0804: "Pumpkin Carving"

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Technical Ben
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Re: 0804: Pumpkin Carving

Postby Technical Ben » Mon Oct 11, 2010 4:28 pm UTC

Oh, and is it not cheating to say "finite number of pieces" over an "infinite" amount of points/locations? Like me saying I can cut it up in an infinite amount of pieces made of finite points?

Oh, and the "cutting a baby in half" argument is kind of missing the point. These people were not thinking rationally. One had lost a baby, the other was about to. Their emotions were at play. So giving them an even greater situation to deal with, brought out the thoughts and emotions even more. The one who thought "I don't care, I've already lost my child" was shown to be thinking just that, the other "as long as my child lives, I will be happy". We are human after all.
[edit]
We occasionally get people lying in disaster situations. But 99% of the population who shout out "my child is trapped in that car/house" will be telling the truth.
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Re: 0804: Pumpkin Carving

Postby Paladin65536 » Mon Oct 11, 2010 4:31 pm UTC

I think I understand why the Banach–Tarski theorem doesn't work on a 2-dimensional circle, but would it work on a 4-dimensional hypersphere? I can't quite wrap my head around the idea =P

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Re: 0804: Pumpkin Carving

Postby Pfhorrest » Mon Oct 11, 2010 4:36 pm UTC

Diadem wrote:And yeah, the Axiom of Choice is evil. Down with the Axiom of Choice!

The Axiom Choice has a well-known liberal bias.

Damn liberals and their being so pro-Choice and all...
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Re: 0804: Pumpkin Carving

Postby tojo940 » Mon Oct 11, 2010 4:45 pm UTC

Pfhorrest wrote:
Diadem wrote:And yeah, the Axiom of Choice is evil. Down with the Axiom of Choice!

The Axiom Choice has a well-known liberal bias.

Damn liberals and their being so pro-Choice and all...

Have you been reading Conservapedia again?

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Lady Freya
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Pumpkin Carving

Postby Lady Freya » Mon Oct 11, 2010 5:46 pm UTC

Not knowing what the Banach–Tarski paradox was I googled it and found the wikipedia, then I chuckled at the punchline.

Then, I wondered how many people saw the comic and didn't know what the Banach–Tarski paradox was.

Then I wondered if enough people had viewed the XKCD comic and googled "Banach–Tarski paradox" to influence a google trend, so I typed Banach–Tarski paradox into google trends. Unfortunately it is so rarely searched for that it has no trend.

I think this needs to change.

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Re: 0804: Pumpkin Carving

Postby pizzazz » Mon Oct 11, 2010 6:02 pm UTC

This comic is pretty much genius.

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Re: 0804: Pumpkin Carving

Postby jonas » Mon Oct 11, 2010 6:21 pm UTC

The fourth guy actually just assembled two smaller pumpkins from pieces of a larger one.

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Re: 0804: Pumpkin Carving

Postby Nollidge » Mon Oct 11, 2010 6:24 pm UTC

What is panel 3 supposed to be about?

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Re: 0804: Pumpkin Carving

Postby chapel » Mon Oct 11, 2010 7:06 pm UTC

tojo940 wrote:
Pfhorrest wrote:
Diadem wrote:And yeah, the Axiom of Choice is evil. Down with the Axiom of Choice!

The Axiom Choice has a well-known liberal bias.

Damn liberals and their being so pro-Choice and all...

Have you been reading Conservapedia again?


I can't tell you the number of times I have double checked that just to make sure that it really said that. I bet Wiles is pissed to find out that he didn't really prove Fermat's Last.

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Re: 0804: Pumpkin Carving

Postby thefool » Mon Oct 11, 2010 8:02 pm UTC

I hope the next comic on this topic involves constructing a ball pit out of one pumpkin.

Though it unfortunately may turn back into 1 pumpkin at the stroke of midnight.

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Re: 0804: Pumpkin Carving

Postby existentialpanda » Mon Oct 11, 2010 8:06 pm UTC

willpellmn wrote:(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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Re: 0804: Pumpkin Carving

Postby dbmag9 » Mon Oct 11, 2010 8:19 pm UTC

I second the enquiry as to what any references are in panel 3.
-dbmag9

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Re: 0804: Pumpkin Carving

Postby The_Mexican » Mon Oct 11, 2010 9:11 pm UTC

willpellmn wrote:(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?)


Randall draws backgrounds more like once a month, give the guy a break. (The most recent one was about 3 weeks ago: http://xkcd.com/795/)

Some other ones: http://xkcd.com/789/, http://xkcd.com/787/, http://xkcd.com/781/, http://xkcd.com/780/, http://xkcd.com/772/ The list goes on and on, it's much more frequent than you think.
Last edited by The_Mexican on Mon Oct 11, 2010 9:14 pm UTC, edited 2 times in total.

