Consideration:

• Gather useful information and insights from experts in countries foreign to you, the farther away the better. (Use the internet, jet travel, etc for this.)
• Read this information into the chronophone.
• This should produce insights from experts Archimedes would have had comparatively much more trouble contacting, because you have better tools available to you for the execution of the same cognitive strategy.

I'd like to point out that the statistical value of human life is used by economists for calculations such as Eliezer mentions, so at some point someone has managed to do the math.

Any mind that I can model sufficiently well to be accurate ceases to be an agent at that point.

If I can predict what you are going to do with 100% certainty, then it doesn't matter what internal processes lead you to take that action. I don't need to see into the black box to predict the action of the machine.

People I know well maintain their agenthood by virtue of the fact that they are sufficiently complex to think in ways I do not.

For these reasons, I rarely attempt to model the mental processes of minds I consider to be stronger than mine (in the rational sense.) Attempting to ask myself what a powerful rationalist would do is not a useful heuristic, as my model of a strong rationalist is not, in itself, stronger than my own understanding of rationalism.