Re: Numbers and math

taliesin the storyteller <taliesin@...> wrote:
>
> A classic question is: how do you count to ten in your conlang?
> Generalizing:
>  - do you form ordinals from cardinals? how? if not, how?
>  - do you have a zero?
>  - can numbers be negative?
>  - fractions? percentiles? if it's not a decimal system, is there
>    something instead of percentiles?
>  - how do you add, subtract, multiply and divide? (if you know how)
>  - what about raising to the nth power and n-roots?
    As a mathematician, or at least someone educated as one, these
questions were among the first I answered when designing Gladilatian, along
with similar ones you left off, such as how to say "two pi".
    Most of the following was lifted from my website.

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    Gladilatian uses a base six number system.  I will append a (6) to a
numeral to indicate base six.  E.g. 25(6) = 17.
    The basic form for a number is the adjectival form.  The noun form is
constructed with the suffix "ot".

>>>>>> Naturals
These are the natural numbers which have their own names.

_mro_   "zero"
_zno_   "one"
_fsut_  "two"
_hrnu_  "three"
_srut_  "four"
_wefe_  "five"
_mu_    "six"
_hzut_  "seven"
_zo_    "eight"
_hrhr_  "nine"
_mrut_  "ten"
_mefe_  "eleven"
_mumu_  "twelve"
_hrmu_  "eighteen" = 30(6)
_srmu_  "twenty-four" = 40(6)
_wemu_  "thirty" = 50(6)
_zla_   "thirty-six" = 100(6)
_fyat_  "two hundred sixteen" = 1000(6)
_sflo_  "1296" = 10000(6)
_sflosflo_ "1679616" = 100000000(6)

    Numbers less than 100(6) which don't have their own name are formed by
combining a multiple of six with a number less than six as one word, e.g.
_hrmufsut_ "twenty" = 32(6).  Numbers greater than 100(6) and less than
10000(6) are formed by combining a multiple of 100(6) with a number less
than 100(6).  E.g. _srmuhrnuzlasrmusrut_ "1000" = 4344(6).  Higher numbers
are formed similarly with powers of 10000(6) and coefficients, with
coefficients of one and components having a coefficient of zero left off.
E.g. _hrnusflosflomumu_ "5038860" = 30000020(6).  Powers of _sflo_ greater
than two are formed by prepending the ordinal of the power.  When this
happens a coefficient must be used to distinguish it from a regular ordinal
e.g. _znozmrwefesflo_ = 6^20.

>>>>>> Negatives
Negatives are formed with the state _lr_.  E.g. _lrfsut_ "minus two".

>>>>>> Ordinals
Ordinals are formed with the state _zmr_.  E.g. _zmrfsut_ "second".  The
ordinal of minus one, _zmrlrzno_ means "last", the ordinal of minus two,
_zmrlrfsut_, means "penultimate", etc.  The ordinal of zero, _zmrmro_ means
"not in the list".

>>>>>> Transfinite Cardinals
Two transfinite cardinals have their own names:

_srmo_      the cardinality of the integers
_fryma_     the cardinality of the reals

    The aleph and beth systems are formed by modifying _msoru_ "aleph" and
_msuto_ "beth" with ordinals.  N.B. Gladilatian ordinals for the aleph and
beth notations are one off from English.  So _zmrzno msoru_, literally
"first aleph", is "aleph naught", and _zmrfsut msoru_, literally "second
aleph", is "aleph one".

>>>>>> Rationals
    Fractions are formed by using the preposition _mnat_ with the noun form
of the denominator, so _mnatsrutot_hrnu_ would be "three fourths".  Note
the difference between _mnatsrutot_zno_rek_ "one fourth of a cake" and
_mnatsrutu_zno_rek_ "one cake divided into four pieces".

>>>>>> Transcendentals
    Here are the two most important trancendentals.  Note that Gladilatian
avoided the historical accident which resulted in English having a name for
half of two pi but not for two pi itself.

_ryt_   "two pi"
_mxo_   "e"

>>>>>> Arithmetic
    Addition is denoted with the preposition _het_, e.g.
_hetfsutot_hrnuot_wefeot_ "2 + 3 = 5".

    Multiplication is denoted by having one number modify the other e.g.
_fsut_hrnuot_muot_ "2 * 3 = 6".

    Exponentiation is denoted by having the exponent, with the attribute
_nmut_, modify the base e.g.
_nmuthrnu_fsutot_zohot_ "2 ^ 3 = 8".

    Subtraction is addition with negative numbers, and division is
expressed the same way as rationals.

    Relatives may be used for grouping, e.g.
_mep_hethrnuot_srutot_fsut_u_fsut_hethrnuot_fsut_srutot_
"2 * (3 + 4) = 2 * 3 + 2 * 4".

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    I still need to deal with the equivalent of decimals (sexals?), omega
(and other infinite ordinals), complex numbers, modular arithmetic, linear
algebra, calculus, topology, geometry, etc.  I want to think about each
field a bit before I do, though, since I don't want to simply relexify
modern mathematics.
    I also need to put Gladilatian numerals, which I have designed, on the
web.

 ===========================================================================

             Dennis Paul Himes    <>    dennis@himes.connix.com
             homepage: http://www.connix.com/~dennis/dennis.htm
        Gladilatian page: http://www.connix.com/~dennis/glad/lang.htm

Disclaimer: "True, I talk of dreams; which are the children of an idle
brain, begot of nothing but vain fantasy; which is as thin of substance as
the air."                      - Romeo & Juliet, Act I Scene iv Verse 96-99