2^8 = 256. No further explanation needed, really.

2^16 = 65,536. A big number, certainly, but hardly astromonical.

2^24 = 16,777,216. Now that's quite large.

2^32 = 4,294,967,296. In other words, 4.3 billion. Now we're getting 
into the territory that normal English is inadequat to describe.



2^64 = 1.844 * 10^19.

Now let's stop and think about that for a moment. Just how large *is* 
that, exactly?

Wolfram Alpha claims that the volume of the world's oceans is about 
1.338 * 10^21 L. (This estimate probably varies wildly depending on who 
you ask.) So that's slightly larger than 2^64 L. [Actually 2^64 L = 1.4% 
of the volume of the oceans.]

Wolfram Alpha also claims that the number of grains of sand on this 
planet is "between 10^20 and 10^24". So again, 2^64 is somewhat less 
than the number of individual grains of sand on our entire planet.

I asked Alpha for "the number of fish in the sea". Well, it gave me an 
"estimate of total ocean fish biomass", which comes out to about 3 
gigatons. Even if you measure in grams, it's still 2 * 10^15 g. So 2^64 
g is [vastly] more than the total weight of all the fish in the sea.

The estimated total number of cells in the human body is a piffling 
10^14. So 2^64 is about a hundred thousand times bigger. So... the total 
number of living cells in a hundred thousand people then?

The number of stars in the observable universe is reported as 10^22, so 
that's somewhat larger than 2^64.

Apparently 2^64 atoms of Carbon-12 works out to just 30.6 micrograms. 
And that's pretty unimpressive. So it seems better to quote that against 
the number of cells rather than the number of atoms. (Atoms being JUST 
SLIGHTLY SMALLER than entire cells of course.)

2^64 seconds = roughly 600 billion years. That's 43 times the current 
age of the universe. So that's quite impressive.

2^64 meters = 1,950 light years. That's about a quarter of the distance 
from here to the Crab Nebula. Or 3% of the galactic radius.



Now, here's a thought. MD5 produces a 128-bit hash value. So what are 
the changes of two random datums having the same hash?

2^128 = 3.40 * 10^38

Hooookay then. That's one God-damned big number!

It's easily way, way more than the number of stars in the observable 
portion of the universe. (About 5 * 10^15 times more, in fact.)

2^128 atoms of C12 is 5.65 megatons. (!!) That's apparently about twice 
the mass of all the humans on Earth currently alive.

In terms of time, that's obviously going to be stupidly huge, given 
thatn 2^64 seconds is already far older than the universe itself.

In distance, 2^128 m = 3.597 * 10^22 light years. (!) Which is almost 
quadruple the diameter of the observable universe. (!!)

2^128 L = 1.2 * volume of Betelgeuse. (That actually exists??)

Personally I think the number of "things" type of comparison is the most 
impressive (we're thinking about combinations originally, right?), but 
I'm struggling to come up with things that there can be 10^38 of.

2^128 E. coli cells would have a volume about 1/5th of planet Earth. 
(That's total volume, of course. The cells are actually tubular, so 
there'd be some extra space. But then, maybe the cell size depends on 
the surrounding pressure anyway? Who knows!)

2^64 E. coli cells weighs about twice as much as a large elephant, or 
half the typical weight of a blue whale. But 2^128 cells? That's 4% of 
the mass of planet Earth.

Oh, and look at that. Wikipedia claims that the total number of 
bacterial cells alive on our planet right now is roughly 10^30. Well 
that makes sense then...



When we reach 2^256, Wolfram Alpha happily informs me that this is 0.12% 
of the number of atoms in the observable universe. (!!!)

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