Blah, blah, blah. In the past almost thirteen years I’ve been writing this blog, I know I’ve said it here a lot about our Universe and its infinity.
But think of the possibilities. The probabilities. We, humans, tend to consider things from our own experiences. So we try to conceive this subject of infinity and endless space in terms of our earthly awareness.
There’s a bit of a debate over the topic of infinity. Is our Universe truly infinite? Most say yes. Some say no. Either way, its enormity is mind-boggling.
We don’t know with any certainty what shape the universe as a whole takes. There are all sorts of models out there. Maybe it’s a closed cosmic “donut.” It could be a flat plain stretching like an endless piece of paper (perhaps to go along with the Flat Earthers). Or it could be some giant sphere in a state of constant expansion. We just don’t know.
However. We do know the observable universe — the part we can visibly see and measure — began around 13.8 billion years ago with the Big Bang. Unfathomable to me.
So yes. When we think of the endlessness of the Universe, we look outward toward the heavens.
But what about in the other direction? The small.
Is smallness infinity?
Is there such a thing? Does the small keep going endlessly?
Theoretically, there is no philosophical reason why we cannot keep subdividing space an infinite number of times. You know, keep slicing something in half. Or keep saying minus one.
But according to the most current scientific theory, there comes the point when you reach what is known as the Planck length. This is where we could not discern a smaller region of space. Planck. Arrrrgghhhh Matey. Walk the Planck.
I was reminded of all this infinity, great and small, because today is the birthday of John Wallis. He was a mathematician and cryptographer. A cryptographer is someone who can perform the art of writing or solving codes.
Yes, John Wallis was born in Ashford, England on December 3, 1616. He kicked around here on the big blue ball for 86 years and left again on October 28, 1703.
John Wallis was the most important English Mathematician until Isaac Newton. In fact, Wallis’ work influenced Newton’s work. He published a work called “Arithmetica Infinitorum” in 1656. As a result of his findings, he is given partial credit for developing infinitesimal calculus.
Now, I’ve called calculus many things, but never infinitesimal.
But wait. There’s more. Much more. In that same work, Wallis introduced the symbol for infinity — this one: ∞. And he similarly used 1/∞ for an infinitesimal. In case not knowing these things keeps you up at night.
In mathematics, an infinitesimal or infinitesimal number is a quantity closer to zero than any standard real number, but that is not zero.
Finally, the dictionary tells us that in·fin·i·tes·i·mal means something that is “extremely small.”
Tiny, minuscule, barely perceptible, indiscernible, wee, teeny, and little-bitty.
Yes, my friends, we are surrounded both ways by the endless. By all things great and small.
We cannot see these things — large or little — with our naked eyes. So just remember that important fact. There are worlds around us that we cannot see. So much we do not know.
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I get scared thinking about the yawning void of space and the maddening smallness of our solar system in it, and the smallness of our planet in that solar system and of my own voice in the dark.
— Joey Comeau
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No one can grow if he does not accept his smallness.
— Pope Francis
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If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.
— Bertrand Russell
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Big. Small. We cannot see. We do not know.
