Philosophers and/or mathemeticians wanted for enigmatic haiku translation....

Forums: Haiku, Enigma, Prime Numbers, Existential Riddle
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The following comic is way over my head. Can anyone translate this translate this mathematical enigma into layperson's English?

http://imgs.xkcd.com/comics/haiku_proof.png

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Type: Question • Score: 6 • Views: 7,599 • Replies: 21

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@tsarstepan,

I dont understand warp drive either

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We are looking at a classroom
The student asks a difficult question
The teacher answers using a poem and appears to be floating out of the room
The student (after being sleep deprived for 48 hours) thinks that lectures can get very interesting...............

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@sullyfish6,

Ummm... I get that part of the whole comic. I don't need a transcription service for the legally blind. Rolling Eyes

I don't understand Q.E.D. or quod erat demonstrandum or that which was to be demonstrated in the context of "top prime divisor's ... [being a] product (plus one) factor..." I'm assuming this is legitimate high function math theory.

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@sullyfish6,

wow

just wow

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Doesn't make sense to me.
Call the "Top Prime" P.
No matter how big P is, its only divisors are P and 1.
The product of P's divisors are, of course, P.
P+1 is not a prime number because it is divisible by 2.
Its factors must be 2 and (P+1)/2.
I don't see how that proves anything.

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http://en.wikipedia.org/wiki/Prime_number

Euclid's theorem:

Quote:

Consider any finite set of primes. Multiply all of them together and add 1 (see Euclid number). The resulting number is not divisible by any of the primes in the finite set we considered, because dividing by any of these would give a remainder of 1. Because all non-prime numbers can be decomposed into a product of underlying primes, then either this resultant number is prime itself, or there is a prime number or prime numbers which the resultant number could be decomposed into but are not in the original finite set of primes. Either way, there is at least one more prime that was not in the finite set we started with. This argument applies no matter what finite set we began with. So there are more primes than any given finite number. (Euclid, Elements: Book IX, Proposition 20)

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@tsarstepan,

Tsar, why do you assume that the teacher's answer is sensible? (It's even poor haiku!) The student is suffering from 48 hours of sleep deprivation. There's a sugestion in that last panel that the student might be imagining the whole sequence.

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@Merry Andrew,

You may be ultimately right.

But its mostly on the heady credentials of the comic artist/writer. He or they have a solid history of drawing comics revolving physics, engineering, mathematics, and the history of science.

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@DrewDad,

A Dead Greek wrote:

Consider any finite set of primes. Multiply all of them together and add 1 (see
Euclid number).

So how do you get "TOP PRIME'S DIVISOR'S PRODUCT (PLUS ONE)'S
FACTORS" out of that?

3 Replies

@George,

George - you get it via the Sieve of Eratosthenes:

Quote:

new number q, equal to the product of all primes between 2 and p, plus 1.

http://www.arachnoid.com/prime_numbers/index.html

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@tsarstepan,

couldn't the floating teacher be a representation of 'going over one's head'

makes sense if the students last remark is taken as sarcastic. it does use itallics...

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@High Seas,

Yet another Greek.
Quidquid id est, timeo Danaos et dona ferentes
OK, but how does that jibe with the cartoon I've quoted above?
(BTW, thanks for that reference, it was very interesting. )

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@George,

"Top Prime" is the largest known prime number. (I think that's what it means.)

"Top Prime's Divisors" would be one and the top prime itself. A finite set of one prime number.

Technically, one is not a prime number, but a) we're dealing with a comic strip haiku and b) it doesn't affect the outcome of the calculation.

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@George,

I'll also suggest that "top prime's divisors" means the set of all known primes. The author took poetic license and used the word "divisors" to mean all smaller primes, even though they aren't technically divisors.

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@DrewDad,

Quote:

I'll also suggest that "top prime's divisors" means the set of all known primes.

Bit of a stretch, but, granting that -- reluctantly -- I agree.

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@tsarstepan,

Here's the official XKCD forum thread on that comic.

1 Reply

@DrewDad,

We seem to have done the same thing in far fewer iterations.

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@George,

. . . and I'm still not real happy with that "product of all primes" thing.

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@George,

So there.

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Philosophers and/or mathemeticians wanted for enigmatic haiku translation....

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