gwern comments on Best of Rationality Quotes, 2012 Edition - Less Wrong

31 Post author: DanielVarga 26 January 2013 03:03AM

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Comment author: gwern 25 January 2013 07:51:18PM *  2 points [-]

I tried some stuff in R. While it looks exponential, none of the code or fitting functions gave good results on the highest-karma quotes - I guess because all the other thousand quotes look so linear. Of course, I could have just messed up in any of the following:

Open http://people.mokk.bme.hu/~daniel/rationality_quotes_2012/rq.html in Firefox; C-a; then:

$ xclip -o | grep Permalink | grep points | cut -f 1 -d' ' | tr '\n' ','
$ R
R> karma <- sort(c(105,73,66,64,63,62,60,60,58,58,57,57,57,57,57,56,56,55,55,54,53,51,50,50,49,49,
48,48,48,47,47,46,46,45,45,44,44,44,43,43,43,43,43,43,43,43,43,42,42,41,41,41,
41,41,40,40,40,40,39,39,38,38,38,38,38,38,38,38,37,37,37,37,37,37,37,37,36,36,
36,36,36,36,36,35,35,35,35,35,34,34,34,34,34,34,34,34,34,34,34,34,34,34,33,33,
33,33,33,33,33,32,32,32,32,32,32,32,32,32,32,32,32,32,31,31,31,31,31,31,31,31,
31,31,31,31,31,30,30,30,30,30,30,30,30,30,30,30,29,29,29,29,29,29,29,29,29,29,
29,29,29,29,29,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,27,27,
27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,26,26,26,26,26,26,
26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,25,25,25,25,
25,25,25,25,25,25,25,25,25,25,25,25,25,25,24,24,24,24,24,24,24,24,24,24,24,24,
24,24,24,24,24,24,24,24,24,24,24,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,
23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,22,22,22,22,22,
22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,
22,22,22,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,
21,21,21,21,21,21,21,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,
20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,19,19,19,19,19,19,19,
19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,
19,19,19,19,19,19,19,19,19,19,19,19,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,17,17,17,17,17,17,17,17,17,17,17,
17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,
17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,
17,17,17,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
16,16,16,16,16,16,16,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,14,14,14,14,
14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
14,14,14,14,14,14,14,14,14,14,14,14,14,13,13,13,13,13,13,13,13,13,13,13,13,13,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,12,12,12,12,12,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
11,11,11,11,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10))
R> summary(karma)
Min. 1st Qu. Median Mean 3rd Qu. Max.
10.0 12.0 17.0 19.5 23.0 105.0
R> n <- seq(length(karma))
R> temp <- data.frame(y = karma, x = n)
# first try, fitting a nonlinear model
R> plot(temp$x, temp$y)
R> mod <- nls(y ~ exp(a + b * x), data = temp, start = list(a = 0, b = 0))
R> lines(temp$x, predict(mod, list(x = temp$x))); mod
Nonlinear regression model
model: y ~ exp(a + b * x)
data: temp
a b
1.9094 0.0016
residual sum-of-squares: 17684
Number of iterations to convergence: 9
Achieved convergence tolerance: 8.9e-06

Fitted exponential

# second try, fitting a quadratic
R> lm(temp$y ~ temp$x + I(temp$x^2))
Call:
lm(formula = temp$y ~ temp$x + I(temp$x^2))
Coefficients:
(Intercept) temp$x I(temp$x^2)
1.33e+01 -1.91e-02 3.96e-05
# third try, log transform
R> exp(fitted(lm(log(temp$y) ~ temp$x)))
....
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134
35.080 35.123 35.167 35.211 35.255 35.299 35.343 35.387 35.431 35.475 35.520 35.564 35.608 35.653
1135 1136 1137 1138 1139 1140
35.697 35.742 35.786 35.831 35.876 35.920
# fourth and final try, log variation
R> cc <- coef(lm(log(temp$y) ~ temp$x)); cc
(Intercept) temp$x
2.160310 0.001246
R> with(temp, fitted(nls(y ~ exp(a + b*x), start = list(a = cc[1], b = cc[2]))))
...
[1106] 39.594 39.657 39.721 39.784 39.848 39.912 39.976 40.040 40.104 40.168 40.232 40.297 40.361
[1119] 40.426 40.491 40.556 40.620 40.686 40.751 40.816 40.881 40.947 41.012 41.078 41.144 41.210
[1132] 41.276 41.342 41.408 41.474 41.541 41.607 41.674 41.740 41.807
attr(,"label")
[1] "Fitted values"
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