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### 0816: "Applied Math"

Posted: Mon Nov 08, 2010 5:01 am UTC

Alt text: "Dear Reader: Enclosed is a check for ninety-eight cents. Using your work, I have proven that this equals the amount you requested."

The principle of explosion returns.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:03 am UTC
A logical proof that disproves logic? How interesting!

HI JOEE!

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:04 am UTC
Only 1,317,408 errors?

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:04 am UTC
cjmcjmcjmcjm wrote:A logical proof that disproves logic? How interesting!

HI JOEE!

Today, mes amis, I've ordered the metaphysics special with a side of GĂ¶del's incompleteness theorems. I expect our discussion will be as lively as ever.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:04 am UTC
I'll bet she divided by zero somewhere in there... -_-

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:05 am UTC
Randall hasn't updated the >| button yet.
Edit: Now he has.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:05 am UTC
A flowchart? Seriously? Real mathematicians use 4pt serif font when writing on the blackboard. Because secretly, it's all done with tex. (Insert comment about knuth here.)

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:05 am UTC
Alright, I need an explanation. Did the book author promise to send someone money if they found errors in his/her book?

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:06 am UTC
HI JOEE x INFINITY

Also, the pricely sum of 2^8 x 10-2 per error is nice.

edit: wow, I only just read http://en.wikipedia.org/wiki/Knuth_reward_check from the link below.. that man is awesome.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:06 am UTC
black_hat_guy wrote:Randall hasn't updated the >| button yet.

He has not changed it. And he will not. It points to xkcd.com/, not any specific number. So it is /always/ up-to-date.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:08 am UTC
mikebolt wrote:Alright, I need an explanation. Did the book author promise to send someone money if they found errors in his/her book?

Yup. Donald Knuth's http://en.wikipedia.org/wiki/Art_of_Computer_Programming

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:08 am UTC
mikebolt wrote:Alright, I need an explanation. Did the book author promise to send someone money if they found errors in his/her book?

This isn't restricted to mathematics; my classics professors will send in grammar errors and assorted typos that they catch in our references.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:09 am UTC
Of course, since we all know $0.98 is the same thing as$0.098, that check's not worth the paper it's printed on.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:09 am UTC
bytbox wrote:
black_hat_guy wrote:Randall hasn't updated the >| button yet.

He has not changed it. And he will not. It points to xkcd.com/, not any specific number. So it is /always/ up-to-date.

That's a good point. I've come to expect that xkcd.com has the latest comic on it.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:13 am UTC
http://plato.stanford.edu/entries/dialetheism/

seriously not terribly high-level logic here, guy

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:14 am UTC
Inb4 .02 cents!

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:15 am UTC
Turing Machine wrote:http://plato.stanford.edu/entries/dialetheism/

seriously not terribly high-level logic here, guy

The point is that it could be derived from an arbitrary P with the bare minimum of assumptions used in most useful problems, thus proving any P impossible.

Of course, hasn't it been proven that such a proof is impossible?

Finally, keep in mind that the Incompleteness Theorem, as the name suggests, showed only that a system cannot be both complete and consistent, that is to say, it can't precisely address every question that could possibly be posed to it (which would have to include "will this system answer 'no' to this question?") without running into an inconsistency.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:21 am UTC
Apparent inconsistency of logic arises from assuming logic is complete. Logic is not complete since it's consistent.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:25 am UTC
Man, I walked in to say that Knuth proved that the reader requested an amount of money equal to 98 cents by the reason of that other comic where assuming contradictory premises led to any true conclusion the thinker liked.

Um...oh dear, how to contribute now...? I've got it! Poorly-executed computer science joke!

So, I notice that the conclusion here is P and not-P. Now, we have a pretty good guess that P != NP, but does not-P = NP?

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:27 am UTC
This just made me realize that there should be a Knuth Facts website to accompany the Schneier one.

The man's a legend.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:29 am UTC
memcginn wrote:Man, I walked in to say that Knuth proved that the reader requested an amount of money equal to 98 cents by the reason of that other comic where assuming contradictory premises led to any true conclusion the thinker liked.

Um...oh dear, how to contribute now...? I've got it! Poorly-executed computer science joke!

So, I notice that the conclusion here is P and not-P. Now, we have a pretty good guess that P != NP, but does not-P = NP?

If P!=NP, then that must mean P=NP!

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:30 am UTC
I expect she'll be killed at a zebra crossing.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:34 am UTC
StClair wrote:I expect she'll be killed at a zebra crossing.

Yes. And Donald Knuth will disappear in a puff of logic.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 5:56 am UTC
I notice she would have gotten nearly twice as much money by pointing out that she proved all of the Millennium Prize Problems. In any case, I'm sure they'd consider that more important than any of them, and the should at least give her one million-dollar prize.

Shouldn't she use a proof checker? I wouldn't trust a human with something like that. Or just one proof checker for that matter.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 6:00 am UTC
Women start from the conclusion and work backwards.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 6:02 am UTC
black_hat_guy wrote:
StClair wrote:I expect she'll be killed at a zebra crossing.

Yes. And Donald Knuth will disappear in a puff of logic.

that makes little sense if you're american and dont know that zebra crossing is crosswalk.
Thats what I have taken away from this topic...

