Pons Asinorum

When I was in college my freshman mathematics tutorial required going through each of Euclid's Elements from memory on a chalk board. Day in, day out. Each student had a proposition or two assigned to them for the week, but they were expected to know the other propositions as well in case their fellow class mate couldn't make it out.

I was assigned I. 4 that day. To inscribe a circle with a triangle.

Not the most magical stuff of Euclid, but a fun little proof, easily accomplished, and most importantly, easily remembered. I. 4 is one of those propositions that shows it is true that memory and mastery are cousins. The more you remember about that proposition, the more you have it mastered. Its simple.

My somewhat sadistic freshman math teacher, however, thought different.

"Well sir, it seems your colleague assigned to perform I. 5 failed to show today didn't he?"

I nodded.

"One four is fairly simple isn't, it not?" "Oh its simple enough." I replied.

"Good then. Why don't you get us started on I. 5 then and everyone, please review I. 4 tonight on your own."

In case you aren't familiar with proposition 5 of book one, its a pain in the ass. Indeed it has the nickname "bridge of asses" or "Pons asinorum" as Johnnies are want to say. I struggled like hell that day. I hadn't prepared the proposition very well, I took almost the entire class time just getting the basics of it sketched out, and I barely eeked out a proof by the closing bell. What little bit I did remember, was pretty much unhelpful. I had to really think through it as I was going along. Trying different approaches until I finally (and with the help of my guide through gentle questioning) caught the scent of the trail and finished off what otherwise was a total waste.

But I learned more in that utter failure than I ever learned from proposition four, or any other proposition for that matter (I still have trouble with I. 47 for example, but I have prop. 5 down cold.)

When I went on to study Ptolemy and the higher disciplines, I realized something... the experience failing at something very difficult is altogether a liberating experience.

While I have been on the Administration's ass about Iraq for quite awhile, I can't help but think that even after all the wasted blood, wasted treasure, and wasted dreams, the entire saga will be seen by history as the crucial Pons asinorum of our age.

Or as Aristotle said: there is no royal road to geometry.