The very concept of transcendance is mind-boggling – especially as applied or demonstrated in mathematics, philosophy, and space! The question of where or if the universe ends, and what exists beyond it, and its cousin consideration of whether anything can go on *forever* are an endless source of wonder, frustration, inspiration, and curiosity for me. This unendingly unanswerable question of how big is the biggest – and why the “biggest” cannot get bigger still – has caused me to lose track of myself and my thoughts since before I had the words to explain it.
“I bet you a buck the sub won’t collect the homework?”
“You’re so stupid! Mrs. Crabapple probably told the sub to get it so she can grade it at home! Duh!”
“At home? What’re you, on crack? No WAY! She’s NEVER out! She’s gotta be so bad she can’t hardly move! I bet she’s barfing a lung, dude!”
“I betcha TWO bucks she’s not.”
“I bet you a hundred bucks we have to pass in our homework, AND that Mrs. Crabapple will have her ‘no recess’ list before school even starts tomorrow!”
“I bet you a MILLION she won’t!”
“Well, I bet you…*INFINITI* she will!”
“Oh, yeah? I bet you infiniti PLUS ONE!”
“…wh…hey….you can’t…….that’s so…..so stupid!”
Is it? I don’t have an answer yet. And, the implications for applied research into this question are rather discouraging for one person to ponder alone. How can we investigate the infiniteness of space when we have very definitely a *finite* amount of living time in which to do so? This is uniquely easy to translate conceptually. We cannot measure a limitless quantity (space) with limited resources (time).
But not all is necessarily lost! Let’s think outside of the box. No, we just learned that there are limits to that direction of inquiry. Let’s instead think not just inside the box, but way, way WAY inside. Let the box be our maxima our infinity! How? By exploring infinity in the OPPOSITE direction! Why can’t we investigate, or at least discuss, the limitless *minima*! We do not even have to get up out of our chairs to explore the infinitesimality of something right before us! That is, we can ask ourselves to ponder the infinite DIVISIBILITY of matter! How small is the smallest? And why cannot you cut that in half, getting even smaller still, forever and ever?
“I bet I can write my name smaller than you”
“Oh, yeah? I bet I can write mine so small you’ll need a magnifying glass to read it.”
“Big deal, I’ll just write half as small as that! Yeah! Inuhhh..in-MINUS-finity!”
“Dude, that’s so stupid!”
Science, and most especially molecular science and physics, are exploring exactly these maxima and minima of our staggeringly, and yes, even stupefyingly puzzling world, both abstract and physical. We have been blessed to discover the atom, and have tried ever so hard to gain an appreciation of both its purity and essentiality by really, for the layperson anyway, no less clumsy a tool than the metaphor.
“Okay, class, I want you to imagine a grain of sand on a beach. Your body is the beach. One grain of sand is an atom”
“Now, we used to be able to go no smaller than that. But this is the wonder and beauty of science, people! Atoms are made up of electrons, protons, and neutrons. The protons and neutrons are at the center, and the electron or electrons are orbiting around it much like planets to stars! Now imagine that we’re in the gym. The entire gym is an atom. At the very center of the gym is a soccer ball. Imagine a golf ball orbiting around that soccer ball, travelling around the edges of the gym. That golf ball is an electron!”
Way. And it gets even more infinitely amazing. Now we know of these particles called quarks. Even as electrons and protons and neutrons are as teeny to the tiny atom, they are giants, again *metaphorically*, compared to the quark! I emphasize metaphorically because most scientists regard it as meaningless to discuss subatomic particles in terms of “size”. Not just because they are so “small” but, in different atoms, their “smallness” is also relative. But for the sake of wonder and amazement let me get back to my metaphor!
“Yes! We can now study SUB-atomic particles! Which reminds me – your teacher told me that you had a homework assignment to turn it today?”
“I *told* you, dumbass!”
“You were all supposed to look up the definition of the subatomic particle called the quark’. Before I collect that from you, I’ll ask you to think of that golfball-slash-electron. Now look closely at the golfball. See those dozens of little dimples all over and around it? Imagine that those are quarks!”
“Yuh-huh. Why, some of you look a little worried. Panicked even. Hmmm Could it be that some of you thought a, um, SUB, wouldn’t collect your homework? Thought the odds were pretty big, eh? Now I want you to look at just one dimple. If you were to put it under a microscope, you’d see little specks and spots inside ONE dimple.”
“Yeah, but like, what’s that got to do with you not collecting our homework?”
“Your odds are smaller than one of those specks.”