Avidity Blog

Truth and Beauty

Beauty is truth, truth beauty, that is all
Ye know on earth, and all ye need to know.
John Keats's "Ode on a Grecian Urn"
Beauty itself is but the sensible image of the Infinite.
Francis Bacon
The search for differences or fundamental contrasts between the phenomena of organic and inorganic, of animate and inanimate things, has occupied many men’s minds, while the search for community of principles or essential similitudes has been pursued by few; and the contrasts are apt to loom too large, great though they may be.
D’arcy Thompson, from On Growth and Form

Scientists throughout the ages have wrestled with the concept of beauty. In physics and mathematics an ugly theorem or proof is looked upon with skepticism. I ran across a book review of Ian Stewart’s “Why Beauty is Truth: A History of Symmetry” written by Martin Gardener (Scientific American, April 2007). Stewart concludes that 1) "In physics, beauty does not automatically ensure truth, but it helps.”; and 2) “ In mathematics beauty must be true--because anything false is ugly." Gardener’s review is a good discussion and gives examples of beautiful proofs that are not true, and some ugly solutions that are.
The concept of symmetry as beauty in physics or mathematics requires a group-- a relationship of the elements to each other so that as the group is manipulated or rotated the relationship is maintained. Symmetry arises out of the connections and relationships of the group. Symmetry is beautiful, not because symmetry in itself is beautiful, but because it allows us to make sense—to see—the connections of the elements. Therefore, it is NOT symmetry that is beautiful, but that we see the connections or the underlying relationships that give rise to the symmetry.
In biology, the symmetry we see is a physical manifestation of the physical principles that give rise to the form. One needs only to look at the spirals of a cone shell, or the intricate patterns in an animal’s coat to see Beauty. D’arcy Thompson’s mathematical treatments of these forms give us a deeper appreciation, and a deeper sense of wonder-- as Bacon describes-“making sense of the Infinite.” Mandelbrot’s fractal, a repetition of a geometric pattern at different scales, really just extends the work started by Thomson. The insight from fractal’s that many of the forms (all?) we see in nature can be replicated by a repeated pattern at different scales really doesn’t inform much of the underlying principles.
Thompson’s reductionist approach “essential similitudes” that all biology may ultimately be explained by mathematics and physics, is something that Thompson acknowledges may not be adequate to explain the complexity of systems seen in biology. How can physics explain self-awareness? Stuart A. Kauffman, in his excellent book “Re-inventing the Sacred: A New View of Science, Reason, and Religion” , takes the reductionist approach head-on and offers an alternative view that is worth reading.
We see symmetry in biology, and this physical manifestation of the underlying principles is beautiful in that we are able to connect disparate organisms, and even see the similar patterns in inanimate objects, because the same principles are working to generate these patterns. But there is a deeper Beauty. My previous Blog talked about the awe that I felt at seeing the evolutionary connections between micro-organisms. There was no symmetry in the recognition of the relationship of convergent and divergent nucleotides. There is great Beauty in recognizing the connections—making sense of the Infinite. And there is great Truth in this Beauty.

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