Sometimes, science leaves you dissatisfied

What's that? Am I trying to be just another crank, dissatisfied with science? Well, no - who said that science has to be satisfying? Not every scientific result can be as satisfying as a bowl of hot chicken noodle soup on a cold winter day - I would venture a guess that even physicists are sometimes deeply dissatisfied with the results of, let's say, quantum mechanics. The satisfaction of answers that are comprehensive and plausible is not a scientific requirement - it's our "common sense" that is satisfied by it. Like by a bowl of chicken soup - or steak and lobster, for that matter. Which leads directly to why I started writing this post in the first place.

Today's edition of the Science Times is dedicated solely to puzzles. And on the second-to-last page, I came across a math puzzle, which - when answered correctly - left me deeply dissatisfied. Here's the riddle:

A surf and turf holiday buffet costs only $5.95. But you must pick one of 38 covered plates, without looking, and only one of them has any food: lobster and steak worth $208. If you're a purely economical holiday gourmand, is the buffet worth the price? Now imagine the other 37 plates have a conciliatory chocolate worth $1. Is the buffet now a good buy?

For those who want to solve it themselves, I will leave some space here
.
.
.
.
.
.
.
.
.
.
Let's continue with the solution, as offered by the Times. The first deal is definitely not worth the price: You have a 1/38 chance to win the plate, which gives you an average value of $5.47 for your $5.95. But adding the dollar's worth of chocolate increases this value to $6.45 (5.47 plus 37/38 of one Dollar) - and thus it becomes a "good deal." Q.e.d.

Well, I for my part was left unsatisfied, and I think that even a statistician would reject this offer in real life. Not so much for the odds, but because it only makes statistical sense - it plays in your favor only when you can play it many times over and over, or in a large aggregate, i.e. with a large number of friends, who can share the lobster and steak (208 Dollars should buy you quite a lot of it, even in an expensive Manhattan restaurant.) But as an individual one-time player - you're hungry here and now - you have only two possible outcomes: most likely you'll be left with a cheap piece of chocolate, that you could have gotten at any corner store for a dollar or less, or with a huge plate of lobster and steak, which is probably more than you would want to eat (or otherwise ridiculously overpriced) anyhow. Neither of the two solutions seem attractive - regardless that they may be mathematically "reasonable."

Let's ignore for the moment that most certainly, some economic expert in game theory will have a solution in his desk drawer, which can address these weighted preferences elegantly and with scientific accuracy: Form argument's sake, I will assume that the given solution is the only one that's scientifically correct - yet dissatisfying. And, obviously, common sense tells me, that it must be "wrong."

And this is what happens to many "sceptics of science" (don't call them "cranks" - yet!) - their "gut" feels not fully satisfied by the theory of evolution, relativity, quantum mechanics ... or whatever. And because it doesn't feel right, it must be wrong - right? But, as I said before: Science can't always satisfy our craving for full answers. And that's often a good thing: The less "delightful" the answer, the more likely scientist will keep on digging deeper. And that's what science is all about.


Und manchmal ist Wissenschaft auch unbefriedigend