. O’Leary’s Christian inspirational talk, k8a18.

< Tuning up Your Number Base>, a thread at the DozensOnline Forum, h8aaa→. The thread examines the notion of “tuning” the selection of a number base by observing the number-theoretical effects on products in multiplication tables, intuitive divisibility tests, and in expansions of unit fractions.

“Turbulent Candidates”, a paper and all work associated with determination and study of the necessary but insufficient condition A288784 for the “Highly Regular Numbers” sequence, A244052. Many of the terms m in A244052 are in A060735; the primorials A002110 appear and by observations of A275280, must appear; these primorials p_T organize A244052 into “tiers” T wherein all terms p_T# ≤ m < p_{(T − 1)}# must have ω(m) = T. The terms m that are in A060735 = k p_T# with 1 ≤ k < p_{(T + 1)}, must appear in A244052 as they are “reapplications” of the most efficient configuration of primes in tier T, i.e., primorial p_T#. Among the terms m in each tier are certain terms that do not appear in A060735. These terms, when examined through multiplicity notation or MN(m), have an appearance that does not conform to a “word” with T multiplicities e > 0, but instead has a “turbulent” appearance. Hence the designation “turbulent candidate” for A244052. These turbulent candidates appear in A288813, and must be tested via A010846 to determine if they set records. The paper has its nucleus at w9374 but remains unpublished as of late 2017. This work gave its name to the nine dozen ninth xrgâ of late 2016, aligned with the US presidential election of that year, which is notorious for its turbulent candidates.

Tuscany: unfinished sketch of Piazza del Campo, Siena s45b0a17, unfinished sketch of Torre del Mangia, Siena a45b0a18, Monte San Savino ceiling s5810a06, Arezzo hospital room s5810a07, Palazzo Vecchio s5810a06, s5810a09, architectural analyses of stone arches s6861a03, architectural analysis of an infilled Roman arcade in Lucca s6861a04, Torre del Mangia (Siena) by night s6861b02. Imagined scene at Piazza del Campo, Siena s5231a16. Imagined scene in the Val di Chiana s5231a24.

Twelve, a number that goes far beyond being my favorite. A superior highly composite number, third in the series, {2, 6, 12, 60, 120, 360, 2520, …}. Twelve has six divisors {1, 2, 3, 4, 6, 12}, half of its digits. Twelve has four totatives {1, 5, 7, 11}, one-third of its digits are relatively prime to twelve. A number system based on twelve has a richly patterned multiplication table that facilitates human computation. I believe base-twelve is the optimum number base for general intuitive human computation. Since middle school I have maintained an interest in duodecimal numeration, “institutionalizing” the system in my writing and business since early high school years (the three-dozen third xrga). Set of duodecimal numerals s5231a25, fractions s5231a91, divisors of the cube of 12 s5231a95, fractions and irrational numbers s5231a98, s7836a41. “The Optimized Sequence” s7836a19. Powers of primes p ≤ 7 s7836a34. Powers of 10, 16, and 60 s7836a36, powers of 12 in bases 16, 60, and 120 s7836a36. Factorials s5231a37. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03. A 2011 paper on merits, “Dozenal FAQs”, 5.6Mb PDF d8907. All tayya dates and Vinci LLC project numbers are duodecimal. Lrixe: ñiçme. See duodecimal, dozenal.

Typography, simulated: Serif j3b84. s3964a00, s45b0a11, s45b0a12; s5231a00, s5231a07, s5231a14, s5231a18, s5231a21, s5231a23; s7836a00; in logos s5231a31, s5810a00. Sans serif s3964a01, s45b0a06, s45b0a11, s45b0a17, s45b0a1a; s5231a14, s5231a25, in logos s5231a31, s5231a41, s5231a43, in drawings s5231a46. Copperplate s45b0a1a. Distressed, Impact s5231a16; in drawings s5231a44, s5231s48, s5231a49, s5231a51, s5231a70, s5231a71, poster study s5231a80. Fin de Siecle s611ba09. Stylized/decorative k8a18, s3964a04, s45b0a1a, s45b0a24, s45b0b81, s5231a01, s5231a49, s5231a51, s5231a56. Gilt s5231a50. Russian style lrixe (conlang) j3b84. Cursive lrixe (conlang) s5231a00, s5231a01, s5231a10, s5810a00, s5231a70, s611ba00, Invented numberforms: duodecimal s5231a25, the argam arimaxa s45b0b80, argam for superior highly composite numbers s7836a01. Typography and letterforms, graphic design in general, has often figured in drawings and sketches since childhood.

Þabirâ /thuh-BEE-shung/, a pistol or gun.

Þabirallisal /thuh-bih-JAWL-lis-ull/, from þabire ke rallisme, “of guns and riots”, the name of the Life-Phase of “Unrest and Downfall” or nine dozen fourth xrgâ of autumn-winter 2014. Representative work: r9408, a9423, a9431, a9440, a9455, a9460, a9492. The local scene saw the Ferguson riots and general pall that hung over arynluimy; the socialist riots became international news. Internally, this life-phase is perhaps most representative of midlife and was thoroughly journalled as was previous xrgyn 46-47 (The Sugar Factory), 4a-4b (The Threshold), 57-59 (Dynamic City). This phase saw the completion of reneyan political conversion to conservatism that had its start in the nixaþine.

University: here this phrase means the years between August 1988 and May 1993 at the Illinois Institute of Technology’s College of Architecture in Chicago. Roughly coterminous with Safrine or “the Life Stage of Enlightenment”. A positive era of growth following a rocky Ralysine (Life Stage of Rebellion, 1984-1989) and preceded by an upwardly mobile but insecure Ñixaþine (Life Stage of the Apprenticeship, 1993-1998).

Urbanism / City Planning: Place de la Université, Aix-en-Provence, France s5810a03, Joliet close s5231a63. Seattle suburban off-road parking lane and mass transit s5231a77, downtown plaza s5231a78.

Uþþarminal /ooth-THAWR-mee-null/, “(of the) business engagement”. Name of the seven dozen fourth xrgâ of early 2005. Exemplary work: a7418, j7458, a746a.

Vaðanaral /vuh-the-NAW-jull/, “(of the) new wealth”. Name of the six dozenth xrgâ of winter 1998-1999. Representative work: s3964a13.

Vard /VAWRD/, “world”, map of s5231a45.

Venice, Italy: Torre d’Orologio (Clock Tower) Piazza S. Marco s45b0a14, Canaletto and Piazza S. Marco s45b0a16.

Verakrexal /vuh-shuh-KRAY-shull/, “(of the) resurgence”. Name of the six dozen eleventh xrgâ of mid 2003. Representative work: j6b53; includes interactive presentations and digital renderings that are not yet part of the portfolio.

Verhixtoral /vush-hisht-AWR-ull/, “truly winter storm”, name of the nine-dozen-second xrgâ of early-2014. Polar vortices. Intense office work begins to subside. Major projects were a9224, a9247, a9285.

Verlunðe /vur-LOON-the/, coworker at tavnemikâ; drawing with s3964a05, drawing sold to j6b53.

Vernacular: s5810a02. Masonry details j6284, j6285. Neighborhood in snow j6295. Foreground homes j6304. Profane side of high rises j63b6. Stately masonry home j6400. McRee Town neighborhood, j6786, j6789. Part of a montage j6924.

(Jimalmyne) Verone /vuh-JO-nuh/, “inversed”, a drawing style involving colored pencil on black paper, intended to draw light rather than shade in mass. This style dominated the añikçine (Commitment) era drawings of 1998-2003. Examples of verone studies and sketches: j6284, j6786, drawings j63b6, j6580.

Verso /VAYR-soh/, coworker at tavnemikâ and a stellar urban planner; collaboration with s5231a63, result of collaboration with s5231a74, gift to j6b53.

Verykenâ /ve-RÜ-kay-nung/, female coworker at tavnemikâ; pictured along with other coworkers in Icarus countercurrent s5810a06. Also Aðivrukâ /uh-thee-VROO-kung/, Xoxanaveryka /sho-shah-nuh-ve-RÜ-kung/, Syðanaveryka /sü-dthaw-nuh-ve-RÜ-kung/.

Vianjal Egajen /vee-AWN-zhull ay-GAW-zhen/, literally “Split Steel Crisis”, the deepest part of the Great Teenage Depression, at age 15. The event at tayya 3310 (Wednesday 27 November 1995) utterly changed the trajectory of life, from a cowering and bullied biracial boy to a militant and increasingly confident talent. Name of the three dozen third xrgâ of late 1985-early 1986. Representative work: j339a. The troubles in this life-phase set the stage for an explosion of artistic expression in the following phase, Ayuleyal xrga.

