Eliezer, although the comments did eventually get better, don't despair for the early comments on this post. Remember yourself, all you are finding in the comments is evidence confirming the belief that no one reading this blog is learning anything. I conjecture that those who have learned something just don't get excited enough to post because they don't disagree with you strongly enough or aren't sufficiently surprised to thank you publicly.

Of course, I still suspect, as you probably do, from years of experience that most readers of this blog believe they are learning to overcome bias when in fact they are just convincing themselves that they are learning to overcome bias because they have read about it and believe it's a virtue to overcome bias. And I don't exclude myself from this group either, because although I don't feel as though I'm thinking this way, that doesn't mean I might not secretly be and I will be revealed when I discover a serious error in my behavior and beliefs.

The best thing about grad school is when you finish taking courses. To make it through the math courses you have to play the game, writing down proofs you know aren't right but that will get you some credit. Once you're done with that, then you can actually step back and learn something. Study only one or two things at a time, set a reasonable pace that will allow you time to think (and will be paced relative to your own speed of thought), and actually gain some understanding. Of course, some students use this as an excuse to be lazy, but a good advisor will know the difference.

As I see it, what's most important is to make a division between rationality and emotions in terms of where they fit in the equations. Rationality describes the equations, emotions provide a source of evidence that must be applied correctly. If an outcome makes me happy, that should make me desire that outcome more, but not make me think that outcome more likely than if it made me sad (unless, of course, I'm evaluating the probability that I will be motivated to do something).

Unfortunately, I think this model of mind is not how the human mind actually works. Emotions appear to change the equations, not their arguments, so eliminating emotions seems like an appropriate measure to increase the human brain's approximation of a rational process. Maybe you can allow yourself feel happy or sad at an outcome without it affecting the outcome, but getting to that point may require an unemotional transition period as you change your thinking to match that of a rational process.

zzz, I think you underestimate how people perceive gambles. Investing in financial markets isn't perceived as a bet, since we like to believe that if you only knew enough, you could make the right choices (whether you actually can or not is another matter). With lotteries and other forms of gambling, it doesn't matter how much you know, you can't anticipate the outcome any better than if you had no additional information. That, I think, is part of why gambling is much more popular than investment: even the least skilled person has the same chance of winning as the most.

As I've thought about the chronophone, a big part of the trouble with it is that we can't successfully transmit any idea where we already know what result we want. Thus to pick something desirable now that will be translated into something desirable then is essentially impossible, since if I already know it to be desirable, I must know enough of the result to know it's desirable, hence tainting all my thoughts. At best, I can tell Archimedes about things I'm working on now that are non-obvious and hope that they translate into something similarly non-obvious that would have generated from the same motivation in his own time. That is, if my motion to have fun causes me to research mathematical topic X, his motivation to have fun will cause him to research topic Y in his favorite field. X and Y may not even be analogues, just generated by the same kind of line of thinking.

I still haven't come up with something that I feel fits the spirit of the question, but my start is that I could tell Archimedes about atheism. Up until I was maybe 11 or 12 years old I never really considered the question of religion. My parents taught me the basic Christian tradition, but I never attended church or was deeply indoctrinated. At that age, though, other kids started asking me about religion as they began to become adult members of their religions. "What religion are you?" they would ask and my answer was "I don't know". Someone asked if I celebrated Christmas and I said yes so they told me I was a Christian, but I didn't really know what that meant. But over the next several years the more I learned about religion the less it seemed to make sense to me, until eventually someone shunned me for being an atheist, so then that put me on the path to actively learning what atheism was and seriously thinking about the question of whether anything supernatural exists.

In the end I concluded on atheism. If I recounted my steps to Archimedes, I think they would come through clearly, except rather than the Cult of Jesus he might hear Cult of Zeus. To what extent this might actually improve things I don't know, since I'm not even sure if promoting atheism for its own sake is a good idea.

In sum, I agree, but one small issue I take is when you argue that someone acts contrary to their learning it demonstrates that they don't really understand it. I'm sure this is often the case, but sometimes it's a matter of akrasia: the person knows what they should do and why, even deep down inside, yet finds themselves unable to do it.

Humans suffer heavily from their biases. I recall at in middle school I came to the conclusion that no deities existed, yet it took me a long while to act on it because of social pressures, so I continued to behave contrary to my beliefs out of fear. It was only later in life that I gained the self-confidence and bravery to act upon my beliefs, no matter how contrary to the social norm.

You might say that I didn't really understand and that if I did I would have acted differently, but I find this contrary to my own experience, and this is only one such example. The human brain is a mine field, and even when we understand, we may still fail to act correctly.