Monday, May 6, 2013

Ergodic Samsara

Reflecting on precious human birth and on the illustrations that demonstrate its rarity, it strikes me that underlying the argument is a vision of samsara as an ergodic system. Ergodicity is a notion from physics, from statistical mechanics in particular. Statistical mechanics deals with bulk matter, with big heaps of reasonably uniform stuff, for example a big tub of water.

A big tub of water is composed of many water molecules. Each of these water molecules is doing its own particular thing, has its own particular location and velocity at one time and then a different location and velocity a bit later etc. If you watch a single water molecule dance around for a long time, you can get a sense of for its general pattern, what locations it spends the most time in, what velocities it is likely to have, etc. But another way to study a tub of water is not to watch a single water molecule over a long period of time, but to look at the whole collection of water molecules over a very short time. What are the locations and velocities that are most common among all those water molecules?

Well-behaved systems, systems where statistical mechanics works well, systems that we can understand, are ergodic. This means that two approaches above will give the same results. I can watch a single molecule for a long time to learn about the most common locations and velocities, or study all the molecules for a short time. Either way, the distribution of locations and velocities will be the same.

When we read about precious human birth, the illustrations provided are about other sentient beings. For example, when we looking around we see many more insects than we see human beings. What we should infer from this is that if we look at our own series of births, many more of them will be as an insect than will be as a human.

The reliance of this argument on the ergodicity of samsara is quite exact. An individual sentient is like an individual molecule. The birth realm of a sentient being is like the location and velocity of a molecule. The distribution of an individual's series of births among the realms matches the distribution of births of all beings at any single time, in just the way that the distribution over time of the locations and velocities of a single molecule matches the distribution at a single time of a whole collection of molecules.

I'm not sure what exactly the value of this observation might be. It might help to clarify for some people the notion of a precious human birth. For some people, it might help strengthen their faith in the Buddhadharma, to see how the reasoning incorporated in the Dharma is at least similar in sophistication to that of modern science. Perhaps it could be a step along the way to a mathematical model for samsara, the evolution of experience of deluded beings. Ultimate truth surely transcends any sort of mathematical or logical analysis, but clear reasoning can surely help us let go, step by step, of our clinging to delusions.

1 comment:

  1. Contemplation on the rarity of a precious human birth is generally intended to work as a spur for practice. The defining quality of a precious human birth is that it provides the opportunity to practice Dharma, to liberate oneself from samsara or at least to make substantive progress on the path. If one fails to take advantage of this opportunity, one will generally experience a long series of births without any such opportunity before again experiencing a precious human birth.

    If one misses the twist in the argument where time, one's own future births, replaces space, the present births of other beings, then there is real danger that contemplating the births of other beings could have the opposite effect, could provoke complacency. A precious human birth is indeed special. But sentient beings cannot themselves be categorized as special or not special. All sentient beings cycle through the same sorts of births, the rare special ones and the much more common ones that are not special.

    If one infers from one's own present rare and special precious human birth that one is a special being, one might then conclude that such a special being as oneself can safely presume to take rare and special birth in the future as a matter of routine. So then there would not be much urgency in the need to practice. If not this lifetime, soon enough, since opportunities are abundant. But this would be a catastrophic confusion!

    The selflessness at the core of Buddhism is exactly the point that beings themselves cannot be divided up into distinct categories. Certainly at any time each being has a unique combination of characteristics and so can be categorized in many ways. But over time these characteristics are constantly shifting. Beings are constantly crossing the boundaries of whatever categories we might use to classify them.