Re: Kurzweil vs. Dertouzos

From: Jim Fehlinger (
Date: Thu Dec 21 2000 - 17:32:28 MST

Joseph Sterlynne wrote:
> An exchange between Ray Kurzweil and Michael Dertouzos in MIT's _Technology
> Review_ over future technological progress:
> Kurzweil vs. Dertouzos

In this letter, Ray Kurzweil makes the same claim I heard him
make in his keynote address this past summer at PC Expo in New
York -- namely, that the 21st century will encompass 20,000 years
of technological progress, measured as the amount of progress
accomplished in one calendar year at the current (year 2000)
rate, because (Kurzweil claims) technological progress is and
will continue to be described by an exponential curve. He made
the same claim at that Spiritual Robots seminar at Stanford
hosted by Douglas Hofstadter and in a recent article in an
on-line magazine called "Business 2.0" at

This statement (that the next century will see the equivalent of
20,000 years of progress at today's rate) is certainly a very
potent rhetorical device, which rivets the audience's attention
and gets their adrenaline surging (either out or fear or
anticipation!) A friend of mine, who was with me at PC Expo,
asked me later exactly how this 20,000 years will be distributed
over the next century, and apart from saying that most of it will
be stuffed into the last decades, I never bothered to provide him
with a better answer.

However, I later resurrected some college calculus, and after a
bit of stumbling around, came up with an exponential function (a
pair of them, actually -- one is the derivative of the other)
that, if I did the math correctly, gives some interesting
intermediate numbers between now and 2100, and fits Kurzweil's
20,000-year figure closely enough.

The function E(x), which gives the total elapsed technological
progress (in years at current year 2000 rate of progress) between
now (year 2000, x=0) and a century from now (year 2100, x=100)

E(x) = (13.8 * e^.0725x) - 13.8

The function I(x), which gives the instantaneous rate of progress
relative to the current (year 2000) rate, is:

I(x) = d/dx E(x) = e^.0725x

Here are some representative values:

        Elapsed E(x) I(x)
        Time (yrs) (Total Progress since 2000) (Instantaneous Rate)
Year (since 2000) (years at 2000 rate) (compared to 2000 rate)

2000 0 0 1
2001 1 1.034 1.075
2002 2 2.153 1.156
2005 5 6.029 1.437
2010 10 14.69 2.065
2015 15 27.14 2.967
2020 20 45.03 4.263
2025 25 70.74 6.128
2030 30 107.7 8.802
2035 35 160.7 12.65
2040 40 237.0 18.17
2045 45 346.6 26.11
2050 50 504.0 37.52
2060 60 1055 77.48
2070 70 2194 160.0
2080 80 4544 330.3
2090 90 9398 682.0
2100 100 19420 1408

As you can see, it kind of sneaks up on you!

HOWEVER, it later occurred to me that these numerically
impressive "years at current rate of progress" numbers start to
look a little fluffy if you shift your Year 0 point of view
backward a few decades (which I've already lived long enough to
do while staying within the span of years encompassed by my own
personal memories) and use the formula to compute "years at
then-current rate of progress" looking forward to the present
from that past vantage point. For example, according to the
exponential function I plotted (derived from Kurzweil's
20,000-years-in-the-next-century statement), between now and
2040, there will be 237 years of progress at the year 2000 rate.
OK, so that also means (assuming the same curve was in effect)
that there's been 237 years of progress at the **1960** rate of
progress between 1960 and now.

I was thinking of a science-fiction story by Robert A. Heinlein
called _The Door Into Summer_ (there are, of course, hundreds of
similar examples), which was written in 1956. This story starts
around 1970 (only 14 years in the future, from the point of view
of its authorship), by which time, Heinlein imagines, there will
be household robots (the hero of the story is an engineer and
entrepreneur who had founded a company called "Hired Girl, Inc."
[now **that** really dates the story!] and is forced out by his
business partners).

Now, looking forward from 1956, Heinlein plausibly (for the time)
imagined useful robots by 1970, 14 years later. Remember, those
were the heady days of the earliest commercial digital computers
("electronic brains") and Alan Turing's speculations about the
possibility of artificial intelligence, as well as of the
post-war consumer electronics boom (the beginning of the Age of
Television). Heinlein might have been mildly disappointed if
you'd told him that consumer housecleaning robots wouldn't have
been invented even by the year 2000, 44 years later. He would
**certainly** have been disappointed if you'd gone on to tell him
that, since progress is exponential, that 44-year gap is really
equivalent to something like 350 years at the "1956 rate of
progress". He might think, "wow, 350 years ain't what it's
cracked up to be!". He would probably have been appalled if
you'd then added that technology optimists in 2000 now anticipate
that such devices might start showing up around 2040, after
**more than six thousand years** of progress at the 1956 rate!!

I suspect our **expectations** of the future may be exponential
in some sense, too. In other words, we can imagine all sorts of
things we'd like to have or do, and even portray them to the masses
by means of TV shows like _Star Trek_, many of which (like
intelligent machines or immortality) are out of reach to an
indeterminate degree compared to what is possible with today's
technology. Kurzweil says we've all adapted to and internalized the
current rate of change, which causes us to underestimate the
progress that will occur during a future calendar period (like
the next century), but I wonder if our unbounded hopes for
the future make our linear view the more realistic one, even
if Kurzweil's exponential curve is accurate.

There's a special edition of _Newsweek_ magazine on the
newsstands right now entitled "Issues 2001" which has a section
called "The Technological Human" starting on p. 46 and containing
nine articles. One of these, on p. 50, is entitled "2001: Why
HAL Never Happened". The article's author, Steven Levy, says
that "Marvin Minsky, the celebrated MIT computer scientist who
was one of Kubrick's gurus on the subject, had blurted to _Life_
magazine [sometime in the late 60's, presumably] that within a
few years, 'we will have a machine that will be able to read
Shakespeare, grease a car, play office politics, tell a joke,
have a fight.'" Levy then goes on to say, "More recently, to
author David Stork, [Minsky] has called the quote a joke, and
says that he has always believed we'll have HAL-like computers
'in between four and 400 years'". Minsky means calendar years,

Let's see -- in terms of "years at the current (Y2K) rate of
progress" (blending Kurzweil's exponential math and Minsky's
revised timeline for AI) we should expect HAL-like computers
after anywhere between about 4.6 years and 54 trillion years
of continued technological progress (at the current year 2000 rate).

That sounds about right! ;-> ;-> ;->

Jim F.

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