[OBJECTIVE SCIENCE.COM] As I explained in part 1 of this series, the purpose of what follows is to identify the causes in philosophy of physicists' obsession with mathematical formalism -- and the incredible superficiality to which this leads. We will thereby also explode the myth that it was scientific discoveries that led physicists to reject the need for causal explanations of their formalisms. The rejection of the physical world in favor of mathematical formalism comes from the influence of two philosophers -- Plato and Kant -- and not from any 20th century scientific laboratory. Indeed, the Primacy of Mathematics attitude is nearly as old as Western Civilization itself. Let us, then, begin with the originator of the Primacy of Mathematics, the man who planted a seed which Plato turned into a complete philosophic system: Pythagoras in Ancient Greece.

Pythagoras and his followers were the first to realize the ubiquity of mathematical relationships in the natural world. They discovered that harmonious musical tones are produced by lyre strings with simple mathematical ratios, and noticed the precise mathematical regularity of the progression of seasons and tides. They then extrapolated, coming to regard mathematics as the essence of a mystical supernatural realm which governed reality. The Pythagoreans shunned the lowly material world and worshipped the abstract mathematics that they thought was the key to reality.

Plato adopted and systematized this Pythagorean mysticism. His solution to the problem of concepts was to project an entire supernatural world -- the world of the Forms -- in which resided the abstract, everlasting, mathematically perfect abstractions to which our concepts referred. Metaphysically, the world of Forms was regarded as fully real, while the familiar physical world of perception was downgraded. Physical entities in this world, according to Plato, were mere shadows, imperfect copies of the Forms. True knowledge, therefore, meant knowledge of the immaterial Forms, and not of the grubby ever-changing imperfect material world.

The causal primacy of Plato's supernatural world of Forms was presented most eloquently in his creation myth, the Timeaus. Here he tells the story of how, in the beginning, there was only a chaotic undifferentiated blob of matter. Then a god (a symbol for the Forms) enters and imposes identity and structure on the matter, bringing about the orderly physical world we see around us today. The important point here is that, according to Plato, physical matter - the stuff of this world - left to itself is essentially passive or worse: positively chaotic. An external force is therefore required to explain the apparent orderliness of the world around us.

In Plato's physics, then, the mathematical laws of nature are not a human grasp of the causal sequences arising from the identity of physical objects. Rather, the laws are metaphysically distinct supernatural abstractions which impose identity on otherwise chaotic matter. So in physics as in other areas, true knowledge is knowledge of the abstract Form - in this case, the mathematical laws - and not of any causal sequence involving physical matter. Indeed, for Plato, the abstract mathematical law is the causal factor: it is what imposes order on the material world.

Plato's Primacy of Mathematics also comes out in his attempt to reduce the physical elements to "pure geometry." He argues that the four elements (earth, air, water, and fire) could be identified with four regular geometrical solids: earth with the cube, fire with the tetrahedron, etc. So again here, the idea is that the physical world of material substances is not fully real. The physical world is ultimately reducible to nothing but geometrical shapes: the triangles and squares which make up the geometrical solids.

Platonism, to summarize, shuns the physical world in favor of a supernatural world of pure abstractions. The latter is fully real where the former is not, and true knowledge in physics, therefore, is knowledge of the true causal primaries: the abstract mathematical laws which impose identity and order on the lowly material realm.

This Platonic attitude is alive and well in physics today. We see it, for example, in the standard interpretation of general relativity, Einstein's theory of gravity. Here, Einstein attempts to reduce gravitational forces to the geometrical properties of empty space. When two bodies attract gravitationally, he says, they don't "really" move toward each other. Rather, they move along locally straight lines and it is the geometry of space -- the global curvature of locally straight lines -- which explains the "apparent" attractive force. Thus, the gravitational field, the physical medium by which gravitational influences are transmitted, disappears and is reduced to the purely geometric curvature of empty space.

A more general form of Platonic mysticism exists in the tendency of some physicists to reify the mathematical laws of nature. For example, some physicists believe that the laws existed prior to the creation of the physical universe in the so-called big bang. Nobel laureate Leon Lederman writes: "In the very beginning there was a void -- a curious form of vacuum -- a nothingness containing no space, no time, no matter, no light, no sound. Yet the laws of nature were in place, and this curious vacuum held potential." [2]

Stephen Hawking agrees about the priority of the mathematical laws, asking "What is it that breathes fire into the equations and makes a universe for them to describe?" [3] Or, as one contemporary philosopher of science describes the difference between natural law and mere fact, "Implicit in the concept of a natural law is the idea that the laws of nature govern the universe." [4, emphasis in orig.] Even the great Einstein concurs, writing that "Nature is the realization of the simplest conceivable mathematical ideas." [5]

This projection of the mathematical laws of nature into a higher or prior existence is an obvious expression of Platonism -- and a major source of the Primacy of Mathematics in contemporary physics. It is part of the reason why causal sequences involving the material world are scorned in favor of "elegant" mathematical formalism.


To be continued next month in part 3.

 

 

References:

[2] Leon Lederman, The God Particle, page 1.

[3] Hawking, A Brief History of Time, page 174.

[4] Lange, Natural Laws in Scientific Practice, pg. 49

[5] Quantum Questions, page 146

Copyright 2001 Travis Norsen/ Objective Science. All rights reserved. Permission granted to link to this article only; but, permission is not granted to republish it. 

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