0622: "Haiku Proof"

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dissonant
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Re: "Haiku Proof" discussion

Postby dissonant » Wed Aug 12, 2009 5:48 am UTC

revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid

This seems to be the proof Randall is using, but I'm not exactly sure what the divisors part is meant to be. Bad wording?


The proof of the infinitude of the primes irks me more than any other! People always tack on a little superfluous (false) information right at the end, or even worse, just state that p1p2...pn+1 is prime.

pgn674
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Re: "Haiku Proof" discussion

Postby pgn674 » Wed Aug 12, 2009 5:54 am UTC

ndookie wrote:Why doesn't the second panel have a border :S...
It does; you're hallucinating.

The wording does not match up with the proof (as explained by revolutionx897) that he's trying to use.
Top prime's divisors' product (plus one)'s factors are...? Q.E.D., bitches!
It means: Take the highest prime you can think of. Now take its divisors, which are 1 and the prime. Now take the product of those two divisors, which is the prime itself. Now add one. Now think about and list the factors for this number. Somehow, that makes you realise that there are infinite primes. But there really is nothing special about the next number over a prime, or its factors, I don't think.

A bunch of people have been suggesting various fixes to make it follow the intended proof properly while maintaining the Haiku. I wonder if Randal will alter the comic?

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A_of_s_t
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Re: "Haiku Proof" discussion

Postby A_of_s_t » Wed Aug 12, 2009 5:57 am UTC

Begin with Euler,
Write as a product with primes.
Primes are infinite.

God, that's hard to write Euler's proof of the infinitude of primes...
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Max2009
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Re: "Haiku Proof" discussion

Postby Max2009 » Wed Aug 12, 2009 6:01 am UTC

Wow. I never thought I'd see so many mathematical proofs and haikus in the same place.

Joee, Glasnt I've been meaning to ask for a long time, what is UP with that :?:
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glasnt
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Re: "Haiku Proof" discussion

Postby glasnt » Wed Aug 12, 2009 6:09 am UTC

Max2009 wrote:
Joee, Glasnt I've been meaning to ask for a long time, what is UP with that :?:


Mmm.. what do you mean?
I don't see anything wrong...
Hallucinating?



edit:
Spoiler:
In all ser'ousness
It started as a lil' joke
But now it's a meme

Do not blame me, though
I blame Miss Joee in full
It is all her fault ;)

opal
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Re: "Haiku Proof" discussion

Postby opal » Wed Aug 12, 2009 6:22 am UTC

halucinated
one summers morning, stayed
awake for a friend.

(also 48 hours is a pretty good guess; might have been somthing arround 53, when everthing started coming alive, and i REALLY knew i need some sleep. - other possible reaction i observed once, is falling in a coma-like-sleep: this guy had his eyes open while beeing passed out, and was clearly a case for the doctors at that point (hacked away for about 2 and a half days before)luckilly, it did no serious harm to him)

Deciheximal
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Re: "Haiku Proof" discussion

Postby Deciheximal » Wed Aug 12, 2009 6:42 am UTC

It means: Take the highest prime you can think of. Now take its divisors, which are 1 and the prime. Now take the product of those two divisors, which is the prime itself. Now add one. Now think about and list the factors for this number. Somehow, that makes you realise that there are infinite primes. But there really is nothing special about the next number over a prime, or its factors, I don't think.

Assume 7 is the highest known prime.

7 & 1 (divisors of 7)
7 * 1= 7 (product of those two divisors, which is the prime itself)
+ 1 (now add one)
= 8
2 & 4 (Factors for this number)

2 is prime, but this is less than 7, and therefore assumed already known. Where did I go wrong?
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Max2009
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Re: "Haiku Proof" discussion

Postby Max2009 » Wed Aug 12, 2009 6:43 am UTC

Are we counting how long we've been up?

