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Wolfram: A New Kind of Science

  
  

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Lurid Archive
12:30 / 12.07.02
Has anyone read Stephen Wolfram's book, A New Kind of Science?

To anyone who doesn't know about it, his website has a summary here. From the summary,

Starting from a collection of simple computer experiments--illustrated in the book by striking computer graphics--Stephen Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.

Wolfram uses his approach to tackle a remarkable array of fundamental problems in science, from the origins of apparent randomness in physical systems, to the development of complexity in biology, the ultimate scope and limitations of mathematics, the possibility of a truly fundamental theory of physics, the interplay between free will and determinism, and the character of intelligence in the universe.


He wants to overturn conventional methods and use rule based "cellular automata" that create complex patterns to describe nature. Naturally, not everyone agrees that this will be as revolutionary as he hopes. See here, for some first impressions by scientists. Another review by Kurzweil here and a long article at Wired here.
 
 
Fist Fun
15:10 / 14.07.02
I think I posted a link to this a wee while ago. Sounds great, in quite possibly an entirely deluded way. The worlds need genius scientists to do this kind of thing though. Apparently the print run sold out as soon as it was made available. You thinking about trying to get your hands on a copy?
 
 
glassonion
19:35 / 14.07.02
i don't trust him. too rich
 
 
Lurid Archive
12:29 / 15.07.02
I'm not going to buy it, but I'll read it when my library gets it. Not sure how long that will be.
 
 
Sebastian
17:26 / 15.07.02
Your choice Lurid: Hardcover, 1197 pages

"I have come to view [my discovery] as one of the more important single discoveries in the whole history of theoretical science."

I know its easy and to laugh at these sort of statements, but whomever makes them should also be aware of how easily they can be mocked upon.
 
 
grant
19:17 / 15.07.02
From the Wired article:
"Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. My purpose in this book is to initiate another such transformation, and to introduce a new kind of science that is based on the much more general types of rules that can be embodied in simple computer programs."

He goes on to explain that by applying a single key observation - that the most complicated behavior imaginable arises from very simple rules - one can view and understand the universe with previously unattainable clarity and insight. The idea of complexity arising from simple rules - and that the universe can best be understood by way of the computation it requires to grind out results from those rules - is at the center of the book. The big idea is that the algorithm is mightier than the equation.

"Stephen makes the point that Newton developed calculus before Babbage invented computing - but what if it had been the other way?" says Rocky Kolb, a physicist at the Swiss physics laboratory CERN.

Wolfram is not satisfied with simply explaining and justifying his contentions, but instead makes substantial efforts to apply his insights to dozens of fields. "What's basically happened is that I had this idea of how to use simple programs to understand things about nature, the universe, other stuff," he says. "And you can start looking at questions that have been around forever, and you really get somewhere." He invariably introduces each topic in a similar fashion: Curious to know about _______ [CHOOSE ANY SCIENTIFIC DISCIPLINE] and how his new theories might apply, he decides to take a look at the history of the field. Amazingly, he concludes, for hundreds of years so-called experts have failed to answer key questions that should have been easily resolved centuries ago. (Wolfram's disappointment in his predecessors is bottomless.) But when Wolfram applies the ideas from A New Kind of Science, he begins making progress and expresses the hunch that not long after his ideas are understood, the biggest problems will quickly be resolved, transforming the field.


To list only a few examples: Wolfram finds an exception to the second law of thermodynamics; conjectures why extraterrestrials might be communicating with us in messages we can't perceive; explains seeming randomness in financial markets; defines randomness; elaborates on why the "apparent freedom of human will" is so convincing; reconstructs the foundations of mathematics; devises a new way to perform encryption; insists that Darwinian natural selection is an overrated component in evolution; and, oh, theorizes that there's a "definite ultimate model for the universe." What might this be? The mother of all rules; a single, simple "ultimate rule" that computes everything from quantum physics to reality television.

