date:20140518

Re: Free Will Universe Model - James Tagg

2014-05-18 Thread Bruno Marchal



On 18 May 2014, at 21:37, Craig Weinberg wrote:




On Sunday, May 18, 2014 1:56:48 PM UTC-4, Bruno Marchal wrote:

On 18 May 2014, at 17:43, Craig Weinberg wrote:

Free Will Universe Model: Non-computability and its relationship to  
the ‘hardware’ of our Universe


I saw his poster presentation at the TSC conference in Tucson and  
thought it was pretty impressive. I'm not qualified to comment on  
the math, but I don't see any obvious problems with his general  
approach:


http://jamestagg.com/2014/04/26/free-will-universe-paper-text-pdf/

Some highlights:


Some Diophantine equations are easily solved
automatically, for example:
∃𝑥, ∃𝑦 𝑥² = 𝑦² , 𝑥 & 𝑦 ∈ ℤ
Any pair of integers will do, and a computer programmed
to step through all the possible solutions will find one
immediately at ‘1,1’. An analytical tool such as Mathematica,
Mathcad or Maple would also immediately give symbolic
solutions to this problem therefore these can be solved
mechanically. But, Hilbert did not ask if ‘some’ equations
could be solved, he asked if there was a general way to solve
any Diophantine equation.

...
Consequence
In 1995 Andrew Wiles – who had been secretly working on
Fermat’s ‘arbitrary equation’ since age eight – announced he
had found a proof. We now had the answers to both of our
questions: Fermat’s last theorem is provable (therefore
obviously decidable) and no algorithm could have found this
proof. This leads to a question; If no algorithm can have
found the proof what thought process did Wiles use to answer
the question: Put another way, Andrew Wiles can not be a
computer.

Also, he is the inventor of the LCD touchscreen, so that gives him  
some credibility as well.


http://www.trustedreviews.com/news/i-never-expected-them-to-take-off-says-inventor-of-the-touchscreen-display


You will not convince Andrew Wiles or anyone with argument like that.

1) it is an open question if the use of non elementary means can be  
eliminated from Wiles proof. Usually non elementary means are  
eliminated after some time in Number theory, and there are  
conjectures that this could be a case of general law.

2) machine can use non elementary means in searching proofs too.

Does computationalism necessarily include all that is done by what  
we consider machines,


Only digital machines.



or does computationalism have to be grounded, by definition, in  
elementary means?


It does not, but always can, by Church Thesis.






You did not provide evidence that they cannot do that.

His evidence was the negative answer to Hilbert's 10th problem.



By using Church thesis. The proof consists in showing that the 10th  
problem of Hilbert is Turing complete. Diophantine polynomials are  
Turing universal. See below for an example of UD written as a system  
of Diophantine equations (exponent are abbreviation here(*)






And you could'nt as a machine like ZF, or ZF + kappa, can prove  
things with quite non elementary means.


What theory addresses the emergence of non elementary means?


Mathematical logic, theoretical computer science.



Maybe there is something about the implementation of those machines  
which is introducing it rather than computational factors?


?

Bruno


(*)
Nu = ((ZUY)^2 + U)^2 + Y

ELG^2 + Al = (B - XY)Q^2

Qu = B^(5^60)

La + Qu^4 = 1 + LaB^5

Th +  2Z = B^5

L = U + TTh

E = Y + MTh

N = Q^16

R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + +  
LaB^5Q^4)Q^4](N^2 -N)

 + [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)

P = 2W(S^2)(R^2)N^2

(P^2)K^2 - K^2 + 1 = Ta^2

4(c - KSN^2)^2 + Et = K^2

K = R + 1 + HP - H

A = (WN^2 + 1)RSN^2

C = 2R + 1 Ph

D = BW + CA -2C + 4AGa -5Ga

D^2 = (A^2 - 1)C^2 + 1

F^2 = (A^2 - 1)(I^2)C^4 + 1

(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1

(unknowns range on the non negative integers (= 0 included)
31 unknowns: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S,  
T, W, Z, U, Y, Al, Ga, Et, Th, La, Ta, Ph, and two parameters:  Nu and  
X. The polynomial emulates the universal question "X is in w_Nu", or
"phi_Nu(X) stops".




Craig


Bruno






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http://iridia.ulb.ac.be/~marchal/




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Re: So, a new kind of non-boolean, non-digital, computer architecture

2014-05-18 Thread Bruno Marchal



On 18 May 2014, at 21:16, ghib...@gmail.com wrote:


Does this computer architecture assume not-comp?


No. Elementary arithmetic emulates n-synchronized oscillators for all  
n, even infinite enumerable set of oscillators. You would need a  
continuum of oscillators, with an explicit special non computable  
hamiltonian. Today, there is nothing in nature which would threat  
comp, except the collapse of the wave packet in theories where this is  
a physical phenomenon. Even in that case, it would be a computation  
with oracle, and not change much of the consequences. Anyway, I am not  
sure I can make sense of the wave collapse being a physical  
phenomenon, and even less that this play a role in the brain  
computation.


