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The Universe in 4 Lines of Code?
serendigital writes "Stephen Wolfram, founder of Wolfram Research and creator of Mathematica has, after 10 years+ finished his book, "A New Kind of Science." In a "Wired" article entitled: The Man Who Cracked The Code to Everything ...," Steven Levy talks about how and why the book was written and more importantly, what it is about. The best part of the article is in this exchange: 'I've got to ask you,' I say. 'How long do you envision this rule of the universe to be?' ... 'I don't know. In Mathematica, for example, perhaps three, four lines of code.'" This book seems a little... nutty. But it's been submitted a bunch of times. If anyone wants to review it, go right ahead.
Stephen is an amazing guy, and I'm sure what he's done is something absolutely marvellous. I'm also sure, however, that his attitude will continue to suck for great lengths of time. He's probably one of the most arrogant people on this planet. I think he said it best himself regarding what he thinks people will say about his book:
my opinion of the world at large isn't high enough for me really to be interested in what they have to say
Now, if that's not a bad attitude I don't know what is. I suppose he could be excused though. He's pretty much as close to the stereotype mad scientist recluse as anyone will ever get.
"If you think education is expensive, try ignorance" - Derek Bok
He got these ideas when one day he found that extremely complex events can be expressed in relatively simple equations. Seeing that complex events can be so reduced, that's where is '4 lines of code' is coming from. He believes that the falling of a raindrop is of equal complexity as the behavior of gases in a nebula - a single equation can predict both.
Maybe it can't be proven, per se, but nothing scientific can be. All scientific theories are that - just theories. None of it should be dogma, for that would violate the principles of science. There's nothing lost if such equations must be considered hypotheses that have yet to be proven wrong.
This isn't meant to create a tidy artificial universe. It's to prove that the real universe can be predicted by simple equations. Whether he succeeds or not - that's the problem. There's no middle ground. Either this will be the waste of a brilliant mind (read his background in the latest Wired) or the greatest revolution in the history of science and a certain Nobel Prize.
________
"And if the fool, or the pig, are of a different opinion...." -- J.S. Mill
Well, it can. Sort of. Pure mathematics is great for predicting a single event of a simple system. For modeling the complex behavior of many interacting systems (nuclear reactions, protein folding, sociology), we've got no single equation that can do it. You can't predict it, but you can simulate it, using the basic equations to predict one event at a time. We don't have an equation of gravity that works for more then two bodies of mass, but what we can do is model each pair interaction for a short time interval, modify the system accordingly, advance the timer one tick, and repeat.
Dyolf Knip
He's just trying to sell more copies of Mathematica!
That's not it. Wolfram is saying the exact opposite. He is saying the universe uses very little math. Just a few simple rules. Fancy math is a red herring, in my opinion. It explains nothing. On the contrary, it is our equations that are in dire need of an explanation, from Newton's gravity equation to Einstein's GR/SR equations. They only describe the evolution of matter but do not explain the causal mechanisms.
Real science is about causal mechanisms at the fundamental level where simple rules rule! This is where Wolfram's ideas are revolutionary. They will not be well received in academic circles. Academics hate simplicity because they can't show off with it.
... as if there's something meaningful in knowning those "4 lines of code". You can even presuppose that those rules exist and we can find them. What do you have? The entire premise is "the Wolfram worldview focuses on simple rules that generate counterintuitively complex results...".
Does there exist math to go from those simple rules to complex results? The problem is, and this part of it was as at least elluded to in the Wired article, that the complexity doesn't exist inherently in the system but in our perceptions of the system. And our definition of complexity is about as slippery as snot on teflon -- implicitly defined by our own analogies of our experiences of being human and our colored perceptions of everything in nature.
To go from "simple rules" to "complex results" seems intractible. You still may be reduced to discovering complex and interesting results in the crufty scientific way. And those 4 rules may just be sitting up on the mantle doing the only thing they can do: looking pretty.
Isn't this a fallacy of undistributed middle term:
Simple iterative functions produce complex structure.
The Universe has instances of similar complex structure.
Therefore the complex structure observed in the universe is modeled by simple iterative functions.
It won't be a "waste of a brilliant mind". If he succeeds, it's not a waste. If he fails, he's shown that there are no easy answers in that direction, so then other people will try other directions of research which might be more fruitful.
Speaking as a former student that learned Mathmatica in Calculus labs ( for I, II, and III ) and Maple for engineering classes...
I completely agree with you about how powerful Mathematica is, but when I started doing PChem research on Fourier transforms I found MathCAD to be the easiest for documentation. I have since only used MathCAD, as it doesn't require learning the cryptic code... just learning the interface which is fairly intuitive.
As far as speed... We pitted two PPro 200s of equal specs: one with Mathematica, one with MathCAD. We calculated the Riemann Sum of several functions, and MathCAD appeared to be the quickest.
But... just a suggestion that you MAY wanna try... if you haven't already...
--JamesT
--Chemguru
I'd just like to contend that Mathematica does actually handle documentation remarkably well. I've documented my entire Elementary Number Theory course using MMA including all the really really nasty formula (2^(p^(p-1.....))) in nice 2D. There is no performance loss in its display and creating them is such a breeze if you know the keyboard shortcuts (Ctrl^6 etc.). The Mathematica file format is based on Latex so anything you can do in Latex you can probably do in Mathematica too. (Well, enough anyway) I'll choose Mathematica whenever possible
;)
Don't try serious number crunching with Mathematica. True! Tbe Runge-Kutta's and P-C methods for solving ODE's run about 100 times slower than the same in fortran. But it only took 10 lines of code so I didn't mind too much
Finally, for those who want to see just how good (better IMO) Mathematica is at WYSYWIG Latex like editing, check out my ccourse notes (800kbs gzipped postscript). It has impressive formatting
I think you mean:
printf("Hahahahaha!%c",13);
Also, check the man page for ascii. 13 is '\r', 10 is '\n'. Please try harder next time.
I haven't read the book (already ordered it), but I have a bone to pick with it. The first thing that is new about it is that it avoids peer review prior to publication.
We all know that the best way to advance in an area of knowledge is by getting criticism to our new ideas. The reason to do so before publication is that any scientists know how easy it is to fool one self and tries to avoid it, not by asking a few friends to read our stuff, but by asking the biggest experts in the best magazines (or by posting for free in a web site so everybody gets a crack at it).
By failing to follow this procedure Dr. Wolfram has open himself up to criticism that his book is not a scientific enterprise, but a commercial one...
Disclosure: I am a mathematician...
An algorithm is a pure expression of process; it has no meaning with execution and data contexts. Thus, I think Wolfram has gone beyond science into faith and religion... he may answer "how", but that is only part of an entire description of the universe that also asks "why" and "what."
Be that as it may, I am fond of heretics who shake the foundations of science with unorthodoxy. Wolfram is brilliant, if erratic, and I'll read his book simply to have my viewpoints challenged.
All about me
All lengths of space or time are either multiples or one over a multiple of length.
... ?
So the allowable multiplicative factors are:
...5, 4, 3, 2, 1, 1/2, 1/3, 1/4, 1/5,
Closure under addition produces the rational numbers.
By a density argument we might as well call it a continuum.
That last one is the most problematic. Wolfram says he doesn't expect people to understand him, or to get a negative reaction from the scientific community, and -- worse -- that this negative reaction is only to be expected etc. These are the early hallmarks of the crank.
Things to expect soon: A legion of amateur readers proclaiming him a genius and arguing that the indifferent reaction of mainstream science is somehow evidence that the book is right. Just remember: P(Cranky and Weird | Work of Genius) = High. P(Work of Genius | Cranky and Weird) = Very low.