The Newtonian Mechanics of Motivation

My three year old son’s favourite thing to do is go on the swing in our garden. When I push him on the swing he always demands “go higher daddy!”. He yells this even when I have only just started pushing and he is impatient to get to full velocity! Of course I oblige, and I also take it as an opportunity to expose him to the concepts of velocity and acceleration. (He can learn the equations later). Sometimes I wonder how easy it is to make the same mistake of confusing position, velocity, and acceleration in other contexts.

When trying to achieve something — a project, a goal, or simply going faster on the swing — the rule of thumb I have developed is to be gentle on yourself at lower orders of motion and harsher at higher orders. Your current position is a function of the past. Your current velocity is also a function of the past. Neither can be changed directly. The only thing you can do in this moment is apply force. In applying force, as per Newton, you change the direction and/or magnitude of your acceleration. Over time, acceleration changes velocity and position.

The idea also applies to situations that may appear discouraging at first glance. You may be currently going in the wrong direction. Let’s say you are in the habit of eating a lot of sugar and want to eliminate sugar from your diet. You have the body that you have this second and there is nothing you can do to change it instantaneously. Rather, your sphere of influence is that of acceleration, meaning, as you read these words, time is passing when you are not (presumably) consuming more sugar, and this fact alone means the amount of kg/s of sugar being consumed is not increasing. The question is whether that force can be maintained over time.

If acceleration is the only thing that we have power over, then why bother with position and velocity? Sometimes it’s hard to tell if you have been applying the right force because acceleration is not easy to perceive. On the other hand, velocity is accumulated acceleration and position is accumulated velocity and they both seem to be easier to perceive. Whether that’s because the magnitudes are larger or just a fact of our evolved perception is unclear. Position is also what largely determines value in the world: a healthy body, an acquired skill, a supportive network.

So the tragedy and struggle of achieving is that the things we have power over (force/acceleration) are hard to perceive and hard to value while the things we have little power over (position/velocity) are much easier to perceive and value. The connection between the two is that, ultimately, being in a good position is a delayed outcome of acceleration. In this light, productivity is a reinforcement learning problem where the value function is the wisdom to know what forces to apply to our situation at any moment in time.