# Drinking an infinite amount of beer without getting drunk?

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 1371117.  Fri Jan 08, 2021 6:33 pm On QI series P Sandi poses the question: 'how do you drink an infinite amount of beer without getting drunk?'. The answer given is that you drink one pint, then a half, then a quarter and so on. Therefore the amount you drink is equal to 1+1/2+1/4+1/8+...+(1/2)^n where n varies from 0 to infinity. To evaluate this you notice that it is a geometric series summed to infinity with (modulus of) common ratio less than one. This yields the result 1/(1-1/2) which is 2 pints as stated in the show. The issue with this as it assumes that you can drink an infinitesimally small amount of beer; in summing the sequence from n=0 to n=infinity we imply that it is possible to drink an arbitrarily small amount of beer. The issue is that this involves making a continuous approximation to a discrete quantity. Beer is a mixture of molecules (and at its most fundamental is composed of atoms). Estimates for the number of atoms in the universe are around 10^(78) to 10^(82). Therefore, it is not possible at its most fundamental to drink 1/10^(100) of a pint as this would imply there are more atoms in the beer than there are in the universe. As a result, we cannot take the sum to infinity; at some point the quantity of beer you are consuming is so small that you could not possibly call it beer (indeed there could be no atoms in your glass). Therefore, we reach the stage where the next beer glass we drink is empty. As a result, we are not drinking an infinite amount of beers, we are drinking a finite amount of beers and then gulping from empty glasses- not quite the same.

1371125.  Sat Jan 09, 2021 4:47 am

What you say is correct, but isn't there a rather more fundamental objection?

 geometricsequencepints wrote: On QI series P Sandi poses the question: 'how do you drink an infinite amount of beer without getting drunk?'. The answer given is that you drink one pint, then a half, then a quarter and so on.

As you say, that sums to two pints, which is not an infinite amount of beer!

I didn't see the programme in question, but it would have made more sense if she'd said "an infinite number of beers" (though still subject to your valid objection).

Of course another valid objection is that it's impossible to drink an infinite number of beers, since it would take an infinitely long time.

 1371128.  Sat Jan 09, 2021 5:08 am Yes this is true- to be fair the original phrasing is ‘how can you enjoy unlimited glasses of beer without getting drunk’

 1371134.  Sat Jan 09, 2021 5:55 am I would question how anyone could genuinely "enjoy" a glass containing only a few molecules of beer! Bit of a silly question really - if glasses containing arbitrarily small quantities are allowed, then there's no point in filling even the first one. Just drink an insignificant amount of beer out of each glass.

 1371135.  Sat Jan 09, 2021 6:31 am If it was typical american "beer" I can assure you I would get more enjoyment from a glass containing a few molecules of the stuff than one containing a quantity that was actually discernible by my tongue... But this surely is just another example of people being unable to understand the difference between counting quantity and counting numbers. In any infinite series there are an infinite number of elements/iterations but (as you point out) there may well be a finite sum to the value of the elements. It possibly illustrates the difference between science and philosophy. In Tom Stoppard's play "Jumpers" the main character is a philosopher who struggles with the idea that an infinite number of terms can have a finite sum as illustrated by (a misunderstanding of) Zeno's Arrow Paradox. But in science it's not a problem because the mathematical language can describe both concepts in the same frame of reference. For some reason there are people who can't grasp that an infinite term multiplied by an infinitesimal term actually evaluates as unity. Or in a more common example - that 0.99recurring doesn't "approximate to 1", but it actually *is* 1 (ie it's just an alternative way of writing it), and similarly 0.33recurring is also identically equal to a third. PDR

1371143.  Sat Jan 09, 2021 7:48 am

 Brock wrote: I would question how anyone could genuinely "enjoy" a glass containing only a few molecules of beer!

And of course, there is no such thing as a "beer molecule" anyway.

My stepdaughter would be able to quote proper chemistry at you since she works in the brewing industry. I won't ask her to do that right now, but isn't beer essentially ethanol in aqueous solution, with soluble flavourings added?

The drinking of pure ethanol is not recommended, although there are those who do it. I would imagine that it tastes more like cheap vodka than like any other alcoholic beverage.

There must be a smallest quantity of beer which you would actually recognise as being beer. What that amount of beer is, I don't know.

If we did a blind tasting, and I told that you that the three liquids in sealed containers were (shall we say) beer, Coca Cola, and urine, I have little doubt that you'd be able to tell which was which from a full mouthful of each. But if you were given only a teaspoonful of each liquid? A mustard spoonful?

 1371146.  Sat Jan 09, 2021 7:56 am Is it possible to distinguish american beer from urine? I think I'd want to see a properly scrutineered double-blind test before I'd accept that assertion at face value... PDR

 1371147.  Sat Jan 09, 2021 8:00 am Shouldn't this thread be transferred to a more appropriate forum?

 1371148.  Sat Jan 09, 2021 8:01 am The simplest way to drink infinite beer without getting drunk is surely to do it so slowly that you just keep a small amount of alcohol in your system at any one time. Of course you’d need a reasonably watertight definition of what constitutes being drunk.

 1371150.  Sat Jan 09, 2021 8:04 am If the "beer" used for the experiment were American Budweiser, I think I'd have to concede PDR's point. Then again, if the "beer" were Newcastle Brown Ale, I'm not confident that I would be able to distinguish it from cold tea. But I have to protect my investment. If anyone wishes to try the experiment at home, I suggest using the best Danish lager in the whole of Northamptonshire. Numerophile makes a fair point; this discussion is better placed in The Green Room since it's a point arising from the TV show. By the powers of QuIM, I've moved it there.

1371165.  Sat Jan 09, 2021 1:38 pm

Since the OP arose from the P series (I'm not sure how - P for pint, perhaps?), might I further suggest that it doesn't belong with
 Quote: Your queries, niggles, footnotes and favourite moments from the current series.
either?

1371281.  Sun Jan 10, 2021 6:39 pm

Numerophile wrote:
Since the OP arose from the P series (I'm not sure how - P for pint, perhaps?), might I further suggest that it doesn't belong with
 Quote: Your queries, niggles, footnotes and favourite moments from the current series.
either?

Pop just ate itself (again)

1371309.  Mon Jan 11, 2021 6:23 am

 Alfred E Neuman wrote: The simplest way to drink infinite beer without getting drunk is surely to do it so slowly that you just keep a small amount of alcohol in your system at any one time.

That would only work if you had an infinite lifespan.

Unless there's something you want to share with the group, I'm guessing that's where it falls down ;-)

1371312.  Mon Jan 11, 2021 6:53 am

 Numerophile wrote: Since the OP arose from the P series (I'm not sure how - P for pint, perhaps?),

P for american beer, as I mentioned above...

PDR

1371350.  Mon Jan 11, 2021 12:29 pm

 dr.bob wrote: That would only work if you had an infinite lifespan

There's this old married couple who are interested in exploring the idea, given that they do have that last thing. Infinite amounts of beer need to be submitted to Windsor Castle, Windsor, Berkshire SL4 1PD.

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