Thursday, September 28, 2006

I refute it thus!

I just reread "Paradigms Lost", by John Casti. Published in 1989 (17 years ago), it presents examinations of the progression of thought on six "Big Questions" around humanity and its place in the Universe: Origin of Life, Sources of Human Behavior, Language Acquisition, Artificial Intelligence, Extraterrestrial Life, and the Nature of Reality. Although some of the science is dated, these questions remain as unanswered today as they were a generation ago.

These are all topics that fascinate me, and the temptation is to blog a bit about each. But instead, I want to blog about a related topic that I've been thinking about a lot. The way we posit a problem, the very symbols we use to represent it and manipulate it, contain in them boundaries and obstacles that often can get in the way of finding clear solutions (or at least clear paths).

Although terribly oversimplified, I'd like to use math to make my point. The number 12 can be represented in (literally) countless ways: 12, sqrt(144), 3 times 4, 2 times 6, 2 times 2 times 3, six plus 6, 144/ get my point, right?

Now, say the problem you wanted to solve was to divide 12 eggs among three people. Some of the representations above make the problem trivial. And some make it very awkward to solve. If wrote the problem as "If the number of eggs is one gross divided by sqrt(2x2x2x2x3x3), how many eggs should go to each of (30 +3)/11 people", it would be a bit harder to see the solution at a glance - you might have to work your way through it a bit.

All problems are like this. The path we take to a solution (if we can find our way to one at all) depends on the way the problem is formed, and the symbols we use to manipulate the problem space.

For the Big Problems, we tend to get stuck in paradigms of our own making (and perpetuated by cultural transmission, like a disease). These paradigms guide and restrict our thinking about a problem, such that often we can never see what is right before us in Objective Reality.

In fact, the concept of Objective Reality itself has often come under attack. Many ideas that reality is only as much as we perceive, or even that it requires our perception for reality to even exist.

An Example. The elevation of the measurement function to special status by Copenhagen Interpretation of Quantum Physics should have been sliced to bits at birth by Occam's Razor. If quantum probabilities required an observer to collapse into a single "real" state, then who in the universe was doing the obligatory observing for the 13 billion years it took for man to arrive on the scene?

Even if you take some mish mash Creationhagen view that the universe sprang fully formed once viewed by the "first consciousness", then when along the continuum of nervous system evolution did this occur? Humans? Protohumans? Anthropoids? Mammals? Eukaryotes? Viruses? Proteins? Molecules? And since we can't even firmly define what we mean by consciousness to this day, using it as the foundation for another theory seems to be building on quicksand.

No, reality existed long before we came onto the stage, and will exist long after. (Maybe - depends whether or not we make it through the singularity awaiting the end of man's childhood. If we do, there's a chance we could stick around till the end). Critical thinking skills seem to be rarely taught, either via informal cultural transmission or formal education. And it should be. When we are able to question the tenets of our thoughts back to their very foundations in Descartes like fashion, such that we can identify and recognize the boundaries of our paradigms, we can make progress in true understanding of the Universe As It Is.

It seems to be recognizing the truth through the fog of our paradigms that is the tough part, even when you're about to trip over it.
After we came out of the church, we stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it -- "I refute it thus."
--Boswell: Life
Usually the path reveals itself by its very simplicity. But its not enough to ask the right questions (a tough enough proposition).

You have to ask them the right way.


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