Comments on: Stephen Wolfram
http://www.metafilter.com/17255/Stephen-Wolfram/
Comments on MetaFilter post Stephen WolframMon, 20 May 2002 11:32:02 -0800Mon, 20 May 2002 11:32:02 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Stephen Wolfram
http://www.metafilter.com/17255/Stephen-Wolfram
<a href="http://www.stephenwolfram.com/">Stephen Wolfram</a> has finished his book, "<a href="http://www.wired.com/wired/archive/10.06/wolfram_pr.html">A New Kind of Science</a>," which purpotedly is being espoused as a paradigm shift in many fields. But, I'm starting to see a very reductionistic attitude in many of the main theorists of complextity theory and emergent phenomena. Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea? Isn't math a man made mapping and can the Universe be reduced to an equation by a man? Still this book is going to be groundbreaking. Read the following exceperpt from the <a href="http://www.wired.com/wired/archive/10.06/wolfram_pr.html">wired.com</a> article:
q: "I've got to ask you," I say. "How long do you envision this rule of the universe to be?"<br>
w: "I'm guessing it's really very short."<br>
q: "Like how long?"<br>
w: "I don't know. In Mathematica, for example, perhaps three, four lines of code."<br>
link via <a href="http://www.protofunk.org">protofunk.org</a>, old similar <a href="http://www.metafilter.com/mefi/14205">thread</a>post:www.metafilter.com,2002:site.17255Mon, 20 May 2002 11:16:42 -0800nakedjonStephenWolframWolframsciencemathematicsphysicsWiredBy: gordian knot
http://www.metafilter.com/17255/Stephen-Wolfram#278431
I wondered how long it would take before someone brought up the "reductionistic" argument. Just because something can be expressed in a few lines of code, that doesn't mean it's nothing more than those few lines. Maybe the whole idea of reductionism is nothing more than an interpretation by the literal minded. And just what kind of gender-bias would you have to come up with if Wolfram happened to be a woman instead of a man?comment:www.metafilter.com,2002:site.17255-278431Mon, 20 May 2002 11:32:02 -0800gordian knotBy: rcade
http://www.metafilter.com/17255/Stephen-Wolfram#278432
<a href="http://www.metafilter.com/mefi/17072#274995">Quintuple post</a>.comment:www.metafilter.com,2002:site.17255-278432Mon, 20 May 2002 11:33:12 -0800rcadeBy: atom128
http://www.metafilter.com/17255/Stephen-Wolfram#278458
The more I read about Wolfram (and it's interesting, I look forward to the book eagerly), the more I like the philosophies of Camus. Create your own meaning.comment:www.metafilter.com,2002:site.17255-278458Mon, 20 May 2002 12:15:57 -0800atom128By: hob
http://www.metafilter.com/17255/Stephen-Wolfram#278459
<i>Quintuple post.</i>
Yeah, and we'll probably have at least one more in a couple of months once somebody's managed to plough through it.
<i>Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea?</i>
What if it is? That doesn't make it untrue and it doesn't make those lines of code less worth knowing.comment:www.metafilter.com,2002:site.17255-278459Mon, 20 May 2002 12:17:59 -0800hobBy: Su
http://www.metafilter.com/17255/Stephen-Wolfram#278460
Kurzweil <a href="http://www.kurzweilai.net/articles/art0464.html?printable=1">rips him a new one</a>.
Okay, it's not that bad, but he tries to point out some major holes in the idea.comment:www.metafilter.com,2002:site.17255-278460Mon, 20 May 2002 12:18:02 -0800SuBy: josh
http://www.metafilter.com/17255/Stephen-Wolfram#278461
Seriously now, not only has this been posted a zillion times, but I fail to understand what is either phallic or somehow 'male' about this idea. Superficially speaking, I would think it was the 1,100 page <i>book</i> that was 'phallic' or 'egocentric' or what have you -- not the compressed equation. And speaking more pointedly, isn't all of science, at least physics, reductionist in intent? And isn't that what Wolfram is trying to <i>undo</i>? As I understand it, his contention is that it is impossible to reduce certain complex behaviors into physical laws; he's saying that a 'few lines of code' generate 'complexity' within which behaviors occur unpredictably and spontaneously. He is generating <i>models</i>, not laws.
