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Hey Daniel, have you heard of Zeno's paradox?

Hey Daniel, have you heard of Zeno's paradox?

Yeah?

Yeah?

Is that the one where you can't get some work because you keep going half the distance and then half that distance and half that distance.

Is that the one where you can't get some work because you keep going half the distance and then half that distance and half that distance.

Yeah. It's kind of like this thought experiment where you say, all right, I'm trying to get home, so I'm gonna get to half of the distance to my home. And then you stop and you say, all right, now I'm gonna get half of the distance to my home. And so you go another half of that and you say, now I'm going to go half of the distance to my home, and you do that half, and so the question is will you ever get home? I mean, it sounds like you would always get there because you're always going half of what's left, but you might never get there.

Yeah. It's kind of like this thought experiment where you say, all right, I'm trying to get home, so I'm gonna get to half of the distance to my home. And then you stop and you say, all right, now I'm gonna get half of the distance to my home. And so you go another half of that and you say, now I'm going to go half of the distance to my home, and you do that half, and so the question is will you ever get home? I mean, it sounds like you would always get there because you're always going half of what's left, but you might never get there.

Right. It raises an interesting question, right because if you can cut a mile and a half and then cut that in a half to a quarter mile, and cut that in half to an eighth of a mile, can you keep cutting it to infinitely small distances? Like are those distances even meaningful on a physics point of view? Or is there a shortest possible distance in the universe? Afterwards, Zeno has to actually take that step.

Right. It raises an interesting question, right because if you can cut a mile and a half and then cut that in a half to a quarter mile, and cut that in half to an eighth of a mile, can you keep cutting it to infinitely small distances? Like are those distances even meaningful on a physics point of view? Or is there a shortest possible distance in the universe? Afterwards, Zeno has to actually take that step.

Right, So physics could be like Xeno's paradox, more like Xeno's para nut.

Right, So physics could be like Xeno's paradox, more like Xeno's para nut.

That's right, Zeno's paradox unraveled. Hi am Jorge and I'm Daniel, and welcome to our podcast. Daniel and Jorge explain the universe.

That's right, Zeno's paradox unraveled. Hi am Jorge and I'm Daniel, and welcome to our podcast. Daniel and Jorge explain the universe.

Where we take the universe, cut it in half, and then cut it in half again, and cut it in half again and again until it's small enough for everybody to understand and happily digest. This is Daniel Jorges podcast paradox.

Where we take the universe, cut it in half, and then cut it in half again, and cut it in half again and again until it's small enough for everybody to understand and happily digest. This is Daniel Jorges podcast paradox.

And unlike that paradox, this will actually end at some point in about thirty to thirty five minutes.

And unlike that paradox, this will actually end at some point in about thirty to thirty five minutes.

That's right. Not If you listen to half the podcast and then half it was left, and then half of what's left right and infinitely slicing the podcast, you can enjoy it forever.

That's right. Not If you listen to half the podcast and then half it was left, and then half of what's left right and infinitely slicing the podcast, you can enjoy it forever.

Yeah, at some point you'll be like, uh, that's.

Yeah, at some point you'll be like, uh, that's.

Right, you'd be listening to one unit of laughter. But that's sort of the question we want to talk about today. Can you slice up space into smaller and smaller pieces, Can you divide it into shorter and shorter distances?

Right, you'd be listening to one unit of laughter. But that's sort of the question we want to talk about today. Can you slice up space into smaller and smaller pieces, Can you divide it into shorter and shorter distances?

Or is space pixelated like a video game?

Or is space pixelated like a video game?

That's right, or your latest iPhone. You look around you and it seems like the universe is continuous and smooth, right, But it might be that the universe is actually pixelated. That you can be here or the adjacent pixel, but you can't be in between. That there's the shortest possible distance to the universe.

That's right, or your latest iPhone. You look around you and it seems like the universe is continuous and smooth, right, But it might be that the universe is actually pixelated. That you can be here or the adjacent pixel, but you can't be in between. That there's the shortest possible distance to the universe.

So not the stuff is pixelated, but the actual like the universe itself, the space in it is like a video game. It's pixelated. It's not continuous and infinite resolution.