Well, I never counted, but I do remember one week where I didn't sleep from Tuesday morning until Friday night.
Cogito ergo surf - I think therefore I network

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JulienW
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Re: "Haiku Proof" discussion

Postby JulienW » Wed Aug 12, 2009 7:10 am UTC

revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid


In 3., isn't it "so it must either be prime or divisible by another prime" ? I can't think of a reason why the new prime would be larger, p1..pn aren't necessarely the first primes.

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Re: "Haiku Proof" discussion

Postby Al-pocalypse » Wed Aug 12, 2009 7:16 am UTC

I didn't find this comic funny. Then again I am not a maths geek and i cannot stand poetry, especially haikus!
Ali ;)

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Kisama
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Re: "Haiku Proof" discussion

Postby Kisama » Wed Aug 12, 2009 7:25 am UTC

Warui desu
Eigo no haiku
Kore mou ne
cd880b726e0a0dbd4237f10d15da46f4

VDOgamez
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Re: "Haiku Proof" discussion

Postby VDOgamez » Wed Aug 12, 2009 7:30 am UTC

I definitely know what that state of mind feels like. I hate it, it makes it hard to think properly. I keep catching myself staring suspiciously at the faces in the smiley box... Get out of my bed head, Randall!

meh1936
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Re: "Haiku Proof" discussion

Postby meh1936 » Wed Aug 12, 2009 7:30 am UTC

dissonant wrote:
revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid

This seems to be the proof Randall is using, but I'm not exactly sure what the divisors part is meant to be. Bad wording?


The proof of the infinitude of the primes irks me more than any other! People always tack on a little superfluous (false) information right at the end, or even worse, just state that p1p2...pn+1 is prime.


It is necessary because it isn't superfluous/false information. p1p2...pn+1 isn't necessarily prime.

(2 × 3 × 5 × 7 × 11 × 13) + 1 = 30,031 = 59 × 509

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Re: "Haiku Proof" discussion

Postby Arancaytar » Wed Aug 12, 2009 8:04 am UTC

It's just a hallucination? Aw, I'd hoped that the sheer awesomeness of haiku mathematics conferred the power of flight.
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nuke
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Re: "Haiku Proof" discussion

Postby nuke » Wed Aug 12, 2009 8:07 am UTC

JulienW wrote:
revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid


In 3., isn't it "so it must either be prime or divisible by another prime" ? I can't think of a reason why the new prime would be larger, p1..pn aren't necessarely the first primes.


Read 1 again - "Assume a finite number of primes". Next, read 2 again - "Take the product of all primes". p1..pn are necessarily the only (leave alone the first) primes as per the assumption. This is an example of reductio ad absurdum proof technique, or proof by contradiction.

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Re: "Haiku Proof" discussion

Postby disq » Wed Aug 12, 2009 8:33 am UTC

Deciheximal wrote:Assume 7 is the highest known prime.

7 & 1 (divisors of 7)
7 * 1= 7 (product of those two divisors, which is the prime itself)
+ 1 (now add one)
= 8
2 & 4 (Factors for this number)

2 is prime, but this is less than 7, and therefore assumed already known. Where did I go wrong?


Assuming 7 is the highest known prime, we take 2, 3, 5 and 7.

2 * 3 * 5 * 7 is, 210. Add 1, it's 211, a prime number.
(See http://en.wikipedia.org/wiki/Primorial_prime )

dantendo
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Re: "Haiku Proof" discussion

Postby dantendo » Wed Aug 12, 2009 8:36 am UTC

sorry disq, you are wrong. p1p2p3...pn+1 is not necessarily a prime.

meh1936 wrote:
dissonant wrote:
revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid

This seems to be the proof Randall is using, but I'm not exactly sure what the divisors part is meant to be. Bad wording?


The proof of the infinitude of the primes irks me more than any other! People always tack on a little superfluous (false) information right at the end, or even worse, just state that p1p2...pn+1 is prime.


It is necessary because it isn't superfluous/false information. p1p2...pn+1 isn't necessarily prime.

