Zen Satori and P vs. NP

Suzuki says satori is irrational, it cannot be explained.

Logical positivism says that we can only talk meaningfully about things which refer to experience. See for example Hempel’s “The Empiricist Criterion of Meaning” in Ayer's Logical Positivism

Are these incompatible? I claim they are not, because even holding to the requirements of the positivists, there is still an area that allows things which cannot be explained, which I explain by analogy with the computational classes of P vs. NP. In computer science – and by computer science I mean math – P and NP are groups describing the difficulty of computing functions. P stands for Polynomial time, meaning that functions in P can be computed in a time proportional to a polynomial function of the length of the input. The simplest example of this is probably multiplication of two numbers. It’s easy to see that the simple method you learned in school takes time proportional to the multiple of the lengths of the two numbers, or in other words, it takes O(n2) time. On the other hand, there is no such efficient method for factoring a number into its composite primes. If you want to know the prime factors of 987654321, you pretty much have to just try every prime up to the square root of the number*. NP stands for Nondeterministic Polynomial time, which you don’t need to worry about and but just remember it is the class of all problems which can be verified quickly.

So here we have two groups of problems, P which are those things which we can find the answers to, and NP which are the things we cannot find the answers to, but can verify the answers are correct once we have them. (See Sipser p. 243 for the key concept I will use.) These problems, both those in P and those in NP are still well defined problems. We’re not even including things like “is this sentence false?” or “what’s the last digit of Pi”. We will refer to these last as undecidable problems.

For the positivists, all statements fall into three groups. First are those statements that are analytic, which are true or false solely by virtue of their form, also known as a priori knowledge. In this class are the statements of math and logic. Next are those statements which are synthetic statements, empirical knowledge. All statements in this class refer directly or indirectly to knowledge about the world, that can be perceived by the senses. In the third class are the metaphysical statements which are neither analytic, nor statements which refer to things which can be perceived by the senses. This includes statements like “God loves you” and “colorless green ideas sleep furiously”. These statements are meaningless. I don’t mean that they are confusing, or difficult to understand, but because they are neither analytic nor synthetic, there is no observation or chain of reasoning from observations which can have bearing on the truth value of these statements. (I’m skipping a whole section here where I should talk about Wittgenstein and Humpty Dumpty, but eventually this would result in the same conclusions but would be much more difficult to read and follow.)

Generally, religious thought falls into the second and third categories. Claims that the earth is 6000 years old, or that all your psychological problems are caused by things you overheard while unconscious are synthetic (though clearly false) statements. Claims that Jesus is simultaneous different from and the same as his father would fall into the category of metaphysical or meaningless statements. It is neither true nor false that God is Love.

So what do we make of Zen? “There is something,” says Suzuki, “in Zen that defies explanation, and to which no master however ingenious can lead his disciples through intellectual analysis.” (Zen Buddhism) Let us consider a master who wants to instill a particular state of mind in the student. If the state of mind is something like understanding Euclidean geometry, there are well established means to accomplish this task. The master will proceed by teaching the student certain axioms, showing him the relation between these, and so on. To put it in terms that Java programmers can understand, Euclidean geometry implements Serializable.

This ability to express a concept in words, in such a manner that the concept can be clearly communicated from master to student, will correspond to P in my analogy. Just as some problems (P) can be calculated, so some ideas are explainable. And I claim that satori, while not explainable, is testable. That is, a master cannot impart satori to the student, but the master can identify whether the student understands Zen / has experienced satori / is enlightened (choose your favorite characterization of this phenomenon). So while I claim that Satori is a meaningful concept, and does refer to an empirically verifiable state of the world (of which the mind of the supposed zen master is part), it is also impossible to explain. This shouldn’t be taken to mean that I think all sorts of religious nonsense falls in the same category. Zen is the only thing I’ve found so far which I think meets this criterion.

To formalize somewhat, I believe that a core claim of Zen Buddhism is of this general form. There exists a state of mind, or world view, which we we call satori, that once adopted, is persistent and stable. Satori offers peace of mind, the absence of fear of death, the lack of desire for worldly goods, happiness, and the desire to pass it on to others. Etc., etc. Satori cannot be explained in the sense that there is no known sequence of experiences which will consistently cause this state of mind. Satori can however be recognized by the responses of one who has experiences satori to certain experiences or situations (e.g. the stories where the master smiles when he sees that the student is finally enlightened).

What’s important is that you will note that the above contains no mention of anything metaphysical. This is what makes it a meaningful statement. I consider satori of questionable desirability due to my personality (I have no desire to lose desire), but I consider it a real phenomenon. Actually, I consider it a single example of a phenomenon that occurs to people of all sorts of religious backgrounds, but the Buddhists are better at intentionally triggering it and have a framework which allows them to see it as closer to what it actually is than those who experienced this state of mind in the context of 1st century Judaism or 7th century Arab polytheism. This last part is totally unsupported and I’m open to other interpretations.

Join me next time when I answer the koan, “who is the great master who makes the grass green?”

\*Yes, I know this is wrong. I'm sure since you are such a transcendent genius that you remember that factoring is sub-exponential and in the next paragraph I outright assume that P != NP, you've already figured out where I'm going with this and don't need to read the wrong parts anyway. Aren't you missing a Star Trek re-run?