How big is infinity?

Ok, I'm not talking really about infinity. Instead, I'm talking about unfathomably large numbers. For example, one googol, which is one followed by a hundred zeroes. Now, this is pretty big, but it's not incomprehensible. In fact, it seem quite underwhelming for how big it sounds: it is just 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000. But what about a googolplex? For those of you who don't know, a googolplex is 1 followed by a googol zeroes. That, my friends, is very, very, very, very big. So big that we cannot really grasp its "bigness", so let me put it into perspective. Imagine the length of that number, on a screen. The "1" (at least here on this screen), has a length of around 1/32 of an inch (sorry metric system people). Each "0" has a length of around a little more than 1/16th, but we'll call it 1/16th of an inch anyway. Now, imagine that someone wrote out googolplex and wrote it out on a piece of paper (assuming the paper is as long as required by the number). That would be a length of:

1/32 in + (1/16 * 10^100) in

Disregarding the 1/32in, that is

10^100/16 in

Obviously, that's a big number, but it is still too big to really understand, so let me put it into perspective – That paper is long enough to cross the circumference of the galaxy

1.864432 * 10^75 times or approximately 1,800,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times, or, in word form, that piece of paper would wrap around the galaxy one quattuorvigintillion eight hundred sixty-four trevigintillion four hundred thirty-two duovigintillion times.

Yeah.

That's a lot.





Here's the math for those of you interested:

The first step is to convert 10^100/16 inches to light-years to get a measurement comparable to the galaxy. One inch is equal to about 0.000000000000000002684782 light-years. If you multiple 10^100/16 by 0.000000000000000002684782, the result is 1.67798882e+81 light-years, so that is the length of the paper.

The next step is to find the circumference of the galaxy:

  1. The Milky Way galaxy is in the approximate shape of an ellipse, which has a circumference of 2 * π * the square root of (a^2 + b^2)/2, with a and b equal to the minor and major axis of the ellipse.

  2. In the Milky Way, a = ~100000 and b = ~175000.

  3. Thus, the circumference is 2 * π * √(100000^2 + 175000^2)/2 or around 900000 light-years

Now comes division: 1.67798882e+81/900000 gives you around 1.864432E75.