On Thursday, September 6, 2012 2:19:40 AM UTC-6, Vince Virgilio wrote: > To borrow a pithy from Wheeler: It-from-Bit?
That's a great example of how psychology drives the preferences of scientists and mathematicians. Dualism is a powerful psychological drive in human beings, but it gets little support from reality. Is it true that Pluto is a planet? That's a big deal to some people, but it matters little. "Planet" is the name of a simple (and rather shifty) story we tell about celestial objects. "Pluto" is the name of another story, but that's much more complex. The concrete reality behind the story is easier to find, and we can relate it to other stories (e.g. "methane"). Dualism is actually a barrier to real understanding here.
The powerful instinct to dualism misleads in other ways. Many people have a superstitious faith in its elaboration, (two-valued) logic. But while logic is useful in elucidating the relationships between hypotheses, it cannot determine truth. Logic steps from falsehood to falsehood as easily as it steps from truth to truth.
Then note that Boole believed his algebra (a further elaboration of dualism) to represent the "Laws of Thought". But we've constructed machines that can evaluate Boolean expressions trillions of times faster and more accurately than we humans can. Actual thought based on Boolean mechanism remains elusive. I thus think Boole's belief has been comprehensibly falsified.
One might note that bits are decent raw material for some kinds of mathematical modeling. Still, they have unfortunate limitations. A newly synthesized simple molecule can find its "ground" configuration in picoseconds, while a highly complex binary supercomputer takes hours or days to compute the same thing. It thus seems unreasonable to think that bits are fundamental to anything physical.
The gnurdiest fortune cookie fortune I ever saw read "Digital devices are composed of analog components." A fine piece of wisdom.
Wheeler was an example of the kind of theoretical "physicist" who forgets that physics is fundamentally, well, physical. The mathematical stories we tell are not fundamental: in the end, they are only stories. The physical phenomena themselves are fundamental.
But clearly, dualism is an expression of a very important cognitive mechanism for the practice of mathematics. So, while we might wish to dismiss it as a bad metal habit, that would surely be a mistake. Indeed, this message is full of dualism: while dualism isn't very true to how the world works, it seems essential to human communication. Can we, in mathematics and science education, learn to better exploit this mechanism while also teaching awareness of its profound difficulties?