What do we mean when we speak of Fitness? For ants, fitness might be discovering a source of food that is abundant and easy to reach. For a city, fitness might be moving the maximum number of people in the minimum amount of time. But fitness criteria can also vary - what might be fit for one agent isn't necessarily fit for another. 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.
Accordingly, 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 the system to determine what factors are at play.
That said, there are certain principles that remain somewhat more constant, 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. 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 depends on the nature of the goal.
Example: Returning to the example 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 to have 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 of these interacting parameters that 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 they are willing to expend over the course of their travel. One package might hold their money, one might hold their time, and one might hold their patience to deal 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 preserve them for other needs. 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 available to spend on time, and others will have more energy to go towards 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 these 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.
In the above example the agents (room seekers), employ cognitive decision-making processes to determine what a 'fit' regime is. But physical systems also 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 surface area that minimizes surface area and therefore frictions. The soap bubble can therefore be considered as an energy minimizing emergent phenomena (if you want a detailed explanantion, then follow the 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.
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