Smallness
And Then Smaller Still
Nothing is so small that you cannot cut it in half
This is a truth worth pondering, and here is also your chance to prove that a penny dropped will never, in fact, reach the floor.
I know, but sometimes logic doesn’t quite synchronize with reality, for logic suggests that if you drop a penny, it will, obeying gravity all the way, first have to fall half the distance to the floor, and from there: it now has to fall half the remaining distance and then half the new remaining distance, and then… you can always halve any remaining distance, no matter how small by now; and since you can do this, indefinitely, as in eternally, the penny will, logically, never reach the floor: there is always half the distance to go, and then the new remaining half ad infinitum.
In other words, the noise you hear when the penny clatters to the floor is all in your imagination.
But that’s all an amusing aside. What set me pondering about halving distances and sizes was the incredible smallness of the micro-cosmos.
We’ve all seen and played with the school models of atoms and molecules, and these models are certainly large enough to see and then further to envision; but the thing is that atoms and molecules have yet to be directly observed — even the strongest microscope is nowhere near strong enough to provide a visual of the atom, or electron; their sizes are but conjecture, still.
So, how small is small, the conjectured small? Say a water molecule. Well, I read in a book by Schrödinger that if you fill a glass with water and then, by some magical means, mark each and every water molecule — say, paint them orange — and then pour this glass of orange water molecules into the ocean somewhere and then, by some other magical means, mix the oceans so well that your glass of water is equally dispersed throughout the seven seas, all the way down to the 10,000 meters depths. If you did this and now use your original (now empty) glass and fill it with ocean water from anywhere in the world, at any depth, you will now scoop up at least a few hundred of your original (orange) water molecules.
I think that paints an incredible picture of smallness.
And, of course, you can halve this size.
And then halve that size.
And then halve that size.
Ad infinitum.
© Wolfstuff