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 6:04 am UTC
The title text burnt my cheese.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 6:11 am UTC
Godel's theorem comes in two parts: one implies that predicate logic is incomplete. It's actually the second part that's weirder, it says that any sufficiently powerful axiom system CANNOT prove itself to be CONSISTENT! Yes I'm serious. It's really weird. But let's say even if a system COULD prove itself consistent: this wouldn't actually mean anything, because it might still be an inconsistent system, since inconsistent systems CAN prove themselves to be consistent, it's just that they can also prove themselves to be inconsistent, and all sorts of other contradictions. There IS no proof, and cannot be, that second order predicate logic will never prove 1 = 0 and A = not A, although (hopefully?) it is true. Weird. http://everything2.com/title/Godel%2527 ... e+syllable you might want to check out the wikipdedia page also. And here's a talk I just found going into what it would actually mean if the current foundations of mathematics were to be found inconsistent! (Which actually happened once before when it was attempted to build up mathematics from naive set theory which lead to russel's paradox. http://en.wikipedia.org/wiki/Russel%27s_paradox)

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 7:40 am UTC
SocialSceneRepairman wrote:Of course, hasn't it been proven that such a proof is impossible?

So tell me, what would you actually use to make such a proof?

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 8:13 am UTC
To be a small sticker on notation:

where it says [imath]P \Lambda \bar{P}[/imath], what you probably meant, the adjoint (conjugate transpose for finite-dimensional spaces), is usually written [imath]P^*[/imath] rather than [imath]\bar{P}[/imath] to distinguish it from only doing complex conjugate (without doing transpose) of all the elements in the matrix. So [imath]P \Lambda P^*[/imath] is how you usually see it. Unless this was the hidden joke and Randall was trying to troll mathematicians or something.

Also I don't really see what the comic has to do with applied math at all. Consistency of logic systems is about as far from applied math as you can get (restricting yourself to the realm of math). Unless this is part of the joke too? I don't know.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 8:30 am UTC
mafaraxas wrote:Also I don't really see what the comic has to do with applied math at all.

The application is getting the \$3,372,564.48.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 8:37 am UTC
mafaraxas wrote:To be a small sticker on notation:

where it says [imath]P \Lambda \bar{P}[/imath], what you probably meant, the adjoint (conjugate transpose for finite-dimensional spaces), is usually written [imath]P^*[/imath] rather than [imath]\bar{P}[/imath] to distinguish it from only doing complex conjugate (without doing transpose) of all the elements in the matrix. So [imath]P \Lambda P^*[/imath] is how you usually see it. Unless this was the hidden joke and Randall was trying to troll mathematicians or something.

Also I don't really see what the comic has to do with applied math at all. Consistency of logic systems is about as far from applied math as you can get (restricting yourself to the realm of math). Unless this is part of the joke too? I don't know.

P is a proposition, not a matrix. The girl has proved "P and not P."

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 9:04 am UTC
I was under the impression that The Art of Computer Programming was in italics because the writer was referring to the very foundations of computer programming, and thus, based on the gravity of this revelation, was using italics for emphasis!

I see now that it's a book. Also, I know what the deal is with the cheque. Much funnier now.

### Re: 0816: "Applied Math"

Posted: Mon Nov 08, 2010 10:40 am UTC
I had a burning cheese problem with this one.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 11:04 am UTC
SocialSceneRepairman wrote:Of course, hasn't it been proven that such a proof is impossible?

You forget the subject. If logic itself is inconsistent, then an apparently solid proof that something can't be proven might be also provably false, as you could prove contradictory and false things. By the very nature of the question to prove that such a proof is impossible would be irrelevant as the production of such a proof would show that the proof of its inability to be proved was invalid.

A more troubling objection is that all proofs rely on basic logic, so such a proof of logic's invalidity would thus prove itself to be invalid and unable to be relied on to prove anything, including logic being invalid.

### Re: 0816: "Applied Math"

Posted: Mon Nov 08, 2010 11:30 am UTC
SocialSceneRepairman wrote:Of course, hasn't it been proven that such a proof is impossible?

Of course. But it's also been proven that such a proof is possible.

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 12:21 pm UTC
Turing Machine wrote:http://plato.stanford.edu/entries/dialetheism/

seriously not terribly high-level logic here, guy

(5) (5) is false, or neither true nor false, or the fourth thing.

And that's still supposed to be paradoxical, but I don't see how. Why can't 'the fourth thing' be a true thing? In which case, (5) is the fourth thing, and true. Which is not paradoxical.

Surely it would only be paradoxical if it was
(5) (5) is false, AND neither true nor false, or the fourth thing
or any other arrangement that says it can't be the fourth thing and true. Hahaha, what about
(5) (5) is false, or neither true nor false, or a paradox

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 12:48 pm UTC
SocialSceneRepairman wrote:Of course, hasn't it been proven that such a proof is impossible?

Assume such a proof exists. Then P and not P. Contradiction. Therefore, no such proof exists.

### Re: 0816: "Applied Math"

Posted: Mon Nov 08, 2010 1:26 pm UTC
Assume such a proof exists. Then P and not P. Contradiction. Therefore, no such proof exists.

If you assume such a proof exists, that is, that logic is invalid, then you can't use logic to make the rest of your proof, can you?

### Re: 0816: Applied Math

Posted: Mon Nov 08, 2010 2:05 pm UTC
Ezbez wrote:
SocialSceneRepairman wrote:Of course, hasn't it been proven that such a proof is impossible?

Assume such a proof exists. Then P and not P. Contradiction. Therefore, no such proof exists.

It happens that "P is provable; therefore, P is true" is not valid mathematical reasoning. In fact, adding this as an axiom to our systems of logic would make them inconsistent.