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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...
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.
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?
is directly proportional to the perceived knowledge required to post.
You must be new around here. When it comes to biology, everyone seems to think they are experts. Because there are so many computer people here, at least when it comes to math, more of them know that they know nothing...
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!
Proofreading? On Slashdot? You must be new here!
Please correct me if I got my facts wrong.
"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.
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
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.
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.
Im more interested in the mathematical errors being discussed than grammatical ones. Anyone got anything to say about these 44 conjectures or the guy who made them?
// MD_Update(&m,buf,j);
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.
s/Disproved/Improved/
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.
Every knows that biology is weak, and Math is strong.
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).
Clearly he's on a first name basis with Every One. This is good for him since as they say, you have to pretty much know Every One to get ahead in this world. On the other hand, when I ask who truly understands any complicated subject, the response is always "not Every One". Truly, like so many of our leaders, this Every One character is simply an influential dullard.
In Repressive Burma, it's not just your connection that dies. slashdot.org/comments.pl?sid=314547&cid=20819199
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).
This reminds me of a paper by Putnam (IIRC) I read a long time ago. He puts forward two different set-theoretic constructions of the integers, with the major distinction that in one construction, x y implies x is a subset of y; this does not hold in the other construction. Both constructions describe the same properties of the integers, but they also introduce arbitrary mathematical artifacts particular to the set-theoretic underpinnings adopted.
What is Wolfram attempting to do where it would matter that that the chosen basis was linearly independent?
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).
It's actually fairly simple: Wolfram created a table with 256 logical formulae in them that modelled all possible 3 input boolean truth tables. He apparently conjectured that these were the shortest. The article corrects Wolfram in providing, for 44 of these cases, that there exists a shorter formula. Wolfram was apparently not smart enough to simply enumerate all the formulae until he found the shortest. Given the size of the search space this would have taken all of three seconds.
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'. :-)
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An interesting review: http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/