Speaker 1: Welcome to Stuff to Blow Your Mind from how Stuff
Speaker 1: Works dot com. Hey, you're welcome to Stuff to Blow
Speaker 1: your Mind. My name is Robert Lamb and um Julie Douglas,
Speaker 1: and this is our second episode on infinity. If you
Speaker 1: missed the first one, if you recommend you go back
Speaker 1: and listen to that one. But we are going to
Speaker 1: do a little recap here in case any of the
Speaker 1: information has fallen out of your head in the time being. Yeah,
Speaker 1: so let's talk about what infinity is and what it
Speaker 1: is not, because that's our nice little baseline there. It
Speaker 1: is not a real number, because we discussed before. You
Speaker 1: can't say that infinity is X number. You can't write
Speaker 1: it on a check. You can use a symbol, I guess,
Speaker 1: but good luck cashing it. Uh, why have I never
Speaker 1: done that? Uh? It cannot be measured. Of course, that
Speaker 1: is tied back to it not being a real number.
Speaker 1: It's not something that's growing, it's not doing anything. It's
Speaker 1: the ultimate Zen concept. It just is yes. And of
Speaker 1: course this has been an important topic to philosophers, uh, theologians,
Speaker 1: great thinkers throughout time, and that's one of the primary
Speaker 1: things we discussed in our last episode because Ultimately you
Speaker 1: get into discussions about the boundless, about the limits of things.
Speaker 1: I mean, you're dealing with everything from the basic human experience.
Speaker 1: You know, how do I deal with the fact that
Speaker 1: my life only stretches on until so so long? How
Speaker 1: do I deal with the fact that I can only
Speaker 1: perceive the universe with a certain bubble of perception. And
Speaker 1: then you start imagining a god and you're trying to
Speaker 1: figure out how that works. Is God is God? Infinite?
Speaker 1: Is God physically infinite? Is God infinite in quality as
Speaker 1: opposed to quantity. It's to say the biggest idea is
Speaker 1: it is the the the infinite idea that the humanity
Speaker 1: has tackled with over the ages. Yeah, and we talked
Speaker 1: about George Tvorski writing for Ion nine, and he used
Speaker 1: the chess board to illustrate this idea, saying that all
Speaker 1: the other pieces having number assigned to it except for
Speaker 1: the king, whose number value is infinite. Yeah, that chess
Speaker 1: is It is interesting because we mentioned before, you have
Speaker 1: a finite number of playable games for chess, and then
Speaker 1: you then you have this king that has an infinite
Speaker 1: importance within the game, So you have two different types
Speaker 1: of infinity going on there. Yeah, you lose, you lose
Speaker 1: the king, You lose the game because zer or some
Speaker 1: game if you get rid of the king, and so
Speaker 1: again it ties back to this whole idea about eternity
Speaker 1: even consciousness uh embedded in there with infinity. So of
Speaker 1: course it becomes with this great uh media area for
Speaker 1: philosophers to really tussle with, because it's got the afterlife there,
Speaker 1: it's got the idea and the question of God, and
Speaker 1: by its very nature, it's an idea that we cannot
Speaker 1: fully contain and we cannot really completely grasp it, and
Speaker 1: yet we try to and so did philosophers as we
Speaker 1: discussed the last episode, and they used to try to
Speaker 1: prove this out or try to make their arguments even
Speaker 1: more persuasive. So today we're gonna look at some examples
Speaker 1: in math and physics to see how well we can
Speaker 1: contain the idea of infinity and reach some sort of meaning,
Speaker 1: which we already talked about as sort of impossible, like
Speaker 1: meaning is infinite in itself for various reasons. To just
Speaker 1: to recap mathematics and infinity, you voluencountered numbers like twelve
Speaker 1: point one to nine, eight, seven, six, five, three, two, one, zero, one,
Speaker 1: just on on and on forever. You just have to
Speaker 1: stop counting those numbers. After a while, you have to
Speaker 1: stop recording them because it becomes a pointless exercise. You
Speaker 1: just round up, right. Is that because humans are finite
Speaker 1: and we kind of continue to count infinitely. Yeah, that's
Speaker 1: that's Uh, that's kind of the big topic of discussion here.
