Zero to Fourier…
One thing I know I've wanted to do is write a very concise exposition that goes from zero to Fourier in as few lines as possible. This could be very useful in conversations with others, and would, I hope, help me separate the gluten from the chaff.
A) Here is a simple image that tells a useful story.
1) Think of people or other conscious agents as bubbles floating together in the air. Their experience of others and of any activity outside those bubbles is mediated entirely by the effects of those activities on the surface of their bubbles -- deformations, impingements, vibrations, what have you. Our mental and physical experiences intrinsically involve those impingements -- our actions/reactions begin with them. Mentation is about de-scribing ("unwriting") and ex-plaining ("reflattening") differences from sphericality of the bubble surface. Our minds are only aware of the world through these dings, dents, and deformations and through our efforts to undo them.
2) So the surface of such a bubble is a sort of 3D graph, and our job as conscious agents is to deconstruct that graph into salient components and thus develop a mental map of the world of activity happening around us so that we can undo the perturbations to the bubble, since that's our only way to perceive what's outside of ourselves. Smoothness good, perturbations bad. Or Survival of the smoothest. Perception is deeply tied to self-regulation and self-preservation. Our idea of truth, I daresay, will involve the components that do the best job for us in this regard.
3) Those of a certain mathematical or computational background might hear "deconstruct a graph" and immediately think of Fourier analysis or maybe wavelets. Briefly, these are techniques by which simple off-the-shelf objects are employed to reproduce (and, equivalently, undo) graphs of unknown origin -- sine waves in the former case and little Gaussian curves in the latter. I'll give a fake version of the Fourier process that's close enough for my purposes. Start with a very squiggly graph. Find a sine wave that maximally matches it (by minimizing the integral of their difference). That first sine wave is the fundamental part of our "de-scription." Subtract the sine wave from the graph, and we have new second-order graph that still needs decomposing but is starting in the direction of looking like a flat line. Again find an optimal sine wave (generally of higher frequency and smaller amplitude), and repeat the process until the resulting graph is as close to a flat line as you choose. My proposition is that something analogous to this process is what mentation is about. Let that sink in.
4) The good news is that this subtraction process is almost bound to work in the long run no matter what off the shelf objects are employed. Unfortunately that's also the bad news. From the standpoint of one who wants there to be true descriptions and explanations, I'm afraid you're out of luck. There may be efficiencies and optimization but no one-way to skin a kumquat. All explanations are Ptolemaic.
B) Suppose I say "All explanations are Ptolemaic." When the unsuspecting person I'm talking to says, "What the hell does that mean?" I can say:
[In this phony historical sketch,] Ptolemy was a 2nd century Alexandrian astronomer who produced very accurate tables of the positions of heavenly bodies that were the standard in astronomy for over 1000 years. What's interesting is how he arrived at the calculations. He believed along with everyone else that the Earth was the center of the universe and that the motion of the heavens could be accounted for by the motions of rotating Earth-centered spheres containing those bodies -- separate spheres for the Moon, Sun, each planet, and one for all of the "fixed" stars. If the sphere for Mars behaved in the simplest way, when Mars was viewed every midnight, it's position in the sky would be the same (if synchronized with the motion of the Sun) or moved by some fixed distance every day. Mars, in fact, usually seems to be moving in this very regular way, but at times the "constant" nightly shift in the sky grows or shrinks; in fact it sometimes changes direction -- so-called retrograde motion. Dedicated as he was to his model of circular motion, Ptolemy patched his theory to account for this discrepancy with things called deferents and epicycles. The epicycles are smaller circular paths tacked onto the original circular paths -- making Spirograph like motions possible. Even the epicycles can have their own epicycles. If one is careful and ingenious enough, one can come up with epicycles that mimic any possible observed motion without abandoning the primacy of circles. In modern parlance we can say that in the face of the failure of the circular motion argument, Ptolemy kept doubling down on the circle explanation until it worked.