 
 
Lurid Archive
20:51 / 15.07.02
I tend to agree with Sebastian that its likely to be a load of tosh - I've got some inkling of what he's trying to do and it seems interesting but not as revolutionary as he would have us believe. He is a very bright guy despite the arrogance.

The one problem I see is that while his claims for the applications of his ideas know no bounds, from what I understand he hasn't actually discovered anything new, apart from the methods themselves. If you read the claims carefully they are mostly speculative or limited.

Perhaps it will explode and and revolutionise science but my own suspicion is that people will find some interesting applications and gain something from the ideas but it will fall far short of the publicity. But to be sure, I'll give the book a skim.
 
 
cusm
20:27 / 17.07.02
Wolfram is quite smart. He wrote the Mathematica program I used in college, which is impressive to begin with. So far, I find the descriptions of his ideas to follow a type of thinking I've been exploring myself in recent years, and had success with. That is, complex systems can be reduced to simple relations and algorythms, and that intelligence can be contained in self-referencing systems. I'd love to get a read of it. I'd love to have the time to sift through 1200 pages. I'd also love for the time to read more than a couple of chapters in Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid as well, though all of these are pretty unlikely at present.
 
 
odd jest on horn
02:58 / 18.07.02
I haven't actually read the book yet, but this sounds suspiciously old and dated. The whole complexity thing hasn't given us anything new yet ('cept for pretty pictures) and it's been around for 20 years or so.

Gonna read it soon (got some inside coneections in the city library :-) and if he can convince me in his physics chapter that cellular automata rules can reproduce the randomness and/or non-locality of quantum physics, I might have to reasses my opinion. Those physicists weren't too impressed though.
 
 
Gibreel
04:01 / 18.07.02
Wolfram: A New Kind of Bullshitting?

I am not mathematically educated enough to critique his methods, his public statements are unappealingly arrogant. He crops up as a character study here:

http://www.amazon.com/exec/obidos/ASIN/0201122782/qid=1026968255/sr=1-1/ref=sr_1_1/103-4237331-2415061

Where he appears as bright and self-confident (surprise, surprise).

One thing to note is that "complexity" theories are starting to take off in the business community (touted by MBA schools and management consultancies), so may be Wolfram is going for a different market than expected at first glance.
 
 
Lurid Archive
05:20 / 18.07.02
His arrogance will probably ensure that there will be a good deal of opposition to his ideas.


I think that there is a philosophical problem to his ideas - that of emphasising algorithms rather than "elementary properties". It is entirely possible that one arrives at a descriptive algorithm for a physical situation without any understanding of why it works. This makes for interesting predictive power with little chance for further progress in the same direction. You can end up with scientific dead ends.

On the other hand, if one takes a more babalnced approach and uses both conventional ideas and complexity, genetic algorithms and so on, it might prove fruitful.
 
 
Sebastian
12:27 / 18.07.02
I was wondering, would anybody say this guy is a phiolosopher, a scientist, or an ultimate pragmatist? I would only be interested in the last option.
 
 
Lurid Archive
13:25 / 18.07.02
All three probably. But I don't really understand the point of your quesion.
 
 
odd jest on horn
22:59 / 18.07.02
Lurid:
Some people think that the brain can be simulated with neural networks. However the analysis of neural networks is NP complete, so you can't ever analyse a neural network of sufficient complexity. Meaning that you could possibly build a brain that was as smart as a human's, but you'd be no closer to understanding it than a human's either. Neural networks are much closer to elementary properties than an algorithm, but it still doesn't really help us.
 
 
Sebastian
12:25 / 19.07.02
But I don't really understand the point of your quesion.

Just speculating. In the Wired article it is mentioned that Wolfram finds an exception to the second law of thermodynamics; conjectures why extraterrestrials might be communicating with us in messages we can't perceive; explains seeming randomness in financial markets; defines randomness;, which is fine, but if he were a pragmatist I think he would be actually contacting the extraterrestrials, or comming up at least with a fair methodology to do so, or putting upside down the industrial world of engineering through the exception to thermodynamics 2nd law, which anyway we don't know if he is already doing. Ultimately, only time will tell.
 
