Port 80

Reader’s Note: This is what comes of thinking too hard about Zen koans, memes, and complex numbers. I assure you that no mind-altering substances were used in the creation of this post.

This post begins with the famous Zen koan: “What is the sound of one hand clapping?” The koan poses an interesting puzzle, as two hands are required to clap. However, the riddle specifies that only one hand is doing the clapping - in other words, the question is self-contradictory. Although the question is a perfect sentence in English (or in any other language), the rules of that same language prevent that question from ever being answered.

This familiar puzzle is of interest because of the existence of an almost parallel problem in mathematics: What number times itself is equal to -1? Alternately, and more commonly, what is the square root of -1? Again, the problem makes perfect sense in mathematical terms, but that same system of mathematics prevents an answer — any number multiplied by itself must be positive. Period.

Those readers who have studied more advanced algebra already know that the mathematical question has an answer: i, the imaginary number, which is defined as the square root of -1. With the introduction of imaginary numbers, the familiar number line becomes a plane: Some numbers are real, some numbers are complex, and some numbers are a little bit of both.

This is where the interesting pontificating begins: Mathematics is a sort of language, in a sense. It is a language designed to very accurately describe quantities, and to allow for easy manipulation and examination of those quantities. English is also a language, designed to accurately and conveniently describe the interaction of humanity with the rest of the world. However, because English (or whatever your native language is) is so pervasive in our daily lives, it’s easy to forget that the language is only a description of a system. Just as a tire does not have 35 psi, but rather a certain amount of molecular motion which we like to describe as 35 psi, so are physical objects, such as “hands,” by no means tied down by the language we use. A “hand” is simply a arbitrarily defined portion of a larger discrete organism.

The point of all this circumlocution is thus: If there are numbers not described in mathematics, such as imaginary numbers, that do in fact exist, what is there to say that there are not concepts which are not defined in language that do in fact exist? What if the sound of one hand clapping is an imaginary concept in the mathematical sense?

Certainly there is precedent for this sort of thing. Consider descriptions of higher spatial dimensions: Although they may very well exist, we don’t deal with them every day. Our language — and more to the point, our minds — are not adapted to deal with their existence. Like the sound of one hand clapping, they are imaginary concepts as far as our language is concerned. We can name them, certainly, just as we can name i. But try to visualize them — and likewise, tell me if i apples are more or less than two apples.

What are the possible applications of imaginary concepts (or imaginary memes, although it stretches the definition of meme a bit)? Aside from simply describing the divorce between our conceptions and the limits of what can be conceived, imaginary concepts such as these can serve a test for the limits of logic and reason. Consider the age-old philosophical debate about whether God (typically a Judeo-Christian God) exists. According to most Christian theologies, God existed before time, exists throughout all time, exists in all locations simultaneously, knows all, and is all-powerful. The idea of “existing before time” alone is clearly self-contradictory, not to mention the endless possibilities for self-contradiction arising from “all-powerful” (how many fifth-graders have asked if God could make a rock He couldn’t move?). Clearly, a Judeo-Christian God is an imaginary concept.

Unfortunately for those atheists reading this, I haven’t just sealed God’s fate. Rather, I am simply stating that the idea of God is beyond the comprehension of language and reason, just as imaginary numbers lie beyond the real numbers. This is why every philosophical attempt to prove the existence or nonexistence of God has always been blown to pieces — the task faced by these philosophers is similar to the task of a mathematician who tries to find two real numbers which add to i. Although God may or may not exist (I have my own views, or course), neither philosophy or science nor any rational expression of religion has the ability to prove or deny His existence.

Those who are familiar with Zen and the Art of Motorcycle Maintainence are likely to notice a striking similarity between the “imaginary concept” and Robert Pirsig’s definition of Quality. Pirsig likened Quality to the Tao: Although it exists, it exists before any intellectual comprehension. In fact, Pirsig stated that no definition of Quality was possible, as any definition would be bounded by the limits of intellectual thought and unable of capturing the true essence of Quality.

The only catch is that Pirsig thought his undefinable Quality was unique. Now, we are faced with a whole bevy of imaginary ideas. I will let this concept rest for now, but may come back and play with it later. And, as always, feel free to leave a comment or send an e-mail if you’ve got anything on your mind.

Herbal, I’m no stranger to stoner logic, but… — “Sketchy”, Dark Angel