(2 × 3 × 5 × 7 × 11 × 13) + 1 = 30,031 = 59 × 509


from http://primes.utm.edu/notes/proofs/infinite/euclids.html:

It is a common mistake to think that this proof says the product p1p2...pr+1 is prime. The proof actually only uses the fact that there is a prime dividing this product (see primorial primes).


We are saying that any prime divisor of p1p2p3...pn+1 must be a prime larger than pn, meaning that primes are infinite.

Zenexer
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Re: "Haiku Proof" discussion

Postby Zenexer » Wed Aug 12, 2009 8:40 am UTC

Funny, I actually had a physics teacher who would pretty much go, "QED, bitches!" Except, he only thought he was proving stuff... I think he had a mental problem or two. Nothing like having a mad scientist spend an hour proving that 1 + 1 = banana. He actually believed half of it, too. He would always terminate his proofs with "QED," though the exact symbol that he used varied (it generally resembled a triangle--close enough to the actual thing). So much for AP Physics. I love physics, but that guy killed it.

MSTK
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Re: "Haiku Proof" discussion

Postby MSTK » Wed Aug 12, 2009 8:42 am UTC

I would subscribe to any blog or buy any book with important mathematical proofs in Haiku form.

nickbmx
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Re: "Haiku Proof" discussion

Postby nickbmx » Wed Aug 12, 2009 9:53 am UTC

The cartoon's definitely wrong. My friend directed me here after I pointed it out to him so I would stop ranting at him (he doesn't seem interested in my critique and explanation of the actual proof). Anyway, most of the suggested alternatives don't include the 'assume there are a finite number of primes' line, and the proof doesn't work without it. Dougallj came closest, but assumes the product is a prime (and lawsuits do not constitute a reason to excise 'bitches').

Primes being finite,
Take product of all, add one.
A prime! Q.E.D.


This is as close as I could get, but at the expense of treating Q.E.D. as an acronym and not an initialism, so anyone reading it aloud would be immediately identified as an idiot, which might rather undermine the point...

Assume finite primes.
Product of 'em all, plus one.
Factors are...? QED, slag!

Also, syllable restraints mean I've replaced the insult with a more English one. For full impact, a Cockney accent should be effected.

P.S. What the hell is up with the captchas on this forum? Who in hell can read this: Image

darktalon
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Re: "Haiku Proof" discussion

Postby darktalon » Wed Aug 12, 2009 10:26 am UTC

Another XKCD where Randall seems to have got inside my head. I remember well the effects of sleep deprivation on undergrad lectures. On reflection I have to wonder how I managed to get a 2i.

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jules.LT
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Re: "Haiku Proof" discussion

Postby jules.LT » Wed Aug 12, 2009 10:52 am UTC

Tarquin wrote:A previous poster mentioned that this is doable via modular arithmetic, which I'm sure is accurate, but without thinking about it more in that vein this claim is not self evident. In particular, it's obvious that for sufficiently high values of ai, it's possible to have a1p1.......anpn greater than x, so what we're really trying to prove here is that THERE DOES NOT EXIST A COMBINATION OF INTEGERS a1.....an such that a1p1 *.... * anpn = (p1 * p2 *...... * pn) + 1, which strikes me as not immediately self-evident Can someone explain how best to go about this proof and why it might be considered obvious?


I never heard of modular maths, but I understood it as:

1 - Assume a finite number of primes p1 ... pn
2 - pick one: pj other than 1
3 - [(p1*...*pn)+1]/pj = (p1*...*p(j-1)*p(j+1)*...*pn)+1/pj
4 - The first part is a product of integers, so it is an integer, but 1/pj is not an integer.
5 - Therefore (p1*...*pn)+1 is not divisible by pj
6 - Therefore this number is either prime or divisible by a prime that is not in the list
7 - ...
8 - Win!
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Richard Feynman & many others wrote:Keep an open mind – but not so open that your brain falls out

dissonant
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Re: "Haiku Proof" discussion

Postby dissonant » Wed Aug 12, 2009 11:41 am UTC

dantendo wrote:sorry disq, you are wrong. p1p2p3...pn+1 is not necessarily a prime.

meh1936 wrote:
dissonant wrote:
revolutionx897 wrote:... 3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid ...


