Monkey Business
By Kevin

A Monkey Publication
If you get a monkey to sit in front of the computer/typewriter and type forever, it is definite that it will produce the works of Shakespeare somewhere in that whole writing.
How true is that? That is the Infinite Monkey Theorem. In any case, it illustrates how we cannot think of infinity as a very large finite number. It is not a number, we need to think of it as a 'flow', or like a horizon - it is a concept but not something that physically exists. If you think about the monkey analogy, it is not just the lifespan of the monkey that is in concern
Years ago, a team of lecturers and students from the University of Plymouth took the idea pretty seriously and tried to see how it works out in reality. They placed a computer in the zoo with six Celebes Crested Macaques and see what they'd produce. In a month, they produced quite a huge mess and a five page document, which was actually published and sold for 25 UK Pounds.
I find the experiment pretty interesting and the result is kind of hilarious. Of course, animal behaviour was the more important segment for this 'study' but when you look at the document from the monkeys, you must seriously reconsider the idea that monkeys are potential random number generators. They obviously approach the activity of typing with some sort of intent, albeit it transcends typing - it included 'interacting' (mostly involving urinating and defecating on it) with the computer and provoking it (like attacking it with a stone).
Chart Play
By Kevin
I learnt about Google Charts API quite a while back but didn't quite found time to explore it. I had wanted to use it to create charts to showcase certain data trends on ERPZ so that I don't have to generate Microsoft Office graphics to be uploaded. For my experiment, I decided to use the same data set for the distance fares to generate a chart using the Google Charts API. I took the following that I used in the previous entry:
Using the wizard provided by Google and then tweaking the codes a bit here and there, I managed to create the following:
Adult Bus Fares MC curve (By Google)
It actually looks great and I guess in future, when I need to present any data on ERPZ, I'll be using this API.
Mathematics of Warfare
By Kevin
ERPZ have always been rather social science oriented, doing analysis mostly on social/economic/political matters and lots of writing in just plain language (ie. no greek symbols or mathematical operators). Nevertheless, economics is fundamentally somewhat about logic and it attempts to connect the maths and science of our society with reality. Sean Gourley, a physicist is doing the same sort of analysis in his research on the mathematics of war, which he presented on TED.com.

Gourley's Equation
The most interesting idea presented in the talk is that even within the chaos of conflict, there are universal principles and relationships between the myriad of different variables in the field (in this case, fatality and frequency of attacks). More importantly, the use of alpha as a measure of fragmentation of insurgency is an interesting result and hopefully can be exploited as a means to achieve peace more quickly during a conflict.
This research paper that eventually resulted from his collaboration with the various experts of different fields was recently published on Nature magazine. TED Blogs features a Q&A with Gourley about the research. It's great that scientists and mathematicians are using their tools to learn more about complex reality and uncover patterns previously hidden from us; the applications of these mathematics, however, remains to be discovered. As science is often the neutral party, it is important to note also that the same tools can be used by the opposing parties. Strategic thinking, remains an important means of conducting these affairs.
Bad Markets
By Kevin

Better Be Good
I first heard about Benoit Mandelbrot a while back, I believe in JC1 when we had a guest speaker who specially came in to talk about Mathematics. I didn't remember the purpose of the entire event; it was some sort of Maths day or something, organized by the Maths Club (or some CCA with a name like that and deals with Mathematics in general). He spoke of golden ratio, Fibonacci sequence, self-similarity and therefore fractals.
It was an interesting talk that included loads of graphics, something pretty rare in our mathematics syllabus which emphasized more on calculus and probabilities than on geometry, though the former have their sort of diagrams. Nevertheless, golden ratio and self-similarity of fractals merely appeared to me as fancy stuff without much applications. Turns out that my impression is pretty wrong and as Maths had it for Physics towards the beginning of the 21th Century where advances in mathematical manipulation of space gave birth to Einstein's Theories on Relativity, Fractals could have some relevance in the complex systems that exhibits wildness. The stock market happens to be one so when I picked up The (Mis)Behavior of Markets, I expected to see these applications.
And of course it did, but as a book for the layman, it spent a substantial amount of text explaining the clues that built up to the notion that fractals could be used to model the wildness of the markets. It was written in a clear and simple manner for people to understand but don't expect to pick up any mathematical calculation tools on the way to help you predict or describe the market in any ways because you won't be given any high-level stuff to play with in this book. Besides that, Benoit goes all out to demonstrate the stupidity of those who assumes normal distribution of events in the stock market despite evidence that suggests otherwise. He will definitely succeed in convincing you that the market is not somewhere fun or great to be in. Unfortunately the study is not well-established enough to replace the tools used in Finance industry despite a general acknowledgment of the inadequacies of the current tools. Thus there's little examples of how the fractals improves our 'skills' of riding the market or gaining from it in any particular way.
During the lecture the guest speaker gave, I clearly remembered he described Benoit as an arrogant man who thought too highly of himself. Benoit's defensive tones of his discovery and findings as well as the offense he seem to have taken on his opponents in the book seem to confirm if not suggest that the guest speaker who came to my institution might be right after all. It'll be a good read for those interested in mathematical economics/finance stuff but probably not a good one for those looking to exploit the stock market and hope for extraordinary gains.

