This is the first post of a series on what I’ve been calling “moral physics”—a theory of morality and human nature which will borrow heavily from theories in physics.

A bit of context. I find the process of thinking to be quite a lot like working on a jigsaw puzzle: we do not immediately know the end state of our thinking (there’s no box with an image on it); instead we have in our minds fragments of many thought patterns, like puzzle pieces, which, in trying to form an argument or follow the thread of an idea, we fit a few of together, tentatively. If they snap into place the pieces will remain attached, and the combined piece can then act as a single element in larger thought-patterns; if not we dismantle the thought, forget it, and try another. Much of the labor of thinking, then, consist of the sorting of ideas into clusters, just as we would start a puzzle by sorting the pieces by color or pattern. It is ideas which are especially concrete—like math, logic, and physics—which play the role of “edge pieces”, serving as a stable scaffold to which other ideas may be attached. Much of the intellectual development in history has, in this way, grown inward from the math and physics of its time.

I will begin, therefore, with some physics. The presentation will be high-level and informal, but explicit. Everything here can be made technically precise.



Fairly generically, a physical system evolving in time can be described by an energy function, which I’ll denote by for simplicity. The energy function can in turn be divided into two kinds of “terms”:

  • kinetic energy terms, written , which represents “inertial” motion: an object in motion remains in motion; one at rest remains at rest.
  • potential energy terms, written , which describe “interactions” among the constituents of the system, or with the external world.

Given full knowledge of the energy function, and all the definitions going into it, you can more-or-less predict the entire dynamical evolution of a system.

Imagine, say, a system of billiard balls rolling around on a level surface and bouncing into each other.

The dynamics would consist of the inertial motion of each of the rolling balls, each described by a term alone, plus a term for each pairwise collision. The overall energy function is:

The kinetic terms have nothing to do with each other, and we can just as easily combine them into a single term:

Likewise we can merge all of the collisions into a single term:

The full energy function is then:

It now looks we have a single object whose inertia is described by experiencing a single potential . But the dynamics will be exactly the same as under the original energy function.



If instead the surface was uneven or sloped surface, then we’d have to account for the surface with a second potential term, an interaction between the balls and the surface:

A full solution for the trajectory of the balls would have to incorporate both effects, as well as the interplay of the two: perhaps a ball rolls, then collides and changes course; now it is rolling in a new direction and will experience the effects of the surface differently than if it hadn’t collided.

But there is nothing about the rolling on the hills and valleys of a “surface” that truly distinguishes it from “inertial motion”. We can freely consider consider as a single inertial term which representing “rolling on an uneven surface”:

Assuming perfect mathematical accuracy, the dynamics given by this rewritten energy function will be exactly the same as when we treated the surface as an interaction. The math cannot tell what is “inertia” and what is an “interaction”—everything in the sum going into is treated equivalently. What distinguishes inertia and interactions is, first, the kinds of formulas that usually appear—inertial terms are those which produce motion we would call “inertia”, after all—and second and more fundamentally that inertial terms tend to be very general, applying to the same object in many different situations, whether realized or only hypothetical or counterfactuals, and also to many types of objects, whereas potentials tend to be distinct to a particular problem.

(The basic gesture of Einstein’s theory of gravity is exactly the one here: treating gravity not as an interaction but as inertial motion on a curved surface.)



Let us now imagine launching our bunch of billiard balls into space or something. It will be easier to imagine if we take away the surface and attach the balls together with strings or springs instead, so we can visualize them flying as a group:

The energy function is:

Another way of writing this is to separate out the “overall” motion of the cluster—the motion of its center of mass, which travels in a straight line—from the “internal” or “relative” motion of the individual balls:

The second term must also contain all the information about how this object would react to a collision with some external object, like a wall, as the result of such a collision sould depend on the internal state. The ball closest to the wall will hit first, and if the springs are compressed, it the cluster as a whole might be launched away sharply, whereas if the springs are extended when it hits it might bounce away lightly, or it could even conceivably to a stop, sticking to the wall.

Here we have a model of elasticity. For the purposes of describing the motion of the cluster, we can forget about the internal motions and springs entirely and simply describe the elastic behavior of the ball in any interaction it might experience:

And actually, our billiard balls are the same idea: they are composed of a huge number of atoms linked by atomic bonds, which we ignore when we conceive of a single ball with a singular inertia and some small elasticity. This conception is only an approximation, but it will be a good one up until the point where we need to deal with the squishiness of the ball very precisely, or until we hit one so hard it blows up.



Interestingly, if our cluster of balls-and-springs went through multiple collisions in a row, the latter collisions’ effect, which depend on the precise internal state of the cluster, must therefore depend also on the results of the earlier collisions. This cluster of balls, viewed as a whole, turns out to possess a rudimentary “memory”—how it interacts depends on what has happened in its past. We can therefore write the energy function in a different way:

Here is a new kind of term which has taken the place of the two terms in our original expression. It is not exactly equal to these; instead the term is found by first working out the internal motion for a generic overall motion, and then reinserting that solution into . The resulting term will look kind of like an inertial term, but it will depend on the entire history up to the point in time it describes. (Not a very inertial behavior, if you ask me.)



Earlier we merged an interaction term into to get a single inertial term which describes “inertial motion on a surface”. The math had no objection: it can’t truly tell one term in a sum apart from the others.

Why not go further? There is nothing to stop us from viewing even inter-ball interactions like or part of the inertial term, too:

An “inertial” solution to this problem will be exactly equivalent to a full solution of the original problem. Arguably this is all it means to come up with a “solution” for some scenario of physics: working out the new inertial motion in the presence of some interactions. In this view all physics ultimately reduces to straight-line, inertial motion—the entire universe is evolving forward in the only way it can.

