The singularity and the knife-edge
I’ve been too busy thinking about all the fun I’ll have with my magic pony, designing my private planet and so on, to write up a proper review of Ray Kurzweil’s book, The Singularity is Near. The general response seems to have been a polite version of DD’s “bollocks”, and the book certainly has a high nonsense to signal ratio. Kurzweil lost me on biotech, for example, when he revealed that he had invented his own cure for middle age, involving the daily consumption of a vast range of pills and supplements, supposedly keeping his biological age at 40 for the last 15 years (the photo on the dustjacket is that of a man in his early 50s). In any case, I haven’t seen anything coming out of biotech in the last few decades remotely comparable to penicillin and the Pill for medical and social impact.
But Kurzweil’s appeal to Moore’s Law seems worth taking seriously. There’s no sign that the rate of progress in computer technology is slowing down noticeably. A doubling time of two years for chip speed, memory capacity and so on implies a thousand-fold increase over twenty years. There are two very different things this could mean. One is that computers in twenty years time will do mostly the same things as at present, but very fast and at almost zero cost. The other is that digital technologies will displace analog for a steadily growing proportion of productive activity, in both the economy and the household sector, as has already happened with communications, photography, music and so on. Once that transition is made these sectors share the rapid growth of the computer sector.
In the first case, the contribution of computer technology to economic growth gradually declines to zero, as computing services become an effectively free good, and the rest of the economy continues as usual. Since productivity growth outside the sectors affected by computers has been slowing down for decades, the likely outcome is something close to a stationary equilibrium for the economy as a whole.
But in the second case, the rate of growth for a steadily expanding proportion of the economy accelerates to the pace dictated by Moore’s Law. Again, communications provides an illustration – after decades of steady productivity growth at 4 or 5 per cent a year, the rate of technical progress jumped to 70 per cent a year around 1990, at least for those types of communication that can be digitized (the move from 2400-baud modems to megabit broadband in the space of 15 years illustrates this). A generalized Moore’s law might not exactly produce Kurzweil’s singularity, but a few years of growth at 70 per cent a year would make most current economic calculations irrelevant.
One way of expressing this dichotomy is in terms of the aggregate elasticity of demand for computation. If it’s greater than one, the share of computing in the economy, expressed in value terms, rises steadily as computing gets cheaper. If it’s less than one, the share falls. It’s only if the elasticity is very close to one that we continue on the path of the last couple of decades, with continuing growth at a rate of around 3 per cent.
This kind of result, where only a single value of a key parameter is consistent with stable growth, is sometimes called a knife-edge. Reasoning like this can be tricky – maybe there are good reasons why the elasticity of demand for computation should be very close to one. One reason this might be so is if most problems eventually reach a point, similar to that of weather forecasting, where linear improvements in performance require exponential growth in computation (I still need to work through this one, as you can see).
So far it seems as if the elasticity of demand for computation is a bit greater than one, but not a lot. The share of IT in total investment has risen significantly, but the share of the economy driven primarily by IT remains small. In addition, non-economic activity like blogging has expanded rapidly, but also remains small. The whole thing could easily bog down in an economy-wide version of â€˜Intel giveth and Microsoft taketh away’.
I don’t know how much probability weight to put on the generalized Moore’s Law scenario. But as Daniel points out, even a small probability would make a big difference to a mean projection of future growth. Since the Singularity (plus or minus pony) has already been taken, I’ll claim this bit of the upper tail as my onw pundit turf.