The Parable of the Free Beer

There is a classic logic problem that goes like this: you are on an island where some of the natives always lie and others always tell the truth.  You find yourself at a fork in the road where one branch leads to the village, the other into the jungle, and you wish to determine which branch is which.  There is a native standing at the fork, of whom you may ask one yes-no question.  What do you ask?

The usual, nerdy answer goes something like, "If I were to ask you if the left path is the way to the village, would you say yes?"  The problem with this answer is that the native may as well decide that by the time he sorts out the hypotheticals, the cannibals will have emerged from the jungle and had both of you for lunch.  So in the real world (and I may as well warn you now, this post will require a certain level of suspension of disbelief) he is as likely to say, "Bugger off" or "WTF?" as he is to say yes or no.

Martin Gardner suggested a brilliant, practical solution: you should ask, "Did you know they are serving free beer in the village?"  Then you ignore the answer, and just follow the villager whichever way he goes.

This solution is cute, but not without its issues.  It assumes, for example, that your interlocutor likes beer, that he doesn't have urgent business in the jungle, that he is not an "artful deceiver" willing to forego a shot at free beer in order to mislead a foreigner, etc.  Furthermore, it assumes that the native is not considering the possibility that you might be a deceiver, and that you are asking the question not because there is, in point of fact, free beer in the village, but that you have (as indeed you do) some hidden agenda that has nothing at all to do with beer.

In this post I want to consider the inverse problem: suppose you know the way to the village and a native comes up to you and says, "Did you know they are serving free beer in the village?"  How would you respond?  Assume for the sake of argument that you like beer, and all else being equal you'd rather pay less than more.  But in this case all else is not equal.  To act on the information that is (apparently) being provided to you, you have to walk to the village.  If you get there and discover that they are not, in fact, serving free beer then you have incurred, at the very least, an opportunity cost.  Since you are wise in the ways of wily natives, you decide to make further inquiries, and the following conversation ensues:

You: No, I did not know they are serving free beer in the village.  Are they in fact serving free beer in the village, or are you trying to trick me into showing you the way to the village?  Because if it's the latter, all you have to do is ask.  This isn't a logic puzzle.

Native: Oh no, I assure you, there is no trickery, and I have no hidden agenda.  They are indeed serving free beer in the village.  Do you like beer?

You: Indeed I do.

Native: Then why are you not at this very moment rushing off to the village?  It's right over there.

You: It's because I'm a little skeptical.  It seems odd that they should be serving free beer.  As far as I know, there is no reason for them to be doing so.  Is there a festival going on that I didn't hear about?  Or maybe the beer company is running a promotion?

Native: No, nothing like that.  The barkeep is just a particularly generous fellow.

You: I see.  So he sometimes serves free beer just out of the goodness of his heart, does he?

Native: Not sometimes.  Always.  Twenty-four by seven.  All you have to do is walk into the pub and ask.

You: That seems a tad implausible.  How does he stay in business?

Native: Tips.

You: You'll have to pardon me if I'm not convinced.

Native: Oh, it's true.  Ask anyone.  Say, Fred, come over here a second?

Fred: What can I do for you?

Native: This foreigner here doesn't believe that they serve free beer in the village.

Fred: Oh, they do.  I've availed myself of it many times.

[So you go to the village and enter the bar.]

Barkeep: Welcome, stranger!  What can I get for you?

You: I hear you're serving free beer.

Barkeep: Indeed we are.  And not just any old beer.  It's the best beer you've ever had.

You: Can't wait to try it.

Barkeep: Well, as soon as you're dead, you can.

You: What?!

Barkeep:  Oh yeah, didn't they tell you?  You can only have this beer in the afterlife.

You: I knew there had to be a catch.

Barkeep: It's not a catch.  This beer is so good that if you had it while you were alive your head would explode.

You: Do you have any idea how ridiculous that sounds?

Barkeep: Yeah, I know, but it's true.

You: What makes you think so?

Barkeep: Oh, the evidence is overwhelming.  People have written books about the beer.  2000 years ago people were actually able to try it.  And even today, while you can't actually drink it until after you're dead, you can experience it.

You: How?  (And what does it even mean to experience beer without drinking it?)

Barkeep: You have to believe in the beer, and then the beer will reveal itself to you.

You: That is the most absurd thing I have ever heard in my life.

Barkeep: Be that as it may, you really want to believe in the beer.

You: Why?

Barkeep: Because if you don't then when you die you will go to the Hostelry of Eternal Liquor Lossage, which is a very bad place.

You: What makes it such a bad place?

Barkeep: No beer.

You: Hm, that does sound unpleasant.  Can I take some time to think about it?

Barkeep: Sure, but don't take too long.  Once you're dead, that's it, no do-overs.  And you never know when you might get hit by a bus.

You: I'll be careful.  Thank you, and good bye.

Barkeep:  Good bye. Oh, before you go, take a copy of the Beer Insider's and Brew Lover's Encyclopedia.  It will tell you all about the beer.  How it was made, what makes it so special, why you can't get it any more except after you're dead...

[He hands you a thick book.]

You: Thank you.

[You exit the bar, making a mental note to be very careful to look both ways before you cross the street.  On the sidewalk outside you encounter another villager.]

Villager: Say, stranger, did you know that they are serving free wine in the next village?