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Re: 0804: Pumpkin Carving

Postby Pterosaur » Mon Oct 11, 2010 9:13 pm UTC

Panel 1: Teeheehee!
Panel 2: The warning label negates liability. Nice.
Panel 3: Way to bum me out, Ms. Mopey McBuzzkill.

As for Panel 4:

Lady Freya wrote:Then I wondered if enough people had viewed the XKCD comic and googled "Banach–Tarski paradox" to influence a google trend, so I typed Banach–Tarski paradox into google trends. Unfortunately it is so rarely searched for that it has no trend.

I think this needs to change.


I’m sure that this is Randall’s true intention in these obscure comic punch lines. He wants to see “Banach–Tarski paradox” in the trend list between “Emma Watson hot” and “kitten in paper bag.”
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Re: 0804: Pumpkin Carving

Postby BcNexus » Mon Oct 11, 2010 9:48 pm UTC

So...does the second pumpkin have any volume or not?

Assuming the second pumpkin has no volume, that means there's no icky guts to scoop out. This is awesome! Geometry has saved me from scooping out icky pumpkin guts!

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Re: 0804: Pumpkin Carving

Postby SpringLoaded12 » Mon Oct 11, 2010 10:55 pm UTC

Take out Panel 3, and this is the perfect xkcd halloween special comic.

(Beret Guy was the best, especially if you read his line with an enthusiastic voice)
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Re: 0804: Pumpkin Carving

Postby neoliminal » Mon Oct 11, 2010 11:36 pm UTC

StClair wrote:Panel 1:
Recursion is fun.


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Re: 0804: Pumpkin Carving

Postby mikekearn » Tue Oct 12, 2010 1:45 am UTC

Crosshair wrote: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".

Peeper spray? Is that legal?
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Re: 0804: Pumpkin Carving

Postby Ghandi 2 » Tue Oct 12, 2010 4:25 am UTC

Just terrible.

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Re: 0804: Pumpkin Carving

Postby mcv » Tue Oct 12, 2010 9:02 am 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.

This logic holds up wonderfully. Solomon didn't want to cut up the baby, he wanted to know who the real mother was. The mother of the live baby just wanted her baby to live. The mother of the dead baby was jealous of the mother with the living baby, and wouldn't mind seeing it dead. Then at least she wouldn't be alone in her misery.

That you're even considering that someone might have any use for half a baby means you're thinking on completely the wrong level here. It's not about math, it's about psychology and emotion, and playing those by applying devious logic. There's plenty of practical wisdom in the bible, but this is definitely the most devious application of it.

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Re: 0804: Pumpkin Carving

Postby stardragon » Tue Oct 12, 2010 9:30 am UTC

Exactly what are the two people on the side of the nitroglycerin box doing?

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Re: 0804: Pumpkin Carving

Postby melladh » Tue Oct 12, 2010 9:35 am UTC

I hope this will get a followup comic regarding the nitro one
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Re: 0804: Pumpkin Carving

Postby ReverendJohn » Tue Oct 12, 2010 2:20 pm UTC

The Existentialist's head looks like an acorn.

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Karilyn
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Re: 0804: Pumpkin Carving

Postby Karilyn » Tue Oct 12, 2010 4:14 pm UTC

willpellmn wrote: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.

The specific detail of the story that was left out was that the two women hated each other. The non-mother was satisfied with the idea, because it would kill the mother's child, which was just as good as taking it away from the mother. The goal was not to get a child, but to hurt the mother.

Sadly, the exact same attitude seems to be common in parenting disputes between divorced parents, with one parent who doesn't give a shit about the child, fighting tooth and nail for singular custody, purely to hurt the parent which does care about the child. The tragedy is compounded by the fact that the legal system overwhelmingly favors the mother, which makes it all the more horrific when the father is the parent which cares about the child, and the mother couldn't give two rats ass if the child died tomorrow, because the mother will probably get singular custody without even having to really put in much effort over it.
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Re: 0804: Pumpkin Carving

Postby cjm » Tue Oct 12, 2010 8:00 pm UTC

This entire comic is pretty brilliant.

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Re: 0804: Pumpkin Carving

Postby Pfhorrest » Tue Oct 12, 2010 8:57 pm UTC

I don't see why so many people dislike the third panel. I think the mood whiplash between the different characters is part of the humor of the comic: (1) silly, (2) sadistic, (3) sad, (4) gwaaah..?
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Re: 0804: Pumpkin Carving

Postby phillipsjk » Tue Oct 12, 2010 9:16 pm UTC

I confess I did not know about it until today, but The Banach-Tarski theorem sounds like rounding error.

Essentially, you break the object into an uncountable number of pieces points. When you re-assemble the pieces into countable objects again, the count does not have to be the same.