The proof of the infinitude of the primes irks me more than any other! People always tack on a little superfluous (false) information right at the end, or even worse, just state that p1p2...pn+1 is prime.


It is necessary because it isn't superfluous/false information. p1p2...pn+1 isn't necessarily prime.

(2 × 3 × 5 × 7 × 11 × 13) + 1 = 30,031 = 59 × 509


from http://primes.utm.edu/notes/proofs/infinite/euclids.html:

It is a common mistake to think that this proof says the product p1p2...pr+1 is prime. The proof actually only uses the fact that there is a prime dividing this product (see primorial primes).


We are saying that any prime divisor of p1p2p3...pn+1 must be a prime larger than pn, meaning that primes are infinite.


The argument works for any finite set of primes, not necessarily the first n. It is superfluous and false to state that any prime divisor of p1p2...pn+1 must be larger than pn. It even says this on the page you linked to. For example, consider {2,7}.

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Re: "Haiku Proof" discussion

Postby tiedyeina » Wed Aug 12, 2009 12:01 pm UTC

Bit of a strained haiku but:

Euclid's Theorem works;
Infinite primes must exist
Or this would be false

Full credit for the proof to SMBC:

Spoiler:
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Last edited by tiedyeina on Wed Aug 12, 2009 12:04 pm UTC, edited 1 time in total.

JulienW
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Re: "Haiku Proof" discussion

Postby JulienW » Wed Aug 12, 2009 12:03 pm UTC

nuke wrote:Read 1 again - "Assume a finite number of primes". Next, read 2 again - "Take the product of all primes". p1..pn are necessarily the only (leave alone the first) primes as per the assumption. This is an example of reductio ad absurdum proof technique, or proof by contradiction.


I'm ok with that, I was just saying, as others did, that if (p1pn+1) has a dividor, this dividor isn't necessarily larger than all pi. (and even if it is, it isn't necessary to prove that prime numbers are infinite).

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sorceror
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Re: "Haiku Proof" discussion

Postby sorceror » Wed Aug 12, 2009 12:33 pm UTC

Dang, I thought this thread would be full of sleep-deprivation stories, or at least sleeping-in-class stories. Ah, well - I'll add a few.

1) I've never hallucinated due to lack of sleep, but once, after about a month of nowhere near enough sleep, my alarm went off, I sat up... and for a solid 30 seconds not a thought went through my head. Nothing. Blank carrier wave. Finally, I snapped out of it, made a sound like "Wuh!", shook my head, and - very frightened - resolved to get plenty of sleep the next night.

2) My brother had an 8am organic chemistry class that was taught by a man who spoke in a monotone, and usually turned off the lights, teaching by projected transparency. My brother called him "Dr. Morpheus". He would literally watch other students collapse onto their desks, or make random note-taking motions with glazed eyes. Sometimes he'd take some 'interesting' notes himself.

3) I had a 9am intro chem class freshman year - large auditorium, much sleeping got done. Until the day the prof was demonstrating photoreactivity. He used a flashbulb on a plastic bag filled with gas - pop! Then he turned to the blackboard and explained what had happened. After about half an hour, he turned back. A few rows in front of me, one guy had fallen asleep, spread out over three chairs, gently snoring.

The prof pulled out another inflated plastic bag and did it again. But someone had put way too much reactant in there - this time it wasn't "pop", it was BANG!! The prof stepped back, stunned but thankfully not hurt. I saw dust shaken off the blackboard. The sleeping guy shot straight up to a standing position, shouting "WIIAAAAHHHH!" - and then, the focus of many stares, slowly sat back down and tried to be inconspicuous thereafter.

funda
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Re: "Haiku Proof" discussion

Postby funda » Wed Aug 12, 2009 12:47 pm UTC

glasnt wrote:
FCN wrote:Top prime's divisors? Huh?