So not the stuff is pixelated, but the actual like the universe itself, the space in it is like a video game. It's pixelated. It's not continuous and infinite resolution.

Exactly, And it's a perfect analogy to the stuff. Right. In particle physics, we love taking things apart. We say your body is made of molecules, and those molecules are made of atoms, and those atoms are made of smaller particles, and those little particles get down to quarks and leptons. We're looking for the tiniest particle, the base particle out of which everything is built. But in a completely parallel track, we can ask the same questions about space. Is a mile built out of half miles, is built out of quarter miles, which eventually is built out of the smallest unit? Or can you infinitely divide it?

Exactly, And it's a perfect analogy to the stuff. Right. In particle physics, we love taking things apart. We say your body is made of molecules, and those molecules are made of atoms, and those atoms are made of smaller particles, and those little particles get down to quarks and leptons. We're looking for the tiniest particle, the base particle out of which everything is built. But in a completely parallel track, we can ask the same questions about space. Is a mile built out of half miles, is built out of quarter miles, which eventually is built out of the smallest unit? Or can you infinitely divide it?

So this is a mind blowing question, and so we were curious what you thought. The answer was, do you think the universe is pixelated?

So this is a mind blowing question, and so we were curious what you thought. The answer was, do you think the universe is pixelated?

Yeah? So I went around. I asked a random selection of U see Irvine undergraduates who were not put off by a weird physics professor holding a mic in their face, and ask them this question.

Yeah? So I went around. I asked a random selection of U see Irvine undergraduates who were not put off by a weird physics professor holding a mic in their face, and ask them this question.

Do you think the universe is pixelated?

Do you think the universe is pixelated?

Here's what they had to say.

Here's what they had to say.

It's quantized basically, so atoms cannot be I mean, of course they're made by some atomic articles. But I think at the after that like, it can't be continuous. I think it's particulate. I think it's like I can ask him some of what you reach smaller and smaller and smaller and smaller and smaller.

It's quantized basically, so atoms cannot be I mean, of course they're made by some atomic articles. But I think at the after that like, it can't be continuous. I think it's particulate. I think it's like I can ask him some of what you reach smaller and smaller and smaller and smaller and smaller.

But you never get to like a finite like this is the smallest thing.

But you never get to like a finite like this is the smallest thing.

I think it would probably get smaller and smaller forever.

I think it would probably get smaller and smaller forever.

I ready don't know about this. This is a tough onextround, here's a tough question. Yeah right, what's your best guess? What do you think you got to say?

I ready don't know about this. This is a tough onextround, here's a tough question. Yeah right, what's your best guess? What do you think you got to say?

Really? You know, this one is really beyond my understanding of this whole word right now?

Really? You know, this one is really beyond my understanding of this whole word right now?

Yeah, all right, So people were kind of skeptical about this.

Yeah, all right, So people were kind of skeptical about this.

It was a whole spectrum of answers. I mean, some people are like, no, you can chop down infinitely far. Other people are like, no, quantum mechanic says everything is quantized and therefore there must be pixels. And other people are like what, wow, I have no idea what are you talking about? And I totally regret agreeing to answer your question.

It was a whole spectrum of answers. I mean, some people are like, no, you can chop down infinitely far. Other people are like, no, quantum mechanic says everything is quantized and therefore there must be pixels. And other people are like what, wow, I have no idea what are you talking about? And I totally regret agreeing to answer your question.

It's like, I've never heard these two words at the same time, universe and pixels.

It's like, I've never heard these two words at the same time, universe and pixels.

That's right, that's right, And it is a weird question, you know. But the pixels is a perfect analogy because, like, if you have a modern iPhone and you look at the screen, it seems like the pictures are fluid, they're smooth, right, You can't see the pixels because they have this retina display. It gives the illusion that is completely smooth.

That's right, that's right, And it is a weird question, you know. But the pixels is a perfect analogy because, like, if you have a modern iPhone and you look at the screen, it seems like the pictures are fluid, they're smooth, right, You can't see the pixels because they have this retina display. It gives the illusion that is completely smooth.