Given my current understanding of the theorem, it should be possible to get 1 or 0 objects from two, but I am probably missing an important detail.
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Re: 0804: Pumpkin Carving

Postby Gd8908 » Tue Oct 12, 2010 9:58 pm UTC

lol. If only there was some way to split the atoms without... well, destroying the pumpkin. I'm gonna go to the store to buy a whittling knife now... and a pumpkin...

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Re: 0804: Pumpkin Carving

Postby Pfhorrest » Wed Oct 13, 2010 2:39 am UTC

phillipsjk wrote:Given my current understanding of the theorem, it should be possible to get 1 or 0 objects from two, but I am probably missing an important detail.


You can't just split up the sphere into arbitrarily many (or few) spheres (though 1 is trivially easy: do nothing).

The crux of it is that you can divide up certain sets into subsets in a way that any one of those subsets can be put into one-to-one correspondence with several other of those subsets (including itself): similar to how the numbers between 1 and 2 can be put into one-to-one correspondence with the numbers between, say, 0 and 4, or any other arbitrary interval. (The functions which do this kind of transformation are good ol' multiplication and division).

As the linked IrregularWebcomic explanation put it (ignoring the requisite fifth subset): You can divide it up into sets A, B, C, and D. Then take A and C off to one side, and put B and D off somewhere else. Nothing fancy so far, right? You've just split up the set into two parts.

The trick is, the way A, B, C, and D were defined, there is a function that transforms C into (B and C and D); so A and C can be transformed into A and (B and C and D), i.e. the whole set.

Meanwhile you still have B and D sitting off somewhere else; now you can do the same with B, and turn it into (A and B and C), then put that together with D and voila! You've got another of the whole set!

Which doesn't sound any more crazy than anything else in set theory (e.g. there being as many numbers between 1 and 2 as there are on the entire number line), until you model the elements of the set as points on a geometric object, and suddenly you see you can turn one geometric object into two... provided the object really is continuous, which actual physical objects never are.

Then again, with a truly continuous sphere you could just spread the same number of points out over twice the area (or volume, or whatever you choose), without decreasing the density of points in the sphere; then distort the sphere in the right way to get two conjoined spheres of equal area (or volume or whatever) to the first.
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Re: 0804: Pumpkin Carving

Postby Have_A_SnApple » Wed Oct 13, 2010 3:55 am UTC

Look what this comic did to searches for "Axiom of Choice":
http://www.google.com/trends?q=%22axiom+of+choice%22&ctab=0&geo=all&date=mtd&sort=0

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Re: 0804: Pumpkin Carving

Postby ConMan » Wed Oct 13, 2010 4:41 am UTC

Pfhorrest wrote:
phillipsjk wrote:Given my current understanding of the theorem, it should be possible to get 1 or 0 objects from two, but I am probably missing an important detail.


You can't just split up the sphere into arbitrarily many (or few) spheres (though 1 is trivially easy: do nothing).

The crux of it is that you can divide up certain sets into subsets in a way that any one of those subsets can be put into one-to-one correspondence with several other of those subsets (including itself): similar to how the numbers between 1 and 2 can be put into one-to-one correspondence with the numbers between, say, 0 and 4, or any other arbitrary interval. (The functions which do this kind of transformation are good ol' multiplication and division).

As the linked IrregularWebcomic explanation put it (ignoring the requisite fifth subset): You can divide it up into sets A, B, C, and D. Then take A and C off to one side, and put B and D off somewhere else. Nothing fancy so far, right? You've just split up the set into two parts.

The trick is, the way A, B, C, and D were defined, there is a function that transforms C into (B and C and D); so A and C can be transformed into A and (B and C and D), i.e. the whole set.

Meanwhile you still have B and D sitting off somewhere else; now you can do the same with B, and turn it into (A and B and C), then put that together with D and voila! You've got another of the whole set!

Which doesn't sound any more crazy than anything else in set theory (e.g. there being as many numbers between 1 and 2 as there are on the entire number line), until you model the elements of the set as points on a geometric object, and suddenly you see you can turn one geometric object into two... provided the object really is continuous, which actual physical objects never are.

Then again, with a truly continuous sphere you could just spread the same number of points out over twice the area (or volume, or whatever you choose), without decreasing the density of points in the sphere; then distort the sphere in the right way to get two conjoined spheres of equal area (or volume or whatever) to the first.


The other important part of BT is the fact that the sets of points are achieved solely through rotations around the centre of the sphere, an operation which is normally assumed to be "measure preserving", i.e. if you rotate something it should take up the same volume, so the fact that only by performing these rotations you can double the volume is the really surprising effect.
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Re: 0804: Pumpkin Carving

Postby phillipsjk » Wed Oct 13, 2010 4:11 pm UTC

I got lost where he started splitting the sets:

ABA-1B-1 != (AA-1)+(BB-1) => ABA-1B-1 != (A)+(A-1)+(B)+(B-1)

And I did not feel like delving into a formal or longer treatment to try to understand what was glossed over.

