Thursday, August 13, 2009

Comic 622: Left To The Reader

today Hought Carding blogs, but then I got so mad at this comic that I went on a rant about it too, and it was so angry that I made it one of my 'Angriest Rants'. That's at the end though. Sorry, Hought. You will have to share the spotlight with me.

it's fucking wrong!
Huh.

Well...

I really don't know where to start with this one.

I mean, it's not funny. I can start there.

The thing is, that it goes beyond being just 'not funny'. It leaves to discernible impression. It's very zen - being almost not there at all - approaching oblivion. Although that's giving it far too much credit.

So, what do we have here? We have maths. Randy likes maths. Can I call him Randy? We also have fun and games with maths! Haiku! The inherent hilarity of putting something that's not a Haiku into a Haiku! Haiku! Also we have nerd girls. Perhaps not Nerd Girls, but girls who share Randy's passion for maths. Yaaayyyyy. Then there's a, um, 'punchline'. In the loosest sense of the word.

Not so much a punchline, as a weak justification for making a joke and turning Randy's speculative poetry about prime numbers into a comic.

Alt-text also leaves me uninspired. Maybe if I indulge in some sleep deprivation, this bland comic will metamorphose into something good, like new horribleville comics or marmite.

One theory I might cautiously put forward is that Randy didn't write this; instead, a computer program, possibly written by NASA, analyzed many of the trends that appear throughout XKCD, and came out with this. Which would explain why this comic has no soul.

To conclude; this comic makes me remember the 'least interesting man in the world' comic, and smile fondly. Mostly because those beer adds that the comic were based on were kinda sweet.

Oh yeah; the art in this one is a pile of horse-ass too. I mean, obviously, the art is also bland, but sleep deprivation/hallucinations is one subject particularly suited to be shown through compelling art. You could have the teachers head and expression exaggerated and bulbous, while the sleep deprived student's eyes red raw, and bloodshot, with the visuals getting gradually more ludicrous towards the end of the comic [see, for example, the latest Subnormality - carl]. But, none of that, because Randy draws stick people. Always stick people.


-Hought Carding away!
=================
Carl again: I'm going to break some of my Summer of MADNESS rules and add my own post to this. Because I hated this comic a lot more than usual, and probably a lot more than most of you. And it's been a while since I all out blogged.

This comic is a drowning man, grasping for small molecules of humor to keep him a live another week, another month. Randall loves math and used to love drawing comics about math, because for a while there it was a rare thing on the internet so he kind of cornered that market. So here he tosses out another lame math reference for his math-nerd fans. It's not a complicated one - all the math and science in xkcd has been getting simpler over time to appeal to more people. Perhaps you didn't understand it, you stupid idiot you, but it is a pretty basic proof for those who are into math (I recall a friend explaining it to me in 7th grade).

So he's basically just trying to appeal to lots of nerds for sheer nerdery's sake. Because if you don't already know that proof (and there's more on this later) there is no way you are going to understand this one. That's a function of space, sure. For 17 syllables (well, really just 12 without the "QED") it's a fine attempt, but why the fuck write a haiku of a proof, however simple? to be a fucker. That's why. Just to say you did. fucker. Just so you could use the phrase "QED bitches". you're a bit of a QED bitch yourself, randall.

But that's not enough for him. He doesn't just present his little haiku, he has to think of some other justification for it (since "because I am a douche" might look a little odd there). So he makes it some sleep deprivation joke. But not one that makes sense. "Lectures get interesting after 48 hours of sleep deprivation"? What? What does that mean? After 48 hours, things just get horribly tedious and you just want to sleep. Lectures don't magically turn into haiku form. That doesn't make sense. In any way. Making ideas into haikus takes more work and concentration, not less. You are stupid. Maybe if you said "being on acid makes lectures more interesting" that would work a little better.

Randall: You did a good sleep-dep joke already. A long time ago. I'm not saying not to do it again, I'm just pointing out what a good joke looks like. Being tired means that the tired person gets confused easily and perhaps falls asleep randomly, not that the people around them suddenly speak in haikus and fly. god.

But all that is usual xkcd sucks stuff. Not funny, stupid, etc. That's not, on its own, enough for me to upstage Hought Carding like this. Here's why I have to write my own part. Now it's a little math heavy so you can skip it and just read the bold part down below for the gist.

Let's talk about the proof that primes go on forever. Here it is in short: If there were a finite number of primes, then there would be one prime, Q, that was the largest (see, interestingly enough, yesterday's dinosaur comic on a similar idea). So you arrange all the prime numbers, from 2 to Q. And you multiply them together. 2 * 3 * 5 * 7 * 11 *.....* Q. And that will be a crazy huge number that I will name, oh let's say Z. Now Z is of course clearly not prime, because it is divisible by all those numbers. BUT - Z+1 will not be divisible by any of those numbers. That's just what happens when you multiply a bunch of numbers together and add 1. The result is not a multiple of any of them (this makes intuitive sense; if there's a number that was, say, a multiple of 11, you'd need to add 11 more to it to get a new multiple of 11. Just adding 1 isn't enough. Likewise for any other divisor). So Z+1 is not divisible by any prime, and all composite numbers are (hence "composite," because they are "composed" of primes). SO therefore Z+1 is prime, so your list at the beginning was not the list of all possibly primes, so you are wrong, and stupid, the end.

