gwern comments on Best of Rationality Quotes, 2012 Edition

[gwern]

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

# 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"