Infinity + One

I don't know, we're gonna find out. Yeah, because we're taking two episodes to discuss infinity only infinite amounts, right, We're taking a finite number of episodes in each episode is uh you know, consists of a finite uh number of minutes. There only there's only so much time and energy we can throw at the topic. And the topic is the the infinite, the boundless, the pretty much one of the biggest, most mind staggering concepts you could attempt

to try and comprehend. So you're gonna get lost along the way. We're gonna get lost along the way, and hopefully we will not all remain lost for an infinite amount of time and just completely lose our minds. But yeah, in full disclosure, at some point I'm going to have the math sweats but you know, we're all going to wait into the deep end of the pool to gather the deep end of the philosophical pool, the theological pool,

the mathematical pool, to the physical pool. Uh, we're all going to go together and hopefully none of us will sink beneath the waters infinitely. But in the meantime, let's get our hands and our minds around the concept of infinity, because we use it all the time, or at least my kid does. When she's really excited about something, she'll say, infinity plus one. I totally want to go to Chuck

E Cheese, which is its own infinite hell um. But again, it's we find this parlance um a way to try to describe something that feels like it's going to go on forever and ever. Yeah, and you know, also another big pop culture mentioned of this that our pretty certain knowledge is pointed out to infinity and beyond toy story movies, which on one level kind of sounds like ridiculous but actually is kind of key to some of the discussions we're going to have about the nature of infinity um um,

which is kind of clever in its own way. But but indeed, infinity is this thing that we kind of pick up on even at an early age, even if

we're not giving it a lot of serious consideration. UM, for your part, what was what was your earliest interaction with infinity, your earliest even attempt to utilize infinity as a concept or to think about it, or I think just when I was considering the universe and the place that I had on Earth and then Earth's place out there, and so that was the first sort of inkling of like, wow, things might go on forever and ever and ever. What

about you? I definitely remember the idea of a never ending pit being the thing that came to my mind.

I think this came out of like playing with Masters the Universe action figures or watching Heman cartoon and somehow getting the idea that you know, you would have not only would you have these action figures fighting on the edge of a cliff, which would probably be the back of a couch, but that this would be a cliff above just an endless chasm that they would if they start you started falling, you would just never reach the bottom. And uh, and so we would when we would play

basically the Floor's Lava. Our version was the floor is a never ending pit. Oh that really amps up the the sorry by the again. Oh that really ups the anti there. Yeah, and and so I would I would think I remember thinking about the concept sometimes because then you you have to ask yourself, well, if this is a never ending pit, what does that mean? Are their walls to this pit? Do the walls go on uh at infiniteum and uh? And and if so, where is

this pit? Where are the walls? Where is the universe? So you do kind of go down the wormhole a little bit and even trying to you to figure out that the rules of this fantastic childhood concept. You know what I love about this is that the band The Handsome Family has a song about a never ending pit, bottomless, bottomless pitt in this guy's backyard, and he's obsessed with it. And it's, as of course, depressing and beautiful, but it deals with that same sort of concept of just the

never ending fall. Yeah, but I believe in the song his his wife lowers him down and like a bathtub or something, on a rope, and eventually the rope gives way and he's just endlessly falling down for this whole That's what I love about that band too, you know it was a cloth footub. Yeah, of course, you know you want to go down and style. Sure, all right, perhaps we should talk about what infinity is not because we've got that sort of simple idea of it's going

on on forever and ever. Infinity is not a real number. We can't say, you know, it's this number of things. There's an infinite number of things. We can say an infinite amount because we don't know specifically, specifically what that number would ever be. Yeah, there's no there's no number that we can say is infinity. We just have the symbol for infinity, which of course is essentially an eight on its side, and you can think of as a little little like childhood train track that circles back in

on itself. Yeah, it's actually called a Lemna skit. And John Wallace began using the symbol for infinity in sixteen fifty five. Um. Now, infinity cannot be measured, of course, which also ties into it not being a real number.

It's not something that's growing, it's not doing anything. It just is okay, Yeah, so it's it's not a situation of the bottomless pit, the endless pit, an everything pit actually getting deeper and deeper it is, right, right, Yeah, And infinity comes from that Latin word infinitis, which means unbounded nous, which is a good way to look at that that pit. It is not bound to anything physically,

it's just going on for an infinity. Now, the reason why this is an important concept is because it really flavors different fields of study, like mathematics and physics and philosophy.

And today we're going to focus more on philosophy because I think this is really at the heart of the matter for humans of course, right, it's pretty much the the underpinnings, you know, because once you get into the mathematics, in the in the physics, uh, it's kind of the tip of the spear and uh and philosophy is kind of the shaft. And also having the philosophy in mind really helps you better grasp the mathematics and physics of

the issue. Yeah, there's uh an article by George Divarsky writing for Ion nine, and he talks about why infinity is such an interest in and media concept and he says, quote, as every chess player knows, each piece is assigned a numerical value according to its tactical importance and strength These values range from one ponds to nine the queen, and are often used to keep a kind of score as the game progresses. But he says the King is a signed infinite value, and for a very good reason. He says,

losing the king is fatal. It's instant game over, regardless of whatever else might be happening in the match. The King's worth therefore cannot be bound within a finite set of values. And he goes on to say therein lies another kind of infinity death right because you kin gets knocked out, as he says, it's game over. And he says, assuming that nothing awaits us in the afterlife, the termination of our lives represents a kind of eternity. It's an

internity of nothingness, but an internity nonetheless. Indeed, I mean, infinity is often a concept in the religions and worldviews. And and you go back to our episode on the problem of mortality, I mean, that's that the key to that is our struggling with the whole question, you know, we what does it mean that we're not infinite? We're finite? And maybe could we become infinite? And is there anything about us or humanity or the universe that is infinite.

