Wanted: punch line for joke
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Wanted: punch line for joke
A while ago, when I was on Math Camp¹, I had a really weird math dream. I awoke with a question in my head that sounded just like the beginning of a very funny, nerdy joke in a genre comparable to "changing a light bulb". However, no matter how often I tried, I've never been able to dream of a punch line to the joke. Maybe someone with more imagination than me can help me out, and finish it for me?
The question is:
How many topologists² can you fit inside a soda can?
Looking forward to your responses.
ThijsJohan
Department of Mathematics, Leiden University
¹: Yes, this is a real thing: http://www.vierkantvoorwiskunde.nl/
²: A topologist is someone who specializes in the field of Topology. Note that any topologist would likely interpret the outside of the soda can as the inside, therefore the can would contain every topologist in the universe. This comment is in itself an excellent suggestion for an answer, that, in most audiences, would at least produce a titter or two. However, anyone familiar with the study of topology would think this rather obvious. I'm looking for an answer slightly more creative than this.
The question is:
How many topologists² can you fit inside a soda can?
Looking forward to your responses.
ThijsJohan
Department of Mathematics, Leiden University
¹: Yes, this is a real thing: http://www.vierkantvoorwiskunde.nl/
²: A topologist is someone who specializes in the field of Topology. Note that any topologist would likely interpret the outside of the soda can as the inside, therefore the can would contain every topologist in the universe. This comment is in itself an excellent suggestion for an answer, that, in most audiences, would at least produce a titter or two. However, anyone familiar with the study of topology would think this rather obvious. I'm looking for an answer slightly more creative than this.
Re: Wanted: punch line for joke
ametheus wrote:How many topologists can you fit inside a soda can?
Spoiler:
or (variation on the same theme)
Spoiler:
Last edited by Qaanol on Wed Apr 21, 2010 12:01 am UTC, edited 5 times in total.
wee free kings
Re: Wanted: punch line for joke
How many topologists can you fit inside a soda can?
Spoiler:
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.
Re: Wanted: punch line for joke
Spoiler:
Re: Wanted: punch line for joke
Spoiler:
Yakk wrote:hey look, the algorithm is a FSM. Thus, by his noodly appendage, QED
 skeptical scientist
 closedminded spiritualist
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Re: Wanted: punch line for joke
I came up with one similar to Qaanol's, but Z4lis was the only one who made me chuckle.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
Re: Wanted: punch line for joke
avoiding the math punchlines I'll just go with the:
Are we talking 12 oz soda or those wimpy 8oz cans?
Are we talking 12 oz soda or those wimpy 8oz cans?
 Yakk
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Re: Wanted: punch line for joke
If we where to open the can, there would be no inside or outside, so clearly we must deal with a closed can. To determine the topological properties of the can, however, we can imagine opening the can by rotating it by pi/2. When we do so, bubbles form in a continuous process inside as they grow from the infinitesimal. Without loss of generality, we'll presume that the bubbles form an open cover of the can  and, as a finite quantity of bubbles leaves the can, there must be a finite subcover. Thus the can is compact. As compacted cans are recycled, this implies that the fundamental group of the 4can is trivial. If we then show that the can can can can can be pathconnected, and we presume the axiom of choice, we can then show that the can can can can can be deformed into the surface of the can can can can can if we can go that far. And as the following diagram commutes:
the answer is 6.
Code: Select all
... ... ... ...
   
s_0 v s_1 v s_2 v s_3 v s_4
... > Can > Can Can > Can Can Can > Can Can Can Can > ...
 d_1  d_2  d_3  d_4
v v v v
... < Glug < Gluglug < Glugluglug < Gluglugluglug < ...
c_00  c_01  c_02  c_03  c_04
v v v v
... ... ... ...
the answer is 6.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: Wanted: punch line for joke
How about
Or
Spoiler:
Or
Spoiler:
Re: Wanted: punch line for joke
Maybe you all thought of this and discarded it. But how about..
Spoiler:
Now these points of data make a beautiful line.
How's things?
Entropy is winning.
How's things?
Entropy is winning.
Re: Wanted: punch line for joke
Yes, I did; it's in my original post.
I'd like to thank everyone for their replies, I think I'm going with Yakk's answer if that's okay with him.
Cheers,
Thijs
I'd like to thank everyone for their replies, I think I'm going with Yakk's answer if that's okay with him.
Cheers,
Thijs
 Yakk
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Re: Wanted: punch line for joke
Sure? But do clean it up. I got a bit silly at the end.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Re: Wanted: punch line for joke
I like silly; it's sort of the point.
Re: Wanted: punch line for joke
Yakk wrote:Sure? But do clean it up. I got a bit silly at the end.
I'm having trouble parsing "the can can can can can". Could you explain what the first 4 cans mean?
 Yakk
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 Posts: 11129
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Re: Wanted: punch line for joke
I took the term 4can (the 4 dimensional can), and expanded it to a can can can can (4 cans). I then used the word can immediately afterwards to make it sillier.
To fully ruin the joke, such as it is:
I think I caught all of my silliness above?
To fully ruin the joke, such as it is:
Spoiler:
I think I caught all of my silliness above?
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Re: Wanted: punch line for joke
Really? I thought you meant the Canonical map (which is often abbreviated with "can"), and had applied it four times on the can, thus resulting in can[can[can[can[can]]]]. The quotient groups of two of such entities are quite commonly standard nonabelian groups such as D_4.
This way, your diagram actually almost makes sense. (Apart from it being absolute nonsense, of course.)
This way, your diagram actually almost makes sense. (Apart from it being absolute nonsense, of course.)
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