Stephen Wolfram's A New Kind Of Science: Computing A Theory Of Everything
#13
(09-Aug-2011, 02:33 PM)Kanad Kanhere Wrote: Ajita, Dr Wadhawan,
I have some queries for you. I went through the TED talk and then the link sent by murthmail. I am absolutely novice in this field and my knowledge in this field is next to nothing, so Sorry in advance if my queries sound stupid.
The link, as per me, had two strong points
1. "Wolfram is just proposing a new kind of computational method, not a new kind of science"
2. "Wolfram's theory lacks explanatory power. Not everything that is useful is explanatory"
What is your take on these?

Doesn't this method sound like a brute force method of figuring out fundamental laws of nature?

The answers to your questions are discussed in detail in Chapters 12 and 15 of my book 'Complexity Science'.

http://www.amazon.com/COMPLEXITY-SCIENCE...108&sr=8-1

Trying to give a brief and simplistic answer would be unfair to Wolfram's work. So I shall just give you a feel for what is at stake here.

There are 'simple' (or simplifiable, or computationally reducible) systems, and there are 'complex' systems. Practically all our present science deals only with simple systems. For such systems it is possible to make models, and make testable predictions. Most of the complex systems are such that it is impossible to model them sensibly. Any model involves approximations, and for complex systems approximations usually lead to disastrous, runaway, consequences (e.g. in chaotic systems). Real Nature is mostly about complex systems. Mathematical equations are not good enough for modelling them sensibly. So what do we do? Wolfram's 'New Kind of Science' (NKS) offers a way out.

His approach is born out of a question he asked long ago: 'What secret it is that allows Nature seemingly so effortlessly to produce so much that appears to us so complex?' His answer is that all natural processes are just computations, i.e. the running of what he calls 'simple computer programs'. Any process that follows definite rules can be regarded as a computation. Thus cellular automata (CA) can carry out computation, as can Turing machines, and many other systems in Nature. In computations carried out by humans on computers, the computer programs define the rules of computation. In Nature, the rules of computation are nothing but the laws of Nature.

As Wolfram emphasizes, the whole idea of doing science with mathematical formulas makes sense only for 'computationally reducible' systems. For other systems there are no computational shortcuts; practically the only way of knowing a future configuration is to actually run through all the evolutionary time steps. And Wolfram’s NKS is ideally suited for that purpose. Exploiting the immense power of modern computers, one can generate a huge repertoire of the consequences of all sorts of simple programs as embodied in the corresponding CA. For understanding the basics of a given complex system observed in Nature, one can try to see if the observed behaviour pattern can be matched with any of the archived CA. If yes, then the simple program used for generating that particular CA pattern is the explanation of the time or space evolution of the complex behaviour observed in the actual physical system under study.

Whether we like it or not, there are not many other ways of understanding complex systems. That is why Wolfram's NKS cannot be ignored. It is important.
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#14
(17-Jun-2010, 05:08 PM)Ajita Kamal Wrote: Of course, there is good reason why many scientists are not thrilled with Wolfram. He is, in many ways, what they all wish they could be. He has his own very successful company (which indirectly works to test his ideas in the real world) and doesn't publish papers or write grants. He doesn't have his ideas scrutinized by his peers and is making grandiose claims about the importance of his work.

It is unfair to paint all his critics with the same brush. A mathematician of the calibre of Steven Krantz is unlikely to criticize Wolfram for any of these reasons!

I have not read Wolfram's book in its entirety, and don't intend to do so, given how much I admire Krantz ("Techniques of Problem Solving," "The Proof is in the Pudding") and his opinions. But I have read much about cellular automata, Wolfram, and his contributions to science.

So instead of saying anything more about your review, I'll just ask you how you would address the following criticism by Krantz:

1. Cellular automata may reproduce various patterns and theories. But don't we also get patterns from a monkey sitting at a keyboard (I swear I do not intend the monkey reference to mock Wolfram Wink )? How about the occurrence of every conceivable special sequence of numbers in the digits of pi? Is there anything insightful about finding a sequence of several 9's in the digits of pi? Krantz's review proposes that Wolfram's claim about the power of cellular automata is something similar.