Speaker 1: And so you kind of have two schools of thought
Speaker 1: in mathematics, right when when it comes to to struggling
Speaker 1: with the infinite, and it kind of comes down to
Speaker 1: some of the core arguments with mathematics itself. So is
Speaker 1: is mathematical infinity? Is this a mere human creation, an
Speaker 1: extrapolation into the world where there's no truth? Or does
Speaker 1: mathematical infinity actually exist? Well, this comes down to the
Speaker 1: question of God to rite. There are some observable things
Speaker 1: of how infinity works in mathematics, um, and I say observable,
Speaker 1: but you can it's just as we discussed in your example.
Speaker 1: There numbers can go on and on forever, and we
Speaker 1: have finite lives. Uh, we can't see God in Therefore,
Speaker 1: some people would say he or she or it does
Speaker 1: not exist. So you're grappling with some of the same
Speaker 1: concepts in math and in infinity. So if you were
Speaker 1: to ask the constructivists or the institutionists, they would say
Speaker 1: that classical mathematics, well, they deal with the sort of
Speaker 1: math that God would do. An infinite God he can
Speaker 1: tackle with infinite numbers. Uh, and and and the idea
Speaker 1: of a mathematical infinity. But we are humans, we are finite,
Speaker 1: and we would rather focus with human mathematics with finite
Speaker 1: numbers because that ultimately is what relates to what we do.
Speaker 1: You know what I hear with that, my brain hurts.
Speaker 1: I'll just I'll just leave it to God. He or
Speaker 1: she or it can deal with it. Yeah, I mean,
Speaker 1: it's kind of the idea that infinity is an interesting
Speaker 1: topic to tackle with as an abstraction, but does it
Speaker 1: really relate to the work that I'm doing here, the
Speaker 1: work that mathematics needs to do in the world. And
Speaker 1: then they're the formalist Now. Formalism is a theory that
Speaker 1: holds that statements of mathematics and logic can be thought
Speaker 1: of as statements about the consequences of certain certain string
Speaker 1: manipulation rules. Um systematic formulation of the concept of mathematical
Speaker 1: formulism arose directly as a reaction to the paradox discovered
Speaker 1: within set theory, which studies the concept of infinity. According
Speaker 1: to twenty century mathematician Abraham Robinson, infinite totalities do not exist,
Speaker 1: either really or ideally. Any mentioned of infinite totalities is meaningless. Still,
Speaker 1: the business of mathematics must continue as if infinite totalities
Speaker 1: actually do exist. Right, we said, there are a couple
Speaker 1: of things that we're talking about. A system here in
Speaker 1: this idea that you can again capture infinity. You can
Speaker 1: define it um and then set theory, which is something
Speaker 1: that a man named Georg Cantor came up with. And
Speaker 1: he's sort of the rabble rouser here. According to Natalie
Speaker 1: while cover writing for Quantum magazine, infinity was boxed and
Speaker 1: sold to the mathematical community in the late night concentury
Speaker 1: by the German mathematician Georg Cantor, who invented a branch
Speaker 1: of mathematics dealing with sets collections of elements that ranged
Speaker 1: from empty the equivalent of the number zero to infinite.
Speaker 1: So Cantra stepped in there really and began to define
Speaker 1: infinity in a much more specific way. Yeah, and uh
Speaker 1: he was he was a one of these individuals who
Speaker 1: was hated as well as love, depending on who you're asking,
Speaker 1: because he was bringing up some really mind blowing, disturbing
Speaker 1: takes on infinity. Yeah. Natalie Walquiver says that other mathematicians
Speaker 1: initially despise what they called this mess of infinities. And
Speaker 1: we'll talk more about this because it's largely due to
Speaker 1: his ideas of set theory, and one of his colleagues
Speaker 1: called them a grave disease. Another called him a corrupter
Speaker 1: of you. Uh. Sadly, he was so vilified that he
Speaker 1: actually um fill into a lifelong depression after that. Um.
Speaker 1: But I think it tells you how radical some of
Speaker 1: these ideas were at the time and still are really,
Speaker 1: because what it does is it just sets minds ablaze
Speaker 1: as to what what reality is and isn't. Essentially, Yeah,
Speaker 1: I mean, one of the core concepts to come out
Speaker 1: of it is that there are different kinds of infinity
Speaker 1: and some are bigger than others. Well, that that's thinking
Speaker 1: for a second. Yeah, let me let's get into the
Speaker 1: math sweats here. I'm having the math sweats right now. Uh.
