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A Cup Of Wine And Thou

Dave North

Mentioning Omar Khayyam and libration in the same sentence is definitely an invitation to make the classic confusion of "libration" and "libation."

There's only one letter difference, and of course the line Omar is most famous for? "A loaf of bread, a jug of wine, and thou." One of the best-known libation phrases of all time.

But it's libration that concerns us here - in this case, the shifting view we get of the edges of the moon, sometimes revealing things that are otherwise impossible to see.

Just off the west edge of the Moon, in the northern quadrant, is the crater named for Omar Khayyam - and though the strongest western exposure for the month doesn't happen until the 23rd, the northern libration is out of sync. As a result, we have a rare opportunity to see the finer details of OK on the first of the month.

But wait a minute! Why does an author of sappy love poems (much adored by parapostpubescent teenyboppers) have a lunar crater named after him? Is it because "crater" means "cup," and he did more to popularize wine cups than anyone else?


It's because he was (get this) one of the foremost mathematicians of his time (which was 1048 to 1131, a remarkable old age for those times).

And, of course, mathematicians are well-represented on the Moon.

First, the crater itself: not all that special, but definitely challenging to locate in this light. When you see it, you'll be able to feast on a nearly edge-on plain old everyday 70Km crater with no discernible central peak and reasonably well-preserved walls.

The terminator position will be just about perfect, though, to inspire your imagination to reverie on the curious stories behind the man for whom the crater is named.

For example, the symmetry and clean shape of the crater bring to mind the orderly logic of Algebra, Omar's true devotion. We can only regret that there were no telescopes, and no way for Omar ...

...hold on a minute. Omar? His full name was Ghiyath al-Din Abu'l-Fath Umar ibn Ibrahim Al-Nisaburi al-Khayyami. I suppose the "Umar" is where "Omar" comes from, but I can't help but prefer OK to UK, so we'll call him "Omar" since I have it on excellent authority (Thomas Edward Lawrence) that arabic pronunciation is somewhat mercurial, and english transcriptions should reflect that happy approach...

...Omar had no way to observe his own crater, as telescopes were not yet popular. Nevertheless, he's also known as one of the premier astronomers of his age!

Not happy with that, he composed a groundbreaking proto Music Of The Spheres - Problems of Arithmetic, a book on music and algebra - before he was 25 years old. Later, he wrote what became a classic in the field: Treatise on Demonstration of Problems of Algebra.

During this time Khayyam led work on compiling astronomical tables, also contributing to calendar reform (a popular Arabic pastime) in 1079.

Astronomy was often his chosen venue to illustrate the uses of Algebra, and the precision possible with only crude tools.

For example, Khayyam measured the length of the year as 365.24219858156 days. For his time, it is outstandingly accurate, and was useful in all manner of computations (including discovering that the length of the year was changing!)

Cubic equations may be his greatest legacy.

Khayyam solved the cubic equation x^3 + 200x = 20x^2 + 2000 and found a positive root by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. Perhaps even more remarkable is the fact that Khayyam states that the solution of this cubic requires the use of conic sections and that it cannot be solved by ruler and compass methods, a result which would not be proved for another 750 years.

In the end, Khayyam himself seems to have been the first to conceive a general theory of cubic equations.

Okay, by now you've probably pointed your scope at the Moon and seen the curious problems inherent in such observations - a perfect example of how odd the moon itself is. And how you can see a crater in much the same way that Omar could see ideas: with the eye of your mind.

You start out with a Rubaiyat and end up with a guy who also extended several of Euclid's geometric principals.

But should he be so remembered for his poems? Probably not; versions of the forms and verses used in the Rubaiyat existed in Persian literature before Khayyam, and only about 120 of the verses can be attributed to him with certainty. But if I understand it correctly, he does own the patent to this:

The Moving Finger writes, and, having writ,

Moves on: nor all thy Piety nor Wit

Shall lure it back to cancel half a Line,

Nor all thy Tears wash out a Word of it.

It's ironic to me that The Finger would have served Omar so well had it in fact recorded all that he did, but instead it inscribed most deeply perhaps his least important contributions.

Then again, consider it a marketing "loss leader." Enticed by the poems, we discover the substance of the man.

Enticed by a chance to see the crater, we come to understand the name. That both enticements are insubstantial is unimportant.

If nothing else, the next time someone quotes his poetry at you, it might serve you well to point out what he really was:

An astro nerd.

Mail to: Dave North
Copyright © 2001 San Jose Astronomical Association
Last updated: July 19, 2007

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