Wolfram's New Kind of Science Now Online 480
gotscheme writes "When Stephen Wolfram of Mathematica fame self-published A New Kind of Science in 2002, he raised the suspicions of many in scientific communities that he was taking advantage of a lot of other people's work for his sole financial gain and that he was going against the open nature of academia by using restrictive copyright. Yesterday, Wolfram and company released the entire contents of NKS for free on the Web (short registration required). Perhaps Wolfram is giving back to the scientific community; perhaps it is simply clever marketing for a framework that is beginning to gain momentum. For any matter, the entire encyclopedic volume is online, and this appears to be a positive step for scientific writing."
Nothing to see here (Score:2, Insightful)
Wolfram doesn't care, he's made a nice pile from it, generated some nice PR for himself; refused all peer review; got a bunch of sycophantic reviews -- largely from non-scientists -- took his short term profit, then bailed.
If he was poor, he'd've been dismissed as a kook, but the rich can lay on some nice junkets, so they get treated as genius, even when their ideas are rotten.
Move along.
Or perhaps... (Score:4, Insightful)
ANKOS is not a groundbreaking book, and it's conclusions (that all creation is fundamentally programmed into it) is specious. He is adamant that there is no God which created everything, yet he points to artificial order which could only be created by an intelligent designer.
He totally discounts the view that these patterns are the result of accepted scientific theories like evolution and geology and says that evolution and geology are directed by the patterns. It's a completely inside-out view of the universe and despite its obvious attraction for pseudo-intellectual navel gazers, the book and its contents are neither anything new nor anything that could be construed as vaguely scientfic.
Neat marketing ... (Score:5, Insightful)
A forum at the site for peer review would be nice. Then the issues of credit for work and contentious elements of the theory could be debated dynamically and publicly. Of course maybe it exists already. Can't get to the site at the moment.
Not Interested (Score:5, Insightful)
He may be a smart guy, but I think he might just be recycling old material and calling it the Next Big Thing (TM). Again, I won't find out unless this book catches on, because most of my book purchases are by word of mouth or by trusted source (sorry, Slashdot, you do not fit into this category), and if it's going to get to me and my small circle of friends and acquiantences, it had better start selling.
But good luck to the guy. At least he's writing a book, rather than writing all of his prose in Slashdot comments!
Oh yeah... (Score:4, Insightful)
I remember THAT book. That's the book where Wolfram compares himself to Newton in the first paragraph of the introduction.
Wolfram is a great math pro, but the only way he could help Newton is to shine his shoes.
It's like the von Neumann bottleneck, where 10 % of the code is run 90 % of the time. Truth be told, the REAL von Neumann bottleneck is that only 10 % of computer scientists are even 90 % as smart as von Neumann.
I'm voting for clever marketing (Score:5, Insightful)
Also, you need Mathematica to run the programs.
So, if you get hooked by the online text, Wolfram can count on 1 book sale, and maybe 1 Mathematica license (if, like me, you don't study/work somewhere with a site license).
A Good Step Forward (Score:4, Insightful)
Wolfram's broad sharing of his work, while still limited (you still need an internet connection, at least momentarily, to save or print it) is a terrific step forward in sharing information with a broader audience that may be interested in his work. I was one of the purchasers of his book when it was first published, but it was expensive enough (even while heavily subsidized by Wolfram himself) that not everyone who was interested could find a copy.
By publishing on-line, Wolfram does something courageous as well - rather than simply submitting his work to academia and using their vetting procedure, he's opening up his work for criticism from a much, much wider body of critics. Forums like /. give us the opportunity to discuss the merits of his work - by the end of today, there will be many critiques of his work on this page, and everyone who takes the time to read those will come away from the discussion with many different perspectives that they might never have stumbled upon.
It's true that Wolfram has his own agenda to push here, and it might be compared to self-publishing a newspaper that only focuses on what you want, but one could argue that about nearly anything that's published, and I'd rather have the material disseminated so that I can read it and come to my own conclusions.
