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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 reality — but the emotion, the physical neurendocrine experience of betrayal, was quite real. And I've been able to return to it ever since, and if I'm ever in a situation where I might be working from a cached plan, I can relive a hint of it and ask myself, "Now, you don't want to feel that again, do you?"
Unfortunately, this experience strongly ties the five-second skill of "check consequentialism" to the emotion of betrayal in my mind. It is very easy for me to construct social experiments in which the teacher radically betrays her students, and then turns around and says, "Don't let anyone do that to you again!" But that is horrible teaching. It's a lot more difficult for me to imagine what "check consequentialism" would feel like if it carried a strictly positive emotional association, and then extrapolate outward to what kind of social situation would provide that emotional/cognitive link.
Students must abandon a cached plan, and evaluate the real-world consequences of their actions instead, at precisely the moment they get a strong positive emotional charge. Preferably "fun." Preferably in the sense of a party game, not a strategy game: both because people who have learned to win without disrupting social bonds (or who care more about winning than about socialization) have often already learned this skill, and because the moment I construct "winning" as a state which disrupts social bonds, I've set up a false dilemma which misleads my students about what rational thought actually is.
But what's the chain of causation? A dispassionate experimenter times the payoff to correlate with the decision? That seems awfully Pavlovian. Leaving the plan causes a reward which provides an emotional payoff? Maybe, but if a student only leaves the plan in expectation of reward, they haven't actually learned anything beyond the latest professorial password. The excitement of getting the right answer to a puzzle inspires leaving the plan? I suspect this is the way to go. But then what sort of puzzle?
I'm going to press the "Comment" button now, even though I don't think I've contributed much beyond a restatement of your original dilemma. Perhaps having done so, I'll think of some specific scenarios overnight.
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. Not that anybody here could have caught the error, but however much eleven years between events might feel like two decades, it really, really isn't.
Oh, that and for commenting on Luke's post when he specifically asked for emails.
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 enough working nerves to accept any new sensory input, including pain? How likely is it that I'll be able to maintain enough memories to preserve a link to my 2011-era self? How likely is it that my awareness, running on a dying brain, will process thoughts at even a fraction of my current rate?
I suspect that after death, I'll quickly drift into an awareness that's so dreamlike, solipsistic, and time-lapsed that it's a bit iffy calling me an awareness at all. I may last until the end of time, but I won't see or do anything very interesting while I'm there. And no worries about the universe clotting with ghosts: as my entropy increases, I'll quickly become mathematically indistinguishable from everyone else, just as one molecule of hydrogen is very like another.
Quantum immortality is pretty certainly real, but it also has to add up to normality.
(Ooh, I like that first problem. It reframes in all sorts of interesting directions.)
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.
Well, perhaps this answers Yvain's question on the thread above: if we link to the original post, instead of quoting it, then its "next" buttons will work….
Well, how embarrassing. Ten months of lurking and I still hadn't noticed that for myself. Thank you!
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 which Sequence it was part of.
By now I know about the "all posts by year" lists, but as a newbie I couldn't find them. And if I had found them, I wouldn't have known which posts were relevant from their titles alone. I'd have used a naïve all-Eliezer-all-the-time heuristic, and assembled the same list that you're intelligently avoiding.
And … honestly … even if there were a single, coherent, easy to find, chronological list of all Sequence posts … the act of going there, looking up the blog I just finished, and visiting the one beneath it is just the sort of trivial inconvenience that discourages new readers. It's easy, but it's not obvious. We can make it easier.
So as long as we're re-running the Sequences from a template — could there please be a "next" button?
Pray forgive me that I dodge this question. My brother prefers to keep his personal & professional lives separate; now that I've outed myself as his sister on a Googlable forum, I feel awkward identifying precisely whose sister I am.
I didn't like it at all, the first time I read it.
Many years later, after reading and enjoying A Deepness in the Sky, I gave it another try, and this time liked it very much. Even though the books were written in the opposite order, I wonder whether it helps to read Deepness first?
My brother is one of the actors on this show.
This brings me absolutely no inside knowledge or wisdom, but a great deal of pleasure when somebody brings it up on a rationalist message board.
Thank you; I had hit "Show more comments above" without effect, but hadn't referred back to the original post.
pb.com is a site which sells postage meters...?
