A New Kind of Science 530
| A New Kind Of Science | |
| author | Stephen Wolfram |
| pages | 1197 (plus 62 page index) |
| publisher | Wolfram Media, Inc. |
| rating | 10 |
| reviewer | cybrpnk2 |
| ISBN | 1-57955-008-8 |
| summary | A long awaited treatise that cellular automations, not mathematics, holds the key to understanding reality |
First things first - have I read this book? Hell, no, and if anybody else says THEY have in the next year, they're lying thru their teeth. This book is so dense that if Wolfram had added a single additional page, the whole thing would have imploded into a black hole. That's got to be the only reason he quit writing and finally went to press.
I've been waiting for years for ANKOS to come out. I ordered my copy Tuesday when it was released, got it on Thursday and I've been skimming it like mad since. To give you some idea of how engrossing this book is, I was reading it Friday morning at 4 AM in the bathroom of a Motel 6, curled up in a bedspread on the tile floor to keep from disturbing my wife and stepdaughter during a trip to my stepson's graduation. I've got four college degrees, one in math and two from MIT, and bottom line - this sucker's gonna take a while to digest. However, it's theoretically straightforward enough that anybody with a high enough level of obsession and a few years to stay glued to it can follow it in its entirety. In ANKOS, Wolfram certainly comes across as arrogantly cocky but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.
ANKOS is 1250+ pages divided into 850 pages of breezy exposition followed by 350 pages of fine-print notes. The exposition is composed of 12 chapters and the notes have about a paragraph per page of topic- and name-dropping technobabble to let you know where to go next for more details on whichever of Wolfram's tangents strike your fancy. Topping the whole thing off is a 60+ page index with thousands of entries in even smaller typeface than the notes.
Despite its length, ANKOS is not a rigorous mathematical proof of anything as much as it is a superficial survey of a vast new intellectual landscape. And what a landscape Wolfram has laid before us. It's all about cellular automations, which have traditionally been relegated to the realm of mathematical recreations. Start with a black square in the center grid square (cell) on the top line of a sheet of graph paper. Think up a few rules about whether a square gets colored black or white on the next line down depending on the colors of its neighbors. Apply these rules to the squares on the next line of the sheet of graph paper. Repeat. Watch what happens. Sounds simple. It isn't.
The first short chapter outlines Wolfram's central thesis: That three hundred years of mathematics based on the equals sign have failed to provide true insight into various complex systems in nature, and that algorithms based on the DO loop can succeed in this endeavor where mathematics has failed. The reason, claims Wolfram, is that deceptively simple algorithms can produce heretofore undreamed of levels of complexity. He claims that while frontier intellectual efforts such as chaos theory, fractals, AI, cybernetics and so forth have hinted at this concept for years, his decade of isolation studying cellular automata has taken the idea of simple algorithms or rules embodying universal complexity to the level of a new paradigm.
The second chapter outlines what Wolfram calls his crucial experiment: the systematic analysis of the 256 simplest rule sets for the most basic cellular automatons. He discovers this "universe" of rules is sufficient to produce his four so-called "classes" of complex systems: order, self-similar nested patterns, structures and most importantly, true randomness. The first two lead to somewhat familiar checkerboard-type patterns and leaf-type fractals; the last two, unforeseen unique shapes and unpredictable sequences. Wolfram stresses that the ability of simple iterative algorithms to produce complex and unique non-fractal shapes as well as truly random sequences of output is in fact a revolutionary new discovery with subtle and profound implications.
The third chapter expands his initial 256-rule-set universe of simple algorithms with many others Wolfram has researched for years in the dead of night while others slept. Rule sets involving multiple colors beyond black-and-white, rule sets that update only one grid square instead of a whole row, rule sets that embody full-blown Turing machines, rule sets that substitute entire sets of patterned blocks into single grid cells, that tag end point grid squares with new patterns, that implement "registers" and "symbols" - Wolfram has examined them all in excruciating detail. And no matter how complex the rule set is he explores, it ends up generating still more and more unexpected complex behavior with many notable features as the rule sets are implemented. This ever-escalating spiral of complexity leads Wolfram to believe that cellular automatons are a viable alternative to mathematics in modeling - in fact, embodying - the inherent complexity of the natural world.