It's not the money, it's the claims (Score:5, Insightful)
I think the thing that offended most people is that Wolfram seemed to be taking credit for other people's ideas. And also, he comes off as being tremendously pompous. He hid away for ten or more years, then comes out with a book claiming, as per the title, to have invented an entirely new way to solve problems. What's he got? Algorithms and cellular automata.
Re:Or perhaps... (Score:2, Insightful)
Science is, in a nutshell, a clearly defined mapping from reality towards a formal structure.
In this sense he is doing science.
Science is the better the simpler the formal structure, compared to the amounts of reality mapped into it.
Theoretical Physics is arguably furthest along this road.
Is it good science? From what I've read of it, no. He maps an emergent phenomenon in reality into an emergent phenomenon in a cellular automata.
However, his CAs provide a wide array of well defined mathematically sound emergent patterns, which have been notoriously elusive. So his approach to match the emergent patterns in mathematics with those in reality does indeed constitute a new kind of science. But it's not good science. And it doesn't show new ways of creating new good science, because there is no understanding involved, no reduction in the structure of reality into simpler formal structures.
Ultimately we are still at the very beginning with understanding emergent structures, and Wolframs book doesn't push the frontier a lot, but his approach is as valid as any other in this area.
-Frank
Re:obligatory (Score:2, Insightful)
For a change, this is actually a legitimate question. Having browsed through a friend's copy (thank god I didn't splash out for one of my own) I have come to the conclusion that it is "whack". A colossal exercise in vanity publishing, nothing else (except for the gratuitious advertising for his own software). Pretty pictures though.
review (Score:2, Insightful)
I saw Wolfram speak shortly after the book came out, and it was almost laughable. He made a sequence of sweeping generalizations and, so far as I could tell, backed none of them up.
That said, there is some useful stuff in the book (albeit, not all contributed by Wolfram) but it is a beautiful example of why the standard process of peer review and sharing work with your colleagues is a good idea. Wolfram did neither of these things and the book is the poorer for it.
Re:So What's the Deal? (Score:2, Insightful)
So what's the deal? Outside of Wolfram's ego, of course.
The "deal" is that he's trying to appear cutting edge and jump the genetics/bioscience bandwagon by using biological metaphors. That's all there is to the book, as far as I can tell.
thinking this is crap? (Score:2, Insightful)
This is not how science works... (Score:5, Insightful)
From one of the links [wikipedia.org] discussing Wolfram's use of others' work:
This really highlights what a megalomaniac Wolfram is. While he may be remembered after his death, I imagine it will be for his insufferable ego, not for his scientific achievements.
Oh, and regarding Mathematica: its use by students should be banned until they are able to outperform it in terms of mathematical sophistication. Its overuse in universities is leading to an intellectually-stunted generation.
Re:thinking this is crap? (Score:3, Insightful)
Elgon
Re:Before anybody complains about Wolfram's book, (Score:5, Insightful)
True. The universe is described by complicated equations wrought by the human mind.
Re:New Kind of Hype? (Score:4, Insightful)
Pretty much any idea, if expressed sufficiently broadly and vaguely, will seem "neither unique nor unexpected."
Re:New Kind of Hype? (Score:5, Insightful)
And you the mighty gowen have contributed so much to society. Wolfram is indeed a genius.He is up there with the likes of Stephen Hawking, just in a different field. He did build some of his work off of other people's, but that is what science is. Modern Physics was built off of Newton's work which was then in turn added to by others until it has reached its amazing point in this day and age where we can send a small robot to a crater on a planet millions of miles away. Quantum Mechanics is also commonly contributed to Albert Einstein who's work was then contributed to by others. But before Einstein there was Max Planck. The reason the human race has progressed as such is because we learn from our predecessors and build on that knowledge. Yes Wolfram used a lot of work based on others (and he cites it all), but he has also studied Cellular Automata for somewhere between 12 to 20 years.The guy is smart and I've read this entire book cover to cover and have referenced it several times. He makes insights into the field that no one has ever mentioned before. And after hearing him speak at one of his conferences in New York I have the upmost respect for him and his brilliance. If you still don't believe me, read the book, or just go to his website and browse it. Even better, try to duplicate Mathematica and see how far you get.I'm not trying to start a flame or anythign like that, but unless you are really familar with this guy then you can't really comment. I've followed his works for at least 5 years now.