But it's kind of interesting because if you look at an old phone, like just from five to ten years ago, it looks horribly pixelated, that's right. It looks crunchy and chunky, and you think, how could I ever have seen this and thought that this was anything of quality?

But it's kind of interesting because if you look at an old phone, like just from five to ten years ago, it looks horribly pixelated, that's right. It looks crunchy and chunky, and you think, how could I ever have seen this and thought that this was anything of quality?

That's right. And you know, even old fashioned photographs, the ones that are analog not digital, ones that use chemistry, those in effect have pixels as well, they're just so small that you can't see them because you know, the development process is a chemical process, and so it's based on you know, molecules and drops of fluid in whatever. It's just the pixels are so small. So if the pixels are small enough that you can't see them, it gives you the illusion that it's perfectly continuous and that you could you know, zoom in forever and see more and more details, you know, like on that on those cop shows where they're like enhance the image and they can just like zoom in forever and read the time on somebody's watch, or something.

That's right. And you know, even old fashioned photographs, the ones that are analog not digital, ones that use chemistry, those in effect have pixels as well, they're just so small that you can't see them because you know, the development process is a chemical process, and so it's based on you know, molecules and drops of fluid in whatever. It's just the pixels are so small. So if the pixels are small enough that you can't see them, it gives you the illusion that it's perfectly continuous and that you could you know, zoom in forever and see more and more details, you know, like on that on those cop shows where they're like enhance the image and they can just like zoom in forever and read the time on somebody's watch, or something.

Right right, or get like a face match.

Right right, or get like a face match.

Yeah, but in a real picture, there's a limit to the information that's been captured. And if you look from far away, it looks like you could zoom in forever, but at some point, as you start zooming in, you notice the pixels. And so that's the question we're wondering about today, Like, sure, space seems continuous around us, but is it possible that if we zoomed in far enough, the pixels could appear at some point.

Yeah, but in a real picture, there's a limit to the information that's been captured. And if you look from far away, it looks like you could zoom in forever, but at some point, as you start zooming in, you notice the pixels. And so that's the question we're wondering about today, Like, sure, space seems continuous around us, but is it possible that if we zoomed in far enough, the pixels could appear at some point.

Yeah, So that's kind of related to the question of space itself. Like we know stuff is made the little bits, but is space itself also pixelated like an iPhone screen or an old photograph.

Yeah, So that's kind of related to the question of space itself. Like we know stuff is made the little bits, but is space itself also pixelated like an iPhone screen or an old photograph.

Yeah, and this question is newly fascinating because we're only recently learning what space is, right, Like, the question of is space pixelated is a reasonable question in parallel to is matter quantized and made out of smallest particles, because we've recently realized that space really is a thing. Also, it's not just like emptiness. Those of you are out there saying this is silly. Space is nothing, and so of course you could be anywhere in it and you can divide it infinitely. We've recently realized this space is not nothing.

Yeah, and this question is newly fascinating because we're only recently learning what space is, right, Like, the question of is space pixelated is a reasonable question in parallel to is matter quantized and made out of smallest particles, because we've recently realized that space really is a thing. Also, it's not just like emptiness. Those of you are out there saying this is silly. Space is nothing, and so of course you could be anywhere in it and you can divide it infinitely. We've recently realized this space is not nothing.

Before we thought it was nothing, just the absence of anything, But actually it's not right. It's almost like a medium, or like what the ocean is to fish.

Before we thought it was nothing, just the absence of anything, But actually it's not right. It's almost like a medium, or like what the ocean is to fish.

Yeah, exactly, it's a thing. It has dynamical properties. Right. We know that it's not nothing because you can do things that nothing can't do.

Yeah, exactly, it's a thing. It has dynamical properties. Right. We know that it's not nothing because you can do things that nothing can't do.

Right.

Right.

For example, space can expand that's what dark energy is. And for those of you whose minds were just blown about the meaning of the phrase, space can expand, go off and listen to our dark energy episode where we talk all about that. And space can wiggle, right like things in space can expand and contract with these wiggles as gravitational waves pass through them. And you know, those of you interested in that, go off and listen to our gravitational waves episode. And we also know that space can bend, right, that's what general relativity tells us. It tells us that gravity is not a force, but instead it's a bending of space. So space definitely is a thing. It has properties, and we've only just recently discovered that it's a thing and begun to investigate it. And so it's a very reasonable question to ask, is space pixelated like we think matter might be.

