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Is growth linear, not exponential?

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Re: Is growth linear, not exponential?

#71

Post by lupire »

marginalia_nu wrote: post #38
epgui wrote: post #35

Earlier 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.

That applies to linear growths too. In the long run almost everything is eventually a constant, approximately step function from intitial to terminal condition.

Re: Is growth linear, not exponential?

#72

Post by lupire »

marginalia_nu wrote: post #40
21723 wrote: post #28

It'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.

It's all epicycles of exponents on exponents. The world is a Fourier series.

Re: Is growth linear, not exponential?

#73

Post by lupire »

ravi-delia wrote: post #55
daniel-cussen wrote: post #51

Earlier quoted context omitted.

> Corrupt elites often shut growth down. Yeah so that's oncologists for one, suppose I go to Cuba to a real doctor the likes of which cannot be found in America and get treated for cancer. That's precisely what I want is for that doctor to shut the growth of the tumor down, be a corrupt elite to that tumor, tell it the show's over. It's part of my body like the runaway growth thing is part of the economy, but if eith…

Exponential growth can't go on forever (according to our current understanding of physics anyway), but we're a long way away from the cap. Plenty of resources in the solar system, after all. I'm not unconcerned that our resources can only grow as fast as our lightcone, but I don't lose much sleep either.

I used to worry about the heat death of the Universe, before I realized life will annihilate itself first.

Re: Is growth linear, not exponential?

#74

Post by daniel-cussen »

lupire wrote: post #70
daniel-cussen wrote: post #49

Earlier quoted context omitted.

Yeah there's always economic miracles or Moore's law but for diodes or some shit, something, they all peter out. All of them. No exceptions. All of them. 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…

Exponential compound interest is just linear simple interest with a fixed term loan with auto renewal of non -paid balance. Why would anyone ever pay back a loan if it had zero additional interest for extending the term?

Why would anyone ever pay back a loan if it had zero additional interest for extending the term?

I have excellent answers to that. Well first off I would, because I pay loans in order from most benevolent to least benevolent. Second I figure out the mathematical theory that generalizes interest, and includes all types of interest as special cases, and compound interest is the special case number infinity, the most morally wrong case.

Re: Is growth linear, not exponential?

#75

Post by marginalia_nu »

lupire wrote: post #72
marginalia_nu wrote: post #40

Earlier quoted context omitted.

If the rate of growth varies dynamically over time, then it is not exponential growth. Exponential growth only varies in proportion to itself.

It's all epicycles of exponents on exponents. The world is a Fourier series.

You can likewise argue that all the world is a bunch of polynomials or whatever based on Taylor series. It's not particularly informative.

Re: Is growth linear, not exponential?

#76

Post by ravi-delia »

lupire wrote: post #73
ravi-delia wrote: post #55

Earlier quoted context omitted.

Exponential growth can't go on forever (according to our current understanding of physics anyway), but we're a long way away from the cap. Plenty of resources in the solar system, after all. I'm not unconcerned that our resources can only grow as fast as our lightcone, but I don't lose much sleep either.

I used to worry about the heat death of the Universe, before I realized life will annihilate itself first.

Eh, we're a hardy weed. Barring a threat like none we've seen thus far, we'll get there.

Re: Is growth linear, not exponential?

#77

Post by aidenn0 »

Animats wrote: post #60
aidenn0 wrote: post #3

Is this new? I remember reading an article a long time ago (maybe 15 years?) discussing how growth in aircraft speed was overall exponential, but linear for each new technology that was introduced.

Aircraft speed maxed out a long time ago. "All the aircraft which went significantly over Mach 3 are now in museums." - Scott Crossfield, former X-15 test pilot.

Well any exponential growth curve in the real world is actually a logistic growth curve in disguise. A civilization would have to go from Kardashev II to Kardashev III in about the same time as it went from I to II to maintain exponential energy growth.

As an aside, the Falcon 9 flew 30 times last year and goes significantly over Mach 3.

Re: Is growth linear, not exponential?

#78

Post by aidenn0 »

leetcrew wrote: post #23
heavenlyblue wrote: post #15

Earlier quoted context omitted.

How is aircraft limited to the speed of sound still?

they're not? it just turns out that the most efficient cruising airspeed for passenger jets is in the upper end of the subsonic range. most people can't afford supersonic travel, and the ones that can overwhelming prefer to spend the extra money on a more comfortable subsonic flight. interestingly, extremely high speeds turn out not to be that useful for military aircraft either. the fastest production fighter jet of…

Also, we don't really build dedicated interceptors anymore; the F-106 is the last US interceptor I can think of.

The F-15 was designed primarily as an air-superiority fighter (and in fact misinterpretation of the Mig-25 design was motivation for increasing its maneuverability; the Mig-25 was a dedicated interceptor).

[edit]

In general the Soviets seemed to really like interceptors, the MiG-31 is arguably faster than the Mig-25; altitude and willingness to destroy the engines affect the calculation.

Re: Is growth linear, not exponential?

#79

Post by brandmeyer »

freemint wrote: post #68

The last time i did a similar fit with world GDP between 1920ish and now it came out as O(x^a) where a was between 4 and 5. Actually i fitted the ODE dx/dt = \beta*x^\alpha to data, the fitted looked nice. I wish i wrote a blog post about it.

There's an old joke that all growth looks exponential when plotted on log-log paper with a fat marker.
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