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 sometimes right on top of you. They can be a good marker for your position, but not for your orientation. You need an orientation marker.
So instead, look in the other direction, the most featureless cardinal direction you can find. Then imagine a huge, fictional geographic element just over the horizon, and tell yourself it's in that direction: living in Edmonton at the time, I used the mantra, "The desert is west."
This is a fictional desert. (Or sea, or taiga, or forest.) It is always west. (Or east, or southeast, or north.) For this process to work, you can't actually pick a real landscape, or it becomes possible to walk around it, at which point your directions are confused again. If you're like me, a fictional landmark will help you orient yourself — but please don't make the mistake of believing it's real.
Now take a few minutes to walk around, keeping the desert in your awareness. Which way are you facing when it's straight ahead? Which way are you facing when it's behind you?
After a remarkably short time, you'll find that you always know where the desert is. And that will tell you where all your directions are. And then you're oriented. And now you can look at that downtown core and notice, "When I am standing at Broadway & Commercial, downtown is to my northwest."
Repeat this process in a few different outdoor locations, and you'll be ready to try it indoors. Just before you walk into a building, note where your imaginary forest is. As you turn corners, keep it in mind. Since the forest is fictional, you've never seen it anyhow; the fact that there are no windows in this university won't matter so much.
Oh, and if you're driving, remember that the centrifugal force you feel is proportional to your speed! The faster you're going, the more quickly you feel as though you're turning — at highway speeds, it takes quite a long time to turn 90 degrees, and a 270-degree cloverleaf seems to go on forever. Unless your city is laid out with perpendicular streets and no freeways, it's a lot easier to orient yourself when you're walking or cycling than when you're driving. On a mountain highway, I'm still lost. I navigate by the sun or use a map.
So…this strategy worked for me. I've never taught it to anybody else; I have no idea which bits of it are necessary and which are superfluous. Although it uses magical thinking, I'll point out that it's easier to imagine a specific, concrete object — like a wide desert just over the horizon — than to imagine an abstract notion like "west." My problem was too much abstraction; this strategy makes the compass real.
Thanks - edited for proper italics.
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 experimental error.
But when I was just 50% confident of a fact, I was almost always wrong. Far more often than anyone could achieve by random guessing: my wrongness was thorough and integrated and systematic.
Clearly, that feeling of slight concern which I've always interpreted as, "I think I remember X, but it could go either way," actually means something closer to, "X is not true; my beliefs are inconsistent."
If I'm sure I know something, I probably do. If I'm sure I'm clueless, I probably am. But if I think I might know something, then I almost certainly have it backwards.
Is this a common bias which I should have read about by now?
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-circles-around-it. Really this is the sort of mistake which could only have happened to me. :)
I'm glad that they're teaching these sort of strategies in US schools. My experience tutoring elementary school math (my son attended an alternative school in which parents all volunteered their own skills & experience) is that every kid has a slightly different conception of how numbers interact. The most important thing I could teach them was that every consistent way of approaching math is correct; if you don't understand the textbook's prescription for subtracting, there are dozens of other right ways to think about the problem; it doesn't matter how you get to the answer as long as you follow the axioms.
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 single point.
I was confused. There was nothing wrong with 11 - 6 = 7. Why would my TA have deducted a point? Everyone knew that 11 - 6 = 7, because it was just the reverse of 7 + 6 = wait-a-minute-here.
Pen. Paper. I grabbed eleven coins and carefully counted six of them away. There were not seven of them left. I started writing down remembered subtraction problems. 11 - 4 = 7. 11 - 5 = 6. 11 - 6 = 7. 11 - 7 = 4. One of these sums was clearly not like the others. I tried addition, and found that both 7 + 6 = 13 and 6 + 7 = 13.
The evidence was overwhelming. I was convinced. Confused, yes—fascinated by where my error could have come from, and how I could have held onto it so long—but convinced. I set to work memorizing 11 - 6 = 5 instead.
It didn't entirely take. Twenty years later, the equation 11 - 6 = 7 still feels so right and familiar and uncontroversial that I've had to memorize 11 - 6 = stop. I know the answer is probably either 5 or 7, but I work it out manually every time.