I go through this boring math stuff A) to prove I know it, B) because the nerd in me really does find it elegant in a way, and C) Because Randall got it fucking wrong. he got it wrong. Randall wrote that the proof is to take the "Top Prime's Divisors' Product + 1", and see what its factors are, the implication being that there are none and so you have a new higher prime.

What he is claiming, using my terms, is that the product of Q's divisors + 1 is prime. But of course, Q doesn't have any divisors other than 1 and Q, because it's a prime (the "top prime" as Randy calls it). So the product of the top prime's divisors is just the top prime, Q, again. And that plus one will have a ton of divisors! Probably. It's one higher than a prime number, which is (except in the case of the number 2) always going to be even, for one thing, so divisible by at least 2, probably more.

Here's an example - 31, could be your pretend "top prime" (obviously it's not, but no prime will be, that's the point). So you take the "top primes's divisors product +1 " = (31*1)+1=32. It's "Factors are..." 1, 2, 4, 8, 16 and 32. So...there's a bunch of them!

Luckily some forumites noticed this problem, and at least one even corrected it in a new, better, haiku.

So let me now, with that clearly explained, be nice and clear about this next part. Let's even use some bold.

Randall. You draw a webcomic three times a week. Its motto is that it is a webcomic of "Romance, Sarcasm, Math, and Language." "Math" is one of those. You also worked for NASA. Doing math and physics. You hang around with MIT kids, who are mostly good at math. You do not have to spend much time on your comic. You have a good career. SO WHY CAN'T YOU JUST TAKE THE TIME TO NOT FUCK UP? You are an irresponsible hack of a cartoonist.

the end.

114 comments:

  1. I thought it was laughable that Randall doesn't even seem to check over his work, so even his simple proofs are dead wrong. More credence to the "draw these right before midnight" idea.

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  2. The biggest failing of this XKCD for me was that it ISN'T EVEN BLOODY HAIKU!!!!

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  3. It's a shame Rob doesn't know haiku either.

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  4. Not that I don't think the joke is terrible, but it should really be pointed out that many who get quite sleepy in lectures can attest to the bizarre effect where the explanations of the lecturers begin to merge with daydreams to produce very trippy results

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  5. "FB gurersbe M+1 vf cevzr, fb lbhe yvfg ng gur ortvaavat jnf abg gur yvfg bs nyy cbffvoyl cevzrf, fb lbh ner jebat, naq fghcvq, gur raq."

    Guvf vf inyvq sbe gur checbfr bs gur cebbs, ohg zvfyrnqvat. V pna'g jnvg gb frr fbzr hajvggvat nzngrhe "areq" gb nggnpx guvf nf snyfr. :c

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  6. Thank you, Carl.

    The guest review wasn't bad, but it was pretty lacklustre, lacking substance. There was A LOT to criticise on yesterday's comic, yet the review was extraordinarily empty. You filled that gap nicely. Thank you.

    The strip itself is so bad in so many different aspects, I can't even be bothered to write about it. The worst thing, though, is that the strip is just a mess of "ready" ingredients to get the fans raving: Euclid's theorem, haiku, and sleep deprivation. What's depressing is that the fans will rave merely about the PRESENCE of those ingredients, not whether they're well combined or not. But then again, what's to expect from xkcd fans? (yes, people, I'm NOT counting myself as an "xkcd fan". I may enjoy it a little too often, but I refuse to call myself a fan)

    And what's with haiku, anyway? It's even stupid to call that idiotic americanized thing "haiku", since actual haiku is so much more than that. What's the point in shoving text into a 5-7-5 structure that often has a horrible flow and rhythm, and sometimes barely makes sense? People write it just to show they can count syllables, and people read them just to show they can count syllables. It's stupid. I hate that thing.

    While we're discussing poetry, I actually think xkcd has done it well in the past: remember the Slashdot limerick and the My Generation spoof? I enjoy those.

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  7. Fernie: there's a whole lot of good american haiku. Its just the way they teach it in school that makes it seem so bad; a lot of people never get past that 5-7-5,no-flow part but keep writing them anyways.

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  8. Thanks for the correction. I probably trampled all over the legacy of respectable poets, like a crazed elephant, and I should have been more specific since I was thinking of the memetic Internet haiku sort of thing. My bad. Also, I didn't know it was taught in schools. I think the "three short verses" format can be interesting to exercise brevity and conciseness (sic?) in writing (I definitely should learn that), but people just stick to the 5-7-5 rule and ruin everything else. And Randall did exactly that.

    I'm glad none of my acquaintances are rabid xkcd fans, because if I saw a person wearing a "Q.E.D. bitches" T-shirt, I'd punch him in the jaw.

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  9. hurray, I have fans again! all it took was asserting some basic knowledge. HI ANONYMOUS LET'S HAVE CRAZY SEX IN MY TRAILER

    I do agree with fernie, which is annoying. haiku can be a wonderfully elegant form, and it is annoying to see people just stick a 5/7/5 pattern out there and say "look I wrote haiku!" and it is kind of terrible. very short writing has been my field of study for quite some time. which is why I like trolling 5/7/5 people so very much, and hence why I have a new fan--HI ANONYMOUS HUGS AND KISSES.

