# 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:** 3

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**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\
**Post date:** [April 1, 2021, 2:00pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/41 "2021-04-01T14:00:20Z")

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Not really; or at least not much.

Since we’re halving at each step and the 568ml pint is only 20% bigger than the 473ml pint, that difference won’t buy us even a single additional subdivision.

It might be the case that the inferior US pint could get us to e.g. not quite 26 mathematicians, so we settle for 25, while the superior British pint gets just over the hump to 26 mathematicians. But that’s the maximum improvement: 1 extra mathematician.

Far more likely is that both the US & British pints get us to e.g. 25, but not to 26. So no extra mathematician at all.

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**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\
**Post date:** [April 1, 2021, 2:58pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/42 "2021-04-01T14:58:49Z")

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> [@Dr.Strangelove](#):
>
> To a zeroth approximation, a human-scale quantity of anything has about 1024 molecules. The number of halvings until you get to 1 is log2 of that number, and log2 of a number is a little over triple the base-10 exponent. So triple 24 to 72, then round up to 80. About 80 mathematicians.

Sounds reasonable. Thanks.

I’ll still use ‘infinite’ in the joke though, because it’s funnier that way. 😉

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**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\
**Post date:** [April 1, 2021, 4:21pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/43 "2021-04-01T16:21:40Z")

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An infinite number of mathematicians walk into a bar. The rest of them (also an infinite number) duck.

Kinda lame, I’m not feelin’ it.

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 1, 2021, 5:28pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/44 "2021-04-01T17:28:41Z")

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> [@Senegoid](#):
>
> [aside]  
> @markn_1 : If you quote by highlighting some text then clicking the Quote button, then yes, Discourse loses most or all of the formatting information. But if you quote by clicking on the Reply button at the bottom of the post, then any formatting information is preserved.  
> [/aside]

Og be damned, when did Discourse break the “[aside]” tag?

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**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\
**Post date:** [April 1, 2021, 7:05pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/45 "2021-04-01T19:05:38Z")

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Huh? Color me baffled.

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**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\
**Post date:** [April 1, 2021, 7:09pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/46 "2021-04-01T19:09:33Z")

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[whoosh]  
Looks like those aren’t the only tags Discourse broke…  
[/whoosh]

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**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\
**Post date:** [April 1, 2021, 7:16pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/47 "2021-04-01T19:16:35Z")

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The Dirty Rotten Bastards!™; they killed the whoosh too! 😉  
Just color me embarrassed. Which we don’t seem to have a good smilie for.

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**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\
**Post date:** [April 1, 2021, 7:43pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/48 "2021-04-01T19:43:08Z")

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It works with “\<” and “\>”

For example:

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**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\
**Post date:** [April 1, 2021, 7:57pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/49 "2021-04-01T19:57:48Z")

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> [@chappachula](#):
>
> But nobody has yet discussed the most important inconsistency within the OP:  
> Guinness is not beer!!!

The OP didn’t mention Guinness.

I’m not really a big Guinness fan, but I don’t really get the hate. It’s not all that thick or bitter - it’s far less bitter than a good IPA, and it has fewer carbs and calories than a Budweiser. 🤷‍♂️

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**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\
**Post date:** [April 1, 2021, 7:58pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/50 "2021-04-01T19:58:39Z")

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> [@Munch](#):
>
> The OP didn’t mention Guinness.

I intended to, just to have a specific beer for the sake of argument. And I did mention it later. 😉

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**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\
**Post date:** [April 1, 2021, 10:05pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/51 "2021-04-01T22:05:55Z")

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But are the mathemeaticians really going to get out a molecular analyzer and separate the beer into its individual components, to reconstitute them at the end? Probably not their mathematicians not chemists. They are just going to pour them into smaller and smaller cups and hope for the best.

The problem of course is that if one of the later mathematicians is actually slumming statistician he may complain that his may not have contained any actual molecules of beerium. So the question becomes how many molecules of beer can the smallest drink have to make sure that every glass has at least one beerium molecule.

Well if we use the simplified model that each molecule in the beer has p probability of being beerium, and that p is much smaller than 1, then the probability that a glass containing N molecules will have no beerium is approximately exp(-N\*p). If I want to make 95% sure that my final glass has at least on beerium I want  
N\>log(0.05)/p or in other words about 3/p. If the last glass has a probability greater than 95% than the other glass will have a near certainty of containing beerium.

