Anton Howes

Hi there - Anton Howes here, an economic historian. My speciality is the Industrial Revolution, and especially the causes of accelerating invention. Stephen Clare emailed me about this debate in the comments, and asked for my take.

A few things that I don't think have been mentioned, or perhaps might do with being made a little more explicit (though apologies if I missed them - has been a lot to catch up on reading through):

Each individual technological or institutional boost to economic growth theoretically follows a logarithmic pattern. That is, a particular technology's adoption has diminishing marginal returns, and is ultimately finite. Classic hypothetical example is the tractor superseding the plough - the first few hundred adopters may see huge gains to productivity, followed by some for whom it's good but not amazing, followed by the part-time farmers let's say, then the hobbyists or something, until every farm uses the new technology. The same diminishing marginal returns pattern applies to every single event, or level effect, that raises GDP (or GDP/capita), regardless of the kind of growth, be it extensive, intensive, or Smithian - so lowering tariffs (finite, as you can't lower them below 0), conquest (you eventually run out of lands to conquer), particular technologies (you run out of lands to which to apply the new tractor).
So when we look at the overall curves, what appears to be exponential is, at the more zoomed in level, really just a whole lot of logarithmic curves strung together. When those curves are closer together, then it can appear exponential, as it has for the past two or three centuries. When they are a further apart, there appears to be stagnation. So if we're lucky, then the rate at which we have things that give us level effects increases, such that we never approach the stage where things plateau.
Tangentially, but importantly, the effect of each level effect on overall growth rates is very much determined by the size of the sector of the economy that they affect. So you might get an astonishing improvement to manufacturing in, say, the year 1300, but as the vast majority of the economy was agricultural, it might thus have a negligible effect on overall measured GDP. (A similar point is neatly illustrated in Gregory Clark's book Farewell to Alms, on p.255, fig.12.12, which compares the real purchasing power of workers with historical vs modern tastes - from the perspective of a farm labourer at the time, living standards according to his data in the Middle Ages were only superseded in the 19thC after a period of decline; when using the typical consumption basket of an American middle-class person today, however, there was steady improvement since about 1500).
The same principles apply for service improvements in the era when the majority of GDP was in manufacturing. And the same today, in which there have lately been astonishing advancements in the productivity of agriculture and manufacturing - I mean truly mind-blowing stuff that would make Jethro Tull or Richard Arkwright break down in tears if they saw them - but because they are now such a small proportion of overall GDP (and employment, too) they don't appear to make much difference to the overall figures.

Does Economic History Point Toward a Singularity?

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Anton Howes

A few things that I don't think have been mentioned, or perhaps might do with being made a little more explicit (though apologies if I missed them - has been a lot to catch up on reading through):

Each individual technological or institutional boost to economic growth theoretically follows a logarithmic pattern. That is, a particular technology's adoption has diminishing marginal returns, and is ultimately finite. Classic hypothetical example is the tractor superseding the plough - the first few hundred adopters may see huge gains to productivity, followed by some for whom it's good but not amazing, followed by the part-time farmers let's say, then the hobbyists or something, until every farm uses the new technology. The same diminishing marginal returns pattern applies to every single event, or level effect, that raises GDP (or GDP/capita), regardless of the kind of growth, be it extensive, intensive, or Smithian - so lowering tariffs (finite, as you can't lower them below 0), conquest (you eventually run out of lands to conquer), particular technologies (you run out of lands to which to apply the new tractor).
So when we look at the overall curves, what appears to be exponential is, at the more zoomed in level, really just a whole lot of logarithmic curves strung together. When those curves are closer together, then it can appear exponential, as it has for the past two or three centuries. When they are a further apart, there appears to be stagnation. So if we're lucky, then the rate at which we have things that give us level effects increases, such that we never approach the stage where things plateau.
Tangentially, but importantly, the effect of each level effect on overall growth rates is very much determined by the size of the sector of the economy that they affect. So you might get an astonishing improvement to manufacturing in, say, the year 1300, but as the vast majority of the economy was agricultural, it might thus have a negligible effect on overall measured GDP. (A similar point is neatly illustrated in Gregory Clark's book Farewell to Alms, on p.255, fig.12.12, which compares the real purchasing power of workers with historical vs modern tastes - from the perspective of a farm labourer at the time, living standards according to his data in the Middle Ages were only superseded in the 19thC after a period of decline; when using the typical consumption basket of an American middle-class person today, however, there was steady improvement since about 1500).
The same principles apply for service improvements in the era when the majority of GDP was in manufacturing. And the same today, in which there have lately been astonishing advancements in the productivity of agriculture and manufacturing - I mean truly mind-blowing stuff that would make Jethro Tull or Richard Arkwright break down in tears if they saw them - but because they are now such a small proportion of overall GDP (and employment, too) they don't appear to make much difference to the overall figures.