Luminara

Defend the world from the wrath of the polygons!

This Blog

After boldly proclaiming that I am Boba Fett it seems appropriate to introduce the real me, or at least how I see myself, and talk a bit about what this blog is. Going on a diatribe about myself sounds narcissistic and silly, especially since there are only about ten visitors per week (although it was much higher during the competition). So rather, I'll try and layout a few of my qualities that I hope will at least seed the topics of this blog.

From an early age I was fascinated by numbers. Apparently I did pretty well on some standardized tests when I was little because my parents accelerated me in math programs and I can recall being in a something called "project think" in middle school when I lived in West Texas. From the my discovery of the "variable" beyond, my love of mathematics grew. In Middle School I competed all over Texas in all types of Math competitions like mental math, math olympiad and I was one of the best in the calculator competition (calculator of choice: TI-86). For a few years I became intensely interested in fractals and Chaos Theory after reading Gleick's book and others. During that time I can recall being amazed by a chaotic waterwheel I saw at a science fair and feeling blown away by the simplistic complexity of the logistic equation and Mandelbrot set. Once, I ran into my parents bedroom late at night when I programmed my TI-86 to plot and explore the logistic map (seen above). The observation of self similarity is something I am very fond of and will discuss at length in a future post. By the way, self similarity is certainly a profitable concept in the world of market price analysis. Aronofsky's film Pi remains one of my favorites and it has always been a dream of mine to make films with strong mathematical influences, maybe I'll write about a few of those ideas in the future. Sometime in middle school I came up with "pythagoruz" as an AIM alias, then a hotmail account, and now it is my internet persona in various disciplines, anywhere you see it, thats me.

I'm now 24, have degrees in electrical engineering and physics from UCSB and am working on a Ph.D in materials science at UIUC. In my research I look at very small scale crystal structure ("nanocrystals" or quantum dots) and aim to control the growth geometry. I'll talk more about this later, but it basically involves chemistry and 3D geometry(see TEM image at the end). My favorite subject in Physics was Relativity at one point but has since changed to Quantum Mechanics because of the beautiful mathematical construct created around QM. I am also an active trader with an eye for reading charts, you can find out more about that at Stock Geometry. Also, you may have noticed that I recently competed in a auto-trading software competition using this site as a venue for posting trades. In my experience, all good traders have a eye for spotting patterns and a comfort with numbers.

In short, I love to talk and think about mathematics, always have. Over the years I have met others like me and the internet has provided a great venue for such topics. So while I may digress, e.g. Star Wars, the idea here is to celebrate the beauty of mathematics, not unlike Pythagoras and his Pythagoreans did the 500's BC. I would love to get feedback along the way and get some discussions going so please feel free to comment with any thoughts or suggestions you have. From wiki:

Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. According to Iamblichus, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons."

I took this image of some Iron Oxide nanocrystals i made a few weeks ago. They formed a ring as the solvent evaporated off the thin carbon film on which they rest for transmission electron microscopy(TEM). Can you see the self similarity?

I'm Boba Fett

I just took the Star Wars personality test and was worried that I might end up being someone lame like Grand Moff Tarkin. Well, he wasn't all that lame but since he was into engineering the death star and all I just figured... But as it turns out I have the most in common with Boba Fett, the biggest bad ass in all of the Star Wars universe! Sweet! Ya know, now that I think about it they really nailed it.

This is what they told me at the end:

No Pi for Mr. Palais Please

Its understandable that with the development of Mathematics over the years by countless numbers of highly intelligent people that it has become difficult to contribute meaningfully to the field. It must be pretty tough for up and coming mathematicians to make a name for them selves with the level of complexity that goes into new research and progress. Just about the only field that requires new mathematics is theoretical physics, mainly string theory, and lets just say that 11 dimensional topology is very complex. That being said, I offer no excuses and no sympathy for the attention seeking author of Pi is Wrong.

Let me start by saying that I think it would be inappropriate to change any fundamental constant of nature or mathematics. A massive body of knowledge has been built on the basic principles of math and physics, not to mention civilization as we know it. These principles are apart of who we are, not unlike how history defines culture. To change these constants would in a way be like trying to re-write history. But there is also the issue of it being impractical. Ask any kid what the area of a circle is and he will tell you "pi R squared," ask him what pi is and he'll say "3.14 something." Everybody knows what pi is and what it means. Its written in millions of textbooks, programmed into millions of calculators and taught in thousands of classrooms. Simply put, redefining pi would cause confusion and add complexity. You can imagine some theoretical physicists are working on a groundbreaking problem in string theory, on the verge of a breakthrough, when all of a sudden someone asks "which pi are we talking about?" The train of thought breaks and the geniuses are now caught up in an argument about pi, needlessly.