Is that reductionist (or even what his book is about)? I have no firm idea but it seems to me that if it is, it is different in character and intent from the 'reductionism' (or, as it were, 'science') practiced by others. Explain this phallo-centrism/reductionism/Wolfram link more. Has anybody read the book who can comment?comment:www.metafilter.com,2002:site.17255-278461Mon, 20 May 2002 12:18:39 -0800joshBy: n9
http://www.metafilter.com/17255/Stephen-Wolfram#278465
I bought this book yesterday (it was actually hard to find in NYC, finally spied it at St. Mark's Books) and read the first 45 pages.
The ideas are *quite* reductivist in a way very different than nakedjon is implying. Having read a whopping 3-4% of the book already I see that he is making the case for the Universe not being equations so much as algorithms. Very, very different things, these two. Algorithms are functional, procedural concepts and express something far different than an equation. You express an algorithm in some finite numbers of code-lines, but they have a life of their own, so to speak, and this book seeks to point out that it doesn't take a lot of complexity in the algorithm to generate a *lot* of complexity in the function/output of that algo. It's pretty cool stuff, despite Wolfram's universe-sized ego.
And, BTW: <i>"phallus-extension/masculine overdriven idea"</i>? I think that this is a pretty dumb way to dismiss an idea. Actually incredibly dumb.
And, Kurzweil is a complete nimrod. The man's books are jsut one big parade of fallacy... it makes my day complete that he is poking a hole in someone else's ideas. I've met him a couple of times and he jsut oozes self-absorbed bullshit to the point that I have to resist the temptation to make it my life's work to prove everything he says wrong. Not that Wolfram's going to turn out any different, mind you.comment:www.metafilter.com,2002:site.17255-278465Mon, 20 May 2002 12:22:38 -0800n9By: Hieronymous Coward
http://www.metafilter.com/17255/Stephen-Wolfram#278466
<i>nakedjon: Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea?</i>
Oh please.
This idea may or may not have merit; its merit will be determined by the same processes that determine the merit of any other scientific idea. The notion that the laws of physics are the <em>unique</em> product of a sexual or political bias does not hold up to scrutiny -- at least, not to <a href="http://www.physics.nyu.edu/faculty/sokal/lingua_franca_v4/lingua_franca_v4.html">much</a> scrutiny.
Unless there's a Wimmin's version of Newton's Law out there... F=2ma? I'd love to see the experiments...comment:www.metafilter.com,2002:site.17255-278466Mon, 20 May 2002 12:22:42 -0800Hieronymous CowardBy: n9
http://www.metafilter.com/17255/Stephen-Wolfram#278476
ok, I read the whole Kurzweil response. He doesn't rip anyone a new asshole. He just goes on and on about how Wolfram's book can't be all that important because it doesn't resemble Kurzweil's own thinking about strong AI, which has little to do with Wolfram's book. I guess Kurzweil thinks there is only enough room for one meglomanaical my-big-idea-will-change-everything kid on the block. Man, I feel all gross from reading that essay... Ray is just, man, such an intellectual <i>pig</i>.
his dismissals seem to follow along the track that Wolfram's 1-d and 2-d algos don't 'evolve' into AIs:
"...they are interesting (and intelligent) only to a degree. Moreover, they do not continue to evolve into anything more complex, nor do they develop new types of features. One could run these automata for trillions or even trillions of trillions of iterations, and the image would remain at the same limited level of complexity. They do not evolve into, say, insects, or humans, or Chopin preludes, or anything else that we might consider of a higher order of complexity than the streaks and intermingling triangles that we see in these images."
