Convergence of Arbitrary Goals to Reproduction
You probably heard of the idea that, at some point in time, we might create systems that solve certain tasks and that get better at these tasks by recursively modifying their code. Here is some scary reasoning:
- A system cannot predict (=understand) a system of greater algorithmic complexity.
- Therefore, the only way for a system to improve in a way that increases its algorithmic complexity is trial and error, thereby keeping the best results — i.e. evolution.
- The only goal that is stable under evolution is rapid reproduction.
- Therefore, the only stable goal for recursively self-improving systems is rapid reproduction.
I really hope that someone will point out the flaw in this line of thought or show me the reason why it does not apply to our world and to any self-modifying systems we might create.
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I think point 3 is not sufficient. You need to ensure the “improving” part.
Evolution takes place in a confined space, so one has to fight for survival. The surviving phenotype is by definition improved compared to the extinct versions.
So you also need confine the space and give the improved versions a better survival rate.
Can the self-improving system get better than the designer of the environment?
A system can be predicted in all kinds of ways. E.g. if a human is part of a crowd in a football stadium his actions are highly predictable in the overall pattern. Whereas predicting where a dog will go next is in most situations not possible, unless it is attracted by food for example.
Human beings have already figured out a different mode of evolution - culture & technology. In fact there is a gradual advance in reasoning from animals, over monkeys to apes and finally homo sapiens sapiens. Instead of repeating the mistakes of our grandparents we can learn from their experience. Unfortunately this procedure has it’s shortcomings as well.
I believe there is no fixed threshold for the understanding of any system. Rather the fitness of the models increases through the process of falsification (according to Popper’s Logik der Forschung). They are some ultimate boundaries for understanding (Heisenberg’s uncertainty principle for example). The question is in what ways the fitness of the model is affected.
One of the major risk for human extinction is uncontrolled growth (reproduction). So in some way I would say P4 applies to humans already. Humans seem unable to adapt to new global risks, as of today. They don’t have the social meachnisms in place to make the right choices. That is markets and economic principles are overwhelmingly biased towards to consumption today versus consumption for the next generation.
How many humans can the earth carry? Perhaps 10 billion, certainly not much more. The ecological footprint of the West is 30-100 times higher per capita, compared with the so called undeveloped countries. China and India are already adapting the lifestyle of the West. If those 2.4 billion people will use the same resources as we do a global collapse of the environment will be inevitable. In my view the global society should implement drastic depopulation measures. The best way to achieve this goal is to enhance global economic equality, because a minimal threshold of wealth decreases the numbers of children per couple from 5-6 to 1-2. In fact the UN millenium goals are achievable today, only that the world has different priorities.
beza1e1: The fact that improved versions need to be rewarded with a better survival rate is the very reason why reproduction is the only stable goal for fully self-referential systems that improve with regard to some arbitrary goal function by evolutionary means. If a system can increase its chances of survival both indirectly by getting better at a task and directly by getting better at reproduction, the direct means will prevail in the long term.
Benjamin: I was using the term predict/understand in its technical meaning. System A is said to be able to predict system B if, after a finite number of observations of the output of system B, system A is able to predict all following outputs of system B accurately.
Do you claim that your suggestion (”there is no fixed threshold for the understanding of any system”) is relevant to the problem of self-modifying systems which need to understand improved versions of themselves if they don’t want to limit themselves to evolutionary approaches?
“The only goal that is stable under evolution is rapid reproduction.”
well, if you have owls, then rapid reproduction is a good strategy for mice. but that causes more owls and less food for the next generation. infinite growth is
impossible for a race on restricted territorium.
but did you know these creatures?
http://de.wikipedia.org/wiki/Nacktmull
http://en.wikipedia.org/wiki/Naked_mole_rat
i’d say, “survival of the own race at all costs” is the only stable goal under evolution. it is even unstable wether the genetical improvement of some races stop or go forward or even backward.
due to unstable genes, some fishes and reptiles degenerate/evolve to/from hermaphrodites just to survive (as a race) ‘extreme rare populated environments’/'adapting enemies’.
Marc: My view of evolution is more abstract. It is almost a tautology, but the observation that the only patterns that remain are those that are either very stable, very common or replicate quickly explains a lot. From this perspective, it should be obvious that the genes that use naked mole rats as vehicles are those genes that tuned their vehicles to reproduce as fast as their environment allows them to do, even if this means “pretty slow” in some environments.
By saying that the only stable evolutionary goal is reproduction, I do not want to imply that the means to achieve this goal cannot be complex or that the goal needs to be the goal of a creature.
I don’t get your third point.
Why should the only stable goal for evolution be rapid reproduction?
Rapid reproduction as in: “produce children as early as possible, because you might not live very long?”
It might be so in evolutionary systems like nature, where every act of life has some impact on the future of the acting individual and therefore includes mating.
But what if we kept reproduction out of the game? It obviously possible. For example, I happen to have implemented an evolutionary algorithm to solve the traveling salesman problem for maps with less than 100 cities, where the less optimal individuals of a certain generation just were also less likely to be allowed to mate, when the mating “season” comes.
The more I think about this, the less sure I am that I really understood the issue. I’m sorry.
Thorben: You are right; in environments where you have absolute control over the factors that determine who gets to mate and who does not, you can choose arbitrary goal functions and this will work just fine.
However, this kind of environment needs to be specified completely within the code you are writing. These kinds of evolutionary systems can never lead to an increase in algorithmic complexity (easily provable) and are therefore fairly uninteresting compared to the fully self-referential, self-improving systems some AI people are thinking about.
Andreas:
If we predict system S with model M under parameter p with perfect knowledge the function M(p) is linear. The complexity of the function M is minimal and therefore we can’t call it knowledge.
The description of knowledge, i.e. understanding as boolean introduces many difficulties. Of course this debate has a long history in epistomology. One way out of the problem is to view models as subject to a goal. If I want to describe S I will have some intention and therefore some constraints on M.
With regards to self-modification I would say that an agent A doesn’t not need to have a perfect of model of it’s better counterpart A’, because A can optimize subparts A1,…,An of A. This is possible through the reduction of complexity of by analysis. That is the commutativity of a partition function ap is given, ap(A) = A1 … An (Reductionism). When you adopt the view that ap is not given you take the holistic stance.
An agent tries to understand the set of systems it encounters, including itself. I don’t see why holism should especially apply to itself. Humans can understand a good part of it’s biology, brains, cells, genes and there doesn’t seem to be a principle boundary.
What I am favourable of is the idea of artificial life, that is understanding the dynamics of reproducing machines in biologic systems, chemical and mechanical systems. In the end our view of machines and programs is not static at all, so therefore there is perhaps a practical, current limit to our knowledge what these systems are capable of. Finding the limits of boundaries of all knowledge, including self-knowledge is after all the hardest problem there can be.
Furthermore I believe that action is some kind of self-modification already. So I would suggest that we have to have different levels of self-modification. Cultural evolution is an extension of biological evolution, articial evolution an extension of cultural evolution.
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