Regards,
Steve
P.S. Another guy worth checking out who is affiliated with Wolfram is Eric Weisstein who has a great website and sells an encyclopedia [amazon.com] for mathematics, which I also own and couldn't live without
Re:Either way a good thing (Score:3, Insightful)
Well... geeks I know wouldn't have a problem. They fork 100$ (or whatever, I'm no Star Wars freak) for an AT-AT walker, or 500$ for home stereo system, and so on. And yet always whine about not having enough money for anything, boss being a prick for not giving a raise, and so on. :-)
Plus, don't computer games nowadays cost about that much ("when I was a kid, games came in tapes, and cost just 6 guids!") as well? I've yet to meet a game junkie that does NOT buy latest sequel to their favourite series, due to price.
So, 45$ wouldn't be much of a problem with any geek with a job; IF they were interested in it. Of course buying a 5$ paperback would be easier purchase, but it really comes down to interests.
You should ! (Score:5, Insightful)
This is quite true, notwithstanding the fact that he is precisely the source for much of this old material in the first place ! Wolfram is really a strange guy, and he does have weird ideas (especially on evolution), but at the end of the day he really started something deep.
Wolfram did not invent cellular automata, but he was the first one to study them in a scientific way. And he did find interesting things (papers here [stephenwolfram.com] - caution, big hairy theoretical physics maths inside, but the central idea is quite clear)
First: very simple rules (a 1-D cellular automaton in which each cell depends only on its current state and that of each of its neighbour) can lead to arbitrarily complex behaviours regardless of initial conditions. But this is not the really interesting thing.
Second: Possible behaviours for a simple cellular automaton can fall in 4 categories: frozen (nothing changes), periodic, chaotic (measurably chaotic behaviour in which no recognizable pattern appears), and most importantly "complex": patterns emerge, propagate through the system, interact together in complex and non-trivial ways. Conway's game of Life is the most famous exemple of a class-IV cellular automaton, but Wolfram found a few much simpler ones.
There is something deep there. You probably heard about "chaos theory". Well what Wolfram says is that this is not the really cool stuff. If you think of it, chaos is just as boring as frozen, non-changing states. If you modify something in a frozen state, well your modification either stays there forever, or is immediately swallowed into oblivion. In the chaotic state, any modification you make will instantaneously disappear in the general whirlwind.
But there is a small zone between these two extremes, in which a modification may give rise to patterns, structures, complex bursts of information that appear, grow, propagate and interact. This is what Doyne Farmer and Chris Langton later called the "Edge of Chaos" [viawest.net], where interesting stuff can happen : an actual phase transition, often governed by a small set of parameters (possibly just one), between boring order and completely chaotic states. Around this pahase transition, interesting things can appear.
The world exist because the laws of physics are at the edge of chaos. Would the physical world be chaotic, no structure would ever appear, it would instantaneously be dissolved. In a frozen state, the universe is a black rock. Similaraly, life exists because chemistry is also on the edge of chaos. Molecules can assemble, interact in complex ways and produce order, patterns, structure.
There is something deep there. This guy, together with people like Chris Langton, Doyne Farmer, Stuart Kauffman, is one of the Founding Fathers of complexity sciences. "How do complex systems arise ? If I have a system, what are the condtions under which it can produce freeze, go straight away to chaos, or produce interesting things ? How do structures emerge in a given system ?" Take any paper by any of these four, and you immediately get into mind-boggling stuff. "Life, the universe, everything" - and it's a bit more complicated than 42.
