army1987 comments on SMBC comic: poorly programmed average-utility-maximizing AI - Less Wrong

9 Post author: Jonathan_Graehl 06 April 2012 07:18AM

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Comment author: Rhwawn 06 April 2012 08:50:19PM 3 points [-]

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).

Comment author: [deleted] 06 April 2012 10:49:22PM 0 points [-]

Let's pretend Egyptian tourism followed a linear growth

The first approximation which springs in my mind would be an exponential growth rather than a linear one.

Comment author: gwern 07 April 2012 12:11:59AM 1 point [-]

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.

Comment author: [deleted] 07 April 2012 10:41:59AM 3 points [-]

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!)

Comment author: gwern 07 April 2012 09:14:53PM *  1 point [-]

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.