0804: "Pumpkin Carving"

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glasnt
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0804: "Pumpkin Carving"

Postby glasnt » Mon Oct 11, 2010 4:01 am UTC

Image
URL: http://xkcd.com/804/
Original Title Text: If only King Solomon had known about the Banach-Tarski theorem ...
"New and Improved" iTitleText 2.0: The Banach-Tarski theorem was actually first developed by King Solomon, but his gruesome attempts to apply it set back set theory for centuries.


Pumpkins. Carving. Australians don't get it.

Hi joee!

Also, 65000 threads. Woo!
Last edited by glasnt on Mon Oct 11, 2010 4:13 am UTC, edited 2 times in total.

link3000
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Re: 0804: Pumpkin Carving

Postby link3000 » Mon Oct 11, 2010 4:03 am UTC

Beat me to it.

I liked the comic. But who was the narrator? The white hat guy, I'll bet.
Last edited by link3000 on Mon Oct 11, 2010 4:03 am UTC, edited 1 time in total.

SocialSceneRepairman
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Re: 0804: Pumpkin Carving

Postby SocialSceneRepairman » Mon Oct 11, 2010 4:03 am UTC

Don't take the Axiom of Choice? You won't tell me how to carve my pumpkins, Andrew Schafley!

wackojacko1138
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Re: 0804: Pumpkin Carving

Postby wackojacko1138 » Mon Oct 11, 2010 4:04 am UTC

The best explanation of the Banach-Tarski theorem I've ever seen is in the commentary to an "Irregular Webcomic." Damned if I can find it, though.

EDIT: HERE IT IS: http://www.irregularwebcomic.net/2339.html

Also, it's spelled "Schlafly."

Meem1029
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Re: 0804: Pumpkin Carving

Postby Meem1029 » Mon Oct 11, 2010 4:05 am UTC

Nice comic. Also, congratulations on being exactly thread 65000, not that it matters at all. It's just cool.

And I think the combination of Nitro Glycerin and Pumpkins sounds like it could be entertaining.
cjmcjmcjmcjm wrote:If it can't be done in an 80x24 terminal, it's not worth doing

wackojacko1138
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Re: 0804: Pumpkin Carving

Postby wackojacko1138 » Mon Oct 11, 2010 4:08 am UTC

I suppose it's not really important that the Banach-Tarksi theorem doesn't apply to real objects...because, you know...atoms...

pgn674
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Re: 0804: Pumpkin Carving

Postby pgn674 » Mon Oct 11, 2010 4:10 am UTC

Isn't the img-title "The Banach-Tarski theorem was actually first developed by King Solomon, but his gruesome attempts to apply it set back set theory for centuries."?

black_hat_guy
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Re: 0804: Pumpkin Carving

Postby black_hat_guy » Mon Oct 11, 2010 4:10 am UTC

You could split the atoms in two, but this would result in not having a pumpkin anymore.
Billy was a chemist.
He isn't any more.
What he thought was H2O
was H2SO4.

black_hat_guy
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Re: 0804: Pumpkin Carving

Postby black_hat_guy » Mon Oct 11, 2010 4:11 am UTC

Whoa! You're right. The title text changed since this came out.
Billy was a chemist.
He isn't any more.
What he thought was H2O
was H2SO4.

Klye
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Re: 0804: Pumpkin Carving

Postby Klye » Mon Oct 11, 2010 4:17 am UTC

From Halloween 2009:
Image
Phi wrote: Be careful when touching it though. It really expands.

Why would she say that?!?

A1lion835
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Re: 0804: Pumpkin Carving

Postby A1lion835 » Mon Oct 11, 2010 4:20 am UTC

I actually liked this comic, mostly because of it's miraculous inclusion of a punchline. However, Randy managed to screw that up a bit: I don't see much use for any text after the Banach-Tarski idea. Just let it sink in. "I told you not to take the axiom of choice," distracts from the punchline and doesn't add anything. Other than that, good.

(It's my first post here :D)

pgn674
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Re: 0804: Pumpkin Carving

Postby pgn674 » Mon Oct 11, 2010 4:24 am UTC

Can anyone explain why you can do this doubling thing with solid spheres, but not with sphere surfaces, solid circle disks, or circle outlines?

