Wikipedia:Reference desk/Archives/Mathematics/2008 September 2

= September 2 =

exponential increase
Since the sexes come in pairs it is quite possible the binary base system of counting was known many centuries prior to computers. Aside from that possibility I have two parents and they have two parents or $$ p = 2^{n} $$, where $$ n $$ is the number of prior generations. If $$ p $$ is the minimum size of the population, assuming persons in any generation have parents from only and do not share any parents from the previous generation, at some point $$ p $$ will become so large as to be impossible. So can one assume this is the limit for number of previous generations? —Preceding unsigned comment added by 71.100.6.185 (talk) 13:36, 2 September 2008 (UTC)


 * No, the limit on the generations wouldn't fit the fossil record (it would be far too small). The apparently impossible population size is because of your assumption that nobody shares parents, that assumption is clearly not true and in fact becomes more and more inaccurate the more generations back you go (basically, you've assumed that no-one alive today is related to anyone else alive today, going back to further generations means taking into account more and more distant relationships). If you go far enough back, everyone shares the same ancestors (see Identical ancestors point), and that number of ancestors is far far smaller than doubling the population n times would suggest (it's actually going to be far smaller than the current population, since the population has been growing over time). --Tango (talk) 13:57, 2 September 2008 (UTC)
 * Yes, but if you reduce your base from 2 to 1.1 the population still reaches max at only ~13,000 years in the past. What is the equation you are using? —Preceding unsigned comment added by 71.100.6.185 (talk) 00:10, 3 September 2008 (UTC)
 * No exponential curve is going to be a good fit, regardless of the base. Your number of ancestors in a given generation grows exponentially at first, but then reaches a saturation point and levels off. Eventually it will actually start decreasing. It probably looks something like a logistic function. Most apparently exponential growth patterns are really the leading end of a logistic curve. -- BenRG (talk) 11:48, 3 September 2008 (UTC)