 
Lurid Archive
13:29 / 19.07.02
Sebastian: I've started to read his pronouncements with a pinch of salt. What I think he is saying is that his ideas are so wonderful that it will, at some point manage to solve all the big science problems. In addition, the technique is soooo powerful that it will no doubt be essential in someday decoding alien transmissions. etc etc.

jest: Not sure I get your point, but I'm going to have to get geeky to address it. I'll have to work up the courage for that, but Church's Thesis and the openness of the NP=P conjecture seem pertinent points.
 
 
cusm
20:45 / 19.07.02
If I get his approach, he's seeking to explain natural phenomenon through relations between elements and the systems these suggest rather than discrete evaluations of their composition and effect as in more "classical" science. I wonder, isn't this similar to the mythic approach?

By that, myth is a means used by man to explain the world through observation, much as science. Encoded within the story and personification of natural elements are relations that were observed. For example, stories of the sun god who dies and is ressurected. The observation this is based on is the cycle of day and night, or the turning of the seasons from cold (dead) to warm (living). The story is a means to remember the relation. Observation of that relation initially is a procedure of science, before it was understood in the media of myth rather than math.

So I wonder if this is an approach he's taking here, to some extent. Applying these methods to modern science to create his much touted "new type of thinking."
 
 
Caleigh
09:11 / 22.02.03
in theory his work is stating that if you knew the iterative equation that drives the universe you could start a new one. that everything is following a path set by the original "seed" # as it is processed by the equation of the universe.

a=original seed value

a*sin(a+a2)=b

b=new state of univese

b*sin(a+b2)=c

c= new state of universe

etc.


this equation does not work in all likelihood (since i just made it up now) it would either expand continuously until it was infinite (too fast expanding universe) or it would find an attractor (universe crunches back into black hole) but there are equations which can be iterated infinitely without having attractor nor growing out of a boundary. i've done some of them in qbasic and have created graphic outputs. interesting take on process of universe.
 
 
dithered
14:54 / 17.05.04
http://www.mazenw.com
 
 
FinderWolf
13:34 / 01.06.04
This is clearly a servant of the Wolf, the Ram and the Hart. (ANGEL reference there for those who don't get it)
 
 
eye landed
04:31 / 02.06.04
It makes sense to the ghost of Carl Jung.
 
 
Henningjohnathan
20:05 / 02.06.04
I haven't read the entire book, but it seems to fit in with the directions science (or mathematics) is already moving. Most of the big breakthroughs in physics are actually simply breakthroughs in interpreting information. Also, I don't know what Wolfram's contributed to the concept of "emergence", but his work seems to mirror discoveries in the same field.

In the end, however, I think that there may be a kind of disconnect to these concepts that I haven't fully been able to conceptualize. I can only use Magritte's painting "This is not a Pipe" for a metaphor or analogy. We see the image, but the image does not contain the substance. I think that this cutting edge field of science is more about the limitations of human intelligence and less about the "real world" outside our perceptions of it.
 
 
TeN
19:52 / 11.06.04
I haven't read the book, but I just found this: Automatous Monk, which is "an algorithmic music composition program that uses cellular automata to generate musical pieces." sound's neato, so I'm gonna download it and check it out.
 
 
Wombat
21:13 / 11.06.04
Most of the book is `just` experiment and results. Some of which are very impressive. ( can`t really comment on most of it...but the fluid dynamics results were excellent...lots of remote sensing scientists are useing this to study coastal zones)

The conclusion he reaches is probably a lot more interesting.
The Principle of Computational Equivalence.

"almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication"

He`s not saying that a computational model will gain you extra understanding. (his fluid dynamics model has water moving in only six directions and the interactions between water particles being very simple.....then throw lots of computer power at the problem. Average the results over a few billion highly un-realistic water particles and you have a better model for fluids than any pre-wolfram fluid dynamics simulation)

In a lot of ways he`s abandoning actual understanding and simply using whatever works. Computaion can be represented as mathematics...but why do so when computation is so much easier.
Also why assume that mathematics CAN represent a physical event. It can model it certainly. So can computation.

I`m not sure that a mathematical model increases understanding. I may have a good enough model of an electron to calculate it`s flow across doped silicon. So I can build transistors and computers...The mathematics is possible ....I don`t have any knowledge about what an electron actually is. I can use it. But I don`t understand it.

more to the point...how many people actually read the book before posting an uninformed opinion on it`s contents?
 
 
Henningjohnathan
18:56 / 12.06.04
What is the difference between mathematics and computation? Isn't computation a form of mathematics?

For example, we can describe the laws of the universe using English, but mathematics is more precise and verifiable. In the end, math is the quest for truth and it seems computation would have to break down into mathematic principles at some point. Perhaps it is somehow less aristotelian than classical mathematics (in the same way fuzzy logic and Godel's theorem defy classical interpretations).
 
 
Cat Chant
13:58 / 14.06.04
It is entirely possible that one arrives at a descriptive algorithm for a physical situation without any understanding of why it works. This makes for interesting predictive power with little chance for further progress in the same direction. You can end up with scientific dead ends.

This is interesting. Can you explain why not knowing the why leads to a dead end - or (I suspect this is a related question, about the definition of a "dead end" maybe) what scientific progress would be, if not improved/total predictive power (the ability to predict future states of a physical situation from their present state)?

I am just asking because I'm ignorant, by the way, not because I am attempting to lead you into a subtle Socratic trap or anything
 
 
DecayingInsect
16:02 / 14.06.04
Has anyone noticed that there are fads in the application of mathematics to the sciences?

Anyone remember Catastrophe Theory? Fractals? Fuzzy Logic?

While all the above had success in certain areas would it be fair to say that they were not, after all, paradigm-shattering breakthroughs?

I wonder if it will be the same with Wolfram's speculations on cellular automata in ANKOS?
 
 
Wombat
18:01 / 14.06.04
What is the difference between mathematics and computation? Isn't computation a form of mathematics?

For example, we can describe the laws of the universe using English, but mathematics is more precise and verifiable. In the end, math is the quest for truth and it seems computation would have to break down into mathematic principles at some point.

A simple example would be Conways game of life.

A computational approach would be

Draw a grid. Colour in random dots. Coloured dots are populated.

create a new grid using these rules
For a space that is 'populated':
Each cell with one or no neighbors dies, as if by loneliness.
Each cell with four or more neighbors dies, as if by overpopulation.
Each cell with two or three neighbors survives.
For a space that is 'empty' or 'unpopulated'
Each cell with three neighbors becomes populated.

repeat 2000 times.

Traditional Mathematical approach. Has never been done and is probably incredibly complicated.

Wolfram suggests that for some systems the computational approach is a simpler and clearer description of what is happening than the traditional mathematical approach. (by traditional I mean the type of mathematics currently used by most sciences...calculus, matrix, geometry , arithmetic, complex numbers, statistics)
Basically just adding one more mathematical tool to our repertoire. A tool that can increase our understanding of what is really going on. (if that`s possible...but I`ll save that for another thread)
It`s already a use-full tool. Perhaps `new kind of science` and revolution are overstating the case. But judge on results not arrogance.
 
 
Lurid Archive
13:15 / 15.06.04
I still haven't read the book, though I really do intend to. I think it would help if I met someone who didn't think that Wolfram is a loony.

