**From:** CE Whitehead (*cewcathar@hotmail.com*)

**Date:** Mon Jun 07 2010 - 21:36:48 CDT

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Hi, I've gotten a bit behind on this discussion; oh well.

It really does seem to be getting circular (and getting away from the concerns of encoding) unless Luke comes back with a list of facebook users, his private use encoding system, etc. and shows that his system is in use.

From: Luke-Jr (luke@dashjr.org)

Date: Sat Jun 05 2010 - 10:29:03 CDT

On Saturday 05 June 2010 09:33:03 am Otto Stolz wrote:

*>> In the decimal systems, you can easier divide by 2, 5,
*

*>> and powers of 10, whilst in the hexadekadic system,
*

*>> you can easier divide by many powers of two, and all
*

*>> powers of 16.
*

*> And 4, and 8. Many repeating fractions also become more accurate with base 16.
*

*>> For arbitrary divisors, the decimal system seems to be
*

*>> easier, as you would use the same division algorithm,
*

*>> in both systems, however with different tables (dubbed
*

*>> “multiplication table” or, less formally, “times table”)
*

*>> that comprise 100 vs. 256 entries. Hence, the the hexa-
*

*>> dekadic multiplication table should be 2½ times as hard
*

*>> to learn, and memorize, as the decimal one.
*

*> Does anyone seriously memorise multiplication tables...?
*

Doing so can speed up test taking for persons who have to pass entrance examinations -- not to mention

of course rapid calculations about payments, interest, and more.

(Indeed memorizing tables through 12 by 12 albeit in base 10 was a requirement for promotion to third grade

in my day in school but things have changed I suppose -- for one thing candidates are allowed to take calculators to the S.A.T. now)

*>> This whole deliberation is, of course, purely academic.
*

*>> In real life, you will have to use the decimal system
*

*>> as everybody else does, lest you wont be misunderstood.
*

*> Only when/if you deal with "everybody else".
*

*> And then you need only convert, not use it for your calculations.
*

You need the decimal system for most college entrance exams, prices in the real world (till we change the dollar, get another monetary system -- maybe we need to -- but we are not the only country on a system of one's, one-hundreds, etc; there is the Mexican peso and more -- but the Mexican peso comes from the base 8/16 pieces of eight -- maybe they had computers way back then and we just do not know -- that info got somehow lost; the British however always did their own thing; I'm not a Brit I guess), taxes, etc.

You need the hexadecimal system to 'talk to computers in assembly language' (but need to talk in straight base 2 if you are writing machine code -- otherwise you need a compiler).

You can also use hexa whatever (don't want to say the 'decimal' part here) in books describing assembly language -- books for people even. (Why not? Although it does after all take a human to write the code that makes a computer 'really foul things up;' my dad who has written some code himself always told me that base 16 and base 8 were invented to make it easier for PEOPLE to write code for computers -- thus people would not have to write in 1s and 0s.)

IMO an encoding system for hexadecimals -- inspired by an extant private use set of encodings, having a definable/identifiable community of users with examples of usage online or something -- should fly as a proposal.

There is no real perfect base system but base 6 or 12 or some multiple thereof would facilitate conversion between base 2 and base 3 tertiary but the circuits are going to be complicated.

But base 6 or 12 would make counting on the fingers more difficult.

(But as you've said above people don't memorize tables or use fingers; they all have calculators and computers.)

But we've strayed from unicode concerns in this discussion, I think.

(As for isolation, go ahead yourself, but will your children ever mix? If so will they need to understand base 10?)

*>> You may wonder, why I am using the term “hexadekadic”.
*

*>> This is because, “hexadeka” is the Greek word for 16,
*

*>> whilst the Latin word ist “sedecim”; there is no language
*

*>> known that has “hexadecim”, or anything alike, for 16.
*

*> I prefer "tonal", since "hexadecimal"/"hexadekadic" both imply a decimal base.
*

6 and 10. I don't know whether the base is meant to be six or ten . . .

*> . . .
*

From: Luke-Jr (luke@dashjr.org)

Date: Sat Jun 05 2010 - 12:35:36 CDT

*> I've also created a "Hexadecimal / Tonal Mathematics" group on Facebook, to
*

*> promote using it in daily life. ;)
*

Who else goes to your facebook page? How many friends?

And what system of encoding have you all agreed on for encoding characters?

You might develop your case thus; otherwise I fear that any discussion will be 'circular' and pointless.

Best,

C. E. Whitehead

cewcathar@hotmail.com

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