Friday, March 23, 2007

knowledge and evolution -- asymptotitc understandings

It is easy to combine the notions of what is true with the notion of what humans perceive to be true. I believe that they are likely different, and that acknowledging and understanding that difference may help us in our efforts to discover the two related but different truths -- the actual truth and the human truth.

If we look at the natural world, the actual world, there is very little that is a matter of absolutes, as we perceive them. By absolute, I mean something that admits no qualification, at least not within a given context. For example, that 1+1 is the same as 2 is absolutely true (given a specification of what + means, and what mathematical system we're operating in, etc). But, in fact, this absolute truth is not an actual truth, it is a human truth. We have defined 1+1 to be 2. It is an attempt to model the real world phenomenon that if I have a thing, and take another thing, now there are two of them. But if I have one pile of rice, and I dump another pile of rice onto it, I don't actually have two piles of rice -- I have one bigger pileof rice. And although that bigger pile of rice is in some ways equivalent to twice the two earlier piles, there are many ways in which 1+1=1 (for example, the rice is no whiter) or the bigger pile is otherwise not at all the 'sum' of the earlier piles (for example, it is likely neither twice as high nor taking up twice as much of the surface on which it rests).

This does not discomfort or confuse us, at least not most of us. We are fully able to understand that combining two piles into one pile creates a pile with twice as many items, and that that's all we mean. The instances where it doesn't, where the items may react with each other, well that's because of physical and chemical properties of the items involved, and their environment, and the method of combining. We have theories and models and even laws or rules for all of these things. In other words, we understand that in the real world sometimes we have scenarios where combining, two things, even identical things, results not merely in two of those things, but sometimes leaves us only with one of them (for example, observing the lights are out and then observing again that the lights are out doesn't, at some level, mean the lights are doubly out), and sometimes it leaves us with something completely different.

Mathematicians have developed a broad field for modeling and codifying all of our observations. Most humans can't plow much of that field, and many of us probably can't even keep our balance in parts of that field even if we were to have a guide, but the mathematicians who work that patch of the field are able to grow a number of fascinating raw materials, and are able to provide chemists and physicists and biologists the resources to craft wonderful applications. Those scientists, in turn, generate ample amounts of byproduct that fertilize the field, and sometimes even help remove obstacles and thus expose further parts of the field.

But my point is not the analogy, my point is the cycle, the approximation. Mathematicians and scientists are developing human understanding. In many cases, the rest of humanity blithely accepts that these models run counter to our intuition, although it may be that over time our intuition incorporates these new models. But we are no longer as reluctant to accept models that are counter-intuitive as we were hundred or thousands of years ago -- relativity did not result in Galilean treatment for Einstein, and quantum theory did not have political ramifications for its proponents (so far as I am aware!).

In any case, we accept these developments. And we operate according to them, building computers, designing bridges, flying aircraft, mixing colors, growing food. We operate according to them because they are good enough. But we have always done this -- lived according to the extent that our knowledge was good enough. Pre-historic humanity did not 'need' to know that the earth was not flat, because they didn't travel vast distances and had little need to contemplate the issue. Eighteenth century humans did not need to know about quantum effects because they weren't manipulating material at atomic or subatomic levels. Of course, had they known about such things they might have used such knowledge, but it would be unreasonable to expect them to have it.

This does not mean that actual truth then differed from actual truth now. It's possible that human awareness or contemplation of the earth's roundness caused it to be round, and that our studying of antibiotics caused them to exist and have the properties they have, but I believe that actual truth is independent of human existence. That's not to say it's a static truth and that humans have no effect on it, but we interact with it and live within it -- think of us as fish in the ocean, at least in some ways.

What it means is that human truth evolves as humanity evolves. Whether it's due to the selfish gene, the selfish meme, or the selfish humanity, the point is that our sense of what is true is an approximation of what is absolutely true. It is probably an ever improving approximation, but it is also probably asymptotic at best.

That last point is not necessary, and reflects my belief that the universe is infinite and of such a nature that almost everything we currently consider impossible (i.e., contrary to human intuition and current human truth) exists somewhere (or did exist, or will exist) and in such a way that it does not conflict with current human truth but is revealed to be complementary to them.

For example, early human truth held that the world was flat. This was reinforced by the development of euclidean geometry, which dealt with planes and lines and, basically, farmers' fields. When planning trails, dividing acreage, and laying out buildings, it is perfectly sufficient to model a flat world (although it's a wonder theoretical non-euclidean geometry did not develop in societies that lived in very hilly country, considering the practical work they did on 'spheres'). It's only when we move to an era of global travel and where we consider the larger cosmos from a practical perspective that we realize that the earth is round(ish) and that lines we had long considered parallel will, in fact, converge. And that all lines of equal length must converge.

But locally, on my desk, in my town, even within my state, I have no particular need to make use of non-euclidean geometry. For any small enough subset of this non-euclidean world, euclidean truth is good enough for me. It is in that sense that I think human truth will always evolve and improve -- what we know hold to be universally true will often turn out to be a special case, or an approximation.

The result, of course, is that we have two very different truths. An actual truth that reflects reality in all its diversity, that encompasses all we understand and all we can't, and a human truth that is locally quite elegant but that displays jagged discontinuities and gaps. Without suggesting that actual reality is 'continuous' or 'smooth' in the way that humans thinks of those words, I do want to suggest a model of turning flat pieces of paper into a sphere. With one sheet of paper you get gaps and bends and holes. As you use more and more smaller and smaller pieces of flat paper to approximate the sphere, you get a better approximation. But it's never an actual sphere, not matter how good it is for us. This is the struggle of humanity to make human truth correspond to actual truth.

All of this is to set the ground for why we totally screw up in philosophy by constantly referring to human understanding and human intuition as a check against ethical theories.

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