Speaker 1: Welcome to Stuff to Blow Your Mind from how Stuff
Speaker 1: Works dot com. Hey, welcome to Stuff to Blow your Mind.
Speaker 1: My name is Robert Lamb and I'm Julie Dougness and Julie,
Speaker 1: I believe this is definitely a case where we're biting
Speaker 1: off more than we can choose an infante amount that
Speaker 1: we can choot and maybe you guys can listen to you.
Speaker 1: I don't know, we're gonna find out. Yeah, because we're
Speaker 1: taking two episodes to discuss infinity only infinite amounts, right,
Speaker 1: We're taking a finite number of episodes in each episode
Speaker 1: is uh you know, consists of a finite uh number
Speaker 1: of minutes. There only there's only so much time and
Speaker 1: energy we can throw at the topic. And the topic
Speaker 1: is the the infinite, the boundless, the pretty much one
Speaker 1: of the biggest, most mind staggering concepts you could attempt
Speaker 1: to try and comprehend. So you're gonna get lost along
Speaker 1: the way. We're gonna get lost along the way, and
Speaker 1: hopefully we will not all remain lost for an infinite
Speaker 1: amount of time and just completely lose our minds. But yeah,
Speaker 1: in full disclosure, at some point I'm going to have
Speaker 1: the math sweats but you know, we're all going to
Speaker 1: wait into the deep end of the pool to gather
Speaker 1: the deep end of the philosophical pool, the theological pool,
Speaker 1: the mathematical pool, to the physical pool. Uh, we're all
Speaker 1: going to go together and hopefully none of us will
Speaker 1: sink beneath the waters infinitely. But in the meantime, let's
Speaker 1: get our hands and our minds around the concept of infinity,
Speaker 1: because we use it all the time, or at least
Speaker 1: my kid does. When she's really excited about something, she'll say,
Speaker 1: infinity plus one. I totally want to go to Chuck
Speaker 1: E Cheese, which is its own infinite hell um. But again,
Speaker 1: it's we find this parlance um a way to try
Speaker 1: to describe something that feels like it's going to go
Speaker 1: on forever and ever. Yeah, and you know, also another
Speaker 1: big pop culture mentioned of this that our pretty certain
Speaker 1: knowledge is pointed out to infinity and beyond toy story movies,
Speaker 1: which on one level kind of sounds like ridiculous but
Speaker 1: actually is kind of key to some of the discussions
Speaker 1: we're going to have about the nature of infinity um um,
Speaker 1: which is kind of clever in its own way. But
Speaker 1: but indeed, infinity is this thing that we kind of
Speaker 1: pick up on even at an early age, even if
Speaker 1: we're not giving it a lot of serious consideration. UM,
Speaker 1: for your part, what was what was your earliest interaction
Speaker 1: with infinity, your earliest even attempt to utilize infinity as
Speaker 1: a concept or to think about it, or I think
Speaker 1: just when I was considering the universe and the place
Speaker 1: that I had on Earth and then Earth's place out there,
Speaker 1: and so that was the first sort of inkling of like, wow,
Speaker 1: things might go on forever and ever and ever. What
Speaker 1: about you? I definitely remember the idea of a never
Speaker 1: ending pit being the thing that came to my mind.
Speaker 1: I think this came out of like playing with Masters
Speaker 1: the Universe action figures or watching Heman cartoon and somehow
Speaker 1: getting the idea that you know, you would have not
Speaker 1: only would you have these action figures fighting on the
Speaker 1: edge of a cliff, which would probably be the back
Speaker 1: of a couch, but that this would be a cliff
Speaker 1: above just an endless chasm that they would if they
Speaker 1: start you started falling, you would just never reach the bottom.
Speaker 1: And uh, and so we would when we would play
Speaker 1: basically the Floor's Lava. Our version was the floor is
Speaker 1: a never ending pit. Oh that really amps up the
Speaker 1: the sorry by the again. Oh that really ups the
Speaker 1: anti there. Yeah, and and so I would I would
Speaker 1: think I remember thinking about the concept sometimes because then
Speaker 1: you you have to ask yourself, well, if this is
Speaker 1: a never ending pit, what does that mean? Are their
Speaker 1: walls to this pit? Do the walls go on uh
Speaker 1: at infiniteum and uh? And and if so, where is
Speaker 1: this pit? Where are the walls? Where is the universe?
Speaker 1: So you do kind of go down the wormhole a
Speaker 1: little bit and even trying to you to figure out
Speaker 1: that the rules of this fantastic childhood concept. You know
Speaker 1: what I love about this is that the band The
Speaker 1: Handsome Family has a song about a never ending pit, bottomless,
Speaker 1: bottomless pitt in this guy's backyard, and he's obsessed with it.
