An optimizing system is a system that has a tendency to evolve towards one of a set of configurations that we will call the target configuration set, when started from any configuration within a larger set of configurations, which we call the basin of attraction, and continues to exhibit this tendency with respect to the same target configuration set despite perturbations.
If I’m reasoning correctly, I think this definition could classify just about anything as an optimizer.
Consider inanimate biological substances, like a leaf. From a wide range of initial configurations of a leaf, effectively all make the leaf evolve towards being dirt, because leafs decompose eventually. Are leaves optimizers?
People tend to get older and wrinklier when aging. From a wide range of states, people would tend to “evolve” towards being aged. Are people optimizers for aging?
If the rock is hotter than the surrounding aid, virtually any initial configuration of the rock would tend towards the rock being somewhere around the temperature of the surrounding air. Are rocks optimizers?
Suppose you have a program with that shows the user a welcome and information blurb the first time they run the program, and then won’t show it again. Consider the target configuration to be “program does not show the welcome blurb”. The program would evolve into such a configuration from any other configuration. Are welcome blurbs optimizers?
Let us now examine a system that is not an optimizing system according to our definition. Consider a billiard table with some billiard balls that are currently bouncing around in motion. Left alone, the balls will eventually come to rest in some configuration. Is this an optimizing system?
In order to qualify as an optimizing system, a system must (1) have a tendency to evolve towards a set of target configurations that are small relative to the basin of attraction, and (2) continue to evolve towards the same set of target configurations if perturbed.
If we reach in while the billiard balls are bouncing around and move one of the balls that is in motion, the system will now come to rest in a different configuration. Therefore this is not an optimizing system, because there is no set of target configurations towards which the system evolves despite perturbations. A system does not need to be robust along all dimensions in order to be an optimizing system, but a billiard table exhibits no such robust dimensions at all, so it is not an optimizing system.
What about taking the target configuration to be any state in which all the billiard balls are stationary? A wide range of states of billiards bouncing around on a table would result in all the balls ending up stationary, so I don’t see how it wouldn’t be classified as an optimization process.
Also, I’ve made my own attempt at defining “optimizer” here, in case you’re interested.
Consider inanimate biological substances, like a leaf. From a wide range of initial configurations of a leaf, effectively all make the leaf evolve towards being dirt, because leafs decompose eventually. Are leaves optimizers?
People tend to get older and wrinklier when aging. From a wide range of states, people would tend to “evolve” towards being aged. Are people optimizers for aging?
It’s a good question. However, the decomposition of a leaf and of the body are both examples of increases in entropy over time, but actually if you look at the size of the “target configuration set” you find that it’s almost as big as the whole configuration space, because most of the configurations of a system are high entropy configurations. So I don’t think a leaf or an aging body qualify as optimizing systems according to the definition in this post. See also this section.
If the rock is hotter than the surrounding aid, virtually any initial configuration of the rock would tend towards the rock being somewhere around the temperature of the surrounding air. Are rocks optimizers?
Well you really have to look at the whole system. It’s true that if you have a system that consists of a hot part and cold part, the system overall will evolve towards configurations in which the parts are the same temperature. But this is again an example of entropy increasing. Most of the configurations of the joint rock+environment system have the rock and the environment at approximately the same temperature, since if you randomly sample a temperature for each particle, the large number of particles in the rock and the environment mean that the average temperature of all the particles in the rock will be very similar to the average temperature of all the particles in the environment, with high probability.
What about taking the target configuration to be any state in which all the billiard balls are stationary? A wide range of states of billiards bouncing around on a table would result in all the balls ending up stationary, so I don’t see how it wouldn’t be classified as an optimization process.
Yes, just like a ball rolling down a hill qualifies as an optimizing system, a table with with billiard balls qualifies as an optimizing system in the sense that you point out.
But the whole point of this post is to get past the notion of “optimizer” and “optimization” to the extent that these concepts imply that there is some “agent” performing optimization, and some thing “being optimized”, which sneaks the agent model into all our thinking and leads to a very confused picture of things.
Also, I’ve made my own attempt at defining “optimizer” here, in case you’re interested.
Yes, just like a ball rolling down a hill qualifies as an optimizing system, a table with with billiard balls qualifies as an optimizing system in the sense that you point out.
Both of these examples also seem like increases in entropy if you consider the full system.
With a fixed amount of energy, there are a tiny number of ways to use it to make the ball move (or to spend energy putting it somewhere other than the bottom of the hill) but an exponentially vast number of ways to use it to increase the temperature of the billiard ball and table (since there are billions of billions of microscopic degrees of freedom that could be vibrating or whatever).