In chapter four, he begins this process, by linking cellular automatons to the natural world concept of numbers. Automatons that multiply and divide, that calculate prime numbers and generate universal constants like pi, that calculate square roots and even more complex numerical functions like partial differential equations - Wolfram details them all. Who needs conscious human minds like those of Pythagoras or Newton to laboriously work out over thousands of years the details of things like trigonometry or calculus? Set up dominos in just the right way, flip the first one and stand back - nature can do such calculations automatically, efficiently and mindlessly.
Chapter five broadens the natural scope of cellular automations from one-dimensional numbers to multi-dimensional entities. Simple X-Y Cartesian coordinates are left behind as Wolfram defines "networks" and "constraints" as the canvas on which updated cellular automatons flourish - always generating the ever-higher levels of complexity. More Turing machines and fractals such as snowflakes and biological cells forming organs spontaneously spring forth. So far we've seen some really neat sleight-of-hand that Martin Gardner or Michael Barnsley might have written. But we're only on page 200 of 850 with seven chapters to go, and Wolfram is just now getting warmed up.
Chapter six is where Wolfram begins to lay the foundation for what he believes is so special about his insights and discoveries. Instead of using rigid and fixed initial conditions as the starting points for the cellular automations he has described, he now explores what happens using random and unknown initial conditions in each of his previously defined four "classes" of systems. He finds that while previously explored checkerboard (Class 1) and fractal (Class 2) systems yield few surprises, his newly-discovered unique (Class 3) and random (Class 4) cellular automaton systems generate still higher levels of complexity and begin to exhibit behavior that can simulate any of the four classes - a telltale hint of universality. Furthermore, their behavior starts to be influenced by "attractors" that guide them to "structure" and self-organization.
With the scent of universality and self-organization in the air, Wolfram begins in chapter seven to compare and contrast his cellular automations to various real-world topics of interest. Billiards, taffy-making, Brownian motion, casino games, the three-body problem, pachinko machines - randomness is obviously a factor in all of these. Yet, Wolfram notes, while randomness is embedded in the initiation and influences the outcomes of each of these processes, none of them actually generate true randomness in the course of running the process itself. The cellular automations he has catalogued, particularly his beloved Rule 30, do. The realization that cellular automations can uniquely serve as an initiator or generator of true randomness is a crucial insight, leading to the difference between continuity and discreteness and ultimately to the origins of simple behaviors. How, you ask? Hey, Wolfram takes most of the chapter to lay it out in a manner that I'm still trying to follow: no way can I summarize it in a sentence or two.
By chapter eight, Wolfram believes he has laid out sufficient rationale for why you, me and everybody else should think cellular automations are indeed the mirror we should be looking in to find true reflections of the world around us. Forget the Navier-Stokes equations - if you want to understand fluid flow, you have to think of it as a cellular automation process. Ditto for crystal growth. Ditto for fracture mechanics. Ditto for Wall Street. Most definitely ditto for biological systems like leaf growth, seashell growth and pigmentation patterns. This is very convincing stuff - tables of Mathematica-generated cellular automation shapes side by side with the photos of corresponding leaves or seashells or pigment patterns found in nature. Yes, you've seen this before in all of the fractals textbooks. The difference between fractals and cellular automations: fractals are a way to mathematically catalog the points that make up the object while cellular automations are a way to actually physically create the object via a growth process. It's a somewhat subtle difference - and a key Wolfram point.
