Accelerating Change?

From Wise Nano

A lot has changed in the last year. 10% of mankind purchased a cell-phone. The phrase nanotechnology became main-stream enough that ordinary business people recognize it. Several companies explicitly dedicated to the development of anti-aging technologies were founded. A massive depreciation of the dollar vs. the Euro suggests the first hint that the US global economic hegemony is not necessarily as invulnerable to irresponsible policy as it may have appeared. On the other hand, a lot happened in 1904, and in 1905, and 1906… There are very strong logical arguments supporting the claim that technological growth is accelerating exponentially, and just enough real technological growth that such claims aren’t blatantly false, but an actual look at history still tells me that such claims fail the empirical reality check unless it is proposed that technological change is accelerating very slowly. An acceleration of perhaps .5%/year on average might be consistent with an unbiased overview of the last century. This rate of acceleration is rather consistent with the worlds built by science-fiction authors who claim to believe in much faster technological acceleration but is entirely inconsistent with the theoretical reasons for believing in accelerating change. The world of 2004 has almost four times as many people as that of 1904, and almost forty times as many people with university degrees in science. The Flynn effect suggests that there are hundreds people alive today who would qualify as “geniuses” by the standards of 1905 for every one such person then. Total world funding for research and development approaches a trillion dollars, meaning that today’s scientists each have on average dozens of times as much funding at their disposal as their ancestors did while discovering quantum theory, inventing electricity and combustion, and wiping out most of the infectious diseases that had plagued the developed world for centuries. They also have tools that appear to increase the productivity of many branches research by an order of magnitude or more from decade to decade. If the rate of technological and scientific progress was to be assessed on purely theoretical grounds, someone would have to project, as some few people in the early 20th century did, that our understanding of the universe and ability to manipulate it would increase by more during every year of the 21st century than they did during the whole of human history prior to the 20th century. I ask all of you, how many hours has it been since a theory overturned the prior world-view to the degree that natural selection or relativity once did? What gadget invented in the last week do you find contributes more to your quality of live than electric light or running water? A more systematic experimental test of what I am saying is as follows. Look at a list of Nobel prizes and comparing their chronological sequence to the order of their relative importance. The bizarrely modest contribution of a spectacularly empowered R&D framework to the actual structure of people’s lives and minds needs explanation. Any suggestions would be appreciated. Below is an elaboration on the question of how changes can appear exponential by formal metrics without actually being exponential in a meaningful sense.

Economic aggregate output has historically increased at a linear exponential rate, but that is at best a linear rate of change, and more realistically isn't even linear. The difference between $1/day and $2/day is much more substantial than the difference between $100/day and $200/day, even though you can call the latter 100x "bigger". For most people there doesn't seem to be any personal utility difference between $10,000/day and $20,000 per day. At this level there remains a status benefit to being twice as rich, but a stock boom that makes you and your peers twice as rich is a wash. In general, with respect to money, the relevant unit, utility, shows sub-linear growth, while an irrelevant unit, dollars, grows exponentially. The diminishing utility of wealth is well verified by casual introspection but is surprisingly extreme when assessed from international polls of subjective well-being. That wealth diminish in value at least exponentially is fundamental to economics. Without this fact no-one would ever spend any money. Instead they would always invest it for returns of exponentially growing value.

Generally, the shape of a growth curve is determined by the unit one chooses to measure. The challenge, to someone promoting an agenda, such as Kurzweil or John Smart, is to find the unit that produces exponential or increasing asymptotic results. The challenge for someone trying to predict and optimize the future is to find the most relevant unit. Here are some other examples. Computing power, the classical example of exponential growth, becomes an asymptotically fading time savings when evaluated in terms of time to perform any given calculation. It grows massively hyper-exponentially if evaluated in terms of the set of potential calculations that can be completed within some time limit, but appears to grow about linearly if evaluated in terms of the set of known useful programs that can be run at practical speeds, if useful is weighted by degree of utility. Engine horsepower has grown geometrically with time, but a more relevant unit, maximum speed, has grown linearly. A more relevant unit still, commute time, has been constant, but the most relevant unit, commute distance, has grown sub-linearly.

You can look at the archives from Phillip Goetz's speach at Transvision 2004 for more on this topic.