Vigesimal, a number system based on twenty rather than ten, common in the Pre-Columbian Americas and in pre-Christian Celtic cultures: divisors of the cube of 20 in base 20 s5231a95. Powers of primes p ≤ 7 s7836a34. Powers of 20 in sexagesimal and base 120 s7836a36. Irrational numbers s7836a41. Reciprocals of primes 2 ≤ p ≤ 37 s7836a41. Abbreviated multiplication table for use with complementary divisor method s7836b03.

Viðanâ /vi-DHAW-nung/, “balance”; the name of the eighth xisaën, the Era of Life-Balance, 6 May 2008 — 28 January 2013. This stage included the highest-earning years where Vinci LLC saw its greatest successes, as well as the Great Recession, followed by a rebound in business and expansion to the mid Atlantic. The era encompassed krúnþimálle (mid life crisis) and was the last life stage before the dawn of “red pill” thought. The life-stage ended with asmíð vívixe (midlife day).

Viðnírâ /vidth-NEE-jung/, “balance”. Also viðníra señû (balance sign), viðníriñe (balance-tide), perehónme (early-virilitas). The sixth of a dozen señunin tivanal that in the case of vixsáën or the lifetime, represent periods of 1600 tayyin = 2592 days, or roughly 7 years 1 month, three such periods to the 4600 tayyin (7776 day) life-season or xiómðe. Viðnírâ begins the third of four life-seasons, namely the start of xiómðe vhónmal (Autumntide/Adult life-season, “Virilitas”), tayyin 9000–a600 (2013 0128-2020 0303). The zodiac equivalent of viðnírâ is Libra. This señû started with midlife day, and is characterized by sustained business in Colorado and the mid Atlantic, a return to the fecundity of the "golden years" of Vinci LLC, followed by a decline. Notable work inlcudes many wastewater treatment plant proposals and key Cornell University academic buildings. Children were middle to high school age. The inversion of politics took place in þábirallýsal xrgâ (autumn 2014). Wife was injured in kárnaþmóllal xrgâ (spring 2015). The Great Pilgrimage took place in aléysminal xrgâ (April 2017). Several tracts in the journal were written as stream-of-consciousness novel-like segments, chief among these are The Sugar Factory (covering the Semester Abroad, Káxa Maïrénal, and the Summer in Val di Chiana), The Commuting Summer, But It's South. In avnadéhinal xrgâ (November 2017) the transection was attempted through jeléynyn. In eĝájñalékxiðanal xrgâ (August 2018) the Firsts Transection commenced. This work yielded two novels otherworld_son and The Official Troublemaker in xiórral xrgâ (autumn 2019). The runup to the covid lockdowns closed the era.

Vinci LLC, xarika vince /SHAW-jee-kuh VEEN-cheh/, the construction visualization and graphic design company I started in St. Louis at tayya 7307, 26 October 2004. See the portfolio of professional work here.

“Virilitas”, “manhood” > Latin, the third life season or xiómðe, i.e., the Xiómðe Vhónmal (Autumntide/adulthood life-season) starting at Asmíð Vívixe (midlife turning) at táyyâ 9000 (about age 42½), and lasting 4600 táyyin (7776 days) till Asmíð Aðéliñe (senior turning).

Volterra, Tuscany: architectural analysis of a stone arch s6861a03.

Voþþarminal /voth-THAWR-mee-null/, “(of the) new business engagement”. Name of the eight dozen ninth xrgâ of early 2012. Exemplary work: a8930, a8937, a8948, a8966, a8987, a8995. I write the paper “Dozenal FAQs”, on the merits of duodecimal numeration (5.6Mb PDF d8907). The article “Exploring Number Bases as Tools”, a peer-reviewed article I wrote in January 2012, is published in the March 2012 edition of ACM-Inroads, a magazine of computer science education. The article examines the relationship of digits and number bases, using digit maps, examining the manifestations of the relationships on multiplication tables, divisibility tests, and fractions.

