Re: Numbers in Leibniz

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On 29 Oct 2012, at 06:15, Roger Clough wrote:```
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```Hi Bruno

Still waiting for the storm to shut things down.
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Take care.

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Numbers are not discussed specifically as far as I can find yet,
in my books on Leibniz. Which probably means that
they are simply numbers, with no ontological status.
Sort of like space or time. Inextended and everywhere.
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I can be OK. I think that numbers are not even 'inextended' as extension does not apply to them. Then, of course variant of extension, like length in base 10, or number of Kb, can of course be defined.
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Numbers are definitely not monads, because no
corporeal  body is attached.
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For me, numbers, body, language, machine, etc. are basically synonymous. There are nuances, be they are not useful before they play a (usually relative) rĂ´le.
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```Although they can
whenever thought of appear in the minds of
particular men in the intellects of their monads.

Leibniz does refer to a proposed "universal"
language, which is simply everywhere
as well as possibly in each head.
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I think Leibniz got the intuition of universal number (machine, language, program, etc.).
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```Numbers would
no doubt be the same, both everywhere and
in individual minds at times.
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OK.

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So numbers are universal and can be treated
mathematically as always.
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They are universal in that sense. But some numbers are universal in the Turing sense, and, as language, might be closer to Leibniz intuition. Such universal numbers can emulate the behavior of all other number. typical incarnation: the brain, the computer, the three bodies problem, the quantum zero body problem, game of life, fortran, lisp, algol, c++, combinators, arithmetic, etc. They all faithfully mirrors each other.
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They are like the golem. You can instruct them by using words, or numbers, so that they become slave, like your PC or MAC. Like the golem, the math explain it is risky and that you can loose control. With comp, you can make them becoming yourself, and an infinitely of them already are.
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Bruno

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Roger Clough, rclo...@verizon.net
10/29/2012
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content -----
From: Roger Clough
Time: 2012-10-28, 18:31:25
Subject: Re: Re: A mirror of the universe.

Hi Bruno Marchal

I still haven't sorted the issue of numbers out.
I suppose I ought to do some research in my Leibniz books.

Aside from that, monads have to be attached to corporeal bodies,
and numbers aren't like that. I find the following unsatisfactory,
but since numbers are like ideas, they can be
in the minds of individual homunculi in individual monads,
but that doesn't sound satisfactoriy to me.
Not universakl enough.

My best guess for now is that the supreme monad (the One) undoubtedly
somehow possesses the numbers.

Hurricane coming.

Roger Clough, rclo...@verizon.net
10/28/2012
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content -----
From: Bruno Marchal
Time: 2012-10-27, 09:31:59
Subject: Re: A mirror of the universe.

On 26 Oct 2012, at 14:44, Roger Clough wrote:

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```Dear Bruno and Alberto,

I agree some what with both of you. As to the idea of a "genetic
algorithm can isolate anticipative programs", I think that
anticipation
is the analogue of inertia for computations, as Mach saw inertia. It
is
a relation between any one and the class of computations that it
belongs
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to such that any incomplete string has a completion in the collections
```of others like it. This is like an error correction or compression
mechanism.

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-- Onward!
```
Stephen

ROGER: For what it's worth--- like Mach's inertia, each monad
mirrors the rest of the universe.
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In arithmetic, each universal numbers mirrors all other universal
numbers. The tiny Turing universal part of arithmetical truth is

Bruno

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