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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."
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...
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.
Yes the difference are "slight"...
but according to Georgiadis's paper, they're different in nature. Wolfram guess they're 'minimal' in size (plz see the Georgiadis paper for the exact definition) but they are discovered not to be so.
I'm not one in the circle of CA and I don't understand all the significance about these arguments. But I don't think disproving some conjectures are "inflammatory" in mathematics. It seems some people are not satisfied with Wolfram's style (e.g. his failure in acknowledgin/interpreting other people's researches), but as for the FA it is essentially an objective argument about some mathematical facts.
Correct me if I make a mistake.
Colorless green Cthulhu waits dreaming furiously.
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.
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.
s/Disproved/Improved/
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).
Not to be a jerk or anything, but two years of calculus and a PDE course don't prepare you to understand all that much. In this case some course in logic and the theory of computation might be in order.