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  10. I wanked to the thought of Rob's hugs and kisses.

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  11. But Rob is so fat.

    SOOO fat.

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  12. At least Randall hasn't claimed to have gotten the proof wrong on purpose, since it's a hallucination. ...Yet.

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  13. yeah from the brief look at the forum i took (from carl's link) i already saw someone shrug off the non-proof as a side effect of sleep dep.

    ughhhhh

    captcha: popen. I'M POOPIN

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  14. Five seven five bitch
    In mothafuckin' haiku
    Leaves fade in autumn

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  15. WTF @ new comic

    history lesson?

    or is it a joke that no one lives in oregon or something?

    alt text referencing Oregon Trail

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  16. new comic is a super unfunny... joke, I guess, about Oregon Trail. "largely children and adolescents, mostly bring bullets for hunting"--children and teenagers mostly played oregon trail so they could hunt, and accordingly only brought bullets for hunting.

    not that it's funny, just. you know.

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  17. Blarg, way to write down everything that can happen in Oregon Trail without adding a joke of your own, RANDALL.
    Uhg, and I like list based jokes (and flow chart jokes) because I love finding throw-away jokes hidden in the larger text, but then Randall goes and forgets to write a joke at all. And here I was optimistic when I first glanced at the comic!
    My dreams are crushed again.

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  18. That's, like, not even a joke. That does not in any way have the structure of a joke.

    Also I knew it was going to be about Oregon Trail after I read the first line. Way to use the element of surprise, Randy.

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  19. ROB. That trailer is for you to write guest posts in and NOTHING ELSE. PS if you want to guest post after the MADNESS has ended, for like a week, i am going to need someone. and you have that posting-trailer just sitting there.

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  20. doesn't "dysentry" have another e in it

    dysentery

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  21. Congrats, A-man-da, you've busted Randall :p

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  22. dammit linty i thought you were my friend

    i may have to do some re-thinking

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  23. Z+1 isn't necessarily prime; it's also possible that its prime factors are simply not in the original list. For example, (2 * 3 * 5 * 7 * 11 * 13) + 1 = 30,031, which has the prime factorization 59 x 509.

    But enough of me showing off; the comic was awful, and you two did a great job tearing it apart.

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  24. Prime: well, if the list consisted of all of the primes up to the very largest, then it couldn't have prime factors that weren't on the original list, because they are by definition included in the original list.

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  25. Right. So the proof is still valid in either case; I was just responding to Carl's statement that "Z+1 is not divisible by any prime" and "therefor [sic] Z+1 is prime". Nothing more than a bit of nitpicking.


    As for 623: Okay, Randall? Hi. Now, I know you like read TV Tropes. That's great; so do I. It is an entertaining and informative website.

    If you have a moment, there are two articles that I'd like you to take a look at. Take your time and let them soak in. Ponder their implications. Consider their possible utility vis-a-vis your own life and work. This information will be on the quiz Monday. Thank you for your time.

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  26. ah. i actually think he covered that in his proof; he defined Q as the largest prime number, and defined Z as the product of all of the primes, from 2-Q.

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  27. @Amanda

    Well, *somebody's* got to take Femalethoth's old gender!

    "unrad". I guess captcha hates me and my not-surfing ways. :(

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  28. Haha, it's the things that happen in Oregon Trail, but in list form.

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  29. I played Oregon Trail! Randall, get out of my head!!

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  30. Damn you Amanda, I was gonna comment on his spelling fail.

    And if you played Oregon Trail II it started in 1840. QED, bitches.

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  31. I KNEW that there was something iffy about his proof! Other than the lame way it was presented. Bit gutted that I couldn't work it out for myself though.

    Also, I really wish that Randall would stop calling anyone who doesn't get science a "bitch":
    http://xkcd.com/54/

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  32. Wait.

    In his alt text he speaks of them leaving Oregon on said trail. The game is GOING to Oregon.

    Fail.

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  33. I don't get which post is Carl's and which is Hought Carding's. Does "Hought Carding away!" mean that he's going away, so that the previous post was his, or is it meant in the superhero sense, as if he's springing into action and about to go into some heavy guest-posting?

    Not that I don't think the joke is terrible, but it should really be pointed out that many who get quite sleepy in lectures can attest to the bizarre effect where the explanations of the lecturers begin to merge with daydreams to produce very trippy results

    No. This has never happened for me, and it has also never happened for anyone I know. And I and my college friends slept/daydreamed through a lot of lectures. The only thing that happens is that you miss a sizeable chunk of time. Nobody I've known has ever hallucinated due to staying up and working for 48 hours. It may happen, granted, but "many can attest"? No.

    New comic: lame as FUCK. Jesus, The Oregon Trail? Is there anything more cliché in geek canon to make a joke about? What's next, a comic about the cruel and dangerous passtime of jumping on turtles and migrating mushrooms that many Italian plumbers indulge in?

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  34. Also: "OMG I also know about oregon trail because everybody on the fucking internet has made a joke about it already. Get out of my head, Randall!"

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  35. Fred: second post is Carl's.

    btw coviza i had meant to ask what the hell your comment says

    why did no one else ask

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  36. I am not american. As such, I have never played origon trail.