For example, space can expand that's what dark energy is. And for those of you whose minds were just blown about the meaning of the phrase, space can expand, go off and listen to our dark energy episode where we talk all about that. And space can wiggle, right like things in space can expand and contract with these wiggles as gravitational waves pass through them. And you know, those of you interested in that, go off and listen to our gravitational waves episode. And we also know that space can bend, right, that's what general relativity tells us. It tells us that gravity is not a force, but instead it's a bending of space. So space definitely is a thing. It has properties, and we've only just recently discovered that it's a thing and begun to investigate it. And so it's a very reasonable question to ask, is space pixelated like we think matter might be.

Like what is it made out of? What's it like? Really? You know, it's not nothing, So if it's something.

Like what is it made out of? What's it like? Really? You know, it's not nothing, So if it's something.

It's like space is some famous celebrity, you know, right, what's space like, you know, on the weekend. Is it egotistical? It seems egotistical, you know, seems so into itself.

It's like space is some famous celebrity, you know, right, what's space like, you know, on the weekend. Is it egotistical? It seems egotistical, you know, seems so into itself.

What space's favorite color?

What space's favorite color?

Black?

Black?

Black?

Black?

The code that one. I think we know that's a subtle question in science. No, I think it's important to think about this question, like what is the smallest unit of space? Right? What is space built out of? And I think the analogy, you know, understanding what matter is built out of works there, Like is space built out of these little bits, right, these pixels? And then the next question if you discover space is built out of pixels, is what are those pixels made out of? Yeah, it could be that those pixels are made out of something smaller and deeper that's nothing like space. So that space itself is an emergent phenomenon, not a fundamental thing in our universe. That's something that arises, you know, like wetness or economics, you know, so not something that's built in at the very beginning of the universe, but something that comes out of how things interact.

The code that one. I think we know that's a subtle question in science. No, I think it's important to think about this question, like what is the smallest unit of space? Right? What is space built out of? And I think the analogy, you know, understanding what matter is built out of works there, Like is space built out of these little bits, right, these pixels? And then the next question if you discover space is built out of pixels, is what are those pixels made out of? Yeah, it could be that those pixels are made out of something smaller and deeper that's nothing like space. So that space itself is an emergent phenomenon, not a fundamental thing in our universe. That's something that arises, you know, like wetness or economics, you know, so not something that's built in at the very beginning of the universe, but something that comes out of how things interact.

Well, let's take this approach. So let's assume that space is pixelated. Okay, what does a space pixel mean or feel like or look like? Or what would it do to things?

Well, let's take this approach. So let's assume that space is pixelated. Okay, what does a space pixel mean or feel like or look like? Or what would it do to things?

Yeah, it would mean is that you can't be just anywhere you want in space, you know, just like Xeno the beginning of this episode. It would mean that at some point, if you're small enough or you can zoom down enough, it would mean that you have to make a choice. Are you at location N or location N plus one? Right, it would mean that space is discrete the way integers are, instead of being continuous the way real numbers are. Right, there's an infinite number of numbers. For example, between one and two, there's one, one point five, one point two, seven eighty four, and you can always squeeze more numbers in there. There's an infinite amount of numbers between one and two if you're talking about real numbers, a continuous line of numbers. But for integers, like there's just one and there's too, there's no more integers in between. Space could be like that, where you're like, I'm at this spot, and if I want to take a step, there's the shortest distance I can step, and so you have to go to two.

Yeah, it would mean is that you can't be just anywhere you want in space, you know, just like Xeno the beginning of this episode. It would mean that at some point, if you're small enough or you can zoom down enough, it would mean that you have to make a choice. Are you at location N or location N plus one? Right, it would mean that space is discrete the way integers are, instead of being continuous the way real numbers are. Right, there's an infinite number of numbers. For example, between one and two, there's one, one point five, one point two, seven eighty four, and you can always squeeze more numbers in there. There's an infinite amount of numbers between one and two if you're talking about real numbers, a continuous line of numbers. But for integers, like there's just one and there's too, there's no more integers in between. Space could be like that, where you're like, I'm at this spot, and if I want to take a step, there's the shortest distance I can step, and so you have to go to two.

