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44 Conjectures of Stephen Wolfram Disproved

kdawson posted more than 6 years ago | from the new-kind-of-error dept.

Math 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."

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Slightly different boolean formula (2, Interesting)

Ed Pegg (613755) | more than 6 years ago | (#21799380)

That is a very inflammatory title. The page in question is: http://www.wolframscience.com/nksonline/page-884 [wolframscience.com] Comparing the items in the paper to this page, there isn't much here.

Re:Slightly different boolean formula (-1, Troll)

Asstrophene (1204460) | more than 6 years ago | (#21799508)

Ah but you left out a crucial point [tinyurl.com]

Re:Slightly different boolean formula (0)

Anonymous Coward | more than 6 years ago | (#21800310)

What's Zermelo-Fraenkel set theory that link mentions? And why does Wolfram seem to want to modify it. I thoguht it was supposed to be an axiom. I've had 2 years of university calc and partial Def EQs and i'm completely lost.

Re:Slightly different boolean formula (5, Informative)

poopdeville (841677) | more than 6 years ago | (#21800588)

Zermelo-Frankel Set Theory is an axiomatization of set theory. That is to say, it is a list of axioms describing properties of any structure that is meant to be a collection of sets. There are alternative structures and alternative axiomatizations to generate those structures. (FYI, a consequence of Godel's Incompleteness Theorem is that there are infinitely distinct (in a non-trivial sense) axiomatizations of the natural numbers.)

Since you've studied Diff Eqs, I'll give you a little example of why axioms of this kind are needed. You were studying differentiable functions. Many of their properties are due to the completeness of the real numbers. Many of their properties are due the real numbers being ordered. Some are due to the fact that the real numbers form a field. And while tools like linear algebra might be necessary to study differential equations, all the properties of differentiable functions are caused by at least one of these three (and the definition of a differentiable function).

It turns out the real numbers can be characterized as the complete ordered field. To axiomatize the real numbers -- to write sentences from which all the others follow -- we just have to group together the completeness axiom (Every Cauchy sequence converges in the set), the field axioms, and the order axioms. If, for example, you drop the completeness axiom, you would also be writing about things like the rational numbers since they're an ordered field that happens to not be complete.

Axioms aren't about truth. They have a specific meaning in logic, and more importantly act as a sign post to the audience saying: this is what I'm going to talk about, and how I'm going to talk about it. Of course, in practice, mathematicians don't explicitly state these axioms unless they are the subject of the paper. But they are implicitly "contained" in the jargon.

Re:Slightly different boolean formula (1)

Hoch (603322) | more than 6 years ago | (#21802184)

Completeness in the real numbers is not that every Cauchy sequence converges, it is that every set bounded above has an upper bound. That real Cauchy sequences converge follows from this property, but not the other way around. For an example take rational functions as your field with an order on their coefficients(ie 1x+1 > 1x > 1 > 1/x). Showing that cauchy sequences converge and that this not equivalent to the reader is left as an exercise to the reader.

Re:Slightly different boolean formula (1)

miskatonic alumnus (668722) | more than 6 years ago | (#21802294)

Completeness in the real numbers is not that every Cauchy sequence converges, it is that every set bounded above has an upper bound.

That should be "has a LEAST upper bound."

That real Cauchy sequences converge follows from this property, but not the other way around.

False. One way to construct the reals is to consider equivalence classes of Cauchy sequences of rationals. The reals constructed in this manner have the least upper bound property.

For an example take rational functions as your field with an order on their coefficients(ie 1x+1 > 1x > 1 > 1/x). Showing that cauchy sequences converge and that this not equivalent to the reader is left as an exercise to the reader.

What topology are you considering on this space of functions?

Re:Slightly different boolean formula (1)

poopdeville (841677) | more than 6 years ago | (#21802380)

Completeness in the real numbers is not that every Cauchy sequence converges, it is that every set bounded above has an upper bound.

You mean a supremum, or least upper bound. Having just an upper bound is trivial, since every number is finite. The "axioms" happen to be equivalent.

http://en.wikipedia.org/wiki/Complete_space [wikipedia.org]
http://www.mathology.net/mathology/vis_articolo.asp?id=44&lang=ita [mathology.net]

To prove that they are equivalent, note that there is a bijective correspondence between elements of convergent sequences and least upper bounds on finite sets. Use the face that the sequence is Cauchy.

