I’ll begin this morning with Pythagoras and a little lesson in geometry. Pythagoras was a Greek philosopher, mathematician, musician, mystic, cult leader. Job descriptions weren’t so specialized in those days. His fundamental insight had to do with harmony and the way things could be organized in terms of ratios, ratios of whole numbers, particularly starting with musical notes and the way changing the ratio with the stop of a plucked string generates different notes and harmonies. He built up a whole system to understand the order of the universe and we all seem to have a very strong wish to find order in this universe one way or another, built on this notion of harmony and of ratios.
There’s a certain irony in how he’s best remembered now by the Pythagorean Theorem because that gives a very strange result within his own system of harmonies. If you picture a square, a dimension of one on each side, it’s easy to say that the distance around the edges, the perimeter, is 4 x 1 = 4. It’s easy to say that the area is 1 x 1 = 1 squared. Now draw a diagonal line between two corners to make two triangles. It’s easy to say what the area of each of the triangles are: half the area of the square = ½. But something very strange happens when you try to figure out the length of that diagonal. Pythagoras gave his name to a solution to the problem, where he says that the sum of the squares of the two sides equals the square of that diagonal. So if the two sides are 1, it’s 1 sq. + 1 sq. = 2. And it means that the length of that equals the square root of 2. Now the dilemma is that you can’t find the square root of 2 in the whole system of the ratio of integers. The square root of 2 is literally an unsalable number. You can create a symbol to designate it but it’s called an irrational number because it generates a series of decimals that are infinite and never repeat. It’s an extremely peculiar idea. If you look at the number ⅓, that generates decimals .33333 and it goes on forever, it repeats and you can see the pattern in it. But you can’t do that with the square root of 2.
So here you’ve got this guy, Pythagoras, who’s got this whole system of the world that is built on the harmony of the ratio of things, and the simplest picture you can have actually generates something that is totally at odds with it, creates this impossible number, this anomaly. So there’s something about irrational numbers, the square root of 2, that became a kind of mystery at the center of the Pythagorean cult. It was as if there was this secret that we can’t really let out about this anomalous fact at the center of this harmonious universe.
There’s an interesting article by Errol Morris, who most of you would know as a documentary filmmaker, who in a previous life was a graduate student in philosophy with Thomas Kuhn, who is known by his book, The Structure of Scientific Revolutions, the idea of radical paradigm shifts. Kuhn cited the information about Pythagoras as one of the ways he got the idea of the incommensurability of paradigms, that mathematically, incommensurable means that you can’t describe something in another system, so the square root of 2 is incommensurable in the system of ratios. So he took that idea and said that there are all sorts of systems of thought that we have, ways of explaining the world that may be incommensurable with each other. It’s a complicated idea. It’s the problem at the core of translation, of empathy, the problem of knowing other minds, knowing to what extent we ever understand a different culture, a different historical period, and Kuhn was in this strange position of being an historian of science who was trying to reconstruct the world views of previous generations and at the same time saying that those points of view were incommensurable, not fundamentally understandable by us.
Now, the way all of this connects to our practice is that we’re always dealing with something that is our own personal system of explanation, of meaning, of order in the world, in our lives, and it may be something that we share with a group, a religious or cultural vision or idea of how the world works or it may be very personal, our own personal way of organizing or thinking about our lives. And yet it’s fundamentally true that whatever system we have, however logical or reasonable or sane a picture we have, one day something will come into that picture that’s an anomaly. It just does not compute. That can take many, many forms.
If we have a view of life as basically good, orderly, having some purpose or meaning, one day we will bump into the fact of trauma, and trauma will shatter our picture of an orderly universe, a universe that is just or predictable. On the other hand, if we have a picture of ourselves as deficient, lacking something, that our lives are meaningless, fragmented, we may suddenly have a moment of kensho, which is an anomaly in that system, which suddenly refutes our basic assumption of anything missing at all, of there being anything wrong whatsoever. And suddenly everything shifts and we have to figure out how to accommodate that experience into our worldview.
