# Thought and inertia

Relative to decision-making, I believe we can distinguish two ways in which the brain generates action. There is reflexive action that takes almost no time. This is the speed of light or thought reaction. There is reflective action that takes significantly more thought and time before action results. The extreme is when time stands still and the action seems to take forever. I use this to introduce the concept of inertia. Inertia is a measure that determines the mixture of these two types of actions. Zero inertia would be the speed of light and infinite inertia would be action that takes forever. The real world stands between these two extremes.

I also introduce the notion of inertial time. This is how time appears to slow down as decisions are made based on thoughtful reflection. Inertial time or reflection provides the possibility of social structures such as codes of conduct. These are strategies that are conserved and appear static or unchanging. Physical time becomes stationary for stationary flow behaviors, though this is not the same as static behavior. In electrical engineering the analogy is a constant current, which allows for the creation of magnetic fields, which for decisions I identify as payoffs. Static charges allow only electric fields and no wave propagation.

What then is inertia? I start with the idea that everything is described by its energy and momenta. It is a geometric structure called a tensor. The characteristics of this structure depend on what it describes. If it is meant to describe something with a property that allows one to see the world from a perspective at rest, then its properties will be characterized by the flow or rate of change to get to that perspective. At rest it will have a rest energy density and by the characteristics we can call stresses that indicate forces to move along specific strategic directions. Technically, these ideas are captured by the statement that the energy momentum is a second order tensor structure that has a time like eigenvector called flow and a positive scalar called the rest energy density.

Though common sense, these concepts are not part of the normal discourse about decision-making. With these concepts we can approach subjects such as entitlement and engagement. For example, we can view an artificial state of a world in which everyone is entitled, which is to say that everyone sees a payoff that is their own creation and is not impacted by decisions made by anyone else. This is possible only if they are totally disengaged from everyone; their own actions and actions by others have no consequences. I say this is an artificial state to the extent that their entitled payoffs lead to no consequences. If there are severe consequences, either positive or negative, then the theory and common sense suggest that a player becomes engaged. As they become engaged, again theory and common sense suggest that their notion of the payoffs will also change. As part of these changes I expect that the energy density will be stronger in some strategic areas than others and hence inertial behaviors will drive what will become the stable collective behaviors of players as they become engaged and whose behavior ceases to be totally entitled.

In many ways this discussion can be carried on without recourse to theory, just to common sense. Where theory comes in is its ability to deal simultaneously with many different mechanisms that are each plausible but mutually interactive. This is as true for this discussion as it is for industrial systems. Our ability to understand deeply is usually limited to essentially linear effects that extend over some small domain. We have difficulty viewing how many mutually interacting linear effects result in non-linear composite behavior. The theory provides the machinery for such visualizations. I have carried out a number of numerical calculations to illustrate this, and a specific example for inertia can be found in The Dynamics of Decision Processes, figure 8-21 to figure 8-24 of section 8.7.1.