Haiku's are awesome.
But they don't have to make sense...
Refrigerator.


Making Haiku is easy. :lol:

“This would be haiku
If it had just one fewer
Syllable in this line..”

I have a problem
With my 1337 haiku technique
I always put too many syllables into the last line


One, two, three, four, five.
But now I can't count to sev-...
Stupid syllables...


I hate all haiku
Because they can only have
Seventeen syllab--

Haikus are quite fun
But they need a fourth line too
Not a haiku? Bah!
I make fourth line anyway
and perhaps a fifth.
Poorly updated Blog http://johndasfundas.blogspot.com
Yes, I will clean it up.... later
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funda
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Re: "Haiku Proof" discussion

Postby funda » Wed Aug 12, 2009 12:53 pm UTC

nickbmx wrote:The cartoon's definitely wrong. My friend directed me here after I pointed it out to him so I would stop ranting at him (he doesn't seem interested in my critique and explanation of the actual proof). Anyway, most of the suggested alternatives don't include the 'assume there are a finite number of primes' line, and the proof doesn't work without it. Dougallj came closest, but assumes the product is a prime (and lawsuits do not constitute a reason to excise 'bitches').



P.S. What the hell is up with the captchas on this forum? Who in hell can read this: Image



Is it 2R5I ?

Me thinks i'm going colour blind
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Yes, I will clean it up.... later
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Armadillo Al
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Re: "Haiku Proof" discussion

Postby Armadillo Al » Wed Aug 12, 2009 1:17 pm UTC

That opening question really looks like it should be a haiku too...but it's only 4-6-4. Frown.
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Re: "Haiku Proof" discussion

Postby Deciheximal » Wed Aug 12, 2009 1:21 pm UTC

pgn674 wrote: It means: Take the highest prime you can think of. Now take its divisors, which are 1 and the prime. Now take the product of those two divisors, which is the prime itself. Now add one. Now think about and list the factors for this number. Somehow, that makes you realise that there are infinite primes. But there really is nothing special about the next number over a prime, or its factors, I don't think.


Deciheximal wrote:
Assume 7 is the highest known prime.

7 & 1 (divisors of 7)
7 * 1= 7 (product of those two divisors, which is the prime itself)
+ 1 (now add one)
= 8
2 & 4 (Factors for this number)

2 is prime, but this is less than 7, and therefore assumed already known. Where did I go wrong?


disq wrote: Assuming 7 is the highest known prime, we take 2, 3, 5 and 7.

2 * 3 * 5 * 7 is, 210. Add 1, it's 211, a prime number.
(See http://en.wikipedia.org/wiki/Primorial_prime )


Yes, but that's not at all what the poster I quoted instructed.

And what you wrote peters out at 13. 2 * 3 * 5 * 7 * 11 * 13 = 30030 + 1 = 30031. 30031 divides by 59 and 509.

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Quicksilver
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Re: "Haiku Proof" discussion

Postby Quicksilver » Wed Aug 12, 2009 1:37 pm UTC

I think this warrants further investigation. I've been to lectures high and drunk (filled up a 2 litre bottle with vodka), sleep deprived sounds interesting. I've been tired, but not so far as all nighters and going to a lecture the next day.

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SirMustapha
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Re: "Haiku Proof" discussion

Postby SirMustapha » Wed Aug 12, 2009 1:44 pm UTC

Five seven and five
Everyone is doing it
Fuck haiku

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fenrir_darkwolf
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Re: "Haiku Proof" discussion

Postby fenrir_darkwolf » Wed Aug 12, 2009 1:48 pm UTC

mrsaturn wrote:Holy crap, after reading this
ideas to optimize a prime number finder thing i was working on entered my brain.