It's kind of like if you were on your iPhone you were animating one pixel dot black dot on a white background. This dot can't just be anywhere on the screen. It has to move from one box to the next box.

It's kind of like if you were on your iPhone you were animating one pixel dot black dot on a white background. This dot can't just be anywhere on the screen. It has to move from one box to the next box.

That's right. It can't like cross over the boundary. You can't be halfway between one pixel and another, because then each pixel would have to be half white and half black, which if they can't be right, a pixel is the basic unit. It's either on or it's off.

That's right. It can't like cross over the boundary. You can't be halfway between one pixel and another, because then each pixel would have to be half white and half black, which if they can't be right, a pixel is the basic unit. It's either on or it's off.

So like, if you look at the iPhone from a distance, this dot would look like it's moving smoothly across the screen, but really it's taking little jumps between squares, right, Like it's in the square ones at this moment, and then it's suddenly in the next square, and then suddenly it's in the next square. You're saying that maybe, like I'm not really moving continuously through space, Maybe I'm just kind of like jumping from one box to the next exactly.

So like, if you look at the iPhone from a distance, this dot would look like it's moving smoothly across the screen, but really it's taking little jumps between squares, right, Like it's in the square ones at this moment, and then it's suddenly in the next square, and then suddenly it's in the next square. You're saying that maybe, like I'm not really moving continuously through space, Maybe I'm just kind of like jumping from one box to the next exactly.

And the illusion of smoothness, the way you feel that you are moving smoothly, is your brain stitching that together. And it's easy to do because the pixels, if they exist, would be super duper tiny, But they only have to be smaller than you can notice. You know, for example, if you slow down a movie, it's nothing but a bunch of still images right right, And if you watch them fast enough, the key is faster than your eye can register the differences. Then it appears to be an infinitely smooth sequence. It seems like you're watching something in real life. Slow it down, of course you can see, Oh, it's just a bunch of still images. In the same way, space might be discrete. We just haven't noticed. But that if you get small enough, you realize that these nodes. You know, it's like you can't get off halfway between subway stations, right, It might be that space is like that, that every location in space is like a subway stop. You don't want to get off the train halfway between stasions and get stuck in the tunnel. You can't, right, the universe forbids it.

And the illusion of smoothness, the way you feel that you are moving smoothly, is your brain stitching that together. And it's easy to do because the pixels, if they exist, would be super duper tiny, But they only have to be smaller than you can notice. You know, for example, if you slow down a movie, it's nothing but a bunch of still images right right, And if you watch them fast enough, the key is faster than your eye can register the differences. Then it appears to be an infinitely smooth sequence. It seems like you're watching something in real life. Slow it down, of course you can see, Oh, it's just a bunch of still images. In the same way, space might be discrete. We just haven't noticed. But that if you get small enough, you realize that these nodes. You know, it's like you can't get off halfway between subway stations, right, It might be that space is like that, that every location in space is like a subway stop. You don't want to get off the train halfway between stasions and get stuck in the tunnel. You can't, right, the universe forbids it.

Right. But if you're the pixel, like in a screen, the pixel isn't really moving, You just turn it off in one square and you turn it on the next square, so it sort of disappears and it appears.

Right. But if you're the pixel, like in a screen, the pixel isn't really moving, You just turn it off in one square and you turn it on the next square, so it sort of disappears and it appears.

Yes, are you going to ask if that's really like teleportation?

Yes, are you going to ask if that's really like teleportation?

Yeah? Right, like that, as I'm moving through space, I'm actually like disappearing here and appearing in the next spot.

Yeah? Right, like that, as I'm moving through space, I'm actually like disappearing here and appearing in the next spot.

Yeah, I guess it does you know. I guess it means that you zap from one spot to the other without going in between them, right, and so that really is a kind of teleportation. I hadn't thought of that before. It's sort of awesome in the same way like if time is quantized, then you know, you're sort of slicing your way through time in the same way. That's fascinating. Yeah, so we're if space is pixelated, that we're all teleporting right now all the time.

