Wolfram's Future Math
started 4/23/2004; 10:10:11 PM  last post 5/21/2004; 11:43:41 PM


Mark Evans  Wolfram's Future Math
4/23/2004; 10:10:11 PM (reads: 12970, responses: 12)


Wolfram's Future Math 
Offerings include Turing machines and register machines, including "the smallest register machine with complex behavior."
Posted to theory by Mark Evans on 4/23/04; 10:10:48 PM




guevara  Re: Wolfram's Future Math
4/24/2004; 8:17:08 AM (reads: 916, responses: 0)


Silly browser trick...
Browserbased cellular automata. No applets
and validates as XHTML strict:
http://www.xefer.com/cell
:)


Kalani Thielen  Re: Wolfram's Future Math
4/24/2004; 9:05:12 AM (reads: 897, responses: 0)


This is essentially straight out of his book 'A New Kind of Science' (ANKoS). There are some other interesting documents on that website (I've had the chance to read them since I've been on the ANKoS mailing list for a while). I really like the diagrams he's used to visualize different computational models.
Is anybody aware of interesting work that's taken off from ANKoS? Wolfram and Fredkin have some interesting things to say about directions for discrete (computational) theories of physics, but it's all still very preliminary.


Dimitry Gashinsky  Re: Wolfram's Future Math
4/24/2004; 9:48:24 AM (reads: 883, responses: 0)



Mark Evans  Re: Wolfram's Future Math
4/24/2004; 2:30:44 PM (reads: 808, responses: 0)


Yes the talk summarizes the book, which is also online.


andrew cooke  Re: Wolfram's Future Math
4/24/2004; 2:39:20 PM (reads: 813, responses: 0)


is this new? it looks very like the kind of thing coved in "the computation beauty of nature" (for example)?


Sergey Goldgaber  Re: Wolfram's Future Math
4/30/2004; 12:25:36 AM (reads: 358, responses: 1)


Ray Kurzweil has written an interesting review of Wolfram's ANKoS. But I'm afraid it's not very flattering.


andrew cooke  Re: Wolfram's Future Math
4/30/2004; 4:16:18 AM (reads: 354, responses: 0)


thanks  i didn't realise the book was only about cellular automata (i thought it was another general chaos book). kurtzweil's later comments remind me of feynman (in the character of physical law) where he discusses the difficulty of making a discrete phyiscs (one that is quantised spatially). i don't suppose it's relelvant. anyway, it doesn't seem that damning a review to me.


Andris Birkmanis  Re: Wolfram's Future Math
4/30/2004; 5:16:43 AM (reads: 348, responses: 0)


One can mimic Kurzweil and to review his reiew in the same spirit.
E.g., for
To build strong AI, we will short circuit this process, however, by reverse engineering the human brain, a project well under way...
one could reply in amazement  oh, why do you think that intelligence is anywhere in the structure of the human brain? Also, the brain is very intricate, no doubts, but it never evolves into an insect or Chopin prelude. And, hmm, these people love their brains very much, so much they've spent years of their lives studying them.


Mark Evans  Re: Wolfram's Future Math
5/1/2004; 1:50:11 PM (reads: 302, responses: 0)


The reason for this post was just the CS theory. Even that wideranging review considers the book's highlight to be its Turing Machine:
In what is perhaps the most impressive analysis in his book, Wolfram shows how a Turing Machine with only two states and five possible colors can be a Universal Turing Machine. For forty years, we've thought that a Universal Turing Machine had to be more complex than this. Also impressive is Wolfram's demonstration that Cellular Automaton Rule 110 is capable of universal computation (given the right software).
As for broader issues, the review makes a valid critique about the theory's failure to quantify degrees of complexity. That is a mathematical study unto itself (see Dembski, others). Baumgardner echoes the "patternist" concept from the review in noting that "Einstein pointed to the nature and origin of symbolic information as one of the profound questions about the world as we know it."


Chris Rathman  Re: Wolfram's Future Math
5/1/2004; 3:42:11 PM (reads: 309, responses: 1)


From a pure logic standpoint, wouldn't the SK combinators be the simplest way to get a Universal Turing Machine?


Dave Herman  Re: Wolfram's Future Math
5/2/2004; 3:09:29 PM (reads: 292, responses: 0)



Mark Evans  Re: Wolfram's Future Math
5/21/2004; 11:43:41 PM (reads: 72, responses: 0)


Peter William Lount says:
Wolfram has discovered that there is a threshold that when crossed enables very simple systems to generate complexity as complex as any complex system can generate....Wolfram has demonstrated that they can generate systems of equal complexity as any complex system.
That proposition may be true or false. Wolfram may or may not assert it (citation?). Without a quantitative metric for "complexity," the proposition contains no scientific meaning.