    After the first line, I knew the joke would be about oregon trail.

    I was wrong

    There was no joke.

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  37. Person 1 get out of this blog you flag burning commie.

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  38. Sorry, Hought Carding, you're "wrong, and stupid, the end" too.

    The product of all the primes up to your 'top prime' plus one (Z+1) isn't necessarily prime - it may be the product of two or more prime numbers that all happen to be greater than the supposed 'top prime', which still proves that there's a prime higher than the supposed 'top prime', but not in the way you think it does.

    Oh well, it's more fun for the rest of us when you botch the proof yourself while you're being all critical of someone else getting it wrong.

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  39. uncivlengr, you are "wrong, and stupid, the end". The assumption was that the Q is the largest prime. You don't need to check for primes larger than Q, because under the assumption there are none. Learn how reduction ad absurdum argument works before trying to be a smartass.

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  40. Uncivlengr; I wrote the first one. Carl wrote the second one - I didn't know shit about proving infinite primes, so I declined to comment on it. Although it is kinda nice to get mixed up with Carls stuff since I reckon his is funnier than mine.

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  41. The comic was truly awful, but one thing worth noting is that sleep deprivation can cause some sick hallucinations. At least, with me.

    That, and napping while sick. I once tried to use the fundamental theorem of calculus applied in three dimensions to solve the volume of the comic book character, Rorschach, during a nap while sick.

    That, and the hallucianations are incredibly "painful". Not literally, but they just hurt in some way.

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  42. Gunax lbh, Phqqyrsvfu Cevzr naq hapviyrate sbe pbasvezvat zl cerqvpgvbaf.

    Naq, Nznaqn, lbh pna svaq bhg jung guvf vf nyy nobhg ng guvf jrofvgr.

    V nz xvaq bs na nffubyr sbe genafyngvat fbzr bs gur jrofvgr hey, ohg oybttre sbeprq zr gb, gb znxr fher gur yvax jbhyq jbex (fbeg bs).

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  43. (gung fubhyq or genafyngvat bayl fbzr bs gur jrofvgr hey)

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  44. I didn't know about "The Oregon Trail" at all before today; I don't think that game was ever popular in Brazil. But even if I knew the game, I think I wouldn't like the comic too much; the humour's too banal and predictable. Maybe I'd get a chuckle, but that's that. At least it was better than the haiku catastrophe, but then again, ANYTHING would have been.

    Also, "concision". Thank you, John. I knew I should have checked the dictionary, but NOOOO, I cannot spend mere ten seconds on that.

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  45. Timofei: yes, you start with the assumption that Q is the largest prime, which is tested by trying to find a prime larger than Q. When a larger prime is found (which is either Z+1 *OR* a factor of Z+1), we know that the assumption is false, and there is not a finite number of primes.

    If you don't attempt to prove your assumption wrong, what the hell is the point of the proof? "I'm going to assume there's a finite number of primes, therefore I'm not going to bother checking, but that still somehow proves there isn't a finite number of primes." Brilliant.

    Hought Carding: sorry, consider it directed towards Carl.

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  46. Sbe Nznaqn naq nalbar ryfr jub fgvyy unfa'g penpxrq zl pbqr, vg vf na rkgerzryl rnfl pbqr gb penpx, vs lbh unir rira gur fyvtugrfg nzbhag bs fxvyy va penpxvat pbqrf naq erpbtavmvat cnggreaf (naq, ernyyl, gur sbezre vzcyvrf gur ynggre). Urer'f n srj uvagf:

    Gur pbqr vf bayl yrggref gb yrggref. Chapghngvba erznvaf hapunatrq.
    Gur xrl sbe rapbqvat naq gur xrl sbe qrpbqvat ner gur fnzr xrl. Va bgure jbeqf, gur pbqr pbafvfgf bs cnvef bs yrggref orvat rkpunatrq.
    Lbh arrq bayl qrpbqr gur yvax, bapr lbh'ir svtherq bhg gur pbqr, nf gung jrofvgr jvyy qb nyy gur jbex sbe lbh.

    Guvf jbhyq cebonoyl or zber urycshy vs V qvqa'g rapvcure vg...

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  47. Bu, zl SHPXVAT Tbq, hapviyrate, lbh'er ernyyl fghcvq!

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  48. uncivlengr: there are no primes larger than Q. This is the assumption. You multiply ALL the primes to get Z. What are the factors of Z+1? Well, assuming the condition is true, its only Z+1 and 1.

    When you do this you're forgetting the assumption you made from the start. If you have to check that there are higher primes that might divide Z+1, you're assuming the assumption is false, which is the wrong way to do the proof.

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  49. hapviyrate, Pney'f cebbs vf cresrpgyl inyvq. Vg'f n cebbs ol pbagenqvpgvba; gur ynfg fgngrzrag pbagenqvpgf gur svefg, rira gubhtu vg sbyybjf ybtvpnyyl sebz gur svefg, gurersber gur svefg fgngrzrag zhfg or snyfr.

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  50. Amanda: He's writing in ROT13. To understand it all without having to spend time substituting all the individual letters manually, paste text here.

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  51. The complete absence of humor in today's xkcd has given me a nosebleed.