Yet this is too reductive. Not all motion is inertial, not for any useful definition of the word “inertial”. The universe really is composed of “distinct things” interacting with each other, so long as we define a “distinct thing” appropriately.

What makes an object like a ball a “distinct thing”, then, in spite of its being composed of innumerable atoms? So long as the ball remains in-tact, the motions of its atoms will be extremely closely-correlated with each other. I can basically describe the location of any atom in a ball to great precision just by its location and orientation, and this description will continue to work so long as the ball is not put under so much pressure it collapses or explodes. This mental or mathematical operation, by which we reduce a whole ball to its center-of-mass inertial motion, therefore will discard only a minimal amount of predictive power about the trajectories of its atoms, while discarding nearly all of the fine-grained information about the atoms. If we can do this without losing much, it’s a distinct object. (This is essentially an argument from information theory.)

Note the notion of “distinct thing” we get here is not universal, but is relative to a choice of time-scale, length-scale, and conditions. This is fine: we don’t feel it necessary to consider each billiard ball when describing the motion of the earth, or each bacterium on our own skin, nor is it useful to imagine what would happen to a billiard ball after being shot into the sun. As human beings, we are mostly concerned with things on the scales of our own lives.

We could give an alternative definition in terms of the “memory” phenomena just discussed. Any old cluster of atoms would exhibit a little memory, but a stable and self-contained system will tend to smooth out the effect of external reactions rapidly and completely, relative to its own inertia and the strength of its interactions with the world. (Biological or computer systems represent an exception to this: their memory effects are disproportionately strong for how self-contained they are, as their internal dynamics have been fine-tuned to be extremely stable.)

The point here has only been to sure up the description of physics in terms of which we started out with. Despite the mathematical equivalence which allows us to merge and terms into a single inertial term, there are other senses in which these description really are inequivalent, and the unmerged description is actually the real one. I mention this to counter the tendency of the human mind, when acquainted with mathematics, to overeagerly interpret mathematical properties to be “truth”—here the associativity of the sum . If we can so easily think of a joint system as a single system evolving interitally, we should also remember the way back home, to the mindset where two balls are genuinely separate objects, and where their collision represents a genuine interaction—a point of contact with something other than themselves.

I have been careful to limit the present discussion to “inertial” motion, and have said nothing of “determinism”. All our descriptions—any combinations of , , etc.—are deterministic, and the arguments against collapsing everything into inertial motion do not apply for determinism. Yet it is my instinct that most people’s uneasiness about determinism does not really make a distinction between the two, determinism and inertia, and winds up assigning to a deterministic universe more of an inertial character than is really appropriate. But the universe is not purely inertial; interactions genuinely exist; memory exists; distinctness is real; everything is not one thing—to believe it is is to take the mathematics much too literally.



In practice, problems of physics are attacked by employing specific and judicious redescriptions. For the intearctions in a gas, we might divide the potential into an “average” component which represents the background contribution of all the other gas particles, and a much smaller component representing the collisions:

Under typical conditions, collisions are rare, and we might try ignoring the collisions term entirely. The “ideal” in “Ideal Gas Law” refers exactly to this idealization.



This freedom in how we represent physical systems also leads to the correct sense of “wave-particle duality”, a concept which is otherwise quite mystifying. Consider the atoms in a crystal:

Each atom can vibrate in place. As it does so, it will transmit forces through its bonds with its neighbors, causing them to vibrate also; vibrations therefore propagate through the crystal. A travelling vibration is a “sound wave”, and these sound waves can only be created or destroyed in discrete units. These units are their associated “particle”, which is called a “phonon”. (Phonons are somewhat easier to think about than “photons” of light.)

Such a crystal can be described by an energy function in three equivalent ways.

  • The first describes the positions of each atom in terms of their own inertias , and interactions like between neighbors.
  • The second describes the propagation of sound waves of different frequencies by a different set of terms like , whose interactions do not involve neighbors at all.
  • The third describes the same waves but in terms of the number of particles with that particular frequency. Its terms do not even look explicitly like “kinetic” or “potential” terms, so I’ll just write them like .

All three descriptions are correct; each describes the same full system. But they make different “distinctions”—treating different parts of the system as the “natural” subdivision.

The first treats atoms as distinct, and is most natural if you want to measure or predict the position of individual atoms, or perhaps to add or remove atoms. This model will continue to work well even if the crystal explodes—atoms are atoms, after all.

The second treats waves as distinct, and is a good description of how sound waves propagate through the crystal. This view is applicable so long as the wavelengths are longer than the spacing of the atoms, but not as large as the crystal itself.

The third description is best for describing how energy will exchange with the external world—one phonon at a time. This view, like the second, is applicable mainly to an intermediate range of wavelengths, but the phonon description alone gives the correct thermodynamic behavior of the crystal (which is how phonons were discovered).

A great deal of physics, it turns out, can be described by models like this one: some underlying medium or “field” in which waves can propagate, along with a set of interactions between the particles of those waves.

(The Standard Model of particle physics has essentially this form, except that it features a whole zoo of distinct particles interacting with one another.)



What I have tried to convey here is the proper sense of physics, and of a universe modeled by physics. The informal equations help to make precise what can otherwise be vague and disorganized.

The next step is to apply this framework to human nature.

Our first task will be to work out a good description of a human being in terms like those employed here, and to try to find a place for the thing called “free will” along the way.

Our next task will be to consider the nature of human collectives; the model of wave-particle duality in a crystal will be a useful reference.

Our eventual aim will be to describe where “morality” arises clearly, and to see what kind of thing it is, without having to imagine it as apart from the determinism of the universe; my belief is the apparent incompatability of the two will turn out to be a tremendous misunderstanding (of physics, mainly).