An important concept here on LW is that of a singularity of intelligence, or at least a very rapid growth. Although it seems mostly hopeless, it would be nice if we could find a mathematical approach to quantify these things. I think the first point to note is that intelligence...
Hello. This is a concept that I have not seen formulated before and I think the people here might find interesting. I am a new LW user and so I do not know if this has been formulated before. In this case I suppose you can refer me to it...
What do you mean by a product topology here? The product topology being used for a stochastic processes? That requires a topology on the state space in the first place. Right now I have not specified any topologies.
Regarding the stochastic aspect, I have thought about that, but so far I have not yet seen a benefit by including it because any stochastic approach can somehow be seen as just a deterministic approach on the level of distributions. I.e. if a Model M is actually a random variable, and a task T is also a random variable, then the important thing, which is the function and which would now be a random object, can... (read more)
An important concept here on LW is that of a singularity of intelligence, or at least a very rapid growth. Although it seems mostly hopeless, it would be nice if we could find a mathematical approach to quantify these things. I think the first point to note is that intelligence is is surely not one-dimensional. The concept of general intelligence suggest that it might be approximately one-dimensional, in some sense. But how can we really know what is true? I would like to get a better understanding of the geometry of intelligence. To do this, a good starting point is to look for natural operations on intelligence, as operations can lead to... (read 1128 more words →)
Let me try rephrase is in more conventional probability theory. You are looking at a metric space of universes . You probably want to take the Borel-sigma algebra as your collection of events. We think of propositions as sets , which really just means is a subset which is not too irregular. Then thebindicator function is if A holds in universe and otherwise.
Your elaborations do not depend much on the time so we set .
You now talk about picking a universe uniformly from a ball . This is a problem. On finite dimensional vector spaces we have the lebesgue measurenand we can have such a uniform distribution. On... (read more)
Hello. This is a concept that I have not seen formulated before and I think the people here might find interesting. I am a new LW user and so I do not know if this has been formulated before. In this case I suppose you can refer me to it and close this post or something like that.
This "cryptographic life" I will describe now should be seen as a plausible example of how a lifeform/consciousness could span a volume measured in hundreds of lightyears without being fixed to any particular physical objects.
Here are my premises:
P1: We assume that AGI is of course possible and can be implemented on classical computers. It is... (read 770 more words →)
Although we can not rigorously say this yet since we have not chosen a definition of agent, I think this intuitively applies and therefore (H2) can only hold when you are restricted to some set of tasks, perhaps "reasonable tasks", yea.
I wonder if in the stochastic inteprretation of task this issue disappears because "No Free Lunch" tasks that "diagonalize against a model in a particular fashion have very low probability.