14 Mar That’s so Random!

Random Probability Theory

Some things are difficult to predict, and some are nearly impossible to predict. The further a thing gets from predictable, the more nearly it approaches randomness. It may seem silly to try to define chaos or randomness or anything that spends its entire existence trying to defy definition, but some of us have this compulsive desire to try. Besides, in the scientific community there are two significantly different definitions for random. If we are to develop a framework for designing intelligent systems, we need to incorporate intelligent components, including random or chaotic factors in our “fuzzy” logic, if these prove useful in yielding the desired results. So far, I strongly believe random factors improve outcomes, as long as they are implemented with care and monitoring.

Understanding Context Cross-Reference
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Section 5 #18

Table of Context

A random probability is something that, given no external influences, will yield all equally likely results with relatively equal regularity. It will yield all unlikely results with relatively predictable irregularity. If we permit the participation of external influences and factor them into the equation, perhaps we could get a relatively accurate prediction of future events in the domain we are studying. In fact, equations based on statistical probability and laced (or doped) with random factors have proven to be profoundly good at predicting future events in the domains being studied. When we take randomness to infinity and beyond, we may get strange results.

In Hitchhiker’s Guide to the Galaxy, entropy and random probability theory crop up occasionally, as when some philosophers have been accused of demanding “rigidly defined areas of doubt and uncertainty” or at least “the total absence of solid facts” (Adams, 1986, pp. 114-115). Douglas Adams invented a spacecraft called the Heart of Gold for his stories. Its engine was called the infinite improbability drive. The only faster craft in the galaxy was a Bistro in which quality and timely service was absolutely inconceivable. On such a spacecraft, “tiny furry little hands were squeezing themselves through the cracks, their fingers were ink-stained; tiny voices chattered insanely. Arthur looked up. ‘Ford!’ he said, ‘there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet  they’ve worked out'” (Adams, 1986). We’ll look at that script in tomorrow’s post. But in the mean time, there is yet another illustration of the infinitely random theory I have heard.

The Ball in the Box

If we take random probability theory to its limits (infinity) we can produce theories like the following ball and box theory. This version of the ball and box theory of random probability goes like this:

• Given a ball sitting next to a box      AND
• assuming absolutely no external influences,
• at some point in eternity
• the ball is inside the box.

The reason this is possible is that there is a definition of random probability that is asymptotic. In other words, though the probability of an event may decrease infinitely, it will never reach zero. We may sum up the assumption that random probability is asymptotic with the words “anything is possible.” Philosophically, this is an intriguing argument and leads to interesting experimentation. The philosophically seductive argument, however, may be scientifically flawed. A possible flaw exists if, in reality, not everything is possible. If, for example, all events are governed by physical laws (including those we do not yet understand), then the asymptotic model may be incorrect.

We may be better off adopting a common definition of random as “events not explainable by laws we currently understand” to overcome this challenge. This is the commonly held definition in mathematics. This approach speaks to the question of implementation I articulated in the prior post. So, at the risk of disappointing Douglas Adams and others who pursue infinite improbability, let’s opt for a more pragmatic, finite model for our fuzzy logic.

The button at random.org generates random values. Click it a few times and see if you can tell what type of parameters govern the probability of the ball in the box.

Click below to look in each Understanding Context section

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