Is there a good way for me to know if I'm actually any good at anything?

I recommend empirical reality. The kind that exists outside of your (and other people's) head.

Having followed your posts here and on #lesswrong, I got an impression of your personality as a bizarre mix of insecurities and narcissism (but without any malice), and this comment is no exception. You are certainly in need of a few sessions with a good therapist, but, judging by your past posts, you are not likely to actually go for it, so that's a catch 22. Alternatively, taking a Dale Carnegie course and actually taking its lessons to heart and putting an effort into it might be a good idea. Or a similar interpersonal relationship course you can find locally and afford.

Some things are easier to tell whether you're good at than others. I guess you aren't talking about the more assessable things (school/university studies, job, competitive sport, weightlifting, ...) but about things with a strong element of judgement (quality as a friend or lover, skill in painting, ...) or a lot of noise mixed with any signal there might be (stock-picking[1], running a successful startup company, ...).

[1] Index funds are the canonical answer to that one, but you know that already.

So, anyway, the answer to "how do I tell if I'm any good at X?" depends strongly on X.

But maybe you really mean not "(know if I'm actually any good at) anything" but know if I'm actually (any good at anything)" -- i.e., the question isn't "am I any good at X?" but "is there anything I'm any good at?". The answer to that is almost certainly yes; if someone is seriously suggesting otherwise then they are almost certainly dishonest or stupid or malicious or some combination of those, and should be ignored unless they have actual power to harm you; if some bit of your brain is seriously suggesting otherwise then you should learn to ignore it.

There are almost certainly specific X you have good evidence of being good at, which will imply a positive answer to "is there anything I'm good at?". Pick a few, inspect them as closely as you feel you have to to be sure you aren't fooling yourself, and remember the answer.

If someone else is declaring publicly that you are a pretentious idiot and full of shit, it is likely that what's going on is not at all that they're trying to make an objective assessment of your capabilities or character, but that they are engaged in some sort of fight over status or influence or something, and are saying whatever seems like it may do damage. I expect you have good reasons for getting into that sort of fight, so I'll just say: bear in mind when you do that this is a thing that happens, and that such comments are usually not useful feedback for self-assessment.

If you want to mention some specific X, I expect you'll get some advice on ways to assess whether you're any good at it/them. But I think the most important thing here is that the thing that's provoking your self-doubt, although it looks like an assessment of your capabilities, really isn't any such thing.

You could take a cognitive psych approach to some of this. What are the other person's qualifications?

I recommend exploring the concept of good enough.

There's a bit in Nathaniel Branden about "a primitive sense of self-affirmation"-- which I take to be the assurance that babies start out with that they get to care about their pain and pleasure. It isn't even a question for them. And animals are pretty much the same.

You don't need to have a right to be on your own side, you can just be on your own side.

Something I've been working on is getting past the idea that the universe is keeping score, and I have to get everything right.

What I believe about your situation is that you've been siding with your internal attack voice, and you need to associate your sense of self with other aspects of yourself like overall physical sensations.

Do you have people who are on your side? If so, can you explore taking their opinion seriously?

The attack voice comes on so strong it seems like the voice of reality, but it's just a voice. I've found that it's hard work to change my relationship to my attack voice, but it's possible.

For what it's worth, I think your prose is good. It's clear, and the style (as distinct from the subject matter) is pleasant.

The purpose of the Templeton Foundation is [...] to try to blur the lines between science and religion and corrupt the public discourse.

What's your basis for this interpretation? And particularly the "corrupt the public discourse" bit? I read your link, and I remember it getting briefly badmouthed in The God Delusion, but I'd prefer something a little more solid to go on, since this seems to lie on the sharp side of Hanlon's razor.

Evolutionary Psychology: The New Science of the Mind, by David Buss is a pretty good, mainstream, and accessible introduction to the field. I don't regret reading it.

I found TMA was too full of just so stories. I also think it disturbingly rationalized a particular brand of sexism$ and overemphazised status which was very unexpected since I don't think I'm squeamish at all on those fronts. I don't think it helped me to predict human behavior better.

This said I'd be interested too if someone could recommend some other book.

