Can you really assume the agent to have a utility function that is both linear in paperclips (which implies risk neutrality) and bounded + monotonic?

When I was eight or nine i got one of those electricity/magnetism experiment kits. Boy, did I love that kit! I did that motor, electric bell and electromagnet experiment over and over again for maybe a year and then moved on to building my own electronic stuff from components I found tearing old TV's and radios apart. I soon had a little club at home teaching my friends!

Some years ago when my cousin just had turned nine I got him a kit and hoped to see him become as interested in electronics as I was in his age. But he hardly opened the box, and when I came to visit a year later that kit was long gone and forgotten. It simply could not stand the competition against the video games and toy guns.

I don't want to demotivate you with this story. Just want to say that stimulating a kid towards some interest is much more than buying a set of object for them. The key is the time you spend and how you spend it. Make it a step by step project. Ask her; maybe there are things among your alternatives that are more interesting to her than other. Followup and communicate. Visit museums etc..

People don’t use [calculus, physics, chemistry, etc] in daily life unless they are professionals.

Isn't this statement true?

Do you really mean that people would be better off never being exposed to ("interesting but useless") natural science? Would you prefer a society where most people doesn't have a clue about how things around them came to be or how they work?

I suspect that your are making and destroying a straw man here. The original (admittedly rather rambling) post did not advocate never exposing students to science, but rather a specific way of doing it, a sort of a loose version of Socratic questioning.

Calculus, mechanical physics, chemistry, microbiology etc are areas describing objective reality. They explain how the world we live in works on a fundamental level, i.e the very fabric of reality. Not only do they give answers to basic questions of human life, they also activate the students toward systematic analytical thinking and questioning.

Do you really mean that people would be better off never being exposed to ("interesting but useless") natural science? Would you prefer a society where most people doesn't have a clue about how things around them came to be or how they work? How would a potential engineer or a researcher build up its interest towards science if never exposed to it systematically?

Learning about music and art is good, but not at expense of science!

This problem reminds me of the movie Memento. The lead character was unable to make any new memories and his mind was reset every two or three minutes. Nevertheless was he trying to find his wifes killer, and kept record of new leads by taking pictures with a Polaroid camera, keeping notes and tattooing pieces of information to his body. Great movie!

An interesting related question would be: What would people in a big population Q choose if given alternatives: extreme pain with probability p=1/Q or tiny pain with probability p=1. In the framework of expected utility theory you'd have to include not only the sizes of the pains and size of populations but also the risk aversion of the person asked. So its not only about adding up small utilities.

Further: Any chain of reasoning leading to a constrained set of available locations followed by randomization could be used by B to constrain the set of locations to search. Is it therefore possible to beat complete randomization?

Yes. You need to weight locations according to the time it takes to search them and then make a random selection from that weighted set; that'll give you longer search times on average than an unweighted random pick from a large set where most of the elements take a trivially small time to search. I could take a stab at proving that mathematically, if you're comfortable with some abstraction.

You can beat even that by cleverly exploiting features of the setup, as I and muflax did in our responses to the OP, but that's admittedly not quite in keeping with the spirit of the problem.

As some comments has pointed out there are some loopholes in the original formulation, and I will do my best to close these or accept the fact that they're not closeable (which would be interesting in its own right).

Lets try a simpler formulation.. Basically what is being asked here is that given two intelligences A and B, where A and B are identical (perfect copies), can A have a strategy that minimizes the probability of B finding the coin?

Further: Any chain of reasoning leading to a constrained set of available locations followed by randomization could be used by B to constrain the set of locations to search. Is it therefore possible to beat complete randomization?