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44 Conjectures of Stephen Wolfram Disproved
Richard Pritches writes in to let us know that MIT errata expert Evangelos Georgiadis has disproved 44 conjectures set by Dr. Stephen Wolfram (founder of Mathematica) in A New Kind of Science. The paper was published in the latest issue of the Journal of Cellular Automata and can be read in PDF form at Prof Edwin Clark's collection of reviews of Wolfram's ANKS. "The formulas provided by Wolfram for these [44] rules are not minimal. Moreover for 8 of these cannot be minimal even by simple inspection since minimal formula sizes for 3-input Boolean functions over this basis never exceeds 5."
That is a very inflammatory title. The page in question is: http://www.wolframscience.com/nksonline/page-884 Comparing the items in the paper to this page, there isn't much here.
"has disproving"
is it that hard to write a summary without such huge errors??
i'm not a native english speaker, and it even pokes out my eyes...
Terrible grammatical errors in this. Yes I am the Grammar Nazi.
Sure baby, I'll give you my phone number...in Hex
Doesn't Evangelos know that Wolfram is the Chuck Norris of Math?
Nobody disproves Chuck Norris and lives to publish about it!
When information is power, privacy is freedom.
Tim's cellular automata FAQ may be of some help in understanding all of this.
run a beowulf cluster?
*Beer. It's not just for breakfast anymore!
is directly proportional to the knowledge required to post
Sigs are dangerous coy things
Ahh, yes. But the great thing about math is that whether or not you have a grudge, everybody can look at the proof and see if you're right or not.
Personally, if I were a mathemetician, I might have something of a grudge against Stephen Wolfram too. An arrogant person who hypes his own name and abilities far beyond what is justified by the available material then publishes a giant tome of half-baked reasoning that everybody fawns over because of his hyped reputation.
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when I say...
Huh?
Whose name is he supposed to hype? Yours?
For particularly small values of "everyone" of course.
Nobody's.
And no hype either.
That is because the supposed subject of all this is Science. And hype and personality cults are to science as money is to politics: corrupting, destructive, counter-prodctive forces.
Reason, peer review, rigourous analysis, unassailable demonstration of proof, etc are the ways of science, not ascension to prominence via grooming oneself for mass-media "stardom" by boggling the "minds" of the rather feebly-minded general public.
Wait a minute, that's what I do!
"The formulas provided by Wolfram for these [44] rules are not minimal. Moreover for 8 of these cannot be minimal even by simple inspection since minimal formula sizes for 3-input Boolean functions over this basis never exceeds 5."
Oh, SNAP!
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The author of the article, Evangelos Georgiadis, has participated in two of the "New Kind of Science" summer schools (2003, 2005; the link above is from 2003). I must suspect, then, that he is somewhat sympathetic to Wolfram's work, and his papers are not intended to be hostile attacks. Indeed, his paper really doesn't read that way, from my perspective as an academic; it is simply a correction of errors. Indeed, if anything, this work tends to buttress Stephen Wolfram's basic point (whether it is true or not) because it further reduces the complexity of CA implementations.
No, it was not necessary. You and all the other clowns who say "somebody had to", please fuck off.
I admit my youth, but I have never heard of Science such as you describe it. Surely, you are mistaken?
You're thinking small. Why miniaturize the laser, when we could instead enlarge the sharks? -John Searle
Is that I can't believe that Feynman was wrong. No. Must not be. Cannot be.
But apart from that, he seems to be an _____.
All the author does is show that 44 of the boolean equations [out the 256 3 input equations in 1-D cellular autmata] Wolfram provides are not minimal.
The author also shows that 8 of these are not minimal by inspection, since the maximum size of the minimal equations over this basis is 5.
Likewise, the fact that Stephen Wolfram is an arrogant blowhard should not prevent people from making a reasoned assessment of his work. And that is, in my view, what seems to be happening. Sure, Wolfram is hogging some undue spotlight right now. But his work is absolutely useless unless it can be reproduced, verified, built upon, and applied by others. Give it 20-50 years and we'll see what happens. My prediction is that Wolfram's claims about the work, in particular its wide applicability, will be proven to be wildly overstated. But my prediction is as valuable as the bandwidth it is transmitted upon.