$ rigid view of differences between the sexes, incompatible with my experience (which does suggest the sexes are different)

She understood the concept quickly, but it would be much more reliable and eloquent to actually define it.

You think she would've understood the concept even more quickly if you had a definition? I think people underestimate the value of showing people examples as a way of communicating a concept (and overestimate the value of definitions).

To a "regular person", I might say something like "a logical fallacy is a form of reasoning that seems good to many humans, but actually isn't very good".

I don't think this is so simple to explain, because to really understand logical fallacies you need to understand what a proof is. Not a lot of people understand what a proof is.

I think the big fear is stasis. In each case you're put in a certain state of being without any recourse to get out of it, but wireheading seems to be like a state of living death.

Speaking for myself, I consider wireheading to be very negative, but better than information-theoretic death, and better than a number of scenarios I can think of.

I would assume that it's considered worse than death by some because with death it's easier to ignore the opportunity cost. Wireheading makes that cost clearer, which also explains why it's considered negative compared to potential alternatives.

1. People can change (e.g. update on beliefs, self-improve).
2. How to choose your actions - think about your goals, think what steps achieve them in the best way, act on those steps.
3. There is such a thing as objective truth.

Amazing how the basic pillars of rationality are things other people so often don't agree with, even though they seem so dead obvious to me.

You can frequently make your life better by paying attention to what you're doing, looking for possible improvements, trying your ideas, and observing whether the improvements happen.

I run on hardware that was optimized by millions of years of evolution to do the sort of things my ancestors did tens of thousands of years ago, not the sort of things I do now.

There is no magic.
I am not in a story.
Words are detachable handles.

This is a fun exercise. The list could be a lot longer than I originally expected.

• belief is about evidence
• 0 and 1 are not probabilities
• Occam's razor
• strawman and steelman
• privileging the hypothesis
• tabooing
• instrumental-terminal distinction of values
• don't pull probabilities out of your posterior
• introspection is often wrong
• intuitions are often wrong
• general concept of heuristics and biases
• confirmation and disconfirmation bias
• halo effect
• knowing about biases doesn't unbias you
• denotations and connotations
• many more

Yes by judging someone on their credentials in other fields, you can't tell if they are just making stuff up on this subject vs. studied it for 15 years.

Wells's book: Apocalypse when.

I took a quick skim through the book. Your focused criticism of Wells's book is somewhat unfair. The majority of the book (ch. 1–4) is about a survival analysis of doomsday risks. The scenario you quoted is in the last chapter (ch. 5), which looks like an afterthought to the main intent of the book (i.e., providing the survival analysis), and is prepended by the following disclaimer:

This set serves as a foil to the balanced discussions by Rees, Leslie, Powell, and others. The choice of eight examples is purely arbitrary. Their purpose is not orderly coverage but merely examples that indicate a range of possibilities. The actual number of such complex unorthodox scenarios is virtually infinite, hence the high risk.

I think it is fair to criticize the crackpot scenario that he gave as an example, but your criticism seems to suggest that his entire book is of the same crackpot nature, which it is not. It is unfortunate that PR articles and public attention focuses on the insubstantial parts of the book, but I am sure you know what that is like as the same occurs frequently to MIRI/SIAI's ideas.

Orthogonal notes on the book's content: Wells seems unaware of Bostrom's work on observation selection effects, and it appears that he implicitly uses SSA. (I have not carefully read enough of his book to form an opinion on his analysis, nor do I currently know enough about survival analysis to know whether what he does is standard.)

Yes, I'm an academic and I get a similar reaction from telling people I study the Singularity as when I say I've signed up for cryonics. Thankfully, I have tenure.

Academic futurism has low status. This causes people interested in futurism to ignore those academics and instead listen to people who talk about futurism after gaining high status via focusing on other topics. As a result, the people who are listened to on the future tend to be amateurs, not specialists. And this is why "we" know a lot less about the future than we could.

I don't think that's the case. Most people who are listened to on the future don't tend to speak to an audience primarily consisting of futurists.

There are think tanks who employee people to think about the future and those think tanks tend generally to be quite good at influencing the public debate.