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  52. Uijt qptufs xjmm OFWFS tjmfodf ijntfmg

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  53. DEATH TO AMERICA

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  54. I'm finding this comic hard to rationalize. Randall does not work. He does not go to school. He hasn't, for months, or is it years? Point is, he has no reason to be in a lecture, much less have to miss 2 nights of sleep in order to get into it. So he's... Is he aiming to be an outsider spokesperson expressing a certain group's (undergrads and high school students) feelings? Isn't that a bit arrogant and patronizing?

    I sure feel patronized, as an undergrad in the sciences and utter geek.

    The Mandall's never complained about "ordinary school things" back when he was associated with academia, either. And besides, back then it would make sense- the early comics were from his "school years", the most natural time in which to find a bored-at-lecture trope.

    But even when he *was* a student, he didn't write/draw about boring lectures. Makes sense. He's supposed to be a math nerd, math nerds don't get bored at math lectures.

    The Oregon Trail comic: It's established fact that the Mandall enjoys 4chan, and enjoys telling the rest of the internet about all his wacky adventures in the wacky land of 4chan with all those cool kids.

    Now, I don't really go there that often, but one of the quirks of 4chan is an obsession with Oregon Trail. Really, I don't think I've even seen OT mentioned anywhere else. Now, Anonymous being Anonymous, he (they?) often fails miserably whenever he (they?) tries to play the game, the game is not really absurdly hard for a sane and singular player. So that's two links to 4chan, and no other reason to mention OT except for pseudo-meme status.

    This is another stealth 4chan joke. Another display of meme-vocabulary. Another COMMON JOKE ON THE INTERNET! comic. Well, to be sure, 4chan. Not Internet. But isn't the category for silly meme references, anyway?

    And, what's up with that guy desperately posting in rot 13? It's bizarre!
    I sure feel patronized, as an undergrad in the sciences and utter geek.

    The Mandall's never complained about "ordinary school things" back when he was associated with academia. And besides, back then it would make sense- the early comics were from his "school years", the most natural time in which to find a bored-at-lecture trope.

    But even when he *was* a student, he didn't write/draw about boring lectures. Makes sense. He's supposed to be a math nerd, math nerds don't get bored at math lectures.

    The Oregon Trail comic: It's established fact that the Mandall enjoys 4chan, and enjoys telling the rest of the internet about all his wacky adventures in the wacky land of 4chan with all those cool kids.

    Now, I don't really go there that often, but one of the quirks of 4chan is an obsession with Oregon Trail. Really, I don't think I've even seen OT mentioned anywhere else. Now, Anonymous being Anonymous, he (they?) often fails miserably whenever he (they?) tries to play the game, the game is not really absurdly hard for a sane and singular player. So that's two links to 4chan, and no other reason to mention OT except for pseudo-meme status.

    This is another stealth 4chan joke! Another display of meme-vocabulary. Another COMMON JOKE ON THE INTERNET! comic. Well, to be sure, 4chan. Not Internet. But isn't the category for silly meme references, anyway?

    Also, did Caesar throw a beer party or something? What's with the rot13?

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  55. Anonymous: by multiplying all the prime numbers and adding one and stating that it's necessarily prime, you're contradicting the original assumption that the list contained all the primes, too.

    The *whole point* is to contractict the assumption that the list of prime numbers is finite.

    The problem with your method is that you're testing two assumptions: that your list contains all primes, and that the list is finite. When you falsify the assumption that that all the primes are in the list, it doesn't directly follow that the list is infinite, just that your list is incomplete. You'll need to add something to demonstrate the infinite nature of the list.

    In the manner that it's presented in Euclid's theorem, you only need to choose any arbitrary finite list of primes (whether it's complete or not), and you can prove that there's always a prime higher than the last prime in your list. In this way you can prove that the *actual* list of all primes is infinite.

    But hey, I'm sure you guys understand Euclid's proof better than Euclid did.

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  56. uncivlengr: The brilliance of what Carl did is that the proof is correct. Go back and read it carefully.

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  57. Gur ebg13 vf fb hapviyrate unf ab vqrn V'z qvffvat uvz nf ur fcrnxf, naq gung V cerqvpgrq ur jbhyq fubj hc naq znxr fhpu n oybbql sbby bs uvzfrys.

    Ubjrire, ur fgvyy frrzf gb unir ab vqrn, qrfcvgr univat orra fubja rknpgyl ubj gb genafyngr gurfr cbfgf. Vg'f trggvat xvaq bs obevat, ernyyl...

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  58. Except that Z+1 isn't necessarily prime, of course... you keep forgetting that.

    He's saying that Z+1 is prime even though it's not in the list, but it must not be the product of *two* prime numbers that aren't in the list, because that invalidates the assumption that those numbers would have been on the list. That's taking the invalidation of the assumption as a proof in one case, and as an logical flaw in the other.

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  59. uncivlengr: think of it this way. The proof is not that there are an infinite number of primes, but that there is no highest prime. The proof shows that if there is a highest prime, there is a prime higher. Thus, there must be either no primes, or an infinite number of primes.

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  60. Ar-Pharazon: Excellent post.

    Ar-Pharazon: Excellent post.

