| | Ed:
There is a professor emeritus at Colorado, totally unrelated to me in any way, Albert Bartlett, who is the geometric progression go to guy. He's a modern day Malthusian. I ran across some of his lectures recently while looking into something totally unrelated. But the focus of his many presentations on geometric progression does expose some common sense insights into things related to growth.
For example, he amply illustrates that, approx., 7% growth is a 10 year doubling time, as one example, and 2% growth is a 35 year doubling time, and so on, simple facts of compounded steady growth.
One part of his commn sense insight is, no matter what the 'doubling' period is, that once doubled, the newly doubled amount of whatever exceeds the sum of all previous growth combined.
You can easily see this:
1>0
2>1
4>3
8>7
16>15... and so on.
It's not only 'twice as big' as the last value, it is in total greater than the historical -sum- of all previous doubled values.
(Aside: he illustrated this with the chess board story; the inventor asked the king who commissioned the game to be rewarded with a single grain of wheat on the first square, two grains on the second square, four grains on the thrid square, 8 grains on the fourth square, and so on. The King was happy to (try) to oblige to come up with 2^64-1 grains of wheat...)
The last doubling is always a monumental increase. For example, Man is >> ape. (I am not arguing that Man is 2*ape. The same logic applies to tripling or quadrupling or even, any multiple factor > 1.0; doubling is an arbitrary illustration.)
1] Any constant positive growth in something results in a finite doubling time, longer or shorter is just a matter of time. Evolution has operated over a long time.
2] Eventually, the tyranny of geometric progression, if that is maintained, _tends_ to fill the universe with that something. Or, the rate of growth levels off, or even, goes negative.
3] Filling the universe is not possible for every such something(like 'McDonald's), though, it may be possible for some somethings. A concept -- well, it is more than a concept, but 'Intelligence' might be an example of that something.
The increase in intelligence between ape and man might be enourmous. And, unless evolution as a process is done, the next such doubling(or whatever)may well make the difference between mankind and apes look small, just like all geometric progression elements.
Until that step, we are indeed special. There is nothing wrong with enjoying being at the top of the local heap, a local temporal maximus.
Is evolution done? I don't know. Do you?
I've been going back and searching out alot of Feynman's talks recently. He was talking about religion and fatih, but one of the topics he talked about was a scepticism of some of the myths that have arisen about the 'special nature of man.' His criticism was that 'they are too local--too parochial.' He could not look at the universe and conclude that it was a mankind centric event.
I tend to agree with him. We're here, we're capable, we're intelligent. But I stop short of deifying the special nature of our intelligence.
The point of this is, there is distance, and there is distance.
(Edited by Fred Bartlett on 2/27, 10:04am)
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