Re:Slightly different boolean formula (3, Insightful)

2.7182 (819680) | more than 6 years ago | (#21801716)

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.

WARNING DO NOT CLICK LINK (0, Insightful)

Anonymous Coward | more than 6 years ago | (#21800342)

I don't know what it is, I just know not to click it.

DON'T BE SUCH A PUSSY (-1, Troll)

Anonymous Coward | more than 6 years ago | (#21801286)

You are a gigantic pussy. That by itself is already bad enough, but now you're trying to push your pussyness onto others and turn other people into gigantic pussies. Nobody likes you, so just die already.

Re:DON'T BE SUCH A PUSSY (0, Flamebait)

Anonymous Coward | more than 6 years ago | (#21801772)

The link is just another myminicity thing. He was right. And you're an idiot.

Re:Slightly different boolean formula (3, Insightful)

gzipped_tar (1151931) | more than 6 years ago | (#21799774)

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.

Re:Slightly different boolean formula (0, Troll)

Nimey (114278) | more than 6 years ago | (#21800068)

That is a very inflammatory title.
On Slashdot?. Never!

Re:Slightly different boolean formula (0)

theunderground-Check (1207120) | more than 6 years ago | (#21800418)

U kiddin me? on slashdot nothing is. U must be from the Wolfram clan, then.

Re:Slightly different boolean formula (1)

jacquesm (154384) | more than 6 years ago | (#21800448)

Doesn't Wolfram have a stake in that journal ?

Re:Slightly different boolean formula (0)

Anonymous Coward | more than 6 years ago | (#21800538)

Luckily not yet. I bet he will after this though. Money can unfortunately nowadays. But go check it out, the Editor in Chief is amazing prof. Andrew Adamaztky. Hopefully, the editorial board will stay clean from Wolfram.

Re:Slightly different boolean formula (1)

theunderground-Check (1207120) | more than 6 years ago | (#21800882)

Luckily not yet and hopefully for the sake of science the editorial board of Journal of Cellular Automata will never allow this.

Do not click? It's the subject of the article! (1)

Ed Pegg (613755) | more than 6 years ago | (#21800508)

The paper at the heart of this slashdot discussion deals directly with http://www.wolframscience.com/nksonline/page-884 [wolframscience.com] There are 256 boolean expressions on this page from Stephen Wolfram's book The paper claims to give 44 shorter expressions.

English anyone?? (4, Funny)

Racemaniac (1099281) | more than 6 years ago | (#21799388)

"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...

Re:English anyone?? (0)

Anonymous Coward | more than 6 years ago | (#21799414)

Glass houses and such.

Re:English anyone?? (5, Funny)

rxmd (205533) | more than 6 years ago | (#21799476)

"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...
You have assuming that the editors can reading!

Obligatory (-1, Redundant)

PPH (736903) | more than 6 years ago | (#21799768)

OK, somebody has to do it:


All your proofreaders are belong to us!

Re:Obligatory (0, Flamebait)

uberchicken (121048) | more than 6 years ago | (#21799912)

No, it was not necessary. You and all the other clowns who say "somebody had to", please fuck off.

Re:English anyone?? (4, Funny)

Sky Cry (872584) | more than 6 years ago | (#21799908)

Surely you meaning righting, not reading!

Re:English anyone?? (0)

Anonymous Coward | more than 6 years ago | (#21799944)

Me fail English? That's unpossable!

Re:English anyone?? (1)

The Famous Druid (89404) | more than 6 years ago | (#21802262)

I think we have an answer to Gearge W Bush's famous question "Is our children learning?"

No, they aren'ting.

Re:English anyone?? (4, Funny)

evanbd (210358) | more than 6 years ago | (#21799486)

If your shift key is broken, it is permissible to use your caps lock key for the duration of the required capital letter. I know that key is abhorrent to most here, but it does have uses in the event a sudden failure of both shift keys.

Re:English anyone?? (0, Redundant)

marcello_dl (667940) | more than 6 years ago | (#21799518)

Let me disprove the usefulness of parent post for failure to assume laziness of GP poster.

