Imagine a surface representing a function z with independent variables x and t.
(This is just a random image from Google to help out the visualization a little.)
The height of the function z(x, t) represents the amount of anxiety an economic actor feels over time, t, and the range of his available choices x. We assume that an economic actor will seek the lowest anxiety possible. Therefore:
Immediate natural inclination (of man) = – grad of Anxiety = -(dz/dt + dz/dx)
If an actor has no understanding of material cause and effect, like a newborn infant, then as they move forward through time they will choose (modifying the variable x) whichever path ahead of them has the most downward slope, even if this leads them to make a choice that will cause them a great deal of anxiety in the future (like the discomfort of sitting in a poop-filled diaper). This is because they are future-blind. But with experience and observation, we develop the ability to make predictions about the anxiety levels following certain decisions that are similar to previous decisions, and therefore make better decisions.
To make sense of this, we have to introduce another graph for “perceived future anxiety” which is more or less similar to the real graph of future anxiety, z(x, t), if a person is pretty good at predicting the future. It could be wildly different if they are bad at predicting the future, but much more often it is just more “fuzzy” as t increases. That is, a person will perceive many possible anxiety levels distributed along the z-axis, representing perceived possible outcomes for each choice of x (each with its own likelihood).
Okay, that was an awful lot of setup for this next one.
Expected anxiety for choice = Sum (or integral) of (outcome’s anxiety * outcome’s probability) for all conceivable outcomes
Time preference is a personality trait weighting decisions toward immediate gratification (reduction of anxiety. It should be visualized as a weight distribution. For each individual, it can be expressed as a function of “time distance from the present time”, or delta t. A person’s time preference can change over their lifetime, but it tends to stay the same.
(Corrected) natural inclination = – grad (Time preference * Expected anxiety)
The multiplication there is for two distributions. Think dot product. I can’t think of a better way to describe it right now.