Ugh. Like he often does, he wholly missing the point. The book demonstrates the foundation of a different mode of thought. You don't dismiss Calculus because performing differentiation doesn't resemble driving a Porsche. Most of his responses seem shallow and full of context switching and fallacies. Wolfram might be arrogant and he may turn out to be wrong, but at least he's not as pompous a jerk as R.K.comment:www.metafilter.com,2002:site.17255-278476Mon, 20 May 2002 12:46:57 -0800n9By: davidgentle
http://www.metafilter.com/17255/Stephen-Wolfram#278477
Wolframfilter?comment:www.metafilter.com,2002:site.17255-278477Mon, 20 May 2002 12:48:02 -0800davidgentleBy: RevGreg
http://www.metafilter.com/17255/Stephen-Wolfram#278492
<cite>Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea?</cite>
Sure it is, in the same manner that anything that can be even remotely associated with any action that contains the most vague and/or obscure male attributes can be dismissed for that overdriven reason rather than being accepted or dismissed by it's own merits.
Quid pro quo.comment:www.metafilter.com,2002:site.17255-278492Mon, 20 May 2002 13:14:47 -0800RevGregBy: nakedjon
http://www.metafilter.com/17255/Stephen-Wolfram#278499
What's the cultural, gender, and class makeup of mefi members anyway? Just kidding! The megalomaniac/egomaniac complex of many proprietors in different fields astounds me to the point of harkening warhol out of his grave. I'm more interested in how complexity theory is a description of a large network of intermingling parts and functions, yet it is one dude discussing the ideas and <b>specifically</b> addressing these ideas as his own. The wired article at least paints a picture of this guys taking the credit for all the people who are working on his book. I could see a book like this being written by a cast of characters like MeFi; an advanced network of social organization. But give me a break on this feudal lord commanding thunder. Its like hitler getting trippy on us again man.<br>
<b>I am a big proponent of complexity theory and emergent phenomena though and of both Kurzweil and Wolfram's work and vision in the field.</b>
<br>
The interesting discussion about the masculine/feminine argument in relationship to science is that it is historically framed and continues in history to reduce the viewing range of the field. I mean come on, we map our entire concept of mathematics onto the world just like we [humans] map onto the Universe the concept of time and increments.comment:www.metafilter.com,2002:site.17255-278499Mon, 20 May 2002 13:20:05 -0800nakedjonBy: nakedjon
http://www.metafilter.com/17255/Stephen-Wolfram#278500
Those ideas aren't dismissed, but critiqued, discussed, and talked about. Just as Wolfram is probably trying to stir up a stagnant pond, why don't we jump in for a swim and mix it up some more [ie, phallus comment].comment:www.metafilter.com,2002:site.17255-278500Mon, 20 May 2002 13:21:52 -0800nakedjonBy: bshort
http://www.metafilter.com/17255/Stephen-Wolfram#278507
NakedJon, just so you know, mathematics exists independantly of us. We're not mapping math onto the universe, we're hoping to understand the universe through math. The math was there first. 2 is the only even prime whether or not there's anyone in the forest to observe it.comment:www.metafilter.com,2002:site.17255-278507Mon, 20 May 2002 13:32:02 -0800bshortBy: sonofsamiam
http://www.metafilter.com/17255/Stephen-Wolfram#278518
bshort:
Math exists in the heads of humans. Only the counting numbers can be said (arguably, imo) to be 'natural;' all other math constructs are abastractions and generalizations of them. ('1/2' only means anything if a 'whole' is defined, where in nature can you find an irrational? etc.)
<i>we're hoping to understand the universe through math.</i>
The formulas of physics are lossy compression of observable data. We are indeed mapping math onto the universe. There is not necessarily one special set of equations that can predict the entire universe; the universe may be incompressible (and if it is, it's certainly not compressible below it's kolmogorov complexity).comment:www.metafilter.com,2002:site.17255-278518Mon, 20 May 2002 13:48:16 -0800sonofsamiamBy: fold_and_mutilate
http://www.metafilter.com/17255/Stephen-Wolfram#278526
<i> NakedJon, just so you know, mathematics exists independantly of us. We're not mapping math onto the universe, we're hoping to understand the universe through math. The math was there first. 2 is the only even prime whether or not there's anyone in the forest to observe it. </i>
~laugh~
Tautologies R Us, eh? (That annoying sound you heard was an electric can opener liberating annelids.)