Ok, so aside from the obvious reasons why no fundamental constant should be changed, how does Mr. Palais's argument stack up? His angle of attack is basically aimed at the semi-common factor of two that appears in front of pi, if it is so common 2pi must be the "real" fundamental constant he says. Now this wouldn't be the first time a constant had an annoying factor. In physics it is rare to see plank's constant without it being divided by two pi. The physicists of the early 1900s became so tired of having to write h/2pi that they created a new constant h-bar which was equal to h/2pi. In many cases this new constant h-bar eliminated not only the factor of two but also the pi, so for those equations the argument is mute. You may recognize plank's constant from the equation of a photon's energy:
As I've already mentioned, the equation for the area of a circle has no factor of two and the volume of a sphere has a factor of four thirds, so no help there. The circumference of a circle is equal to two pi R, but if you write it in terms of the diameter of a circle the factor of two goes away. Besides, why is Mr. Palais so interested in two dimensional geometry, after all we live in a three dimensional world. The surface area of a sphere is four pi R squared, so maybe he should argue that pi should become four pi. I will give him credit for ponying up to the fact that all the angles in a triangle add up to pi radians, strong evidence against his argument. Then we have Euler's identity, which Richard Feynman called the "most remarkable formula in mathematics," no factor of two there. In fact, if you go through all the major formulas that define pi very few actually have the factor of two. In wikipedia's entry on pi I counted only five equations out of 55 listed from mathematics and science where re-defining pi would eliminate a factor. In fact, from a cursory glance, a factor of one half seems much more common. Here are a couple that I ran into:
His argument about the factor of two being everywhere is bogus, laughable really. Mr. Palais really shines when he tries to say that the equation for the area of a circle should look like the equation for kinetic energy. Yes, isn't it obvious, since one half mass times velocity squared is kinetic energy, one half pi (his new version) R squared should be the area of a circle! Genius! I jest, but this is no laughing matter. Pi beautifully appears in many, many equations. Sometimes it appears with other factors, but those factors are not two much more often than they are. Mr. Palais's claim is not only disrespectful the the beauty of pi but outright wrong.


Theres nothing like a blatantly absurd statement like "I believe pi is wrong" to get attention for yourself, and it worked. I found this article doing my daily scan through digg.com as it was one of the most "digged" articles on the web that week. I can only hope that those who "dugg" the article did so because they were amused by the author's idiocy, in fact I was.

Pi is Perfect

Ok, I was gonna wait a little longer to begin posting here in full force but some punk at Utah State has brought me out of the woodwork with his blasphemy. Let me just say that pi is irrational, impenetrable, indivisible and all powerful. Yes pi is the ultimate number. I will give a full explanation of why pi is so great and the complete opposite of wrong this weekend. But in the mean time read the link I posted above and think of pi as your own little tiny dancer, magic really:

10th Place

The results are out and I placed 10th! They have me down for a 27.254% profit over the eight weeks that the Interactive Brokers College Olympiad ran, slightly above where I thought I ended up. I'm am very pleased with this result considering this is the first of hopefully many more years of competing. I'm eligible so long as I'm in school and I've only finished a year towards a PhD in Materials Science at the University of Illinois (4-6 yrs). With all the experience I picked up in the 2007 competition, next year things could get interesting. 10th is good, but it leaves alot of room for improvement! Thanks for your support and feel free to drop me an email at pythagoruz@yahoo.com if you have questions about the software. You can find my weekly market thoughts at StockGeometry.

Update & Happy Pi Day (3/14)

I got curious today to see how the portfolio has been doing over the last three days since the competition ended. I was still able to log on and I found that the account is now $125,531. In other words it made $2k in the last three days while the software wasn't running! I'm sure the current account value will not count towards the final standing but it was nice to see that the software was in the right positions. Otherwise, I have heard no word from IB about the competition. I even sent them an email about when/if i need to send in my code. I'll will be sure to post a follow up about my final standing.

As you may have guess from the name of the blog and my alias I enjoy the beauty inherent in nature, geometry and math. There are a number of topics in this area I will eventually be discussing in this space from my materials research to more abstract ideas in number theory. I don't intend to start this project until things are wrapped up with the olympiad, but in the meantime take a moment to appreciate the coolest number in existence, if you are comfortable saying numbers exist that is:


3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...............
all images taken from http://en.wikipedia.org/