Speaker 1: And it's, as of course, depressing and beautiful, but it
Speaker 1: deals with that same sort of concept of just the
Speaker 1: never ending fall. Yeah, but I believe in the song
Speaker 1: his his wife lowers him down and like a bathtub
Speaker 1: or something, on a rope, and eventually the rope gives
Speaker 1: way and he's just endlessly falling down for this whole
Speaker 1: That's what I love about that band too, you know
Speaker 1: it was a cloth footub. Yeah, of course, you know
Speaker 1: you want to go down and style. Sure, all right,
Speaker 1: perhaps we should talk about what infinity is not because
Speaker 1: we've got that sort of simple idea of it's going
Speaker 1: on on forever and ever. Infinity is not a real number.
Speaker 1: We can't say, you know, it's this number of things.
Speaker 1: There's an infinite number of things. We can say an
Speaker 1: infinite amount because we don't know specifically, specifically what that
Speaker 1: number would ever be. Yeah, there's no there's no number
Speaker 1: that we can say is infinity. We just have the
Speaker 1: symbol for infinity, which of course is essentially an eight
Speaker 1: on its side, and you can think of as a
Speaker 1: little little like childhood train track that circles back in
Speaker 1: on itself. Yeah, it's actually called a Lemna skit. And
Speaker 1: John Wallace began using the symbol for infinity in sixteen
Speaker 1: fifty five. Um. Now, infinity cannot be measured, of course,
Speaker 1: which also ties into it not being a real number.
Speaker 1: It's not something that's growing, it's not doing anything. It
Speaker 1: just is okay, Yeah, so it's it's not a situation
Speaker 1: of the bottomless pit, the endless pit, an everything pit
Speaker 1: actually getting deeper and deeper it is, right, right, Yeah,
Speaker 1: And infinity comes from that Latin word infinitis, which means
Speaker 1: unbounded nous, which is a good way to look at
Speaker 1: that that pit. It is not bound to anything physically,
Speaker 1: it's just going on for an infinity. Now, the reason
Speaker 1: why this is an important concept is because it really
Speaker 1: flavors different fields of study, like mathematics and physics and philosophy.
Speaker 1: And today we're going to focus more on philosophy because
Speaker 1: I think this is really at the heart of the
Speaker 1: matter for humans of course, right, it's pretty much the
Speaker 1: the underpinnings, you know, because once you get into the mathematics,
Speaker 1: in the in the physics, uh, it's kind of the
Speaker 1: tip of the spear and uh and philosophy is kind
Speaker 1: of the shaft. And also having the philosophy in mind
Speaker 1: really helps you better grasp the mathematics and physics of
Speaker 1: the issue. Yeah, there's uh an article by George Divarsky
Speaker 1: writing for Ion nine, and he talks about why infinity
Speaker 1: is such an interest in and media concept and he says, quote,
Speaker 1: as every chess player knows, each piece is assigned a
Speaker 1: numerical value according to its tactical importance and strength These
Speaker 1: values range from one ponds to nine the queen, and
Speaker 1: are often used to keep a kind of score as
Speaker 1: the game progresses. But he says the King is a
Speaker 1: signed infinite value, and for a very good reason. He says,
Speaker 1: losing the king is fatal. It's instant game over, regardless
Speaker 1: of whatever else might be happening in the match. The
Speaker 1: King's worth therefore cannot be bound within a finite set
Speaker 1: of values. And he goes on to say therein lies
Speaker 1: another kind of infinity death right because you kin gets
Speaker 1: knocked out, as he says, it's game over. And he says,
Speaker 1: assuming that nothing awaits us in the afterlife, the termination
Speaker 1: of our lives represents a kind of eternity. It's an
Speaker 1: internity of nothingness, but an internity nonetheless. Indeed, I mean,
Speaker 1: infinity is often a concept in the religions and worldviews.
Speaker 1: And and you go back to our episode on the
Speaker 1: problem of mortality, I mean, that's that the key to
Speaker 1: that is our struggling with the whole question, you know,
Speaker 1: we what does it mean that we're not infinite? We're finite?
Speaker 1: And maybe could we become infinite? And is there anything
Speaker 1: about us or humanity or the universe that is infinite.
