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A New Kind of Science
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.
I suggest seeing pi if you like this story.
Great soundtrack too.
Trolls, it must be cool to be that bored.
"Can you give us the answer to life?", they asked the computer.
Deep Thought pondered their question.
"Yes," he said. "But it will be tricky. And first I have to write Mathmatica."
(apologies to Mr. Adams fans)
Well thought out review
Wolfram is looking at a piece of the puzzle, IMHO. Though his book seems to be a tour de force of applying specific cellular automata to generate all sorts of neat things, I don't see it as being particularly new. This is more a book to bring it to the attention of people in other fields who may be able to make use of it. Rather like Mandelbrot's The Fractal Geometry of Nature.
I am disappointed that a Physics PhD could miss out on some fundamental issues here. First of all: anybody who has worked their way through an undergraduate curriculum in Physics understands in a visceral fashion that there is an extreme difference between MODELLING the world with a construct, mathematical, computational or otherwise, and saying that the world IS such a construct. We are in possession of many equations that model certain interactions between different kinds of substances via different forces in the world. Traditional mathematics has yielded many useful tools for modelling these processes. Stating that computational theory or cellular automata may yield useful models as well is an obvious inference. Saying that all physical processes are fundamentally composed of elements that ARE cellular automata seems to me to be a non sequitor. Hell, we don't KNOW what anything in quantum physics or beyond IS really, we just know that certain relationships hold mathetmatically that we can translate in physical conceptions and understanding.
Now, the concept of emergent complexity and complexity theory in general - as I understand it, this is stuff that folks at the Santa Fe Institute and elsewhere have been working on for years, and that the understanding has been around for years that you can model many real-world processes well by systems such as cellular automata or other rule-based systems with complex emergent behaviors.
So... I am left wondering what to make of this book. Ultimately, it will speak for itself when I read it. But it sounds like it's a mix of already known fact with ego and some intuitionist insights into certain physical processes in a monolithic volume. If he PROVES anything interesting and fundamental about certain areas of physics or fluid dynamics, or presents models more useful and meaningful (i.e. that provide information NOT obtainable through current models) than he has produced a valuable scientific work. Otherwise, it's just an interesting treatise that may inspire more meaningful work by others who are more willing to work within the establishment and processes of the mainstream scientific world (not to say that those outside it CAN'T do excellent work, just that I'm not sure if Wolfram can).
...goes into a decade of seclusion to discover the secrets of the universe
I worry about that. Science isn't practiced very well in a vaccuum. One feature of the scientific act of discovery that makes it so effective is that the scientists involved are constantly examining each others musings, to keep any one of them from going off the deep end. Genius and madness go hand in hand, after all, and nothing can drive you nuts quite like being alone with your own thoughts. Especially if those thoughts are exceptional.
I just hope this book doen't show that dear Dr. Wolfram has lost it.
"I like to wear big boy pants."
From the introduction to Bit String Physics:
Seastead this.
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.
Wolfram will probably end up having a place on the intellectual fringes, worshipped by people who are often smart but who haven't bothered/aren't trained well enough to see why specialists don't really pay attention to them. In nerd idea-space Ayn Rand is the other main example of this type.
The best comment I've read about Wolfram's book comes from Cosma Shalizi, a physicist working at the Santa Fe institute, who specializes in cellular automata. He comments [scroll down on link]:
Dis-recommended: Stephen Wolfram, A New Kind of Science [This is almost, but not quite, a case for the immortal ``What is true is not new, and what is new is not true''. The one new, true thing is a proof that the elementary CA rule 110 can support universal, Turing-complete computation. (One of Wolfram's earlier books states that such a thing is obviously impossible.) This however was shown not by Wolfram but by Matthew Cook (this is the ``technical content and proofs'' for which Wolfram acknowledges Cook, in six point type, in his frontmatter). In any case it cannot bear the weight Wolfram places on it. Watch This Space for a detailed critique of this book, a rare blend of monster raving egomania and utter batshit insanity.]
I await solid arguments to the contrary --- ie, arguments that don't start from any of the following premises:
1. But he was a boy genius at CalTech and Feynman said so!
2. But he wrote Mathematica, which is obviously really hard!
3. But if he's right this will change the world!
4. But other Scientists are ignoring/laughing at/refuting him only because they are jealous of his enormous brain!
5. But he only ignored peer review because he's so brilliant!
6. But every work of genius always seems crazy when it first appears!
I leave it was an exercise to the reader to show why Wolfram's supporters shouldn't rely on these points (although Wolfram himself apparently does).
