Since I'm not allowed to do math in the Red Room, and I'm terrible at math as it is, I figured I'd show my work here so someone can tell me where and how I fucked up. "One in one quadrillion to the power of four," works out to be one novemdecillion, or 10^60. I was thinking about sand, so I googled "How many grains of sand could fit in the observable universe?" and the number it gave me was 10^63, 1000 times more. So, I multiplied the average volume of a grain of sand by 1000 and got roughly 1 cubic centimeter. So, if I divide the number of grains of sand that can fit in the universe by 1000, I get the volume of the universe in cubic centimeters. 10^63/1000 = 10^60 The volume of the universe is "one quadrillion to the power of four" cubic centimeters. Edit: I googled "volume of the observable universe" and according to Wikipedia it's 4 * 10^80 cubic meters. If that's true, the grains of sand that could fit is WAY off.
Sand grains have diameters of an average of .4mm. pi x (.4mm)^3 x 4 / 3 =~.268cmm=.000268ccm. So it's more like 4000. Also, 10^63 is Archimedes' number, and while his maths was impressive for his time, he didn't quite have an inkling of the size we imagine the universe to be today.
The Sand Reckoner! That's a classic. Yes, old Archimedes could do the math, but his cosmology was a bit...understated.
I didn't actually measure the volume of a .4mm sphere myself, I googled the answer and it said .009 cm^3, which is wrong. I'll actually do the math myself (by typing the radius into a sphere calculator) and... 0.00034 cm^3 Hmm... Oh, you plugged the diameter into the equation, not the radius. Anyway, this is all dumb and precisely why I dropped out of college. After double-checking, yes, the thing I saw was the Archemedes thing. I saw the number was off by three orders of magnitude and my confirmation bias got the best of me. In the RR I estimated that the galaxy was 10^60 liters, let's see how close that is: 8 billion cubic light years is 6.8 * 10^60 liters. So, a volume of 7ish liters gets me the probability I need. So, yeah, one is to one novemdecillion as a basketball's volume is to the Milky Way's volume. Science!