Wolfram goes on. He (and his students) proved that even elementary cellular automaton can actually be universal Turing machines (unsurprisingly, these are class-IV automata). Thus the undecidability principle must be applied to them: you cannot guess, for a given cellular automaton, what the result will be after N iterations - or at least, you cannot do it with less calculations than it would take to actually perform these N calculations.
If such a simple thing as an elementary CA can give rise to universal computation, then universal computation and (most importantly) un
Re:Nothing to see here (Score:3, Insightful)
Yes: he is arguing that, at a very high level, current scientific approaches to large systems are flawed. I understand that that's off-putting to many, but you can't expect such a broad change in perspective to be done a) from the bottom-up nor b) without substantial leaning on the research of others. It's a theory, and a big one at that, so you accept that it's there and you don't base any substantial work or other theory on it until it is beaten on a bit. All I see in these responses is An Old Kind of Science that has been practiced by entrenched organizations like churches for thousands of years.
This kind of knee-jerk ostricization of bright people with ideas is just plain wrong. Maybe he's wrong about the idea, but you don't smack a guy down just for writing his ideas down, you correct where wrong if you want to be helpful or ignore if you don't. Being rude just isn't called for.
He claims no where in the book that I could find that others had not also covered much of this ground, but I don't think it's at all fair to say that that makes this book wholely unoriginal or at all ignorable. After all, he's relying on a body of mathematics that has been carved out over the last 3000 years! I also don't think that it's fair to say that ideas that he shares in common with others were not his. He's a bright enough guy that I think it's quite possible that in 10 years of cloistering himself off and working on this, he re-invented a few wheels. So what? That should neither diminish him nor those who covered the same ground before or in parallel with him (I don't think any less of Liebnitz, even though I'm not sure how to spell his name
Let's all just calm down, take a deep breath and try not to be the Church of Established Science for a moment.
has anybody actually read the whole book? (Score:4, Insightful)
I have to say (not having read it) that when someone says they have written something that breaks conventional wisdom, and the only response is from people saying it's rubbish EVEN THOUGH THEY HAVE NOT READ THE ENTIRE BOOK, I begin to mistrust the views of anyone saying it's rubbish.
If you haven't read the thing, having any definitive view on it is bogus. Trying to convince others that your view is correct is even more bogus. The closest we've got to a review is "I read a review by someone else and...." WTF? What makes you think that reviewer read it either?
And these same people say this wolfram guy is a charlaton? His critics seem worse, somehow.
Re:New Kind of Hype? (Score:3, Insightful)
You're still more succinct than Wolfram, who over the course of these 600 pages reiterates his position several thousand times without ever really stating what it is he's claiming. It's damned annoying, considering I spent $45 to get thusly annoyed.
Here's what I got from Wolfram's book. Anything around you that seems completely random, impossible to generate, isn't necessarily so. There are patterns in the randomness which are the result of the interaction between the intracicies of the process and the data, ones that act one each other regarless of the starting form. And the end result of that, is that complex ordered forms are to be expected even when performing very simple comparisons.
I know, you've heard all this before. You assumed everybody agreed with it. What Wolfram's done is give a "pep talk" to people trying to perform complicated models that they should step back and see if they can't get their model to create itself by simplifying the rules. That's the "new kind of science"...boiling complex multivariable equations down to the processes that generated them.
If anything, AKOS is a computer-science primer for everybody BUT physcists. There's a chapter on applications of it (chapter 8 i think). It's the most useful one in the book.
A note to those pursuing academic careers.. (Score:4, Insightful)
I've seen this reaction across any number of technical or non-technical academic fields. Sometimes the thrashing is justified, usually it's not. But it always happens.
As someone once said: "The politics in academia are so nasty only because the stakes are so small."