Re:English anyone?? (1)

nospam007 (722110) | more than 6 years ago | (#21799648)

If your shift key is broken, it is permissible to use your caps lock key for the
duration of the required capital letter. I know that key is abhorrent to most here, but it does have uses in the event a sudden failure of both shift keys.
___

On every new machine I get, first thing I do is siwtch off the capslock key and redirecting it to left-shift, I assume many people do the same, so we have 3 Shifts.

BTW for the machine I got a few days ago I googled a nice utility which does it nicely, no registry hacks I never remember.
So if you capslock your password entry more than once a day...
http://www.randyrants.com/2006/07/sharpkeys_211.html [randyrants.com]

Re:English anyone?? (1)

pthisis (27352) | more than 6 years ago | (#21799782)

On every new machine I get, first thing I do is siwtch off the capslock key and redirecting it to left-shift, I assume many people do the same, so we have 3 Shifts.

What you map it to usually depends on your editor. Emacs users map it to ctrl, vi users map it to esc.

(I've never heard of mapping shift before, and given that it's right next to a shift key that doesn't seem like a big help to me but if it helps you then do it!)'

Re:English anyone?? (0, Offtopic)

nhaines (622289) | more than 6 years ago | (#21799802)

Actually, that was originally the location of Ctrl. I'm not sure why the changed it, but if I were to remap my CapsLock, it would definitely be to Ctrl.

On the other hand, the OLPC XO-1 is mapped that way and I haven't become used to it yet... So for now I'll leave everything where it is until I can get a nice keyboard with generic keycaps (although I'd substitute a Tux icon for a "Super" label...).

Re:English anyone?? (1)

osu-neko (2604) | more than 6 years ago | (#21800920)

I do precisely that. Control key sequences, especially the vital Ctrl-S and Ctrl-Q, are much easier to type when you put the control key back where God intended it to be. ;)

Re:English anyone?? (1)

und0 (928711) | more than 6 years ago | (#21801430)

[...] especially the vital Ctrl-S and Ctrl-Q, are much easier to type when you put the control key back where God intended it to be. ;)

Near your right pinkie? ^__^

Re:English anyone?? (0)

Anonymous Coward | more than 6 years ago | (#21799926)

What caps lock key? My keyboard doesn't have one of those. It has two left Control keys instead.

(Yeah, I actually popped off the keycap and replaced it with a Control keycap from a spare keyboard, I'm that geeky.)

Re:English anyone?? (1)

psu_whammy (940612) | more than 6 years ago | (#21800574)

Or, quit being a damn cheapskate and go pay 20 bucks for a keyboard!

Oh, you're you on a laptop? Quit typing so damn hard!

Re:English anyone?? (1)

Phleg (523632) | more than 6 years ago | (#21800890)

i switched to colemak [colemak.com] , you insensitive clod!

Re:English anyone?? (2, Funny)

rcw-home (122017) | more than 6 years ago | (#21799730)

"has disproving" is it that hard to write a summary without such huge errors??

One word: havening [nanc.com] .

Re:English anyone?? (4, Funny)

flyingfsck (986395) | more than 6 years ago | (#21799764)

Slashdot Engrish is to be informating and not to be laughful at.

Re:English anyone?? (1)

rm999 (775449) | more than 6 years ago | (#21799918)

Funny thing is, the sentence is about a person whose job (hobby?) is to look for errors in grammar.

Look at his correction of this textbook:
http://www-math.mit.edu/~sipser/itoc-errs2.1.html [mit.edu]

Re:English anyone?? (1, Troll)

OrangeTide (124937) | more than 6 years ago | (#21799956)

People on the internet are too busy typing to be bothered with reading.

Re:English anyone?? (1)

raddan (519638) | more than 6 years ago | (#21800532)

Actually, I think it was supposed to be "Can has disproving!"

What happened to proofreading? (0)

Token_Internet_Girl (1131287) | more than 6 years ago | (#21799390)

Terrible grammatical errors in this. Yes I am the Grammar Nazi.

Re:What happened to proofreading? (1, Troll)

RAMMS+EIN (578166) | more than 6 years ago | (#21799772)

Proofreading? On Slashdot? You must be new here!

Re:What happened to proofreading? (0)

Anonymous Coward | more than 6 years ago | (#21799878)

Can it be postulated that you are only a grammar Nazi after stating it is so? It's the only thing that will save you, given that your first "sentence" is actually a sentence fragment.