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joee
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Re: 0804: Pumpkin Carving

Postby joee » Mon Oct 11, 2010 4:31 am UTC

glasnt wrote:Pumpkins. Carving. Australians don't get it.

Hi joee!

Also, 65000 threads. Woo!


HI CRACK GLASNT BOOM!

My housemates' kids were taken pumpkin carving last year. I thought it was super-weird.
Hi glasnt.

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Qaanol
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Re: 0804: Pumpkin Carving

Postby Qaanol » Mon Oct 11, 2010 4:41 am UTC

pgn674 wrote:Can anyone explain why you can do this doubling thing with solid spheres, but not with sphere surfaces, solid circle disks, or circle outlines?

The Irregular Webcomic linked above should give you a pretty solid intuition for that. You could also check Wikipedia or MathWorld, and if still not satisfied then ask here.
wee free kings

lingomaniac88
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Re: 0804: Pumpkin Carving

Postby lingomaniac88 » Mon Oct 11, 2010 5:09 am UTC

That Irregular Webcomic link does a great job of explaining how Banach-Tarski works. I've always wondered about that.
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glasnt
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Re: 0804: Pumpkin Carving

Postby glasnt » Mon Oct 11, 2010 5:10 am UTC

Just think, if this is what a hammer + ng does...

http://www.youtube.com/watch?v=r17czTWHFmU

From boingboing <3

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aurumelectrum13
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Re: 0804: Pumpkin Carving

Postby aurumelectrum13 » Mon Oct 11, 2010 5:11 am UTC

joee wrote:
glasnt wrote:Pumpkins. Carving. Australians don't get it.

Hi joee!

Also, 65000 threads. Woo!


HI CRACK GLASNT BOOM!

My housemates' kids were taken pumpkin carving last year. I thought it was super-weird.


Weird as opposed to what?

Also: this year, I shall be following the existentialist.

Draco18s
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Re: 0804: Pumpkin Carving

Postby Draco18s » Mon Oct 11, 2010 5:12 am UTC

I think my brain exploded.

I get it, but, ow.

Crosshair
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Re: 0804: Pumpkin Carving

Postby Crosshair » Mon Oct 11, 2010 5:17 am UTC

I like the second frame the best. :twisted:

For something slightly more legal, just cover your pumpkins in peeper spray to "keep the squirrels off of them".

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Icalasari
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Re: 0804: Pumpkin Carving

Postby Icalasari » Mon Oct 11, 2010 5:17 am UTC

"I carved a PUMPKIN!"

Honestly, that was the funniest panel to me :D

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Re: 0804: Pumpkin Carving

Postby Uninfinity » Mon Oct 11, 2010 5:32 am UTC

You know, I wouldn't mind knowing what King Solomon has to do with that theorum...

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Re: 0804: Pumpkin Carving

Postby SlyReaper » Mon Oct 11, 2010 5:44 am UTC

A1lion835 wrote:I actually liked this comic, mostly because of it's miraculous inclusion of a punchline. However, Randy managed to screw that up a bit: I don't see much use for any text after the Banach-Tarski idea. Just let it sink in. "I told you not to take the axiom of choice," distracts from the punchline and doesn't add anything. Other than that, good.

(It's my first post here :D)


Well it does. The axiom of choice is necessary for the Banach-Tarski theorem to work.
Image
What would Baron Harkonnen do?

++$_
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Re: 0804: Pumpkin Carving

Postby ++$_ » Mon Oct 11, 2010 5:44 am UTC

Uninfinity wrote:You know, I wouldn't mind knowing what King Solomon has to do with that theorum...
Think babies.

Shay Guy
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Re: 0804: Pumpkin Carving

Postby Shay Guy » Mon Oct 11, 2010 5:58 am UTC

Yo dawg, I heard you like pumpkins, so I put a pumpkin in your pumpkin so you can carve while you carve.
Sorry.

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StClair
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Re: 0804: Pumpkin Carving

Postby StClair » Mon Oct 11, 2010 6:04 am UTC

Panel 1:
Recursion is fun.

L!me
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Re: 0804: Pumpkin Carving

Postby L!me » Mon Oct 11, 2010 6:38 am UTC

pgn674 wrote:Can anyone explain why you can do this doubling thing with solid spheres, but not with sphere surfaces, solid circle disks, or circle outlines?


