Figure 1: Financial markets exhibit variations at all time scales with amplitude proportional to period. Based on data from stockcharts.com.
Yesterday kicked off the first day of the NIWeek 2009. This is the annual National Instruments user group meeting. NI to followers of this company, makes hardware and software for data acquisition and control applications. For general engineering and research laboratory software, the company's LabVIEW product enjoys a dominant position. The way the company has built and maintains this position is by working hard to anticipate major technology trends that will affect their users, and what their executives learn from this ongoing exercise comes out in comments during keynote speeches at NIWeek.
During NI Chairman James Truchard's opening comments this year, he expressed the opinion that some of the economic difficulties we have experienced globally over the past year can be traced to inappropriate use of mathematics in finance
"... Mathematics, the way it has been taught in business schools the last few years," he said, "has a serious problem ..."
Dr T, as he is known to his friends in the industry, also trotted out the oft-quoted comment by Warren Buffet: "It seems like the higher mathematics, with more false precision, should help you, but it doesn't."
This reminded me of a couple of themes I've been studying over the past few years chaos and fuzzy logic as they apply to things in general, and financial markets in particular. These are surprisingly easy to understand, easy to explain, and universal in application.
Mathematically, chaotic systems can most easily recognized by being in constant motion with cycles represented at all time scales, and the amplitudes of these motions are roughly proportional to their periods. Thus, weekly fluctuations tend to have an amplitude 5-10 times larger than daily fluctuations, with the largest amplitude movements appearing on decades-long time scales.
What makes chaos important is that it can be shown to govern the operation of virtually every complex system, from ocean waves to all human history. If it's a large dynamic system with lots of independently moving parts, its behavior most likely is chaotic.
Fuzzy logic, on the other hand, seems unmathematical for a different reason. The term sounds like a synonym for "fuzzy thinking," which people associate with foolishness and ignorance. Mathematically, however, fuzzy logic is a way of dealing logically with things that cannot be precisely quantified.
Humans, in fact, make nearly all personal decisions - especially life-and-death decisions - using fuzzy logic.
When you merge your car into a busy traffic lane, for example, you don't get out a radar gun to precisely measure the speeds of vehicles already in the lane, then analyze video images of the spacings between cars, then do a calculation based on the measured data plus known performance of your vehicle at various settings of throttle and steering controls. You don't have the equipment available to make the measurements, and you wouldn't have time available to make the calculations if you did.
Instead, your brain converts sense impressions and memories from previous encounters into more-or-less broad categories. Spaces between other cars, for example, are "tight," "okay," or "really big." Their speeds are "slow," "medium," or "fast." Your car "accelerates fast," "moves out okay," or "handles like a dead whale." Instead of a dozens of variables with 12-bit precision, your brain reduces the data set to a handful of variables with at most two-bit precision. It also doesn't use arithmetic to work out the answer, but a fuzzy logic algorithm that resembles a decision tree. The answer comes back as "it's safe - go for it;" "gee, it's borderline," or "that looks like a trip to the emergency ward." The final fuzzy calculation says "no" in the last instance, causes you to look further in the middle instance, and spurs you into action in the first instance.
That's fuzzy logic. It's the fastest and most reliable way to make difficult decisions when time is limited (as it always is). It's also virtually the only way to deal with chaotic systems, which, as I said above, almost all real systems are.
Probably (in a fuzzy-logic sense) the way to solve the problem Truchard and Buffet identified, is by mentally taking chaos and fuzzy logic out of the "advanced mathematics" cubbyhole, and teach it to high-school freshman. If we did that, we'd quickly have a generation with the mental tools needed to analyze and deal with the real world, rather than a hypothetical world of mathematical abstractions.
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