Insufferable pedantry is at its most annoying when it comes from the mouth of a fool. Learn your shit and get some humility.

Re:What happened to proofreading? (0)

Anonymous Coward | more than 6 years ago | (#21800284)

Actually, no, that isn't a fragment. It is written as dialogue, the question marks are standing in the place of commas to better reflect the tone of voice. That is one of the rules that can be suspended when trying to write natural sounding dialogue.

If you say it out loud, then say the same thing with commas instead, you'll see the point. The tone of voice is totally different, with longer pauses between the words than you would get with commas.

Re:What happened to proofreading? (1)

kayditty (641006) | more than 6 years ago | (#21800318)

Like anyone should take your advice on English grammar. Standing in the place of a comma? I suppose it should read: "What happened to proofreading, terrible grammatical errors in this."

No matter; you made a similar error yourself.

"It is written as dialogue, the question marks are standing in the place of commas to better reflect the tone of voice."

What the hell does that mean? Oh, that's right. It was a comma splice.

That is one of the rules that can be suspended when trying to write natural sounding dialogue.

That is one of the rules WHICH [may] be suspended.

If you say it out loud, then say the same thing with commas instead, you'll see the point.
Can you says omething "with commas?"

And the original poster should've said "Yes, I am a grammar nazi."

Re:What happened to proofreading? (1)

kestasjk (933987) | more than 6 years ago | (#21800476)

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?

Watch out for the roundhouse kick (5, Funny)

Jah-Wren Ryel (80510) | more than 6 years ago | (#21799396)

Doesn't Evangelos know that Wolfram is the Chuck Norris of Math?
Nobody disproves Chuck Norris and lives to publish about it!

Re:Watch out for the roundhouse kick (-1, Troll)

Anonymous Coward | more than 6 years ago | (#21799448)

Re:Watch out for the roundhouse kick (1)

jargon82 (996613) | more than 6 years ago | (#21799478)

more minicity crap

Re:Watch out for the roundhouse kick (0)

Anonymous Coward | more than 6 years ago | (#21799952)

Hey! Don't ruin it for everyone else!! [ripway.com]

Re:Watch out for the roundhouse kick (0)

Anonymous Coward | more than 6 years ago | (#21800260)

Chuck Norris is the Chuck Norris of Math.

More info (3, Informative)

the_kanzure (1100087) | more than 6 years ago | (#21799408)

Tim's cellular automata FAQ [cafaq.com] may be of some help in understanding all of this.

Can this 'Cellular Automata'.... (0)

Anonymous Coward | more than 6 years ago | (#21799424)

run a beowulf cluster?

*Beer. It's not just for breakfast anymore!

!Clearly the lack of posts (0)

peripatetic_bum (211859) | more than 6 years ago | (#21799434)

is directly proportional to the knowledge required to post

Re:!Clearly the lack of posts (0)

Anonymous Coward | more than 6 years ago | (#21799522)

is directly proportional to the level of interest in this battle of the egos... no one gives a crap.

Re:!Clearly the lack of posts (4, Insightful)

hung_himself (774451) | more than 6 years ago | (#21799604)

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...

Re:!Clearly the lack of posts (0)

Anonymous Coward | more than 6 years ago | (#21800240)

I find it humorous that you, who have a higher UID, have the audacity to assert that the OP is "new" to /.

Re:!Clearly the lack of posts (0)

Anonymous Coward | more than 6 years ago | (#21800278)

You must be new here.

Re:!Clearly the lack of posts (1)

crosson (1204404) | more than 6 years ago | (#21801214)

Every knows that biology is weak, and Math is strong.

Re:!Clearly the lack of posts (1)

zanaxagoras (1116047) | more than 6 years ago | (#21801514)

Every knows that biology is weak, and Math is strong.
Don't know who this Every person might be, but he/she is utterly wrong...

Re:!Clearly the lack of posts (1)

The One and Only (691315) | more than 6 years ago | (#21801876)

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.

Humm... (-1, Flamebait)

BrookHarty (9119) | more than 6 years ago | (#21799442)

With all the personal attacks against Wolfram on the website, it really shows someone with a grudge against Wolfram. (Not very professional)

Re:Humm... (5, Interesting)

Omnifarious (11933) | more than 6 years ago | (#21799466)

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:Humm... (0)

Anonymous Coward | more than 6 years ago | (#21799558)

Whose name is he supposed to hype? Yours?

