Thursday, August 16, 2007

Not my two cent

Not only that theoretical physicists should be able to estimate any number (or at least its exponent), we feel that we can say something intelligent about almost any topic especially if it involves numbers. So today, I will give a shot at economics.

As a grad student, I had proposed to a friend (fellow string theory PhD student) that I would guess that with about three months study it should be possible to publish a research paper in economics. That was most likely complete hybris but I never made the effort (but I would like to point out that still my best cited paper(364 and counting) was written after only three months as a summer student stating from scratch in biophysics (but of course with great company who, however at that point were also biophysics amateurs)).

About the same time, I helped a friend with the math (linear inequalities mostly) his thesis in macro-economics only to find out his contribution to money market theory was the introduction of new variable to the theory which he showed to be too important to neglect but which unfortunately is not an observable... (it was about the amount of a currency not in its natural country but somewhere else which makes the central bank underestimate the relative change when they issue a certain absolute amount of that currency into the market. For example about two thirds of the US$760 billion are estimated to be overseas and the US dollar is even the official currency in a number of countries other than the US according to Wikipedia). Economics is great for theoretical physicists as large parts are governed by a Schödinger equation missing an i (a.k.a. diffusion equation or Black-Scholes equation) and thus path integral techniques come in handy when computing derivative prices. However, it's probably the deviations from BS where the money is made as I learned from a nice book written by ex-physicists now making money by telling other people how to make money. Of course this is a bit worrying: Why do consultants consult rather than make money directly? This is probably connected with my problem of understanding economic theory at stage one: All these derivations start out with the assumption that prices are fair and there cannot be arbitrage which is just a fancy way of saying that you cannot make profit or at least that prices immediately equalize such that you make the same profit with whatever you buy. If there is a random element involved it applies to the expectation value and the only thing that varies or that you can influence is the variance. This just means that you cannot expect to make profit. So why bother? There are however at least four possibilities to still make profit: • You counsel other people how to make money and charge by the hour. Note that you get your money even if your advice was wrong. And of course it can be hard to tell that your advice was wrong: If you suggest to play Roulette and always put money on red and double when you lose most people will make (small) money following these instructions. Too bad a few people (assuming the limit is high enough) will have big losses. But in a poll many people will be happy with your advice. You don't even have to charge by the hour, you can sell your advice with full money back guarantee, in that way you participate in winnings but not in losses and that's already enough. • You could actually produce something (even something non-material) and convert your resources (including your time and effort) into profit. But that's surplus and old fashioned. Note that at least infinitessimally your profit at time t is proportional to the economic activity A(t), i.e. as long as there is demand the more sausages the butcher produces the more money he makes. • You trade for other people in the money market and receive a commission per transaction. As transactions are performed when the situation changes your will make profit proportional to the (absolute value) of the time derivative of A(t). Thus you have an interest that the situation is not too stable and stationary. This includes banks and rating agencies and many more. • Finally, there is the early bird strategy: You get hold of a commodity (think: share in a dot-com company or high-risk mortgages) and then convince other people that this commodity is profitable so they as well will buy it. The price goes up (even if the true value is constant or zero) and indeed the people early in the game make profits. Of course if the true value is zero these profits are paid by the people who join too late as in any other pyramid scheme or chain letter. The core of all these models of course is as Walter Kunhardt pointed out to me Give me$100. Then you can ask two other people to give you \$100.
Of course, people following strategy three above like it if there is some activity of this type going on...

Thursday, August 09, 2007

Julius Wess 1934-2007

Just got an email form Hermann Nicolai:

Dear All,

this is to inform you of the passing away of Julius Wess who
was a teacher and friend to many of us. His untimely death (at the age of 72) is particularly tragic in view of the fact that he
would have been a sure candidate for the Nobel Prize in physics if supersymmetry
is discovered at LHC. We will always remember him as a great physicist
and human being.

Monday, August 06, 2007

Giraffes, Elephants and other scalings

It's not the first time I am blogging about the as I find amazing fact that with some simple scaling arguments you can estimate quite a number of things without knowing them a priori. You could even argue that this is a core competence of the theoretical physicist: If you consider your self as being one you should be able to guesstimate any number and at least get the order of magnitude right . I have been told of ob interviews for business consultant jobs where the candidates were asked how many bricks the Empire State Building was build from and it's the physicists who usually are quite good at this.

Today, on the arxiv, Don Page gives some more examples of such calculations which I find quite entertaining (even if Lubos argues that they are too anthropocentric and apparently does not understand the concept of order of magnitude calculation where one sets not only h=G=c=1 but 2=pi=1 (ever tried this in mathematica and done further calculations?) as well): Page aims to compute the size of the tallest land animals from first principles and get it basically right.

The basic argument goes like this: First you assume chemistry (i.e. the science of molecules) is essential for the existence and dynamics of the animals. Then the mass of the electron and the fine structure constant give you a Rydberg which is the typical energy scale for atoms (and via the Bohr radius and the mass of a proton gives you estimates for the density both of planets and animal bodies). Molecular excitation energies are down by a factor of proton over electron mass. This implies the typical temperature: It should not be so high that all molecules fly apart but still be warm enough that not all molecular dynamics freeze out.

From this and the assumption that at this temperature atmospheric gases should not at a large scale have thermal energies higher than the gravitational binding energies to the planet gives you an estimate on the size of a the planet and the gravity there. The final step is to either make sure that the animals do not break whenever they fall or to make sure the animals do not overheat when they move or that gravity can be overcome to make sure all parts of the body can be reached by blood (this is where the Giraffes come in).

Of course these arguments assume that some facts about animals are not too different from what we find here (and some assumptions do not hold if all happens within a liquid, the pressure argument and the argument about falling which is why whales can be much bigger than land animals), but still I find it very interesting that one can "prove" why we are not much smaller or larger.

There is a very entertaining paper which makes similar arguments just the other way round (the title is misleading, its really about physics rather than biology): It argues why things common in B movies (people/animals much too large or too small) would not work in real life: King Kong for example would immediately break all his bones if he made one step. On the other hand, if we were a bit smaller, we could fall from any height as the terminal velocity would be much smaller. But simultaneously the surface tension of water would pose severe problems with drinking.

I would recommend this paper especially to the author of an article in this week's "Die Zeit" about nano scale machines that reports amongst other things about a nano-car with four wheels made of bucky balls. Understanding how things change when you try to scale things down show how the whole concept of wheels and rolling does not make sense at very small scales: First of all Brownian movement poses real threats, and then roughness of surfaces at the atomic scale would make any ride very bumpy (the author mentions these two things). But what I think is much more important is that gravity is completely negligible as your nano car would either float in the air or be glued by electrostatic forces (which for example cause most of the experimental headaches to people building submillimeter Cavendish pendulums to check the 1/r law or its modifications due to large extra dimensions) to the surface both perspectives not compatible with wheels and a rolling.

So there are good reasons why we are between one and two meters tall and why our engines and factories are not much smaller.