A Squirrel’s Tale

By Bobby Neal Winters

I received the following report from the Bureau of Unlikely Seeming Happenings, Bulsh for short.

Cletus T. Gnasher was out hunting squirrels one day in order to put a little meat on the table when he came upon a strange sight. He saw a squirrel go into one end of a ten foot long hollow limb.  He took out his trusty 22 rifle and aimed it toward the squirrel.  One minute later the squirrel came out the other end.  

Cletus was about to squeeze off a round when the squirrel ducked back into the hollow limb.  Not about to give up this easily, Cletus kept his eyes on the tree.  At the end of 30 seconds, the squirrels head was out of the other end.  Again, before Cletus could squeeze off a shot, the squirrel had ducked back inside the hollow limb.

The squirrel went again to the other end of the hollow limb and this time in only took 15 second before the little head poked out the other side.

It is at the point some began to doubt the veracity of the report because Cletus said that something funny began to happen. The squirrel continued to go back and forth  between the ends of the hollow limb until at one point it appeared he was looking out of both ends at once.  How long did this take?

This was presented to the Bulsh board and reports were requested.  The first report came from a mathematician.  It was very succinct.  This is an infinite series problem.  To determine the time expended, sum one minute plus one-half minute plus one-fourth minute and so on, i.e. 1+ 1/2 + 1/4+ ... .  This is a geometric series whose sum is 2.

The second response was from another mathematician who didn’t offer a solution, but said that this one couldn’t be correct because it assumed the squirrel would be transversing the tree limb an infinite number of times.  As the length of the limb was fixed, being 10 feet, transversing it at infinite number of times would require the squirrel to go an infinite distance.  That is to say that while the infinite series for time-passed converged, the series for distance traveled diverged.

At this point, a physicist chimed in, saying that the problem was reached long before infinity.  The first time the squirrel went through the limb, he was going at a speed of 0.1136 miles per hour.  However, by halving the length of time through the limb each time, he was doubling his speed. Taking the liberty of converting this to 0.05784 meters per second to make sure no one forgot he was a physicist, he said that after 33 more times through the limb, the squirrel would be going 4.36 times 10 to the 8 meters per second which is greater than the 3.0 times 10 to the 8 meters per second that light travels.  At this point, one of the mathematicians corrected him to 2.998 times 10 to the 8 meters per second.  The physicist wrote back something that best not be repeated here and a flame war ensued.  

After the verbal abuse subsided, the physicist calculated that, because of relativity, a one pound squirrel would weigh 1.45 pounds after 32 trips through the limb.  One of the mathematicians asked him whether he meant a one kilogram squirrel would have the mass of 1.45 kilograms, but fortunately the irony was lost on him, and then he was distracted by the following question from an engineer.

The engineer noted that Cletus only said that it looked as if the squirrel were looking out of both ends at the same time.  An image persists on the retina for one-sixteenth of a second.  According to his calculations, it would only take 10 trips through the limb to be making it in that amount of time.  This is a speed of 58 meters per second.

The first mathematician then calculated that this would take 1.998 minutes which was only 2 one thousands off his original estimate. The second mathematician said, “Yeah, your original WRONG estimate.”

This was beginning to degenerate into something nasty then the physicist said, “You know this would require an acceleration of almost 12 times the force of gravity to accomplish.  The squirrel would be  mush.”

At that point, one of the animal-rights folks on the committee said this was something you couldn’t even talk about doing not even to a theoretical squirrel. As this was a supposedly real squirrel, an investigation would have to be launched.

One of the mathematicians said, “By academic freedom..."

And the reply was that he could be free to seek another academic job if he said one more word.