From mmiller@pcsia.com Mon Oct 25 19:56:26 1999 Date: Wed, 20 Oct 1999 12:09:51 -0500 From: mmiller@pcsia.com To: sanet-mg@ces.ncsu.edu Subject: Population Growth & Sustainability A while back, there was a thread about the earth's population reaching 6,000,000,000 souls. One respondent said something that reminded me of a paper published back in the energy crisis days that seems to be relevant. It has to do with when we realize we that we have exceeded the carrying capacity of the system. This paper just surfaced on my desk again, mainly because I have no filing system for papers, ... mumble, mumble... So here is little excerpt from Am J. Phys, 46(9), Sept. 1978 pgs. 876-888 Forgotten fundamentals of the energy crisis Albert A. Bartlett, Dept of Physics, Uof Colorado, Boulder IV. Exponential Growth in a Finite Environment Bacteria grow by division so that 1 bacterium becomes 2, the 2 divide to give 4, the 4 divide to give 8,etc.. Consider a hypothetical strain of bacteria for which this division time is one minute. The number of bacteria grows exponentially with a doubling time of one minute. One bacterium is put in a bottle at 11 a.m. and it is observed that the bottle is full of bacteria by 12:00 noon. Here is a simple example of exponential growth in a finite environment. This is mathematically identical to the case of the exponentially growing consumption of our finite resources of fossil fuels. Keep this in mind as you ponder three questions about the bacteria: 1. When was the bottle half-full? Answer: 11:59 a.m.! 2. If you were an average bacterium in the bottle, at what time would you first realize that you were running out of spaced? Answer: There is no unique answer to this question, so let's ask, "At 11:55 a.m., when the bottle is only three percent filled(1/32) and is 97% open space (just yearning for development) would you preceive that there was a problem?" (snip time dated illustration) See below. 11:54 am 1/64 full 11:55 am 1/32 full 11:56 am 1/16 full 11:57 am 1/8 full 11:58 am 1/4 full 11:59 am 1/2 full 12:00 noon full Suppose that at 11:58 a.m. some far sighted bacteria realize that they are running out of space and consequently, with a great expenditure effort and funds, they launch a search for new bottles. (Snip time dated material) and at 11:59 a.m. they discover three new empty bottles. Great sighs of relief come from all the worried bacteria, because this magnificent discovery is three times the number of bottles that had hitherto been known. This discovery quadruples the total space resource known to the bacteria. Surely this will solve the problem so that the bacteria can be self-sufficient in space. 3. How long can the bacterial growth continue if the total space resources are quadrupled? Answer: Two more doubling times (minutes). See below. 11:58 am Bottle 1 is 1/4 full 11:59 am Bottle 1 is 1/2 full 12:00 noon Bottle 1 is full 12:01 pm Bottle 1 and 2 are both full 12:02 pm Bottles 1,2,3,4 are all full Well there it is. Sorry it is so long but it illustrates an imporatant point about our ability to preceive a problem with something in exponential growth and still have time to do something about it. After pondering this one maybe Prozac is more in order than coffee :>) Mike Miller To Unsubscribe: Email majordomo@ces.ncsu.edu with the command "unsubscribe sanet-mg". If you receive the digest format, use the command "unsubscribe sanet-mg-digest". To Subscribe to Digest: Email majordomo@ces.ncsu.edu with the command "subscribe sanet-mg-digest". All messages to sanet-mg are archived at: http://www.sare.org/san/htdocs/hypermail