[Short version: Repeated and careful use of one tool will eventually get the job done -- maybe better to have a Swiss Army knife than a stick, but in the end it doesn't matter]
This is what I mean by "All explanations are Ptolemaic." Choose a point of view and find a way to double down on it until it works. This is the way of human knowledge. Copernicus's heliocentrism and Kepler's ellipses may simplify the calculations, but Ptolemy can legitimately stick to his geocentrism; it gives equally good answers. Let Occam's parsimony be damned. We too can generally stick to our guns without ultimate contradiction -- despite the scorn of others. I'm not suggesting that people are easily fooled into accepting geocentrism when the correct heliocentrism is available. In my view, heliocentrism (or any supposedly superior or correct explanation) is just another Ptolemaic explanation -- even if we can't immediately see the epicycles. The world isn't "made" to be explained. BUT humans are totally committed to explanation and narrative over observations, facts, and measurements. A little perspective, a little humility, is called for, I think when we purport to possess knowledge -- especially knowledge that involves a correct explanation. You can say "I know how to build a functioning radio" but you can't say "and that's the only way that works."
In a Ptolemaic world, where everyone is equally trapped by their own sledgehammer metaphors and all the resultant worldviews have equal (and scant) ontological legitimacy, what is the basis for real criticism and disagreement between worldviews? I don't know. Here's something that definitely doesn't form such a basis: "My way of looking at things is right because it is based on and thus leads to real knowledge about the world, and yours doesn't.'' That is, there is no real knowledge, only different versions of knowledge based on different worldviews. I'm leaving aside for now disagreements about objective facts -- Hillary Clinton either has or hasn't run a child cannibalism ring out of a DC pizza parlor, for instance.
C) How about "My explanation enables me to build fantastic technologies and save lives, and yours doesn't.'' Not bad. "My version of events gives every child an equal chance at success and happiness, and yours doesn't." Thus, maybe we can disagree based on our goals and the metaphors best suited to achieving those goals. So legitimate disagreements are about different goals or hoped for outcomes. This sounds like moral reasoning based on moral assumptions. About preferred social conditions -- more or less technological convenience, more or less social justice. Am I arguing in a way that all "philosophical" disagreement is "moral" disagreement? Maybe. I'll have to think about it some more. Ptolemy's approach was moral or at least religious or esthetic. Circles are perfect, God is perfect, so God makes circles.
D) Here's something simmering underneath this. As a rather politically liberal fellow, I'd very much like to dismiss crazy conservatives as simply "wrong" (and there is room for them to be factually wrong about Jewish space lasers, the real motivations behind the Civil War, etc.), but maybe I have to settle for dismissing them as differing with me about preferred outcomes. That is, they are assholes not idiots. Elsewhere, in discussing the bubble-beacon meta-model of reality, I tried to argue that all systems (human and otherwise) are selfish. They only differ in which of various selves get emphasized through differing identification (which is itself mostly automatic and unconscious). Altruistic sorts identify more strongly with the humanity bubble or living things bubble of which they are sub-bubbles, while those on the icky right identify more closely with the individual bubble, the tribal bubble, the racial bubble, etc.
E) I also have been thinking about mathematical attraction. How it's a kind of magic bullet that gives insight into wholeness without any mystical mumbo jumbo. I should write about it -- especially the part where the simple mathematics of it hooks up to real life: the passage of time, the evolution of systems. Feedback and recursion, powerful though they are, just don't fit easily into the human preference for linear narrative.
F) Yes and --ape mind. How strange that we could possibly have the illusion that our ideas stand in relation to reality as anything other than very circumscribed noodlings. If you won't tend to give much credence to opinions expressed by clever apes, there are certainly at least theoretical creatures as far above us as we are above apes who wouldn't put much stock in our impassioned expressions of truth. One seeming implication of this observation that I hate is the notion that, if we were smart enough (like Martians maybe) we really would understand, but the deficit is not totally an intelligence deficit; it's an ontological deficit. The universe does not ultimately admit of the sort of knowledge we like to say we have. Hammering out dents in our bubbles is ill-suited to transcendent understanding.