... It's easy to find prime numbers... finding them sequentially without missing any is hard...
"You're gonna have to learn everything anyway, so which is first is not essential."
-Richard Feynman

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SteveMB
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Re: "Haiku Proof" discussion

Postby SteveMB » Wed Aug 12, 2009 2:06 pm UTC

Product, divisor
I've been awake till I
Forgot which is which

LdyGray
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Re: "Haiku Proof" discussion

Postby LdyGray » Wed Aug 12, 2009 2:28 pm UTC

Please can there be a t-shirt that says "Q.E.D., Bitches!"?

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Re: "Haiku Proof" discussion

Postby cparker15 » Wed Aug 12, 2009 2:33 pm UTC

A meta haiku:
A haiku about haiku.
[insert punch line here]
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Re: "Haiku Proof" discussion

Postby disq » Wed Aug 12, 2009 2:44 pm UTC

Deciheximal wrote:
pgn674 wrote: It means: Take the highest prime you can think of. Now take its divisors, which are 1 and the prime. Now take the product of those two divisors, which is the prime itself. Now add one. Now think about and list the factors for this number. Somehow, that makes you realise that there are infinite primes. But there really is nothing special about the next number over a prime, or its factors, I don't think.


Deciheximal wrote:
Assume 7 is the highest known prime.

7 & 1 (divisors of 7)
7 * 1= 7 (product of those two divisors, which is the prime itself)
+ 1 (now add one)
= 8
2 & 4 (Factors for this number)

2 is prime, but this is less than 7, and therefore assumed already known. Where did I go wrong?


disq wrote: Assuming 7 is the highest known prime, we take 2, 3, 5 and 7.

2 * 3 * 5 * 7 is, 210. Add 1, it's 211, a prime number.
(See http://en.wikipedia.org/wiki/Primorial_prime )


Yes, but that's not at all what the poster I quoted instructed.

And what you wrote peters out at 13. 2 * 3 * 5 * 7 * 11 * 13 = 30030 + 1 = 30031. 30031 divides by 59 and 509.


30031 is not a prime, yes, but that's how it was instructed in the comic. (30029 is a prime, however)

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Re: "Haiku Proof" discussion

Postby sonicseaweed » Wed Aug 12, 2009 2:52 pm UTC

It is not exactly true that The product of consecutive primes plus one is a prime, it is just likely to be.

For instance 2*3*5*7*11*13+1 = 30031 but it is a product of 59 and 509, therefore not a prime (both 59 and 509 are prime by the way).

The reason that it does not work to get a prime is that it does not take into account prime numbers between the string of consecutive primes and the final answer, like 59 and 509 are primes between 13 and 30031. Would be nice if it always worked though.

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cellocgw
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Re: "Haiku Proof" discussion

Postby cellocgw » Wed Aug 12, 2009 3:50 pm UTC

Is it just me, or did anyone else see the title and think, "Cool: a comic about how to make yourself safe from people assaulting you with (bad) Haiku"?
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eds01
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Re: "Haiku Proof" discussion

Postby eds01 » Wed Aug 12, 2009 4:00 pm UTC

A haiku isn't 5-7-5 syllables, but 5-7-5 morae. The form of a haiku doesn't translate into english.

For example, a japanese haiku:
furu ike ya
kawazu tobikomu
mizu no oto

compare that to:
Three things are certain:
Death, taxes and lost data.
Guess which has occurred.

In particular, a mora is at most 3 letters long (in English letters), but generally 1 or 2. It's either a vowel, a consonant followed by a vowel, or an n (the only consonant which can be a mora on it's own). Oto, for example, is 2 morae - o and to. Tsu is one mora, and the mora with ts as the consonant are the only reason a mora could have more than 2 characters when represented in english.

A syllable can be so much longer than a mora that it really makes zero sense to equivocate them for the haiku.


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