Speaker 1: Set theory is essentially a useful language for describing mathematical objects.
Speaker 1: And what we're talking about is a nine item list
Speaker 1: of rules that Cantor came up with called Zermelo Frankel
Speaker 1: set theory with the axiom of choice or the z
Speaker 1: f C, established and widely adopted in math by the
Speaker 1: nineteen twenties. Okay Um. One of the axioms says that
Speaker 1: two sets are equal if they contain the same elements.
Speaker 1: Another simply asserts that infinite sets exist. So you can
Speaker 1: have these infinite sets that are one to one equal
Speaker 1: to each other, and you have them going on forever
Speaker 1: and ever and ever and ever. And Cantor showed that
Speaker 1: for any infinite set, forming a new set made of
Speaker 1: all the subsets of the original sets represents a bigger
Speaker 1: infinity than that original set. So once you have one infinity,
Speaker 1: you can always make a bigger one by creating a
Speaker 1: subset the original set, and then an even bigger one
Speaker 1: by making a set of all the subsets, and so
Speaker 1: on and so forth. And there are an infinite amount
Speaker 1: of infinities in different sizes. And he also proved doubt
Speaker 1: that an infinite set of even numbers like two, four,
Speaker 1: or six could be put in that one to one
Speaker 1: correspondence with all counting numbers like one to three. So
Speaker 1: that came to this idea that there are as many
Speaker 1: evens as there are odds and evens in an infinite set.
Speaker 1: There's one problem with this, though, real numbers, yes, like
Speaker 1: the one that you talked about earlier. You know that
Speaker 1: for example point zero zero zero one or pie right
Speaker 1: three point one four or so on and so forth,
Speaker 1: blah blah blah blah. They go on for an ever
Speaker 1: and they are uncountable, and they don't correspond in a
Speaker 1: one to one fashion with counting numbers. But hold on
Speaker 1: because we will get back to that. If that didn't
Speaker 1: thinking completely. Will return to the unccountability of real numbers
Speaker 1: in a minute, once we have a structure in which
Speaker 1: to house them. All right, I am going to dab
Speaker 1: at the infinite number of sweat molecules dripping off of
Speaker 1: me right now. Uh No, it's not too bad actually,
Speaker 1: Uh And let's take a break. When we get back,
Speaker 1: you'll talk more about the infinite hotel. If you're out
Speaker 1: there and you're thinking, I don't know what they're talking
Speaker 1: about there, they're losing me. I'm sinking beneath the waters
Speaker 1: here in the It is the in the deep end
Speaker 1: of the mathematical, philosophical, theological, physical pool. I need help,
Speaker 1: while we need help to for the love of infinity,
Speaker 1: give me an example. Yes, we do have, We do
Speaker 1: have an example. We have a flotation device. And it
Speaker 1: is a thought experiment, because the thought of experiments, as
Speaker 1: always they can take some very difficult to grasp ideas
Speaker 1: and concepts and put them into into a metaphorical form
Speaker 1: that we can latch onto and then and then actually
Speaker 1: explore the concept a little more easily and sometimes a
Speaker 1: little a little deeper. Right, And what could be more
Speaker 1: of a form inaccessible than a building, which is essentially
Speaker 1: what we're talking about. Um, this is an infinite building,
Speaker 1: an infinite hotel. And this was created by German mathematician
Speaker 1: David Hilbert who was obsessed with cantors work and and
Speaker 1: came up with us little ditty to try to explain
Speaker 1: a hotel with an infinite number of rooms. All right,
Speaker 1: it's so it's a hotel, infinite number of rooms? How
Speaker 1: many how many rooms? Does it have to like an
Speaker 1: infinite amount? Oh but accountable infinite amount, which is going
Speaker 1: to turn out to be important. All right, So let's
Speaker 1: say just to just to roll out the basic entry
Speaker 1: level portion of the thought experiment. I show up to
Speaker 1: the Infinity Hotel, all right, and and I need a
Speaker 1: room for the night. I know there's a convention in town. Uh,
Speaker 1: the local set theory convention maybe, and uh, and I
Speaker 1: I know that all the hotels are booked, but I
Speaker 1: really need a room. So the Infinity Hotel sounds like
Speaker 1: a good place to go, all right, So let me
Speaker 1: a my jaunty little manager's bellhop cap here. What I
Speaker 1: am going to do is, I'm going to ask the
Speaker 1: guests in room do you have vacancy? Always? We have
Speaker 1: an infinite amount of rooms. Okay, I see a lot
Speaker 1: of cars in the parking lot. Hold up, okay, just
Speaker 1: look at a magazine or something. We'll figure this out.
