Once upon a time I scored a 42 on the Putnam. Two decades later I placed 23rd at the World Puzzle Championships. I'd be happy to help if I can.
But honestly? This website holds many mathematicians far better than I. Really I'm replying more from a desire to assuage my own curiosity, than from a strong belief that there exists a problem that uniquely I can solve. All I can promise you is that if I don't know the answer, I'll say so.
ETA: If anything, folks, this comment is worth downvoting for committing terrible math while bragging of being good at it. ...
I generally resolve this issue with the observation that the awareness of misery takes quite a lot of coherent brainpower. By the time my perceptions are 200 years old, I suspect that they won't be running on a substrate capable of very much computational power — that is, once I pass a certain (theoretically calculable) maximum decrepitude, any remaining personal awareness is more likely to live in a Boltzmann brain than in my current body.
You see, after the vast majority of possible worlds perceive that I am dead, how likely is it that I will still have ...
Speaking only for myself: Eliezer's sequences first lured me to Less Wrong, but your posts on decision theory were what convinced me to stick around and keep checking the front page.
I confess I don't understand all of the math. It's been decades since I studied mathematics with any rigour; these days I can follow some fairly advanced theory, but have difficulty reproducing it, and cannot in general extend it. I have had nothing substantial to add, and so I haven't previously commented on one of your posts. Somehow LW didn't seem like the best place to go all fangirl…
It's not only the contributors who are following your work on decision theory. I hope you'll continue to share it with the rest of us.
My own biggest annoyance, after discovering this site last summer and delving into the Sequences, is that it was often very difficult to figure out which post came next.
Finding dependencies was easy — even when there isn't an explicit "Follows:" tag at the start, Eliezer's generosity of hyperlinks meant that I could quickly assemble a screenful of tabs — but whenever I finished a particularly exciting post, especially one I'd reached on the third hyperlink down, I didn't know how to find its follow-up. Early on, I didn't even know how to guess w...
No, nor that they print their own names. They just have to sign their names and date the signature. It's also a good idea to have each of them initial every (numbered) page of your will; this proves that no pages have been inserted or deleted.
When I first started asking how to write a will, a couple of years ago, the best advice I got was to write the will myself — because this is free — and then reread it in a few months. Repeat this process until I couldn't think of anything to add or change. Then visit a lawyer and have them translate it into legalese.
I do not know if this is a practical, general or transferable solution, but it worked for me: throughout my childhood I couldn't orient myself, and I finally taught myself at the age of 24.
Start from a place where you can see quite some distance in all (or most) directions. Outside is best. If you can see, but are not within, a downtown core, you're in a good spot. Ditto mountains, or other tall landmarks.
Now ignore those landmarks. They're untrustworthy. If you can see them, they're close enough that sometimes they'll be north and sometimes west and...
Inspired by your final paragraph, I sought out a variety of test questions on the web -- both on Steven's blog and elsewhere. I was expecting systematic overconfidence, with a smaller chance of systematic underconfidence, throughout the probability spectrum.
Instead I found a very interesting pattern.
When I was 90% or 95% certain of a fact, I was slightly overconfident. My 90% estimates shook out at about 80%, and my 95% estimates shook out around 90%. When I was completely uncertain of a fact, I was also slightly overconfident, but within the realm of e...
Well, it's so much easier and more robust that way! Instead of a long list of confoundingly similar equations, you're left with a single clear understanding of why trigonometry works. After that you can memorize a few formulas as shortcuts if it helps.
Of course this principle completely breaks down when you start working with a child who's already convinced that they can't do math—or with a group of 30 kids at once, a third of whose mathematical intuitions will be far enough from the textbook norm that no one teacher has enough time to guide them through to that first epiphany.
I don't know very much about the American curriculum, having grown up with the Canadian one. But I also didn't pay very much attention in math class. I preferred to read the textbook myself, early in the year, and then play around with as many derivations and theorems as I could figure out, occasionally popping my head above water long enough for a test.
I wrote and memorized my own subtraction tables, and invented a baroque and complicated system for writing negative numbers -- for example, 1 - 2 = 9-with-a-circle-around-it, and 5 - 17 = 8-with-two-circl...
In fact I once had this sort of mathematical experience.
Somehow, while memorizing tables of arithmetic in the first grade, I learned that 11 - 6 = 7. This equation didn't come up very often in elementary school arithmetic, and even more seldom in high school algebra, and so I seldom got any math questions marked wrong. Then one day at university, I received back a Math 300 homework assignment on which I'd casually asserted that 11 - 6 - 7. My TA had drawn a red circle around the statement, punctuating it with three question marks and the loss of a singl...
The day-to-day cognitive skills I've mastered most completely (I will not say "rationalist skills," because this is true of my countless irrational skills too) are the ones which I learned during a moment of strong emotion — any emotion, excitement or curiosity or joy or surprise or depression or fear or betrayal.
In the case of this particular skill, it was betrayal. I brought it on myself — the details aren't important; suffice it that I spent two weeks living in the "should-universe" (I like this term) before a rude reminder of reali... (read more)