Comments on: Exponential growth doesn’t mean what you think it means http://www.johndcook.com/blog/2008/08/25/exponential-growth-doesnt-mean-what-you-think-it-means/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: John http://www.johndcook.com/blog/2008/08/25/exponential-growth-doesnt-mean-what-you-think-it-means/comment-page-1/#comment-5080 John Wed, 27 Aug 2008 02:31:04 +0000 http://www.johndcook.com/blog/2008/08/25/exponential-growth-doesnt-mean-what-you-think-it-means/#comment-5080 What I find more interesting is that so many things actually <em>do</em> grow exponentially for a while, sometimes for a long while. What I find more interesting is that so many things actually do grow exponentially for a while, sometimes for a long while.

]]> By: John Venier http://www.johndcook.com/blog/2008/08/25/exponential-growth-doesnt-mean-what-you-think-it-means/comment-page-1/#comment-5026 John Venier Tue, 26 Aug 2008 18:08:13 +0000 http://www.johndcook.com/blog/2008/08/25/exponential-growth-doesnt-mean-what-you-think-it-means/#comment-5026 I like your note that nothing grows exponentially forever. In grad school I took a class in branching processes and we proved it. The professor noted that this is why pyramid schemes (Ponzi schemes) are doomed to fail. More interesting was our analysis of chain mail propogation. The one we looked at was a common one which claims to have been around the world several times and to bring good fortune if reproduced and bad fortune if not. These claims were backed up by specific examples. IIRC this letter has been in circulation for decades in essentially unchanged form. It can be shown that for this to be the case under any reasonable assumptions regarding the distribution of number of offspring letters, people must have been ressurecting the chain letter from time to time. That is to say, there must have been people who for whatever reason started mailing out the letter spontaneously, and that this must have been happening throughout the period that the letter was circulating. Otherwise the letter would have either died out or blown up to enormous circulation relatively quickly. I like your note that nothing grows exponentially forever. In grad school I took a class in branching processes and we proved it. The professor noted that this is why pyramid schemes (Ponzi schemes) are doomed to fail.

More interesting was our analysis of chain mail propogation. The one we looked at was a common one which claims to have been around the world several times and to bring good fortune if reproduced and bad fortune if not. These claims were backed up by specific examples. IIRC this letter has been in circulation for decades in essentially unchanged form.

It can be shown that for this to be the case under any reasonable assumptions regarding the distribution of number of offspring letters, people must have been ressurecting the chain letter from time to time. That is to say, there must have been people who for whatever reason started mailing out the letter spontaneously, and that this must have been happening throughout the period that the letter was circulating. Otherwise the letter would have either died out or blown up to enormous circulation relatively quickly.

]]>