A Lesson on Exponential

Went to a speaker today, something todo with the past, present and future of technology. Anyways, the speaker pointed out something about exponentials, so 2^x. Then he gives this example (from Mathworld)

Assuming it were possible to fold paper without restriction, the height of a piece of folded paper would double in thickness each time it was folded. Since one sheet of typical 20-pound paper has a thickness of about 0.1 millimeter, folding 50 times (if this were physically possible, which of course it is not) would produce a wad of height 1.13*10^11 meters, and folding one more time would make the stack higher than the distance between the Earth and Sun.

I didn't believe it at first, I did some rough calculation, so 2^50, then to simplify, 2^10 = 1024 then 1024^5 is approx 10^(15). Big number, then I go, ok, assuming the paper is 1 cm thick, so in meter terms, move 2 zeroes over, so 10^12 m. OK, still sizable I think, Earth's bigger than that I thought. So I go home, look at my friend Wikipedia, and found out that Earth's diameter is only 12,742 km. I go what, only that much? And Mount Everest is 8,848 m above local sea level and the Mariana Trench is 10,911 m below local sea level.

Hmmm.... I guess he was right after all, gotta work on my familiarity on how big stuff are, but at least I learned something new :D

Some more numbers (Wikipedia)

• football field length 100 yd (91 m) long. Including the end zones it is 120 yd (110 m),
• empire state building 449 m
• speed of light 3.00×10^{8 m/s (btw, I should've known that the diameter of earth should be less than this!)}