[greymule]

Very interesting question, and a lot of fun to think about. Here's my two cents:

The notion that there cannot be a tie is dependent on the notion that the moment the ball contacts the glove and the moment the runner's foot contacts the base can be defined such that they are infinitesimal points of time, that with perfect measuring equipment, the exact moment of contact could be defined as a unique instant. But it can't.

Perhaps with the best measuring devices, some sort of atomic stopwatches, ball-glove and foot-base moment of contact could be differentiated to a billionth of a second. Who knows?—maybe a trillionth. But obviously not an "infinitesmal" part of a second. And at the subatomic level, "moment of contact" begins to fall apart. If we stop-framed at a trillionth of a second and viewed such that electrons were the size of baseballs, "moment of contact" would be ambiguous. We could not say, "Aha! Right there! Foot touched base at frame number 889,268,141,006." Throw in relativity and the angle of the observer to the play, and the fact that the ball is moving faster than the runner could make the play look safe to one observer and out to another.

A similar philosophical-theoretical problem applies to the notion that no two raindrops hit the ground at exactly the same time. The question breaks down with the definition of "hit."

It would be interesting to know how accurate a human eye would be. Out by one second is out by a mile; you wouldn't even have to call it. I would guess that out by a tenth of a second would be close but clear. But how about a hundredth of a second? Certainly at some point not too far from there we'd have an apparent tie.

A friend of mine, a professor of aerospace engineering at Princeton, says he knows a theoretical physicist baseball fan who has written on the physics of baseball, things like just how much bat speed, weight, hardness, give, etc., affect distance. I think he says that if pitchers could get just a little more spin on their curve balls, the breaks would be much larger. Anyway, maybe that guy could be persuaded to write on the theoretics of ties.

In the meantime, maybe it's better to say, "Apparent tie goes to the runner."