Speaker 1: And chance is also such an interesting concept because another
Speaker 1: uh interplay between chess and infinity is of course that
Speaker 1: there are there are a finite number of chess games
Speaker 1: start to finish when you start thinking about, all right,
Speaker 1: I could move this, uh, this pond, and then my
Speaker 1: opponent could move this pond, and then all the moves
Speaker 1: that could they could go, you know, they could transcend
Speaker 1: from the from that point there there's a finite number
Speaker 1: of chess games that exist, uh, and it's beyond our
Speaker 1: human ability to comprehend them all. But but there is
Speaker 1: a limit. If you look, if you were to look
Speaker 1: at a map of the universe of chess from an
Speaker 1: impossibly high leveled where you could see it all, you
Speaker 1: could see the collection here are the chess games, all
Speaker 1: the chess games that are possible. Yeah, and that's it's
Speaker 1: such an elegant metaphor for us grappling with the concept.
Speaker 1: And you can really see why philosophers get bound up
Speaker 1: in the idea of infinity, because the idea is if
Speaker 1: if you could solve infinity, you could solve meaning, and
Speaker 1: if you solve meaning, you could maybe solve death, or
Speaker 1: maybe you could even prove the existence of God for
Speaker 1: some philosophers. All Right, we're gonna take a quick break
Speaker 1: and we come back. We're gonna talk about some of
Speaker 1: the notable philosophers and thinkers throughout the ages that have
Speaker 1: taken their minds and tried to contain within it infinity.
Speaker 1: All Right, we're back, and we're discussing infinity. We're discussing
Speaker 1: the history of infinity in the way that various great
Speaker 1: thinkers throughout the ages have have tackled the topic. And
Speaker 1: I actually got to hear Philip Clayton, the theo logian
Speaker 1: and philosopher, discussed this at the World Science Festival few
Speaker 1: years back. Uh And he in fact highlighted several of
Speaker 1: these individuals we're gonna discuss right here. Um. A good
Speaker 1: starting point is to go back to the fifth fifth
Speaker 1: century b c e. To the philosopher Zeno of Elia. Uh. Now,
Speaker 1: he introduced the concept in the West of infinity, playing
Speaker 1: on an earlier idea of the boundless by an Aximander,
Speaker 1: which show you have to think think about this. Put
Speaker 1: yourself in the mindset of the ancient Greeks. You know,
Speaker 1: if you're big on architecture and picking out the form
Speaker 1: of things and here's the scary concept of the boundless
Speaker 1: of the infinite, and so Zino came up with several
Speaker 1: different paradox Zeno's paradox is including Achilles and the tortoise,
Speaker 1: which is an interesting little thought experiment that if you
Speaker 1: if you really focus on it too much, it means
Speaker 1: that that movement isn't really possible. It gets kind of crazy.
Speaker 1: But the basic idea here is that if a tortoise
Speaker 1: has a headstart in a race against the mythic Achilles,
Speaker 1: then Achilles can never actually catch up to the tortoise.
Speaker 1: It's gonna take the Achilles a certain amount of time
Speaker 1: to reach the point where the tortoise stopped. And then
Speaker 1: you have all these different increments in the UH, the
Speaker 1: shrinking space between the two UH. And so it means
Speaker 1: that something finite can be divided an infinite number of times.
Speaker 1: And I've seen it pointed out that that if you
Speaker 1: if you have a mortgage or any kind of arrangement
Speaker 1: with a bank on a loan, you can see that
Speaker 1: that's possible because it seems like they find a way
Speaker 1: to take a finite amount of money and make paying
Speaker 1: it back last forever. What I like about this thought
Speaker 1: experiment is that it really illustrates this concept of infinite continuum,
Speaker 1: this continuum that goes on and on forever and ever,
Speaker 1: even though you have these little finite parts of it,
Speaker 1: that that Tortoise and Achilles are forever divided by a
Speaker 1: certain space of time. Do you move onto another notable
Speaker 1: Greek thinker, there's of course Pythagoras, Greek philosopher and mathematician,
Speaker 1: invented the notion of mathematics that which can be learned,
Speaker 1: and he said that that each integer has its own
Speaker 1: spiritual meaning. Most notably, he launched the Pythagoryan theorem. Uh.
Speaker 1: Just to to run through that one again, said the
Speaker 1: square of a hypothenuse is equal to the sum of
Speaker 1: the squares of the other two sides. If you plug
Speaker 1: some ones in there. Uh, And the square root of
Speaker 1: two requires infinite digits with no repeating patterns. You can
Speaker 1: see infinity popping up right, because I mean, we've all
Speaker 1: encountered that in in in our even basic mathematics classrooms.