Sounds to me like you're still Waiting For Godel, and buddy, lemme give you a hint: he's already been here and gone.comment:www.metafilter.com,2002:site.17255-278526Mon, 20 May 2002 13:56:36 -0800fold_and_mutilateBy: n9
http://www.metafilter.com/17255/Stephen-Wolfram#278555
Einstein was known to say that he was skeptical if numeracy, that there was something 'off' about numbers being here first.comment:www.metafilter.com,2002:site.17255-278555Mon, 20 May 2002 14:58:51 -0800n9By: vacapinta
http://www.metafilter.com/17255/Stephen-Wolfram#278575
<i>Einstein was known to say that he was skeptical if numeracy</i>
I am skeptical too. I am especially suspicous of how physicist often find that the mathematics for what they are trying to describe has already been invented. Riemann's geometry, matrix mechanics, Galois theory, Lie algebras were all mathematics invented as pure theory and later adopted as essential practical tools by physicists.
Its as if mathematics, as an extension of logic, tells us what sorts of things our mind can comprehend, lays out the basic templates. Later, in our encounters with reality, we search for and find or invent the particular "bucket" which can contain these new revelations.comment:www.metafilter.com,2002:site.17255-278575Mon, 20 May 2002 15:24:20 -0800vacapintaBy: Dark Messiah
http://www.metafilter.com/17255/Stephen-Wolfram#278584
I made it 4 paragraphs into R.K.'s mindless essay. I gave up after I got tired of being talked down to. Aside from that, even with my sore lacking of deep scientific knowledge, I could see R.K. completely missing the point and just latching on to irrelevancies and addressing them -- and though he was getting to the 'heart' of the issue.
Clearly, Kurzweil likes to hear the sound of his fingers hitting the keys and loves to waste server-space with his tripe. We get the idea, you're a "smarty man". Now go away and leave discussion to those who address the relevant points and don't automatically assume we're right.
I can't stand people who take themselves too seriously.comment:www.metafilter.com,2002:site.17255-278584Mon, 20 May 2002 15:37:41 -0800Dark MessiahBy: bshort
http://www.metafilter.com/17255/Stephen-Wolfram#278619
sonofsamiam: <cite>"The formulas of physics are lossy compression of observable data."</cite> Well, sure. And it turns out that's exactly what Wolfram is saying. The smooth, continuous formulas that are so easy to predict don't necessarily crop up all that often in the real world. We work with them because they are really good shortcuts. By plugging in a few known variables we can see what values a smooth, continuous function has at any point in the given metric space. Wolfram is saying that some things can only be computed, not predicted. Oh, and, pi is pretty darn irrational.
Fold: <cite>"Sounds to me like you're still Waiting For Godel..."</cite> Godel's theorem puts restrictions on systems of logic and the resolvability of those systems into provable theorems. This turns out, for the most part, to be a mathematical curiosity, and doesn't hinder the existence of mathematical objects. For instance, the fact that Goldbach's conjecture is just a conjecture, and is not known to be provable does not hinder us from discovering other theorems and proving or disproving them.comment:www.metafilter.com,2002:site.17255-278619Mon, 20 May 2002 16:41:40 -0800bshortBy: RevGreg
http://www.metafilter.com/17255/Stephen-Wolfram#278625
<cite>I could see R.K. completely missing the point and just latching on to irrelevancies and addressing them </cite>
Kurzweil seems overly excited by the concept that complex things are made up of lots of simple things - and that there is an underlying logic to the behaviors of these simple things that is correspondingly simple, yet these simple behaviors when combined produce more complex behaviors.