Wanderlust (craving travel): Reminiscent of recent Andalusian travels s5231a01, of Seville and planning French travel a5231a08, memories of travels past s5231a12. Past “pilgrimages” and favorite destinations s5231a14. Siena, a favorite destination, serves as backdrop for Icarus and Mairenâ, married s5231a16. Vignettes of exotic destinations s5231a18. Travel as elements of a list of things boys like s5231a19. Planning the Kaxa Lecorbu s5231a20, s5231a21. Considering a trip to Greece s5231a25. Map of fluencies toward potential travel s5231a45. Map of southeast Europe s5231a66.

Wár, Wárd /WARR, WARD/ The lřixe word meaning “world” or “planet”. The lrixe names of the planets are Féälwar /FEY-al-war/ “Mercury” (fleeting), Kimálwar /kee-MALL-war/ “Venus” (beauty), Téffwar /TEFF-war/ “Mars” (conflict), Káçynwar /KAUTCH-ün-war/ “Jupiter” (father of gods kát rýnor, kxán jánor), Sáënnwar /SAWN-war/ “Saturn” (ages), Kóximwar /KOSH-im-war/ “Uranus” (spaces), Móywar /MOY-war/ “Neptune” (seas). The earth is called Řðâ /UR-thung/ (earth) or Tárr /TARR/ (lands).

Watercolor: architectural analyses s6861a03, s6861a04.

Weird Letters: The constructed language lrixe is now predominantly conveyed by a standard transliteration into English orthography. The language had an alphabet that increasingly became cursive and nonmodular: the late-1996 manifestation of the alphabet can be seen at a5231b05. After the 2002 cessation of the development of lrixe, the English transliteration became the sole conveyance of the language. There are sounds in the language that are conveyed by special letters. The letter Ð/ð, “eth”, strictly conveys the “th” sound in “lathe”, while the letter Þ/þ, “thorn”, strictly conveys the “th” in “athlete”. These are former Old English letters that are still used in Iceland, and are heavily used in lrixe because ð and þ are more common than d and t or z and s. The letter Ç/ç represents the sound in Scottish “ch” in “loch”, Spanish “j” in “baja”, while plain c represents the “ch” in “matchbox”. The letter x represents the “sh” sound in “flashlight”. The q is either a heavy q not found in English but in Arabic Qatar, or it stands for the “ng” sound as in “singer”. The letter y is one of the lrixe main vowels midway between i and u, the “u” in French “amusée”, but it is also a consonant like in English y in “yard”. The letter j is pronounced as the s in “pleasure” or “leisure”. The lrixe r has often mutated into a “sh” or “zh” sound, though it sometimes retains a familiar rhotic quality (standard r) in stressed syllables. The lrixe rr or reinforced r guarantees the rhotic sound, but it is trilled like is found in Spanish or Italian.

Weird Numbers: My standard number base is duodecimal, based on twelve rather than ten. Because twelve is larger than ten, transdecimal numerals become necessary. See “argam”.

Woods, Lebbeus, influence: s5231a02. Mr. Woods is a conceptual architect and futurist trending toward dystopia, famous in the early 1990s for deserted scenes in cities whose highly patinated layerized buildings are usually presented in a state of decay.

Xajiranviþatelal /shu-jir-un-vi-THOT-el-ull/, “shaky choice”, usually translated as “turbulent candidates”. This refers to the autumn 2016 work and paper, “Turbulent Candidates” regarding the ncessary-but-insufficient condition A288784 for the “Highly Regular Numbers” sequence, A244052. The work aligned interestingly with a US presidential campaign season full of turbulent candidates. Name of the nine dozen ninth xrgâ of late 2016 and early 2017. The period was dominated by very large projects. Representative work: a9906, a9908, a9940, a9977, g9990-a9a09.

Xannaprnâ /shan-na-PURR-nung/, Naprnâ /nuh-PURR-nung/, coworker Susan, s5810a06. Also Aðiprcnâ /uh-thee-PERCH-nung/, Aðisyðanâ /uh-thee-sü-DTHAW-nung/, Aðixoxanâ /uh-thee-SHO-sha-nung/.

Xarika vince /SHAW-jee-kuh VEEN-cheh/, Vinci LLC, the construction visualization and graphic design company I started in St. Louis at tayya 7307, 26 October 2004. See the portfolio of professional work here. Name of the seven dozen third xrgâ of late 2004, beginning of the Vinci era. Representative work: a7326, a7337, a7367, a7386.