Speaker 1: I'm going to ask the guests in room one to
Speaker 1: move to room two, and then the guests in room
Speaker 1: two to move to room three, and so on and
Speaker 1: so forth. Every guest moves to room N plus one.
Speaker 1: And since there are an infinite amount of rooms here,
Speaker 1: then there's room for every guest to move into a
Speaker 1: different room. So you're saying that even though they're already
Speaker 1: infinite guests at the infinity hotel. Occupying the infinite rooms,
Speaker 1: you can still make everyone move over one room and
Speaker 1: thus open up a single room for me to stay
Speaker 1: in this evening. You, a whole person, a whole number,
Speaker 1: a natural person, a natural number, may and are into
Speaker 1: this hotel in fact, and if forty other people want
Speaker 1: to join you, they can, I mean not in your room. Obviously,
Speaker 1: you don't want to sleep with forty other people in
Speaker 1: your room. But forty other people would like to get
Speaker 1: forty rooms. Well, hey guess what they can. And all
Speaker 1: I have to do is have everybody gather their luggage
Speaker 1: and move to room N plus forty. So if you
Speaker 1: are in room two, now you move to room two.
Speaker 1: That sounds reasonable. I'm gonna pick up my bags, I'm
Speaker 1: gonna move on in and hopeful I'm gonna be a
Speaker 1: sleep in an hour or two. Oh. By the way,
Speaker 1: I see a bus coming around the corner. Looks like
Speaker 1: some more guests are arriving. Thus containing a countardly infinite
Speaker 1: number of people arriving. No problem. All I have to
Speaker 1: do is ask each guest to move to room N
Speaker 1: to room number two N. So room one moves room
Speaker 1: to room two to four Room three to six and
Speaker 1: four to eight, and this fills up all the infinite
Speaker 1: rooms and empties all the infinite odd rooms. So you're
Speaker 1: telling me that the Infinity Hotel, which is currently filled
Speaker 1: up with infinite number of guests, has room to take
Speaker 1: care of the guests the infinite number of guests arriving
Speaker 1: in an infinity bus. That's right, because all it is
Speaker 1: is shifted to everybody to the infinite even number rooms
Speaker 1: to accommodate all the infinite amount of people coming off
Speaker 1: the infinite buses. I'm gonna put them all in odd
Speaker 1: number rooms. And you remember Cantor in his infinite sets.
Speaker 1: This is an example of those one to one matches,
Speaker 1: not to mention, underscoring the idea that Cantor had that
Speaker 1: there are an infinite odd and even amount of numbers.
Speaker 1: So so, so far, the Infinity Hotel thought experiment is
Speaker 1: holding up. But of course, one of the the fun
Speaker 1: things about thought experiments is that you can continue to
Speaker 1: experience with them in an attempt to break them, to
Speaker 1: push them to the absolute limits. Break come on, Okay, Well,
Speaker 1: so far the Infinity Hotel has been able to deal
Speaker 1: with one new occupant. It's been able to deal with
Speaker 1: a bus full of infinite new occupants. But what does
Speaker 1: it do of coming around the corner? Are infinite buses
Speaker 1: and each bus has infinite yes, I mean just an
Speaker 1: infinite line of infinitely filled buses. All right, well, maybe
Speaker 1: I remember that youklid said that they're an infinite number
Speaker 1: of prime numbers. Yep, I just remembered that. And so
Speaker 1: current occupants of rooms are assigned the prime number two.
Speaker 1: So for instance, the current occupant of room number seven
Speaker 1: goes to two to the seventh power or room. Then
Speaker 1: the next group they're all assigned to the prime number three,
Speaker 1: and they take their bus seat numbers to figure out
Speaker 1: their room numbers. So seat number seven goes to three
Speaker 1: to the seventh power or room two thousand and seven.
