Any time the current growth rate depends linearly on the size of the current population, you get exponential growth.
For instance, given effectively boundless food, the number of bacteria will double every regular time period because, in that time period, each bacterium can split into more.
Similarly, human populations grow exponentially (up to environmental bounds like food supply, war, etc.) because after roughly twenty years, humans beget more humans. With a population as gargantuan as Earth’s, that growth rate is practically continuous.
Kurzweil’s argument is that this applies to many technological industries, too. Faster, more powerful computers make it easier and faster to design the next technological generation. Thus when you measure computing power with any one well-defined scale like transistor count, you’ll find that the growth rate depends on the current number. Ergo, exponential.
I’m not sure what’s going on with the GDP, but if it’s really keeping so nicely to an exponential curve like that, then I’d expect it means that the growth in GDP depends primarily on the current GDP and that it has been this way for a very long time.
I don’t know whether this is what’s really going on. As others here have pointed out, there might be some biases playing a role here. And as I suspect has been beaten to death here before, Kurzweil hides a number of dubious assumptions about market forces and human creativity in his projections. But I do know that if you really, honestly have a strongly exponential growth pattern, it’s most likely that you’ll find some reason why the growth rate depends on the current population.
the growth in GDP depends primarily on the current GDP and that it has been this way for a very long time.
If this were the case, we should expect any noise to accumulate as a random walk. After the Great Depression, the data goes back to where it would have been without the interruption.
GDP trend related to population, not to previous GDP? Over the period of time covered by the above GDP graph, the log graph of US population (seen on http://www.wolframalpha.com/input/?i=united+states+population) looks pretty much like a straight line. GDP per person looks exponential over the last ~60 years (also wolframalpha) [edit] looks linear in constant dollars (from wikipedia)[/edit]
Unless an economic disruption is big enough to greatly change the birth or death rates, the GDP will tend to go back to the straight line, it seems.
If there is easy-to-find GDP data going back to the 1600s, when the log(population) graph is not on the same line as recently, my guess could be tested.
I should perhaps have said in the OP that I understand the natural examples perfectly well; what startles me is that here I’d expect certain exogenous factors (the introduction of income tax and its later peak and descent, the rise and fall of the automobile industry, World War I and the Cold War, etc) to have some significant effects on the growth rate, and different effects in different eras.
Instead, it looks to me (with the exception of the Great Depression and recovery) like the growth rate never leaves the 3-4% range, once you average over decades to iron out the fluctuations. I noticed that this confused me.
Could there be an economic-technocratic explanation of the steadiness of growth since 1950? That is, did someone decide that annual GNP growth should be 3.5% (which is 2% growth per capita, according to Kehoe’s graph), and has policy been determined accordingly?
The Federal Reserve does play a relevant role, and it may well have tried to keep growth within a narrow band over the last two decades. If so, then the financial crisis might have started to show that the official GDP numbers of the last decade were a house of cards based on overvaluation of some sectors of the economy, and that we’ve actually been growing at a lower rate for quite some time.
I don’t have evidence of this, but it is a hypothesis that confuses me less than the hypotheses of coincidence or a natural propensity to a 3.5% growth rate.
Any time the current growth rate depends linearly on the size of the current population, you get exponential growth.
For instance, given effectively boundless food, the number of bacteria will double every regular time period because, in that time period, each bacterium can split into more.
Similarly, human populations grow exponentially (up to environmental bounds like food supply, war, etc.) because after roughly twenty years, humans beget more humans. With a population as gargantuan as Earth’s, that growth rate is practically continuous.
Kurzweil’s argument is that this applies to many technological industries, too. Faster, more powerful computers make it easier and faster to design the next technological generation. Thus when you measure computing power with any one well-defined scale like transistor count, you’ll find that the growth rate depends on the current number. Ergo, exponential.
I’m not sure what’s going on with the GDP, but if it’s really keeping so nicely to an exponential curve like that, then I’d expect it means that the growth in GDP depends primarily on the current GDP and that it has been this way for a very long time.
I don’t know whether this is what’s really going on. As others here have pointed out, there might be some biases playing a role here. And as I suspect has been beaten to death here before, Kurzweil hides a number of dubious assumptions about market forces and human creativity in his projections. But I do know that if you really, honestly have a strongly exponential growth pattern, it’s most likely that you’ll find some reason why the growth rate depends on the current population.
If this were the case, we should expect any noise to accumulate as a random walk. After the Great Depression, the data goes back to where it would have been without the interruption.
GDP trend related to population, not to previous GDP? Over the period of time covered by the above GDP graph, the log graph of US population (seen on http://www.wolframalpha.com/input/?i=united+states+population) looks pretty much like a straight line. GDP per person looks exponential over the last ~60 years (also wolframalpha) [edit] looks linear in constant dollars (from wikipedia)[/edit]
Unless an economic disruption is big enough to greatly change the birth or death rates, the GDP will tend to go back to the straight line, it seems.
If there is easy-to-find GDP data going back to the 1600s, when the log(population) graph is not on the same line as recently, my guess could be tested.
Alternatively, we could examine both datasets closely to see if non-trend-predicted variation in one is reflected in the other.
I should perhaps have said in the OP that I understand the natural examples perfectly well; what startles me is that here I’d expect certain exogenous factors (the introduction of income tax and its later peak and descent, the rise and fall of the automobile industry, World War I and the Cold War, etc) to have some significant effects on the growth rate, and different effects in different eras.
Instead, it looks to me (with the exception of the Great Depression and recovery) like the growth rate never leaves the 3-4% range, once you average over decades to iron out the fluctuations. I noticed that this confused me.
US population, 1790-2000.
US GNP per capita, 1875-2010.
Could there be an economic-technocratic explanation of the steadiness of growth since 1950? That is, did someone decide that annual GNP growth should be 3.5% (which is 2% growth per capita, according to Kehoe’s graph), and has policy been determined accordingly?
The Federal Reserve does play a relevant role, and it may well have tried to keep growth within a narrow band over the last two decades. If so, then the financial crisis might have started to show that the official GDP numbers of the last decade were a house of cards based on overvaluation of some sectors of the economy, and that we’ve actually been growing at a lower rate for quite some time.
I don’t have evidence of this, but it is a hypothesis that confuses me less than the hypotheses of coincidence or a natural propensity to a 3.5% growth rate.