Xaþdoxxal /shuth-DAW-shull/, “build the baths”, usually translated as “construction of the baths”. This refers to the spring 2016 rehabilitation and building of new baths at Avindelor, our home. Name of the nine dozen eighth xrgâ of mid 2016. This was a period of vigorous demand from several clients and expansion of services. Representative work: a9820, b9828, a9841.

Xaþtivanal /shuth-tee-VAW-null/, “build the heavens”, usually translated as “construction of the Zodiac”. “Zodiac” was the project name associated with rehabbing the upper story of Avindelor, our home. In the summer of 2004, “Zodiac” was drywalled and finished, and would serve as the home of Vinci LLC until February 2005. Name of the seven dozen second xrgâ of mid 2004. This period brought about a deepening relationship with clients and a stronger compulsion toward entrepreneurship. Representative work: a7294, a72ab.

Xegriwâ /sheh-GREE-wung/, “marriage”, name of the six dozen second xrgâ of late 1999. Portrait of engagement s611ba01, married s611ba08. Representative work from the six dozen second includes technical architectural drawings that are not yet part of the portfolio.

Xele Kinþre /SHELL-eh KEEN-threh/, “program a computer”, name of the two dozen third xrga of early 1981.

Xensley /SHENS-leh-ee/, “Social fortune”, name for the city of Chicago, IL. As a favorite destination s5231a14.

Xereney /SHEH-je-ne-ee/, “Reney is cast out”, name for the city of Joliet, IL. Camélia at an industrial riverfront s5697a01. Noted as a favorite destination s5231a14. Vignette showing a factory in Joliet s5231a18. A page of vignettes showing industrial buildings around town s5231a57. Joliet urbanistic close s5231a63. Setting of _otherworld son_ and The Official Troublemaker.

Xibane /shee-BAW-nuh/, a name for Imani, s3964a02, stylized s5231a10, memory study s5231a21. Seeing Xibane and I reflected in a biracial couple playing chess at a coffeeshop s5231a41. Thoughts penned while waiting on at Lambert Airport s5231a59.

Xiomðe /shi-ONG-the/, “generation”, a lrixe calendar period of 7776 days or 30 xrgyn, equivalent to a quarter lifetime or a generation, about 21 years 3 months long.

Xiorrâ, /SHYOR-rung/, “heavy, passing front”, lit. the feminine/intensifier prefix xi- and the lrixe word for “storm”; a lrixe word describing the windy cold that follows a passing storm front. The term also refers to one’s life or the feeling after a significant correction or revelation that causes conversion of thought. In these times, one is left rethinking actions and methodologies, often shocked at one’s behavior. This is often the start of a major turning point in life. Name of the ten dozen fifth xrgâ of winter 2019-2020, featuring the Xiorrine Metanoia.

Xisaën /shi-SAW-en/, “life-stage”, a red-calendar period of 1728 days or 12 xrgyn, about 4 years 10 months long. The xisaën roughly represents a life development stage.

Xiübanâ /shi-oo-BAW-nung/, laxubanâ /luh-shoo-BAW-nung/, “splendor”. Name of the five dozen sixth xrgâ of late 1996, beginning of the Amherst era. Representative work: s5231a13, s5697a01.

Xiwlâ /SHEEW-lung/, Xtriâ /SHTREE-ung/, Jenâ /ZHAYN-ung/, “woman”. Adevanâ s5231b00. Aðijamyse s3964a00. Aðilyrâ s3964a13, s5231a59, dedicatee s611ba01, s611ba08. Akaisone/Ayntô s3964a04. Akimakinâs45b0a14. Amagal s5810a06, s5231a44, s5231a50. Amyñikâ s5231a07. Amyqâ s5810a06. Arebinâ s5231a09, Dedicatee j4656. Asayme a5231a11, s5231a51. Asmarâ s5231a31, s5231a46. Aveacrixe/Ymalhyna s5231a43. Avikari s45b0a14. Aymanî/Xibane s3964a02, s5231a10, s5231a21. Ayuleyâ s3964a01. Camélia/Akimalâ/Axanthi s3964a06, s45b0a12, s45b0a13, s5231a31, s5231b00, s5697a01. Ðebninâ s45b0a12. Mairenâ a45b0a1a, s5231a12, s5231a16, s5231a24. Ñimanþyñe s5231a49, s5231a67. Samaðenâ dedicatee s5810a00, s5231a41. Xrine s5231a28, s5231a49.

