Great idea!
I actually think an accurate approximation would involve an
impredicative hierarchical model. I don't think one can isolate
technology from the humans that create it.
But absent the time to put that together, I'll go with something like:
{ 1/(1+e^-(h-h_o)), h near h_o
p(h) = {
{ 1/(1+e^(h+h_f)), h >> h_o
where h is the population of humans and h_o is some
tech-accelerating-maximum population of humans. h_o becomes some sort
of "optimal clique size". h_f is some sort of failure size larger than h_o.
Grant Holland wrote at 05/17/2013 11:51 AM:
> Glen's latest retort on this thread (see below) gave me this thought: It
> would be interesting if you guys could offer an (admittedly
> oversimplified) analytical model of your best guesses on what the
> productivity function and the acceleration function (2nd derivative of
> the production function) of "technology" over time would be. Such a
> model, though simplistic, would force some careful thinking.
>
> For example, if you believe that the production of technology over time
> (p) is linear, or p = mt, then the acceleration would be 0. If you think
> p is strict exponential, or p = e**t (as Steve might), then the
> acceleration would be e**t. If you think it is cyclical (periodic) (say,
> p = sin(t)), then the growth rate is cyclical, e.g. p = -sin(t). (Maybe
> Glen thinks something like that.) Of course, the productivity function
> is actually none of these but probably some analytic series, or whatever.
>
> Anyway, this kind of thinking could at least be subjected to past
> history and be a more quantifiable conversation promoter.
>
> Just an idea.
--
glen e. p. ropella, 971-255-2847, http://tempusdictum.com
Liberty is the only thing you can't have unless you give it to others.
-- William Allen White
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