And chance is also such an interesting concept because another uh interplay between chess and infinity is of course that there are there are a finite number of chess games start to finish when you start thinking about, all right, I could move this, uh, this pond, and then my opponent could move this pond, and then all the moves that could they could go, you know, they could transcend from the from that point there there's a finite number of chess games that exist, uh, and it's beyond our

human ability to comprehend them all. But but there is a limit. If you look, if you were to look at a map of the universe of chess from an impossibly high leveled where you could see it all, you could see the collection here are the chess games, all the chess games that are possible. Yeah, and that's it's such an elegant metaphor for us grappling with the concept.

And you can really see why philosophers get bound up in the idea of infinity, because the idea is if if you could solve infinity, you could solve meaning, and if you solve meaning, you could maybe solve death, or maybe you could even prove the existence of God for some philosophers. All Right, we're gonna take a quick break

and we come back. We're gonna talk about some of the notable philosophers and thinkers throughout the ages that have taken their minds and tried to contain within it infinity. All Right, we're back, and we're discussing infinity. We're discussing the history of infinity in the way that various great thinkers throughout the ages have have tackled the topic. And I actually got to hear Philip Clayton, the theo logian and philosopher, discussed this at the World Science Festival few

years back. Uh And he in fact highlighted several of these individuals we're gonna discuss right here. Um. A good starting point is to go back to the fifth fifth century b c e. To the philosopher Zeno of Elia. Uh. Now, he introduced the concept in the West of infinity, playing on an earlier idea of the boundless by an Aximander, which show you have to think think about this. Put

yourself in the mindset of the ancient Greeks. You know, if you're big on architecture and picking out the form of things and here's the scary concept of the boundless of the infinite, and so Zino came up with several different paradox Zeno's paradox is including Achilles and the tortoise, which is an interesting little thought experiment that if you if you really focus on it too much, it means that that movement isn't really possible. It gets kind of crazy.

But the basic idea here is that if a tortoise has a headstart in a race against the mythic Achilles, then Achilles can never actually catch up to the tortoise. It's gonna take the Achilles a certain amount of time to reach the point where the tortoise stopped. And then you have all these different increments in the UH, the shrinking space between the two UH. And so it means that something finite can be divided an infinite number of times.

And I've seen it pointed out that that if you if you have a mortgage or any kind of arrangement with a bank on a loan, you can see that that's possible because it seems like they find a way to take a finite amount of money and make paying

it back last forever. What I like about this thought experiment is that it really illustrates this concept of infinite continuum, this continuum that goes on and on forever and ever, even though you have these little finite parts of it, that that Tortoise and Achilles are forever divided by a

certain space of time. Do you move onto another notable Greek thinker, there's of course Pythagoras, Greek philosopher and mathematician, invented the notion of mathematics that which can be learned, and he said that that each integer has its own spiritual meaning. Most notably, he launched the Pythagoryan theorem. Uh. Just to to run through that one again, said the square of a hypothenuse is equal to the sum of the squares of the other two sides. If you plug

some ones in there. Uh, And the square root of two requires infinite digits with no repeating patterns. You can see infinity popping up right, because I mean, we've all encountered that in in in our even basic mathematics classrooms.

You have that number and it has a remainder that just that repeats forever, and you just have to give up on it after a while, because the human mind can only deal with so much so that you have this infinite continuum the basis of that with Zino, with Pythagoras, you have infinite digits just going on and on, no repeating pattern. And then you have the Jain religion, the Maharivad years ago, who begin to look at the infinite

and pars it in terms of different types. And they're coming up with the concepts of an infinite length and infinite volume, the concept of innumerable as represented by in and now we have even more building blocks of conceiving of infinity again within the field of mathematics, even though these are philosophers essentially grappling with grappling with the idea of infinity. Yeah, and in fact different infinities. And that's where things start getting really weird, when you start realizing

there's not just the one infinity. They're different takes on infinity. Um. This leads us to Aristotle. Of course, everything seems to come back around the Aristotle when you start talking about um history of thought, especially in Western traditions um and uh. He found that with with actual infinities, physics doesn't work that well. And we'll discuss more about this later. But Aristotle said that there exists no actual infinities in the physical world, so he'd banished them two more or less.

The realm of forms um and you can count. In the basis here is you can count as long as you want you can, but you experience finite results in a finite lifetime. You can divide all day or you're gonna run out of time. So you see this division between between. So even though we're talking about infinity, where of course finite minds and finite bodies and finite world. Yeah, and this he describes as the notion of potential infinity.

