Further, the kinds of computations that would increase that ratio are the sorts of things that would be like the continuation of human history in a non-catastrophic way.
This is not obvious to me. I concur with Manfred's point that "any solution that doesn't have very good evidence that it will satisfy human values, will very likely not do so (small target in a big space)."
To be concrete, consider the implementation that runs a lot of Monte Carlo simulations of human history from now on, with differences in the starting conditions based on the granularity of the h term and with simulations of exogenous shocks.
Why couldn't they just scan everyone's brain then store the information in a big hard drive in a maximum-security facility while the robots wipe every living person out and start anew? Perhaps it's possible that by doing that you vastly increase resilience to exogenous shocks, making it preferable. And about 'using the computational gains of humanity', that could just as easily be achieved by doing the opposite of what humans would have done.
Non-catastrophic with respect to existence, not with respect to "human values." I'm leaving values out of the equation for now, focusing only on the problem of existence. If species suicide is on the table as something that might be what our morality ultimately points to, then this whole formulation of the problem has way deeper issues.
My point is that starting anew without taking into account the computational gains, you are increasing D(u) efficiently and D(u/h) inefficiently, which is not favored by the objective function.
If there's something ...
I attended Nick Bostrom's talk at UC Berkeley last Friday and got intrigued by these problems again. I wanted to pitch an idea here, with the question: Have any of you seen work along these lines before? Can you recommend any papers or posts? Are you interested in collaborating on this angle in further depth?
The problem I'm thinking about (surely naively, relative to y'all) is: What would you want to program an omnipotent machine to optimize?
For the sake of avoiding some baggage, I'm not going to assume this machine is "superintelligent" or an AGI. Rather, I'm going to call it a supercontroller, just something omnipotently effective at optimizing some function of what it perceives in its environment.
As has been noted in other arguments, a supercontroller that optimizes the number of paperclips in the universe would be a disaster. Maybe any supercontroller that was insensitive to human values would be a disaster. What constitutes a disaster? An end of human history. If we're all killed and our memories wiped out to make more efficient paperclip-making machines, then it's as if we never existed. That is existential risk.
The challenge is: how can one formulate an abstract objective function that would preserve human history and its evolving continuity?
I'd like to propose an answer that depends on the notion of logical depth as proposed by C.H. Bennett and outlined in section 7.7 of Li and Vitanyi's An Introduction to Kolmogorov Complexity and Its Applications which I'm sure many of you have handy. Logical depth is a super fascinating complexity measure that Li and Vitanyi summarize thusly:
The mathematics is fascinating and better read in the original Bennett paper than here. Suffice it presently to summarize some of its interesting properties, for the sake of intuition.