# Maximum number of mathematicians in this joke
**URL:** https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113
**Category:** Factual Questions
**Created:** [March 31, 2021, 8:22pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113 "2021-03-31T20:22:29Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [March 31, 2021, 8:22pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/1 "2021-03-31T20:22:29Z")
> [@More Jokes](https://boards.straightdope.com/t/more-jokes/848629/1):
>
> An infinite number of mathematicians walks into a bar. The first one orders a beer. The second one orders a half a beer. The third one orders a quarter of a beer. The fourth one orders an eight of a beer…
> The bartender pours two beers, and says, “You figure it out!”
Funny joke, but an infinite number of mathematicians is too many. There are only so many molecules in a pint of beer. To make it even more complex, there aren’t ‘beer molecules’, but a number of molecules that, in combination, constitute ‘beer’.
Given one pint (473.176 ml) of a given beer, between how many mathematicians may it be divided before 1) a hypothetical 'beer molecule cannot be divided; or 2) any more divisions would create a substance that does not constitute ‘beer’ because one of the ingredient molecules is missing?
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### Author:  [@pjd](https://boards.straightdope.com/u/pjd)
#### Post date: [March 31, 2021, 8:30pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/2 "2021-03-31T20:30:34Z")
What brand of beer are we talking about here ?
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### Author:  [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)
#### Post date: [March 31, 2021, 8:32pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/3 "2021-03-31T20:32:50Z")
I was going to say ‘Let’s call it Guinness, because I like Guinness’ in the OP, but didn’t.
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### Author:  [@F.U.Shakespeare](https://boards.straightdope.com/u/F.U.Shakespeare)
#### Post date: [March 31, 2021, 8:33pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/4 "2021-03-31T20:33:12Z")
Maybe there should also be some chemists and physicists.
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### Author:  [@TriPolar](https://boards.straightdope.com/u/TriPolar)
#### Post date: [March 31, 2021, 8:33pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/5 "2021-03-31T20:33:21Z")
Why did the bartender pour 2 beers?
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### Author:  [@F.U.Shakespeare](https://boards.straightdope.com/u/F.U.Shakespeare)
#### Post date: [March 31, 2021, 8:37pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/6 "2021-03-31T20:37:22Z")
One on the house?
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### Author:  [@pjd](https://boards.straightdope.com/u/pjd)
#### Post date: [March 31, 2021, 8:38pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/7 "2021-03-31T20:38:25Z")
136 would probably be enough.
…or 142 maybe.
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### Author:  [@markn\_1](https://boards.straightdope.com/u/markn_1)
#### Post date: [March 31, 2021, 8:38pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/8 "2021-03-31T20:38:37Z")
Beer is over 90% water, so to a first approximation we can just assume it’s all water. 473 ml of water weighs 473 grams, and the molecular weight of H2O is 18 g/mol, so the pint contains 473/18 = 26.3 moles = 1.6 x 1025 molecules. That’s about 284, so the 85th mathematician gets one molecule and everyone after him has to go to another bar.
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### Author:  [@Prof.Pepperwinkle](https://boards.straightdope.com/u/Prof.Pepperwinkle)
#### Post date: [March 31, 2021, 8:41pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/9 "2021-03-31T20:41:51Z")
> [@Johnny\_L.A](#):
>
> Funny joke, but an infinite number of mathematicians is too many. There are only so many molecules in a pint of beer. To make it even more complex, there aren’t ‘beer molecules’, but a number of molecules that, in combination, constitute ‘beer’.
>
> Given one pint (473.176 ml) of a given beer, between how many mathematicians may it be divided before 1) a hypothetical 'beer molecule cannot be divided; or 2) any more divisions would create a substance that does not constitute ‘beer’ because one of the ingredient molecules is missing
Ah, but an infinite number of mathematicians, skilled in the use of irrational, unreal, transfinite and imaginary numbers, can always find a way to throttle an answer out of such a situation.
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### Author:  [@Dewey\_Finn](https://boards.straightdope.com/u/Dewey_Finn)
#### Post date: [March 31, 2021, 8:44pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/10 "2021-03-31T20:44:08Z")
> [@TriPolar](#):
>
> Why did the bartender pour 2 beers?
Because the first person received a full glass, the second received half, the third a quarter and so forth. It should add up to two glasses.
