John Tierney of the New York times shows a figure from Ray Kurzweil of a log-log plot of the time between changes in history, such as the appearance of life multicellular organisms to new technologies like televisions and computers. His graph shows power law scaling with an exponent of negative one, which I obtained by eyeballing the curve. In other words, if dT is the time between the appearance of the next great change then it scales as 1/T where T is the time. I haven’t read Kurzweil’s book so maybe I’m misinterpreting the graph. The fact that there is scaling over such a long time is interesting but I want to discuss a different point. Let’s take the latter part of the curve regarding technological innovation. Kurzweil’s argument is that the pace of change is accelerating so we’ll soon be enraptured in the Singularity (see previous post). However, the rate of appearance of new ideas seems to be only increasing linearly with T. So the number of new ideas are accumulating as T^2, which is far from exponential. Additionally, the population is increasing exponentially (at least in the last few hundred years). Hence the number of ideas per person is obeying t^2 Exp(-t). I’m not sure where we are on the curve but after an initial increase, the number of ideas per person actually decreases exponentially. I was proposing in the last post that the number of good ideas was scaling with the population but according to Kurzweil I was being super optimistic. Did I make a mistake somewhere?

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[…] Given that good ideas seem to grow linearly with the population and possibly slower (e.g. see here), going towards the train actually means we should keep growing as fast as we can and hope that […]

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2 thoughts:

1) Most of the population growth is in areas where education is low and/or it is difficult to develop new ideas and spread them. This is changing. E.g., http://www.afronline.org/?p=7197 So perhaps the ideas/capita rate will improve.

2) Affluence tends to retard population growth (e.g., Japan). Perhaps population growth will level out if the global marketplace evens out the rich/poor divide.

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Some good points.

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[…] 3) Exponential growth does not necessarily imply progress. In the same week that the Singularity article appeared in Time magazine, influential economist and blogger Tyler Cowen penned an opinion piece in the New York Times lamenting that innovation has done little in making our lives better recently. He writes: “My grandmother, who was born in 1905, spoke often about the immense changes she had seen, including the widespread adoption of electricity, the automobile, flush toilets, antibiotics and convenient household appliances. Since my birth in 1962, it seems to me, there have not been comparable improvements.” I also posted previously wondering why the growth rate of innovation seemed so slow (see here). […]

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[…] or not happen in the near future or ever. I’ve posted about it in the past (e.g. see here, here and here). What I do want to discuss is whether or not there can exist events or phenomena that […]

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