Yeah, I guess it does you know. I guess it means that you zap from one spot to the other without going in between them, right, and so that really is a kind of teleportation. I hadn't thought of that before. It's sort of awesome in the same way like if time is quantized, then you know, you're sort of slicing your way through time in the same way. That's fascinating. Yeah, so we're if space is pixelated, that we're all teleporting right now all the time.

Only you mood, only mood.

Only you mood, only mood.

Oh my god, we just invented teleportation right here live on the podcast. Amazing. Get the legal team on the patent please, will you?

Oh my god, we just invented teleportation right here live on the podcast. Amazing. Get the legal team on the patent please, will you?

And there goes your physics professorship right out of the door. Right there.

And there goes your physics professorship right out of the door. Right there.

That's right, boom, I'm officially a crackpot.

That's right, boom, I'm officially a crackpot.

Well, let's take a quick break before we go on.

Well, let's take a quick break before we go on.

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Okay, so that's what it means for the universe to be pixelated, that we're all just kind of trapped in an iPhone screen. Then we can't really move anywhere. We have to move within these boxes.

Okay, so that's what it means for the universe to be pixelated, that we're all just kind of trapped in an iPhone screen. Then we can't really move anywhere. We have to move within these boxes.

That's right. But if it is, it's a really fancy, super modern iPhone because the pixels would be super duper tiny, right, and has an awesome graphics processor.

That's right. But if it is, it's a really fancy, super modern iPhone because the pixels would be super duper tiny, right, and has an awesome graphics processor.

What would you call it the iPhone you from universe? It'd be like a quantum display.

What would you call it the iPhone you from universe? It'd be like a quantum display.

That's right, iPhone quse, Tim Cook, give us a call, that's right. Somebody put a trademark on that.

That's right, iPhone quse, Tim Cook, give us a call, that's right. Somebody put a trademark on that.

Man.

Man.

We need like a constant legal team standing by just to you know, get down all the great ideas we come up with.

We need like a constant legal team standing by just to you know, get down all the great ideas we come up with.

One fly, So, how could we tell if we are in a pixelated universe or not?

One fly, So, how could we tell if we are in a pixelated universe or not?

Yeah, well that's hard because to see that we are in a pixelated universe, and we'd have to see the pixels, right, So we have to zoom in somehow far enough to be able to see them. And of course, so far we haven't. So far, everything seems continuous. We don't notice discontinuities in the way things move, and we also have no idea how big these pixels are. Right, so far, we have explored space and matter using high energy particle colliders, and that's let us probe down to about ten to the minus twenty meters. That's zero point than twenty zeros and a one me. That's a tiny little distance. I don't even know what the prefix is for that. It's some super tiny distance. We've studied space down about that distance using particle colliders where we smash these tiny particles together and use the protons so like look inside the other protons, and that lets us study space. So we know that if there are space, they have to be smaller than that.

Yeah, well that's hard because to see that we are in a pixelated universe, and we'd have to see the pixels, right, So we have to zoom in somehow far enough to be able to see them. And of course, so far we haven't. So far, everything seems continuous. We don't notice discontinuities in the way things move, and we also have no idea how big these pixels are. Right, so far, we have explored space and matter using high energy particle colliders, and that's let us probe down to about ten to the minus twenty meters. That's zero point than twenty zeros and a one me. That's a tiny little distance. I don't even know what the prefix is for that. It's some super tiny distance. We've studied space down about that distance using particle colliders where we smash these tiny particles together and use the protons so like look inside the other protons, and that lets us study space. So we know that if there are space, they have to be smaller than that.

Right, you mean at the large hydron collider, you can polke things at that distance, meaning you can tell if things mashed together within that small of a distance apart.

Right, you mean at the large hydron collider, you can polke things at that distance, meaning you can tell if things mashed together within that small of a distance apart.

Right. Yeah. Essentially, our current theory assumes that space is continuous, and our current theory doesn't break down down to ten of the minus twenty and so we would notice some deviation. Something would be different, The calculations would be wrong if space became pixelated and at a level that we didn't expect, and so so far we're pretty sure space seems continuous down to ten to the minus twenty. So the pixels, if they exist, have to be really.

