# [Xmca-l] Re: Verismo and the Gothic

```Hi David,

I am terrible at math word problems! As a result I got dizzy thinking about infinite trips by the Trojan Fly.

Is the answer that the fly is facing up?

In one hour the tortoise and Achilles are 4 miles apart. But I can't determine where the fly would be because it is flying back and forth at 10 mph. Knowing the life of flies, wouldn't it be likely to be dead from flying that fast for that long?

Kind regards,

Annalisa

On Wednesday, February 18, 2015 12:05 AM David H Kirshner <dkirsh@lsu.edu> wrote:

>From a mathematical point of view, there are some interesting paradoxes associated with the notion of a moment in time. Here's a particularly nice one building on the race between Achilles and the tortoise, the latter having been given a head start.
David

The Trojan Fly:

Achilles overtakes the tortoise and runs on into the sunset, exulting. As he does so, a fly leaves the tortoise's back, flies to Achilles, then returns to the tortoise, and continues to oscillate between the two as the distance between them grows, changing direction instantaneously each time. Suppose the tortoise travels at 1 mph, Achilles at 5 mph, and the fly at 10 mph. An hour later, where is the fly, and which way is it facing?

We can find the answer by running the scenario backward, letting the three participants reverse their motions until all three are again abreast. The right answer is the one that returns the fly to the tortoise's back just as Achilles passes it. The paradox is that all solutions do this: Place the fly anywhere between Achilles and the tortoise, run the race backward, and the fly will arrive satisfactorily on the tortoise's back at just the right moment. [The reason this is so is because there are an infinite numbers of zigs and zags in the fly's path--you can get a sense of the infinite oscillation as you move the actors backward in your mind ever closer to the point at which the Achilles and the tortoise are abreast of one another.]

This is puzzling. The conditions of the problem allow us to predict exactly where Achilles and the tortoise will be after an hour's running. But the fly's position admits of an infinite number of solutions.
(From University of Arizona philosopher Wesley Salmon's Space, Time, and Motion, after an idea by A.K. Austin.)

```