Fitness

Getting Fit!

The idea of fitness in any complex system is not necessarily a fixed point. There can be many different kinds of fitness, and we need to examine each specific system to determine what factors are at play. For example, what makes a hotel room 'fit'? Is it location, or price, or cleanliness, or amenities, or all of the above? For different people, these various factors or parameters have different 'weights'. For a backpacker traveling through Europe, maybe the price is the only thing worth worrying about, whereas for a wealthy business person it may not factor in at all.

Despite these variations, there are certain principles that remain somewhat consistent, and this pertains to the idea of minimizing processes. We can imagine that certain behaviors in a system require more or less energy to perform. Agents in a system are always trying to minimize an energy expenditure, but what might entail a high energy expenditure for one agent might be a low energy expenditure for another (depending on what forms of energy they each have available to them. If an ant wants to find food, it prefers to find a source that takes less time to get to than one that is further away. Further, a bigger source of food is better than a smaller source of food, as more ants in the colony can benefit. Complex systems generally gravitate towards regimes that therefore in some way minimize energy expenditure to achieve a particular goal. However, this energy rationing depends both on the nature of the goal, and the resources available to reach it.

Example:

Returning to the example of finding a hotel room, consider the popular website 'Airbnb' as a complex adaptive system. Here, two sets of bottom-up agents (room providers and room seekers) coordinate their actions in order for useful room occupancy patterns to emerge. Some of these patterns might be unexpected. For example, a particular district in Paris might emerge as a very popular neighborhood for travelers to stay in, even though it is not in the center of the city. Perhaps it is just at a 'sweet-spot' in terms of price, amenities, and access to transport to the center. This is an example of an emergent phenomena that might not be predictable but nonetheless emerges over the course of time. In that case, rooms in that district might be more 'fit' than in another, because the factors listed (its relevant parameter settings in that particular zone) are highly appealing to a broad swath of room-seekers.

So in what way is the above example 'energy minimizing'? We can think of the room seekers as having different packages of energy rations they are willing to expend over the course of their holiday. One package might hold money, one might hold time, and one might hold patience for dealing with irritations (noisy neighbors that keep them from sleeping, or willingness to tolerate a dirty bathroom...). Each agent in the system is trying to manage these packets of energy in the most effective way possible to minimize discomfort and maximize holiday pleasure. So if a room is close to the center of the city, it might preserve time energy, but this needs to be balanced with preserving money energy.

We can begin to see that fitness is not going to come in a 'one size fits all' form. Some agents will have more energy resources available to spend on time, and others will have more energy resources to allocate in the form of money. Further, an agent in the system might be willing to spend much more money if it results in much more time being saved, or vice versa. We can imagine that an agent might reach a decision point where two equally viable trajectories are placed in front of them. The choice of time or money might be likened to a flipping of a coin, but the resulting 'fit' regime might appear as very different.

In order to better understand these dynamics, two features of CAS, that of a Fitness Landscape and ideas surrounding Bifurcations, clarify how CAS can unfold in multiple fit trajectories, but despite these differences the underlying principles of energy minimizing holds true.

Avoiding Work and the Prisoner's Dilemma

In the above example the agents (room seekers), employ cognitive decision-making processes to determine what a 'fit' regime is. But physical systems will all naturally gravitate to these energy minimizing regimes.

Example: 

When molecules in a soap bubble solution are subject to being blown through a soap wand, nobody tells them to form a bubble, and the molecules themselves don't consider this outcome. Instead, the bubble is the soap mixture's solution to the problem of finding a form that minimizes surface area and therefore frictions. The soap bubble can therefore be considered as an energy minimizing emergent phenomena  (for a detailed explanination, follow this link to an article on the subject: note the phrase, 'a bubble's surface will minimize until the force of the air pressures within is equal to the 'pull' of the soap film'). We can also think of a sphere as being the natural Attractor States of a soap solution: seeking to absorb maximum air with minimum surface - or doing the most with the least.

We can derive from these examples that one way we can examine complex systems is to equate 'fitness' with avoiding unnecessary work or effort. While this is important for individual cases of agents (specific birds in a flock, or specific fish in a school), what is also interesting in systems exhibiting Self-Organization (bird flocks and fish schools), is that this principle is extended to the include the group level. Thus the system, as a whole, finds a regime that expends the minimum effort to achieve a goal on the part of the group rather than on the part of the individual. This might involve individual sacrifices in order to enable overall group behavior to succeed.

These kinds of dynamics involving individual sacrifices (or trade-offs) where group performance ultimately matters are the subject of game theory. The Prisoner's Dilemma, for example, is a classic case where the most 'fit' long term strategy is for both players to sacrifice some potential individual gain, in favor of longer term collective gain. Fit strategies differ depending on whether or not the game is played once or multiple times, so in natural systems that have ongoing interactions of agents than there are different fitness incentives than in non-repeating scenarios.

Short Explanation of the Prisoner's Dilemma:

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