Anti-Jump Redux

What exactly is my anti-jump-muscles imagery meant to suggest? Well, I've often preferred to let it stand by itself so that it could embrace almost any sort of alternative interpretation, but there is a particular idea that it originally grew from: assumption switching.

I've always been fascinated by Euclid's geometry. In particular, I loved the sort of mathematical dream that stands behind it: If we can identify a set of truly fundamental facts that absolutely compel acceptance, then we can apply rigorous logic to them and build up an edifice of theorems of increasing complexity that could, in theory, eventually encompass all true statements. What a wonderful world that would be.

Now, there are many ways in which this dream can collapse. 1) It might not be possible to develop a good enough set of axioms to actually get anywhere; 2) No matter how excellent our axioms, there might still be some important truths that would evade proof (incompleteness); etc.

But these possible pitfalls are no reason to abandon the task of axiomization and proof. Euclid did it! We might not be able to achieve for morality or politics or even auto-mechanics what Euclid was able to do for geometry, but surely the hard sciences — physics, chemistry, et al. — would benefit from such a program. It's kind of sad to me that nothing like this has ever really gotten off the ground (as far as I know -- and I don't know anything). In fact, (as far as I know) the only example of full axiomization outside of geometry is that carried out for set theory in the late 19th and early 20th centuries as a reaction to certain crises in the foundations of mathematics.

My belief is that Newton had a program of Euclid-like axiomization in mind when he set down his laws of motion. Fundamental laws of physics, in this view, aren't the equivalent of theorems as one might suspect — they are undeniable truths or axioms with which one tries to "prove" the observable facts of the world. That is, we show that, given such-and-such set of laws, the observed facts could not have been otherwise. It can work either way. We can use the laws to churn out predictions which can be tested by experiment, or we can take an observation outside our current knowledge and see if logic can bridge the gap between the laws and the observation. Failure doesn't necessarily show that the laws are wrong — the problem might be with either the observation or the logic. Nor does success prove that the axioms are the right ones.

In mathematics, the axioms are ostensibly the easy part. The crowning achievement for the mathematician is the proof, the theorem. Oddly, it's the other way around for scientific theorists. Their crowning achievements are the axioms, the laws or explanatory principles. To them the observations are the grunt work, and the actual explanations of the observations from the laws, although challenging and creative, are mostly just a matter of grinding it out.

Okay, before I try to hook this back up to anti-jump muscles, I need to develop the idea of assumption switching. The dream of Euclidean certainty in mathematics survived through Newton's era, but in the early 19th century that certainty began to show serious cracks. I'll give a brief exposition (which has been done much better elsewhere). One of Euclid's postulates was that, given a line and a point not on that line, there is exactly one other line in the same plane through the point that will not intersect the line — a line parallel to the original line. Get it? There's exactly one line through a given point parallel to a given line. This postulate seemed to many geometers through the ages to be less self-evident than the other postulates, and extraordinary efforts were made to try to do without it. That is, these geometers tried to derive the parallel postulate from the others. We now know — it's been proved — that such a proof is impossible. The truth of the parallel postulate is independent of the others. But that doesn't mean that the parallel postulate is justified. Some adventurous mathematicians tried to see what geometry would look like if the parallel postulate were actually false — if there were 1) no parallel lines or 2) more than one. In both cases, perfectly valid theorems were produced. In the first case, it produced the geometry of the surface of a sphere, and in the second the geometry of a hyperbolic surface. BTW, there is still some question which of these three geometries is the true geometry of the natural world — whatever that means — and therefore the most fundamental version of geometry.

Anyway, the point is that there turned out to be nothing ultimate about Euclid's postulates. This fact sets up the assumption-switching paradigm. Take a basic "truth," and see what happens when you defiantly and deliberately negate it in some way. Assumption switching like this has been my inspiration, and I keep trying to apply it any- and everywhere.

