Re: Assigning a plane for mapping digits for many different bases

From: Ken Whistler (kenw@sybase.com)
Date: Tue Mar 08 2011 - 16:18:53 CST

• Next message: Hans Aberg: "Re: Assigning a plane for mapping digits for many different bases"

On 3/8/2011 1:16 PM, Tiago Estill de Noronha wrote:
>
> So instead of writing it as 3 digits you gotta write all of that? That
> kinda sounds like when one language is translated into a very
> different one requiring whole sentences to be spelled out to explain
> the meaning of each word in the first language, very awkward.
>
Not at all. And while I may not be getting across here, the alternative
I suggested has
the elegance that it applies equally well to any base you desire.
Suppose I need to
express that same number 1927631 in base 4199, instead of base 360. In
base 4199,
that number can be expressed in just two digits: {{459},{290}}_4199

And again, I don't need to encode 4190 additional digit symbols to do
so. Nor do I even
have to learn a new system -- this particular system is defined so
generically that it
applies to any integral base you might choose. And that general
applicability is
precisely what would make it appeal to the kinds of people who might
actually be
concerned with base 4199 numbers, namely mathematicians.

And if you don't like the need to express the digits and the base
themselves in decimal, you
could always express them in hex or octal or binary, or even apply the
representation
recursively, and express each digit and the base itself, say, in base 23.
>
> People who use CJK learn thousands of characters, someone that
> frequently deals with numbers in a big base coud just as easilly learn
> all the characters.
>

Yeah, but a little acquaintance with Chinese will result in the
observation that
1.3+ billion Chinese get along for numbers (in addition to the European
0-9 digits)
with 10 characters for 0 through 9, plus a character for 10, for 100,
for 1000, for
10,000, and a few more for higher multiples of 10. And have for thousands
of years. So even the users of by far the largest logographic writing system
have not complicated their lives by inventing separate characters for
hundreds
or thousands of additional digits for writing in base systems they don't
use.

> I choose to use a whole plane in the idea for foward compatibility,
> humans might augment their brains with technology, or post-singularity
> AI might become comonplace, or some freak confluence of genes might
> spawn a whole breed of humans capable handling big bases way more
> easilly than lower bases.
>

Well, I won't speculate as to what mutated humans or post-singularity AI's
might or might not be able to do.

But I know that pre-singularity simple algorithms and/or unaugmented
humans with a modicum of mathematical background can currently handle
the kind of representation system I suggested just fine.

--Ken

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