…and he’s now dead. Another victim of … the Curse of the Pharaohs !
oh no !!!
… being ripped out of full life at the untimely age of 84 … as part of the Club-of-84 (w/ Isaac Newton, Franklin, Edison and Leslie Nielsen)
this cannot be just chance - we must investigate this further
To address the mathematical question: What if you did have 2.3 million blocks, all with independent random variations, stacked end-to-end (which is of course not at all the situation with the Pyramids)? How precise would the tolerances on each individual block have to be, to expect a total error of only 1/4"?
Random errors do tend to cancel out somewhat, so it’s not so bad as 1/4" divided by 2.3 million. But they don’t cancel out completely, and it does still get worse overall as you put more blocks together. What actually happens is that, in addition to the standard deviation (roughly, about how far off of nominal do you expect a measurement to be), there’s also something called the variance, which is the square of the standard deviation. And the variance, not the standard deviation, adds up when you add random numbers together (this is sometimes called the “Pythagorean sum”, because if C is the standard deviation of the sum and A and B are the standard deviations of the individual measurements being added together, then you get the familiar A^2+B^2=C^2).
So we want our final stack to have a standard deviation of 0.25 inches, which means a variance of 0.0625 square inches. We then divide that by 2.3 million, for a variance of around 2.72*10^-8 square inches per block. And take the square root of that to find the standard deviation for each block, around 1.65*10^-4 inches, or about 4.19 microns (half a hair’s breadth, or so).