This is interesting. Can you explain why not knowing the why leads to a dead end - or (I suspect this is a related question, about the definition of a "dead end" maybe) what scientific progress would be, if not improved/total predictive power

Sure (with the warning that you should take everything I say with a pinch of salt). One point to make is that predictive power is a measure of success, but not the only goal that scientists have. Most scientists I've met want to understand how the world works and even if, ultimately, one can never answer the why and how questions, this doesn't mean that people want to give up on asking them. And science is as much about finding interesting questions as coming up with useful answers.

I think there is a more practical consideration. One of the striking features of cellular automata is that they produce very complex and difficult to predict behaviour. Great. So you start up a simplified model which on the small scale is only coarsely accurate, plug this into a cellular automaton and watch the pretty patterns producing the large scale emergent behaviour.

Cool. Now how do you know that you haven't just modelled your data samples? Maybe you have gone through a complex process which does little more than encode the information you already had. How can you tell? You can't, because the complexity that produced the result stands in the way of making the structural analysis that lets you answer questions like that.

(This is why I think Mr Spoong's example of Conway's Game of Life actually demonstrates the opposite of what they intend.)

But maybe you find that that you can model lots of situations. Which ones are going to work? When does the simulation break down? What are the significant features of the behaviour of your system (I'm thinking breaking points, resonant frequencies and so on)?

You can run the simulation lots of times in order to get some answers, and that can tell you a great deal, but a gap in understanding is not just a philosophical problem but places serious practical limitations on what you do. A chalk is a really good model of a piece of chalk, and you can learn a lot by smashing it, crushing it and stamping on it. But I don't think anyone would take seriously the notion that we should abandon material science and just test things (even though that is a large part of what material science is). Wolfram seems to be saying, with some added sophistication, something along those lines.

Now, of course, some of this could also be said of conventional science, but part of what Wolfram is doing is setting up a false dichotomy. No one objects to computer simulations (which is on some fundamental level what cellular automata are, albeit with a curious programming language), but why give up on the conventional stuff? You don't get relativity by designing a cellular automaton to model Newtonian collisions.

Has anyone noticed that there are fads in the application of mathematics to the sciences? - Decaying Insect

Yeah, its the sexiness of the paradigm shift, where people want to believe that the old fashioned, relentlessly incremental and rather difficult old stuff is for losers. Smart people use [insert current mathematical fad].
 
 
Henningjohnathan
14:50 / 15.06.04
Great points, however, I'm not sure it addresses what I think may be the essential point of the computation approach as I understand it.
Our minds, our consciousness, is a computational phenomenon. Therefore, to explain the phenomena of the universe to ourselves, we have to reduce it to computation. I think what Wolfram seems to be pointing out is that the basic phenomenal nature of the universe is computational and can't be "broken down" intelligibly past a certain level.
I think this may be a way to get around the basic problems of Quantum Physics which has been that there is no good way to mathematically model the basic interactions of particles and waves on the fundamental level of the universe. Perhaps if we began looking at this universe as an emergent program from the basic probabilities involved in th interactions of systems (rather than particles or waves) on the quantum level, we could develop a better (though not mathematically precise) model of what is actually happening.
As I pointed out earlier, it seems that science is becoming more about defining the limits of our perceptions and thought than describing the world we live in.
 
 
Lurid Archive
09:52 / 16.06.04
I think this may be a way to get around the basic problems of Quantum Physics which has been that there is no good way to mathematically model the basic interactions of particles and waves on the fundamental level of the universe.

Not sure I understand. I thought the problem with QM is that it is inescapably mathematical, to the extent that it can't really be explained outside of math.
 
 
Wombat
16:54 / 16.06.04
Lurid. I`m not sure how modelling something implies a lack of understanding.
He`s using low level knowledge of how something works to predict large level complexity and seeming randomness.

For example. Modelling a water molecule requires understanding it`s interactions with other water molecules. Once you have a model for this one thing you can use his methods to predict large scale fluid flows. (ocean currents..turbulence..etc...)

or. You can use a model of a skin cell. Model the cell splitting and growth. It`s interaction with other cells. Then predict the patterns and colouring of entire animals.

or. You can model interactions between ice crystals. Grow them around a seed and get snowflakes.

etc...etc...

