Tuesday, March 14, 2006

What If--Just What If--the Singularity Really IS Near?

Leonardo Da Vinci, Self-Portrait, c. 1515.

From his birth in 1452 in Vinci, Italy, until his death in 1519 in Cloux, France, Leonardo defined "the archetype of the Renaissance man . . . infinitely curious and infinitely inventive." Leonardo lived to be the ripe old age of 67, at a time in European history when life expectancy was a mere 31 years. During the 500 years between Leonardo's time and today, so much has changed . . . .

(Source: Wikipedia)

The Law of Accelerating Returns

Try to imagine a world where $1000 buys a computer capable of emulating the human brain, where nonbiological intelligence exceeds all human intelligence, and where people can choose to “upload” their brains instead of dying. In his book, The Singularity Is Near (New York: Viking, 2005), artificial intelligence (AI) visionary, Ray Kurzweil, boldly presents his thesis that around the year 2045, we will achieve a “singularity” point, where technology and human intelligence become one--and the universe “wakes up.”

If 2045 is too far into the future to fathom, how about a nearer-term, though equally “futuristic” prediction? With the genetics-nanotechnology-robotics (GNR) revolution in technology now underway, Mr. Kurzweil foresees a dramatic alteration of the PC experience as we currently know it: “By the end of this decade [2010], computers will disappear as distinct physical objects, with displays built in our eyeglasses and electronics woven in our clothing, providing full-immersison visual virtual reality.” And I thought that people appear a little wacky wearing cell phone headsets and seemingly carrying on conversations with themselves while walking down the street. Just imagine how peculiar we will all look typing hands-free in mid-air, while viewing computer screens in our eyeglasses and wearing body-contoured CPUs in our clothes!

Sounds pretty far-fetched, like it’s straight out of science fiction, right? Perhaps. But what if--just what if--the guy is right? Mr. Kurzweil’s thinking is based on a new paradigm, the so-called “law of accelerating returns.” The more commonly accepted view of economic and technological progress is a linear one, built on the belief that the pace of change will continue at its current rate. However, as the increasingly rapid pace of technological evolution evidences (consider the sequentially shorter product cycles in going from radio to TV to computer to cell phone), the actual rate of progress is not linear; instead, history shows that progress accelerates over time.

Accelerating Life Expectancy

In his book Mr. Kurzweil provides an abundance of data on computer chip density, processor speed, information-technology spending as a percentage of GDP, and other indicators of the exponential rate of progress. One area that I find particularly fascinating is human life expectancy over the millennia. How should we understand the rate of change in the following sequence of life expectancy data (from p. 324)?:

Cro-Magnon era (c. 20,000 B.C.): 18 years
Ancient Egypt (c. 1800 B.C.): 25 years
Medieval Europe (c. 1400): 30 years
Industrial Revolution in Europe and U.S. (c. 1800): 37 years
Second Industrial Revolution (c. 1900): 48 years
Internet Age (2002): 78 years

Clearly, human life expectancy is increasing; but at what pace? The three graphs below display these same data points on three different scales--linear, logarithmic and log-log:



The sudden upward rise of the curve in the linear plot (left diagram) shows that during the past century, life expectancy has risen sharply compared to the slower historical trend. The logarithmic plot (center) reveals how the pace of increasing longevity is faster than exponential (since exponential growth would appear as a straight line on a logarithmic plot). Only the log-log plot (right) is capable of capturing the essence of the accelerating rate of change, with the straightness of the plotted line revealing how the exponent of exponential function itself is growing exponentially! In other words, life expectancy may be represented by a growth function of the form exp(x), where x itself is proportional to exp(t), i.e., life expectancy scales as exp(exp(t)).

The apparent exponential growth of the growth rate in the exponent of the life expectancy growth function (now that's almost a tongue twister!) seems to point to a singularity in the making. Sometime over the next 50 years or so, could it be that we reach a point where human life expectancy really does become effectively infinite? With the ongoing technological advances in the GNR revolution, perhaps the day when no one needs to die anymore will be sooner than we think.

Would Anyone Like Eighty Trillion Dollars?

