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.

Comments

I'm reading the book

[Anonymous Coward]

I managed to get it a week ago because I work at a bookstore. I'm about halfway through, and so far it's overrated. The demonsrated cellular automata are very cool, but Wolfram constantly confuses similar behavior for causation. After the first 300 pages describing various kinds of CAs, he slips into pure "I suspect" and "Probably" and "Very likely" mode without really explaining why he suspects the things he does. The wildest thing he's stated so far (without any real evidence, just lots of "It is my strong belief") is that space and time are discrete on a very small scale, and are stuctured as a network of nodes. He doesn't (yet) go so far as saying that the universe is actually a simulation running in a computer. Maybe he will later in the book. Most of the rest of it seems to be concerned with the limits of computation.

In his credit, he does make a good argument that much of nature is based on processes analogous to CAs, particularly the growth of plants and pigmentation patterns on animals. But again there's lots of "I believe" and practically no "I've observed."

Chaos

[QuodEratDemonstratum]

Looks like he's rediscovered chaos theory - simple input intp simple equations give complex outputs; he thinks he can find the simple input which generates the universe from a chaos producing equation.

Mathematica

[gbnewby]

There are probably far fewer slashdotters familiar with Mathematica than PERL, so I wanted to write a few lines about Mathematica. From what he's said, Wolfram wrote Mathematica a lot like Larry Wall wrote PERL: to solve lots of problems by hiding complexity behind the scenes.

As PERL is the swiss army chainsaw of computer programming, Mathematica is the swiss army chainsaw of mathematics. The syntax isn't as forgiving as PERL, but it's not bad. Here's a snippit I use for singular value decomposition:

• svout = SingularValues[N[mydata],Tolerance->0];
• 
  {u, md, v} = svout;
  Print["u is ", u//MatrixForm];

I've done the same thing with LAPACK and CLAPACK (scientific programming libraries) and in 3 lines of FORTRAN, C or C++ you haven't even started to define your data. In Mathematica, you're already done.

Then there's visualization. Running on a PC or via XWindows, Mathematica can do stunning graphics -- including interactive graphics -- with almost no coding. It's not entirely flexible (sort of like using SAS or SPSS' graphics routines), but again you can do astoundingly great things with almost no code.

In short, Mathematica is very close, for mathematics, to what PERL is for programming (or insert your favorite programming language or toolkit - but I think PERL fits best). While in the olden days of CGI everyone would have their own copy of cgi-lib.pl, now PERL has this functionality built in -- we just do stuff like do stuff like "my $query = new CGI;". In Mathematica, the language has evolved similarly so that stuff you needed to write lots of code for previously is now abstracted to a few functions. Like PERL's ability to use modules, you can write your own add-ons for Mathematica. Like PERL's POD, Mathematica can be used for documentation (and *was* used to write the Mathematica Book, and presumably Wolfram's new book).

Just a few words about Mathematica. Give it a try, if you're remotely interested in how this stuff works. You'll probably like it!

Re:Mathematica

[CheshireCatCO]

Speaking as someone who has Mathematica installed on his laptop as well as his workstation (and has it currently, actively working on both machines at the moment), I have to disagree with your review, if only in the light in which you cast MMA.

Mathematica (aka MMA) is a life-saver for some kinds of symbolic manipulations and is great for plotting up formulae. But it has a lot of weak flanks. I refuse to use it for writing things, [La]TeX is much better for that. You might lose a bit of WYSIWYG, yes, but MMA gets really slow after a few pages of serious 2D mathematics. And it's a lot easier to type straight text.

MMA also is far from ideal for data plotting and manipulation. While I knew MMA long before IDL (from RSI), I have long since started doing all of my data I/O, plotting and manipulation in IDL.

Finally, MMA is pretty slow about serious number crunching. Much has been made about doing modelling in MMA, but my observation and my experience is that if you want to use commercial software (as opposed to writing your own C/FORTRAN/whatever code), Matlab and even Maple are better than MMA.

Still, Mathematica is very strong in its niche. I'm not sure it's worth $700+, which is the usual cost. But since I'm still a graudate student, I got my copy for $150 or so. It's been worth that.

All that said, this far from proves that Wolfram has a clue about anything other than MMA.

Re:Mathematica

[mcelrath]

I wonder if Steven Wolfram himself has to call up Wolfram tech support when he gets a new laptop, dig up his registration number, license number, and hardware ID, and explain to them that he wants to transfer his license to a new computer and why he wants to transfer his Mathematica license to a new computer and assure them that yes he will delete the old copy and give them the hardware identifier for his new machine and install a new Big Bro^H^H^H^H^H^H^H^H License Manager...yadda yadda

Sure it's a useful piece of software. But it's an absolute pain in the ass, Wolfram is a paranoid bastard, and it's not worth half the price they ask for it. For my professional work, I choose Maple. Go away Wolfram and annoy someone else. I don't want to talk to you after I have legally purchased your product. It's NONE OF YOUR BUSINESS!

Remember dongles? The things you put on your serial port to keep you running Autocad on only one machine? Mathematica is one big software dongle.

--Bob

What Wolfram is driving at

[vkg]

is that the observable universe is defined by calculus and differential equations in very small areas: planetery motion, for example, or atomic physics.

Phenomena like life, geology and the like are very badly behaved with respect to our standard mathematical tools and we all know this.

