Randomness and Meaning

by Martin Bulgerin

(Originally published in the "TidBits" column of the Fall 2003 issue of JOAC.)

As anyone who has tried to rigorously define the notions of "randomness" and "meaning" knows, they are very slippery, ambiguous ideas. And in common usage, this ambiguity often means the two ideas are confused and intertwined. While I'm obviously not the first person to notice this confusion, I recently had an insight on how removing this confusion relates to oracles in general and the Q-Ching in particular.

Take, for instance, the concept that the yarrow sticks are a "random process" that nonetheless reveals the Tao. Depending upon how you interpret "random" and "meaningful", people seem to split into two or more factions, including the group that believes the yarrow sticks are not random, but conscious. I think a more useful basis for discussion comes about if you only split these two ideas apart.

Let's start by trying to define these intuitions more precisely. "Randomness" is undoubtedly a very complicated idea, having spawned numerous fields of mathematics that try to nail it down. And while there are clearly many "degrees of randomness" that are possible (say, in sequences of symbols comprising a "message" or in geometrical pictures), for our purposes it is sufficient to note the difference between having a pattern or being without a pattern. If there is a pattern in a sequence of symbols (e.g., "abcabcabc..."), then it is easy to describe what the next symbol should be, while if it is random there is no way to "guess" the next character. A random process is essentially unpredictable in the sense that you will never know before the process creates the next answer. Of course, there are infinitely many shades of gray in our ability to describe patterns and this ability has some severe limitations theoretically (see Recursion Theory). As an example, a picture of a square clearly has a simple pattern and a random collection of points on the plane clearly does not. But the Mandelbrot set is both complicated (since it's a fractal) and simple (since it's describable by a single algebraic formula inside a small number of lines of code), which is part of its mystery.

"Meaning" is also very slippery. First of all, "meaning" is not the same as "information", at least in a theoretical sense. Information is what allows you to resolve uncertainty. Meaning, on the other hand, is more of a psychological reaction to information by a conscious being. A meaningful message produces a state of "aha!" in a person, while a meaningless message is just ignored as background noise. I'm hard pressed to believe in "objective meaning", that is, meaning that is independent of an observer. A string of ones and zeros may appear meaningless to one person, but very meaningful to the next person who translates it into hexagrams and consults the Q-Ching for guidance. The ability to "interpret" a message is critical for meaning. Again, there are gray areas and ambiguities. How often have researchers studied their data and thought, "It seems to mean something, but I don't know what it is." Ambiguity is extremely common in oracular messages.

(As an aside, the illusion of meaning may simply be an awareness on the part of the receiver of a message that the sender of the message has a consciousness similar to itself. Such a receiver may not see any meaning in a message from a totally dumb process, nor from a being whose consciousness exceeds or is sufficiently different from itself.)

So, if you tease these two ideas apart and examine them as independent dichotomies, there are four separate categories to look at. In two of the categories, a message is meaningless: it doesn't say anything. These messages can be either with a pattern (such as endlessly repeated jibberish) or random (electronic static or white noise). In most person to person communications, the message is not only meaningful, but full of patterns like linguistic structure or being conceptually coherent. This leaves one last category, namely random-but-meaningful. In the common, confused way of interpreting these terms, this is an oxymoron. However, random-but-meaningful is precisely the kind of messages throwing the yarrow sticks produces. The randomness (i.e., beyond our ability to describe beforehand) is why this is the Tao talking. The meaning is why the oracle makes sense and seems to answer our questions. In fact, many practitioners of the Q-Ching report the experience that the oracle is a "wise being" with a very definite personality for them. If the oracle is indeed meaningful, it's practically inevitable that we'd come to think of it as a person somewhat like ourselves.

I suspect that this idea of random-but-meaningful is a common characteristic of most oracular systems.