Lambda the Ultimate

inactiveTopic 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  blueArrow
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  blueArrow
4/24/2004; 8:17:08 AM (reads: 916, responses: 0)
Silly browser trick...

Browser-based cellular automata. No applets and validates as XHTML strict:


Kalani Thielen - Re: Wolfram's Future Math  blueArrow
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  blueArrow
4/24/2004; 9:48:24 AM (reads: 883, responses: 0)
There is plenty of interesting work going on right now. I am writting this from NKS2004 which is going very well.

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

The reason for this post was just the CS theory. Even that wide-ranging 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  blueArrow
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  blueArrow
5/2/2004; 3:09:29 PM (reads: 292, responses: 0)

I'll see you and lower you a combinator:

One-combinator basis for lambda-terms

Mark Evans - Re: Wolfram's Future Math  blueArrow
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.