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> 5-6% global growth of the 1950s-60s > The overarching story is still faster-than-exponential I've heard a lot of people lately incorrectly using the word "e

by csense 14y ago

> 5-6% global growth of the 1950s-60s > The overarching story is still faster-than-exponential I've heard a lot of people lately incorrectly using the word "exponential" to just mean "pretty fast." It has a specific mathematical meaning which you clearly don't know, but which you should know if you're going to throw around words like "exponential." If growth over the period you're talking about has 6% per year as an upper bound, that's really saying it's bounded above by some curve of the form f(t) = k0*1.06^t where k0 is the GDP at the start of your period. The function f(t) is an exponential function. So your growth is not "faster-than-exponential" since it's bounded above by an exponential function. The only way you can get faster-than-exponential growth is if the percentage growth of GDP is itself growing every year. Needless to say this will eventually become ridiculously fast growth: If we started out with a GDP 1% a year in 1950, and say GDP advanced .5% per year after that, we'd currently be experiencing 31% economic growth per year. Insane!

michaelochurch 14y ago
Actually, I do know what exponential means. Faster-than-exponential means the rate of growth increases as time progresses, e.g. e^(e^t). By "the overarching story is still faster-than-exponential", what I mean is that the rate of economic growth itself is growing-- taking the long (hundreds of years) view. In agrarian times, 0.1% per year was typical. By the 1700s, we were up to 0.3-0.5% per year. By 1825, 1% per year was typical. Now, global economic growth is about 4% per year. If we started out with a GDP 1% a year in 1950, and say GDP advanced .5% per year after that, we'd currently be experiencing 31% economic growth per year. It won't grow that fast. My guess is that the growth rate's own doubling rate is about once every 150 years or so (with noise) meaning we'll see 9-10% growth as the norm in the mid-22nd century. Obviously, there's some limit to this, but once humanity is post-scarcity (ca. 2120) who cares?

by csense 14y ago

michaelochurch 14y ago

Actually, I do know what exponential means. Faster-than-exponential means the rate of growth increases as time progresses, e.g. e^(e^t). By "the overarching story is still faster-than-exponential", what I mean is that the rate of economic growth itself is growing-- taking the long (hundreds of years) view. In agrarian times, 0.1% per year was typical. By the 1700s, we were up to 0.3-0.5% per year. By 1825, 1% per year was typical. Now, global economic growth is about 4% per year. If we started out with a GDP 1% a year in 1950, and say GDP advanced .5% per year after that, we'd currently be experiencing 31% economic growth per year. It won't grow that fast. My guess is that the growth rate's own doubling rate is about once every 150 years or so (with noise) meaning we'll see 9-10% growth as the norm in the mid-22nd century. Obviously, there's some limit to this, but once humanity is post-scarcity (ca. 2120) who cares?