Is Beauty Truth?—Part 2

I believe that the previous posting describes Stewart’s restrictive use of the word beauty. And how about his use of truth? The meaning of truth is where philosophers can really wax endlessly. But let’s narrow the field (according to Stewart) by considering truth to mean physical reality. The main aim of the physicist is to discover nature’s story, to seek nature’s truth. While the mathematician plays with abstract (not necessarily real) concepts, a physicist plays with nature’s rules and behavior—looking to discover the reality of how the world works. Nature holds the truth and the physicist is attempting to uncover her secrets.

When beauty and truth are described this way, I think I see the crux of Stewart’s argument, because as it turns out, the mathematician’s beauty has often been the same as nature’s truth. Time and again physicists, struggling to grasp a given physical reality, have come upon a rule or law (not their law, but nature’s) that previously was neatly expressed by a mathematician who was completely unconcerned with the physical world. The mathematician may have thought the rule was her theoretical and beautiful insight, but nature was already operating that way. Beauty becomes truth.

Another way to view this situation is to note that nature consistently prefers elegance. Time and again physicists have discovered that Mother Nature takes the simple path. When physicists are bumbling about and, say, are positing two different theories of how things might work, they’ve often gotten closer to reality by choosing the simpler one. I’ve written before of how Kepler’s three elegant laws of planetary motion (expressed by three simple—and beautiful—mathematical equations) came to be seen as having far more truth than Ptolemy’s contorted and confusing model of how the planets were supposed to move.

Ian Stewart’s main point is that symmetry can demonstrate to us the equivalence of mathematical beauty and physical truth. I won’t try to describe his definition of symmetry—it’s a little too esoteric for me to try and tackle here. In a general way, however, when something possesses symmetry, we find it has a pleasing quality—for it helps our mind to more easily and fluently grasp it. Symmetry literally helps to smooth our mental processing. Symmetrical things, it turns out, not only appear to us as true, but it’s also pretty much the way that nature works: being both symmetrical and true.

So nature—by definition “The Truth”—is at root beautiful. A giant of pure mathematics and physics, Paul Dirac, once put it, “A physical law must possess mathematical beauty.” Ian Stewart wraps up his book Why Beauty is Truth with, “In physics, beauty does not automatically ensure truth, but it helps. In mathematics, beauty must be true—because anything false is ugly.”

Over the last 2-3 decades I’ve been privileged to become increasingly absorbed in local nature, as I’ve watched the flora and fauna surrounding me. In the process I have come to consider nature as something to be revered. The local creatures and plants have been teaching me their truths as they have been showing me their beauty. The more I learn, the more I can comprehend that the story of nature, at root, is elegant. The totality of it, however, is beyond mere human comprehension. I am in awe of it; I’m overwhelmed by its beauty. Is that not something divine?