Re:You should ! (Score:3, Insightful)
In terms of his "you can explain everything with CA" thesis, Wolfram basically provides little more than preliminary results. The work is intriguing and many aspects appear promising, but as far as I can tell, he hasn't actually solved any major problem in biology or physics using his approach. There have been other examples of mathematical insights that were supposed to revolutionize biology (remember Catastrophe Theory?), and they have rarely turned out to be as revolutionary as their proponents expected. It might be a useful tool, but I'm waiting to see something of value built with it.
Re:Yes (Score:4, Insightful)
The AC is half right. It is not a great work like the Principia Mathematica. He spends way too much time dwelling on his cellular automata. His book could have used an editor willing to tell the brooding genius that his ideas weren't really explained well. His layman's language and reiteration of his WAY understated hypothesis make him seem like more of an amateur than he is.
But he's not doing it for the money. The book is huge, printed using an expensive process and self-published. Even still, it was cheap...$45, less than half the cost of a physics textbook and about what I'd expect to pay for a good poetry collection. To self produce and distribute such a massive and expensive to produce book, even with the massive press behind it, he can't have recouped enough to make the effort worthwhile.
It's my opinion that Stephen really thought he was on to something. It's also my opinion that he was on to something, but that he dwelled too much in the mechanics to really explain what he was doing to people who don't care about cellular automata. I also wonder if his programs are influenced by hidden variables (like his choice of borders, and their effects). Really, this book needs a companion volume written by somebody who can explain what the Stephen's talking about when he says "New Kind of Science" without going on and on about series numbers and alternating gray squares.
Re:Enjoy reading his stuff (Score:4, Insightful)
While that's true the way it's written, I'd say: To do research is a necessary, but not sufficient requirement. A PhD is about gaining expertise in a field of science, and advance the knowledge of that field by doing research (and publishing it, or at least have it publically scrutinised). To prove the 'expertise' part (but not necessarily atain it) you're usually required to take classes.
Note that there's in general no way to skip the first point, by being clever. It takes work even if you're the brightest SOB to be walking around today. The world is full of smartarses of all levels of intelligence that know only of their own ideas, without as much as a clue about anybody elses, past or present.
In my humble opinion, the first part is really the tricky part these days, with so much being published. Staying abrest of your field, so that you can correctly value the judgements of your contributions to the field (or your ideas before they become contributions) is a bit of a chore, and it's easy (too easy in fact) to miss that vital piece of information that puts your work in a whole new light (such as "that's been done before").
Re:I've seen him talk (Score:3, Insightful)
Surprisingly, despite his continuous repetition that this is a great revolution, he doesn't do a great job defending that position. Take his writing on fluid flow and the inadequacy of equations. He rehashes the traditional problem, offers the CA take on it, and fails to give us anything of any practical use. If he could compute a solution faster, with more accuracy, or give the solution to an unsolved problem with this technique, that would be great, but he can't.
Or take his views on biology. He says there could be a small set of genes that are a "leaf generator" and with a few small tweaks, generate all known leaf types. No duh. It isn't the only possible view on it, but its many people's naive theory. Ditto for shells.
This happens all throughout the book. He finds something surprising that I think most wouldn't. He than shows that it's not surprising from the CA perspective, and he basically stops there. Lameness, I say.
(If I'm wrong, do your
Re:Nothing to see here (Score:3, Insightful)
The point is that all Wolfram has done is say "look, cellular automata are cool and they can model complex stuff". We knew that. We knew it 30 years ago. The reason people hate him is that he's utterly convinced that he's a genius, so he arrogates this title of "A New Kind Of Science" to his incredibly old kind of science. Also, he doesn't actually produce any useful results (there's some vague handwavy wibble about modelling a growing leaf with a CA - gee, d'ya think a CELLular automata might be a model of a leaf?), so his New Kind Of Science is all Kinds of useless. Get some experimental results in and come back.
