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.