Speaker 1: And I want to throw in it. This is important
Speaker 1: because if you just did them bust by bus, you
Speaker 1: would never finish onload owning the first bus. Well, yeah,
Speaker 1: first you gotta take uh, you gotta take care of
Speaker 1: your career that's already in in the hotel, right that
Speaker 1: you've given that prime number two, And then yes, you
Speaker 1: have to start referring to bus seat numbers to begin
Speaker 1: applying all the infinite number of prime numbers, so you
Speaker 1: can do this. Each each new group gets a new
Speaker 1: prime number, so you know, you go to the you know,
Speaker 1: prime number five, then prime number seven, eleven, and thirteen,
Speaker 1: and everybody just has to reference that number on their
Speaker 1: bus seat. So again, this is just really it's it's messy,
Speaker 1: but there's an elegant system to take place or to
Speaker 1: make sure that everybody gets their place, and that ensures
Speaker 1: that there are no overlapping room numbers for the infinite
Speaker 1: amount of people filing out of the infinite number of buses.
Speaker 1: Here's here's the thing, though, here's the thing. Okay, here's
Speaker 1: what I don't want to see coming out of those buses.
Speaker 1: I don't want to see any irrational numbers. I'm talking
Speaker 1: about you, pie. I don't want to see you tumbling
Speaker 1: off the bus because this is not going to work.
Speaker 1: I don't need to see a negative seven a representation
Speaker 1: human representation of a negative seven. First, you're you're negative, right,
Speaker 1: you're killing the vibe here in the hotel. Second, I
Speaker 1: don't have negative numbers. I don't have basement number rooms,
Speaker 1: you know, extending infinitely down into my my building here,
Speaker 1: and I don't have half fractional rooms available, because that
Speaker 1: ultimately breaks the hotel, that brings everything crashing down, because
Speaker 1: there's one infinity that's too big, and that's the infinity
Speaker 1: contained in a continuous flying, a continuous line of real
Speaker 1: numbers that goes on forever. If it showed up at
Speaker 1: the hotel, they wouldn't be room for everyone. You wouldn't
Speaker 1: be able to, uh to take that real number and
Speaker 1: count it. You wouldn't be able to put it on
Speaker 1: the guest list. Yeah, and that's yeah exactly, that's the problem.
Speaker 1: I mean, because we can deal with this lowest level
Speaker 1: of infinity, the countable infinity of the natural numbers, but
Speaker 1: that's uh, that real number, that continuum that Cantor had
Speaker 1: described before, that is uncountable, that doesn't behave in that
Speaker 1: one to one set way. And that's what I love
Speaker 1: about the Infinity Hotel is that it describes both these
Speaker 1: different levels of infinity, these larger amounts of infinity, but
Speaker 1: how certain numbers don't work within it or are uncountable.
Speaker 1: Plus you've seen being John Makovitch, right, you know what
Speaker 1: happens when you have a half demension, right, you had
Speaker 1: the half floor of the buildings right where where everything's
Speaker 1: cut in half and you have to stoop. And what happens,
Speaker 1: people will will use that as a vessel to somehow
Speaker 1: infiltrate your mind and hijack your body if you're placed
Speaker 1: in a half room or a half floor. Yeah, and
Speaker 1: that nobody wants that. It's gonna hard hard to retain
Speaker 1: tenants when you have that going on. Exactly, so again
Speaker 1: you have Cantor's continum hype offices. Fit says that there's
Speaker 1: there's no set whose cardinality is strictly between that of
Speaker 1: the integers and the real numbers. Can't prove it's true,
Speaker 1: can't prove it's false, can't measure it, can't hunt for
Speaker 1: a particle or measure anything about it. Yes, those real
Speaker 1: numbers are uncountable in this scenario of infinity. And then
Speaker 1: along uh of of and about nine gun named Goodill
Speaker 1: has a pair of proofs that are just spectacular to
Speaker 1: the math community because essentially he shows that you can
Speaker 1: never prove that the continuum hypothesis is false. And this
Speaker 1: feels like, uh, you're like you're moving the needle here
Speaker 1: on infinity just a bit right, Like we think we've
Speaker 1: grabbed onto something here. The problem is that in nineteen
Speaker 1: sixty or they're about Paul J. Cohen shows that you
Speaker 1: can never prove that the continuum hypothesis is true. And
Speaker 1: why does it all of this matter is because it
Speaker 1: shows that there are unanswerable questions in mathematics, particularly dealing
Speaker 1: with infinity, which just is really a microcosm of the
Speaker 1: macrocosm problem of the unknowability of life in general. So
Speaker 1: if your brain is exploding right now, don't worry, because
Speaker 1: now we're going to take it back to physics. We're
Speaker 1: gonna take it to discussions of the physical world as
Speaker 1: complicated and mind blowing is that whole realm can get
Speaker 1: at least we're dealing with observable physical reality, right, Sure,
Speaker 1: you say that, And now I have the physics sweats,
Speaker 1: which is an entirely different stench here. And that's understandable. Yes,
Speaker 1: but because certainly physics gets very complicated as well. But
Speaker 1: when but here's the thing. When we see infinities in physics, generally,
Speaker 1: it means that we have a problem and means that
Speaker 1: something's really catastrophic wrong unless you get into theoretical physics,
Speaker 1: as we will in a second. Yes, but you know
Speaker 1: basic physics, you're trying to use somebody that's designing. You know,
Speaker 1: you know a new building and you look at the plans.