Having established some credibility for his ideas, Wolfram stretches that credibility to the limit in chapter nine, where he applies his cellular automation ideas to fundamental physics. It was practically inevitable he would do this - his first published paper as a teenager was on particle physics, and that's the field he got his PhD in from Cal Tech at age 20 before going on to write the Mathematica software program and make his millions as a young businessman. Despite his solid background in physics, this seems at first blush to be pretty speculative stuff. He shifts his focus on the cellular automations from randomness to reversibility, and describes several rule-sets that both lead to complexity and are reversible. This behavior is an apparent violation of the Second Law of Thermodynamics. From Wolfram's way of thinking, if the universe is indeed some kind of ongoing cellular automation, then it may well be reversible and the Second Law must not be the whole story, so there must be something more we have yet to learn about the nature of the universe itself. He continues extensive speculations on what this may be, and how space, time, gravity, relativity and quantum mechanics must all be manifestations of this underlying Universal Cellular Automation. The rule set for this ultimate automation, which Wolfram believes might ultimately be expressed as only a few lines of code in Mathematica, takes the place of a mathematically-defined unified field theory in Wolfram's world. This is mind-blowing stuff, but ultimately boils down to Wolfram's opinion. I have great difficulty in comprehending space and time and matter and energy as "mere" manifestations of some cellular automation - if so, what is left to be the "system" on which the automation itself is running? I'm reduced to one of Clarke's Laws: The universe is not only stranger than we imagine, it is stranger than we CAN imagine ...
Wolfram shifts from Kubrick-style religion back to mere philosophy in chapter ten, where he explores how cellular automations are perceived by the human mind. Visual image perception, the human perception of complexity and randomness, cryptography, data compression, statistical analysis, and the nature of mathematics as a mental artifact are all explored. The chapter ends on a discussion of language and the mechanics of thinking itself. Wolfram reaches no real concrete conclusions on any of these, except that once again cellular automation is a revolutionary new tool to use in achieving new insights on all of these topics.
Chapter eleven jumps from the human mind to the machine mind by exploring not the nature of consciousness but the nature of computation instead. He goes here into somewhat deeper detail on ideas he has introduced earlier, about how cellular automations can perform mathematical calculations, emulate other computational systems, and act as universal Turing machines. He focuses on the implications of randomness in Class 4 systems and the universality embodied in systems like that of his Rule 110. His arguments lead up to a closing realization, what he does not call but may one day be named Wolfram's Law.
The final chapter, chapter twelve, discusses what all of Wolfram's years of isolation and work have led him to conclude. He calls it the Principle of Computational Equivalence. What follows is an unavoidably oversimplified distillation of Wolfram's thoughts on the PCE. If indeed cellular automations are somehow at the heart of the universe around us, then the human effort to reduce the universe to understandable models and formulas and simulations is ultimately doomed to failure. Because of the nature of cellular automation computation, there is no way to come up with a shortcut method that will deduce the final outcome of a system in advance of it actually running to completion. We can currently compute a rocket trajectory or a lens shape or a skyscraper framework in advance using mathematics merely because these are ridiculously simple human efforts. New technologies based not on mathematics but instead on cellular-automations like wind-tunnel simulators and nanobot devices will be exciting technological advances but will not lead to a fundamentally new understanding of nature. Issues that humans define as undecidability and intractability will always limit the level of understanding we will ultimately achieve, and will always have impacts on philosophical questions such as predestination and free will. To conclude with Wolfram's own final paragraph in the book:
"And indeed in the end the PCE encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of the universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold."
As noted above, 350+ pages of notes follow this exposition, and trust me, there's no way they can be summarized. To mention one nugget I found amusing as I envisioned Wolfram working towards endless dawns on ANKOS, he thinks sleep has no purpose except to allow removal of built-up brain wastes that cannot be removed while conscious. So much for dreaming.
So what is the bottom line on ANKOS? It is a towering piece of work and an enduring monument to what a focused and disciplined intellect can achieve. It is very thought provoking. It will definitely lead to new work and progress on cellular automation theory and some interesting technological applications we should all look forward to with anticipation. But is it the next Principia, the herald of a new scientific revolution?
Read and decide for yourself. Only time, and a lot of it, will tell.
To read it yourself, you can purchase A New Kind of Science at bn.com. You can read your own book reviews in this space by submitting your reviews after reading the book review guidelines.
Seductive lure of the Game of Life? Bah. (Score:2, Insightful)
I would love to read a book about more mundane concerns written by someone whose education was accelerated like that, to try to see what a world I already know looks like to them.