I don't know what it is, I just know not to click it.
The fact that various people continuously try to remodel Science into a contest of egos and popularities does not change the fundamental fact that Science itself is in the long term immune to such tactics.
And those who attempt it end up, sooner or later, with the only scientific title they deserve: "Crackpot", their "theories" having been ground into dust by the slowly, unglamorously, mundanely, steadily turning wheels of the scientific method.
Bitter that you don't amount to a hill of beans?
nobody attacks you puppie dummy ... it's simply Wolfram is wrong and i'm sorry if u cannot deal with it.
Obviously someone who hasn't read the book...
It's not arrogant to present some of your best work as conjectures—a mathematician's term for "A wild-assed guess, but wouldn't it be interesting if it were true?"
Given that one of the implications of Wolfram's work is that you can do a lot of neat stuff with algorithms that are out of scope for conventional mathematics, many on Slashdot should enjoy reading ANKS. Among other things, committing some of his constructions to code is fun.
I'm a Programmer. That's one level above Software Engineer and one level below Engineer.
The paper at the heart of this slashdot discussion deals directly with http://www.wolframscience.com/nksonline/page-884 There are 256 boolean expressions on this page from Stephen Wolfram's book The paper claims to give 44 shorter expressions.
"8 of these cannot be minimal even by simple inspection since minimal formula sizes for 3-input Boolean functions over this basis never exceeds 5." See, that's just common sense, obviously...Christ, I tried, I tried REAL REAL REAL hard several times to get through NKS without having my eyes gloss over because it was so technically tricky. At least the illustrations were beautiful, I suppose.
s/Disproved/Improved/
Perhaps Wolfram was counting the weight of "not" as zero in his mind when he constructed his table. I'm not going through the reg page to find out what he actually wrote. His error could be as small as *printing* that he was giving weight one to "not" when in fact he hadn't.
Personally, I find it rather arbitrary to give a weight to the unary not operator. It strikes me as more fundamental (and less arbitrary) to take as your basis the set of *all* binary input truth functions.
Suppose you change your basis from and,or,xor,not to nand,or,xor,not and this gives you a different length bound? What is the significance of the length bound then? Stupid.
Here is the thing to check, if anyone is interested. Is Wolfram's table correct if you weight "not" to zero?
I have a lot of respect for the guy for trying, and for getting SOME of it right. That's more than 99% of the slashdot readers! Where would we be if it weren't for the brave few who publish their works for peer review?
Humbly, please tag as "disimprovement"
There's a Starman, waiting in the sky / He'd like to come and meet us, but he hasn't got the time.
You can read the full text of "A New Kind of Science" online for free at http://www.wolframscience.com/nksonline/toc.html
While I'm not surprised to see people refute some of Wolfram's claims, I hate seeing preprints distributed that have key citations that are "Unpublished results". The whole point of peer review is to treat results as believable when they can be independently verified. Citing unpublished work is a bit sketchy. It would be nice if people could wait before distributing results until proper review has taken place (but then again, this is refuting wolfram, the kind of non-peer-reviewed publication).
Ofcourse it is. After I bought the book, ofcourse.
The link is just another myminicity thing. He was right. And you're an idiot.
I think I know why.
You have to spell your adversary's name correctly first.
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
I had all my conjectures and overtures disproved and disapproved. Big deal.
Well, we are talking mathematicians here.
That leads me to an interesting musing, if there were an infinite number of people, would there then be an infinite number of people (even if it were still a small fraction of the total infinite number of people) capable of evaluating the theorems and proofs in Stephen Wolfram's book?
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I wonder how many loopholes Evangelos Georgiadis will find in Wolfram's Turing Machine Prize Proof. Well, if there are any I'm sure he is the best candidate to spot them (excluding Don Knuth who is also an errata expert but too busy at the moment).
On Soviet Slashdot, off fucks you!