Wow. What a concept.comment:www.metafilter.com,2002:site.17255-278625Mon, 20 May 2002 16:51:49 -0800RevGregBy: Dark Messiah
http://www.metafilter.com/17255/Stephen-Wolfram#278655
Rev: are you agreeing with me, or not? I honestly can't tell and, as such, am unsure how to proceede. Help me, my feeble brain is failing me!!comment:www.metafilter.com,2002:site.17255-278655Mon, 20 May 2002 18:00:24 -0800Dark MessiahBy: mstillwell
http://www.metafilter.com/17255/Stephen-Wolfram#278669
E = mc<sup>2</sup>
That's pretty simple, and it has a lot of implications. I can believe four lines.comment:www.metafilter.com,2002:site.17255-278669Mon, 20 May 2002 18:30:58 -0800mstillwellBy: josh
http://www.metafilter.com/17255/Stephen-Wolfram#278694
Believe me, there is <i>nothing</i> more tiresome than a discussion of science/objectivity vs. social theory/subjectivity. <i>Nothing</i>. I come to MeFi to get away from my college courses, not to relive their worst, most nightmarish components. Ugh.
The fact is that, as one would expect, the physical sciences and social theory <i>do not</i> collide except when they are misinterpreted or generalized outside of their proper spheres. No one makes this clearer than Alan Sokal did with his <a href="http://www.physics.nyu.edu/faculty/sokal/lingua_franca_v4/lingua_franca_v4.html">hoax article in <i>Social Text</i></a>. It might be reasonable enough to talk about how psychology, say, has been influenced by social facts. But it is not sensible to talk about how physics has been influenced (and I think you would be hard-pressed to find an actual example of a development in physics that has had to be changed because of changing social ideas -- the heliocentric theory of the Universe, for instance, might have been inspired by the Bible, but was tossed because of observable data, not social change).
Nakedjon, if you think <b>this</b> particular set of theories is somehow 'phallocentric' I would be curious to hear why, but if there's no reason other than "science is masculine" then I don't think there is a discussion to have. Read Sokal's hoax article and tell me it doesn't sound pretty close to the kind of unusable position you're trying to take. (I'm a humanities kid too -- I've been known to <i>read</i> Social Text <i>on my own time!</i>)comment:www.metafilter.com,2002:site.17255-278694Mon, 20 May 2002 19:47:26 -0800joshBy: kfury
http://www.metafilter.com/17255/Stephen-Wolfram#278714
(putting on my egotistical Wolfram hat)
What I haven't heard anyone say is that it's not so reductionist to say that the universe can be summed up in 'three or four lines of Mathematica code.'
Mathematica, in its entirety, is intended to be an algorithm-cruncher, and it's hardly a small program. To say that the universe can be represented in a small amount of code interpreted by that program is to say that the program is already inheirently similar to the universe, and three or four lines of tweaking or 'direction' if you will, is all that is needed to bring the hundreds of thousands of lines of code already written into alignment with our particular universe.
If Wolfram so desired, he could factor those in to the program itself until it only took a few characters to set the right algorithm in motion.
What I (and I believe Wolfram) am(is) saying is not that the universe is as simple as 3 or 4 lines, but that Mathematica already operates on rules and principles very close to the universe.
That said, my book's arriving tomorrow. The first printing run was only 50,000 copies, costing Wolfram $12 apiece because he was so picky about production methods. This morning the book was Amazon's #1 bestseller. This afternoon it was already dropping because estimated delivery times changed from 24 hours to two weeks (and likely far more, waiting for the second printing).