Speaker 1: You have that number and it has a remainder that
Speaker 1: just that repeats forever, and you just have to give
Speaker 1: up on it after a while, because the human mind
Speaker 1: can only deal with so much so that you have
Speaker 1: this infinite continuum the basis of that with Zino, with Pythagoras,
Speaker 1: you have infinite digits just going on and on, no
Speaker 1: repeating pattern. And then you have the Jain religion, the
Speaker 1: Maharivad years ago, who begin to look at the infinite
Speaker 1: and pars it in terms of different types. And they're
Speaker 1: coming up with the concepts of an infinite length and
Speaker 1: infinite volume, the concept of innumerable as represented by in
Speaker 1: and now we have even more building blocks of conceiving
Speaker 1: of infinity again within the field of mathematics, even though
Speaker 1: these are philosophers essentially grappling with grappling with the idea
Speaker 1: of infinity. Yeah, and in fact different infinities. And that's
Speaker 1: where things start getting really weird, when you start realizing
Speaker 1: there's not just the one infinity. They're different takes on infinity. Um.
Speaker 1: This leads us to Aristotle. Of course, everything seems to
Speaker 1: come back around the Aristotle when you start talking about
Speaker 1: um history of thought, especially in Western traditions um and uh.
Speaker 1: He found that with with actual infinities, physics doesn't work
Speaker 1: that well. And we'll discuss more about this later. But
Speaker 1: Aristotle said that there exists no actual infinities in the
Speaker 1: physical world, so he'd banished them two more or less.
Speaker 1: The realm of forms um and you can count. In
Speaker 1: the basis here is you can count as long as
Speaker 1: you want you can, but you experience finite results in
Speaker 1: a finite lifetime. You can divide all day or you're
Speaker 1: gonna run out of time. So you see this division
Speaker 1: between between. So even though we're talking about infinity, where
Speaker 1: of course finite minds and finite bodies and finite world. Yeah,
Speaker 1: and this he describes as the notion of potential infinity.
Speaker 1: And I like this because it kind of it's almost
Speaker 1: like straddling offense between does infinity exists and does infinity
Speaker 1: not exist? It kind of saying there's a potential for infinity.
Speaker 1: And other words, if you have a line mathematics that
Speaker 1: goes on and on forever, it exists there, but in
Speaker 1: the physical world you have a finite line. Yeah. It
Speaker 1: kind of reminds me of being in a Sunday school
Speaker 1: class when I was a kid, and and I was
Speaker 1: always one of the problematic Sunday school kids who would
Speaker 1: want to ask about the really difficult stuff and or
Speaker 1: the really crazy stuff. So I would always ask about
Speaker 1: the Book of Revelation, and I remember this one Sunday
Speaker 1: school techer. He would always just say, I don't worry
Speaker 1: about that, just don't even don't just forget about all
Speaker 1: that stuff, because that only worry about the stuff that
Speaker 1: directly relates to your life. And because that's just a
Speaker 1: bunch of you know, because it's dragons and stuff right
Speaker 1: at the end of times, its codes and all. And
Speaker 1: so you see a bit of that in this separation
Speaker 1: between the between you know, infinities and the finite, right,
Speaker 1: because we are finite and the infinity is ultimately beyond us,
Speaker 1: all right. Another person who is exploring this notion is
Speaker 1: thirteenth century theologian Thomas Aquinas. We've talked about him before too, yes,
Speaker 1: and he was very much to focus on the quality
Speaker 1: of existence rather than the quantity. And it's at least
Speaker 1: as far as infinity is concerned. So he was saying
Speaker 1: that God uh is infinite in quality more so than
Speaker 1: in quantity. So he sees it more as a mode
Speaker 1: of existence. And he identified a separation between mathematical infinity
Speaker 1: and religious infinity. So we see a curious principle emerge
Speaker 1: out of acquaintas is thinking here, even an infinite God
Speaker 1: cannot create an infinite object. So think about that. Yeah,
Speaker 1: now you have Nicholas of Cusa in the fifteenth century.
Speaker 1: He's a philosopher who says everything is included in the
Speaker 1: infinite heresy. Heresy, that's the reaction from the crowd in
Speaker 1: the third and fifteenth century. Uh So, therefore, with this model,
Speaker 1: you would have the world itself um being inside God.
Speaker 1: And he used mathematical examples to describe this God world model.
Speaker 1: And the crutch really is that God is the circle
Speaker 1: whose center is everywhere, and the circ conference is therefore nowhere.
Speaker 1: And this is called a coincidence of opposites because now
Speaker 1: you have humans that the animals that stand at the
Speaker 1: boundary between the eternal and the finite. And here's an
Speaker 1: interesting when this comes from the seventeenth century Jewish philosopher
Speaker 1: Baruk Spinoza, and he was actually kicked out of the
Speaker 1: synagogue for allegedly arguing that God has a body. This
Speaker 1: is where we see metaphysics meeting geometry. Said, if God
Speaker 1: is infinite, then God is the one substance, and the
Speaker 1: substance must have infinite attributes, and we must all be
Speaker 1: modes of the one, which all sounds kind of nice
Speaker 1: and if you feel good to read, I don't see
Speaker 1: why they had to kick him out. It's very gaya
Speaker 1: s so, so in this God is not the personal god.