Re:Humm... (5, Insightful)

IgnoramusMaximus (692000) | more than 6 years ago | (#21799682)

Whose name is he supposed to hype? Yours?

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.

Re:Humm... (1)

PachmanP (881352) | more than 6 years ago | (#21799990)

I admit my youth, but I have never heard of Science such as you describe it. Surely, you are mistaken?

Re:Humm... (3, Insightful)

IgnoramusMaximus (692000) | more than 6 years ago | (#21800388)

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.

Re:Humm... (5, Funny)

ceoyoyo (59147) | more than 6 years ago | (#21799644)

For particularly small values of "everyone" of course.

The only reason I like Wolfram to any degree.... (0)

Anonymous Coward | more than 6 years ago | (#21800146)

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 _____.

What's good for the goose (2, Insightful)

mcg1969 (237263) | more than 6 years ago | (#21800308)

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.

Re:Humm... (0)

Anonymous Coward | more than 6 years ago | (#21800398)

Bitter that you don't amount to a hill of beans?

Re:Humm... (1)

thethibs (882667) | more than 6 years ago | (#21800506)

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.

Re:Humm... (1)

Chapter80 (926879) | more than 6 years ago | (#21801044)

Hey, it takes some guts to go out on a limb. ESPECIALLY in a field where your work can be "proven wrong".

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?

Re:Humm... (0)

Anonymous Coward | more than 6 years ago | (#21800482)

nobody attacks you puppie dummy ... it's simply Wolfram is wrong and i'm sorry if u cannot deal with it.

yuHo fail it... (-1, Troll)

Anonymous Coward | more than 6 years ago | (#21799512)

I think I speak for a lot of people here ... (4, Insightful)

mortonda (5175) | more than 6 years ago | (#21799540)

when I say...

Huh?

Re:I think I speak for a lot of people here ... (1)

h2k1 (661151) | more than 6 years ago | (#21799826)

is there anyone out there willing to translate this post to dumb ass slashdoters?

Re:I think I speak for a lot of people here ... (5, Informative)

emurphy42 (631808) | more than 6 years ago | (#21800224)

As I understand it, it's basically an abstract-logic equivalent of a Perl golf [wikipedia.org] exercise.

Given three Boolean variables (p,q,r), there are 2 possible values (T,F) per variable, thus 2^3 = 8 possible values for the combined set:

  1. T,T,T
  2. T,T,F
  3. T,F,T
  4. T,F,F
  5. F,T,T
  6. F,T,F
  7. F,F,T
  8. F,F,F

Now consider functions f(p,q,r) whose output is a Boolean variable. Each such function can be completely described by what output it produces for each of the 8 combinations listed above, e.g.

  • f(T,T,T) = F
  • f(T,T,F) = F
  • f(T,F,T) = F
  • f(T,F,F) = F
  • f(F,T,T) = F
  • f(F,T,F) = F
  • f(F,F,T) = T
  • f(F,F,F) = F

There are multiple ways to describe the above function, but they're all equivalent to each other because they all give the same results. Thus, there are exactly 2^8 = 256 distinct functions of this sort.

Wolfram published a list of descriptions for all 256 of these functions, attempting to use the minimum number of symbols (p,q,r,not,and,or) in each case. Georgiadis pointed out that he could have done better in 44 cases. For instance, 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

while Georgiadis gave a 6-symbol representation

f(p,q,r) = r and not (p or q)

Re:I think I speak for a lot of people here ... (4, Informative)

fyngyrz (762201) | more than 6 years ago | (#21800364)

First of all, mod parent up. I know you moderators suck ass and the system is broken, but come on - parent post is a precise description of TFA's issue, the first in the thread. If you're going to spend mod points at all and pretend they do something worthwhile, parent post is the place.

Secondly, Wolfram's point - in the book - wasn't that the descriptions were minimal (even if he may have mentioned that he thought they were, which I don't actually recall), his point was that they were a complete set of correct descriptions (which I would add are functionally equivalent to the minimal ones anyway) that one can examine for certain behaviors he thought were significant. Niggling about the description not being minimal does not affect what Wolfram was trying to say to the reader. He may be completely wrong, but this kind of nit-picking can not and will not demonstrate it. It is a complete waste of everyone's time.

use of a conflicting basis? (0)

epine (68316) | more than 6 years ago | (#21801020)

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?

