army1987 comments on SMBC comic: poorly programmed average-utility-maximizing AI - Less Wrong
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Well, it's still a fun Fermi calculation problem, anyway.
Let's see, the Pyramids have been the targets of tourism since at least the original catalogue of wonders of the ancient world, Antipater of Sidon ~140 BC which includes "the great man-made mountains of the lofty pyramids". So that's ~2150 years of tourism (2012+140). Quickly checking, Wikipedia says 12.8 million people visited Egypt for tourism in 2008, but surely not all of them visited the pyramids? Let's halve it to 6 million.
Let's pretend Egyptian tourism followed a linear growth between 140 BC with one visitor (Antipater) and 6 million in 2012 (yes, world population & wealth has grown and so you'd expect tourism to grow a lot, but Egypt has been pretty chaotic recently), over 2150 years. We can just average that to 3 million a year, which gives us a silly total number of tourists of 2150 * 3 million or 6.45 billion visitors.
There are 138 pyramids, WP says, with the Great Pyramid estimated at 100,000 workers. Let's halve it (again with the assumptions!) at 50k workers a pyramid, 50,000 * 138 = 6.9m workers total.
This gives us the visitor:worker ratio of 6.45b:6.9m, or 21,500:23, or 934.8:1.
And of course the pyramids are still there, so whatever the real ratio, it's getting better (modulo issues of maintenance and restoration).
The first approximation which springs in my mind would be an exponential growth rather than a linear one.
Sure - but can you offhand fit an exponential curve and calculate its summation? I'm sure it's doable with the specified endpoints and # of periods (just steal a simple interest formula), but it's more work than halving and multiplying.
Well... integral from t0 to t1 of exp(at+b) dt = (exp(at1+b)-exp(a*t2+b))/a i.e. the difference between the endpoints times the time needed to increase by a factor of e... a 6-million-fold increase is about 22.5 doublings (knowing 2^20 = 1 million), hence about 15 factors of e (knowing that ln 2 = 0.7) i.e. about one in 150... hence the total number of tourists is about 1 billion (about six times less than Rhwawn's estimate -- my eyeballs had told me it would be about one third... close enough!)
I'm actually a little surprised that his such gross approximation puts it off by only 6x. For a Fermi estimate that's perfectly acceptable.