Speaker 1: God in nature one the highest ethic is to live
Speaker 1: in accordance with the laws of nature and in doing
Speaker 1: so be a part of the infinite. So would what
Speaker 1: people were really disgusted by a pen which is how
Speaker 1: terrible to live one with nature? Is that you know,
Speaker 1: he's they're talking about a God that is, you know,
Speaker 1: amorphous and infinite and almost unknowable except by nature. And
Speaker 1: to say that nature might be greater than man at
Speaker 1: that point, obviously would be sort of like, what are
Speaker 1: you talking about? What we're trying to get away from
Speaker 1: our animal selves and you're saying that this God has
Speaker 1: a body in the form of everything. Yeah. Plus, I
Speaker 1: mean he's saying, you know, God is boundless. God is
Speaker 1: you know, ultimately not something you can know. You can't
Speaker 1: contain God, and uh, And really that's what religion is
Speaker 1: all about, containing God, shackling God, creating narrow definitions for
Speaker 1: what God is and what God wants. Yeah, little God kidges. Yeah,
Speaker 1: that's my take. Anyway. What I really like about Spinezza
Speaker 1: is that he wrote ethics in the guise of geometry.
Speaker 1: So he's calling out himself and pretty much saying, I
Speaker 1: intend to to put this in the guise of geometry,
Speaker 1: but I'm saying some pretty radical things for the time.
Speaker 1: All Right, we're gonna take another quick break, and when
Speaker 1: we come back, we're going to talk a little bit
Speaker 1: about where this leads us in the pool of the
Speaker 1: infinite and where are we hope to move on to
Speaker 1: in the next episode. All Right, we are back, and
Speaker 1: hopefully we have laid the groundwork for infinity, what it's not,
Speaker 1: and maybe inching toward a concept of what it is.
Speaker 1: Um you know, the question comes up, does infinity exist?
Speaker 1: Is it like that perfect circle that we've talked about before.
Speaker 1: Is it something that that only exists within mathematics? Does
Speaker 1: it exist within mathematics? It kind of goes to step
Speaker 1: even further than that, which is why the next episode
Speaker 1: is going to deal heavily with us and uh, you know,
Speaker 1: because of then we kind of get into those questions
Speaker 1: that we've grappled with before, we've unwrestled with. Maybe that's
Speaker 1: a better way to describe it is map intrinsic or
Speaker 1: extrinsic to humans. And then that brings up the question
Speaker 1: about infinity itself. Do we exist within infinity? Can you
Speaker 1: exist outside of it? Which brings up the question of
Speaker 1: time existing in and out of time? So all of
Speaker 1: these concepts are bound up with one another and it's ah,
Speaker 1: some good territory to chew over. Yeah. Like another big
Speaker 1: one is when is infinity and acceptable answer to a question?
Speaker 1: Because if if I were to ask my son how
Speaker 1: many cashes would you like and he was to say
Speaker 1: infinite cashows, that would be a problem because I don't
Speaker 1: have infinite cashoes and he cannot eat infinite cashows. I
Speaker 1: don't think you should have more than four, to be honest,
Speaker 1: there's a thought experiment there, my friend. Um, but I think, yeah,
Speaker 1: what this all gets down to is that complete knowledge
Speaker 1: is impossible. Yeah, we've talked about this and they all
Speaker 1: accept for Chuck Norris, who has counted to infinity twice
Speaker 1: And do do you check out the next episode because
Speaker 1: we do have some really great thought experiments in there, uh,
Speaker 1: including the infinite Hotel. Yeah, you get to choose the
Speaker 1: point during the podcast when you go Matt, We're not
Speaker 1: going to tell you when lose your mind. Hey. In
Speaker 1: the meantime, make sure you've got to stuff to Blow
Speaker 1: your Mind dot com. That's where you'll find all the
Speaker 1: podcast episodes, and particularly on on this one. In recent
Speaker 1: episodem you know, trying to include links to up other
Speaker 1: topics that we've covered, being blog form, video form, etcetera
Speaker 1: that are related, as well as links out to some
Speaker 1: important resources related to the podcast. If you are listening
Speaker 1: to and if you have any um infinite ideas that
Speaker 1: you want to express in a finite number of characters,
Speaker 1: you can do that by sending us an email at
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