Saturday, March 7, 2009

use of prime numbers in xyz co-ordinate measurements, decimese, deafese 'mathese'

D: I heard of a language that includes pronouns to denote compound nuances that English cannot.

The following passage is from a book called "Language Death" by David Crystal.

A book review by Danny Yee © 2000
In Language Death David Crystal looks at present and future threats to languages — and at what can be done to counter them. Crystal's relatively unemotional, reasonable, and balanced approach is unlikely to ever gain him the acclaim of more populist science writers, but he is always readable and informative and Language Death is no exception. A succinct overview with a good selection of examples and case studies, it has something for anyone involved with either linguistics or indigenous cultural survival.

Tok Pisin from New Guinea, an officially recognized creole, has the following nuances for pronouns.
mi - I
yumi- we (you and me, inclusive)
yu - you
mipela - we (we, not you, exclusive).

D: this ability to indicate multiple subjects with degrees of inclusive/exclusive is useful. It is handy to do so with brevity. To do so in a methodical fashion would be handy.

I was thinking about yesterday's discussion on describing size.
I was thinking how handy it would be to be able to describe 2 of the 3 Cartesian system co-ordinates in a single robust term.
My very first thought on this went nowhere.
"If we clarify the 1st, 2nd and 3rd dimensions, then add together those numbers, could we denote which 2 of 3 co-ordinates we are describing jointly in a single statement?"
D: of course, this doesn't work. 1 plus 2 is 3, which would be confused with the 3rd-only. Keep in mind that the default quality is assumed to be all three dimensions inclusively.
D: I then attempted to apply prime numbers in ascending order for 1D, 2D and 3D respectively.
This was inspired by some passage I read online years ago. If anybody knows the site, please tell me so I can give them credit. Imitation can be the highest form of flattery, and I wish to be considered an imitator but not a plagiarist.
In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid around 300 BC. The first twenty-five prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

D: technically, since I use 1 also, this is not quite just prime numbers.
So 1, 2, 3, 5, 7, 11, 13...
Now let us look at the implications of this.
We associate 1D (longness, length) with 1.
We associate 2D (wideness, width) with 2.
We associate 3D (deepness, depth) with 3.
Same problem. To revise, we do the following.
1D, 2D, 3D with 1, 3 and 5 respectively.
Let us look at the new addition totals.
1D only, 1. 2D, 2. Same problem at 3.
So we skip 2. Now we have the (near) primes of 1,3,5,7,11...
1D, 1. 2D, 3. 3D, 5.
1D and 2D - 1 plus 3 is 4. No overlap with the revised prime list so far.
1D and 3D - 1 plus 5 is 6. OK.
2D and 3D - 3 plus 5 is 8. OK.
Stacking our revised prime list (missing 2) and these 2-dimension totals, we get
1,2,3,4,5,6, 8.
That works pretty well!
Adding in time as a 'dimension' throws a monkey wrench into the works.
4D (time) is the prime 7.
OK, here we have problems. I am not sure how often this would come up, but if we attempt to describe length (1D) and time (4D), we get 1 plus 7 or 8.
And that is a problem - 8 is already taken by 2D plus 3D.
Hmm, back to the drawing board.
In desperation, I skipped 7 and went to prime 11 as the 4D dimension of time.
1D and 4D have the primes 1 plus 11 for total 12. OK.
And so on, with higher numbers.
Expressing all 4D at the same time would be 1,3,5, 11 added to make 20.
If the Decimese number naming convention can concisely handle 20, there are several benefits. There are sufficient benefits with even just 12.
1) the Imperial measurement system has 12 inches in a foot.
( I know a great but risque joke about this. Ask me. <:)
2) the 60-base ancient number system, still in use in time and angles/degrees.
Sexagesimal (base-sixty) is a numeral system with sixty as the base. It originated with the ancient Sumerians in the 2000s BC, was transmitted to the Babylonians, and is still used—in modified form—for measuring time, angles, and geographic coordinates.

The number 60 has twelve factors, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, of which 2, 3, and 5 are prime. With so many factors, many fractions of sexagesimal numbers are simple. For example, an hour can be divided evenly into segments of 30 minutes, 20 minutes, 15 minutes, etc. 60 is the smallest number divisible by every number from 1 to 6.

D: there is a fabulous book in the WPL on ancient number systems, which I read.
Author Bruno, Leonard C
Title Math and mathematicians : the history of math discoveries around the world / Leonard C. Bruno ; Lawrence W. Baker, editor
Imprint Detroit, MI : UXL, c1999
D: not sure, but I *think* it was this book.

So both 12 and 20 are useful multiples of 60, so have great utility.

Decimese is now misnamed. With SIX (not five) sets of voiced/voiceless consonants, it no longer has a 10-base. It can still express Metric just fine.
Assuming enough planning to use brief number names up to 12 or 20, we have the basis for a very concise shorthand system for describing space/time.
I suppose if some unified theory candidate out there changes the official number of dimensions that my prime system could be simply expanded to reflect this.
There is one claim that there are 9 space and TWO (!) time dimensions.
I suppose my system could handle this.
A out-of-my-butt number naming convention might be as follows:
Special Number Naming convention is heavily aspirated consonant + A + H.
E.g. consonant pairs of pb sz kg fv td ch/sh.
Ergo 1-12 would be pah bah et al.
Of course, this violates the syllable rules of Decimese. A Ygyde-style optional variant system for ease of speaking could also work.
E.g. pahan, haban, et al.
See the post on number naming conventions for why this is undesirable.
The naming convention, based as it is on the binary nature of voiced/voiceless consonant pairs, lends itself to the other binary concepts such as even/odd and the myriad other examples of duality in nature and our social world.

Example. Let us say that we wish to decribe a large piece of paper without denoting that the paper is thicker. Thus we have length, width but not depth.
Length is 1D, width is 2D. 1D is associated with prime 1. 2D with prime 3.
Thus (number 4) and the convention for naming dimensions.

Of course, this borrows heavily from my first language design called Deafese.
Haha, funny that when I quote myself, the plagiarism becomes flattery! [=

For the benefit of English speakers raised on a certain chronological order in the alphabet, the consonant order is B,D,Ch,L,R,Th,V,W. These consonants are sometimes referred to a C1to8, representing the #s 2to9. The sounds for Ch and Th can be written with C and T, if one remembers the sound associated with them.

The #s 2-9 are expressed via C1to9+A. I.e. 2 ba, 3 da, 4, cha(or ca), 5 la, 6 ra, 7 tha(or ta), 8 va, and 9 wa.

CVC. Think of this as the #s CV plus C to clarify the numerical quality involved..
CVC1 or CVb can be the # of dimensions to a geometrical shape.

I can easily express 'dimension' as a concept via reserving CVC1. This in turn frees up all the V-CVC2to8 slots for additional meanings. Having said that, I think that expressing numerical qualities via a consonant added to the numbers themselves is elegant and transparent.

Please note that I plan to post interface rules for lip-readable visemes and the Decimese phonemes, selected for global (and Mandarin) appeal this week.
Sorry, work and career goals get in the way!


I was unable to check spelling today. I am using a bud's computer and the script is disabled.

No comments: