I'd meet on June 6 (tentatively). South side is preferable if there are other people down here.

Your Gian-Carlo Rota link talks about tricks used in proofs, which is different from sub-fields of mathematics. It's certainly true that modern mathematicians and scientists are hyperspecialized, but that's not the same thing.

There is a trick for your parenthesized link: hex-escape the parentheses. Here's the link itself: http://graphics8.nytimes.com/images/blogs/freakonomics/pdf/DeliberatePractice%28PsychologicalReview%29.pdf Here are cute fluffy kittens.

Great topic.

Ask someone who has been in a similar situation or solved a similar question or tried to solve a similar question. This may seem obvious, but is often ignored.

Be ready to recognize a bad answer when you see it. Sometimes, what looks like a good answer at the outset develops fatal problems. Don't vest too deeply in your answer. But don't be afraid to keep your answer just because others view it as different or scary.

Expanding on the go meta point:

Solve many hard problems at once

Whatever solution you give to a hard problem should give insight or be consistent with answers given to other hard problems. This is similar in spirit to: "http://lesswrong.com/lw/1kn/two_truths_and_a_lie/" and a point made by Robin Hanson (Youtube link: the point is at 3:31) "...the first thing to do with puzzles is [to] try to resist the temptation to explain them one at a time. I think the right, disciplined way to deal puzzles is to collect a bunch of them: lay them all out on the table and find a small number of hypotheses that can explain a large number of puzzles at once."

His point as I understand was that people often narrowly focus on a limited number of health-related puzzles and that we could produce better policy if we attempted to attack many puzzles at once (consider things such as fear of death, the need to show we care, status-regulation, human social dynamics: particularly signaling loyalty).

Edit: I had originally meant to point out that solving several problems is a meta-thought about solutions to problems: i.e. they should relate to solutions to other problems

From: You and Your Research

When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you.

Here is another mechanism by which status could make you "stupid", although I'm interpreting stupid in a different sense: as in making one less productive than one otherwise might. Although, I think the critique could be more general.

Its generally only worth talking about things that we can make progress in understanding so if you have an inflated sense of what you can accomplish then you might try to think about and discuss things that you cannot advance. So you end up wasting your mental efforts more and you fall behind on other areas that would have been a better use of your talents.

No, you shouldn't make broad inferences about human behaviour without any data because they are consistent with evolution, unless your application of the theory of evolution is so precise and well-informed that you can consistently pass the Two-Truths-and-a-Lie Test.

This sentence could have beneficially ended after "behavior," "data," or "evolution." The last clause seems to be begging the question - why am I assuming the Two-Truths-and-a-Lie Test is so valuable? Shouldn't the test itself be put to some kind of test to prove its worth?

I think this is cross-validation for tests. There have been several posts on Occam's Razor as a way to find correct theories, but this is the first I have seen on cross-validation.

In machine learning and statistics, a researcher often is trying to find a good predictor for some data and they often have some "training data" on which they can use to select the predictor from a class of potential predictors. Often one has more than one predictor that performs well on the training data so the question is how else can one choose an appropriate predictor.

One way to handle the problem is to use only a class of "simple predictors" (I'm fudging details!) and then use the best one: that's Occam's razor. Theorists like this approach and usually attach the word "information" to it. The other "practitioner" approach is use a bigger class of predictors where you tune some of the parameters on one part of the data and tune other parameters (often hyper-parameters if you know the jargon) on a separate part of the data. That's the cross-validation approach.

There's some results on the asymptotic equivalence of the two approaches. But, what's cool about this post is that I think it offers a way to apply cross-validation to an area where I have never heard it discussed (I think, in part, because its the method of the practitioner and not so much the theorist--there are exceptions of course!)

Sorry about that. Our first diavlog was better, IMHO, and included some material about whether rationality benefits a rationalist - but that diavlog was lost due to audio problems. Maybe we should do another for topics that would interest our respective readers. What would you want me to talk about with Scott?

Each element of the set is characterized by a bunch of probabilities; for example there is p_01101, which is the probability that elements x_{i+1} through x_{i+5} are 01101, for any i. I was thinking of using the topology induced by these maps (i.e. generated by preimages of open sets under them).

How is putting a noninformative prior on the reals hard? With the usual required invariance, the uniform (improper) prior does the job. I don't mind having the prior be improper here either, and as I said I don't know what invariance I should want; I can't think of many interesting group actions that apply. Though of course 0 and 1 should be treated symmetrically; but that's trivial to arrange.

I guess you're right that regularities can be described more generally with computational models; but I expect them to be harder to deal with than this (relatively) simple, noncomputational (though stochastic) model. I'm not looking for regularities among the models, so I'm not sure how a computational model would help me.

Thanks much!

and one has chosen a prior for those parameters such that there is non-zero weight on the true values then the Bernstein-von Mises theorem guarantees that the Bayesian posterior distribution and the maximum likelihood estimate converge to the same probability distribution (although you may need to use improper priors)

What do "non-zero weight" and "improper priors" mean?

EDIT: Improper priors mean priors that don't sum to one. I would guess "non-zero weight" means "non-zero probability". But then I would wonder why anyone would introduce the term "weight". Perhaps "weight" is the term you use to express a value from a probability density function that is not itself a probability.