Speaker 1: If you see infinity on there, you know that something
Speaker 1: is wrong. You do not want to try and stand
Speaker 1: in that building or or or or certainly have an
Speaker 1: office in it. Um it's never an actual measurement. It
Speaker 1: doesn't correspond to to to reality as as we we
Speaker 1: deal with it in our lives right today, for instance,
Speaker 1: quantum mechanics okay um and and and in such an
Speaker 1: important area of studies. So many of our greatest technological
Speaker 1: achievements in recent memory have arisen out of quantum mechanics.
Speaker 1: But even here we see this crisis. The crisis being
Speaker 1: that even though we can predict the the light heat
Speaker 1: power emission of a lamp, it's a finite amount of energy,
Speaker 1: but the various wigglings of waves and atoms creates this
Speaker 1: answer infinite energy, which which we simply can't deal with.
Speaker 1: Right we know that there's not infinite energy coming out
Speaker 1: of off of a lamp, so we afterwards we have
Speaker 1: to begin applying quantum physics to the forces of our universe.
Speaker 1: Quantum field theory, which is of course initially played infinities
Speaker 1: as well, and it takes ends up taking decades to
Speaker 1: flog through it all. You end up, you know, having
Speaker 1: all these infinities, all of these problems in the in
Speaker 1: the theory that have to be eradicated, like like enemies
Speaker 1: floating around in a video game, or which becomes incredibly
Speaker 1: important if you're looking at particle physics, right, because if
Speaker 1: you're trying to isolate the Higgs boson, you're taking these
Speaker 1: finite number of particles that we know and have named
Speaker 1: in seeing how they behave right, you do not need
Speaker 1: infinity in the mix if you're trying to figure out
Speaker 1: the composition of the universe, both from the time in
Speaker 1: which it became to now I mean, take the Higgs
Speaker 1: for example, the search for the Higgs boson, this was
Speaker 1: such the so called god particle, right. Uh. This uh, this,
Speaker 1: this of course been one of the predominant science stories
Speaker 1: in recent years, because the whole idea was that we
Speaker 1: had infinities in the theory, we had to remove them,
Speaker 1: and the thing that could remove it would be this
Speaker 1: Higgs particle. Right, So the whole quest for the Higgs
Speaker 1: particle comes out of this, this this necessity, this need
Speaker 1: to eradicate the infinities from the theory, because again, infinite's
Speaker 1: just don't work in the set and the infinities here
Speaker 1: in the theory said said, all right, we have an infinity.
