Monday, February 9, 2009

tradeoffs and compromises

Tradeoffs are what make optimization interesting, giving functions minima, maxima and saddle points. With only one dimension, one process can increase a utility function in the same direction in which another decreases the function, resulting in a maximum or minimum. In more than one dimension, a function can have a saddle point, which is a maximum in some directions and a minimum in other directions. In one model of system change, we can envision a mostly static environment, represented by a utility function. The system tries to minimize that function. There is a large applied math literature devoted to optimization in one or more dimensions, which is done mostly by computer nowadays. We know that a system can get stuck in a local minimum if the only strategy it employs for finding that minimum is going downhill in a local manner. If the environment changes once (but not continually--we will discuss a model for that later) and then is static again, what used to be a minimum may now no longer be one. In that case, a new minimum will be found, in a time depending on the efficiency of the system in locating the new minimum. The new minimum will not be too different from the old minimum unless a cataclysmic change in the environment has occured which destroyed some surrounding mountains of the old valley. To get to other valleys which might have a lower minimum, the best strategy is to go uphill for some time, to get to a mountain pass (a saddle point) which is the least uphill one has to go. But gradual change in a downhill direction will not get us there.

You can see the obvious application to social change in the age of dwindling petroleum. Insulate your house, purchase a greener car or appliance, build a cob/straw-bale house and a rocket stove all of which make your life more comfortable and you won't achieve much change. Much of the old culture is still right there with you--the exploitation of third world people, the exploitation of those without capital/land by those who own them, hierarchies based on power, egotism and greed, alienation caused by overspecialization and abstraction of production, etc. Any direction that has a chance of getting you to the mountain pass has to be somewhat painful, somewhat decrease your fitness, somewhat not work with the rest of the system as it currently exists. That is the (almost) static model of system change based on optimization. Note this has not much to do with dynamical systems theory where there is no function to be optimized in the dynamics, where you can get strange attractors and chaos. Human life does seem to have some function that it optimizes, whether it be fitness, happiness, freedom, or a combination of these.

Now for a dynamic environment model, where each component of a system influences the functions (environments) of other components by only controlling a few variables, whereas each function depends on all the variables.

In game theory, which applies not just to discrete games but to continuous systems with more than one component, competition in a zero sum game can be modeled nicely by each player (or component/cell/organism/species/culture) having a utility function to minimize which has a saddle point. Around this point, one player trying to decrease his function increases the function of his competitor (a simple realistic case for similar players competing for some resource is the same function with the variables interchanged). A compromise will occur at the saddle point, where though each player does not do as well as they could if they had control of their competitor's variables, the system utility function (defined as the sum of the individual utility functions) is minimized.
I am researching this, so I am not sure yet: if the functions to be minimized are not the same, situations could arise in which the strategy of each player minimizing his utility function with only control over his own variables can lead to being stuck at a point which is not a saddle point of his function. Whether the utility functions of different players are the same or not, it is possible to get stuck at a point which is a local but not global minimum of the system utility function. This can happen even in a cooperative domain (a win-win, not a zero sum) where the players reducing their own utility function are also reducing the other players' utility functions. In order to get out of a local minimum, just like in the static environment model, some players have to become altruistic, undergo some suffering and go uphill for a while in order to either reach a lower minimum for themselves eventually (temporary altruism, or altruism in time), or else they may never reach a better minimum for themselves, but reach a better minimum for the system utility function (altruism in space).

So we see that in both the static environment model and the dynamic environment model, a strategy of always going downhill can get the players stuck in a local minimum, and in order to get unstuck one must go uphill sometimes. It follows that changes that seem to improve things for people in the short run will not lead to a better situation for the whole culture.

Also, compromises which place one in the original valley are not worth making because one will still roll back down to the original minimum. Once the new valley has been reached (by going uphill for a while), all kinds of small changes which lead downhill, or compromises which keep one in the new valley may be made with no damage.

Tradeoffs around the local minimum are going to be different than tradeoffs around the global minimum. Around the global minimum it is possible to do better on both aspects of the tradeoff than around the local minimum, or perhaps much better on one aspect and only a little worse on the other.

What tradeoffs have I encountered?

Solitude vs people around: I like solitude. I can think more clearly, be more calm and grounded. However, having more people around, especially people I like, has some advantages like good conversations, good dances and music making, intellectual comrades, romantic partners, ability to do more of what I love because of specialization, more stability in the face of hardship, and energy/labor savings on shared heat, cooking, tools and building materials.

Freedom vs comfort and security. I would much rather spend time doing physics, dancing, working in the garden or on engineering projects than on having clean clothes, electronic gizmos, appliances and any convenience one can think of. The latter take time away from things I love, or vice versa--time is a limited resource and I would rather spend it doing things I love than being comfortable and secure (beyond a minimal level). Some comfort and security comes from being part of the global economy. Some comes from conforming to the norms of a group. Depending on the structure of the group, it is possible to do better on freedom and not much worse on comfort, so that the total happiness is increased. More generally, tradeoffs are dependent on where the baseline optimum is. I think it is possible to have alot more freedom, love and creativity for most people than in this culture, while sacrificing only a bit of comfort, security and convenience.

Freedom vs collective responsibility. I think that beyond basic needs, I would not want collective responsibility for everyone's individual needs in my community. This would cut down on most people's freedom. If someone needs their own cabin for artistic reasons, let them pay for it with their resources. If someone needs a lab, or expensive film equipment, a washing machine, a vacuum cleaner, or alot of land for agriculture as an avocation or for making money, let them pay for it. I may support some of these and not others, depending on my affinities. On the other hand, I want the whole community to be collectively responsible for basic nutritional needs, soil fertility, tools and labor for the land that provides those needs, and basic communal shelter for people. The freedom each individual gains from such an arrangement seems worth it to me.

Feeding people vs protecting wildlife and biodiversity: I saw this tradeoff being bitterly discussed at Earthaven. I fall on the side of feeding humans first, protecting wildlife second. That does not mean that I don't care about wildlife and will try as much as possible to protect it. There is also the issue that relying on the current food system may be even more harmful to the wild than clearing some wilderness around us in order to feed ourselves.

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