Why not just use minimum description length?
Is growth linear, not exponential?
41–50 of 79 posts
Re: Is growth linear, not exponential?
#42Perhaps even related to a human generation, or even living memory (like physics progresses one funeral at a time). Though the inflection points found lack that duration-scale and periodicity.
Just on curve fitting: you need some penalty for each extra line (noisy data can always be "fitted" better to enough lines). I expect the paper has a large section on this issue of statistical significance, but I can't access it.
I do feel it's kind of hard to say if such a pattern is "really" there, where exactly the breaks are, or if it's just a noisy artifact.
Re: Is growth linear, not exponential?
#43Earlier quoted context omitted.
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?
#44It'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.
Re: Is growth linear, not exponential?
#45So cells. Cells do not multiply exponentially. DNA does not move faster than the speed of light! Nothing in the cell does! It may look exponential but actually that's cubic, they're easily confused, along with a shitty excel library, and bad measurement, measuring it on the small side early on. And what else? A bad education, being told exponential growth is real.
Re: Is growth linear, not exponential?
#46So sometimes it's quadratic, once in a while cubic. Never exponential. Never, never exponential. Rid that of your mind! If there were infinitely many dimensions, exponential growth would be possible. There are not, so it's impossible. So cells. Cells do not multiply exponentially. DNA does not move faster than the speed of light! Nothing in the cell does! It may look exponential but actually that's cubic, they're eas…
Re: Is growth linear, not exponential?
#47So sometimes it's quadratic, once in a while cubic. Never exponential. Never, never exponential. Rid that of your mind! If there were infinitely many dimensions, exponential growth would be possible. There are not, so it's impossible. So cells. Cells do not multiply exponentially. DNA does not move faster than the speed of light! Nothing in the cell does! It may look exponential but actually that's cubic, they're eas…
But bunnies in Australia.
I bet if you actually had bunnies you could say fuck it they double every season and deal with them on that basis. You'd be wrong...but by how much, like get real? Plus the bunnies have the INTENTION of doubling, they each WANT to have lots of bunnies per season. I think that's the crux of it, despite the impossibility nature's program is exponential.
Re: Is growth linear, not exponential?
#48Earlier quoted context omitted.
Not quite! https://en.wikipedia.org/wiki/Weierstrass_function
Heh. Reminds me of how gamers manage to find exploits to cheese speed runs while developers react in dismay.
Re: Is growth linear, not exponential?
#49It'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.
All exponential functions in nature are really S-curves. Slow-downs could absolutely be the result of corruption, but could be natural limits of whatever process enabled the initial growth
Moore's law is in the saggy part of the S-curve, it's been morally dead for fourteen years in some ways, eleven years in others, and for eight years transistors flat out don't shrink at all they just pack more of them in the same space. I saw this coming, I did the math with the size of the transistors and the size of the chips and realized 99.5% of the area on a chip was empty back when 14 nanometer was the smallest. That's what new lithographies go for, they fill up that empty space. It ain't over til it's over, but when it is in fact over, it's over. It's over.
[1] South Korea, China, which is the new one? Is there a new one? A lot of the time it's artificial and carefully presented to market the exponential curve shit, mainly by lying about the beginning of the segment to make it look smaller and the end of the segment to make it look bigger. Shoehorning it. Also defining the segment as unique, like giving it an identity so it's meaningful to isolate it from the bigger picture which is not exponential because it has a past and a future. Moore's Law talks about transistors, why not talk about valves instead and look at the history since the nineteenth century, or since Leibniz for that matter? Like you can make a switch out of wood, people did, they transmitted energy by moving staffs of wood back and forth. Cuckoo clocks. Antikythera mechanism. The abacus. Mental arithmetic.
The big thing there is for usury, usurers have to keep the dream of exponential growth alive to charge exponential compound interest without getting tarred and feathered like so many usurers before them.
Re: Is growth linear, not exponential?
#50It'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.