Wolfram is suggesting that cellular automata provide a simple framework for examining the phenomena outside of the "magic circle" of the calculus: i.e. most of life and the universe.

Of course, for a long time we've confused hard science with the application of calculus, which has effected what we consider "science" to be: if it is not an equation, we don't think it's scientific.

Well,

1> go talk to some biologists

2> get used to it: equations got us this far, but after this it may be increasingly about computation.

Consider, for example, the Four Color Theorem - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

We'll see how Wolfram's work fares over time, but my bet is that it will fare Quite Well.

Re:What Wolfram is driving at

[VFVTHUNTER]

is that the observable universe is defined by calculus and differential equations in very small areas: planetery motion, for example, or atomic physics.

No. The universe can be described by calculus and difficult equations.

Phenomena like life, geology and the like are very badly behaved with respect to our standard mathematical tools and we all know this.

No they're not. It's just that in order to model biological phenomena very well, you have to do finite state analysis on a very fine scale - and getting even the most powerful supercomputer to do the (calculus and difficult equations) calculations on ALL those elements is...unrealistic.

Still don't believe me? Ask IBM - according to their Blue Gene Project, given all the computing power available on the planet right now, it would still take several hundred years to calculate the structure of human proteins.

Still not convinced? OK. The human body is around a trillion cells. Each of these cells has millions of molecules in it. Each of those molecules can be accurately modeled by calculus and DifEq...but you've got trillions of millions of equations to worry about. There's not enough RAM on the planet to hold that matrix. Also consider that you also have trillions of millions of possible boundary conditions.

Wolfram is suggesting that cellular automata provide a simple framework for examining the phenomena outside of the "magic circle" of the calculus: i.e. most of life and the universe.

Wolfram is also supplying the code for the book in Mathematica. I submit to you that Wolfram is trying to sell more software. Which isn't to say I don't own his books, or that I don't have 4.1 minimized on my desktop right now. Because I do. But when someone comes out and says that his book is the be all and the end all of our scientific quandries, I am...skeptical.

You've hit a sort of soft spot here. I love the alternative ways of thinking - wavelets, fuzzy logic, neural networks, AI, and yes cellular automata. Each of these fields has been able to solve (or simplify) problems that have plagued researchers. But every time a researcher uses one of these methods to solve a problem, he or she starts evangelizing it, and hurts its credibility. It's a problem of HYPE - and there's HYPE written all over this book. He should have just published it, sent a copy to some respected scientists, and let THEM speak about it. I could care less when I see fervent hype on the MTV. But I get sick when I see it in scientific publications.

Of course, for a long time we've confused hard science with the application of calculus, which has effected what we consider "science" to be: if it is not an equation, we don't think it's scientific.

1> go talk to some biologists

Biologists are friggin crazy. I know this because I am one :)

2> get used to it: equations got us this far, but after this it may be increasingly about computation.

Consider, for example, the Four Color Theorem [wolfram.com] - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

You seem to be unfamiliar with mathematical proofs. Grinding through many cases does not a valid proof make. In order to prove a theorem, you have to verify its validity for ALL cases, and in order to disprove a theorem, you only have to find one case where it is not valid. Just because you ran your theorem on a supercomputer for three months does not mean you have proved its validity for all cases. Example: You are trying to prove some theorem, and you use only positive integers. The supercomputer runs for a year and finds no holes in your theorem. Then your girlfriend comes over and enters -1, and your supercomputer barfs at you.

We'll see how Wolfram's work fares over time, but my bet is that it will fare Quite Well.

I HOPE it fairs well - I'd love to understand WHY the second law of thermodynamics works as well. But whether it fairs well or not, it would have faired much better without all of the hype and simply on the merits of the work itself.

Re:What Wolfram is driving at

[Alomex]

Consider, for example, the Four Color Theorem [wolfram.com] - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

This was a subject of debate twenty years ago. Currently the computer proof is generally well accepted by mathematicians. What Wolfram proposes is neither new nor revolutionary.

Computer Science itself has spent a good portion of its young life moving away from equation descriptions to constructive, computable descriptions. They are called algorithms. You don't need cellular automata to make a switch from equations to computing. Moreover, I was reading a famous physicist (whose name escapes me) state that physics had move beyond the equation as description and considers now computational descriptions as valid.

Digital Mechanics

[ROBOKATZ]

This sounds a lot like Ed Fredkin's Digital Mechanics theories. Which isn't surpising, considering that Wolfram and Fredkin used to work together.

Re:It should be obvious

[Tony-A]

surely you need relativistic mechanics to describe the orbits themselves
As I vaguely recall from a physics course long long ago, Newton's equations are not wrong. There is a derivative term that everyone assumes is a constant, but written as a derivative, which is not constant under relativistic effects. Written properly, Maxwell's equations would be still be valid with relativistic effects. Classical mechanics is just a simplification of relativistic mechanics.

See Fredkin's Digital Physics book draft online

[hqm]

People interested in the concept of the universe
as a digital computer should look at

http://www.digitalphilosophy.org.

Fredkin was thinking about this stuff long before Wolfram was born.

Re:Silly mathematicians.

[ImaLamer]

read this book:

Shadows of Forgotten Ancestors by Carl Sagan and Ann Druyan...

Love, relationships and most defintely peace is explained by math. Why? Because of DNA, Natural Selection and simply who we are.