Richard Feynmann claimed that he wasn't exceptionally intelligent, but that he focused all his energies on one thing. Of course he was exceptionally intelligent, but he makes a good point.

I think one way to improve your intelligence is to actually try to understand things in a very fundamental way. Rather than just accepting the kind of trite explanations that most people accept - for instance, that electricity is electrons moving along a wire - try to really find out and understand what is actually happening, and you'll begin to find that the world is very different from what you have been taught and you'll be able to make more intelligent observations about it.

http://www.reddit.com/r/askscience/comments/e3yjg/is_there_any_way_to_improve_intelligence_or_are/c153p8w

reddit user jjbcn on trying to improve your intelligence

If you're not a student of physics, The Feynman Lectures on Physics is probably really useful for this purpose. It's free for download!

http://www.feynmanlectures.caltech.edu/

It seems like the Feynman lectures were a bit like the Sequences for those Caltech students:

The intervening years might have glazed their memories with a euphoric tint, but about 80 percent recall Feynman's lectures as highlights of their college years. “It was like going to church.” The lectures were “a transformational experience,” “the experience of a lifetime, probably the most important thing I got from Caltech.” “I was a biology major but Feynman's lectures stand out as a high point in my undergraduate experience … though I must admit I couldn't do the homework at the time and I hardly turned any of it in.” “I was among the least promising of students in this course, and I never missed a lecture. … I remember and can still feel Feynman's joy of discovery. … His lectures had an … emotional impact that was probably lost in the printed Lectures.”

One useful definition of Bayesian vs Frequentist that I've found is the following. Suppose you run an experiment; you have a hypothesis and you gather some data.

• if you try to obtain the probability of the data, given your hypothesis (treating the hypothesis as fixed), then you're doing it the frequentist way
• if you try to obtain the probability of the hypothesis, given the data you have, then you're doing it the Bayesian way.

I'm not sure whether this view holds up to criticism, but if so, I sure find the latter much more interesting than the former.

This has been the most fun, satisfying survey I've ever been part of :) Thanks for posting this. Can't wait to see the results!

One question I'd find interesting is closely related to the probability of life in the universe. Namely, what are the chances that a randomly sampled spacefaring lifeform would have an intelligence similar enough to ours for us to be able to communicate meaningfully, both in its "ways" and in general level of smarts, if we were to meet.

Given that I enjoyed taking part in this, may I suggest that more frequent and in-depth surveys on specialized topics might be worth doing?

Maybe we've finally reached the point where there's no work left to be done

If so, this is superb! This is the end goal. A world in which there is no work left to be done, so we can all enjoy our lives, free from the requirement to work.

The thought that work is desirable has been hammered into our heads so hard that it's a really, really dubious proposition that actually a world where nobody has to work is the ultimate goal. Not one in which everyone works. That world sucks. That's world in which 85% of us live today.

I've first read this about two years ago and it has been an invaluable tool. I'm sure it has saved countless hours of pointless arguments around the world.

When I realise that an inconsistency in how we interpret a specific word is a problem in a certain argument and apply this tool, it instantly transforms arguments which actually are about the meaning of the word to make them a lot more productive (it turns out it can be unobvious that the actual disagreement is about what a specific word means). In other cases it just helps get back on the right track instead of getting distracted by what we mean when we say a certain word that is actually beside the point.

It does occasionally take a while to convince the other party to the argument that I'm not trying to fool or trick them when I ask for us to apply this method. Another observation is that the article on Empty Labels has transformed my attitude towards the meaning of words, so when it turns out we disagree about meanings, I instantly lose interest and this can confuse the other party.

But we know from basic probability theory that for two independent random variables, E(X/Y) > 1 does actually imply E(X) > E(Y).

This does not follow; a counterexample:

Suppose X and Y are independent random variables, with X taking the values {2,100}, and Y the values {1,150}, each with equal probability (i.e., each of X and Y follows the Bernoulli distribution with p = 0.5). Then we have
E(X/Y) = (2/1 + 100/1 + 2/150 + 100/150) / 4 = 25.67 > 1,
but
E(X) = 51 < 75.5 = E(Y).

Keep in mind that the equation E(1/Y) = 1/E(Y) does not hold in general, because taking the inverse is not a linear transformation. To evaluate the expectation after a nonlinear transformation, one requires not just the orignal expectation, but also the pdf of the distribution. (I can't be sure this is what you did, but misapplying this gives: E(X/Y) = E(X)E(1/Y) = E(X)/E(Y). The first equality holds if X and Y are independent or by definition if X and 1/Y are uncorrelated, but the second equality does not hold in general.)

It is aimed at people with only basic command of probabilities

Such people have probably not heard of the two envelopes problem and thus the title is not informative for them.* It seems to me that it would be useful to put something in the title to indicate that this post is about probabilities and maybe that it is fairly introductory. I could be wrong about how people read this site. Maybe everyone clicks through to the article and reads as far as the italicized section, but it seems low cost to give it a more informative title.

* Also, I doubt that people who do associate "two envelopes" with probability are not very likely to think of this particular problem, for what it's worth.

Added: "this site" = discussion. If the plan is to move this to main, the structure makes more sense. But I still think the title could be better.

Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars.

Seems to me the language of this rules out faked video. And to explain it as a newsletter scam would, I think, require postulating 2^100 civilizations that have contact with Omega but not each other. Note that we already have some reason to believe that a powerful and rational observer could predict our actions early on.

So you tell me what we should expect here.

Why is it important to you that the success rate be a frequentialist probability rather than just a bayesian one?

Assume no "future peeking" and Omega only correctly predicting people as difficult to predict as you with 99.9% probability. One-boxing still wins.