I also don't think that academic has any special claim to be specialists about the future. When I think about specialists on futurism names like Stewart Brand or Bruce Sterling.

It might be a worthwhile endeavor to modify our wiki such that it serves not only as a mostly local reference on current terms and jargon, but also as an independent guide to the various arguments for and against various concepts, where applicable. It could create a lot of credibility and exposure to establish a sort of neutral reference guide / an argument map / the history and iterations an idea has gone through, in a neutral voice. Ideally, neutrality regarding PoV works in favor of those with the balance of arguments in their favor.

This need not be entirely new material, but instead simply a few mandatory / recommended headers in each wiki entry, pertaining to history, counterarguments etc. Could be worth it lifting the wiki from relative obscurity, with a new landing page, and marketed potentially as a reference guide for journalists researching current topics. Kruel's LW interview with Shane Legg got linked to in a NYTimes blog, why not a suitable LW wiki article, too?

I do this all the time and it's great!

While you're at it, you probably should also research how much water is too much, because on the other side of the spectrum lies hyponatremia and having suboptimal electrolyte levels from overdosing water could be harmful to your cognition too, although I think it's unlikely anyone here will develop a measurable hyponatremia just from drinking too much water. Sweating a lot for example might change the situation.

this definitely seems like something that's worth researching more because it literally affects every single day of your life

This doesn't look like a selective enough heuristic alone.

More frequent water-drinking makes you urinate more often, which is probably a bad thing for productivity.

Extended sedentary periods are bad for you, so if drinking extra water also makes you get up and walk to the bathroom, that's a win-win.

As far as water consumption goes I feel the difference between drinking one liter or four liter per day. I just feel much better with four liter.

There were times two years ago when unless I had drunk 4 liter by the time I entered my Salsa dancing location in the evening, my muscle coordination was worse and the dancing didn't flow well.

Does that mean that everyone has to drink 4 liters to be at his optimum? No, it doesn't. Get a feel how different amounts of water consumption effect you. For me the effect was clear to see without even needing to do QS. Even it's not as clear for you do QS.

Thanks for writing this up.

this definitely seems like something that's worth researching more because it literally affects every single day of your life

Lots of things fall in to this category :)

"A person's body, during an average day in a temperate climate such as the United Kingdom, loses approximately 2.5 litres of water.[citation needed]"

In case it's not obvious: this probably means in the absence of food/fluid consumption. You can't go on losing 2.5 litres of water a day indefinitely.

This, maybe?

http://lesswrong.com/lw/7k/incremental_progress_and_the_valley/

I'd like to know how many techniques you were taught at the meetup you still use regularly. Also which has had the largest effect on your life.

Romeo Stevens made this comprehensive doc.

Eating a handful of nuts a day.

"Scientists from Dana-Farber Cancer Institute, Brigham and Women's Hospital, and the Harvard School of Public Health came to this conclusion after analyzing data on nearly 120,000 people collected over 30 years."

"The most obvious benefit was a reduction of 29 percent in deaths from heart disease - the major killer of people in America. But we also saw a significant reduction - 11% - in the risk of dying from cancer."

http://www.medicalnewstoday.com/articles/269206.php

I found this list of causes of death by age and gender enlightening (it doesn't necessarily tell you that a particular action will increase your lifespan, but then again neither do correlations). For example, I was surprised by how often people around my age or a bit older die of suicide and "poisoning" (not sure exactly what this covers but I think it covers stuff like alcohol poisoning and accidentally overdosing on medicine?).

Is there a reasonably well researched list of behaviors that correlate positively with lifespan?

Depends on what you'd call "well-researched" but, unfortunately, most of it is fuzzy platitudes. For example:

• Do physical exercise. But not too much.
• Be happy, avoid stress.
• Get happily married.
• Don't get obese.

and most importantly

• Choose your parents well, their genes matter :-P

That's known as Strawman Has A Point (Warning: TVTropes).

Hidden Markov models are a reasoning model to solve a specific problem. If you don't face that specific problem they are no use.

Most of the problems we discuss aren't modeled well with HMMs.

I think for most people who ask this question, the range of fitting jobs is much wider than they think. You learn to like what you become good at.

If I were to pick a career right now, I'd just take a long list of reasonably complex jobs and remove any that contain an obvious obstacle like a skill requirement I'm unlikely to improve at. Then from what is left, I'd narrow the choice by some other criteria than perceived fit, income and future employment prospects for example and then pick one of them either by some additional criteria or randomly. I'm confident I'd learn to like almost any job chosen this way.

If you make money you can do whatever you like in the future even if you chose your job poorly in the first place. So please don't choose to become an English major.

Is there a good way of finding what kind of job might fit a person?

That's a strange question.

Either you want to know how to pick up the skill of being a career adviser. Alternatively you want to find a job for yourself. You might also be a parent who tries to find a job that fits his child instead of letting the child decide for themselves.

I think the answers to those three possibilities are very different.

Not much. The kind of probability relevant to MIRI's interests is not the kind of probability you need calculus to understand (the random variables are usually discrete, etc.). The closest thing to needing a calculus background is maybe numerical analysis (I suspect it would be helpful to at least have the intuition that derivatives measure the sensitivity of a function to changes in its input), but even then I think that's more algorithms. Not an expert on numerical analysis by any means, though.

If you have a general interest in mathematics, I still recommend that you learn some calculus because it's an important foundation for other parts of mathematics and because people, when explaining things to you, will often assume that you know calculus after a certain point and use that as a jumping-off point.

Do you have any material for dealing with chronic pain? Or material that could conceivably be leveraged to apply to chronic pain management?

In my experience memorization often comes for free when you strive for fluency through repetition. You end up remembering the quadratic formula after solving a few hundred quadratic equations. Same with the trig identities. I probably still remember all the most common identities years out of school, owing to the thousands (no exaggeration) of trig problems I had to solve in high school and uni. And can derive the rest in under a minute.

Memorization through solving problems gives you much more than anki decks, however: you end up remembering the roads, not just the signposts, so to speak, which is important for solving test problems quickly.

You are right that "the reduction in mental effort required on basic operations will rapidly compound to allow for much greater fluency with harder problems", I am not sure that anki is the best way to achieve this reduction, though it is certainly worth a try.

In general there the core principle of spaced repetition that you don't put something into the system that you don't already understand.

When trying to memorize mathematical results make sure that you only add cards when you really have a mental understanding. Using Anki to avoid forgetting basic operations is great. If you however add a bunch of information that's complex, you will forget it and waste a lot of time.

Nice, and good luck! I'm glad to see that my post resonated with someone. For rhetorical purposes, I didn't temper my recommendations as much as I could have -- I still think building mental models through deliberate practice in solving difficult problems is at the core of physics education.

I treat even "signpost" flashcards as opportunities to rehearse a web of connections rather than as the quiz "what's on the other side of this card?" If an angle-addition formula came up, I'd want to recall the easy derivation in terms of complex exponentials and visualize some specific cases on the unit circle, at least at first. I also use cards like that in addition to cards which are themselves mini-problems.

Huh. I followed the link to the correction of the Petrov story, and found I'd already upvoted it.

But if you'd asked me yesterday for examples of heroes yesterday, I'd have cited Petrov immediately. S

hows how hard it is to unlearn false information once you've learned it.

On September 26, 1983, Soviet officer Stanislav Petrov saved the world. (Nov 2011)

Eh, not really.

The Wiki link in the linked LW post seems to be closer to "Stanislav Petrov saved the world" than "not really":

Petrov judged the report to be a false alarm, and his decision is credited with having prevented an erroneous retaliatory nuclear attack

...

His colleagues were all professional soldiers with purely military training and, following instructions, would have reported a missile strike if they had been on his shift.

...

Petrov, as an individual, was not in a position where he could single-handedly have launched any of the Soviet missile arsenal. ... But Petrov's role was crucial in providing information to make that decision. According to Bruce Blair, a Cold War nuclear strategies expert and nuclear disarmament advocate, formerly with the Center for Defense Information, "The top leadership, given only a couple of minutes to decide, told that an attack had been launched, would make a decision to retaliate."

A closely related article says:

Petrov's responsibilities included observing the satellite early warning network and notifying his superiors of any impending nuclear missile attack against the Soviet Union. If notification was received from the early warning systems that inbound missiles had been detected, the Soviet Union's strategy was an immediate nuclear counter-attack against the United States (launch on warning), specified in the doctrine of mutual assured destruction.

That he didn't literally have his finger on the "Smite!" button, or that the SU might still not have retaliated if he'd raised the alarm, is not the point.

Smart move not only to review but post the results. Shows humbleness and at the same time prevents being called on it later.

This is an approach I'd like to see more often. Maybe you should add it to the http://lesswrong.com/lw/h7d/grad_student_advice_repository/ or some such.

previous eras' low life expectancy was mostly due to high child mortality.

I have long thought that the very idea of "life expectancy at birth" is a harmful one, because it encourages exactly that sort of confusion. It lumps together two things (child mortality and life expectancy once out of infancy) with sufficiently different causes and sufficiently different effects that they really ought to be kept separate.

Sexy is a quite broad word that probably used by different people in different ways. I think for most people it about what they feel when looking at the person. Those feeling where set up by evolution over large time frames.

Evolution doesn't really care about whether you get a fun intercourse partner.

But it's not only evolution. It also has a lot to do with culture. Culture also doesn't care about whether you get a fun intercourse partner. People who watch a lot of TV get taught that certain characteristics are sexy.

For myself I would guess that most of my cultural imprint regarding what I find sexy comes from dancing interactions. If a woman moves in a way that suggests that she doesn't dance well, that will reduce her sex appeal to me more than it probably does with the average male.

"Sexy" isn't signaling -- it's a characteristic that people (usually) try to signal, more or less successfully. "I'm sexy" basically means "You want me" : note the difference in subjects :-)

Being sexy signals health, youth, and fertility. This is quite well supported by evidence and discussed in many books and articles.

I would agree with what Lumifer says below, but I think sexy can be signalling when many people are involved: look at the sexy people I hang out with. Being with sexy people brings high status because it's high status.

I think this feeling arises from social norms feeling unnatural to you. This feeling should be expected if your interests are relevant to this site, since people are not trying to be rational by default.

The difference between a pathetic misfit and and an admirable eccentric is their level of awesomeness. If you become good enough at anything relevant to other people, you don't have to live through their social expectations. Conform to the norms or rise above them.

Note that I think most social norms are nice to have, but this doesn't mean there aren't enough of the kind that make me feel alienated. It could be that the feeling of alienation is a necessary side effect of some beneficial cognitive change, in which case I'd try to cherish the feeling. I've found that rising to a leadership position diminishes the feeling significantly, however.

I think that feeling is more common than you might think. Especially if you deviate enough from the societal norm (which Less Wrong generally does).

My general strategy for dealing with is social interaction with people who'll probably understand. Just talk it over with them. It's best if you do this with people you care about. It doesn't have to be in person, if you've got someone relevant on Skype, that works as well.

Does anyone else experience the feeling of alienation?

But of course.

And does anyone have a good strategy for dealing with it?

Accept that you're not average and not even typical.

Feeling usually become a problem when you resist them.

My general approach with feelings:

1. Find someone towards which you can express the content behind the feeling. This works best in person. Online communication isn't good for resolving feelings. Speak openly about whatever comes to mind.

2. Track the feeling down in your body. Be aware where it happens to be. Then release it.

Yes, although it would help if you could be a bit more specific, the term is somewhat overloaded.

As for the strategy, depends. Find a better community (than the one you feel alienated from) in the sense of better matching values? We both seem to feel quite at home in this one (for me, if not for the suffocating supremacy of EA).

I have experienced this also, though roughly a month ago, after an extended debate on trans* issues specifically.

I responded by messaging the person I had argued with, and politely asking that, if it was them who had been downvoting me, they please stop going through my comment history. I got no response, but the stream of downvotes seemed to tail off shortly thereafter.

EDIT: As a side note, the person with whom I had been debating/arguing was the same one that showed up in the thread ChrisHallquist linked. It looks like it's a pattern of behavior for him.

I got a seemingly one-time hit of this about a week ago. For what it's worth I had just been posting comments on the subject of rape, but a whole bunch of my unrelated comments got it too.

(Since then it's been having an obnoxious deterrent effect on my commenting, because I feel so precariously close to just accumulating negative karma every time I post, leaving readers with the impression that my ideas have all been identified as worthless by someone probably cleverer than themselves. I'm now consciously trying to avoid thinking like this)

For context, link to past discussion of mass-downvoting.

A quick look at the first page of your recent comments shows most of your recent activity to have been in the recent "Is Less Wrong too scary to marginalized groups?" firestorm.

One of the most recent users to complain about mass downvoting also cited participation in flame-bait topics (specifically gender).

Gah... This is becoming way too common, and it seems like there's pretty good evidence (further supported in this instance) regarding the responsible party. I wish someone with the power to do so would do something about it.

I don't know what you mean precisely by confusion, but I personally can't always control what my immediate primal level response is to certain situations. If I try to strictly avoid certain feelings, I usually end up convincing myself that I'm not feeling that way when actually I am. I'd rather notice what I'm feeling and then move on from there, it's probably easier to control your thinking that way. Just because you're angry doesn't mean you have to act like angry.

Heretical? Well, considering that 'heretic' means 'someone who thinks on their own', I'm not sure how we're supposed to interpret that negatively.

I assume however that you meant 'disagreeing with common positions displayed on LW' - which of those common positions did you differ on, and why, and just how homogeneous do you think LW is on those?

A, which grants -100 utilons with 99.9% chance and +10000 utilons with 0.1%

A has an expected utility of +900.1 utilons

Um, A actually has a utility of -89.9.

That explains why it seems less appealing!

I think the non-intuitive nature of the A choice is because we naturally think of utilons as "things". For any valuable thing (money, moments of pleasure, whatever) anybody who is minimally risk adverse would choose B. But utllons are not things, they are abstractions defined by one's preferences. So that A is the rational choice is a tautology, in the standard versions of utility theory.

It may help to think it the other way around, starting from the actual preference. You would choose a 99.9% chance of losing ten cents and 0.1% chance of winning 10000 dollars over winning one cent with certainty, right? So then perhaps, as long as we don't think of other bets and outcomes, we can map winning 1 cent to +1 utilon, losing 10 cents to -100 utilons and winning 10000 dollars to +10000 utilons. Then we can refine and extend the "outcomes <=> utilons" map by considering your actual preferences under more and more bets. As long as your preferences are self-consistent in the sense of the VNM axioms, then there will a mapping that can be constructed.

ETA: of course, it is possible that your preferences are not self-consistent. The Allais paradox is an example where many people's intuitive preferences are not self-consistent in the VNM sense. But constructing such a case is more complicated that just considering risk-aversion on a single bet.

I'd flip that around. Whatever action you end up choosing reveals what you think has highest utility, according to the information and utility function you have at the time. It's almost a definition of what utility is - if you consistently make choices that rank lower according to what you think your utility function is, then your model of your utility function is wrong.

If the utility function you think you have prefers B over A, and you prefer A over B, then there's some fact that's missing from the utility function you think you have (probably related to risk).

I've recently come to terms with how much fear/anxiety/risk avoidance is in my revealed preferences. I'm working on working with that to do effective long-term planning -- the best trick I have so far is weighing "unacceptable status quo continues" as a risk. That, and making explicit comparisons between anticipated and experienced outcomes of actions (consistently over-estimating risks doesn't help any, and I've been doing that).

This might have been a good call 10 years ago but nowadays Eliezer is participating in regular face to face meetings with skilled mathematicians and scientists in the context of constructing and analyzing theorems and decision strategies. This means that for a large amount of the people who are most important to convince, he gets to screen out all the "evidence" of not having a degree. And to a large extent, someone having the respect of a bunch of math phds is more important a qualifier of talent than having that phd themselves.

There's theoretically still the problem of selling Eliezer to the muggles but I don't think that's anywhere near as important as getting serious thinkers on board.

