Thursday, November 3, 2022

Non-Euclidean Science

Maybe I should call it non-Aristotelean, or non-Platonic, but the exact name isn't the point. Euclid built geometry up from postulates; Aristotle explained motion as objects returning to their natural state; Plato portrayed experience as the shadow play of forms in an ideal realm. In each case, a complex field of phenomena is explained as the outgrowth of some simple essential foundation. Perhaps I should call my proposal non-foundational science. But I am not proposing any kind of freed-floating science. I am proposing a science that is founded on reality, on the vast tangled web of lived experience. Science is an extract, like resin extracted from the sap of a tree. There is a lot more to a tree than such resin. The tree itself is embedded in soil and climate, in an ecological web, flying pollinators and mycorrhizal fungi. The simple essence emerges from the whole, rather than the whole emerging from the simple essence.

Science as a quest for an inner key that explains everything - such science takes us on a quest into ever more remote realms. It distances us from experiencing what is right at hand. Of course, building and launching the James Webb infrared telescope surely involved considerable attention to experiences right at hand - precision torquing of many bolts, etc. Galaxies and quarks are not objects of direct experience, but neither are they disconnected from direct experience. What I am proposing is no neglect of any corner of the world. I am suggesting a shift in how we understand the way all the bits and pieces fit together.

Non-Euclidean geometry provides an excellent analogy. The surface of a sphere, such as the surface of the earth, is a perfect concrete instance. Euclidean geometry is plane geometry, the geometry of a flat surface. At the scale of a few square miles, the earth is extremely close to a flat surface, and can be mapped onto a flat sheet of paper with great precision. But as the area to be mapped increases to include a significant fraction of the earth's surface, inevitably distortions arise. There is no perfect flat map of the earth.

The impossibility of perfection does not mean that we just give up and produce fantastic maps that have lost any connection with the lived experience of moving around on the earth. The value of a map is exactly in how it relates to such lived experience. Whether a map is good or not, that depends on how the map is to be used. A map that is good for navigation will typically not be a good map for estimating agricultural productivity.

Pure science is science that neglects its relationship to its use. Applied science is science that orients itself to its use. The classical scientific attitude is that applied science grows out of pure science. I am proposing that a healthier approach to science is to see pure science growing out of applied science. Applied science connects to the vast complexity of lived experience. Refining our ideas requires chopping out local regions to be precisely mapped. This always involves distortion and omission: the inevitable price of precision. It's like taking a photograph: a fast shutter speed can reduce blurring from movement, but requires opening the aperture which increases blurring from less depth of field.

Our scientific quest for ultimate theories is like the old searches for the alchemical philosopher's stone or the healer's panacea, a medicine to cure all diseases. Good science requires following the clues wherever they lead, but it also requires a perspective on the actual situation so that one doesn't chase clues just for the sake of the chasing. Good science is science that is engaged with the lived reality of an actual situation.