Re:Kurzwiel's Review (Score:5, Insightful)
Have you read the book? Or just reviews of the book?
(No offense meant, but there are a lot of people who seem to think that one can somehow form a meaningful opinion of something just by exposure to other folks opinions of it.)
Phenomenal (Score:2, Insightful)
Re:Talking at work (Score:4, Insightful)
Actually, quantum physics does imply there are a finite number of states. Time, space, energy, motion, even Heisenberg's uncertainty are all descreet, quantisized values. The number of eigenstates that exist before an observation is made that collapses into one observed "event" is not infinite, it is merely a very, very, very big number (made much bigger when one considered the true vastness of the universe on a macro scale, and the number of quantum processes thus contained, many of which are not observed and thus, arguably, never collapsed into one given state or another).
We tend to think of quantum clouds of probability and "alternate universe" scenerios as containing an infinite number of possible states, but that isn't really true. Consider the plank constant (a measure of the smallest possible increment of space, time, or energy, the base unit of the universe, if you will [and if you normalize it to whatever units you are working with]). Now consider a cloud of probability that contains, for example, all possible locations and vectors of an electron within a hydrogen atom, for example. That volume has some descrete limit (though depending on one's interpretation, that limit may be the entire volume of the universe, or more commonly, some small volume around that atom's nucleus). Either way, that volume has an upper limit. We thus have a system with an upper and lower limit on where the electron can be at any moment, and what vectors it may have. This means there is a finite number of possible states that can exist, and while that number is impossibly huge to contemplate, it is not infinite.
Therefor, while Wolfram may or may not be right in his thesis, quantum physics does not in any way conflict with that thesis. Indeed, it might even lend his thesis some support (I have no idea if it does
This isn't to say Wolfram can't be wrong
Re:Crank, crank, crank (Score:3, Insightful)
Re:Are these the tools for decompiling DNA? (Score:3, Insightful)
I can see why DNA would remind you of the sort of CA that Wolfram is working with: it's 1D, linear, and can take on one of several states at each position. However, DNA is not a cellular automaton. With a true CA, the state of the system at iteration i is dependant on the state of the system at iteration i-1 (or earlier). You can describe it as a Markov chain, I think (please correct me if I'm wrong about that). On the other hand, if we consider an "iteration" of the DNA system to be a single round of DNA replication, then the state of the system at iteration i is identical to the state of the system at iteration i-1, with some noise thrown in. If, on the other hand, we consider an iteration to be a single generation of reproduction of the species, then the state at i is dependant on all sorts of things unrelated to i-1: mostly the choice of a mate, which is heavily determined by chance and environment.
Re:An odd definition of "truly random" (Score:5, Insightful)
Apparently this is one of the insights in the book - Wolfram runs every standard test for randomness on his Class IV Cellular Automata - all of which indicate that the data is random, all the while containing very clear and complex structures.
Even if you randomize the choice of your seed value (the initial value for x[0]), you're just choosing an entry point in the cycle, not changing the fundamental fact that it is cyclic and will eventually repeat. That's why we call these things "pseudo-random numbers", not "random numbers".
While they are deterministic, the patterns are not cyclical like the normal pseudo-random numbers you describe. This is a key distinguishing element.
INTERVIEW WOLFRAM! (Score:5, Insightful)
Re:Crank, crank, crank (Score:4, Insightful)
We'd also be using dynamos to generate alternating current, and transformers to change the current to various useful voltages, to power such crazy devices as flourescent lighting and AC motors. Not to mention we'd be transmitting all sorts of signals and communications though the air via radio waves.
Re:Talking at work (Score:5, Insightful)
The quantum simple harmonic oscillator (SHO), a baby among useful quantum phsyics problems has an infinite number of states. The states it may occupy have energies, (1/2 + n)*h-bar*omega_0, for all non-negative integers n. [omega_0 is a property determined by your configuration.] Virtually every useful quantum physics problem also has an infinite number of states, including the electron configuration of atoms.
Higher energy states occur with increasing rareness, and thus for practical purposes scientists often truncate and only deal with the first several states. This does not however mean that nature doesn't concern itself with all of them. (Perhaps, nature truncates too, but Wolfram sure hasn't shown that, and QED experiments would imply that nature sure doesn't truncate early on.)
