Sunday, February 05, 2006

A DREAM (a philosophical tale)

A Dream
(a philosophical tale)

I saw in a dream, reclining under the shade of an ancient tree by a warbling brook — who else but Zeno of Elea, reading to a comely youth out of a tattered scroll.
"If an archer shoots an arrow, the arrow can never reach its target. At any given moment of time, the arrow is in a space equal to its own length. It is therefore at that moment at rest. Hence it is at rest at all moments. An infinite number of positions of rest does not amount to motion. The arrow is at no time in motion and can never reach its target."
The boy was agape, but before he could speak, there suddenly appeared on the spot a white-haired man and a young woman. They were – I knew it by that mystic cognizance with which we are endowed in dreams – a professor and student of physics from a modern university. They stood close by Zeno and the Greek boy but were apparently unaware of their existence. Yet I could see that Zeno and the boy were attentively watching the new couple. The white-haired professor was intently explaining something to the young student.
"Heisenberg showed that a problem arises when you try to measure the position and the momentum of a particle simultaneously. In his 1927 paper he said – and I think I can trust my memory with the exact words –, 'The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.' Which means that an inescapable uncertainty is encountered in attempting to observe a single event with two frames of reference. The two frames substantively complement each other, but at the same time they mutually exclude each other. The juxtaposition of the contradictory frames of reference is necessary to yield an exhaustive view, yet their mutual exclusiveness effectively bars the juxtaposition."
Then Zeno laughed. "What fools! I have been speaking to them in parables for two and a half millennia and they will not understand."
I felt the young girl shiver – I felt it in my own bones – as if a foreign presence had just entered into her being. I saw her eyes shine with a strange brilliance. When she spoke her voice sounded as if it came from remote depths in space-time.
"Professor," she said, I will not even pretend that I have understood your explanation of the Principle of Indeterminacy, but I have just had a notion, a philosophical notion." She stood silent for a while. When she spoke again, I somehow felt as if it was not she that was speaking. "From a philosophical point of view, I would suggest that the principle puts us face to face with the fact that all science operates with fictions; creative, productive fictions, but fictions nevertheless. First, permit me to put forward two preliminary propositions. (1) Theoretical science is not – as the widespread misunderstanding, even among practising scientists has it – concerned with finding facts, but with the interpretation of facts. (2) Real things are whole, active, creative processes. The notions of time, space, inert matter, and so on, are abstractions from the whole."
"Let me now", she continued, sounding more and more entranced, "get back to the Principle of Indeterminacy. Physicists are nonplussed by the fact that they cannot determine the position and the momentum of a particle simultaneously. The reason, to my mind, is simple. Only the whole process is real. Both the notion of momentum and the notion of position in space are fictions. When you speak of momentum (itself the product of two fictions, mass and velocity) you negate the notion of position in space, and when you speak of position in space you negate the notion of momentum. You can only determine the one by ignoring the other, which in fact has no actual existence. So it is impossible to determine both at the same time, because when you do that you are negating both. More generally, you can represent any whole in terms of an elected abstraction, but you cannot exhaust the whole in terms of any set of abstractions."
The girl fell silent and a look of amazement spread over her features. Surely she was wondering what moved her to say what she had just said. The professor was obviously displeased; no, more than displeased, he was pained. He had had hopes for his student. One word escaped his lips. "Nonsense!"
Then out of nowhere I saw the venerable Alfred North Whitehead advancing. He approached, stood for a while silent, then in a sad voice said, "I too had tried to tell them that, in my philosophy of organism, but no one took notice."
Then the whole group vanished, and I heard my alarm-clock ringing.


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