You require a knowledge of how something works at a low level before you can produce a model for large scale phenomena.

Also the reverse is true. If you notice that a large scale thing can be modelled by a few simple rules..then it`s a big clue to how the smallest parts are interacting.

As for QM and relativity. *grin*.
If his views on modelling systems annoyed you then his views on physics are really gonna bug you.
He views the universe as a multipath network. Then uses this simple model with his methods to model gravity, quantum mechanics and general relativity. (although in this chapter there seems to be a lot less evidence than in the other chapters.)
Although I love the idea that the entire universe can be explained by a few simple rules that are totally alien to humanities way of thinking...he might have dropped the ball on this one.
 
 
Lurid Archive
09:58 / 17.06.04
Lurid. I`m not sure how modelling something implies a lack of understanding.

It doesn't. But there are specific ways of modelling that do. Your example of the Game of Life is relevant here. BY saying that math can't deal with it, what you really mean is that we have no idea how to predict its behaviour except by just running it. Given that that is a very simple example of a cellular automaton, I think it has implications of the kind I already outlined.

He`s using low level knowledge of how something works to predict large level complexity and seeming randomness.

And there is nothing wrong with that, and it is hardly new to do so. But this approach has limits.

For example. Modelling a water molecule requires understanding it`s interactions with other water molecules. Once you have a model for this one thing you can use his methods to predict large scale fluid flows. (ocean currents..turbulence..etc...)

Sure. I can also use the ocean itself as a model of the ocean. I see what happens and I find that it is remarkably accurate at predicting what it is going to do. But there is a problem here, I think you'll agree. Cellular automata also suffer from other problems, as I said.
 
 
iconoplast
10:30 / 17.06.04
I read maybe half the book. The first half was full of the phrase "in this book I will..." (revolutionize science, &c, &c). So I skipped to the end, which obliged my by being full of "in this book I have...". However, there didn't seem to be a middle bit which actually did anything.

Here's my problem with Wolfram's Science:

Say you're interested in bird behavior. You get a cellular automata system which is behaving /exactly/ like a flock of birds for the first 1,000 generations. You'd feel pretty spiffy, having "solved" the problem of flock behaviors.

But there is no predictive power. You could very well be using the wrong automaton - the one that, at 1,001 generations, suddenly does nothing. Or that just suddenly stops describing bird flocks. Since you're not bound by old-science's tired insistence on deductive proof and mathematical certainty, you also have a much harder time using induction to predict anything based on the behavior of your cellular system.

...I think.
 
 
Wombat
17:09 / 17.06.04
The celluar automata example was to show the difference between mathematics and computation. Not an example of Wolfram being right.

He`s not suggesting we abandon the scientific method.
Or even abandon traditional mathematical models.
The only relationship between the real world and mathematics is one created by us.
A similar relationship can be created using computational methods. ( I can`t remember Wolfram actually saying this.)

Lurid - I agree with what you are saying. But more. Understanding died when newton published his theory of gravitation. He used the shiny new (fashionable) methods of calculus to create a theory of gravitation. He could predict the motion of planets perfectly. But neglected to provide a mechanism. (I`ll take that back...he said that the laws of physics were the direct result of gods Will) Today quantum mechanics is a load of maths that is beyond human understanding. Superstring theory also defies human understanding. You are fighting a battle that was lost a long time ago. Wolfram is no worse or better than any other modern scientist. Wolframs methods start with a few simple rules and applies them many times. At least the few simple rules are within understanding.
( a possible exception is einstein...who tried to understand rather than model)


iconoplast - it`s also possible to spend hundreds of years using newtonian mechanics. How do you know that going a little bit faster doesn`t change thing completely. How do you know that looking at things a little smaller won`t change things in strange ways.
Sometimes we just get things wrong.
 
  

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