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pedanterrific comments on 2011 Less Wrong Census / Survey - Less Wrong
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First thing I did upon completing the survey: looked up Principia Mathematica and gave a little whoop of self-congratulation.
First thing I did was look up Principia Mathematica and pat myself on the back for providing a sufficiently low confidence estimate.
At least I was in the right century.
My answer was 17 years off, and I gave 60% confidence. (Assuming a Gaussian distribution, 60% confidence for +/- 15 years means a standard deviation of 17.8 years, so I still was within 1 sigma.)
Does a Gaussian distribution really make sense here?
As an approximation that makes calculations easier, I think it does (though it gives too high a probability to Newton publishing his book next week).
Also, “too high”? Seriously? The log-odds against (x − μ)/σ being more than 19 are about 800 dB; I'm not sure I'd be comfortable with assigning such a great confidence about a non-tautological proposition about the real world. (Except “Emile will torture 3^^^3 people unless I give him/her $5” and similar, of course.) :-)
I'll bet 100 bitcoins against .00000001 bitcoins that Sir Isaac Newton will not publish the historical Principia Mathematica next week.
Edit: After considering the additional coinflips required to bring even that large a difference in money up to the relevant level, I think I'm going to withdraw my offer. Before I earned back my stake laying bets like that, I'd run into a situation where time travel had been commonplace for centuries but there was a huge conspiracy to keep it secret from me, or something like that.
100 against .00000001, that is, 10^2 against 10^-7 has a log-odd of 90 dB, very far from 800 dB. Didn't check the 800 dB of army1987, but if he's right on that, your bet is way below his odd.
Edit : wrote 9 dB instead of 90 dB at first, sorry, hope noone saw the broken version ;)
Yup. Unfortunately, bitcoins are not currently subdividable any further than that, and I'm not rich enough to bet more. However, I'd be willing to throw in "and you don't have to pay up the .00000001 bitcoin unless a coin comes up heads 220ish times in a row."
Is this a general method for adjusting bets on long odds that make money impractical? I just thought of it.
I would take that bet, except that I am insufficiently sure in my understandings of the rest of reality if I happen to win to be confident that I'd want 100 bitcoins in that eventuality.
ETA: I should note that I didn't run the numbers, 0.00000001 bit-coins is something I'd be willing to risk on a 1:2^220 chance for the amusement involved. It should not be taken to reflect a general policy of accepting wagers at what my estimate of these odds would be if I did decide to work them out more rigorously...
Well, I think most real-world applications of Gaussian distributions aren't that satisfactory more than about 5 sigma away from the mean, anyway.
Not if for some reason you are nearly sure that it was before/after a certain date (which I wasn't); I felt that to a first approximation a normal distribution described my beliefs (as of the time I was answering) decently enough, but YMMV.
Certainly you're sure that Newton didn't live before 1000 AD and didn't survive to 1800 AD. Immediately a Gaussian prior can be improved, substantially. See Emile's comment above as well.
Meh. On a Gaussian prior of mean fvkgrra friragl, s.d. 18, knowing that it's between 1000 and 1800 (or even between fvkgrra uhaqerq and friragrra svsgl) doesn't change that much, does it.
(Edited to rot-13 the years... sorry for anyone who read them before taking the test.)
I was entirely sure (20 decibels, at least) it was before gur Nzrevpna Eribyhgvba. That plus "some padding but not too much" got me within the margin of error, but I only gave 2 decibels of confidence that it would be.
For myself I confused Newton's birth date and the date of the Principia Mathematica :/ So I was off more than 15 years, but still not too bad. I gave a 50% confidence to it, 15 years is too short on that time frame, my memory of dates isn't good enough.
I made a similar mistake.
Huh. Apparently I was underconfident in that I was only 7 years off from the correct date and for the calibration estimated I was 65% sure I was within +/- 15.
My logic to get my year estimate:
Tnyvyrb qvrq gur fnzr lrne Arjgba jnf obea, naq ur fgnegrq qbvat fhofgnagvny jbex nebhaq fvkgrra uhaqerq. Vg gura gbbx gur Vadhvfvgvba n juvyr gb qb nalguvat naq ur fcrag znal lrnef haqre ubhfr neerfg. Fb Tnyvyrb pbhyq abg unir qvrq zhpu orsber fvkgrra guvegl. Fb Arjgba unq gb unir obea nebhaq fvkgrra guvegl gb fvkgrra sbegl. Arjgba jebgr Cevapvcvn jura ur jnf nyernql fbzrjung byq. Fb +sbegl lrnef tvirf nebhaq fvkgrra rvtugl. V jnf nyfb cerggl fher gung Cevapvcvn jnf choyvfurq fbzrgvzr va gur frpbaq unys bs gur friragrrgu praghel, fb gung jnf n (zvyq) pbafvfgrapl purpx. Ubjrire, V rkcrpgrq zl qngr gb or zber yvxryl bire engure guna haqre naq va guvf ertneq V jnf jebat.
So, rot13 doesn't do much to obscure numbers.
Good point. I've replaced the numbers with numbers that have been spelled out so the rot13 does now obscure them.
That doesn't mean you were underconfident; with a confidence of 65% you are correct 65% of the time.
Yeah, but the fact that my estimate was pretty close to the correct date suggests that some underconfidence may have been at work. If someone had stated the exactly correct year, and had estimated only a 51% chance that they were in the correct zone, we'd probably look at them funny.
Maybe, but getting very close with low confidence is entirely possible with these estimation-calibration tasks: a uniformly chosen year between 1600-1800 could be the exact year but the confidence of such a guess is always 15%.
That's a good point. So a single data point like this doesn't really say much useful for my own calibration.
Yup. You might already know about it, but PredictionBook seems to get touted around here as a good method to calibrate oneself (although I haven't used it myself).
Yes, I've used it quite a bit. So far the main thing I've been convinced of from it is that my calibration is all over the place.
I wasn't...
How far off were you?
One century. I said svsgrra svsgl I think. Or maybe svsgrra friragl svir. I don't remember.
Could you spell out those numbers in rot13? (It kinda gives it away.)
Actually, here: first is 'svsgrra svsgl' and second is 'svsgrra friragl svir'.
Good idea, thanks!
Same thing. It's a calibration test, not a history trivia quiz.
My brain remembered the cover of Principia Mathematica including the date, more or less right. The problem was it was the wrong edition.
V tbg vg zvkrq hc jvgu Qrfpnegr'f Bcgvpf, juvpu V fhfcrpgrq V zvtug. Zl 40% be 45% (pna'g erzrzore juvpu V jrag jvgu) pnyvoengvba jnf onfrq ynetryl ba gur cbffvovyvgl V unq qbar gung.