Probably, we can blame Galileo for the fascination with numbers as reality’s descriptors, but we can’t forget the Pythagoreans for playing an historically longer role in shaping our quest to find meaning in mathematics. Pythagoras and Galileo expressed what many of us think: Underneath ostensible chaos lies an order. Life makes sense because it rests on something describable. With mathematics, we can see Nature’s underlying order, or, at least, that’s what some of us believe thanks to centuries of indoctrination stemming from guys like Pythag and Gal.
But even in the so-called Golden Spiral exhibited by the chambers of a bisected nautilus, we really don’t find a precise order. Chambered nautiluses are organisms, and organisms are subject to chance even in biological or chemical development. That’s probably good news, because it means that there’s a bit of individuality built into the “system.”
Yet, there you are, looking in the mirror to find some mathematical symmetry in your face, standing at a ninety-degree angle in front of the mirror to see whether or not you match some ideal shape, or living by comparison to some unreachable ideal. Face your face; one half is a bit different from the other half, one eye a little more open than the other, one cheekbone a bit higher. But that’s okay.
No ideal is ideal. Everything, including the beautiful spiral chambers of the nautilus, is an approximation. You are an approximation; everyone is. Somehow, most of us have learned to find happiness in our asymmetry. Of course, for some, that means that we just acquiesce to our level of imperfection, that we yield to the mediocre, to the ordinary.
So, let’s say you want to attain perfection, want to have that perfect face or body, and that you work hard and spend lavishly to acquire some Golden Shape. Say you won’t compromise. At what level will you find happiness in your Golden Ideal? Will it be in five decimal places of accuracy? In ten decimal places or even eleven like the accuracy of quantum electrodynamics in describing the hydrogen atom? It really doesn’t matter how many decimal places of accuracy you have toward the ideal. They’re all approximations. Otherwise, they reach infinity, and, as we all know, you can’t be finite and infinite.
Find some reasonable level of approximation in your search for the Golden Ideal; resign yourself to that level as satisfactory for a finite being whose beauty, just like that of the spiraling chambers of the nautilus, is an approximation, a close one, but still an approximation.