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### Author:  [@F.U.Shakespeare](https://boards.straightdope.com/u/F.U.Shakespeare)
#### Post date: [March 31, 2021, 8:45pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/11 "2021-03-31T20:45:01Z")
I wish to apologize for cracking wise before the question had been answered. One doesn’t often get the opportunity to make math jokes.
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### Author:  [@dtilque](https://boards.straightdope.com/u/dtilque)
#### Post date: [March 31, 2021, 8:45pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/12 "2021-03-31T20:45:03Z")
> [@TriPolar](#):
>
> Why did the bartender pour 2 beers?
Explaining jokes always ruins them, so here’s the ruined joke:
1 + 1/2 + 1/4 + 1/8 + … = 2
[Ninja’d but I’ll post anyway.]
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### Author:  [@TriPolar](https://boards.straightdope.com/u/TriPolar)
#### Post date: [March 31, 2021, 8:51pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/13 "2021-03-31T20:51:05Z")
Doh! I assumed the bartender had already poured the first four beers.
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### Author:  [@Deeg](https://boards.straightdope.com/u/Deeg)
#### Post date: [March 31, 2021, 9:01pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/14 "2021-03-31T21:01:18Z")
I wanna know how all those mathematicians fit into the bar in the first place.
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### Author:  [@markn\_1](https://boards.straightdope.com/u/markn_1)
#### Post date: [March 31, 2021, 9:04pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/15 "2021-03-31T21:04:15Z")
It was the bar in [Hilbert’s Hotel](https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel).
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 31, 2021, 9:16pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/16 "2021-03-31T21:16:00Z")
> [@Johnny\_L.A](#):
>
> or 2) any more divisions would create a substance that does not constitute ‘beer’ because one of the ingredient molecules is missing?
Others have handled the first part, so I’ll tackle this one. To a second approximation, beer consists of water and ethanol. Guinness is 4.2% alcohol by volume, which translates to 3.4% alcohol by weight. Ethanol has a molecular mass of 46, compared to water’s 10, so it has about 130 water molecules per ethanol molecule. That’s very nearly 2^7, so requiring each mathematician to have at least one ethanol molecule reduces the number of possible mathematicians by 7.
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### Author:  [@markn\_1](https://boards.straightdope.com/u/markn_1)
#### Post date: [March 31, 2021, 9:32pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/17 "2021-03-31T21:32:50Z")
> [@markn\_1](#):
>
> 473 ml of water weighs 473 grams, and the molecular weight of H2O is 18 g/mol, so the pint contains 473/18 = 26.3 moles = 1.6 x 1025 molecules. That’s about 284, so the 85th mathematician gets one molecule and everyone after him has to go to another bar.
Correction: as Chronos says, water’s mass is 10, not 18, so there are 47.3 moles = 2.8 x 1025 = ~ 285 molecules , which actually doesn’t materially change the result.
(Just noticed that Discourse removes the \< sup \> tags when you quote text, so I manaully added them back. That sucks.)
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 31, 2021, 9:47pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/18 "2021-03-31T21:47:33Z")
Correction to correction: Water’s mass is, in fact, 18. Oxygen has 8 protons, but then also that many neutrons. I had it wrong before.
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### Author:  [@TroutMan](https://boards.straightdope.com/u/TroutMan)
#### Post date: [March 31, 2021, 10:02pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/19 "2021-03-31T22:02:57Z")
> [@Chronos](#):
>
> To a second approximation, beer consists of water and ethanol. Guinness is 4.2% alcohol by volume, which translates to 3.4% alcohol by weight.
We need a better definition of “beer” than water and ethanol, because water with 4.2% v/v ethanol is just watered-down vodka. In order to be considered beer, there needs to be at least some “malt” molecules and “hop oil” molecules, in the proper balance to create the taste of beer.
We can’t ignore those just because they’re in small amounts; in fact, the smallest contributor that must be present to create “beer” will determine how many parts the pint can be split into.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 31, 2021, 10:11pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/20 "2021-03-31T22:11:26Z")
And actually, it gets much worse: Most of the other compounds in beer are going to be much larger molecules than water or ethanol. Which means that the requisite single molecule of one of those will be equal to many water and ethanol molecules, and so will need many more to make the proper proportions.
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