Consider an image with 400 pixels in width and 300 pixels in height, and each pixel can have 65536 different colors. Or 16-bit color depth if you prefer. This picture width is used in most of my thumbnails here. With this picture size, we can practically picture everything imaginable.
By considering that an image like this as a base-65536 number, we can find the number of possible images we could generate. The following output from octave program gives the base-10 logarithm of the possible number of images that could be generated, or in other words, its order of magnitude. For example, 10000 gives 1010000 number of ways. You should know how to read scientific notation as given by most computer programs using ‘e’ notation.
octave:6> (400*300)*log10(65536)
ans = 5.7798e+05
octave:7> (400*300)*log10(256)
ans = 2.8899e+05
octave:8> (400*300)*log10(16)
ans = 1.4449e+05
octave:9> (400*300)*log10(2)
ans = 3.6124e+04
The extra 3 calculations are just my curiosity to see the number of possibilities if we use 8-bit (256 colors), 4-bit (16 colors) and 2-bit (monochrome) color depth instead. Especially for the first two, we still can picture things clearly.
As expected, these numbers are very large. Engineers would say that it is practically infinite. But the mathematicians don’t care. They say it is still finite, possibly we could define a larger number by just simply adding at least one into it.
If you try to follow all the possibilities in sequence, like going from 0000 to 9999 in numerical sense, you will inevitably:
- Witness your own fate.
- Witness the final fate of the universe.
- Seeing how your future looks like, the family picture of your future spouse and future kids.
- Witness the fate of a certain country.
And the list goes on. There are too much possibilities, but you do not know which one. Whatever it is, you already have passed by one of them. At least macroscopically, don’t need to be in fine detail, or you would need even bigger image size, but it would still be finite.
Does quantum mechanics involve in this? Since if you know the final fate at last, we have something like ‘wavefuntion collapse’ …
Or you could be the most sucessful inventor, because you will also inevitably:
- Uncover the theory of everything? Since we can arrange every possible wordings when we picture texts.
- Invent almost everything.
And the list will go on again. Life in this world is very finite indeed.