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  61. Okay, I'm done with this rot13 shit, since it is getting kind of boring, and uncivlengr (and, apparently, Ar-Pharazôn) has been tortured for long enough.

    uncivlengr: The thing you have to realize is that the proof is not intended to produce another prime not in the list. It is intended to assume that there are only a finite number of primes, and show that that assumption leads to a contradiction (that's what a proof by contradiction does). It is valid to say that Z+1 is prime under the assumption that we started with the complete list of primes (which then contradicts that assumption). Of course, it might not be true without that assumption, but that's not the point. The point is that the assumption led to a contradiction, therefore the assumption must be false.

    If you think about it, Euclid's proof is possibly the earliest example of a non-constructive proof, at least as far as I know. Anyone know of any earlier examples?

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  62. "The proof shows that if there is a highest prime, there is a prime higher."

    Exactly, but that prime isn't necessarily Z+1. It could be another prime number between the assumed highest prime and Z+1, but for some reason people here think that this is impossible because it breaks some rule, that the assumption that Z+1 is prime doesn't.

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  63. COVIZAPIBETEFOKY: hah, that's a much better explanation than I gave :)

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  64. No one is arguing that Z+1 is prime. We are merely telling you that stating "Z+1 is prime" is valid for the purposes of the proof.

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  65. COVIZAPIBETEFOKY,

    So you're not just contradicting your assumption that all the primes are in the list, but making a false assumption that a number is prime even though you have no reason to believe that.

    That might be satisfying to you, but making false statements to disprove other false statements isn't nearly as elegant as the actual proof by Euclid.

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  66. It would work if instead of saying "Z+1 is prime" (which is precisely what is said in the post), you just said, "Z+1 isn't divisible by any number in our supposedly complete list of prime numbers".

    It's what you're trying to express without resorting to casually redefining the meaning of 'prime' within the proof.

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  67. coviza: i'm glad you stopped being a dick. Just fyi, insulting someone in a language they do not recognize doesn't make you cool, nor smarter than that someone.

    Though I gotta say, "QNZA LBH NABA" is the funniest outburst I have ever seen.

    Thank you anon 6:58!

    A-P: even though I usually agree with you, the statement "math nerds don't get bored at math lectures" is entirely false.

    But hey, I'm sure you guys understand Euclid's proof better than Euclid did.
    and
    That might be satisfying to you, but making false statements to disprove other false statements isn't nearly as elegant as the actual proof by Euclid.
    okay honestly what is the point of saying that? it's like saying "OH BY THE WAY i'm sure you understand how computers work better than the inventor of computers did! EVEN THOUGH you guys are repeatedly showing me that I am wrong I WILL BE A SNARKY BITCH cuz this is the internet." You, also, stop being a dick.

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  68. In order to show that Z+1 is composite, we have to find some prime factor it has other than itself. But we listed all the primes (and remember, the assumption is that this list is complete), so Z+1 has no prime factors. Therefore Z+1 must be prime.

    Z+1 may not itself actually be prime, but it is valid to assert that it is prime for the purposes of this proof. Here's a rough outline of the steps of the proof:

    1. Assume there are a finite number of prime numbers.
    2. Therefore, we can produce a complete list of prime numbers.
    3. Multiply all the numbers in said list; we call this number Z.
    4. Z+1 is not prime, because it's not in the list (it's larger than any number in the list).
    5. Z+1 is prime, because it is not divisible by any of the prime numbers in our complete list of prime numbers.
    6. Step 1 is false, because steps 4 & 5 contradict each other and they both follow from step 1.
    7. There must be an infinite number of prime numbers.

    Each step is valid and can be derived from the previous steps. It's called a proof by contradiction.

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  69. Amanda: meh; I just wanted everyone to know I predicted someone like uncivlengr would show up. It's not really an amazing prediction, but I was right, wasn't I?

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  70. I almost missed uncivlengr's second post while writing my response to his first post. I did not "casually redefin[e] the meaning of 'prime' within the proof"; it's a theorem in number theory that a number is prime (ie. has no factors other than 1 & itself) iff it has no prime factors other than itself.

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  71. COVIZAPIBETEFOKY: Stating that "Z+1 is prime" is not valid for the purposes of the proof because it's not valid. You may as well say "Z+1 is not prime, therefore there may be finitely many primes". It's true that you don't need to make the strongest possible statement, but the statement itself should be valid.

    uncivlegr: I didn't forget that Z+1 isn't prime, I just assumed that Carl was trolling for the sort of person who would feel the need to correct that common mistake. If you read the proof without that claim, it's still complete. Then again, maybe I give Carl too much credit.

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  72. Just take out the 'prime' bit in 5:

    5. Z+1 is not divisible by any of the prime numbers of our complete list of prime numbers.

    You don't need to say that Z+1 is prime in your proof, and it means you don't need to resort to a modified definition of 'prime'.

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  73. What are you talking about, Way Walker? Steps 4 and 5 in my outline are both valid derivations from previous steps, and the contradiction between them leads to the conclusion that the assumption was false.

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  74. The definition I heard for a prime number is that its only factors are 1 and itself. Saying that a number is prime if its only prime factors are 1 and itself is circular.

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  75. The definition is not modified; it's equivalent. Can you point out the contradiction that arises in your proof?

