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Peter_de_Blanc comments on Complexity of Value ≠ Complexity of Outcome - Less Wrong
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Are you talking about Kolmogorov complexity or something else? Because the outcome which optimizes a simple goal would have a low Kolmogorov complexity.
Kolmogorov complexity is fine by me.
What make you say that? It isn't right.
Filling the universe with orgasmium involves interstellar and intergalactic travel, stellar farming, molecular nanotechnology, coordinating stars to leap between galaxies, mastering nuclear fusion, conquering any other civilisations it might meet along the way - and many other complexity-requiring activities.
Indeed - sorry! The r-pentomino's evolution is not a good example of high Kolmogorov complexity - though as you say, it is complex in other senses.
I had forgotten that I gave that as one of my examples when I retroactively assented to the use Kolmogorov complexity as a metric.
Well, if you had a utility function over a finite set of possible outcomes, then you can run a computer program to check every outcome and pick the one with the highest utility. So the complexity of that outcome is bounded by the complexity of the set of possible outcomes plus the complexity of the utility function plus a constant.
EDIT: And none of those things you mentioned require a lot of complexity.
If the things I mentioned are so simple, perhaps you could explain how to do them?
I would be especially interested in a "simple" method of conquering any other civilisations which we might meet - so perhaps you might like to concentrate on that?
Build AIXItl.
Alas, AIXItl is a whole class of things, many of which are likely to be highly complex.
This contradicts my understanding of AIXI from Shane Legg's Extrobritannia presentation. What's the variable bit? Not the utility function; that's effectively external and after the fact, and AIXI infers it.
I think I answered that in the other sub-thread descended from the parent coment.
If you're referring to the parameters t and l, I'll suggest a googolplex as a sufficiently large number with low Kolmogorov complexity.
No. AIXItl will need to have other complexity - if you want it to work in a reasonable quantity of time - e.g. see, for example:
"Elimination of the factor 2˜l without giving up universality will probably be a very difficult task. One could try to select programs p and prove VA(p) in a more clever way than by mere enumeration. All kinds of ideas like, heuristic search, genetic algorithms, advanced theorem provers, and many more could be incorporated.""
It seems that you think "complex" means "difficult." It doesn't. Complex means "requires a lot of information to specify." There are no simple problems with complex solutions, because any specification of a problem is also a specification of its solution. This is the point of my original post.
So: a galaxy-conquering civilisation has low Kolmogorov complexity - because it has a short description - namely "a galaxy-conquering civilisation"???
If you actually attempted to describe a real galaxy-conquering civilisation, it would take a lot of bits to specify which one you were looking at - because the method of getting there will necessarily have involved time-and-space constraints.
Those bits will have come from the galaxy - which is large and contains lots of information.
More abstractly, "Find a root of y = sin(x)" is a simple problem with many K-complex solutions. Simple problems really can have K-complex solutions.