Re: Exponential growth

From: Greg Kuperberg <greg_at_MATH.UCDAVIS.EDU>
Date: Wed, 8 Nov 2000 15:03:14 -0800

On Wed, Nov 08, 2000 at 09:19:26AM +0000, Stevan Harnad wrote:
> Greg, please give me some technically irreproachable words for saying
> what I am saying, so we can get on with it. I think you know what I mean.

No, I don't really know what you mean. I had supposed that you really
did envision exponential growth, maybe that the number of e-prints in the
"global virtual archive" would double every two years in keeping with
Moore's Law. I also assumed that you ascribed the linear growth of the
arXiv not to the structure of the research community but to limitations
due to format. If this is what you really think then I am not asking
you to change the way that you say it, I simply disagree.

Maybe you want to say more conservatively that new submissions should be
superlinear, i.e., concave up. Superlinear growth includes exponential
growth, but it also includes asymptotically slower things like quadratic
growth. And maybe instead of asymptotics you are interested in the
short term. In that case the right way to say it is that you open
archiving should grow faster in the near term.

After all, if growth is sublinear, that means that there is more growth
now in absolute then there will be later; if it is subexponential,
there is more growth now percentagewise than there will be later.
Subexponential may sound like it means "not fast", but it is closer to
the opposite in the short term. Maybe that is the hidden virtue of the
arXiv's grossly subexponential growth rate, that it means that the arXiv
was first out of the gate.
  /\  Greg Kuperberg (UC Davis)
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Received on Mon Jan 24 2000 - 19:17:43 GMT

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