4 years (or even 1 year if you are super hard-core) of time is a pretty non-trivial investment. I was 2 classes away from a second degree and declined to take them, because the ~100 hours of work it would have taken wasn't worth the additional letters after my name. I also just really don't know anyone relevant who thinks that a college degree or lack thereof particularly matters (although the knowledge and skills acquired in the course of pursuing said degree may matter a lot). Good people will judge you by what you've done to demonstrate skill, not based on a college diploma.

I think IlyaShpitser's comment pretty much nails it.

Has anyone toyed around with the idea of sending him off to get a math degree somewhere?

I think the bigger issue w/ people not taking EY seriously is he does not communicate (e.g. publish peer reviewed papers). Facebook stream of consciousness does not count. Conditional on great papers, credentials don't mean that much (otherwise people would never move up the academic status chain).

Yes it is too bad that writing things down clearly takes a long time.

Here's your tuition and an extra sum of money to cover the opportunity cost of your time

If you buy into the “crunch time” narrative, that's a lot of opportunity cost.

I don't think you understand signaling well.

Eliezer managed signaling well enough to get a billionaire to fund him on his project. A billionaire who fund people who drop out of college systematically in projects like his 20 Under 20 program.

Trying to go the traditional route wouldn't fit into the highly effective image that he already signals.

I don't think that's really what means are. That intuition might fit the median better. One reason means are nice is that they have really nice properties, e.g. they're linear under addition of random variables. That makes them particularly easy to compute with and/or prove theorems about. Another reason means are nice is related to betting and the interpretation of a mean as an expected value; the theorem justifying this interpretation is the law of large numbers.

Nevertheless in many situations the mean of a random variable is a very bad description of it (e.g. mean income is a terrible description of the income distribution and median would be much more appropriate).

Edit: On the other hand, here's one very undesirable property of means: they're not "covariant under increasing changes of coordinates," which on the other hand is true of medians. What I mean is the following: suppose you decide to compute the mean population of all cities in the US, but later decide this is a bad idea because there are some really big cities. If you suspect that city populations grow multiplicatively rather than additively (e.g. the presence of good thing X causes a city to be 1.2x bigger than it otherwise would, as opposed to 200 people bigger), you might decide that instead of looking at population you should look at log population. But the mean of log population is not the log of mean population!

On the other hand, because log is an increasing function, the median of log population is still the log of median population. So taking medians is in some sense insensitive to these sorts of decisions, which is nice.

As a first step, I suggest Dennis Lindley's Understanding Uncertainty. It's written for the layperson, so there's not much in the way of mathematical detail, but it is very good for clarifying the basic concepts, and covers some surprisingly sophisticated topics.

ETA: Ah, I didn't notice that Benito had already recommended this book. Well, consider this a second opinion then.

Read Edwin Jaynes.

The problem with most Probability and Statistics courses is the axiomatic approach. Purely formalism. Here are the rules - you can play by them if you want to.

Jaynes was such a revelation for me, because he starts with something you want, not arbitrary rules and conventions. He builds probability theory on basic desiredata of reason that you that make sense. He had reasons for my "whys?".

Also, standard statistics classes always seemed a bit perverse to me - logically backward. They always just felt wrong. Jaynes approach replaced that tortured backward thinking with clear, straight lines going forward. You're always asking the same basic question "What is the probability of A given that I know B?"

And he also had the best notation. Even if I'm not going to do any math, I'll often formulate a problem using his notation to clarify my thinking.

I too spent a few years with a similar desire to understand probability and statistics at a deeper level, but we might have been stuck on different things. Here's an explanation:

Suppose you have 37 numbers. Purchase a massless ruler and 37 identical weights. For each of your numbers, find the number on the ruler and glue a weight there. You now have a massless ruler with 37 weights glued onto it.

Now try to balance the ruler sideways on a spike sticking out of the ground. The mean of your numbers will be the point on the ruler where it balances.

Now spin the ruler on the spike. It's easy to speed up or slow down the spinning ruler if the weights are close together, but more force is required if the weights are far apart. The variance of your numbers is proportional to the amount the ruler resists changes to its angular velocity -- how hard you have to twist the ruler to make it spin, or to make it stop spinning.

"I'd like to understand this more deeply" is a thought that occurs to people at many levels of study, so this explanation could be too high or low. Where did my comment hit?