Interesting stuff, all right, but what’s the connection to investing? One section (pp. 96-108) of Mr. Kurzweil’s book bears the enticing heading, “Get Eighty Trillion Dollars—Limited Time Only,” with the claim that “You will get eighty trillion dollars just by reading this section and understanding what it says.” Mr. Kurzweil explains how the law of accelerating returns is fundamentally an economic theory, and how the world’s economy is continuing to accelerate, with productivity (economic output per worker) growing exponentially. Specifically, with regard to stock prices:

“. . . [P]resent stock prices are based on future expectations. Given that the (literally) short-sighted linear intuitive view represents the ubiquitous outlook, the common wisdom in economic expectations is dramatically understated. Since stock prices reflect the consensus of a buyer-seller market, the prices reflect the underlying linear assumption that most people share regarding future economic growth. But the law of accelerating returns clearly implies that the growth rate will continue to grow exponentially, because the rate of progress will continue to accelerate.”

However, no sooner than Mr. Kurzweil presents the basis for an incremental tripling of the current $40 trillion value of the global equity markets (2% additional growth for 20 years with a 6% discount rate enhances returns by 200%, or $80 trillion), he backpedals and all but retracts his grand financial prediction with the verbiage:

“Although people realize that stock prices [will] increase rapidly, the same realization also increase[s] the discount rate. . . . Think about it. If we know that stocks are going to increase significantly in a future period, then we’d like to have the stocks now so that we can realize those future gains. So the perception of increased future equity values also increases the discount rate. And that cancels out the expectation of higher future values.”

This last paragraph is where Mr. Kurzweil’s logic eludes me. When I “think about it,” I reach a different conclusion: Assuming that economic growth really is on the verge of accelerating, any investor with the foresight to buy equities today should benefit from the inevitable run-up in prices when everyone else and his brother catch on to the new paradigm and join the expanding wave of buying, thereby lifting the market to its fair value consistent with the law of accelerating returns. I fail to see why the discount rate that investors use to calculate the present value of future profits would increase, since investors demand higher returns (i.e., use a higher discount rate) when future profits become less certain, not when profits become increasingly predictable as they would in the scenario of increasingly apparent accelerating growth of the world’s economy.

If anyone reading this understands why the discount rate would increase as Mr. Kurzweil indicates, would you please take a few minutes to post an enlightening explanation? I look forward to your commentary . . . as much as I do to trading in my laptop PC for an affordable pair of virtual-reality eyeglasses and matching electronic-weave clothing in 2010 (although I remain in the dark on the implications of infinite longevity come 2045). Thanks for your help.

9 Comments:

Blogger Grant said...

...we’d like to have the stocks now....

The use of "now" seems to be an indication that an adjustment will take place automatically and not over a period of time. Once the adjustment is in effect the expectation of any additional return, or required rate, is priced into the security.

The view that the adjustment would be instantaneous and all inclusive seems to lie in the efficient market hypothesis (EMH) school of thought. I do not personally buy into the EMH on a macro-level but if the discussion were to head down this path it would have to be assumed that the realization of accelerating economic progress is already happening in the stock market.

Maybe the reason for disconnect is caused by some other factor, that is just what struck me from the excerpt. What do you think?

12:01 PM, March 15, 2006  
Blogger Oven said...

The Theory of Accelerating Returns is interesting, but as any good investment adviser will tell you, past performance is no indicator of future results. It occurs to me that demand for goods and services is not driven by technological progress, even if the ability to supply those goods and services is. Will technological advancements increase the consumption of hamburgers and T-shirts and disposable razors? I think not, and therefore I suspect the purveyors of those products will not see returns accelerate past the rate of population growth.

1:30 PM, March 16, 2006  
Anonymous Anonymous said...

Because we realise sooner that stocks will rise and will buy the sooner the better, leaving little or no expectation left for the future.(And thus, leaving no will to buy in the future, as we already bought) That's why we'll soon see bigger and bigger bubles.

10:39 PM, March 24, 2006  
Blogger enoughwealth@yahoo.com said...

I like the blog, but some of your musings take dodgy theory and extrapolate it into "likely" outcomes.

For example, in this post you quote increases in life expectancy, and do a plot to show its growing exponentially - so we'll all soon live forever (not).

A little bit of thought shows that life expectancy has mostly increased due to cutting the infant mortality rate. So, while we may soon cut infant mortality down to close to 0%, that won't actually boost life expectancy that much. Maximum life extent has stayed pretty much the same - going from around 60-70 in past times, to a maximum of around 125 today.

5:45 AM, August 26, 2006  
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1:42 PM, August 10, 2007  
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