You can do much the same thing with sphere shells and circle outlines, indeed, the BT theorem uses this in cloning the spheres. Not sure if you can do the solid disks, as I can't remember how the hole generated in the centre of the clone is plugged.
If you're looking for a physical book to read on the subject,I'd recommend The Pea and the Sun: A Mathematical Paradox by one Leonard Wapner; it gives a more in-depth explanation than Irregular Webcomic.

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Re: 0804: Pumpkin Carving

Postby NotAllThere » Mon Oct 11, 2010 7:17 am UTC

++$_ wrote:
Uninfinity wrote:You know, I wouldn't mind knowing what King Solomon has to do with that theorum...
Think babies.

There's even a movie about it, if you haven't read the book.
yangosplat wrote:So many amazing quotes, so little room in 300 characters!

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Quaternia
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Re: 0804: Pumpkin Carving

Postby Quaternia » Mon Oct 11, 2010 8:10 am UTC

Best comic in a long time! An instant-classic in my books = )
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Diadem
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Re: 0804: Pumpkin Carving

Postby Diadem » Mon Oct 11, 2010 9:52 am UTC

This comic was awesome. One of the best in a long time. And the alt-text made me laugh out loud.


And yeah, the Axiom of Choice is evil. Down with the Axiom of Choice!
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
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Tualha
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Re: 0804: Pumpkin Carving

Postby Tualha » Mon Oct 11, 2010 10:40 am UTC

The alt-text made me laugh too. Is panel 3 a reference to something?

KraZug
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Re: 0804: Pumpkin Carving

Postby KraZug » Mon Oct 11, 2010 11:04 am UTC

Given that yesterday afternoon (while I was out) some kids came into my garden, cut the pumpkins I've been growing off the vine and then threw them at each other or just at the floor, I like BHG's plan here!

nazgul92
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Re: 0804: Pumpkin Carving

Postby nazgul92 » Mon Oct 11, 2010 12:37 pm UTC

The last few after the internet 2 have just been awesome.
Keep up the good work!

ancientcampus
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Re: 0804: Pumpkin Carving

Postby ancientcampus » Mon Oct 11, 2010 1:16 pm UTC

Explanation for people who don't get the joke (i.e. me until I checked Wikipedia):

From Wikipedia (because I'm too lazy to paraphrase)
The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3-dimensional space can be split into a finite number of non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball.

There ya go
Link: http://en.wikipedia.org/wiki/Banach%E2% ... ki_paradox

Not_an_S
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Re: 0804: Pumpkin Carving

Postby Not_an_S » Mon Oct 11, 2010 3:14 pm UTC

I liked the last panel the best. Probably because instead of actually caring about the theories I was thinking "I'M CARVING UP ALL THESE PUMPKINS" "I WARNED YOU ABOUT THE AXIOM OF CHOICE I TOLD YOU DOG"

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willpellmn
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Re: 0804: Pumpkin Carving

Postby willpellmn » Mon Oct 11, 2010 3:28 pm UTC

I think this thread is the closest thing XKCD has to a cast page. I can't think of another time when four recurring characters (assuming the guy with no hat is a particular character and not some random nondescript person) are all pictured, let alone pictured at a large size in identical positions so you don't have to parse their motions through the nonexistent background.

(Seriously, Randall, we know you can draw awesome landscapes. Couldn't you actually DO IT at least once in a while? I understand not wanting to do that much work three times a week, but once in three months or so isn't an unreasonable wish. The last strip I remember with color and detailing was "Lighthouse" which was what, in the 400s?)

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willpellmn
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Re: 0804: Pumpkin Carving

Postby willpellmn » Mon Oct 11, 2010 3:38 pm UTC

Okay, I'm a reasonably smart guy, but Wikipedia's attempts to summarize math hurt my brain big-time (you would think Wikipedia, being written in majority BY the layperson, would be written FOR the layperson). I half-comprehend what the Axiom of Choice is about, but could someone tell me what exactly a Choice Function is? That term's own page doesn't even vaguely describe it outside of math jargon in the intro paragraph.

jbo5112
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Re: 0804: Pumpkin Carving

Postby jbo5112 » Mon Oct 11, 2010 3:43 pm UTC

Uninfinity wrote:You know, I wouldn't mind knowing what King Solomon has to do with that theorum...

