Thursday, August 4, 2011

Finite Infinity

It's common knowledge that infinity is, well, infinite. But it's not quite as infinite as it seems!

Not too long ago, I had an idea:

There are a multitude of languages out there, and an even greater number of characters associated with them (letters, numbers, punctuation, symbols). So what if I created a program that would make a copy of every possible character that would fit in a certain area? Let's say 10 x 10 pixels. Just black and white. The program would simply shift / add one pixel to the image at a time until it ended up drawing every possible combination of pixels. Now, most of the images that this program would produce would look nothing like anything. But every once in awhile, the pixels would line up just right to produce a recognizable character.

So I ran the numbers. Well, it turns out that a drawing area of 10 x 10 would create 2^100 or 1,267,650,600,228,229,401,496,703,205,376 unique images. The fastest supercomputer on the planet running 24/7 would take over 5 million years to complete the task.

Obviously, 10 x 10 was not going to happen. How about a 9 x 9? At a mere 2^81 or
2,417,851,639,229,258,349,412,352, it could be done in about a decade. Ah, the power of powers.

If you keep reducing the drawing area, eventually you can find one that can be done within a reasonable amount of time. The downside is, you can't draw nearly as much or as well in a smaller area.

That's when I stopped looking at the idea from a practical perspective, and started seeing it for what it was...

A standard definition TV has a screen resolution of 640 x 480. That's a high enough resolution to display anything, but that also means that it can display everything.

Take a look at this number: 32,000,000^307,200. It is the total number of unique images possible with 32 million colors at a resolution of 640 x 480. The total number of unique images possible. That's profound! What that means is that everything that you can ever see on a TV is contained somewhere within that insanely huge number.

Some examples: 
  • Every picture ever taken
  • Every frame from every videogame, movie, or TV show ever made
  • A childhood memory or a scene from your favorite book
  • Anything that you can possibly imagine

In fact, wherever you are, whatever you are doing, whatever is going on around you this very instant is captured in perfect detail by an image inside that number! There's an image of you and your surroundings from every angle. From what you are currently seeing with your eyes, to 1,000 feet above you, to 1000x magnification of your elbow.

That's not to say that it would be easy to find them. Just as with the 10 x 10 black and white, a vast majority of all of those images would just look like colorful white noise. 

But that's just what can be shown on a TV screen. How about we take that concept even further?

Your senses have limitations based on how many nerve endings, photo receptors, tastebuds, etc your body has. While I don't have the hard numbers to calculate, there is a distinct, finite number of combinations of senses your body is capable of having. That means that everything you could ever experience, whether possible or not, is contained within one astronomically huge number.

It's a finite number that contains what we thought was infinite.

Wednesday, August 3, 2011

My Latest Adventures

Wow! I entirely forgot I had this blog! I suppose I better post something. How about Minecraft? Ever heard of it? Good! Cause it has been a major time sink of mine lately.

Though, I tend to play Minecraft differently than most...