This has NOTHING to do with a state's spatial extent. Of course everything has to fit inside the universe. So what? Suppose I only cared about a 1x1 square, there are still an infinite number of ways to draw a curve from one corner to the opposite corner while staying inside the box. Likewise, you can have infinite variety in quantum states in only a limited volume.
It sounds like you want to cheat and invoke the quantitization of space and say that the electron has some position in space. This simply isn't true, the various proofs of the "No Hidden Variables Theorem" shows that the electron really has no position when not being "measured" and that you truly do have to work in terms of the whole (usually infinite) array of wave functions. The universe simply doesn't operate in terms of point particles.
Actually it's never even been shown that time and space are discrete, though a number of theorists would like them to be. On the other hand though, I don't see any reason why the universe having infinite numbers of states would be an impediment to the use of CAs. Anything being modelled on computer has to be an approximation anyway.
the number of quantum states are finite (Score:3, Insightful)
From the review, wolfram claims to have addition, subtraction, multiplication, and division... with these he can generate all rational numbers... plus he claims to be able to generate trancendental numbers like pi, that seems to imply that he can make all real numbers. I haven't read the book, but I see nothing in the review that would preclude these methods from describing an infinite number of quantum states or even a continuum of states.
By the way, saying that the universe has an infinite number of quantum states is basically just saying that there is no maximum entropy for the universe. (the entropy of a system is a measure of the number of quantum states in a system). However some cosmologies have a 'big crunch' ending the universe which would imply some maximum entropy and therefore a finite number of quantum states in the universe.
What is clear (from the Big Bang theory) is that there currently is a finite number of quantum states in the universe that is increasing with time. That is, the universe currently has some finite entropy that we can assign a number to and that entropy is increasing with time. The entropy is finite because the universe had a set beginning where the entropy was zero (if the universe didn't exist, it didn't have any quantum states).
There are theories other than the big bang (like steady state cosmology) that have no fixed beginning to the universe. However, these all have a finite value for entropy in the universe (at least locally) for other reasons (see the "Heat death of the universe")
peer-review is overrated (Score:4, Insightful)
In academia, if you have a good idea someone will steal it, if you have a great idea they will dismiss you without listening to it. If you don't believe me, look into whether or not Watson and Crick _really_ discovered the structure of DNA or if it was a grad student who's ideas they orginally dismissed.
In academia there's this absurd notion that if someone understands your explanation of a new idea that they somehow helped you come up with it.
So Bravo to Wolfram for thumbing his nose at academia! I just hope he can back it up.
Reviews (Score:1, Insightful)
But I've seen a number of reviews, and a pattern seems to be emerging:
People inside the field think it's interesting, but nothing new save stuff about Rule 110, whatever that is.
People outside of the field think it's amazing.
My impression is that people outside of the field are misattributing their amazement with CA itself to amazement with Wolfram's intellect. That is, this is their first real exposure to CA, and they attribute things to Wolfram that should be attributed to a community of researchers.
Now, you can lambast people all you want for referencing reviews and giving impressions of things based on reading reviews. But I'm on a limited budget, and if I get any whiff of egomaniacal BS, I'm not going to fork $50 over for it.
Examining patterns in reviews is a very worthwhile endeavor. There's no way to purchase everything to evaluate it yourself; we all rely on reviews to some extent to make choices about what we do and don't do. Being aware of impressions based on reviews is just being aware of things at a different level.
They guy in the original post was basically just saying "My impression is such-and-such; you can do whatever you want, read this review yourself." My guess is he might look it over in the bookstore, but not buy it. He's just saying that it's something to think about.
I say, link to more reviews, and give your opinions based on those reviews! If someone can't tell the difference between impressions made based on reviews, and those based on the book, they've got other problems.
Re:Crank, crank, crank (Score:4, Insightful)
From the original review: but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.
The reply: This means he's almost certainly a crank. If actual scientists were arguing heavily about it, there might be a bit more uncertainty. But if the debate is happening amongst people whose knowledge of physics comes mainly from Star Trek, then that pretty much settles the matter in advance.