I love mathematica, and I like books that make me think. Whether this is the next revolution in science or just another Pons and Fleishman, I'm sure it'll make me think, and possibly give me a few insights into the power of Mathematica. $45 well spent.comment:www.metafilter.com,2002:site.17255-278714Mon, 20 May 2002 20:47:23 -0800kfuryBy: nakedjon
http://www.metafilter.com/17255/Stephen-Wolfram#278747
Totally kfury...that was the reason I brought up this topic. I admire Wolfram's embracing of conflict to tweak some noggins and get people to take self-organize into a new structure to support a new science.<br>
Thanks for the article josh : ) . Um, the argument of gender typing of roles was not meant to be a "one liner," or reduction of the man wolfram (just as i said this idea seemed). The phallic comment had more to do with the way Kurzweil and Wolfram talk about themselves as if it is the truth (implying, so don't question it).comment:www.metafilter.com,2002:site.17255-278747Mon, 20 May 2002 22:50:53 -0800nakedjonBy: fold_and_mutilate
http://www.metafilter.com/17255/Stephen-Wolfram#278755
<i> Fold: "Sounds to me like you're still Waiting For Godel..." Godel's theorem puts restrictions on systems of logic and the resolvability of those systems into provable theorems. This turns out, for the most part, to be a mathematical curiosity, and doesn't hinder the existence of
mathematical objects. For instance, the fact that Goldbach's conjecture is just a conjecture, and is not known to be provable does not hinder us from discovering other theorems and proving or disproving them.</i>
Prove them? I'm with ya, friend. But do tell within exactly <i> which system you, a human, have chosen to prove them</i>, or even use them. Ya can't really just say the system is <i>mathematics</i> and leave it at that, as you well know. Believe me, I'm on your side, but I've searched (in vain) for mathematical objects like "2" and "primes" and Goldbach's conjecture and Chebyshev's theorem and even the Banach-Tarski theorem up every tree and down every rabbit hole...and found them all residing whole and *cough*consistent*cough only within the forests...the systems...set up by myself or some other sentient being.
If my hero Paul Erdos' <i>The Book</i> is Out There (and I believe it is), it's name is better just called Nature. Some describe her with Euclidean geometry, some with Riemannian geometry, some with Lobachevskian geometry. Some just sing songs of her. Which system do you want to use? The Book may be a single brass plaque floating somewhere in the plasma streaming out from the far side of the sun, or a crystal thought in the eternal mind of God. But I kinda very much doubt it. Think most mathematicians are Platonists? Could be, but I know many who are squarely in the formalist camp. At least, the issue among mathematicians ain't as clear cut as a blanket assertion that "mathematics is independent of us."
Behold living things, matter that contemplates itself -- recursive little bastards, all. That contemplation includes mathematics.
<i> I'm sure it'll make me think, and possibly give me a few insights into the power of Mathematica. </i>
Well, I'm a big fan of both Mathematica (despite hating the licensing restrictions...consider Reduce or even MacSyma if you're looking for tools) and emergent computation/physics/cognition too, but having played with the <a href="http://www.wolframscience.com/nks/programs/">sample programs</a> from the book, I think you'll find they don't actually express much of what Mathematica is really designed to do, any more than an implementation of CAs in C++ will really turn you on to that language. The programs are fascinating stuff in their own right, however. I'm enjoying the book...shades of Fredkin and Feynman and John Walker Wheeler at their most speculative.comment:www.metafilter.com,2002:site.17255-278755Mon, 20 May 2002 23:24:18 -0800fold_and_mutilateBy: hurkle
http://www.metafilter.com/17255/Stephen-Wolfram#278911
<i>Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea? Isn't math a man made mapping and can the Universe be reduced to an equation by a man? </i><br><br>Oh geez.... He never says that the Universe is in lines of code, just that there are simple rules that drive the complexity of the universe, and makes the comparison to Mathematica to indicate relative size of a ruleset in a complex system... Now how that has anything to do with phalluses is beyond me... <br>Additionally, I wonder why you complain about penis-something, then in the next breath, give man (not woman) all the credit for mapping math (though to what isn't clear). The universe itself <b>cannot</b> be reduced to an equation, but he feels that the equation, or rule that drives the universe can be deduced. Of course, this means absolutely nothing about the predictability of said universe, since he takes many points to indicate that simple rules give rise to complex unpredictable systems...<br><br>Just cause we know the rules to the game of Life (conway), doesn't mean we can predict what the 100th generation will like like without (a) having observed the same initial pattern in the past and watched it for 100 generations, or (b) completely and correctly modeling the Life universe and simulating the generations with the <i>same ruleset</i>. That's the point of computational equivalence...comment:www.metafilter.com,2002:site.17255-278911Tue, 21 May 2002 08:52:44 -0800hurkleBy: sonofsamiam
http://www.metafilter.com/17255/Stephen-Wolfram#278950
bshort: <i>Well, sure. And it turns out that's exactly what Wolfram is saying. The smooth, continuous formulas that are so easy to predict don't necessarily crop up all that often in the real world. We work with them because they are really good shortcuts. By plugging in a few known variables we can see what values a smooth, continuous function has at any point in the given metric space.</i>
That's all it is. <i>A really good shortcut.</i>
Just because you have a formula that describes a physical occurance as accurately as your instruments can measure does <i>not</i> mean that this formula is equivalent to whatever process actually governs the occurance. (and re: continuity, it's not clear that the universe is continuous.) It may be that the formulas that describe the universe's behavior precisely take up an entire universe.
