Some confusion seems to be arising on what “change” means. Let X denote the quantity whose change (in absolute terms) we are referring to. Is X
The number of transistors on a chip (call it N)?
log2(N)?
The utility produced by those chips (which seems like it ought to be proportional to something between N and log2(N))?
or something else?
If Kurzweil is thinking about (1) and you are thinking about (2), then you could easily both be correct (i.e. more transistors are being added to chips this year than ever before, even though the exponent governing the growth is lower).
Put another way: the rate of change may be at historic highs even if the rate of change of the rate of change is not.
Put another way: the rate of change may be at historic highs even if the rate of change of the rate of change is not.
Yes. But I don’t think that’s compatible with his argument. He posits, basically, that progress is locked in a feedback loop, and the “rate of change of the rate of change” is proportional to the rate of change. The situation you just described is therefore impossible in his model.
Some confusion seems to be arising on what “change” means. Let X denote the quantity whose change (in absolute terms) we are referring to. Is X
The number of transistors on a chip (call it N)?
log2(N)?
The utility produced by those chips (which seems like it ought to be proportional to something between N and log2(N))?
or something else?
If Kurzweil is thinking about (1) and you are thinking about (2), then you could easily both be correct (i.e. more transistors are being added to chips this year than ever before, even though the exponent governing the growth is lower).
Put another way: the rate of change may be at historic highs even if the rate of change of the rate of change is not.
Yes. But I don’t think that’s compatible with his argument. He posits, basically, that progress is locked in a feedback loop, and the “rate of change of the rate of change” is proportional to the rate of change. The situation you just described is therefore impossible in his model.