The most familiar of all the axioms of classical physics may well be Newton's first law of motion: an object in motion (or at rest) will remain in that same constant rate of motion unless it's acted on by an outside force. It says that simple continuance of motion is the default state. In our post-Newtonian world, we have internalized this idea and find it almost obvious, but, in Newton's time, this was not at all clear. Everywhere observers saw projectiles arcing through the air but then coming back to earth. They saw balls rolling to a stop, clocks winding down, people growing old and dying. Even when objects like the Moon do stay in motion, their motion isn't constant and linear but curving and accelerating. So Newton was saying that none of the observed world fit in with the natural condition! He conceived and formalized the idea of force (what an amazing job of abstraction that is!) as something capable of accelerating or changing things from their natural condition of changelessness. Frictional force acted on objects to slow them down, and gravitational force acted on objects to alter their paths from the linear and constant to the curving and accelerating. His idea, in other words, was that the default state of motion (or motionlessness) is other than that which he ever actually found in nature. Bold! Might it be valid to develop an alternative to Newtonian physics based on some negation of Newton's first law? I have every confidence that this heretical position is tenable, but I'm not the person for the job. I take my lack of scientific credentials seriously! Some folks might wish I did the same for my lack of philosophical credentials.

I have, however, taken the liberty of generalizing the law of inertia (as it's called). Here is the Generalized Law of Inertia: Nothing changes unless it is caused to do so. Physical cause is taken here as akin to force in Newton's version. Living in a post-Newtonian world, it's hard not to believe this. It's kind of like the definition of causation, for Pete's sake. But it isn't what we actually observe either. Everywhere things are happening kind of inevitably and on their own — aging, evolution, growth, decay (both biological and subatomic), catastrophic extinction, not to mention friction, entropy, and gravity. And many things only stay the same through forces -- hurricanes, people, etc.

It is this generalized law of inertia which I've most often tried to flip — with varying degrees of success. There are many such flipped versions. Heraclitus was an early adopter of one such interpretation: All is change. That is, spontaneous change is the natural condition or default state.

My favorite switched version is close to that of Heraclitus: Everything is trying to happen at once but failing mostly. This of course is not what we see in the world around us (any more or any less than we see objects in constant motion.) Things do sometimes happen (!), but when they do, they seem to happen in a tempered and sequential fashion (explosions aside, I guess). Chairs don't spontaneous morph or disappear. Events tend to wait their turn. By choosing something rare or counterintuitive as the default state, it sets up something else as the primary "agent" — in the case of the Heraclitean axiom, something that controls, reins in, or undoes change.

If this switched assumption has any merit, something must be taking the place of force as the reason everything isn't happening at once. Yes, and if this idea has any merit, that reason is... cancellation! If a ball wants to accelerate to the speed of light, but wants to do so equally in every possible direction, all of these impulses cancel each other out. If this same ball has an impetus to spontaneously disintegrate or morph into a model of the Eiffel Tower, these impetuses must also be mostly countered by some or many impetuses in the opposite direction. (What's the opposite of the Eiffel Tower?) The world is mostly held in an exquisite balance of multitudinous and contradictory tendencies all trying to express themselves. The things that do happen are those that have what I call special status. Something in the symmetry of opposing "forces" has been broken, and the event leaks out of the boundless but frustrated fecundity of nature. The anti-jump muscles somehow relax and we take flight. Picture a circle of 100 fans blowing inward on a beachball in the center of a circular pool. There will be little movement beyond random fluctuations due to turbulance, since all forces on the ball are balanced. But turn off one of the fans (with special status) and ball moves slowly toward it. Either the turned-off fan is having an influence or the fan directly opposite is. Which would you say?

There's something further I want to mention about some forms of cancellation that helps create the world as we know it. Cancellation doesn't mean annihilation. Two waves, for example, can cancel locally and augment each other elsewhere.

And there it is! That's why I find the flippedness of the antijump muscle image appealing.

My essay called Future Influence includes a longish discussion of cancellation-with-special-asymmetries as a major "force" of nature. I put quotes around force because it ain't your grandfather's kind of force.

Let me relate this back to another of the cornerstones of my philosophical system (he says pretentiously) — the World of Describers vs. Be Like Me. From the yin POV, the fundamental activity of conscious agents is to cancel out incoming influence to maintain stability and identity, but beyond the region of cancellation, these efforts actually add to the chatter of the world. These "forces of cancellation" are the counterparts of the "forces of change" that emerge from the yang perspective.