Re: pi, where can you show me a Euclidean circle? At some resolution (atoms and below), it will break down ;)
But foldy has put it better than me.comment:www.metafilter.com,2002:site.17255-278950Tue, 21 May 2002 09:56:03 -0800sonofsamiamBy: clevershark
http://www.metafilter.com/17255/Stephen-Wolfram#278996
I find it quite amusing that this post starts out with what can only be seen as a political attack on material which the poster could hardly have yet digested... this 1200 page brick has been out for all of a week.
Get this nugget: complexity isn't nearly as complex as everyone so far as made it to be. That's the starting point of the book. You don't need to a turing machine with 200 different 'states' in order to generate a complex system from a basic set of rules... just 5. Wolfram himself is man enough to admit that he once missed that particular point in his early analysis of Rule 30.
What politics could possibly have to add to this debate at this point I have yet to fathom, but then again I left college after a BA because I saw the field I was involved it devolve into ritualistic navel-gazing at the graduate level.comment:www.metafilter.com,2002:site.17255-278996Tue, 21 May 2002 10:45:53 -0800cleversharkBy: bshort
http://www.metafilter.com/17255/Stephen-Wolfram#280418
Fold: <cite>"Prove them? I'm with ya, friend. But do tell within exactly which system you, a human, have chosen to prove them, or even use them."</cite>
See, I think you're looking for some sort of external confirmation of proofs. Like looking for spirals in sunflowers or chaotic behaviour in ant trails. I'm not saying that all mathematical objects exist in the real world. On the contrary, I think that mathematical objects (and grammatical object) could better termed to be abstract; i.e. non-spatial and non-temporal. Your insistence on the independant existance of math for it to be valid or universal doesn't really work. Because mathematical (and, indeed, formal) truths are forms of <i>a priori</i> knowledge, they are necessarily objective. If I say 1 = 1 or 2 = 1 + 1, those are true regardless of what you choose to believe. You could insist that mathematics is simply the formal manipulation of signs, but that would imply that different forms of notation would somehow have different truths.
sonofsamiam: <cite>"Just because you have a formula that describes a physical occurance as accurately as your instruments can measure does not mean that this formula is equivalent to whatever process actually governs the occurance."</cite>
Well, true. The formula (or the automaton) is not the same as the physical reality of processes, but you could perhaps argue that it is computationally equivalent, and therefore equivalent in the abstract.
<cite>"Re: pi, where can you show me a Euclidean circle? At some resolution (atoms and below), it will break down ;)"</cite>
As I was saying to fold, mathematical objects are abstract. Pi exists independantly of its approximate expression in nature. After all, if pi was exactly equal to the resolution of our measurement not only would it vary depending on the local curvature of space, but it would vary depending on the scale (an aside: to use it in formulae we would have to specify pi as a circle inscribed on such and such material that is such and such size measured to such and such resolution with a specific measuring device) that we're talking about. Additionally, pi would necessarily be limited by the Planck length, it would vary at a sub atomic level, etc.comment:www.metafilter.com,2002:site.17255-280418Thu, 23 May 2002 13:11:54 -0800bshort