Googology Wiki
Advertisement
Googology Wiki

The Misalian base-naming system is a system for naming various positional numbering bases in English created by jan Misali. The system, itself, is not positional, instead relying on the prime factorization of numbers.[1][2]

The first unexian base names are available as a webpage,[3] while the first biexian base names are available as a text file.[4] See also #External links for an automatic generator.

Roots, prefixes and suffixes

  • Base 0 is "nullary".
  • Base 1 is "unary".
    • Prime bases without a root name are expressed as "one plus number"; for proper names of bases, the prefix is "un-", while for prefix forms, the circumfix is "hen-...-sna-".
  • Base 2 is "binary".
    • "bi-" is a prefix meaning "times two".
  • Base 3 is "trinary".
    • "tri-" is a prefix meaning "times three".
  • Base 4 is "quaternary".
    • "tetra-" is a prefix meaning "times four".
  • Base 5 is "quinary".
    • "penta-" is a prefix meaning "times five".
  • Base 6 is "seximal".
    • "hexa-" is a prefix meaning "times six".
  • Base 7 is "septimal".
    • "hepta-" is a prefix meaning "times seven".
  • Base 8 is "octal".
    • "octo-" is a prefix meaning "times eight".
  • Base 9 is "nonary".
    • "enna-" is a prefix meaning "times nine".
  • Base 10 is "decimal".
    • However, if this name is preceded by a prefix, it becomes "-gesimal".
    • "deca-" is a prefix meaning "times ten".
  • Base 11 is "elevenary".
    • "leva-" is a prefix meaning "times eleven".
  • Base 12 is "dozenal".
    • "doza-" is a prefix meaning "times twelve".
  • Base 13 is "baker's dozenal", a name credited to Kate of Tangerine's Neocities Page.[5]
    • However, if this name is preceded by a prefix, it becomes "-ker's dozenal".
    • "baker-" is a prefix meaning "times thirteen".
  • Base 16 is "hex".
    • "tesser-" is a prefix meaning "times sixteen".
  • Base 17 is "suboptimal". It is named for the fact that it has the worst representations of rational numbers of any base from 2 to 20.[6]
    • "mal-" is a prefix meaning "times seventeen". It is derived from the Esperanto prefix "mal-", which nominally means "opposite", but which jan Misali noted that Romance language speakers could misconstrue as meaning "bad".[2][7]
  • Base 20 is "vigesimal".
    • "icosi-" is a prefix meaning "times twenty".
  • Base 36 is "niftimal". Derived from the seximal word "nif", niftimal has been proposed by jan Misali as a compression method for seximal.[8]
    • "feta-" is a prefix meaning "times thirty-six".
  • Base 100 is "centesimal".
    • "hecto-" is a prefix meaning "times one hundred".
  • "nega-" is a prefix negating the number following it; for example, "negadecimal" is base -10. This extends the system from all natural numbers to all integers.
  • "vot-" or "vöt-" is a prefix for the reciprocal of the number following it; for example, "votdecimal" is base 1/10. It is named after the conlang Vötgil, which, to name numbers, lists their decimal digits in reverse order, thus employing votdecimal. This extends the system to all rational numbers.
  • The final two suffixes, albeit not used together with the standard roots, prefixes and suffixes above, extend the system to all numbers that can be named.
    • "-nary" is a suffix which can be added to the English name of any number less than six to form a name for a system that uses that number as a base.
    • "-imal" is a suffix which can be added to the English name of any number greater than six to form a name for a system that uses that number as a base.

Forming compounds

For any base that is neither prime nor has a basic root form, the algorithm is to take the two closest factors of the number and write the smaller one in prefix form and the larger one in root/suffix form.

For example, 120 can be decomposed into two factors that are either prime or have root forms in two ways: 10 × 12 and 6 × 20. However, as 10 and 12 are closer to each other than 6 and 20, base 120 is known as decadozenal rather than "hexavigesimal".

Abbreviations

In addition to giving each base a full name, the system also gives the abbreviated name, which is no shorter than three letters. It does so by first converting the full name to uppercase and removing any apostrophes, vowels not in the first three letters and the last letter (with the exception of hex), and then, cycles through a space of subsets of this modified name, picking the first one that isn't in use by a smaller base. The space of subsets is composed as follows:

  • Shorter abbreviated names are preferred to longer ones. Out of bases up to 10000, the system only gives a 5-letter name to 196, or 1.96% of them.[2]
  • Within abbreviated names of the same length, ones that use the letters occurring earlier in the name are preferred.
  • An abbreviated name must use the first letter of the full name.

External inks

Sources

Advertisement