**From:** Tyler Emerson (*emerson@intelligence.org*)

**Date:** Thu Sep 29 2005 - 13:59:10 MDT

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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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