Magic Numbers
You learn something new every day. It seems that some strings of random numbers are more random than others. That's kind of interesting, but not really a surprise when you think about it. Whenever we look at the characterisitcs of a string of random digits occuring in Pi or e or some other irrational number, we are looking at only a tiny fraction of the digits. Actually, it may not even be accurate to describe it as a fraction.
The linked article describes how mathematician Steven Pincus made some interesting discoveries when looking at the randomness of the first 280,000 digits of Pi, the square root of 2, and several other irrational numbers. However, even 280,000 isn' t really a fraction of an infinite number, now is it? How many digits would it take before you had a representative sample of an infinite string? I'm not a mathematician, but I'm guessing it would take an infinite string.
But before you wrap your head too tightly around that, consider what Pincus observed when he started comparing these strings of digits: some have higher levels of entropy (randomness), some lower. Then he started looking for the same characteristic of entropy in real-world strings of numbers, such as you might get from tracking, say, the stock market. He discovered that the stock market hits its highest level of entropy right before a crash.
Pincus observes that entropy
appears to be a potentially useful marker of system stability, with rapid increases possibly foreshadowing significant changes in a financial variable.
He goes on to conclude:
Independent of whether one chooses technical analysis, fundamental analysis, or model building, a technology to directly quantify subtle changes in serial structure has considerable real-world utility, allowing an edge to be gained... And this applies whether the market is driven by earnings or by perceptions, for both sort- and long-term investments.
Expect to hear a lot more about entropy and financial markets in the near future. The movie Pi, which I thought was well-made and entertaining, but suffered from a silly premise, may just turn out to be prescient.
via GeekPress