Bruno




15046Synchronized oscillators may allow for computing that works  
like the brain


Expand Messages
richard ruquist
May 15 2:09 PM
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Synchronized oscillators may allow for computing that works like the  
brain

May 15, 2014


This is a cartoon of an oscillating switch, the basis of a new type  
of low-power analog computing (credit: Credit: Nikhil Shukla, Penn  
State)
Computing is currently based on binary (Boolean) logic, but a new  
type of computing architecture created by electrical engineers at  
Penn State stores information in the frequencies and phases of  
periodic signals and could work more like the human brain.
It would use a fraction of the energy necessary for today's  
computers, according to the engineers.
To achieve the new architecture, they used a thin film of vanadium  
oxide on a titanium dioxide substrate to create an oscillating  
switch. Vanadium dioxide is called a "wacky oxide" because it  
transitions from a conducting metal to an insulating semiconductor  
and vice versa with the addition of a small amount of heat or  
electrical current.

Biological synchronization for associative processing
Using a standard electrical engineering trick, Nikhil Shukla,  
graduate student in electrical engineering, added a series resistor  
to the oxide device to stabilize oscillations. When he added a  
second similar oscillating system, he discovered that, over time,  
the two devices began to oscillate in unison, or synchronize.
This coupled system could provide the basis for non-Boolean  
computing. Shukla worked with Suman Datta, professor of electrical  
engineering, and co-advisor Roman Engel-Herbert, assistant professor  
of materials science and engineering, Penn State. They reported  
their results May 14 in Scientific Reports (open access).
"It's called a small-world network," explained Shukla. "You see it  
in lots of biological systems, such as certain species of fireflies.  
The males will flash randomly, but then for some unknown reason the  
flashes synchronize over time." The brain is also a small-world  
network of closely clustered nodes that evolved for more efficient  
information processing.
"Biological synchronization is everywhere," added Datta. "We wanted  
to use it for a different kind of computing called associative  
processing, which is an analog rather than digital way to compute."
An array of oscillators can store patterns -- for instance, the color  
of someone's hair, their height and skin texture. If a second area  
of oscillators has the same pattern, they will begin to synchronize,  
and the degree of match can be read out, without consuming a lot of  
energy and requiring a lot of transistors, as in Boolean computing.

A neuromorphic computer chip
Datta is collaborating with Vijay Narayanan, professor of computer  
science and engineering, Penn State, in exploring the use of these  
coupled oscillations to solve visual recognition problems more  
efficiently than existing embedded vision processors.
Shukla and Datta called on the expertise of Cornell University  
materials scientist Darrell Schlom to make the vanadium dioxide thin  
film, which has extremely high quality similar to single crystal  
silicon. Arijit Raychowdhury, computer engineer, and Abhinav Parihar  
graduate student, both of Georgia Tech, mathematically simulated the  
nonlinear dynamics of coupled phase transitions in the vanadium  
dioxide devices.
Parihar created a short video simulation of the transitions, which  
occur at a rate close to a million times per second, to show the way  
the oscillations synchronize. Venkatraman Gopalan, professor of  
materials science and engineering, Penn State, used the Advanced  
Photon Source at Argonne National Laboratory to visually  
characterize the structural changes occurring in the oxide thin film  
in the midst of the oscillations.
Datta believes it will take seven to 10 years to scale up from their  
current network of two-three coupled oscillators to the 100 million  
or so closely packed oscillators required to make a neuromorphic  
computer chip.
One of the benefits of the novel device is that it will use only  
about one percent of the energy of digital computing, allowing for  
n

RE: Is Consciousness Computable?

2014-05-18 Thread Colin Hales

Hi Folk,

A little more you may find interesting.

RE: The much-discussed arXiv paper

Maguire, Phil, Moser Philippe, Maguire, Rebecca and Griffith, Virgil 2014

'Is Consciousness Computable? Quantifying Integrated Information Using
Algorithmic Information Theory'.

http://arxiv.org/abs/1405.0126v1)

Now there’s an article in New Scientist

http://www.newscientist.com/article/mg9692.800-sentient-robots-not-possible-if-you-do-the-maths.html#.U3liRihGO5L

*‘Sentient robots? Not possible if you do the maths’*

The headline should read:

*‘Sentient robots? Not possible if you use computers’*

Breathtaking blindspot revealed yet again: The presupposition that real AGI
involves formal computing.

Here I am building a robot brain that does not use computing, and New
Scientist guy doesn’t even realise the possibility.

This presupposition is so completely trained-in it’s its..

I have been watching this for >10 years now.

I expect COMP to circle the toilet for a little while yet and then the
penny will drop. I guess.. 1-2 years?

Don’t despair: Brilliant (AGI) robots will happen! They just won’t use
computing as their main cognitive architecture.

Why anyone should be upset about this change of fortune beats me.

Cheers

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