If you just leave it to chance with N=1/p then a quick calculation shows that eveyglass will have beerium only about 53% of the time. If you bump it up to 4/p you get a 98% chance of everyone getting beerium.

TLDR: You may want to cut your mathematician count by a couple just to be 98% sure that everyone gets a molecule.

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 1, 2021, 10:22pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/52 "2021-04-01T22:22:28Z")

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> [@Buck\_Godot](#):
>
> at least one beerium molecule

Slight nitpick: “beerium” is clearly an element, not a compound, so you would not need beerium molecules when singular beerium atoms would suffice.

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**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\
**Post date:** [April 1, 2021, 10:23pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/53 "2021-04-01T22:23:51Z")

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Your right, I used the vernacular rather than the more scientifically accepted term “beerite”.

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**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\
**Post date:** [April 1, 2021, 11:03pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/54 "2021-04-01T23:03:55Z")

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I think the common name is beerium in England and beerinum in the US.

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 1, 2021, 11:26pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/55 "2021-04-01T23:26:42Z")

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In the US, it is “beerium”, but in the UK, it is “beerinium”. The beerium you find in the US has a “flavor” that is best obscured by serving it cold, whereas beerinium is more commonly served at room temperature because the UKians are masochists.

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**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\
**Post date:** [April 1, 2021, 11:33pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/56 "2021-04-01T23:33:37Z")

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Of course “room temperature” in sunny England is about the same as fridge temperature in the US southwest.

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**Author:** ![abcdefghij](https://avatars.discourse-cdn.com/v4/letter/a/43a26b/32.png) [@abcdefghij](https://boards.straightdope.com/u/abcdefghij)\
**Post date:** [April 1, 2021, 11:35pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/57 "2021-04-01T23:35:24Z")

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Actually, if the native ore is beer, then beerium [Br En] and beerum [Am En].

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**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\
**Post date:** [April 1, 2021, 11:49pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/58 "2021-04-01T23:49:46Z")

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Naturally NIH has weighed in on what beerium / beerinium really is:

> **[Beer Molecules and Its Sensory and Biological Properties: A Review](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6515478/)**
>
> The production and consumption of beer plays a significant role in the social, political, and economic activities of many societies. During brewing fermentation step, many volatile and phenolic compounds are produced. They bring several organoleptic...

This learned fellow tells us there are a couple thousand distinct molecular species in beer:

> **[The chemistry of beer](https://www.newfoodmagazine.com/article/9164/the-chemistry-of-beer/)**
>
> It has variously been estimated that there are between 1,000 and 2,000 different chemical species in beer, probably twice as many as are present in wine. It is an extraordinarily complex liquid. Not all of those chemical components make a substantial...

Analyzing any of this is beyond my nodding acquaintance with chemistry.

But ISTM that some of these minor constituents have real high molecular weights, at least compared to simple stuff like water and ethanol. The result of which is that we won’t have to do too many subdivisions before we get the first sample lacking one of the rare and heavy molecules. Our OP’s infinite horde of mathematicians may be culled to a (collossal WAG) mere 10 or so; the rest being disappointed at being left outside the exclusive velvet rope.

Taking @Buck_Godot’s statistical argument at face value, it seems we can’t even count on a single ordinary sized serving of beer containing _all_ the requisite chemistry. So the only way to improve the statistical odds of really having complete beer in your beer is to … have more than one beer.

Do it for Science! 😉

See **[here for even more Science of the “She blinded me with”](http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422000000100019)** kind. Serious chem-geeks only.

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**Author:** ![Terminus\_Est](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/terminus_est/32/3087_2.png) [@Terminus\_Est](https://boards.straightdope.com/u/Terminus_Est)\
**Post date:** [April 2, 2021, 11:48am UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/59 "2021-04-02T11:48:49Z")

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If we can posit an infinite number of mathematicians, then we can also posit the ideal beer, infinitely divisible, composed of ideal beer particles _beerons_, which are infinitely small. Hence a half pint of ideal beer will have only half, but equally infinite, the number of beerons as a full pint of ideal beer.

I will drink a pint of ideal beer any day!

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**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\
**Post date:** [April 2, 2021, 1:47pm UTC](https://boards.straightdope.com/t/maximum-number-of-mathematicians-in-this-joke/939113/60 "2021-04-02T13:47:11Z")

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> [@Terminus\_Est](#):
>
> I will drink a pint of ideal beer any day!

‘Fantastic! And I get two more wishes? I’ll take two more of these!’

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