It’s interesting from a lot of different perspectives the way that kensho and trauma are mirror images of each other. I once got to meet a fellow, I think James Austin, the guy who wrote that big book, Zen and the Brain. It’s a frightening book. He goes on at great length trying to look at the different parts of the brain where he thinks that some kind of kensho or satori experience takes place, and how in a moment some kind of experience can permanently alter the neurophysiology of the brain, so it’s permanently reset by satori. I suggested to him when I met him that I thought his basic thesis could be put on a 3 x 5 card and 650 pages reduced to the basic idea that kensho is the mirror image of trauma, that when we have trauma or PTSD, you can have one experience that permanently resets your experience into a state of hyper-vigilance, hyper-arousal. From then on the brain produces input as threat, intrusion, just automatically on this reset. What he was saying about kensho was just like this mirror image world. Suddenly we reprocess things as part of a unified somehow perfect whole. Anything that comes in has a place in that picture of wholeness, no matter what its content.
To look at these very different world views you might say that the traumatized worldview is truer for most people most of the time, but not all of the people all of the time. We want to try to put together something of those two perspectives in our practice. Partly what we ask as we practice is what kind of difference does a change of perspective make in our lives? In some way, we are engaged in a very physical discipline that resets our world view, our expectations from the body up, not cognitively, but physiologically. In sitting we create a container for a whole range of experience that we learn to simply stay with, leave alone, not judge good or bad, even though it may have a big range in that pain-pleasure continuum where we’re used to dividing everything up. When we sit, somehow those differences don’t usually make a difference. What does it mean to generalize that to the rest of our life? To have the usual differences not make such a difference, to not always divide up everything that happens into likes and dislikes? It’s so automatic for most of us, to just file everything that comes in into one pile or another. It’s just one big sorting machine, and it’s all we do all day: like this, don’t like that, like this, don’t like that. What if we just don’t do it? What if it’s just one undifferentiated heap of experience? What difference would that make? Something about sitting is like that, just letting all the thoughts, all the feelings, pile up in one undifferentiated heap. It makes no sense at all.
See, part of the idea of sorting is that, well, I’ll maximize the good heap and minimize the bad heap. In the long run it doesn’t work but it keeps us really busy. That sense of the unsorted heap of experience is something like at the root of what Bodhidharma says when the emperor asks him, What merit is there in this practice? Who are you? Bodhidharma says, I don’t know. I don’t know. He just doesn’t sort it out at all. And that unsortedness is the root of things.
Now there’s a tendency in this practice to try to create a whole new order, a whole new set of meaning that makes the dharma into something that has content, and the new sorting tool is mindfulness, where we find ourselves being very meticulous about doing everything, if I may characterize it a bit. It’s as if we domesticate our lives through this kind of careful attention to every detail, and everything will be done carefully and mindfully and everything will be put in its place and we will have a new version of an orderly universe because we’re so careful. Zen Centers can run that way, Buddhist centers can run that way. They’re just spotlessly clean. Everything seems perfectly arranged.
There was a very interesting obituary of an old practitioner from the San Francisco Zen Center who died recently. It was some old beatnik who had wandered in there but he was there from the beginning, from the Alan Watts days, and he never really fit into the Japanese Soto style of practice. Even though at some point he was one of the heads of the place, they said, What don’t you like about this style of practice? He said, You know, everybody here is just obsessive about cleaning things and being orderly, and in work practice we clean things that have just been cleaned and we just clean again. The Chinese have a whole different approach to things. And they said, What? And he said, Dirt.
Maybe I’ll just leave you with that. There’s something about it that’s irreducible. You see, dirt is that anomalous, irreducible part. Don’t think that we can clean up our act so perfectly that there will be no irrational number, no irrational thoughts, no dirty thoughts, no dirt. It ain’t gonna happen.