44 Conjectures of Stephen Wolfram Disproved 158
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."
Slightly different boolean formula (Score:3, Interesting)
Re:Humm... (Score:5, Interesting)
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.
Re:I think I speak for a lot of people here ... (Score:5, Interesting)
They are. Wolfram was saying, Look here, for each case, applying the following CA rules gets you the following output set (smaller than the input set) of behaviors. So he was observing - in another way - that the various inputs resulted in a more sparse set of results (speaking as far as they are unique with respect to each other.) Once he identified the various types of behavior possible from these sets, he showed that some were very orderly, some considerably less so, some obviously recognizable - visually - as being members of the same classes of behaviors, and some not so obvious at all except that they certainly weren't in the easy-to-recognize class.
From there - and it gets a lot more murky - he went on to propose that these very behaviors might underlay either everything, or darned near everything. To bolster that assertion, he showed that you could find those very patterns in many interesting and disjoint places - formulas seeming completely unrelated to anything he'd talked about thus far, seashell structure and so forth. That part of the book was downright breathtaking.
It's really a very interesting book. His conclusions far outstrip his ability to back them up, but as far as TFA goes, it's looking at the very start of his chain of reasoning and applying some nitpicking that changes nothing he said or meant to say that had anything at all to do with the proposals and justifications made in the book.
Personally, I could give the south end of a northbound rat if he has a high opinion of himself, or not. What I appreciate is that he provided me with a great read, thought provoking on the one hand, and as far as I could tell, without running into anything I knew that would make me question his approach or conclusions. I've got a good general science background, strong engineering and technical design skills, passable math, and am very creative; I do fairly well at finding little - occasionally large, usually not - holes in new science books and have a huge collection of such volumes full of snippy little annotations of my own (and just for my own benefit, on re-reading.) Aside from a really wonderful book on fuzzy logic which to this day I know of no faults with, this book stood out as almost uniquely solid in the specific area he was clearly trying to explain his thoughts on. I consider it money and time well spent.