Re:New Kind of Hype? (Score:5, Insightful)
Re:has anybody actually read the whole book? (Score:1, Insightful)
I haven't read David Irvings holocaust denial books, so by your logic, I can't say that holocaust denial is wrong.
Re:Nothing to see here (Score:2, Insightful)
It's not enough to be silent on the question of whether others have already covered the ground. A respectable writer has to devote serious effort to documenting previous writings on the subject. It's not even enough to say "this has been done"; you have to say by whom, when, in what journal...
Bibliographies serve an essential and fundamental purpose. They are not just there to make typesetting difficult!
Serious scientific books and papers list everything that's even **related** (well, closely related) to the topic at hand. The burden is on the author, not the reader, to indicate how much of the material is new.
zach
Re:This is not how science works... (Score:3, Insightful)
How is having a computer look up an integral in a database any different from looking it up yourself?
Because it is often the case that the solution to a given math problem is less important than the means used to obtain that solution. For instance, consider Zeno's paradox: to explain how Achilles can overtake the tortoise requires one to consider such concepts as infinite summations and limits. Just to assert that Achilles will overtake the tortoise offers no insight into the paradox whatsoever.
Re:Before anybody complains about Wolfram's book, (Score:4, Insightful)
The book doesn't point out anything more than hints and allegations of what you said. As other people have pointed out, he solves nor resolves NO existing problem with his approach, he just shows how CA behavior maps to real systems behavior and says "aha!" and moves on.
When you combine that with the VAST amount of self-horn-tooting that he engages in, you get a fairly dull book.
Re:This is not how science works... (Score:2, Insightful)
Whats that supposed to mean? Answer a question Mathematica can't? Nearly every college math student I know can do that.
Or perhaps answer every question that Mathematica CAN answer? I highly doubt that there's a mathematician in the world today that can do that.
Mathematica is a tool, the results you get out are only as useful as your understanding of them.
Oh, and intellectually stunted generation? Intellectually stunted because students of today no longer learn several dozen arbitrary tricks to manually solve differential equations? Pullease. Mathematica (or Matlab, or Maple etc) gives students a tool to investigate problems that were previously inaccessible--that hardly makes them intellectually stunted.
Time to call your bluff (Score:3, Insightful)
Who needs to read the whole book? (Score:3, Insightful)
Re:Time to call your bluff (Score:3, Insightful)
Regards,
Steve
P.S. If you still deny that my argument isn't strong enough, just reply and in a few hours when I have time I'll give you some irrefutable information. Take care.
Re:New Kind of Hype? (Score:4, Insightful)
That's probably true by his own estimation. I'm surprised that you say you read the book. I did too, and while there are a few interesting things in there, for the most part it's a lot of chest thumping and self-promotion. He continually trumpets how "simple programs" - i.e., cellular automata - will surely explain all of the mysteries of the universe and that therefore he is the second coming of Isaac Newton. Fair enough; on an intuitive level I can see how this might be so, and I eagerly plowed through the book waiting for some solutions to physical problems that would illustrate his thesis. Nothing of the sort was to be found. All we get is, "Looky here! More pretty patterns from my simple rules!" It was as if Newton, instead of developing the Calculus and actually applying it to physical problems, had just waved his arms and said, "Surely there are mathematical equations that govern the Universe!" and left it at that. Now that's an important insight, but if that's all he did we probably wouldn't even know his name.
While I don't doubt Wolfram's contribution to CA and discrete mathematics, he's trying to join a club for which he hasn't (yet) paid his dues.
Quantum Mechanics is also commonly contributed to Albert Einstein
You're not a physicist, are you? That's just not true. Einstein resisted the ideas behind quantum mechanics for a long time; he couldn't accept that "God plays dice with the Universe". I'm not sure that he ever really accepted it.