2. What exactly is the point of Wolfram's attempt to make his theory accessible to all? Does the statement "the brain is just like a faucet" say much about how our brain works? Is it a necessity that one should be able to explain one's work to the public for it to be fundamental? One can spend all his time devoted to arcane (to the layman) problems in algebraic geometry, and still contribute much to physics and mathematics without ever doing anything that can be explained to a common man. An overwhelming majority of science and scientists work this way. An Einstein, Feynman, or Hawking, with their pleb-friendly, yet scientifically accurate thought experiments and analogies are rare indeed. But before all that, their work was subjected to rigorous peer review. Why should Wolfram take this route to academic glory? The principal victim of this decision of Wolfram's is good science.

3. "...[Wolfram] seems to be confusing the contrary with the contrapositive. Does it necessarily
follow, just because a simple program can produce a picture that resembles the product of some complex mechanism, that the simple program is the same as the complex mechanism, or that it supplants that complex mechanism? I doubt it, and nobody can ever any proof to the contrary."





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#15
Such criticism of NKS baffles me. Instead of getting personal about Wolfram, scientists should come up with better ways of doing complexity science than what he has suggested.
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#16
(16-Oct-2011, 11:08 AM)karatalaamalaka Wrote:
(17-Jun-2010, 05:08 PM)Ajita Kamal Wrote: Of course, there is good reason why many scientists are not thrilled with Wolfram. He is, in many ways, what they all wish they could be. He has his own very successful company (which indirectly works to test his ideas in the real world) and doesn't publish papers or write grants. He doesn't have his ideas scrutinized by his peers and is making grandiose claims about the importance of his work.

It is unfair to paint all his critics with the same brush. A mathematician of the calibre of Steven Krantz is unlikely to criticize Wolfram for any of these reasons!

I do not disagree that there are scientific/mathematical critiques of Wolfram's ideas. Krantz's paper is mostly over my head, as were much of Wolfram's ideas. But the first page of Krantz's paper is a confirmation of what I've stated above. He even goes so far as to use the word "hubris" to describe Wolfram's introduction, attacking Wolfram's apparent impunity for being outside the scientific peer-review system (which I agree is a problem, to address your second criticism). So even if there are good criticisms of Wolfram's science, it is true that his attitude and swashbuckling approach are a good reason for why "many scientists are not thrilled with Wolfram".

1. I don't know enough about Cellular Automata or mathematics to take on this question.

2.I have already made it clear that Wolfram is bypassing the peer-review process, like many charlatans do. I'm interested in whether NKS is really a window into a new kind of science, and I found Wolfram's thinking about complexity to be compelling enough to overlook his decision to bypass peer-review (and historical citation) and give the ideas themselves some thought.

3.
Quote:"...[Wolfram] seems to be confusing the contrary with the contrapositive. Does it necessarily
follow, just because a simple program can produce a picture that resembles the product of some complex mechanism, that the simple program is the same as the complex mechanism, or that it supplants that complex mechanism? I doubt it, and nobody can ever any proof to the contrary."

Yes, he is confusing the converse with the counterpositive, but I disagree that he needs to show absolute proof that he is right, simply because science is not necessarily about proof. The accusation above is applicable to many researchers working on mathematical models and computer simulations. It doesn't make much sense in the context of inductive science, unless we're talking about degrees of certainty (and not absolute proof). If Wolfram's models are shown to be robust based on good science, scientists have a task set before them to demonstrate otherwise. Critics should be able to find counter examples, mathematical anomalies, etc, to falsify his claims. It can't be that difficult for scientists to prove his ideas wrong, after they're done being pissed off at him for not respecting the scientific establishment.

Again, let me state, the interesting thing to me is that Wolfram's ideas seem to have potential to indeed revolutionize the field of complexity, which, as Stephen Hawking said, will be huge in this century ("I think the next century will be the century of complexity".) I think you should read his book, but, in case you haven't already, I would suggest you read Prof Wadhawan's series on complexity first.
"Fossil rabbits in the Precambrian"
~ J.B.S.Haldane, on being asked to falsify evolution.
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#17
Suppose we observe a complex system which it is impossible to model sensibly by conventional analytical science, say by writing a few differential equations and solving them. Suppose we can somehow identify a CA which produces a complex pattern remarkably like the one we have observed in Nature. Suppose we conclude from this that the local rules in the CA are a good description of what is actually happening in Nature. Is this scientific progress or not?
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#18
Please see the attached paper as an example of the application of Wolfram's NKS.


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