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Quasi-NumeralGlossary |
Quasi-Numeral
A quasi-numeral (as opposed to a “natural” or plain numeral as normally regarded) is a group of numerals that serve as surrogates that signify other numbers. (This term is coined in this work.) A decimal example is the quasi-numeral 25, which signifies “a quarter (of a hundred)”, or “repeated 3” (written 3_) which signifies “one third”. Single numerals or digits that evoke another number do not constitute a quasi-numeral as they already are a (natural) numeral of base b. Decimal 5 often serves as a surrogate for the notion of “half, halfway” but is not a quasi-numeral since it already is the numeral 5.
The situation is akin to the English digraph “th”; the phonemes conveyed by the digraph are not related to that conveyed by “t” or “h” alone, but are instead completely unrelated. The quasi-numeral does not always function like a natural numeral, but only alone, at the end, or in front of any number of trailing zeros, expressed in base b. For instance, recall “25” is the decimal quasi-numeral that conveys “one quarter (of a hundred)”. Therefore “325” can be read as “three and a quarter hundred”, or “72500” as “seven and a quarter myriad” but “2539” no longer has “25” interpreted as a quasi-numeral. Of course we may always interpret quasi-numerals strictly according to their normal values, e.g., “2500” as quasi-numeral is “a quarter of a myriad” or “twenty-five hundred”, but surely is two thousand five hundred.
The quasi-numeral does not aid computation but instead the interpretation of a number in base b. It is a subjective figment of human cognition, therefore some enjoy more quasi-numerals depending on their experience with numbers, particularly fractions. For some skilled workers, the quasi-numeral “1875” signifies “three sixteenths (of ten thousand)”, but for most this could simply be “eighteen and three quarters hundred”. The quasi-numeral is a cognitive shortcut that aids in our rapid understanding of a number.
Oftentimes, quasi-numerals and surrogates are interpreted as “round” or semi-round numbers in base b. They serve as convenient “snap points” because of the ease of understanding their significance.
It is anticipated that the natural fractions 1/2, 1/4, 3/4, 1/3, and 2/3 appear as surrogates and quasi-numerals in all bases. This is because of the simplicity and commonness of these fractions in everyday life, and because these fractions can be conveyed by one or two nonrepeating or repeating digits.