Ganesh Swami

Today was the first official day of classes.

My non-linear physics class (PHY484) has just three students. This course is cross-listed with a graduate course (PHYS848) and has one student. That makes four students. Dr. Bechhoefer, my instructor has more or less combined the course with a math course – “The Mathematical Origins of Patterns” by Dr. Muraki. That brings in another five students. Fun.

After we got past the administrative details, Dr. Bechhoefer gave us examples of patterns we see in nature. Because of the multi-disciplinary nature of this course, not all students have the same background. I’m the only engineer in the crowd. We were asked to fill out a three page survey so that the professors can better understand the backgrounds and strengths of the class. Obviously, I took this opportunity to state what I expected to learn from this course: dynamics. Be it fluid dynamics, molecular dynamics, agent based economics or chemistry, hopefully the analysis is transferable between problem domains.

The first class was a “warmup” session, barely leading into the classification of dynamical systems. Broadly, we have two kinds based on the equations of motion:

• Differential Equations (ordinary and partial)
• Iterated Maps (also known as difference equations)

The only difference between the two is whether time is continuous or not. Obviously, iterated maps (with discrete time) translate to computer programs quite easily.

I guess the rest of the week will be looking at trajectories in phase space. Allow me to share this “riddle” that I was once asked when discussing phase space with a friend:

A one-dimensional harmonic oscillator demonstrates oscillations, but one-dimensional systems do not undergo oscillatory motions. What’s wrong?

The answer is that the phase space of the one-dimensional oscillator is actually two-dimensional (space and the first derivative of space.) It is one-dimensional in only space.

The rest of the day was spent running around getting paperwork done. The MIAL is co-directed by people from computing science and engineering, so things are a bit scattered around. Hopefully, all of this is settled by the end of this week.

I’ve been really busy this week preparing for work (at the MIAL), so I’m going to cop out and post a bunch of links that I found interesting:

• A dialogue on Mathematics & Physics by Chaitin and Calude.
• Ultimate physical limits to computation. Physical limits as determined by the speed of light, Planck’s constant and the Gravitation constant.
• Physics of Climate Modeling in Physics Today. Also check out the comments on RealClimate.
• Linux running on the PlayStation3.
• Information Processing: Metric on the space of genomes and scientific basis for race. Plotting genomes of humans leads to easily identifiable clusters of ethnic groups: Europeans, Africans, Asians and Native Americans.
• Comments on Nature’s open peer review experiment and the lack of anonymity by Derek Lowe.
• GigaOm: 2007 is all about monetization of social networks.
• Barclays Ph.D.s Build Hedge Fund Giant Inside Bank. Great article about math, physics and finance.
• rod gets ripped outright. Some strong words, but I understand his feelings. Writing about and pointing to interesting content takes time. On the other hand, I can’t help but paraphrase Zappa: “I should be worried if my music isn’t being copied.”
• Misbehavior of markets by Mandelbrot, the father of fractals. Since I’m taking a non-linear physics course this semester, I went to amazon to check out the reviews — not very appealing. (via rod)

The only way to survive is to do shit and see what happens. You just have to have enough shit going on that some big shit happens. — Tom Peters

Now that 2006 is past us, it’s safe to look back and reflect. My “strategy” for most of 2006 has been to try new and challenging things. Sure, putting myself outside my comfort zone has increased my failure rate, but as a total percentage, I’ve had more success. A hundred percent of nothing is still nothing.

Happy new year!