On 18 Aug 2012, at 15:50, Roger wrote:
Hi Bruno Marchal
BTW how can they know if the calculation of pi is very precise if they
don't really know beforehand what its precise value should be ?
Because PI is a clear concept, and you can prove that some algorithm
computes its exact value, as Archimedes was already aware.
For example, you can prove (convince yourself) that the sequence of
[perimeter of regular polygons divided by they greatest diagonal] will
get closer and closer to PI when the number of sides is bigger and
bigger, and so you can compute PI exactly. Intuitively you might be
able to conceive that a regular (symmetrical) polygon having a large
number of side looks like a circle, and its greatest diagonal looks
like a diameter.
The same for sqrt(2), e, gamma, etc. Those are known as constructive
or computable real numbers, and can be (re)defined as computable
function from N to N, for example the function given the nth decimal,
or more sophisticate one to ensure that the addition and
multiplication of constructive real numbers give constructive real
numbers (which is not the case with the simple minded definition I
just gave).
By Cantor non-enumerability theorem, the computable real numbers
constitute a minority among all real numbers.
Bruno
Roger , rclo...@verizon.net
8/18/2012
Leibniz would say, "If there's no God, we'd have to invent him so
everything could function."
- Receiving the following content -
From: Bruno Marchal
Receiver: everything-list
Time: 2012-08-18, 05:59:32
Subject: Re: Reconciling Bruno's Primitives with Multisense
On 17 Aug 2012, at 19:15, Craig Weinberg wrote:
On Friday, August 17, 2012 10:48:04 AM UTC-4, Bruno Marchal wrote:
Hi Craig,
On 15 Aug 2012, at 11:21, Craig Weinberg wrote:
> in case the special characters don't come out...
>
> I was thinking about your primitive of arithmetic truth (numbers,
0,
> +, and *, right?) and then your concept of ‘the dreams of
> numbers’, interviewing Lobian Machines, etc and came up with
this.
>
> One single irreducible digit (Om) which represents a self-
> dividing continuum of infinite perpendicular dialectics between
> eidetic dream states (in which dream~numbers escape their numerical
> identities as immersive qualitative experiences) and entopic non-
> dream states (in which number~dreams escape their dream nature as
> literal algebra-geometries).
>
I use such term more literally. I am not sure I can understand this,
even if there is some genuine analogy.
Think of it like π, except that instead of circumference and
diameter, there is eidetic-figurative and entopic-literal
presentation modalities.
Pi = ratio of the length or a circle and its diameter. That is
understandable.
"eidetic-figurative and entropic-literal presentation modalities."
is not.
The dreaming number are usually very big concrete number. They dream
by encoding computational state of person, relatively to some
universal number, which are encoding universal machine relatively to
some other one, and the initial one can be chosen arbitrary. Those
are
not symbolic number, but real encoding number, a bit like the genome
if you want.
Why would that result in a dream?
Because I work in the comp theory where we come to the idea that
consciousness can be manifested by abstract relation between
numbers, as they emulate computation. We have already said "yes" to
the doctor.
It seems shrouded in obfuscating self-reference. Why would anything
that has been encoded ever need to be decoded if the machine can
fluently process the encoded form?
To store what we learn. The DNA plays already such a role at the
molecular level. It illustrates also a digital encoding and decoding.
Why would it need any other form - especially if it is all made of
numbers?
Nobody needs a universe. Why do we do babies?
The "truth" is that we have them, we cannot really avoid them. It is
like the prime number and the universal machine. Once you have zero
and + and *, you get Platonia, and a lot of mess in Platonia. It is
a logical consequence.
What I am saying is that if you are going to invoke a possibility
of dreams, that has to be grounded in the terms that you are laying
out as primitive. Why would dreams leap out of mechanical relations?
It is a logical consequence, once you accept the idea that you might
survive with a digital brain.
Even if there was some purpose for it, how could that actually take
place - what are the dreamings made of?
Ontologically: nothing take place. All the computations are there.
Some emulate self-observing machine and the math explain why they
have to be beffudled by existence and conscience.
My view is that it may be the case that everything that is not
matter across space is experience through time - by definition,
ontologically. There is no other form or content possible in the
cosmos. Numbers are expe