Speaker 1: That means there's something finite in the world that we
Speaker 1: haven't discovered yet, and if we discover it, then we
Speaker 1: find our way around that answer. Now, if you sort
Speaker 1: of back up and then begin to take the large
Speaker 1: view of the universe and not just try to contain
Speaker 1: it in this this one model, right, you know that
Speaker 1: the universe is expanding how much infinitely? These are questions
Speaker 1: that come up, and then you begin to say, well,
Speaker 1: how how far does space go? Anyway? And this is
Speaker 1: where theoretical physicists get into infinity and they really have
Speaker 1: some fun um And it's fascinating because here you see
Speaker 1: some examples of infinity played out in ways that you say,
Speaker 1: this is a possibility, because infinity otherwise we just see
Speaker 1: is this sort of you know, the line on the
Speaker 1: piece of paper and mathematics that goes on forever. But
Speaker 1: then you've got these ideas like multiverse existing. Now, when
Speaker 1: I think of the multiverse, I always think of Jorey
Speaker 1: Lewis Borges the Library of Battle, the library that first
Speaker 1: of all contains all books, all written books, but then
Speaker 1: beyond that also contains all possible books, and and and
Speaker 1: and and so being is is ultimately kind of a
Speaker 1: model for a multiverse. Uh, an existence that contains everything
Speaker 1: that is and everything that could be. Again, you go
Speaker 1: back to Cantor, and you're talking about larger infinities, right,
Speaker 1: And essentially that's what we're talking about with multiverses. And
Speaker 1: I'm going to read this from Brian Green's The Elegant Universe. Um,
Speaker 1: we could talk about multiverse in its very own episodes.
Speaker 1: We won't go too deep here, he says, Imagine that
Speaker 1: what we call the universe is actually only one tiny
Speaker 1: part of a vastly larger cosmological expanse, one of the
Speaker 1: nor almost number of island universes scattered across a grand
Speaker 1: cosmological archipelago. Although this might sound rather far fetched, and
Speaker 1: in the end it may well be, Andrei Lynd has
Speaker 1: suggested a concrete mechanism that might lead to such a
Speaker 1: Gargangan universe. Lynn has found that the brief but crucial
Speaker 1: burst of inflationary expanse may not have been a unique
Speaker 1: one time event. Instead, he argues the conditions for inflationary
Speaker 1: expansion may happen repeatedly in isolated regions and the peppered
Speaker 1: throughout the cosmos, which then undergo their own inflationary ballooning
Speaker 1: and size, evolving into new separate universes. And each of
Speaker 1: the universes, the process continues, with new universes sprouting from
Speaker 1: far flung regions in the old, generating a never ending
Speaker 1: web of ballooning cosmic expanses. And this is what he
Speaker 1: calls the multiverse. And that's pretty mind blow I mean,
Speaker 1: even if you you shrink back down to are single universe. Um.
Speaker 1: There was an interesting point that was brought up by
Speaker 1: physicist Raphael Bosso in that World Science Festival talk I
Speaker 1: was mentioning earlier. We will include a link to in
Speaker 1: the landing page for this podcast episode. But he pointed
Speaker 1: out that that when you start start looking at the
Speaker 1: way light travels across the universe, when you start looking
Speaker 1: at this expansion of the universe, you end up with
Speaker 1: a universe that's arbitrarily large. Light can never reach you
Speaker 1: from rapidly expanding regions regions, and so any given observer
Speaker 1: is trapped within a finite sphere of observable universe within
Speaker 1: an expanding infinite. So you kind of get this again.
Speaker 1: You get these ideas of here's this, here's the sphere
Speaker 1: of the finite within the infinite. You can think about
Speaker 1: the infinite, but you're ultimately trapped within that sphere of
Speaker 1: the finite. Yeah, and this is a similar idea that
Speaker 1: Lee Smollen has in terms of the perception of the
Speaker 1: infinite at least. Smallen, by the way, is a cosmologist
Speaker 1: at and State, and his idea is that the conditions
Speaker 1: at the Big Bang and at the centers of black holes,
Speaker 1: each being characterized by a colossal density of crushed matter.