A lot of the examples I pointed out can end up tending towards increasing entropy, but I think there are a lot of things that would be considered optimizer that don’t increase entropy.
For example, consider a leaf out in the sun, drying out and going from a greenish color to a yellow one. Pretty much all configurations of the leaf would result in the leaf getting more yellow over time. Is the leaf optimizing for yellow-ness?
What about a knife that is being used and never sharpened? From a wide range of configurations the knife would tend towards getting duller. Is it optimizing dullness?
What about a spaceship leaving Earth? Is it optimizing for the distance from Earth?
I suppose we could consider these things optimizers if you really want to. But I’m concerned that a definition that include leaves, knives, billiard balls, and rocket ships is overly broad.
More generally, it seems like this definition classifies a lot of things that change in some way over time as an optimizer. In general, if something tends to be different in some ways when it’s young than old, then I think you can say the system is an optimizer optimizing for whatever characteristics correlate with oldness.
If I’m reasoning correctly, I think this definition could classify just about anything as an optimizer.
Consider inanimate biological substances, like a leaf. From a wide range of initial configurations of a leaf, effectively all make the leaf evolve towards being dirt, because leafs decompose eventually. Are leaves optimizers?
People tend to get older and wrinklier when aging. From a wide range of states, people would tend to “evolve” towards being aged. Are people optimizers for aging?
If the rock is hotter than the surrounding aid, virtually any initial configuration of the rock would tend towards the rock being somewhere around the temperature of the surrounding air. Are rocks optimizers?
Suppose you have a program with that shows the user a welcome and information blurb the first time they run the program, and then won’t show it again. Consider the target configuration to be “program does not show the welcome blurb”. The program would evolve into such a configuration from any other configuration. Are welcome blurbs optimizers?
What about taking the target configuration to be any state in which all the billiard balls are stationary? A wide range of states of billiards bouncing around on a table would result in all the balls ending up stationary, so I don’t see how it wouldn’t be classified as an optimization process.
Also, I’ve made my own attempt at defining “optimizer” here, in case you’re interested.
Thank you for this comment Chantiel.
It’s a good question. However, the decomposition of a leaf and of the body are both examples of increases in entropy over time, but actually if you look at the size of the “target configuration set” you find that it’s almost as big as the whole configuration space, because most of the configurations of a system are high entropy configurations. So I don’t think a leaf or an aging body qualify as optimizing systems according to the definition in this post. See also this section.
Well you really have to look at the whole system. It’s true that if you have a system that consists of a hot part and cold part, the system overall will evolve towards configurations in which the parts are the same temperature. But this is again an example of entropy increasing. Most of the configurations of the joint rock+environment system have the rock and the environment at approximately the same temperature, since if you randomly sample a temperature for each particle, the large number of particles in the rock and the environment mean that the average temperature of all the particles in the rock will be very similar to the average temperature of all the particles in the environment, with high probability.
Yes, just like a ball rolling down a hill qualifies as an optimizing system, a table with with billiard balls qualifies as an optimizing system in the sense that you point out.
But the whole point of this post is to get past the notion of “optimizer” and “optimization” to the extent that these concepts imply that there is some “agent” performing optimization, and some thing “being optimized”, which sneaks the agent model into all our thinking and leads to a very confused picture of things.
Thank you for the pointer!
Both of these examples also seem like increases in entropy if you consider the full system.
With a fixed amount of energy, there are a tiny number of ways to use it to make the ball move (or to spend energy putting it somewhere other than the bottom of the hill) but an exponentially vast number of ways to use it to increase the temperature of the billiard ball and table (since there are billions of billions of microscopic degrees of freedom that could be vibrating or whatever).
Thanks for the response.
A lot of the examples I pointed out can end up tending towards increasing entropy, but I think there are a lot of things that would be considered optimizer that don’t increase entropy.
For example, consider a leaf out in the sun, drying out and going from a greenish color to a yellow one. Pretty much all configurations of the leaf would result in the leaf getting more yellow over time. Is the leaf optimizing for yellow-ness?
What about a knife that is being used and never sharpened? From a wide range of configurations the knife would tend towards getting duller. Is it optimizing dullness?
What about a spaceship leaving Earth? Is it optimizing for the distance from Earth?
I suppose we could consider these things optimizers if you really want to. But I’m concerned that a definition that include leaves, knives, billiard balls, and rocket ships is overly broad.
More generally, it seems like this definition classifies a lot of things that change in some way over time as an optimizer. In general, if something tends to be different in some ways when it’s young than old, then I think you can say the system is an optimizer optimizing for whatever characteristics correlate with oldness.