Re:New Kind of Hype? (Score:5, Insightful)
I have worked in several of the labs where Steve has worked. Does not play well with others is a common conclusion.
The big problem with Steve's book is that he is simply unable to see that a large part of what he is proposing is simply stating existing ideas in a different notation.
Einstein surrounded himself by people who he considered his intellectual peers, people like Kurt Goedel. Steve shut himself up in a room for ten years and basically talked only to the people he felt like. He surrounded himself with a bunch of sycophants in the manner of a pop star - we have all seen what that has done to Michael Jackson. I decided not to read the book after I heard the gushing haigographies given by his employees.
It is not surprising that the book got the reception it did. When I heard Steve talking about it I kept thinking 'hammer, nail'. Steve has been working on finite state automata for years. But the standard model of physics today has at its core an idea that is pretty close to being a collection of finite state machines. It is already known that you can simulate one with the other.
I think that the problem that Steve has created here is that the manner of his presentation closely resembles that of a crank. I get letters from cranks calling themselves the new Einstein and Adam Smith combined, actually everyone who has been published in the letters section of the London Times does.
Steve is incredibly bright, but unfortunately no intelligence in history could match his ego, and his does not either.
Re:Open src compute algebra systems, was: Marketin (Score:3, Insightful)
Mathematica is much more of a rewrite of SMP, which was the symbolic math program Wolfram and Chris Cole wrote at Caltech, because Macsyma was too limited for the physics problems they were working on.
To call Mathematica essentially a rewrite of Macsyma is like saying that Java is essentially a rewrite of Altair Basic.
Re:has anybody actually read the whole book? (Score:3, Insightful)
The same is true of NKS. Open it to almost any page, and three things stand out (1) plenty of pretentious claims (2) large number of unatributed ideas, (3) dearth of truly new insight.
God knows we scientists have put up with plenty of arrogant scientists because at the end of the day the could deliver the goods (Millikan comes to mind).
Wolfram's book fails the open at random page test. The book is pseudoscience and I don't have the time, inclination or more importantly the *need* to read the remaining 1400 pages of drivel to prove it.
Re:Skeptic Magazine takes Aim (Score:3, Insightful)
Welcome to specialization (Score:3, Insightful)
I suspect that many people said this about Sir Newton, who was also supposed to be an amazingly arrogant asshole. (This is not to suggest that Dr. Wolfram is Sir Newton's equal, just that someone being arrogant has hardly kept them from fame before.)
Oh, and regarding Mathematica: its use by students should be banned until they are able to outperform it in terms of mathematical sophistication. Its overuse in universities is leading to an intellectually-stunted generation.
I cannot agree.
I agree that it is producing a more highly specialized generation. I assume that you are acquiring or have graduated with a computer science or mathematics degree. When you started on your degree, were you required to learn the philosophical foundation of mathematics? How about the physics and chemistry required to build the computer that any practical implementation of your work would require use of?
At one point, a well-educated man could encompass most of the known fields of work. Later, it was still possible to understand a single field well. You could literally be simply a chemist, a physicist, or a mathematician. As the knowledge present in each field has exploded, the sliver of that field that can be fully known and understood by each person has dwindled. That is not necessarily bad -- it's simply a phenomenon that was abound to happen. It would be ideal for someone to fully understand, from the ground up, the field they work in, but that is less and less practical.
I can cook a nice side of garlic bread. However, I have no knowledge of how to grow garlic itself, or of what processes and safety measures are involved in the production of the flour used in the bread. I don't even really know what goes into the bread. I don't know how to ward off insects from the grain used in the bread. If you removed me from society, I would die. I simply cannot function -- I am too specialized -- without society.
Furthermore, given that knowledge has been increasing, each generation in a field will tend to have less an understanding of the fundamentals than their predecessors. This makes interdiciplinary knowledge sharing more difficult, and easier to make foundational mistakes, but is a prerequisite for the degree of advancement that we have achieved.
