It's not exponential, it's sigmoidal
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It's not exponential, it's sigmoidal
1–9 of 9 posts
Re: It's not exponential, it's sigmoidal
#2Except that's a silly distinction, when you don't yet have any information about what the upper bound is, or any evidence that growth is slowing from its exponential stage. The growth of real-world things clearly has some upper bound, and in saying that it's "exponential" this is understood by all listeners.
Since calling a real-world trend "exponential growth" is always an approximation, pointing out that it's actually "approximately sigmoidal growth, i.e. only approximately exponential until it flattens out sometime in the eventual future" is (you guessed it) a redundant waste of breath.
And to say that pointless pedantry is the same as "mathematical literacy" is even sillier.
Re: It's not exponential, it's sigmoidal
#3Except that's a silly distinction, when you don't yet have any information about what the upper bound is, or any evidence that growth is slowing from its exponential stage. The growth of real-world things clearly has some upper bound, and in saying that it's "exponential" this is understood by all listeners. Since calling a real-world trend "exponential growth" is always an approximation, pointing out that it's actua…
It's not much of a distinction mathematically, but it's an important distinction in emphasis. Saying something is growing exponentially does imply that it will just keep on growing, at least for a long while. Saying growth is sigmoidal emphasizes the eventual slowdown.
Talking about "exponential growth" often leads people into unrealistic hyperbole. Of course, by "people" I mean marketers, investment advisors, and headline writers at Business Week...not us rational computer scientists!
Re: It's not exponential, it's sigmoidal
#4Modding this up is an even truer sign of mathematical illiteracy. The sigmoid itself contains an exponent that is damped at higher values. One could go further and say that it is not even a sigmoid because all web traffic will peter off eventually, with the eventuality in the undefined horizon.
Does anyone really assume an exponential growth in the literal sense with users rushing in via some inter-galactic network when all earth users are exhausted?
Re: It's not exponential, it's sigmoidal
#5"And as Saul noted a few moments later, most of these curves aren't even sigmoidal, they are sinusoidal. (This is, incidentally, why Ray Kurzweil is most likely wrong about the singularity.)"
Am I the only one who gets tired of sweeping bullshit generalizations like this? I can't believe people will pay to hear this kind of nonsense.
He isn't actually saying anything you can rebut.
Re: It's not exponential, it's sigmoidal
#6Except that's a silly distinction, when you don't yet have any information about what the upper bound is, or any evidence that growth is slowing from its exponential stage. The growth of real-world things clearly has some upper bound, and in saying that it's "exponential" this is understood by all listeners. Since calling a real-world trend "exponential growth" is always an approximation, pointing out that it's actua…
Even so, you can't argue that the growth is exponential by simply looking at the graph. It could just as well be polynomial. To conclude that it is exponential you need some kind of analysis, like "every user brings two, those bring two each etc".
Re: It's not exponential, it's sigmoidal
#7Modding this up is an even truer sign of mathematical illiteracy. The sigmoid itself contains an exponent that is damped at higher values. One could go further and say that it is not even a sigmoid because all web traffic will peter off eventually, with the eventuality in the undefined horizon. Does anyone really assume an exponential growth in the literal sense with users rushing in via some inter-galactic network w…
I'm really hoping our fantasy sports site will be popular in the Sombrero Galaxy.
Re: It's not exponential, it's sigmoidal
#8Except that's a silly distinction, when you don't yet have any information about what the upper bound is, or any evidence that growth is slowing from its exponential stage. The growth of real-world things clearly has some upper bound, and in saying that it's "exponential" this is understood by all listeners. Since calling a real-world trend "exponential growth" is always an approximation, pointing out that it's actua…
Even so, you can't argue that the growth is exponential by simply looking at the graph. It could just as well be polynomial. To conclude that it is exponential you need some kind of analysis, like "every user brings two, those bring two each etc".
I believe this article is referencing the the metaphor and the hyperbole of "Exponential Growth!!!"...not a mathematical treatment of growth rates.
That growth eventually slows is a very very simple point, but it's important to never forget. Maybe everybody is making this too complicated because Saul Griffith is supposed to be a 'genius' now?
Re: It's not exponential, it's sigmoidal
#9Modding this up is an even truer sign of mathematical illiteracy. The sigmoid itself contains an exponent that is damped at higher values. One could go further and say that it is not even a sigmoid because all web traffic will peter off eventually, with the eventuality in the undefined horizon. Does anyone really assume an exponential growth in the literal sense with users rushing in via some inter-galactic network w…
"Does anyone really assume an exponential growth in the literal sense with users rushing in via some inter-galactic network when all earth users are exhausted?"
Some valuations for .com companies at the end of the 20th century did seem to have factored this expectation into their analysis.