Friday, August 15, 2014

Delta Calculus

I'm thinking Calculus is too generic a name for the Newton-Leibniz thing, takes up a good word for what I'll call Delta Calculus, as opposed to say Lambda Calculus (different greek letter).

People make fun of Newtonian mechanics for being "mechanistic" (duh) meaning "clock-like" which is where delta calculus hails from:  the world of gear-works and their ratios.  How quickly does this gear turn relative to that one?  dy/dx comes from there.  You're trying to reverse engineer nature by modeling her as a clock-works.  Sure it's primitive, but it actually works pretty well when it comes to planetary orbits and what not, even if we admit to chaotic elements.

The figure below, singled out by Glenn Stockton from the many images flying through his workspace, provides a fine summary of rotational motions "in principle" i.e. what you'd expect just thinking about it, in a somewhat Kantian sense (synthetically a priori in other words):

You've got the magnetic field thing going, as a kind of involution / evolution of toroidal (donut) shape, then the revolving and orbital-precessional.  The solar system "corkscrews" whereas in profile it's sinusoidal, which means sine waves.  We should talk about sine waves more, and their oscilloscope values.  Trigonometry remains such a key, don't let e to an imaginary power divert your attention from the underlying rotational phenomenon.

The rate of change at which something changes gets us back to that "trim tab" idea of the butterfly effect.  Butterflies do not in fact cause climate change individually, yet are a part of the climate collectively, and deltas in butterfly cultures may indeed serve as canary-in-mineshaft warnings or positive omens, of big wheels turning in a helpful or harmful direction (you need a model to figure out about preferences, and a value system).