Le 24-oct.-07, à 20:32, Tom Caylor a écrit :

> This might be of interest to some of you, for instance Bruno, since
> one of the ideals expounded here is "keep it simple".  Sorry I haven't
> been participating here.
>> From Wolfram Science Group:
> We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine
> Research Prize has been won.

Thanks for that very nice news. We have discussed it a lot in Siena.
I am interested in this because, a negative solution would have ruin a 
conjecture of my own: the existence of of a cubic universal diophantine 
equation with no more than 8 variables. Today the simplest universal 
diophantine equation is of degree four and has 154 variables.

> Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a
> 40-page proof that Wolfram's 2,3 Turing machine is indeed universal.
> This result ends a half-century quest to find the simplest possible
> universal Turing machine. It also provides strong further evidence for
> Wolfram's Principle of Computational Equivalence. (PCE)

I don't see why. I should publish this perhaps, but I can prove that 
comp entails the falsity of the PCE.
Frankly, anyone grasping the UDA should see this. The reasoning is the 
same as the one showing Schmidhuberian form of physicalist 
computationalism is incompatible with comp (I have often explain why I 
cannot be myself a digital machine, and at the same time in a purely 
computational universe).

Ah!  I see Wei Dai just posted a message which shows this is not yet 
clear for every one ... Hmmm...

> The official prize
> ceremony is planned for November at Bletchley Park, UK, site of Alan
> Turing's wartime work.
> For more information about the prize and the solution, see:
> http://www.wolframprize.org
> Stephen Wolfram has posted his personal reaction to the prize at:
> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html

Well Wolfram says:

"But is PCE true?  I'm sure it is. But--like many fundamental 
principles in science--it's not the kind of thing one can abstractly 

It is a good test to see if you have grasped the Universal Dovetailer  
Argument: shows that it refutes (even without comp) the PCE, at least 
if you define Nature by what is observable.
Note that the QM observables (in any world/branches, or if you prefer 
Unitary-Evolution+Measurement) refutes it also. If you define Nature by 
the QM mutiverse, as seen from outside (and thus without measurement) , 
then the PCE is not violated, but it has to be violated from inside.



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