Xrgâ /SHUR-ghung/, “life-phase”, also tayyiney /TAW-yi-nay/, tajiney /TAWZH-i-nay/, “a gross / a dozen dozen days”, a red-calendar period of 144 days; 12 xrgyn make a 1728-day xisaën, roughly five months long. The xrgâ roughly represents a phase of psycho-intellectual interest. See a page of named xrgyn along with links to representative work from that era.

Xrine /SHREE-nuh/, “blessed”; my own sister Lisa. Icarus shamefully arguing with s5231a28, with her daughter s5231a49. Namesake of the eighth xrgâ of late 1973. Also Xeline /SHEL-lee-nuh/ “better (one)”, Nixrine /NEE-shree-nuh/, “little sis”.

Xrinkelexinal /shrin-kuh-LAY-shee-null/, “(of) blessings and luck”, i.e., “blessed and lucky life phase”, name of the eight dozen eighth xrgâ of late 2011. My daughter and I visit New York City, business begins to recover, and I tutor algebra. Representative work: a8818, r8847, a8869, r8898. Thoughts on the relationship of digits to number bases develops into the paper “Neutral Digits”, 1.15 Mb PDF d8895.

Xwilkenimaral /shwil-ke-ni-MAW-rull/, “(of) swimming and digits”, i.e., “life phase of digital swimming”, name of the eight dozen sixth xrgâ of late 2010. My daughter participates in a swim team, I am a swim judge, work on digit maps matures. Representative work: a8675: this is the nadir of the construction depression of 2008-2011, with a record low revenue.

Yexua (Hamaxta) /yi-SHOO-ah huh-MAWSH-tah/, Jesus (Christ), the one true Lord and Savior.

Yexuel /yi-SHOO-ell/, a Christian, specifically, a Catholic Christian. The lrixe for any other proper denomination of Christian is kajiyexuel “almost-Christian” or filyexuel “sibling-in-Christ”. Some are ymyexuel “anti-Christian”.

Ymalhynâ /üm-AWL-hü-nung/, “Unanticipated”, a name for Beatrice, shortened: Imallâ /ee-MAWL-lung/, Ymallâ /ü-MAWL-lung/; see also Aveacrixe; s5231a43, dedicatee s5568a00. Beatrice understood the name as Malina, diminutive of Amalia or Emily.

Ymxávral /üm-SHAWV-rull/, “The Void”, here meaning a “void for reflection or thought”, name of the nine dozenth xrgâ of early 2013. This period is nearly devoid of work in the first half, though some significant projects occur late in the period (a9089, a90a0, a90b1). The beginning months, shortly after asmið vivixe (midlife turning, táyyâ 9000) see the remastery of the jeleyn sarynal or the Journal of Paradise, an account of travels in Tuscany, Paris, and Barcelona and significant relationships shortly after asmið galmine (coming of age, táyyâ 4600), half a life ago. The jeleyn sarynal and the resultant account of the Ahilðiñal and Mairenal Xrgyn have become part of the Reneyan Bildungsroman.

Ynþa /ÜN-tha/ The lřixe second person singular pronoun, meaning “you”. Feminine is Ynþi /ÜN-thee/.

Ywa /Ü-wa/ The lřixe third person singular pronoun, meaning “he”. Feminine is Iya /EE-ya/. Accusative suffix is -ak, dative is -hym.

“Zerocode” (0-code), a tally of run-lengths of indices of totatives in the prime decomposition of a number. Suppose we have a number 903210, with multiplicity notation “111110101”. This notation arises from writing the multiplicities of all the prime factors of 903210, i.e., 2 × 3 × 5 × 7 × 11 × 17 × 23, in little-endian positional order, writing a zero for primes coprime to 903210. Using nonzeros in MN(903210) = “111110101” to delimit the run lengths of zeros, we get “000011”. The code is deficient; encoding and decoding yields the squarefree kernel of the original number, and some numbers like 0, 1, and 2 cannot be coded. The code has applications in the study of A288784 and its relationship to A244052 and a related sequence’s relationship to A293555. Zerocode can be easily derived from “π-code” (pi-code, A287352) simply by subtracting 1 from each term.

This page last modified Thursday 20 January 2022, this version first established 4 April 2012.

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