Money is a corruptive force in politics only if allowed to go unchecked. Ditto personality and hype for science.
This reminds me of a tragically vehement argument I had with a good friend about the value of Carl Sagan's work on Cosmos, as well as his overall attempts to publicize space science. I was of the opinion that Sagan was, and perhaps still is, the best thing to happen to space exploration since Von Braun. My friend believed Sagan's methods to be underhanded and self-promoting.
Prominence is a way to get the message out. And where would we scientists and sundry other "smart people" be without that "wow" moment? I fall in love with science all over again when I learn something that floors me. That's not a bad thing.
Yes. Infinity is funny that way.
Wolfram had some interesting ideas, it's too bad he had to go and write a book and call it "A New Kind of Science." That's the title you let someone ELSE put on a book THEY write about your ideas, if your peers agree that they merit it.
Your own book, you call something like "Relativity" (Einstein).
I wouldn't fault Wolfram for making this mistake; people do make mistakes. Wolfram's problem is with science, not bookkeeping: not properly crediting other people, trying to claim results and breakthroughs without having done the hard work to prove them, etc. Wolfram was not the first to formulate the ideas in "A New Kind of Science", and if they should turn out to become the foundation of physics over this century, the key ideas needed for making that happen will not have come from his book. That's the real problem with Wolfram.
It's sort of expected. Every One's brother No was looking out for him, so Every One got all of the good press. When things went well, Every One claimed responsibility. When things when poorly, No One accepted the blame.
Wolfram labeled the function given above as Rule 2, and gave the intuitive 7-symbol representation
f(p,q,r) = (not p) and (not q) and r
Georgiadis gave a 6-symbol representation
f(p,q,r) = r and not (p or q)
In summary, Wolfram failed to simplify the equation properly, so in Georgiadis's mind, Wolfram failed it!
I hate a nit picky math professor, but is there any other kind?
I only look human.
My mother is a halfling and my dad is an ogre, so that makes me an Ogreling
You are confusing fame which comes about as a result of a peer-reviewed, rigorously tested but nevertheless astonishing discovery and attempts to force acceptance of your "theories" via appeals to the mass-media audience. Then there is also simple "popularization" of science, i.e. recasting complicated discoveries in terms more palatable to the public, which is what Sagan was all about.
Fame and efforts at popularization are not a problem. Attempts to use a personality cult to bypass the peer review process are.
As to politics, money is pretty much a universal corruptor. That is why most sane democracies have publicly funded campaigns and strict laws about acceptance of any contributions. It is not foolproof but it reduces the dirty politicos to rather dangerous to them (by the virtue of possibility of detection) methods, such as the one involving cash and brown envelopes.
Yes. Infinity is funny that way.
Well, my thought was maybe there was some sort of cap on the number of people who could understand mathematical concepts that was below infinity. :-)
And regarding the book's title, I agree completely. I was trying to tell a brilliant young (pre-HS age) friend when I was in college that certain titles are conferred upon you by others and you can't assume them yourself without seeming arrogant. And that was for something relatively minor like 'Unix Wizard'. :-)
Need a Python, C++, Unix, Linux develop
i wonder what else is wrong in Wolfram's "highly acclaimed" book NKS apart from being highly "original" it appears to be "highly" flawed.
if you look closely enuff at the results you realize that Georgiadis's paper is rather deep, pinpointing what other major figures such as steven Weinberg criticized Wolfram for namely the lack of inconsistency witnessed when it comes down to definitions. There just isn't one coherent definition in the book or if there is one mentioned it is not followed consistently.
An interesting review: http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/
..by cellular automata expert Shalizi,
http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/
As pointed out previously "if you look closely enuff at the results you realize that Georgiadis's paper is rather deep, pinpointing what other major figures such as steven Weinberg criticized Wolfram for namely the lack of inconsistency witnessed when it comes down to definitions. There just isn't one coherent definition in the book or if there is one mentioned it is not followed consistently."
what does one call a theory that does not stick to any given definition or in fact is not based on definitions at all ?