Mandark said:
If you accept that:
1) The living human population is greater than the populations of all previous humans, who are dead now.
2) Population growth will continue so as to sustain this ratio until the end of the world.
This means:
1) If you blindly selected one human, out of the pool of all humans now living, who ever lived, and who will live in the future, that person would have a chance greater than .5 of being alive at (or at least right up until) the end of the world.
It's a neat little statistical trick, but totally detached from reality. First, it's very, very, very unlikely that population growth would be exponential until the end of the world. This planet has limited resources, so you'd have to either assume a nuclear holocaust in the near future, or expansion to other planets (in which case the end of the world wouldn't be as big a deal).
Secondly, saying "you will probably be alive at the end of the world" is not the same as randomly picking from the pool of humans, regardless of time. We know who we are and what era we're living in.
Finally, the chances of the world ending are not dependent on a ratio of current to past human population. Saying that more or fewer people lived before us would not decrease or increase the likelihood of the Earth blowing up tomorrow.
Someone who took some probabilities course could do a better job at this than I could.
Well, the fact that such exponential population growth would
not be sustainable in the long-run was one of Malthus's very conclusions; this was because he held that agricultural capacity only increased arithmetically, as opposed to exponentially, and its yield would thus be outstripped by a growing population's increasing demands for resources.
As somewhat of a concession to this reality, you point out that population growth would, in all likelihood, not be exponential until the end of the world; this may very well be the case. In making my original post, I had assumed that all such fluctuations in growth-- that is, deviations from the standard model due to attritional factors-- would be more or less randomly distributed throughout time, so that, on average, the model would still hold. If you meant that it (pop. growth) would only
not be exponential in the last few generations of humans, due to a growing awareness of the scarcity of our resources, well then that is another matter entirely.
Your last big paragraph, about the "end of the world" not being dependent upon the ratio of living to dead is, I feel, somewhat misguided (although true)-- because, after all, we can look at "the end of the world" as any arbitrary time, t ; this would merely provide the proper exponential term for the "equation" calculating the population size. The rest would follow as before.
Also, if you
do, in fact, feel that population growth would only stop being exponential in the final generations (and not before at various times) due to dwindling resources, then I would take issue with that. You can view population growth, where bottlenecked by resource concerns such as agricultural limitations, as sort of a "punctuated equilibrium" (to borrow a term from a very different field
)-- that is, stability followed by rapid change (I'm aware of what the term
actually means; this is just an analogy). The stability (equilibrium) would be related to the time during which the dominant modes of agriculture of the day were sufficient to meet the needs of the naturally (exponentially) expanding population base. As people's reproductive rate slowed due to limited resources under the dominant agricultural paradigm, eventually new modes of production would be discovered (improvements such as terraced cropping, domestication of animals, metal-working for the making of implements, more elaborate irrigation methods etc.) which would allow for a greater capacity; people could again reproduce without subsistence concerns looming overhead. My point is that such developments should be more or less evenly placed throughout history, and not confined to only the last few generations of man, whenever that may be.
Obviously, this is not a detailed analysis of the factors which could affect population growth, being focused only on agriculture; I'm quite interested in taking a look at the book White Man mentioned in the "zombie" thread in order to get a feel for the current methodologies being employed by anthropologists in such research.
And I'm still very much looking for an "official" answer as to whether the sum of the preceding terms in an exponential set is greater than the ultimate term, even if it turns out to be irrelevant to this discussion for other reasons. Any mathematicians around?