    Your suggestion, while possible to do, would lead to a much more complicated treatment, in which you would have to consider two cases (Z+1 is prime and Z+1 is not prime), and in the latter case show that there must still be some prime number not in the list that divides Z+1.

    It's easier, and just as valid, to do it the way Carl outlined.

    Also, there are some subtleties involved in the definition of a prime number that haven't been pointed out, but the point is, the standard definition is equivalent to saying there are no prime factors smaller than the given number.

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  76. Also, why didn't you argue against step 4, which also might be false?

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  77. About the latest thingy:

    At first I thought it was one of the "informative" comics Randall does (which I like more than his others), and I was thinking: "That's it? He just lists facts? And uninteresting ones?" Then I reread the list and see what he did there'd. So it's okay. The alt-text is lazy though.

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  78. You're right; step 4 should be:

    4. Z+1 is not in the list of prime numbers.

    If Z+1 is prime, then the list isn't complete. If it isn't prime, then its prime factors are aren't in the list, and therefore the list isn't complete.

    Either way, and without making any unsubstantiated statement about whether or not Z+1 is prime, it's demonstrated that there's prime numbers that aren't in the list, and that's what is to be shown.

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  79. Okay, so you have demonstrated what I already stated (9:28), which is that a proof which requires more complicated treatment can be produced without making any false statements.

    Now, you have yet to explain what's wrong with Carl's version, which is shorter, simpler, and every bit as valid.

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  80. It's not more complicated - I just took out the statements regarding the primality of Z+1. It's simple:

    a) Z+1 isn't in the list of prime numbers
    b) Z+1 isn't a multiple of any of the numbers in the list

    That alone demonstrates that the list isn't complete.

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  81. Yeah... the more complicated treatment lies in showing that a & b imply the that the list isn't complete.

    Let me remind you what you were here to argue in the first place:

    "The product of all the primes up to your 'top prime' plus one (Z+1) isn't necessarily prime - it may be the product of two or more prime numbers that all happen to be greater than the supposed 'top prime', which still proves that there's a prime higher than the supposed 'top prime', but not in the way you think it does."

    You said Carl's proof was wrong. Care to explain?

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  82. But what result are you using to show that Z+1 has no factors other than itself and 1? The fundamental theorem of arithmetic? That says you have a prime factorization which, by assumption, will only give you numbers on your list.

    And you don't have to consider the case that Z+1 is prime and Z+1 is not prime. Just:
    1) Assume there are a finite number of primes.
    2) Produce a complete list of primes.
    3) Let Z be the product of all the numbers in the list.
    4) Z+1 has no prime factorization because it is not divisible by any number in the list.
    5) Z+1 has a prime factorization by the fundamental theorem of arithmetic.
    6) 1 is false because 4 and 5 contradict.
    7) Therefore, there are infinitely many primes.

    I believe a more traditional way is to say
    (1-3)
    4) Z+1 can be factorized into primes by the fundamental theorem of arithmetic.
    5) Z+1 is not divisible by any prime on the list so this prime factorization includes primes not on the list.
    6) 1 is false because 2 and 5 contradict.
    7) Therefore, there are infinitely many primes.

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  83. I have explained - Carl makes the statement that "Z+1 is prime" without basis. That premise alone is a contradiction, because he's justifying it with the assumption that there are no prime numbers that aren't in his list of prime numbers.

    In such an argument, an initial assumption should logically lead to two premises that can be shown to contradict, at which point it's proven that the assumption is invalid, but a premise shouldn't contradict itself.

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  84. Anyway, backtracking through my old posts is a good sign that this conversation is over, so you'll have to deal with what you got.

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  85. oh my god MATH IS SO BORING.

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  86. "I have explained - Carl makes the statement that "Z+1 is prime" without basis. That premise alone is a contradiction, because he's justifying it with the assumption that there are no prime numbers that aren't in his list of prime numbers."

    That's... the point?

    "In such an argument, an initial assumption should logically lead to two premises that can be shown to contradict, at which point it's proven that the assumption is invalid, but a premise shouldn't contradict itself."

    Wait, what?

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  87. Best xkcd ever. This comic captures the complete essence of xkcd.
    Math: This arithmetic/number theory proof was discovered over 200 years ago.
    Language: A haiku is a crappy poem that you learn about in 3rd grade.
    Romance: I love this comic and I want randy to do me without a condom.
    Sarcasm: Well, I guess there's no sarcasm anywhere near here. Close enough.

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  88. y'all need to learn 2 reductio ad absurdum

    CAPTCHA: tedism; as preached in a gospel of Ted.

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  89. uncivlengr is correct but I fear may need some clarification.

    So here it is again.

    We assume that the primes are finite, and so we list them. 2,3,...,Q
    We then take the product of all the primes and add one. 2x3x5x...xQ + 1 = Z + 1

    As we know, Z+1 cannot have any of the primes in the list as factors. This does not necessarily mean that Z+1 is prime. In fact, as Z+1 is far bigger than any number on the list, and every prime is on that list, by our very assumption, Z+1 CANNOT be prime, as Z+1 is not on the list of all primes. We must take the assumption as true still as we have yet to reach a contradiction that disproves it. Claiming that Z+1 is prime at this point would be us discarding out original assumption without reason.

