Freedom's Exponential Math

The general formula for replicative exponential growth is T = 2^N where T is the total number of freedom-seekers at the end of the process and N is the number of periods or cycles of replication. However that assumes there is only one person at the start; there may be several, in which case the expression becomes T = S x 2^N

We don't know how many, on average, each graduate will recruit to become new students, per year; it may be one, or perhaps two or even more. Let it be R, a Replication rate per year. Then the number of years (Y) the whole process will take will come from the expanded fomula

T = S x 2^{(Y x R)} and that can be solved for Y as:

(T/S) = 2^{(Y x R)} and hence
log (T/S) = (Y x R) log 2 or
(Y x R) = (log (T/S)/log 2 and so

Y = (log (T/S)/(R x log 2)

So for example if there is only one person at the get-go then S = 1. If further the replication rate R is only 1 per year (as it may be) then to convert a population of 250 million adults (T) would take

Y = (log (250,000,000 / 1))/(1 x log 2)
    = 28 years.

Conversely if there were 2,048 responders to the one-time promo at launch and the replication rate were two per year, then

Y = (log (250,000,000 / 2048))/(2 x log 2)
    = 8.5 years.

So probably, the job will take somewhere between 8 and 28 years. The sooner the better, of course - but either of those figures is infinitely faster than anything that has been achieved so far.

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