And I like this because it kind of it's almost like straddling offense between does infinity exists and does infinity not exist? It kind of saying there's a potential for infinity. And other words, if you have a line mathematics that goes on and on forever, it exists there, but in

the physical world you have a finite line. Yeah. It kind of reminds me of being in a Sunday school class when I was a kid, and and I was always one of the problematic Sunday school kids who would want to ask about the really difficult stuff and or the really crazy stuff. So I would always ask about the Book of Revelation, and I remember this one Sunday

school techer. He would always just say, I don't worry about that, just don't even don't just forget about all that stuff, because that only worry about the stuff that directly relates to your life. And because that's just a bunch of you know, because it's dragons and stuff right at the end of times, its codes and all. And so you see a bit of that in this separation between the between you know, infinities and the finite, right, because we are finite and the infinity is ultimately beyond us,

all right. Another person who is exploring this notion is thirteenth century theologian Thomas Aquinas. We've talked about him before too, yes, and he was very much to focus on the quality of existence rather than the quantity. And it's at least as far as infinity is concerned. So he was saying that God uh is infinite in quality more so than in quantity. So he sees it more as a mode of existence. And he identified a separation between mathematical infinity

and religious infinity. So we see a curious principle emerge out of acquaintas is thinking here, even an infinite God cannot create an infinite object. So think about that. Yeah, now you have Nicholas of Cusa in the fifteenth century. He's a philosopher who says everything is included in the infinite heresy. Heresy, that's the reaction from the crowd in the third and fifteenth century. Uh So, therefore, with this model, you would have the world itself um being inside God.

And he used mathematical examples to describe this God world model. And the crutch really is that God is the circle whose center is everywhere, and the circ conference is therefore nowhere. And this is called a coincidence of opposites because now you have humans that the animals that stand at the boundary between the eternal and the finite. And here's an interesting when this comes from the seventeenth century Jewish philosopher Baruk Spinoza, and he was actually kicked out of the

synagogue for allegedly arguing that God has a body. This is where we see metaphysics meeting geometry. Said, if God is infinite, then God is the one substance, and the substance must have infinite attributes, and we must all be modes of the one, which all sounds kind of nice and if you feel good to read, I don't see why they had to kick him out. It's very gaya s so, so in this God is not the personal god.

God in nature one the highest ethic is to live in accordance with the laws of nature and in doing so be a part of the infinite. So would what people were really disgusted by a pen which is how terrible to live one with nature? Is that you know, he's they're talking about a God that is, you know, amorphous and infinite and almost unknowable except by nature. And to say that nature might be greater than man at that point, obviously would be sort of like, what are

you talking about? What we're trying to get away from our animal selves and you're saying that this God has a body in the form of everything. Yeah. Plus, I mean he's saying, you know, God is boundless. God is you know, ultimately not something you can know. You can't contain God, and uh, And really that's what religion is all about, containing God, shackling God, creating narrow definitions for what God is and what God wants. Yeah, little God kidges. Yeah,

that's my take. Anyway. What I really like about Spinezza is that he wrote ethics in the guise of geometry. So he's calling out himself and pretty much saying, I intend to to put this in the guise of geometry, but I'm saying some pretty radical things for the time. All Right, we're gonna take another quick break, and when we come back, we're going to talk a little bit about where this leads us in the pool of the infinite and where are we hope to move on to

in the next episode. All Right, we are back, and hopefully we have laid the groundwork for infinity, what it's not, and maybe inching toward a concept of what it is. Um you know, the question comes up, does infinity exist? Is it like that perfect circle that we've talked about before. Is it something that that only exists within mathematics? Does

it exist within mathematics? It kind of goes to step even further than that, which is why the next episode is going to deal heavily with us and uh, you know, because of then we kind of get into those questions that we've grappled with before, we've unwrestled with. Maybe that's a better way to describe it is map intrinsic or extrinsic to humans. And then that brings up the question about infinity itself. Do we exist within infinity? Can you exist outside of it? Which brings up the question of

time existing in and out of time? So all of these concepts are bound up with one another and it's ah, some good territory to chew over. Yeah. Like another big one is when is infinity and acceptable answer to a question? Because if if I were to ask my son how many cashes would you like and he was to say infinite cashows, that would be a problem because I don't have infinite cashoes and he cannot eat infinite cashows. I don't think you should have more than four, to be honest,

there's a thought experiment there, my friend. Um, but I think, yeah, what this all gets down to is that complete knowledge is impossible. Yeah, we've talked about this and they all accept for Chuck Norris, who has counted to infinity twice And do do you check out the next episode because we do have some really great thought experiments in there, uh, including the infinite Hotel. Yeah, you get to choose the point during the podcast when you go Matt, We're not

going to tell you when lose your mind. Hey. In the meantime, make sure you've got to stuff to Blow your Mind dot com. That's where you'll find all the podcast episodes, and particularly on on this one. In recent episodem you know, trying to include links to up other topics that we've covered, being blog form, video form, etcetera that are related, as well as links out to some

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