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Is growth linear, not exponential?
31–40 of 79 posts
Re: Is growth linear, not exponential?
#32This idea was originally discussed by Alexey Guzey back in 2021: https://guzey.com/economics/bloom/#bloom-et-al-appear-to-not... Perhaps there's something I'm missing, but it's weird that he isn't getting any credit for it.
That blog post is cited in the paper the article discusses.
Re: Is growth linear, not exponential?
#33Earlier quoted context omitted.
The dangerous bit is that an exponential curve will also be a fairly good fit for a logistic function that's not yet fully observed.
Every apparent exponential in the real universe must actually be a logistic or some other bounded curve.
Otherwise, we would have about a hundred trillion people infected with Covid by now.
Re: Is growth linear, not exponential?
#34Earlier quoted context omitted.
How is aircraft limited to the speed of sound still?
Adding detail to leetcrew's good reply: the energy of an aircraft in flight is proportional to the square of its velocity. Given steady progress in plane technology you'd expect practical top speed to be limited by cost of energy before too long. That happened more than thirty years ago.
Unless we also had progress in energy technology that could overcome this, which unfortunately we haven't.
Re: Is growth linear, not exponential?
#35It's almost certainly exponential, but the rate of growth depends on a number of dynamic factors. Corrupt elites often shut growth down. It happened in China and Japan several times in the second millennium, and it's happening in the US in the third one; we've backslid since about 1970.
That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacterial colonies, populations of rabbits, compound interest or ROI), but the forces that act on the exponent change over time. It really is this simple.
Re: Is growth linear, not exponential?
#36Earlier quoted context omitted.
If you zoom in far enough every curve looks linear.
Not quite! https://en.wikipedia.org/wiki/Weierstrass_function
> Henri Poincaré famously described them as "monsters" and called Weierstrass' work "an outrage against common sense", while Charles Hermite wrote that they were a "lamentable scourge".
I wonder if there is a really long compound German word for "an achievement whose greatness is best measured by the degree to which it disgusts experts in the field."
Re: Is growth linear, not exponential?
#37It's almost certainly exponential, but the rate of growth depends on a number of dynamic factors. Corrupt elites often shut growth down. It happened in China and Japan several times in the second millennium, and it's happening in the US in the third one; we've backslid since about 1970.
That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacterial colonies, populations of rabbits, compound interest or ROI), but the forces that act on the exponent change over time. It really is this simple.
Oh, and what proof do you have to offer that those exponentials are not sigmoids?
Re: Is growth linear, not exponential?
#38It's almost certainly exponential, but the rate of growth depends on a number of dynamic factors. Corrupt elites often shut growth down. It happened in China and Japan several times in the second millennium, and it's happening in the US in the third one; we've backslid since about 1970.
That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacterial colonies, populations of rabbits, compound interest or ROI), but the forces that act on the exponent change over time. It really is this simple.
Real exponential growth is fairly rare outside mathematical models, it is almost always attenuated by logistical bottlenecks or resource scarcity after some initial phase.
Re: Is growth linear, not exponential?
#39Earlier quoted context omitted.
Adding detail to leetcrew's good reply: the energy of an aircraft in flight is proportional to the square of its velocity. Given steady progress in plane technology you'd expect practical top speed to be limited by cost of energy before too long. That happened more than thirty years ago.
Unless we also had progress in energy technology that could overcome this, which unfortunately we haven't.
You can't make something cheap enough to overcome quadratic growth in demand for very long.
Not even CPU cycles.
Re: Is growth linear, not exponential?
#40It's almost certainly exponential, but the rate of growth depends on a number of dynamic factors. Corrupt elites often shut growth down. It happened in China and Japan several times in the second millennium, and it's happening in the US in the third one; we've backslid since about 1970.
If the rate of growth varies dynamically over time, then it is not exponential growth. Exponential growth only varies in proportion to itself.