Everything List Google Group

Re: Definition of universe

marc...@ulb.ac.be (Bruno Marchal) — Mon, 08 Feb 2010 14:12:11 UT

Actually we have already discussed this a lot, and the work I explain
here (uda, auda) can be considered as an answer to Tegmark (or
Schmidhuber), except that it has been published many years before, and
relies on "philosophy of mind/computer science" or machine's "theology".
The main problem with Tegmark is that he assumes an implicit identity

Re: Definition of universe

tenn...@gmail.com (Brian Tenneson) — Sun, 07 Feb 2010 20:07:48 UT

Assuming a 4-level hierarchy of "universe" as posited by Tegmark here...
[link]
Then the universe would be an aggregate of all mathematical structures.

Re: Definition of universe

marc...@ulb.ac.be (Bruno Marchal) — Fri, 05 Feb 2010 16:53:32 UT

I have still many preprints. People interested can send me their
addresses out of line.
Oops! I just see the axiom "3)" below is not correct. Please replace
"x + 0 = 0" (which says that if you add nothing in your bank account,
you make it empty!), by "x + 0 = x" (which says that if you add
nothing to your bank account then it remains the same).

Re: Definition of universe

ronaldh...@gmail.com (ronaldheld) — Fri, 05 Feb 2010 12:13:42 UT

Bruno:
is there a free version of Theoretical computer science and the
natural
sciences?
Ronald

Re: Definition of universe

marc...@ulb.ac.be (Bruno Marchal) — Thu, 04 Feb 2010 19:45:20 UT

The rule of addition and the rule of multiplication, with some amount
of logic provides a universal programming language. That's correct.
And at the same time this provides a tiny formal theory of arithmetic.
A generator of a tiny subset of Arithmetical Truth (the set of all
true arithmetical sentences, written in first order arithmetical

Re: Definition of universe

jasonre...@gmail.com (Jason Resch) — Thu, 04 Feb 2010 14:28:40 UT

So then it seems the integers, addition, and multiplication (plus some
logic) are the minimum axioms needed to represent and prove true any
computable function, and it is through this representability that the
functions are said to exist. Is this correct?
Could the connection be made between mathematically provable true

Re: measure again '10

m...@dtech.fsnet.co.uk (Nick Prince) — Thu, 04 Feb 2010 00:08:57 UT

NP
OK thanks Jack - this is interesting. Perhaps what I should have said
in the paragraph above was the same but with the word CONTINUATION
rather than TRANSFER so it would read:
“>> Forgetting about MWI for now and just thinking about why I feel
some continuity in my subjective experience. I feel that it must have

Re: Definition of universe

marc...@ulb.ac.be (Bruno Marchal) — Wed, 03 Feb 2010 19:47:13 UT

I guess you ask: how is the existence of a computable function proved
to exist in a theory T. Usually logicians use the notion of
representability. The one variable function f(x) is said to be
representable in the theory T, if there is a formula F(x, y) such that
when f(n) = m, the theory T proves F(n, m), and usually (although not

Re: Definition of universe

jasonre...@gmail.com (Jason Resch) — Wed, 03 Feb 2010 14:49:30 UT

So I suppose that is what I was wondering, given at minimum, those, how is
the existence of a computable function proved to exist? Could you provide
an example of how a simple function, like f(x) = x*2 exists, or is it a very
tedious proof?
Thanks again, things are becoming a little more clear for me. My background

Re: A parable.

marty...@bellsouth.net (m.a.) — Wed, 03 Feb 2010 13:51:42 UT

Autistic God
What worlds
but bipolar?
...No more questions!
Look kid
I am what I am.
Get used to it.
marty abramson
----- Original Message -----
From: Bruno Marchal

Re: A parable.

marc...@ulb.ac.be (Bruno Marchal) — Wed, 03 Feb 2010 12:10:41 UT

Le 02-févr.-10, à 22:29, Brent Meeker a écrit :
I take the word theology (extended on religion) in the sense of the
greek, where theology is a branch of scientific inquiry.
The main reason for doing that is the "modern discovery" that such form
of theology reappear in the study of what machine can and cannot prove

Re: Definition of universe

marc...@ulb.ac.be (Bruno Marchal) — Wed, 03 Feb 2010 09:14:26 UT

Consider the first order arithmetic language in which the number 2 is
denoted by s(s(0)). Now "s(s(0))" is itself a string, and when we
translate meta-arithmetic in arithmetic (like Gödel) that string will
be represented by some number like
2^'s' * 3^'(' * 5^'s' * 7^'0' * 11^')' * 13^')'
(Using some Gödel numbering). Then you can consider the function which

Re: Definition of universe

jasonre...@gmail.com (Jason Resch) — Wed, 03 Feb 2010 02:00:41 UT

Bruno, when you say code here, you are referring to code as in programming
code, correct? I understand how a number can function as code for a
function or a machine, but how can a number be code for another number?
You've said many times that all it takes for everything we see to exist are
the natural numbers, addition and multiplication, but where/how do functions

Re: A parable.

meeke...@dslextreme.com (Brent Meeker) — Tue, 02 Feb 2010 21:29:50 UT

One has to take Bruno's pronouncements on religion with a grain of salt
since he assumes an esoteric definition of religion such that rather
important phrases, such as, "Congress shall make no law respecting an
establishment of religion" and the writings of most of those who have
studied religion incomprehensible:

Re: A parable.

meeke...@dslextreme.com (Brent Meeker) — Tue, 02 Feb 2010 21:28:44 UT

On 01 Feb 2010, at 12:07, W.Tay...@math.canterbury.ac.nz <mailto:W.Tay...@math.canterbu ry.ac.nz>
wrote (FOR list) :

>
The problem with both groups is that both have a tendency to forget

They are not. Religion is a construct, science is a method.
Category mistake.