This is one of my major go-to examples of this really weird linear phenomenon:
150 years of a completely straight line! There were two world wars in there, the development of artificial fertilizer, the broad industrialization of society, the invention of the car. And all throughout the line just carries one, with no significant perturbations.
I’m confused. Moore’s law, GDP growth etc. are linear in log-space. That graph isn’t. Why are these spaces treated as identical for the purposes of carrying the same important and confusing intuition? (E.g. I imagine one could find lots of weird growth functions that are linear in some space. Why are they all important?)
Hmm, in either case a function being linear in a very easy to describe space (i.e. log, log-log or linear) highlights that the relationship the function describes is extremely simple, and seems to be independent of most factors that vary drastically over time. I expect the world to be stochastic and messy, with things going up and down for random reasons and with things over time going up and down quite a bit for very local reasons, but these graphs do not seem to conform with that intuition in a way that I don’t easily know how to reconcile.
It is remarkable how certain industries are protected against shocks, this reminds me of countries who easily bare financial crises as a result of being primary food exporters (NZ). What is even more interesting is the difficulting of fully getting rid of humans in an econmic endevour (latter part of the chart).
Regarding your point on linearity, this chart does show a linear decrease as of 1800. However lets say farming activity halved as a portion of all jobs in the first 100 years, in the latter hundred years it decreased with a multiple of 25. So in the first half it was transformed by X*1/2 and in the second half X*1/25. Is this still linear ? I was wondering about this phenomena, is there something like absolute and relative linearity or exponentiality ?
It seems that the percentage change then is exponential
I think this is just a sigmoid function, but mirrored over the y-axis. If you extended it farther into the past, it would certainly flatten out just below 100%. So I think it’s just another example of how specific technologies are adopted in sigmoid curves, except in reverse, because people are dis-adopting manual farming.
(And I think the question of why tech grows in sigmoid curves is because that’s the solution to the differential equation that models the fundamental dynamics of “grows proportional to position, up to a carrying capacity”.)
This is one of my major go-to examples of this really weird linear phenomenon:
150 years of a completely straight line! There were two world wars in there, the development of artificial fertilizer, the broad industrialization of society, the invention of the car. And all throughout the line just carries one, with no significant perturbations.
I’m confused. Moore’s law, GDP growth etc. are linear in log-space. That graph isn’t. Why are these spaces treated as identical for the purposes of carrying the same important and confusing intuition? (E.g. I imagine one could find lots of weird growth functions that are linear in some space. Why are they all important?)
Hmm, in either case a function being linear in a very easy to describe space (i.e. log, log-log or linear) highlights that the relationship the function describes is extremely simple, and seems to be independent of most factors that vary drastically over time. I expect the world to be stochastic and messy, with things going up and down for random reasons and with things over time going up and down quite a bit for very local reasons, but these graphs do not seem to conform with that intuition in a way that I don’t easily know how to reconcile.
It is remarkable how certain industries are protected against shocks, this reminds me of countries who easily bare financial crises as a result of being primary food exporters (NZ). What is even more interesting is the difficulting of fully getting rid of humans in an econmic endevour (latter part of the chart).
Regarding your point on linearity, this chart does show a linear decrease as of 1800. However lets say farming activity halved as a portion of all jobs in the first 100 years, in the latter hundred years it decreased with a multiple of 25. So in the first half it was transformed by X*1/2 and in the second half X*1/25. Is this still linear ? I was wondering about this phenomena, is there something like absolute and relative linearity or exponentiality ?
It seems that the percentage change then is exponential
I think this is just a sigmoid function, but mirrored over the y-axis. If you extended it farther into the past, it would certainly flatten out just below 100%. So I think it’s just another example of how specific technologies are adopted in sigmoid curves, except in reverse, because people are dis-adopting manual farming.
(And I think the question of why tech grows in sigmoid curves is because that’s the solution to the differential equation that models the fundamental dynamics of “grows proportional to position, up to a carrying capacity”.)