Pfft!
I could have done it in 2 Lines with Perl!
This
What this most made me think of is DNA. DNA is just oodles of four-state variables that represent some kind of program. It is exactly like the cellular automata he's been working with. Looking at the code (the DNA itself) and the output (the organism produced) perhaps we can understand the underlying algorithm that uses the code to produce the output. Unravelling, understanding, decompiling, reverse engineering, or whatever you want to call it, the secrets of how the DNA code is executed could be the biggest scientific advance ever, and Wolfram may have provided the tools to do it.
Suprisingly there was no reference to this in the review, which probably indicates no discussion of it in the book. Cybrpnk2, is it true that he did not discuss DNA?
"I don't know half of you half as well as I should like, and I like less than half of you half as well as you deserve."
As some of my collegues were quick to point out, this is all most likely toss. For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.
... I haven't received my copy of his work yet, much less begun reading it).
... he might be very wrong for all I know. I am merely saying that your coworkers' arguments for dismissing his work out of hand are very, very mistaken.
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
The Future of Human Evolution: Autonomy
Ha, ha, ha, joke's on me :) Actually, my two degrees from MIT are Master's degrees - one in aeronautics and astronautics (what MIT calls aerospace engineering) and the other in interdisciplinary science (I put together a curricula in remote sensing that was accepted by the faculty) both awarded in 1979...My mystery 4th degree is a Bachelor's in physics. It and my Bachelor's math degree are from U of Tennessee (Go Vols!). This was just before the Space Shuttle flew for the first time and I along with thousands of others was racking up whatever it took to be selected as a NASA astronaut - a VERY big deal back then. Detour, I married my first wife. That's another (offtopic) story. As for the book review, I had just returned from a graduation when I started writing this and had been waxing nostalgic about my own college days, which I miss. This spilled over into my stream-of-consciousness writing in the "personal" paragraph of the review. Lest anybody think otherwise, I really wasn't trying to toot my own horn. MIT grads fit a bell curve of their own, and I was pretty much on the tail end of people they've sent down the Infinite Corridor and into the world...
I eventually wrote Wolfram Science an email, partly out of jest:
Only problem was that I originally wrote it without censoring myself, then corrected the censor in my email body, but not my subject. Despite the vulgarity, I still managed to get a very professional response:Oops... ]:)
Please consider making an automatic monthly recurring donation to the EFF
There was an article in NewScientist on the 9th February (subscription required to view the article), "What Lies Beneath", about emergent systems. It discusses that we may never know the true nature of the universe; of what it is made of.
Robert Laughlin (Stanford University) is researching this. What we observe in the universe is model-independent, and we cannot actually see the model itself.
"The laws that govern large-scale phenomena will not be deduced from the laws that govern tiny particles, he says. "It's in the same way that flocking behaviour can be characterised without understanding everything about birds, or superconductivity without understanding atomic theory."
This idea is called emergence. It's a familiar phenomenon in the theory of condensed matter, which is Laughlin's background. Solids and liquids sometimes play host to strange entities that bear little resemblance to the atoms making up the substance."
...
"If what you see is model-independent then you can't learn anything about the underlying equations by observing it," says Laughlin. "You could call this the dark side of emergence."
...
"What we emerge from is unknowable," says Laughlin. "The underlying equations of the Universe cannot be determined from what we know."
The article goes into greater detail than I can here, but it definitely an interesting read.
If all this is true, we can never really know the true mechanics of the universe. It may actually be a simple "4-line" automaton. It could be a billion other things - we'll probably never know.
Science is a cooperative enterprise- building on the insights and mistakes of others. Even fellow eccentric-recluse-genius Isaac Newton said "If I have seen farther than others, it is because I have stood on the shoulder's of giants". Wolfram's insight may be a way of describing things, but it may not be the best way, or the most comprehensive. He's got to work with others.
The review goes on to say how he has been skimming it but the text it too dense to have read within the time of release and the present time -- the first inidication that the poster is responding to very little of the actual review, and not cybrpnk2's whole essay.
;)
But then again, this is Slashdot...
-no broken link
Since, according to the reviewer, nobody will be able to digest this book for at least a year, perhaps we could get a Slashdot interview with Wolfram?
Well, that would explain a lot of things...
Sure, it's a 2-liner, but is anybody going to be able to maintain it 20 billions years from now? Huh?
BBzzzt. Wrong.
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.
We were discussing this at work yesterday. As some of my collegues were quick to point out, this is all most likely toss. For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.
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")
There are 10 types of people in this world, those who can count in binary and those who can't.