Two prostitutes were brought to King Solomon, both of who had given birth recently. One of the babies had died, and both women claimed to be the mother of the living baby.

His solution was to cut the baby in half and give half of it to each woman. The mother protested, and to save the child's life lied. She told Solomon that she wasn't really the mother and he shouldn't kill the baby. I guess the other woman would rather get half the baby than nothing, and Solomon knew to give the baby to the woman who protested against killing the child.

You can read the story here:http://www.biblegateway.com/passage/?search=1%20Kings%203:16-28&version=NIV

Technical Ben
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Re: 0804: Pumpkin Carving

Postby Technical Ben » Mon Oct 11, 2010 4:03 pm UTC

Wait a second. Black hat guy does not wear that type of hat does he?
It's all physics and stamp collecting.
It's not a particle or a wave. It's just an exchange.

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willpellmn
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Re: 0804: Pumpkin Carving

Postby willpellmn » Mon Oct 11, 2010 4:10 pm UTC

jbo5112 wrote:
Uninfinity wrote:You know, I wouldn't mind knowing what King Solomon has to do with that theorum...

Two prostitutes were brought to King Solomon, both of who had given birth recently. One of the babies had died, and both women claimed to be the mother of the living baby.

His solution was to cut the baby in half and give half of it to each woman. The mother protested, and to save the child's life lied. She told Solomon that she wasn't really the mother and he shouldn't kill the baby. I guess the other woman would rather get half the baby than nothing, and Solomon knew to give the baby to the woman who protested against killing the child.

You can read the story here:http://www.biblegateway.com/passage/?search=1%20Kings%203:16-28&version=NIV


As an avowed non-mathist (shut up that's a word), I would protest that the logic is faulty here - regardless of which one was actually the mother, neither one has any use for half a baby - it would just get blood all over her good working dress. So whichever one would rather give up the baby is just the first one to realize that she doesn't want to see a baby get chopped in half just so she can get her clothes soiled.

I suspect that a lot of logic in texts of the Solomonic age holds up about as well as this anecdote when regarded as literally having happened. Makes you wonder if someone is later going to read a transcript of this comic and believe that the ancient Americans actually used to fill their pumpkins with nitroglycerin.

crossalchemist
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Re: 0804: Pumpkin Carving

Postby crossalchemist » Mon Oct 11, 2010 4:16 pm UTC

willpellmn wrote:
jbo5112 wrote:
Uninfinity wrote:You know, I wouldn't mind knowing what King Solomon has to do with that theorum...

Two prostitutes were brought to King Solomon, both of who had given birth recently. One of the babies had died, and both women claimed to be the mother of the living baby.

His solution was to cut the baby in half and give half of it to each woman. The mother protested, and to save the child's life lied. She told Solomon that she wasn't really the mother and he shouldn't kill the baby. I guess the other woman would rather get half the baby than nothing, and Solomon knew to give the baby to the woman who protested against killing the child.

You can read the story here:http://www.biblegateway.com/passage/?search=1%20Kings%203:16-28&version=NIV


As an avowed non-mathist (shut up that's a word), I would protest that the logic is faulty here - regardless of which one was actually the mother, neither one has any use for half a baby - it would just get blood all over her good working dress. So whichever one would rather give up the baby is just the first one to realize that she doesn't want to see a baby get chopped in half just so she can get her clothes soiled.

I suspect that a lot of logic in texts of the Solomonic age holds up about as well as this anecdote when regarded as literally having happened. Makes you wonder if someone is later going to read a transcript of this comic and believe that the ancient Americans actually used to fill their pumpkins with nitroglycerin.


That's not quite the complete story. The true mother was willing to give up her baby to the other woman so that it would live whereas the other woman continued fighting. That was how Solomon knew who the mother was. The one willing to sacrifice. The logic actually works pretty well for the ancient culture Solomon was in.

Also, given Solomon's history from the Bible, I doubt he would have actually killed the baby. If the test didn't work he probably would have given the child to the women in his harem. At least that's my theory anyway, but I am biased.


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