For example -- I have never manually determined a square root. I simply have never had the need to to so, and schools no longer taught one how to find one by the time I went through school. My parents needed to learn this information, but I did not. If you took away all my computers and calculators, I could not determine a square root for you. Oh, I might be able to come up with an inefficient algorithm and manually, slowly, come up with an answer, but I would really be, to some degree, unable to function without my computing devices.
If I needed to implement a calculator one day (and, incidently, calculators use different methods than the manual method we do to obtain numerical approximations of square roots), I could look up how people once did things by hand. However, generally, a specialized profession (calculator designer) has managed to take over and handle much of my work for me.
Using Mathematica to do, say, advanced integration, makes perfect sense to me. Running through a vast collection of tricks to get a stubborn formula to integrate is, frankly, a waste of human time. A phenomenal amount of human time is wasted memorizing and trying to apply integration tricks. Why bother? Sure, it's not inconcievable that one day, I might do something sub-optimally because I lack knowledge in the area. However, if I *know* that I need to know something, I can track down an expert who does know. In the meantime, I will enjoy *known* significant time savings.
I'm sure every generation has complained about this as specialization increases. It isn't new, and I don't believe that it's particularly negative.
Discrete universe makes CA a nice physical model (Score:3, Insightful)
The idea that even space and time are discrete (composed of tiny parts) instead of continuous, could have some very interesting implications. Lots of systems that are discrete appear continuous, but atomic theory made a lot of difference in physics and chemistry.
I don't disagree that Wolfram is a crank, but he's a bright crank who is stealing from interesting people and talking about interesting things. I've met those people before, and they can be worth talking to as long as you keep your perspective. Like a paranoiac who's lead an interesting life. Listen, just don't get too close.
I'll be looking over ANKOS online if the terms aren't too onerous. If they are, I'll buy a used copy of the book. Since he sued to prevent a presentation at a mathematical conference, I'll never buy a new copy. That's just wrong.
Re:Welcome to specialization (Score:3, Insightful)
Thanks for the long, thoughtful reply -- a rather rare occurence on Slashdot, unfortunately. For the record, my training is in astrophysics, so I use math on a daily basis but math is not my 'thing'.
It's Friday night, so I'm only going to write a brief response before knocking off for the weekend. Continuing with your aposite square root analogy, my main point is this: sure, we should be using a calculator to do square roots; but only once we are familiar with what a square root is.
A few years back, I was teaching physics out in a small village in Ghana (Africa). Surprisingly for the poor rural community I was in, a number of kids had calculators. And hell, they could do square roots. But if you asked them what made 2 the square root of 4, they had not a clue. They were able to get by regarding the square root process as a black box, but they had no fundamental understanding of it.
Looking now at integration, when I ask a student why the integral of x wrt x is x^2/2, I don't want to get the answer: 'because Mathematica says so'. I want to hear something which shows at least some understanding of the process of integration. For instance, 'because the derivative of x^2/2 is x, and the fundamental theorem of calculus demonstrates that integration is the inverse operation to differentiation.'
In my day-to-day work, I certainly do use Mathematica to take the tedium out of integration and other problems. However, without Mathematica the chances are that I could still solve these problems, albeit at a much slower rate. Because of this, I feel that I have more insight into the physics of the problems I'm solving.
Returning now to the square root case, ponder this: for someone whose understanding of the square roots is limited to regarding them as black-box functions of calculators, how can they understand why the square root of a negative number causes the calculator to throw an error (assuming real math)? For them to obtain this insight, they need to learn a little more about square roots than the fact that a calculator can calculate them.
Re:[ Doesnt ] work well with others (Score:2, Insightful)
You need to read Gleick's biography of Newton. He makes a very compelling case that when Newton wrote that, he was just kissing ass (it was in a private letter) and that he had absolutely no respect to the "giant" he was addressing it to.
Re:Welcome to specialization (Score:3, Insightful)