Sunday, October 16, 2016

Florensky on evolutionism -- "What is the differential equation?"

From At the Crossroads of Science and Mysticism, Lecture Four:
Renaissance culture also gave attention to the other principal form of being--time. The examination of the concept of time occurred later, and the fragmentation of being in time was performed later than the fragmentation in space: evolutionism came after mechanism.

Evolutionism does have a healthy seed--gentism, according to which an essence does not unfold in some single moment, and the spiritual meaning of an object is not exhausted by some single state, but exists in the totality of its states. But evolutionism errs when it states that this genesis is made up of infinitely small additions, so small that each separately can be considered not a creative act. ...

For example, let us consider the question of the origin of man. Evolutionism denies that there is a qualitative and fundamental difference between man and animals. But if this process occurs discontinuously, if man is descended from the apes, this theory loses its anti-religious character, since a qualitative change suddenly occurs. And if man was created from the dust of the earth by a special creative act, why not then allow in principle--only in principle--that man was created by a momentary addition of spiritual qualities to the ape?
What I am pretty sure Florensky is saying is that one need not take the creation story in the Bible literally to have a Christian worldview, but on the other hand he does insist on a "discontinuous" development of spiritual qualities. On the one hand, I suppose that science can't now and perhaps never will be able to address the important qualitative differences between man and the apes. For example, there will never be a fossil record of spoken language, so we will never know definitively when or how speech developed. On the other hand, Florensky (writing in 1920, mind you) could be taken as throwing his lot in with what might be called the "intelligent design" crowd. How else to interpret this statement, particularly with its wording about "creative acts"?

There's a very thought-provoking passage on how the differential calculus was absorbed into modern science:
For the immediate consciousness rest is opposite to motion, while the essence of science is the fact that we can study motion only by separating it into states as if of rest, with the result being the differential equation. The latter becomes the universal instrument of mathematics, and then of all science and the whole Renaissance epoch, since, to quote Kant, every science is a science insofar as it incorporates mathematics.
 He goes on:
What is the differential equation? Some sort of process is occurring, and we stop it and break it up into a series of instants and see it as if in sectional view. The differential equation is a general formula suitable for the sectioning and study of any process. With this method we are not concerned with the past, with what occurred earlier in time, with whether these are people or whether they are statues who suddenly started moving again after we had stopped them. Only the present is important for us here, not the past; but for many phenomena it is precisely the past that is important.
Writing in 1920, I suppose Florensky could simply not have known about all the modern developments in differential equations. Now it is commonplace to deal with integro-differential equations which were developed to take into account nonlocal interactions across both time and space. I wonder what he would say if he could have lived to see the era in which most differential equations do not involve continuous functions and Taylor series, but rather wild, mysterious functions and generalizations thereof.

Even today, one might think at first glance that Florensky is basically right in his description of differential equations, in that they are meant to break down a process into infinitesimal moments, each of which may be viewed as "not a creative act" but rather a blind obedience to some universal law. But even creative acts or subjective experiences can be modeled quantitatively. The whole use of optimal control theory to predict social behavior comes from the idea not that human beings follow mechanical laws but rather that they exhibit optimizing behavior, i.e. genuine acts of will. Florensky simply could not have seen this, since its development came only after his death.

Still, Florensky challenges me like no other thinker, perhaps because so few theologians know or write anything about differential equations! It would be naive to assume that mathematical objects appeared in a philosophical vaccuum. I should pay closer attention to how today's concepts are used (or could be used) to shape our world view.

To me, there will always be one fundamental discontinuity that cannot be ignored by any scientific theory, and that is the mere fact of existence. Between existence and non-existence there is no continuum. There can be no "probability" that the universe would come into being. Rather, its existence is pure impenetrable mystery. For me, this is basically the same thing as to say that God spoke the universe into being.

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