Pseudo Random Idea

Computer Science Journal – Nov 5th/2008

The lotto, Roulette, pi, evolution, chaos, quantum mechanics, patterns in nature….what do they all have in common?

….hmm

Random numbers! More specifically, the concept of random in general. Which can be defined (from a Computer Science & Mathematics standpoint) as a “fair dance between 0 and 1″, or simply as “a pattern which is impossible for a human to predict”.

Some interesting points:

- A computer (or any computational device or process) cannot generate true random numbers. Instead they generate pseudo random numbers. These numbers are deterministic (they can be predicted) and are eventually periodic. Computer programs always require a changing seed value to build a sequence of numbers from.

- It is impossible to prove whether or not a given series of numbers is random. This can be understood intuitively – is 3 3 3 random? How about 8 9 4? How about 1 2 3 4?

- Nondeterministic number sequences which are normal (evenly distributed) are called true random sequences. In order to generate these sequences humans have tried to roll dice, spin a wheel, flip a coin or measure some chaotic system such as electrical noise, radioactive decay or quantum particle motion.

- In 1996 David H Bailey came up with a simple formula to calculate any digit of pi to the nth digit without calculating the preceding digits (no expansion). Read about it here.

- Pi is an example of a constant which appears normal (a true random sequence) yet has not been proved so. If you are unaware of all the interesting mysteries/myths about this special number click here.

- Do you think you can behave randomly? Well, you can’t – and Casinos know this. Try for yourself:

As you can see, random numbers open up a big can of worms. One which has been thought about for 1000’s of years and is at the heart of a 3.2 trillion dollar gambling industry…among other things. The power of a true random number generator is something worth thinking about. Especially since the only method by which we generate this power is through sampling of natural phenomena.

Keep in mind the Roulette wheel at say Caesars Palace (My favorite spot) is not a device which perfectly generates random numbers. It was first beaten in the 50’s using a neat device built by Claude Shannon, which also happened to be the first wearable computer (click here for paper). This is device works on the principal of wheel bias (no wheel is perfectly balanced in every way) and the fact that you can make late bets in the game after the ball drops. It is based on the principal of guessing probable regions rather then specific numbers. Bets are then placed on neighboring numbers in that region. I’ve read some history and it turns out gambling played an equally important (if not more important) role in advancing Information Theory, as compared to the military – which usually advances everything in Science!