TSIN blog commentary, log-log plot critique

From: Tyler Emerson (emerson@intelligence.org)
Date: Thu Sep 29 2005 - 13:59:10 MDT

If you're tracking the "The Singularity Is Near" blog commentary, I'd like
to see Ray's response to the invalid log-log plot extension inserted into
some of the conversations:

Regarding Kevin Drum's critique (http://makeashorterlink.com/?O3E0214EB) of
Ray's proposed rate of technical innovation expressed on a log-log plot, the
extrapolation of which, when plotted to the present, breaks down, because
log(x) has a singularity at x=0, Ray noted:

"It isn't valid to extend a log-log plot. A progression is valid by showing
exponential growth along a linear time axis, so a graph with a linear x
(time) axis and a log y axis can be validly extended (provided of course
that one has analyzed the paradigm being measured and shown that it will not
saturate to an asymptote). So that is why I analyzed extensively the limits
of matter and energy to support computation and communication, as well as
the specific technologies that could support these densities including
analysis of the heat and energy issues. And an exponential trend (a
straight line on a plot with a linear time axis and a log y axis) or a
double exponential (an exponential on a plot with linear time axis and a log
y axis) does not reach a mathematical singularity but it does reach
fantastic levels eventually.
"So the point of the log-log plot is simply to show that a phenomenon has in
fact accelerated in the past. It is not valid to extend the line. For one
thing the log-log plot cannot go into the future because that is the nature
of the log time axis. If one wanted to extend this trend, one should plot
it on a linear time (x) axis showing exponential progression of the paradigm
shift rate. I did that in another chart where I show the adoption times
(for mass use) of communication technologies such as television, telephone
up to cell phones, etc."

Tyler Emerson | Executive Director | The Singularity Institute
Box 50182 | Palo Alto, CA 94303 | T-F: 866.667.2524
emerson@intelligence.org | http://www.singinst.org

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