    But, as I already said, Z+1 has no factors on the list, therefore Z+1 is not composite either. But it can be proven that every natural number other than 0 or 1 is either a composite or a prime. But we have proven that Z+1 is none of those things, and so we have our contradiction.

    At this point we STILL can't prove if Z+1 is composite or prime, as we know that the list is missing primes so there is no way of knowing whether or not Z+1 is itself a missing prime, or merely a multiple of missing primes.

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  90. maze: sure, if you like being wrong

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  91. COVIZAPIBETEFOKY: Ah so *that's* why you were all doing this rot13 stuff... Looks like it accomplished exactly what it was supposed to be used for. Man, do I feel dumb now.

    Amanda: You know, maybe it's just me but not getting flamed feels weird.

    And yeah, I know. It's not really like that... My statement is meaningless, if you think about it: You could just as easily assert that all math nerds are actually number theory nerds or real analysis nerds or topology nerds or whatever.

    And it's not *entirely* false. More like sometimes false. =p I mean, math people do like at least most of their lectures, right? Right?

    Anyway, yeah. Just liking a subject doesn't guarantee an interesting lecture. (That's one of the wonderful things I've learned in college!) But you'd think some guy who LOVES math would mostly be posting about how awesome his math lecture was. Or at least could have been, if it was like such and such. Not whine about how it was boring boring boring and he'd so much rather be doing something else.

    *shrug* Just my naive assumption, really. That if people like something, they'll complain less about it. I'm sure that this is also, likewise, false... I'd rather naively delude myself to escape the harsh reality, however.

    CAPTCHA: "messes". It's gotta be a sign, man!

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  92. OH AND 0.9999999... TOTALLY EQUALS ONE

    INITIATE DESTRUCTION SEQUENCE

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  93. that is my favorite proof! how did you know this

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  94. I hate Subnormality. I've always had a vague disliking of it but with the 'trolls' comic I became enraged. IF YOU CRITICISE ME YOU ARE A TROLL, OK! I HAVE SOMETHING TO SAY AND I KNOW I'M RIGHT SO SHUT UP ALL OF YOU! OH FORGET IT I'M GOING TO WATCH MY NIRVANA PORN AGAIN.

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  95. Dumb person: (offensive statement)
    Person who uses words he doesn't understand:
    OMG IT'S A TROLL!!!

    Dumb person: (dumb statement)
    Person who uses words he doesn't understand:
    OMG IT'S A TROLL!!!

    Person: (statement disapproving of somethhing PWUWHDU approves of)
    Person who uses words he doesn't understand: OMG IT'S A TROLL!!!

    Captcha: Kuwai. WEEABOO.

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  96. Did someone just say "Weeaboo"?

    'cause I think I just heard someone say "Weeaboo."

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  97. I don't really care what you think. FTW.

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  98. Wow, people. Either there's something you don't get, or you're part of a minority. Randall's comic is read by shitloads of people who find it funny as hell; you can't think he'll stop just because you don't like it. I will give you that the proof doesn't make sense, but otherwise, you don't.

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  99. Anon, do you think that Twilight is good because it's read by shitloads of people who find it amazing as hell?

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  100. No, but I think it's pointless for you to rant on about how xkcd needs to be stopped because a few people dislike it.

    PS Twilight SUCKS.

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  101. Furthermore (and sorry for double posting), this being about what I meant to say earlier, do you really have nothing better to do than to criticize someone whose personal success/failure will not affect you and whose comic you must read only by choice? If you think it's so bad, don't read it in the first place.

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  102. So Twilight sucking is exactly the reason why it is an apt comparison. You can opt not to read it, but you are also subjected to millions of crazy fans and seeing at least a dozen Twilight adverts everywhere you go. xkcd is the Twilight of the internet--it isn't nearly as good as SOME people think, but since that audience tends to be extremely vocal (and do annoying things such as immediately posting xkcd to reddit), we are actually forced to see it even if we don't want to read it.

    I would say that Twilight's success negatively affects me (and our generation) by putting it into the minds of little girls that they can be clingy and weepy and weak and marry a controlling, abusive man, and not abort a baby even if it kills them. I would say that xkcd negatively affects me (and our generation) by putting it into the minds of already pretentious faux-geeks that their pretentiousness is validated.

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  103. except for one thing amanda: twilight fucking ROCKS. it is the best. so your analogy is WRONG.

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  104. fuck you carl

    you are not worthy of captchas anyway

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  105. Just so you know, I am the anon from earlier. You do have a valid point. I'm still going to like xkcd, you're still going to dislike it, and it's time I accept that. Your analogy is completely correct, but I still think complaining about xkcd on the internet is a waste of time. Then again, by the same token, I'm wasting my own time caring about those opinions of yours which are of little importance.


    And Twilight SUCKS. I mean really, the premise is just stupid. I hardly think I could be any worse of a writer, but I believe I could come up with a better idea and make a better story.

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  106. but could you make something more HILARIOUS and find worse actors to be in your movies? I THINK NOT.

    Anyway, consider this: I'm getting a ton of practice writing, which is a good skill I think, not to mention learning about the communication and technical aspects of blogging, which are also really useful.

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  107. of course! one day we will all even meet at a giant xkcd sucks convention somewhere. it'll be crazy! I'll even give ch00f the $10 I promise I'd give him if we ever met in person.

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