Comment author: Armok_GoB 14 April 2011 12:31:26PM *  10 points [-]
Comment author: Osmium_Penguin 15 April 2011 01:08:32AM 9 points [-]

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.

Comment author: Alicorn 23 February 2011 05:30:18PM 0 points [-]

In context it means Prediction Book.

Comment author: Osmium_Penguin 23 February 2011 05:32:20PM 0 points [-]

Thank you; I had hit "Show more comments above" without effect, but hadn't referred back to the original post.

In response to comment by [deleted] on New Year's Predictions Thread (2011)
Comment author: gwern 23 February 2011 05:11:51PM *  0 points [-]

Prediction closed as correct on PredictionBook.com (see other comment for link).

EDIT

Comment author: Osmium_Penguin 23 February 2011 05:27:14PM 0 points [-]

pb.com is a site which sells postage meters...?

Comment author: Alicorn 08 February 2011 05:08:25AM 1 point [-]

Have the witnesses write "witness" next to their signatures.

Is it actually important that the witnesses be the ones to write "witness"? If so, why?

Comment author: Osmium_Penguin 08 February 2011 06:51:03AM 9 points [-]

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.

Comment author: afeller 08 February 2011 04:49:31AM 5 points [-]

I've always assumed that this is something inborn instead of learned -- hopefully, that assumption (which come to think of it I've never really questioned) is wrong -- but I have a very hard time orienting myself. When I'm walking up the stairwell in my apartment, I have no idea whether I am walking towards the road, away from the road, or perpendicular to it. I can sit down with a pencil and paper and draw it and figure it out by looking at it from a 'birds eye' perspective. But when I'm standing in a room with opaque walls and trying to imagine what room is on the other side, I just get really confused.

Comment author: Osmium_Penguin 08 February 2011 06:45:11AM 10 points [-]

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.

Comment author: orthonormal 10 January 2011 02:42:57AM 1 point [-]

Interesting!

By the way, HTML tags don't work here; click "Help" to the lower right of the edit window to see the Markup syntax rules.

Comment author: Osmium_Penguin 10 January 2011 06:27:45PM 0 points [-]

Thanks - edited for proper italics.

Comment author: Osmium_Penguin 10 January 2011 02:15:38AM *  4 points [-]

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?

Comment author: NancyLebovitz 03 August 2010 04:31:06PM 2 points [-]

I never bothered to memorize trig equivalences. Instead, I just reduced sine, cosine, and tangent (and their inverses) to ratios of the sides of a triangle, and then used the Pythagorean theorem.

Comment author: Osmium_Penguin 03 August 2010 04:39:54PM 2 points [-]

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.

Comment author: byrnema 03 August 2010 03:40:47PM 5 points [-]

I don't know if the American elementary curriculum is better than it was (I hope so) but this mistake is less likely to happen now. My niece in 2nd grade is learning different methods of 'knowing' arithmetic. They still memorize tables, but they also spend a lot of time practicing what they call 'strategies for learning the addition facts'.

For example..

11-6 = (10-6)+1 = 5 is the compensation approach.

and 11-6 = 10-5 is the equal additions approach.

They also spend a lot of time doing mental math. I'm impressed with how different things are, and hope that students are doing better with this more empirical, constructivist approach. (My niece is good at math anyway, so I don't know if she's getting more out of it than average.)

Comment author: Osmium_Penguin 03 August 2010 04:22:23PM 3 points [-]

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.

Comment author: Osmium_Penguin 03 August 2010 02:37:14PM 28 points [-]

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.

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