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