Why can't I run a 64-bit program on a 32-bit machine..?

After all, you can run a 32bit program on a 64bit machine, right? So why not the other way around? Well, the answer is actually pretty simple, the code sections don't fit. Ah, that doesn't sound that simple? Ok, no problem.

Imagine for a moment that you have a dozen balls of yarn unwound into a paper bag, all helter-skelter and mixed up. You want to pull the yarn OUT of the bag and handle them in an organized fashion. This is the equivalent of the programs running on your computer, in a very simplistic way. There are dozens of code strings, all waiting to be processed by the computer's brain, the CPU.

Now, the yarn has been separated into sections, divided by knots. Some of the knots are 32" apart, and some of them are 64" apart.

Now we're treading outside the bounds of common sense, but bear with me, because it gets weirder. You have a helper, say a small child. The two of you can only pull out the yarn by sections. You can pull either a 64" piece, or a 32" piece, because either one will fit in your armspan. The child can only pull 32" pieces, because that's all that will fit in their armspan.

I'm sure you've put this together by now, but you represent a 64-bit processor and the child represents a 32-bit processor. Either one of you can handle a string of 32 bits, but only you, a 64-bit processor, can handle a 64-bit string.

It's a good thing to keep in mind about this that running a 32bit program on a 64bit processor is inefficient, so if you have a 64bit processor get 64bit versions of programs whenever possible.