Questioning Nineteenth-Century Assumptions about Knowledge, I by Richard E. Lee

Author:Richard E. Lee [Lee, Richard E.]
Language: eng
Format: epub
ISBN: 9781438433929
Barnesnoble:
Publisher: State University of New York Press
Published: 2010-10-08T00:00:00+00:00

SESSION III

DETERMINISM AND MATHEMATICAL MODELING

Ivar Ekeland

I

Rien ne se perd, rien ne se crée. Nothing gets lost, nothing gets created. This is the basic law of chemistry, as formulated by Lavoisier in the late eighteenth century, precisely the time when the concept of determinism takes shape. Just a few years later, Laplace will make his famous pronouncement that if some rational mind (a demon) was farseeing enough to envision the whole universe at one glance, and agile enough to perform instantly and exactly all the calculations it wanted, then the future and the past would lie before it as an open book.

Indeed, there is a strong similarity between these two views of the universe. Determinism can be understood as Lavoisier's law applied to information. What Lavoisier is saying is that, in spite of all the apparent changes that take place in a chemical reaction, the basic constituents remain unaffected. When sodium and chlorine are put together, they disappear and an innocuous substance appears, namely salt. This is quite a spectacular experiment (not one you would want to perform on your kitchen table), but it is fundamentally an illusion. Neither the chlorine nor the sodium have disappeared, they are hidden in the salt, and they can actually be retrieved with the proper apparatus. The same atoms of chlorine and the same atoms of sodium are still present; they have just been combined in a different way.

Determinism is basically the belief that no information is ever created or destroyed. There can be no gain of information between today and tomorrow (so that, if you know the state of nature today, you should be able to predict the state of nature tomorrow), and there can be no loss of information between today and yesterday (so that, if you know the state of nature today, you should be able to reconstitute the state of nature yesterday). It might be difficult to retrieve that information, just as is it difficult to separate the chlorine from the sodium in ordinary salt, but it is just a matter of having the proper apparatus and being able to perform the calculations.

This is a strange idea, for it runs directly counter to our everyday experience. However, it is well-grounded in religious and philosophical thought. We can refer to the classical idea that God has a great Book, where He has written in advance everything that will happen to everyone, so that we find ourselves miraculously playing our appointed role without ever having learned it, discovering its most unpleasant parts as we go with the word Mektoub, “it is written.” This has the advantage of putting us in the comfortable position of blaming someone else for our own failings, but Leibniz managed to twist the idea around and put the blame back on us. For while Laplace's demon sees only one universe, Leibniz's God sees infinitely many, where there are infinitely many independent copies of myself doing infinitely many different things for infinitely many different reasons. The trick is for God

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