Alright, I must admit I am absolutely influenced by Feynman’s appreciation of Nature and his obsession with Physics. I find myself looking around the shelves for ‘Mathematics’ and ‘Physics’, rather than my typical ‘Economics & Finance’ and ‘Business’. And I was browsing at books that are so boringly titled ‘Fundamental Mathematics for Physics’ when what I normally browse would be some catchy titles like ‘There’s No Free Lunch’ or ‘Bad Samaritans’. The titles of these books doesn’t tell much though. I find myself intrigued by the complex mathematical stuff evoked to study nature and laws of the universe. Take Roger Penrose’s ‘The Road to Reality’ for example. It’s price is really extremely reasonable; at 42 bucks, he introduced the history of scientific inquiry, the mathematical prowess of the ancient Greeks and gave readers lots of mathematical relationships discovered in each of the inquiry he introduced – they span from euclidean geometry, hyperbolic planes and trajectory to wave functions. That is, of course if you have time to read and investigate the issues covered in the book, which is about 1.5 the thickness of my Oxford Dictionary and about the same in terms of area of each page.
I got rather tired after looking at all those symbols that I didn’t understand. I am looking for a technical guide into those mathematical books, I hope I can find it soon. Even better if there’s any hardcore mathematician out there (must be able to speak comprehensible English), who wouldn’t mind being a answer-provider for all my questions on Hamiltonian Mathematics (Quaternion), Vector Analysis, Tensor Calculus, Fractional Calculus and more complex Geometry stuff used in Relativity. You must bear with the ‘elementary’ stuff from me by the way – I am just starting out. Then I am also looking for Feynman Lectures (just like Peng Sing); turned out that those books are so freaking expensive in Singapore. Same for other of those books published by him. Unlike those coffee break books like Johnson Spencer’s (or even Freakonomics), these lecturer series are not the kind you would gladly finish in the bookstore. Perhaps that’s also why I come to like these books; they are worth the money spent because you refer to them and you work on the problems they provide and above that, you refer to them now and then. The books I used to spend my money on are less of this nature.
That doesn’t mean that I have decided to do away with Economics of course! Feynman was describing about how science tells us that different phenomena observed are actually the same phenomena observed at different scales. For example, motion at the smallest scale gives us heat, at just slightly larger scale, it is just the propagation of waves (sounds and ultrasounds); it is only at rather grand scale when it is things changing location and stuff like that. The amazing thing is that a single concept of motion would explain all these seemingly different phenomena. At the same moment, I was wondering if Economics is the same, a rule applied to different scales, resulting in different phenomena. Then I realize it can’t be so. Physics exploits symmetries to make generalizations and aggregate effects of independent particles. That’s to say that even though at any one time, the behaviour of each individual particles are different, their behaviours are restricted to certain rules. By symmetry therefore, it is possible to simulate or calculate aggregate effects of these particles.
In Economics, the individual agents may be restricted to ‘rational rules’ but unlike particles in a substance, these agents can under special circumstances, infringe on those rules, making it rather impossible to sensibly aggregate the effects. Worst, in the physical world, we subject a substance to some conditions (pressure, temperature, presence of any other substance) and we assume the condition’s effect to be uniformly reflected on every single particle in the substance. That does not happen in the economy. Circumstances impact differently on different particular agents. Just think about how you might be able to measure the melting point of an alloy (a mixture of a couple of different metal particles) that is subjected to a few different mysterious forces, which would continually alter the way in which certain type of metal particle in the alloy behave with the other particles. Let’s say there’s a Force A that strengthens and weakens in a sine function; this Force makes the A-Particles in the alloy repel the B-Particles when it strengthens. Then there’s Force B that does something similar to B-Particles and C-Particles. There’s no way you’ll manage to melt the alloy at a particular temperature and then expect the experiment to repeat itself in the same way because the force strength keeps on changing, and then at certain moments some particles are tending towards melting (repelling or pushing away from the other particles) while others are tending towards bond-forming due to the force.
The biggest mistake in marginal analysis have been to make unrealistic assumptions and disregard the dynamic nature of the economy. However, that’s still the best possible way to even attempt to make economics mathematical. Some thinks economics is the science of today because its complexity can only be simulated on computers that have been invented just recently. Still, it does no good to make things more and more complex; it only makes it less accessible and applicable for predictive studies. Right now I have no answers to this problem and I doubt I’ll invest a lifetime to find the answer to such matters of the economy. Somehow the potential of getting an answer is a little too low and the question, like all questions on humans, never yields any sort of answer satisfactory to all. There’s however the branch of Game Theory in Microeconomics that I am interested in and I just got an idea to do a short research on incentive system set up by policies of an institution and matters like that. The first paper will be on late-comers in lectures. It’ll be on my site soon.