Re:use of a conflicting basis? (0)

Anonymous Coward | more than 6 years ago | (#21801684)

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.

They aren't linearly independent. The Scheffer stroke is a generator for this structure.

Re:I think I speak for a lot of people here ... (1)

morcheeba (260908) | more than 6 years ago | (#21800916)

De Morgan [wikipedia.org] wins again! (and the p's and q's are in exactly the same order as on the wikipedia page)

Re:I think I speak for a lot of people here ... (1)

Bananenrepublik (49759) | more than 6 years ago | (#21801154)

For instance, 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




while Georgiadis gave a 6-symbol representation




f(p,q,r) = r and not (p or q)

So Wolfram doesn't know Morgan's rule?

Re:I think I speak for a lot of people here ... (1)

pongo000 (97357) | more than 6 years ago | (#21801168)

So, IOW, careful application of DeMorgan's Theorem results in the simplification of some of Wolfram's functions.

And the impact of this is...what, exactly? Aren't the original functions and new functions still equivalent?

Re:I think I speak for a lot of people here ... (4, Interesting)

fyngyrz (762201) | more than 6 years ago | (#21801726)

Aren't the original functions and new functions still equivalent?

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.

MIT Errata Expert, eh? (4, Funny)

mathcam (937122) | more than 6 years ago | (#21799724)

"...so basically I'm really good at being right about things that other people are wrong about."

Wait a minute, that's what I do!

That's egg on his face. (3, Funny)

yotto (590067) | more than 6 years ago | (#21799812)

"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!

Re:That's egg on his face. (5, Informative)

mcg1969 (237263) | more than 6 years ago | (#21799948)

That's not as much of a SNAP! As you think. The reason that "simple inspection" reveals that the formulas are not minimal is because, in an earlier paper, the same author demonstrates that 5 boolean operators are sufficient. So it actually took a bit more than "simple inspection" to get there.

Re:That's egg on his face. (0)

Anonymous Coward | more than 6 years ago | (#21800294)

Lol, you really need to learn what the expression "Oh, snap" means :)

The paper is not as hostile as the citation (4, Insightful)

mcg1969 (237263) | more than 6 years ago | (#21799846)

The author of the article, Evangelos Georgiadis [wolframscience.com] , 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.

Re:The paper is not as hostile as the citation (5, Informative)

mcg1969 (237263) | more than 6 years ago | (#21799886)

If you go to the NKS Forum [wolframscience.com] , you can find quite a few contributions by the author of this paper, and many of them are error corrections or other disputes with the content. To try it yourself, go to the search page [wolframscience.com] and type in "Evangelos Georgiadis" into the "Search by Author" field, select "Show results as posts", and click "Perform Search."

I think if you read through the posts yourself you'll see his overall interest seems to be in improving the text, not tearing it down. In fact, one of the threads he created is called "Further Improvements and Errata."

Linus is absolutely right (-1, Offtopic)

Anonymous Coward | more than 6 years ago | (#21799850)

I have to agree with Linus on this one.

Not Really (1)

aweinert (969529) | more than 6 years ago | (#21800174)

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.

Obviously! (0)

Anonymous Coward | more than 6 years ago | (#21800528)

"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.

Simple title correction. (4, Insightful)

ksw2 (520093) | more than 6 years ago | (#21800868)

s/Disproved/Improved/

Superb, now the tag (1)

murderlegendre (776042) | more than 6 years ago | (#21801194)

Humbly, please tag as "disimprovement"

Full text of "A New Kind of Science" is online (2, Informative)

slacka (713188) | more than 6 years ago | (#21801338)

You can read the full text of "A New Kind of Science" online for free at http://www.wolframscience.com/nksonline/toc.html [wolframscience.com]

Re:Full text of "A New Kind of Science" is online (1)

Keyframe2 (940074) | more than 6 years ago | (#21801626)

Ofcourse it is. After I bought the book, ofcourse.

citation of unpublished result (1, Insightful)

Anonymous Coward | more than 6 years ago | (#21801518)

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).
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