| Line 2,243: |
Line 2,243: |
| | | | |
| | :::::::August, I have an open mind about this. I don't see how we could so easily find [[conservative]] words that double by century if the underlying pattern were not there. But please explain if you think that is in error.--[[User:Aschlafly|Andy Schlafly]] 22:27, 21 June 2011 (EDT) | | :::::::August, I have an open mind about this. I don't see how we could so easily find [[conservative]] words that double by century if the underlying pattern were not there. But please explain if you think that is in error.--[[User:Aschlafly|Andy Schlafly]] 22:27, 21 June 2011 (EDT) |
| | + | |
| | + | I hope we can agree on the function ''F<sub>theo</sub>'' - it should be uncontroversial: |
| | + | |
| | + | *one layer exists from 1 - 2 - 4 - 8 words, i.e., 2<sup>0</sup>, 2<sup>1</sup>,2<sup>2</sup> and 2<sup>3</sup> |
| | + | *the partial sums are 1 - 3 - 7 - 15, i.e., 2<sup>1</sup>-1, 2<sup>2</sup>-1, 2<sup>3</sup>-1, and 2<sup>4</sup>-1 |
| | + | *so, with the turn of the n-th century, there should be 2<sup>n+1</sup>-1 words |
| | + | *for K layers, the number is K * (2<sup>n+1</sup>-1). Each layer has 15 words, thus, if there are '''N''' feasible words, the number of layers is '''N'''/15 |
| | + | *now adjust for years instead of centuries, and don't start with the first, but with the 17th, and you get the formula <math>F_{theo}(t) = \frac{\#words }{15}</math><math>(2^{\frac{t-1599}{100}}-1)</math>. |
| | + | |
| | + | '''@jcw: ''' ''Another editor has attempted a similar argument above, but without success.'' I read the sections above, and I ''was'' convinced by the argument. |
| | + | |
| | + | '''@Aschlafly:''' ''I don't see how we could so easily find [[conservative]] words that double by century if the underlying pattern were not there.'' The effects of the miscount ([[Talk:Essay:Best_New_Conservative_Words#PERFECTION: 20-40-80-160 BY CENTURY]]) have shown that you are able to match any pattern you were looking for. |
| | + | |
| | + | [[User:AugustO|AugustO]] 12:11, 22 June 2011 (EDT) |
| | | | |
| | == Americanadians == | | == Americanadians == |