Thursday, June 30, 2011

Writing, writing, writing...

This has been a great summer. The weather has been gorgeous and we are home in lovely Pullman. My original summer travel plans, which I was finalizing in early spring, had me flying out to Belgium to collaborate with my former grad student Xavi; and, colleague Koen Clays. Belgium would then be the staging point for my other trips, which included giving a Keynote address in Pretoria, South Africa, a stop in Poland to give a plenary lecture followed by a trip to Italy to present an invited talk in beautiful Cetraro at the NOMA meeting. Before heading back to the U.S., I would have stopped in Dublin to attend ICONO, an international meeting that has its roots in Pullman back in 1991 when I was an upstart faculty member.

However, the ICONO meeting was postponed until September. Since ICONO and NOMA were my two priorities, I decided to cancel all of my other commitments, reducing my travels to 17 days from 45. We took a 6 day break between my colloquium in Rome and the NOMA meeting in the south to drive around Italy with friends. This was an excellent idea, turning a hectic work trip partially into fun.

As a result of these abridged travel plans, I have been in Pullman for a larger fraction of the summer than usual. The weather has been heavenly, and working in my study with a cool breeze through the open windows is rejuvenating.

I had also planned to be writing several proposals now, but these good intentions were also placed on hold. Instead, I am working on almost a dozen papers that I hope will be submitted by the end of the summer. Proposal writing will continue in the fall.

Typically, summer salary comes from my grants. This summer, I decided not to pay myself for two of the three summer months. Part of the motivation was to have enough funds to pay all of my students since one of my grants is running out and a second grant was cancelled in the first year (out of 5) because of budget problems at the air force. As a result, I am working four to eight hours a day rather than the usual sunrise to midnight pace. This has given me time to decompress from a very busy life. Now I can take some time off to water the plants, catch an episode of a mindless comedy, or read the paper without guilt.

Most of my time these days is spent writing papers. Surprisingly, not having so many responsibilities to balance, I have found the process enjoyable. It's akin to organizing a photo album. As one mounts each photo, memories of people and events flow through the mind, leaving the reminiscer in a hypnotic state. Similarly, as I write each sentence of a manuscript, I recall the moments when ideas were conceived and grew. The memory of stimulating discussions with colleagues and students rekindles the flow of endorphins, allowing me to relive in my mind the birth and eventually the development of new theories or the discovery of new phenomena.

After my mornings with new manuscripts, I have a relaxed lunch, then meet with my students in the lab, interpreting new puzzles and germinating new ideas. This summer, life is as I had imagined for an academic. However, I know that the hectic life will return in less then 2 months, so there is some urgency to my rest. In the meantime, I am withdrawing into my blissful state.


Saturday, June 18, 2011

So much to learn...

Our trip to Italy combined some work and fun. After giving my colloquium in Rome, we drove north, stopping in Orvieto, Luca, Florence, Pisa and San Gimignano to see the sights. Then, we drove south to Cetraro (the site of my conference), stopping in Caserta for the night to break up the long drive. In Cetraro, I spent the week at the NOMA conference, where I gave a talk and interacted with many colleagues. Our trip ended with a drive up to Rome to catch our plane back to the US, with a stop in Pompeii to visit the amazing ancient city.

Upon getting back, the work that had piled up during my absence hit me like a wrecking ball. While sitting at my desk writing and responding to zillions of emails, I noticed a delightful message from World Scientific press stating, "We are pleased to introduce a new title that may interest you." Usually, I reflexively delete such emails, but this time I glanced at the title, "Fractional Calculus." Immediately, my mind raced back to my high school days when I was learning calculus concurrently with learning to drive a car.

I had noticed that the second derivative was represented as the square of the derivative operator; so, when taking a differential geometry class at a local university (driving there with my new license), I asked the professor if there was any meaning to a fractional derivative - that is, the derivative operator to a fractional power. He pondered the question for a moment and answered "yes." He then described how one would approach the problem. I was intrigued, but the issue had never come up again, until today.

With a little thought about the basics, the idea of a fractional derivative is quite simple. For example, consider the derivative operator to the 1/2 power. When operating twice, it should give the familiar first derivative. Using this fact allows one to develop the mathematics of fractional calculus. Similarly, a negative power can be expressed as an integral. Even complex powers are possible.

This got me very excited. I was tempted to drop everything to study the topic in great detail. Beginning with the Wikipedia page on fractional calculus, I skimmed over the introductory material that described how the gamma function is an important part of fractional calculus as factorials are to integer calculus. This makes sense given that the gamma function reduces to factorials for the integers; and in the rest of the interval connects the points between the factorial.

I read further, and found that one can formulate fractional calculus using the Laplace transform. Ironically, I had gotten intrigued by the Laplace transform when teaching statistical mechanics last semester. At that time, I had received the Dover book catalog, a treasure trove of inexpensive math and physics books. As I skimmed through the catalogue, I saw a book titled, "The Laplace Transform." I could not resist buying it. I also bought a companion book that teaches mathematically deficient people like me how to do mathematical proofs. Sadly, while those two books sat on my desk for months, I only had enough time to read a few pages.

This fact stifled my temptation to buy the book on fractional calculus. But, I was reminded of all the beautiful and wondrous topics that remain to be learned. Though I do not have the time to chew over all the profound topics that have been produced by the human mind, I take pleasure in the privilege of mastering a microscopic fraction of it all, and having the opportunity to contribute an infinitesimal fraction.

Thursday, June 2, 2011

In awe of majesty

The other day, we drove into the small Italian town of Orvieto, which is nestled in the hills of northern Italy. We parked our car near an old school, paid the parking machine, and walked up the hill to the central square. When we made the turn around the bend, the magnificent Orvieto Cathedral appeared in front of us. It was absolutely stunning.

The photos on the internet do not capture its beauty nor the awe that one feels standing in front of this huge structure, decorated throughout with centimeter-sized tiles laid carefully by teams of craftsmen. It must have taken thousands of man-years to complete.

The next day, we toured the walled town of Lucca, at one time home to a hundred churches and cathedrals. As we we walked from block to block, we saw many of them - magnificent pieces of art as well as impressive feats of engineering. We soaked in similar sights in Florence and Pisa.

In stark contrast, in the Museo Galileo in Florence, I found myself standing in front of a glass showcase with two modest telescopes that appeared to be made of lacquered cardboard. These Galilean creations, inferior both in quality and size to the small finder scopes that are attached to my telescopes, revolutionized our understanding of the solar system through careful observations of Jupiter's moons. In one great insight, Galileo moved the center of the solar system from the earth to the sun, 93 million miles away. I was in awe of his intellect. The beauty of a thousand exquisite cathedrals pale in comparison to the intellectual model of the solar system that he constructed.

In addition to discovering spots on the sun and craters on the moon, which shattered the Church's teaching of the perfection of the heavens, Galileo set the foundations for Newtonian mechanics and the theory of gravity, which describe the motions of the moons of Jupiter, the planets around the sun, the sun around our galaxy, and the motions of galaxies within larger clusters. More important than his discoveries, Galileo opened our eyes and minds to a new way of thinking - leading to an ever-deeper understanding of our universe that continues to our times.

While the priests pontificated on the virtues of ritual and the absolute truths held by the church, Galileo was uncovering the real truth, overturning centuries of dogma. It wasn't until 1822 that the Church lifted its ban on Galileo's writings, more than 200 years after he first turned his telescope to the heavens. In 1992, the Church apologized for its treatment of Galileo. This one man discovered the true beauty of the universe, which will continue to display its splendors well after the cathedrals have crumbled.