Speaker 1: I suggested that every black hole is the seed for
Speaker 1: a new universe that erupts into existence through a Big
Speaker 1: Bang like explosion, but is forever hidden from our view
Speaker 1: by the black holes event horizon. And of course, any
Speaker 1: of these discussions of the physical universe are are even
Speaker 1: more twisted when you when you have coorse draw in
Speaker 1: the fact that time and space are one, and if
Speaker 1: you play with space, you're playing with time, and if
Speaker 1: it were to be flat, then it could stretch out
Speaker 1: for an infinity, right, And then you get all these
Speaker 1: different ideas of well maybe in this case that supports
Speaker 1: this idea of some sort of repeating going on because
Speaker 1: you have a finite number of particles that you have
Speaker 1: infinite space and time, and maybe that repeating pattern creates
Speaker 1: more universes, right, And then you have ever many worlds
Speaker 1: interpretation that says that the universe branches off into distinct
Speaker 1: worlds to accommodate every single possible outcome. And so maybe
Speaker 1: we live in an infinite web of alternate timelines. I mean,
Speaker 1: it gets crazy and crazy as you go along. So yes,
Speaker 1: I mean I don't even have to everyone else's mind
Speaker 1: is extrapolating the possibilities on that. I don't have to
Speaker 1: push you in that direction. And if you guys would
Speaker 1: like some articles to accompany this, uh, we have ever
Speaker 1: many worlds interpretation on how stuff works, and we also
Speaker 1: have some good amount of string theory and multiverse um,
Speaker 1: so we definitely have some stuff for you guys to
Speaker 1: dive into. Yes, on the Internet, which is of course
Speaker 1: a finite world. Even though it is it is a
Speaker 1: finite world. But yet we we can't even grasp what
Speaker 1: We can't even put a number on it. We can't
Speaker 1: say how many pages there actually are on the Internet.
Speaker 1: We can't actually even comprehend it's a finite thing we've created,
Speaker 1: and it is already, at least as far as human
Speaker 1: perception goes, bordering the infinite. Let's supposed to just fine,
Speaker 1: since we can see its growth and we can put
Speaker 1: a number on it. But it feels infinite at times. Alright,
Speaker 1: So we're gonna walk you guys out of this um
Speaker 1: and we're gonna take a little walk into something called
Speaker 1: the infinite monkey theorem to end this section. Yeah good.
Speaker 1: This is an you know, a thought experiment that I
Speaker 1: often forget even really entails infinity, maybe because I just
Speaker 1: get too caught up on the idea of monkeys banging
Speaker 1: on typewriters and now awful that writing room, let's be,
Speaker 1: and I've I've written in some awful rooms before. Uh.
Speaker 1: This states that a monkey hidden keys at random on
Speaker 1: a typewriter keyboard for an infinite amount of time will
Speaker 1: almost surely type a given text, like say, the complete
Speaker 1: works of William Shakespeare. Okay, okay, And so in this context,
Speaker 1: almost surely is a mathematical term, alright, and it has
Speaker 1: a precise meaning, And that monkey is not an actual
Speaker 1: monkey but a metaphor for an abstract device that produces
Speaker 1: a random sequence of letters for an infinity. In the
Speaker 1: theorem illustrates the perils of reasoning about infinity by imagining
Speaker 1: this vast that finite number, and vice versa. So the
Speaker 1: probability is really tiny, right, The probability exists that a
Speaker 1: monkey could eventually write a work as cohesive as say
Speaker 1: Shakespeare's Hamlet, just by pure dumb accident of banging on
Speaker 1: the keys forever and ever and ever endever, which gives
Speaker 1: my fiction writing some hope. Oh you're you're better than
Speaker 1: a monkey. I don't know. I don't know about that,
Speaker 1: and I'm fine with that actually, all right, So if
Speaker 1: you're still with us, then hopefully you have you maybe
Speaker 1: you have a better idea of what infinity is all about.
Speaker 1: Maybe you have more nuanced idea, more expansive idea. Maybe
Speaker 1: this is uh forced you to sort rearrange your your
Speaker 1: contemplation of the infinite and of the boundless, in terms
Speaker 1: of of our human experience, in terms of our cosmos,
Speaker 1: in terms of our ideas of God. So we'd love
Speaker 1: to hear from you. We'd love to hear your thoughts
Speaker 1: about infinity, your personal takes on infinity, your favorite uses
Speaker 1: of infinity and fiction. All of that is fair game. Yeah,
Speaker 1: and before you do that, make sure you stopped at
Speaker 1: Stuff to Blow your Mind dot com. That's right, That's
Speaker 1: where you'll find all the podcast episodes, all the videos,
Speaker 1: all of the blog posts, a finite amount of all
Speaker 1: of those, but certainly plenty of stuff to keep you occupied. Yeah,
Speaker 1: So share those thoughts with us, why don't you? And
Speaker 1: you can do that at below the mind house to
Speaker 1: works dot com. For more on this and thousands of
Speaker 1: other topics, visit how stuff works dot com