> It was, after all, only learning at a geometric rate.  I've wondered ever
> since I first saw the movie why a machine so well connected learned so
> relatively SLOW.  Geometric rate means, of course, that it was learning
> linearly.  It seems to me that the more it knew the more quickly it could
> make sense of new data, and thereby learn at some exponential rate.

Geometric is in fact exponential.

An arithmetic progression is

    Tn+1 = Tn + k

Geometric is

    Tn+1 = Tn x k

So

        Tn+x = Tn x K^x

The bigger it gets the faster it grows.
(The bigger it gets the bigger it gets).

25 days to learn enough to decide that you are sure you are able to take
over the world is actually quite fast by our standards. Even Hitler took a
decade or more. It had to ensure sensor adequacy, resources, security and
more.

In the event, it got it wrong. We think.
(So did Hitler - but we largely have the execrable Joseph Stalin (and his
100 million or so largely commendable friends) to thank for that)
It probably should have waited 26 days.


        RM

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