by Chris Bodenner
More insights from math, religion, literature and pop culture:
Your reader's bit about Douglas Adams' Total Perspective Vortex reminded me of the Master from Doctor Who. In the new series, it was revealed that the cause of the Master's drive to conquer came from looking into the Untempered Schism, a crack in time and space that allowed the viewer to see the infinity of time itself. Only a child at the time, the Master was driven insane by it, and for the rest of his life, he could hear an unending drum beat, calling him to war.
Another reader:
I am enjoying the continued discussion on Infinity. It is indeed interesting to read about the terror that it can induce in human mind. But, as a Hindu, brought up on Bhagavad Gita, this is not surprising at all to me. In the last chapter of Bhagavad Gita, the God reveals His infinite, eternal and universal form to Arjuna. Arjuna finds that vision terrifying. And he prays for God to re-assume His (finite) pleasing form. Even as a child, this portion of the Gita brought in me a terrifying awe – I wanted to imagine this grand and wondrous vision of God but at the same time terrified about it.
Different religion, same conundrum:
Ecclesiastes 3 – 11
10 I have seen the burden God has laid on the human race. 11 He has made everything beautiful in its time. He has also set eternity in the human heart; yet no one can fathom what God has done from beginning to end.
Like many, I approached the concept of infinity for the first time through scripture. Reading the wisdom literature of the Hebrew texts as a young Christian messed with my head. I am still reeling. Though one can read the "burden" as what precedes these verses, I have always wondered if it is our ability to contemplate but not fully comprehend that makes up our human burden.
Another:
A reader wondered if there is a beginning to infinity. Why not? In Biblical terms, "In the beginning…" In my Catholic childhood we said the "Glory be", which ended "as it was in the beginning, is now, and ever shall be, forever and ever. Amen. That's highly imaginable.
In math, choose all numbers between 0 and 10. How many numbers are there? Infinitely many. Or stand on the 10-yard line and do Zeno's paradox toward the goal – infinite number of halfway points until you get there. Turn around and do the reverse, doubling each step instead of halving it. You are at a beginning, but will never reach the end. The Eames film you posted is a fun way to follow that idea.
Another is in the same territory:
Math people always define infinite in a straightforward way. When I say, the limit of the function f(x) = 1/x, is 0, as x grows to infinity, it means something concrete. If you pick some number, d, as small as you want, there will be some number n, for which f(y) < | 0 – d |, for all y > n. If you haven't had calculus, it might not seem simple and concrete, but when you're familiar with it, it's pretty straightforward.
Another idea of infinity comes from set theory – we say that the cardinality of some sets is infinite. That just means that there isn't a finite set whose elements you can put in one to one correspondence with the elements of the original set.
This sounds like a glib point, but I think it's kind of central. The point of math is that it takes stuff that seems mystical or incredibly abstract, and it makes it concrete and mechanical. It takes stuff that's slippery and gives you a solid grip on it. If you want to figure out if a set is infinite, you have a really specific test you can run. One of the keys to math is not looking down. You don't think about infinity, and what it means – you think about the formal definition, and what you can do with it on a practical level.
Easier math to grasp:
Another example of infinity is the relationship between a mathematical point and a line. By definition a mathematical point has no dimension – it is 0 units long, 0 units wide, and 0 units high. A line, which is composed of such points, however has a dimension. Its length is >0. How is it possible to obtain a value >0 by adding only values of 0 together, which is essentially all you do when you place points adjacent to each other to form a line? Normally, any number multiplied by 0 is 0; however, infinity multiplied by 0 is not 0.
Another:
Y'all have infinity exactly wrong. Pressed for time today (consumed by several infinite tasks), I'll refer you to Emmanuel Levinas, who demonstrated again and again in his book-length essay TOTALITY AND INFINITY, beyond all possible refutation, that infinity and ethics are inseparable. From the preface:
Infinity does not first exist, and then reveal itself. Its infinition is produced as revelation, as a positing of its idea in me. It is produced in the improbable feat whereby a separated being fixed in its identity, the same, the I, nonetheless contains in itself what it can neither contain nor receive solely by virtue of its own identity. Subjectivity realizes these impossible exigencies – the astonishing feat of containing more than it is possible to contain.
If infinity hurts your brain, then your brain needs to be hurt. The pain originates in your lethal attachment to one or another totality or totalization that means you no good, that relies on or intends your extinction as a unique individual who matters or could matter at all. Infinity is the only and infinite beginning of all beginnings, the origin of origins.
Another sends "a classic section from Neil Gaimon's "Good Omens"":
I mean, d'you know what eternity is? There's this big mountain, see, a mile high, at the end of the universe, and once every thousand years there's this little bird-"
"What little bird?" said Aziraphale suspiciously.
"This little bird I'm talking about. And every thousand years-"
"The same bird every thousand years?"
Crowley hesitated. "Yeah," he said.
"Bloody ancient bird, then."
"Okay. And every thousand years this bird flies-"
"-limps-"
"flies all the way to this mountain and sharpens its beak-"
"Hold on. You can't do that. Between here and the end of the universe there's loads of-" The angel waved a hand expansively, if a little unsteadily. "Loads of buggerall, dear boy."
"But it gets there anyway," Crowley persevered.
"How?"
"It doesn't matter!"
"It could use a space ship," said the angel.
Crowley subsided a bit. "Yeah," he said. "If you like. Anyway, this bird-"
"Only it is the end of the universe we're talking about," said Aziraphale. "So it'd have to be one of those space ships where your descendants are the ones who get out at the other end. You have to tell your descendants, you say, When you get to the Mountain, you've got to-" He hesitated. "What have
they got to do?"
"Sharpen its beak on the mountain," said Crowley. "And then it flies back-"
"-in the space ship-"
"And after a thousand years it goes and does it all again," said Crowley quickly.
There was a moment of drunken silence,
"Seems a lot of effort just to sharpen a beak," mused Aziraphale.
"Listen," said Crowley urgently, "the point is that when the bird has worn the mountain down to nothing, right, then-"
Aziraphale opened his mouth. Crowley just knew he was going to make some point about the relative hardness of birds' beaks and granite mountains, and plunged on quickly.
"-then you still won't have finished watching The Sound of Music."
Aziraphale froze.
That exchange reminds me of the conservation between Ricky Gervais and Karl Pilkington embedded above.
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