On 06 Jun 2011, at 08:19, Felix Hoenikker wrote:

Has anyone watched the movie "Contact", in which the structure of the
universe was encoded in the transcendental number Pi? What if
something like that is what is going on, and that's the answer to all
paradoxes?

So the physical universe beings with "Pi" encoded in the Big Bang,
chaotically inflates, and eventually cools and contracts back to
itself until it is again, exactly the mathematical description of
"Pi".

All consciousness is thus contain with Pi.

But then, Pi is just like any other transcendental number!

So all transcendental numbers contain all existence


You are confusing existence, and description of existence. This is like confusing "babel library" with universal dovetailing. PI contains all encoding of computations, but does not compute anything, and does not possess the gigantic redundancy of computations of the UD's activity, making the relative measure a real mathematical problem, making the comp theory testable.

Note that instead of PI, you could have taken the natural numbers 0, 1, 2, 3, ..., or the real number 0,12345678910111213141516... This one has the advantage that it is easy to prove that, like the natural numbers, it goes through all descriptions of all computations (for PI it is an open problem, really). But this is trivial. You can't extract from this the "real" physical laws. Many people confuse a computation and a description of a computation. I guess it is a subtle point. Now, if you take 0, 1, 2, 3, .... together with logic and the laws of addition and multiplication, then, assuming we are digital machine, you can extract physics. Indeed, thanks to the Gödel splitting between true and provable, and through the distinction between 1-pov and 3- pov, you can even get both the laws of quanta and the laws of qualia, and their relations.

Bruno




F.H.

On Mon, Jun 6, 2011 at 12:57 AM, Jason Resch <jasonre...@gmail.com> wrote:


On Sat, Jun 4, 2011 at 3:12 PM, Stephen Paul King <stephe...@charter.net >
wrote:

Hi Jason,

    Very interesting reasoning!

Thank you.



From: Jason Resch
Sent: Saturday, June 04, 2011 1:51 PM
To: everything-list@googlegroups.com
Subject: Re: Mathematical closure of consciousness and computation

On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexallen31...@gmail.com>
wrote:

On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jasonre...@gmail.com>
wrote:
One thing I thought of recently which is a good way of showing how
computation occurs due to the objective truth or falsehood of
mathematical
propositions is as follows:

Most would agree that a statement such as "8 is composite" has an
eternal
objective truth.

Assuming certain of axioms and rules of inference, sure.


Godel showed no single axiomatic system captures all mathematical truth, any fixed set of axioms can at best approximate mathematical truth. If mathematical truth cannot be fully captured by a set of axioms, it must
exist outside sets of axioms altogether.

[SPK]

I see two possibilities. 1) Mathematical truth might only exist in our minds. But an infinity of such minds is possible...2) Might it be possible that our mathematical ideas are still too primitive and simplistic to define
the kind of set that is necessary?
**

1) More is answered by:
A: "Math -> Matter -> Minds" (or as Bruno suggests "Math -> Minds ->
Matter") than by
B: "Matter -> Minds -> Math", or
C: "Minds -> (Matter, Math)".
Compared to "B", "A" explains the unreasonable effectiveness of math in the
natural sciences, the apparent fine tuning of the universe (with the
Anthropic Principle), and with computationalism explains QM.
"C" has the least explanatory power, and we must wonder why the experience contained within our minds seems to follow a compressible set of physical laws, and why mathematical objects seem to posses objective properties but
by definition lack reality.
Those who say other universes do not exist are only adding baseless entities to their theory, to define away that which is not observed. It was what led to theories such as the Copenhagen Interpretation, which postulated collapse as a random selection of one possible outcome to be made real and cause the rest to disappear. Similarly, there are string theorists which hope to find some mathematical reason why other possible solutions to string theory are inconsistent, and the one corresponding to the the standard model is the only one that exists. Why? They think this is necessary to make their theory agree with observation, but when the very thing is unobservable
according to the theory it is completely unnecessary.
The situation is reminiscent of DeWitt and Everett:

In his letter, DeWitt had claimed that he could not feel himself split, so, as mathematically attractive as Everett's theory was, he said, it could not be true. Everett replied in his letter to DeWitt that, hundreds of years ago, after Copernicus had made his radical assertion that the Earth revolved around the sun instead of the reverse, his critics had complained that they could not feel the Earth move, so how could it be true? Recalling Everett's response to him decades later, in which he pointed out how Newtonian physics revealed why we don't feel the Earth move, DeWitt wrote, "All I could say
was touché!"

2) I don't know. Godel proved that any sufficiently complex axiomatic system can prove that there are things that are true which it cannot prove. Only more powerful systems can prove the things which are not provable in those other axiomatic systems, but this creates an infinite hierarchy.
 Whether or not there is some ultimate top to it I don't know.




But isn't that true of nearly anything? How many axiomatic systems are
there?


Likewise the statement: the Nth fibbinacci number is X.
Has an objective truth for any integer N no matter how large. Let's
say
N=10 and X = 55. The truth of this depends on the recursive definition
of
the fibbinacci sequence, where future states depend on prior states,
and is
therefore a kind if computation. Since N may be infinitely large, then
in a
sense this mathematical computation proceeds forever. Likewise one
might
say that chaitin's constant = Y has some objective mathematical truth.
For
chaintons constant to have an objective value, the execution of all
programs
must occur.

Simple recursive relations can lead to exraordinary complexity,
consider the
universe of the Mandelbrot set implied by the simple relation Z(n +1)=
Z(n)^2
+ C.  Other recursive formulae may result in the evolution of
structures
such as our universe or the computation of your mind.


The fractal is just an example of a simple formula leading to very complex
output.  The same is true for the UDA:
for i = 0 to inf:
  for each j in set of programs:
    execute single instruction of program j
  add i to set of programs
That simple formula executes all programs.


Is extraordinary complexity required for the manifestation of "mind"?
If so, why?


I don't know what lower bound of information or complexity is required for
minds.

[SPK]
Why are we sure that a “lower bound of information” or “complexity” is required? Seriously, there seems to be a bit of speculation from too few
facts when it comes to consciousness!
**


I should clarify, I don't know what the lower bound is or if there is one. That said I do believe information and computation are importantly related
to consciousness.


Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.

OR:

Recursion is just a label that we apply to some of our implicational
beliefs.

The latter seems more plausible to me.



Through recursion one can implement any form of computation. Recursion is common and easy to show in different mathematical formulas, while showing a Turing machine is more difficult. Many programs which can be easily defined through recursion can also be implemented without recursion, so I was not implying recursion is necessary for minds. For example, implementing the
Fibonacci formula iteratively would look like:

Fib(N)
  X = 1
  Y = 1
  for int i = 2 to N:
    i = X + Y
    X = Y
    Y = i
  print Y

This program iteratively computes successive Fibonacci numbers, and will
output the Nth Fibbonaci number.

Jason

There was a bug in that program, replace the last two "i"s with "j",
otherwise it breaks out of the loop too early.  :-)


--

[SPK]
The existence of such Numbers could be a telltale sign that numbers
require an eternal computation to define them.

I'm not sure, I can define Pi without an infinite description or
computation.  Pi = circumference of a unit circle / 2
I would agree that determining Pi from that definition probably does require
an eternal/infinite amount of computation though.
 Jason

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