Re: MATH: Number Base Models

ChuckKuecker (ckuecker@mcs.net)
Sat, 2 May 1998 19:14:07 -0500 (CDT)

At 15:00 5/2/98 -0400, you wrote:
>lawsd (david.laws@nih.gov) wrote:
>
>>Future silicon based life forms should be able to denote 0, 1,
>>and irrational numbers.
>
>
> IAN: And should be able to distinguish between
> numbers and the realities they connote, such
> a 5 and 5 things, and between 0 & no thing.
> That's where my interest in Base 1 comes
> into play, since B1 maps the reality
> behind numbers by 100%, such that
> 11111 is both 5 and 5 things.
>
> To teach a computer to interface with the
> real world, it seems to me that we have to
> establish a logical interface between B1
> and the higher-order-number bases its
> programs are built upon. The example
> I posted doesn't accomplish that. :(
>
> It's probably easy enough to have a set
> of rules that say 11111(B1) = 101(B2).
>
>
>>In a highly rapid semi-conductor based individual could '*' be treated
>>as irrational numberset? As in *square root of -l?
>
>
> IAN: The square root of -l is the imaginary number i.
> From what I understand, irrational numbers are real
> numbers that cannot be expressed as integers or as
> the quotient of two integers, such as the square
> root of 2 or pi. But I may be missing your point.
>

The idea of base 1 arithmetic is fine as a thought experiment, but it seems
to me that you lose any advantage to 'packing' information. If you want to
express a large number, you will end up with a huge number of 'bits' so to
speak. A useful computer would be awfully complex.

Also, if you only have one symbol for the base one system, how do you
represent zero? No symbols at all?

I think that by the time software evolves to the point of being able to
drive a true AI, the individual bits and underpinnings will matter as much
to this entity as the precise operations of our brains matters to us on a
moment to moment basis. Likely, a digital computer based AI will be a lousy
computer programmer, at least as far as modifying it's own 'brain' on an
instant to instant basis..

Chuck Kuecker