I've gone through peer-review several times and it's mostly an exercise of massaging the egos of people in the field who are 'respected' just for being in the field for so long and who haven't really produced anything new in their lauded carreers. You go through a ton of busywork making sure you have the right damn font and you have all of the right people referenced (whehter or not you actually used their papers) and you get paid nothing, the journal takes your copyright and charges you $10 to make fair use copies of your own damn paper.
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.
There are 10 types of people in this world, those who can count in binary and those who can't.
Fredkin went down this road a few years ago, but didn't succeed either. He and Wolfram used to work together, but they seem to have split up.
If anybody ever finds a simple CA that results in a system that behaves like physics, there will be a short, world-famous paper that will put them down in history with Newton and Einstein. But this isn't it. To Wolfram's credit, he isn't claiming that it is.
So yes, there probably is a breakdown between the mathematics and the physical world, but that's just because our models of the physical world are incorrect. Including, perhaps, the Plank constant.
... there are literally hundreds of other examples, both of experimental evidence demonstrating quantum behavior and validating the underlying models, and of practical applications of quantum mechanical systems in the everyday world.
... I have to get back to work ... it is only fair to characterize it as such) is that mathematics can be misapplied, and an assumption of infinity (e.g. an infinite number of points in a line of finite length) may be mathematically valid while completely inapplicable (indeed, wholey invalid) with repect to the real world because space is quite probably not a smooth continuity (contrary to an axiomatic assumption in that particular branch of mathematics), but a granular matrix defined by the plank length ... if quantum mechanics is to be believed (and at this point all the evidence indicates it is).
... they'd used rational numbers quite effectively for centuries, after all, and irrational numbers simply weren't elegant. That didn't stop rational numbers from existing as such, or the Greeks from being very wrong, while their rejection of emperical evidence to the contrary (in the form of a triangle scratched onto the deck of a ship, with hypotenus length=2) did mean exactly that: elegance or aesthetic preferences aside, they were wrong.
This is quickly becoming a religious discussion.
If you are interested in emperical evidence that has been collected which validates QM, may I humbly suggest a google search on the topic as a starting point. We have electrical devices which rely on quantum tunnelling to function is one example that comes to mind
Your "religious" stance is that mathematics can be used to define and model the physical world at any level (and by implicaton, any physical system), and wherever it cannot, it must be because our view of the physical world, not our mathematics or the application thereof, is wrong.
My "religious" stance (since I'm not going to bother to dig up the references here
Any argument which starts by dismissing emperical evidence as "imperfect and therefor to be dismissed in favor of our elegant models which we hold so dear" (as an aside, the heisenberg uncertaintly principle refers to a particle's position and vector, not the overall, possible constraints thereof. It does not preclude emperical evidence of its existence, measurement of its value, or consiquences, as you mistakenly assume. Indeed, quite the opposite) in favor of appeals to authority ("we've used this approach for thousands of years and it works, so anything we see that conflicts must be wrong!") becomes a religious, or perhaps philisophical, but certainly not scientific, discussion.
The Greeks didn't like the fact that the number two had an irrational square root
The Future of Human Evolution: Autonomy
Hey, I admitted up front that I had not "read" ANKOS (as in, "think about and consider the subtlties of every single word the author has written") because to do otherwise and claim I HAD read the book would generate 10 times the number of negative comments saying, impossible, the reviewer is just blowing smoke. It was meant as a flag to take the review that follows with a grain of salt, altho I ***do*** think what I wrote is a pretty good summary of what a reader will find when they pick up ANKOS for the first time. The release of ANKOS is news - lots of people have been waiting lots of years to see it. Wait until a true "reviewer" has really "read" ANKOS and it's no longer a current event - hey, journalistically it's a damned-if-you-do-and-damned-if-you-don't situation. At least I was up front with what the true situation was and produced something (I think) worthwhile as an orientation to ANKOS. The real next step, as pointed out elsewhere in these posts, is to go straight to the horse's mouth and for Slashdot to interview Wolfram...his contact info is here.
It was Sociology, wasn't it. Nobody wants to admit to a sociology degree.
I have a Sociology degree, and a Robotics/AI degree. Robotics was far easier, and dealt with simpler logical models. Sociology was harder because it dealt with people and social networks -- easily the most complex systems ever discovered in the universe (and I have a background in theoretical physics).
Yes, Sociology attracts flakes, but it also attracts people who like to get to grips with the really difficult, interesting questions that can't be abstracted away into pseudo-code, automata, and heuristics.
Da Blog