I didn't come away with that point of view at all. When the review said "nerds", I didn't take it to mean the folks "whose knowledge of physics comes mainly from Star Trek." And the bit about him being a boy genius and the author of Mathematica didn't sounds like the beginnings of any sort of argument to me. I'm sorry, but it just didn't seem like the reviewer said "He was a boy genius, wrote Mathematica, so he must be absolutely correct."
I had no idea who Wolfram was before reading this - to me, it served as an introduction as to who the author was. That I feel, combined with his 10-year solitude, says quite a bit about the author's personality - something that the reviewer acknoledged in a number of places.
In fact, the reviewer was critical at a number of points, especially when talking about the arrogant tone of the writing and the vagueness of some of what was presented. Didn't sounds to me as if this was one of Wolfram's "followers", but someone who got a very interesting book (that he happened to have been hearing about for awhile and was anxiously awaiting), and was trying to digest it and understand it so as to be better able to form an opinion.
As far as the bit about other scientists ignoring him (and several other statements along similar lines), your post really sounds a bit condescending. The reviewer himself stated that he had a few degrees (one physics, I believe?) and that the reviewer himself didn't fully understand all that was in the book. That right there speaks quite well for the reviewer. I've also read other reviews from other scientists, and I've seen a pretty decent amount of debate so far. Some truly hate it and feel it's pure crap. Others like some of the ideas, but feel it's not enough. It doesn't even seem as if this reviewer thought this book was the be-all-end-all text, the answer to everything.
So far, it looks as if the primary intent (at least of the review - possibly even the book, though who knows?) was to spark a discussion. Not a bunch of namecalling (crank!), but honest discussion.
Peer-review is overrated but some is necessary (Score:1, Insightful)
That having been said, however, as you say, it does weed out crackpots and others, such as those with big egos who have nothing new to say.
I also believe that it does improve the publishing process overall.
The thing about peer-review is that at least some is necessary. What concerns me about Wolfram isn't that he bypassed peer-review, it's that he bypassed it completely. After publishing a bit, it's seemed to me that the worst that can happen is that your paper will end up in a lesser-known source. So even great ideas that are rejected by the community will end up somewhere, they might just not be the best sources. Eventually, if the ideas are good, people will probably get a hold of them.
Wolfram could have published his "findings" in less reputable sources, and then summarized them later in a text such as the one he produced. The way it is now, he releases this enormous tome, proclaims it to be the inspired word of God, and expects us to accept it as the new ten commandments of scientific thought. If he had allowed for discussion of it along the way, we would know more about it, he might have recieved useful feedback, and it might have been a better text. He could have gotten input, thought about that input, and then released his text however he wanted.
It seems clear to me that he's just avoiding getting input from others because he doesn't want to listen to others. If he's going to publish a text himself, he doesn't have to listen to others, but he could have. The fact that he chose not to is what concerns me.
This is not a case of someone rejecting the peer-review process to avoid the worthless bureaucracy. It's a case of someone rejecting any input or discussion of his ideas at all.
Re:Crank, crank, crank (Score:3, Insightful)
Er, I think you'll find that Einstein didn't publish his ideas on special relativity until they were good and ready. The fact that Wolfram's book took so longer than expected to come out, shows he was still revising it for a long time - and what on earth is wrong with wanting to make sure your ideas are polished before publishing them? Given the perceived significance of this book, it makes perfect sense to me that he wouldn't want anything too significant to leak out ahead of time - especially if it contained mistakes!
Peer review comes now. To suggest that there will be no peer review, with Wolfram's book currently #1 on Amazon.com, is beyond ludicrous. If he had published it posthumously, now that might fairly be described as "exhiling himself from scholarly debate".
or claim that any initial skepticism about his ideas was evidence that they were right. Maybe not - but Einstein did say something to the effect of "if experiments don't agree with me, experiments are wrong" - which is far more arrogant on the face of it. However, perhaps he was just joking.
Re:Ahem... (Score:1, Insightful)