Edit: maybe that is where the 5th set comes in; there may exist a set F such that:
ABA-1B-1 == (A)+(A-1)+(B)+(B-1)+(F)

F, of course, appearing to come out of nowhere. Rounding error may not be the precise term. I suspect I have to prove the principle of choice wrong to prove the theorem wrong.
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Re: 0804: Pumpkin Carving

Postby chrth » Wed Oct 13, 2010 6:19 pm UTC

Nollidge wrote:What is panel 3 supposed to be about?


The character is projecting her own issues on to the pumpkin. The joke at the end about "distract...with holiday traditions" is that she tried to carve a pumpkin to stop being so mopey but it didn't work.

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Re: 0804: Pumpkin Carving

Postby SirMustapha » Wed Oct 13, 2010 7:49 pm UTC

The_Mexican wrote:Randall draws backgrounds more like once a month, give the guy a break. (The most recent one was about 3 weeks ago: http://xkcd.com/795/)


Wow, ONCE a MONTH? Man, I definitely would never be able to cope with so much pressure in such a tight schedule!

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Re: 0804: Pumpkin Carving

Postby Platypodes » Wed Oct 13, 2010 9:25 pm UTC

chrth wrote:
Nollidge wrote:What is panel 3 supposed to be about?


The character is projecting her own issues on to the pumpkin. The joke at the end about "distract...with holiday traditions" is that she tried to carve a pumpkin to stop being so mopey but it didn't work.

Also, I think it's this girl doing that thing she does...

mcv wrote:This logic holds up wonderfully. Solomon didn't want to cut up the baby, he wanted to know who the real mother was. The mother of the live baby just wanted her baby to live. The mother of the dead baby was jealous of the mother with the living baby, and wouldn't mind seeing it dead. Then at least she wouldn't be alone in her misery.

Karilyn wrote:The specific detail of the story that was left out was that the two women hated each other. The non-mother was satisfied with the idea, because it would kill the mother's child, which was just as good as taking it away from the mother. The goal was not to get a child, but to hurt the mother.


Thank you both. That makes perfect sense, and I never understood that story before. (I always got hung up how if you wanted a baby, half a baby doesn't get you anywhere.)

By the way, I read an interesting retelling of the story once, in which the king told the women to have a tug-of-war with the baby and the winner would keep it... But then he gave the baby to the woman who let go first, because he knew she was the mother and let go because she couldn't stand to see her child in pain. A nice update for a society in which the idea of cutting babies in half seems so completely appalling that it's hard to get past our automatic response of "but how could anyone ever agree to that?"

Pfhorrest wrote:I don't see why so many people dislike the third panel. I think the mood whiplash between the different characters is part of the humor of the comic: (1) silly, (2) sadistic, (3) sad, (4) gwaaah..?

I'm with you on that. And I thought Panel 3 was funny in its own right, too. :lol:
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Re: 0804: Pumpkin Carving

Postby katylava » Wed Oct 13, 2010 10:33 pm UTC

so, are all the panels supposed to represent axioms of set theory? i can see how 1 fits in, but not the others.

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Re: 0804: Pumpkin Carving

Postby Lady Freya » Sun Oct 17, 2010 4:45 pm UTC

Have_A_SnApple wrote:Look what this comic did to searches for "Axiom of Choice":
http://www.google.com/trends?q=%22axiom+of+choice%22&ctab=0&geo=all&date=mtd&sort=0


Awesome :D

But also, Iran? Why?
http://www.google.com/trends?q=axiom+of ... &date=2010

--

Edit:
Aha, this is why http://www.axiomofchoice.com/bio.htm

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Re: 0804: Pumpkin Carving

Postby guale » Mon Oct 18, 2010 6:25 am UTC

Image
I carved a Jack-o-Lantern!

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Re: 0804: Pumpkin Carving

Postby charonme » Tue Oct 19, 2010 2:47 pm UTC

Is the first guy Willard Van Orman Quine ?

Also, I'd solve the 2mothers1child like this: the child will be assigned randomly to one of them, but both women must bear at least one more son. 15-20 years later it will be examined whether the original child looks like his brother(s) or more like the son(s) of the other woman. If by this comparison the judge will realize that the child had not been assigned to his real mother, the mother will be punished in some horrible way. I bet the false mother would confess on the spot if the child was assigned to her.

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Re: 0804: Pumpkin Carving

Postby masakatsu » Tue Oct 19, 2010 3:51 pm UTC

The last pumkin I carved followed the demon motif and I covered it in the jell from some heat in a can. Lit it up. Was great in my driveway until a kid decided to stomp on it.

Stupid neighborhood hoodlums.
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