Recently, during a talk by a faculty candidate who will remain unnamed, I happened to remark on the racehorse story to several of you. None of you seemed to be familiar with it. I tried to find it in my archives, but couldn't, so I typed it in anew.
I leave it to each of you to decide how/if this applies to any particular candidate.
I also leave it to you to ponder this when I stress that my students usually include some implementation for their PhD theses.
These two friends are drinking one evening in a bar. The first one, Bob, is an engineering professor. And the second one, Al, is a brilliant computer scientist specializing in theory. Both bemoan how they are underpaid and underappreciated.
After a few more beers, Bob gets an idea: "Al, you know all kinds of theory and proofs and things. I have an idea. If you can come up with some way to predict the winners of horse races, I can build whatever is needed to collect the data, and we can both become fabulously rich!"
Al thinks this is a great idea. So, after a couple more beers, Al borrows Bob's pen and starts sketching out some ideas on a napkin. After a few minutes, he gets excited, tells Bob "I think I can do it!" and rushes out the door to get started.
The next day, Bob realizes that Al must have accidentally taken his pen at the bar. So, he stops by Al's place on the way home from work and knocks on the door.
Al answers the door. It looks like he hasn't slept, and he certainly hasn't shaved or changed clothes from the night before. He gives Bob his pen, and then says "That was a great idea last night! I started reading literature on race horses and weather and the history of racing, and there is so much data! However, no one has ever studied the formalisms. I think we're on to something! I've already proved several minor theorems about ponies that I think I can publish later. Be sure to check back with me in a couple of days.
Bob agrees and leaves.
Two days later, Bob stops by again. Al stumbles to the door. He looks terrible. His eyes are red, he looks like he has hardly slept, and his hair is a mess. He still hasn't changed his clothes, and there are coffee stains all over his shirt. He has a somewhat wild look in his eyes. "Bob -- it is amazing! You wouldn't believe the amazing but subtle theoretical complexities of this problem! I've had to study physics and biology and meteorology and.... There are so many variables and so much data.....it is daunting, but I'm determined to find an algorithm so we can get rich!"
Bob is concerned about Al, so he orders a pizza delivery and stays to make sure Al eats a piece, and changes his shirt. Then, shaking his head, he leaves. He is troubled that he may have done something awful by suggesting this problem to his friend Al. Still, he's hopeful that Al can find a solution.
A couple days later, he calls Al to see how he is doing. Al sounds sort of crazy on the phone. He's mumbling things about Turing machines with horseshoes and finite state racing tracks and multi-headed jockeys, and his voice kind of trails off. Then he tells Bob "I'm on the verge of the solution! I'll call you." And he hangs up. Bob is further saddened, but is beginning to get excited. If Al is this focused, he must come up with a solution soon and they'll be rich!
Two more days go by, and and Bob's phone rings in the middle of the night. It's Al. "Come quickly! I have the solution! We're going to be rich!!!" And Al hangs up. Bob throws on his clothes, drives over to Al's, and rings the doorbell.
Al answers the door. He looks awful. He's grown a a partial beard from not shaving. His eyes are sunken and his skin is pale. He's gaunt from not eating, and his eyes have a wild look. He's developed a tremor in his hands. He doesn't smell too good, either, because it appears he hasn't changed his clothes since Bob was by last -- the racehorse problem has been consuming him.
Bob comes in and sees papers all over the floor with diagrams and fomulae on them. There are even scribbles on the walls. Al is gleeful -- "I've got it. I can't wait to show you!"
Al leads Bob into his study. There, Bob sees the old pizza carton, and many half-empty coffee cups. The room is a mess. In the middle, there is a portable blackboard, covered in Venn diagrams. Al makes Bob sit down. His enthusiasm is infectious and Bob sits at the edge of the chair in eager anticipation.
Al starts: "At first, I thought the problem was intractable. There were too many uncertainties and variables. I thought it was beyond human comprehension. Then, I started reducing scope and eliminating variables and collapsing states and found that there is one unique answer. It was awfully difficult to find, but I found it! Bob, we're going to be rich! There's a way to predict the winner of certain horse races ahead of time by using this algorithm!"
Bob encourages him "Tell me -- tell me!"
Al wipes off the blackboard, picks up a piece of chalk and starts "Without loss of generality, assume you have a racetrack in n-space and you have massless, spherical racehorses...."