# Re: MATH: Number Base Models

Ian Goddard (igoddard@erols.com)
Sun, 03 May 1998 05:02:10 -0400

ChuckKuecker (ckuecker@mcs.net) wrote:

>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.

IAN: Absolutely truth. Base 1 is pre-data
compression. The set of positional number
systems is a set of data-compression rou-
tines; base 1 is not a positional system.

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

IAN: You don't need zero in Base 1 (assum-
ing that we define base to allow 1) because
zero operatis as a placeholder in a possitional
number system; yet base 1, or tally-mark numbers,
is not a possitional number system. As such, the
* difference * in the value of any 1 in any base
1 column in the number 11111, = 0, since the
defintion of colum value in base 1 is:

column 1 2 3

base 1: 1^2 1^1 1^0
1 1 1
--------------------------
1 1 1 = 3

The value of each column is the same (or their
value-difference equals zero) unlike that found
in any base n > 1 number system. Value jumping
between columns of all base n > 1 systems is
the very function of data-compression, thus
0 value difference = 0 data compression.

>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.

IAN: Base 1 is significant in that it is the
real "natural number" system. It is how brains
count from "the ground up." Our fingers are
base 1 digits. Real Intelligence (RI) does
not count with the binary base 2 system.

Base 1 is significant in number theory in that
it is the only number system that is a member
of both the set of "conceptual mathematical
systems" and "the real world." Base 1 is the
intersection of the number engine of math and
the real world. 4 (b10) or 0100 (b2), or 10
(b4) must always mean this many things: 1111.

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