doubling time and singularity

From: Spike Jones (
Date: Sat Dec 01 2001 - 18:02:03 MST

A singularity-related topic discussed here is the doubling
time of knowledge. This is a notoriously difficult metric to
calculate, for it is unclear what exactly we mean by a doubling
of knowledge. Many of us intuitively suspect that prior to the
singularity, the doubling time will become exceedingly short,
however we are still open to interpretation exactly what
is meant by doubling of knowledge.

Let us propose some kind of metrics to measure how much
of something is known at what time in history, so we can
estimate knowledge doubling times.

Since the largest known prime record was broken two weeks
ago, I found some historical records regarding the size of the
largest known prime, then calculated how many seconds it took
during those time intervals for the size of the largest known prime
to double. I get the following.

date seconds to double record
1994 600
03-Sep-96 172
13-Nov-96 44
24-Aug-97 16
27-Jan-98 300
01-Jun-99 10.7
14-Nov-01 11.9

(The anomalous 300 seconds for 27 Jan 98 is a result of a
curiously short span between M36 and M37.)

In any case, the doubling time is getting wonderfully short.
I don't know what this has to do with the singularity, if anything,
but I had fun calculating it. {8-] Perhaps Damien will comment
with respect to his notions on page 86 of The Spike. spike

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