Right. Yeah. Essentially, our current theory assumes that space is continuous, and our current theory doesn't break down down to ten of the minus twenty and so we would notice some deviation. Something would be different, The calculations would be wrong if space became pixelated and at a level that we didn't expect, and so so far we're pretty sure space seems continuous down to ten to the minus twenty. So the pixels, if they exist, have to be really.

Small, right. But I wonder, you know, if there is a philosophical limit there, you know, in the sense that like, do you think Super Mario, if he's in the video game and he's a pixelated character, could he tell that the world was pixelated, you know, because he's pixelated and he thinks in pixelated thoughts?

Small, right. But I wonder, you know, if there is a philosophical limit there, you know, in the sense that like, do you think Super Mario, if he's in the video game and he's a pixelated character, could he tell that the world was pixelated, you know, because he's pixelated and he thinks in pixelated thoughts?

Could he notice he thinks in pixelated thoughts?

Could he notice he thinks in pixelated thoughts?

Yeah, you know what I mean, Like.

Yeah, you know what I mean, Like.

I think, in terms of thought units, here's a three pixel unit thought. I think that's an interesting question if the pixels Sabe lives in a universe where the pixels were fairly large in.

I think, in terms of thought units, here's a three pixel unit thought. I think that's an interesting question if the pixels Sabe lives in a universe where the pixels were fairly large in.

Comparison to our bodies Minecraft character.

Comparison to our bodies Minecraft character.

Yeah, I mean, I think that's hard to imagine that realistically, because it would mean there's a pretty strong limit on how complex our bodies could be. I mean, if your body was made out of pixels there were like six centimeters across, then you just couldn't be very complicated if you were meter tall. In order to have enough complication to have an interesting mind, you know, you need a huge, complicated brain, So the brain would have to be enormous compared to the size of the pixels. So I think it's pretty hard to have complex enough life to ask that question and still be small compared to the size of the pixels. So if super Mario is an idiot, then yeah, he'd probably be pretty close to the size of the pixels. But then he's not going to be asking the question why am I pixeling?

Yeah, I mean, I think that's hard to imagine that realistically, because it would mean there's a pretty strong limit on how complex our bodies could be. I mean, if your body was made out of pixels there were like six centimeters across, then you just couldn't be very complicated if you were meter tall. In order to have enough complication to have an interesting mind, you know, you need a huge, complicated brain, So the brain would have to be enormous compared to the size of the pixels. So I think it's pretty hard to have complex enough life to ask that question and still be small compared to the size of the pixels. So if super Mario is an idiot, then yeah, he'd probably be pretty close to the size of the pixels. But then he's not going to be asking the question why am I pixeling?

Well, his intelligence would be pixelated, so you probably have zero units. And then if he takes a mushroom, is that going to grow too?

Well, his intelligence would be pixelated, so you probably have zero units. And then if he takes a mushroom, is that going to grow too?

That's just you know, I've always wondered about those mushrooms, you know, does that change the way he thinks? Like what's going on with those? Where do I get some?

That's just you know, I've always wondered about those mushrooms, you know, does that change the way he thinks? Like what's going on with those? Where do I get some?

He doesn't actually get bigger, it's just his pixels in his mind, that's right.

He doesn't actually get bigger, it's just his pixels in his mind, that's right.

Then The other question is, you know, would he even think to ask the question if pixels were obvious in the universe, you wouldn't ask why is the universe pixelated? It would just be one of the basic assumptions that you accept day to day, you know, And that's one of the things I find fascinating about physics is that we keep unraveling basic assumptions about the universe that we didn't even really think to question, you know, questions like is time the same for everybody? Right? Of course? We used to think, of course, it was like time is time, and a clock here and a clock there are the same, And now we know it's not. Time is relative and depends on your speed and all sorts of weird stuff. So physics is helping us peel back the universe and figure out where our perceptions have led to biases in the way we view the universe. And so that's why this space pixelization is just another one on the list. It might be eventually physics shows us that space is different than the way we always imagined, you know, that's made up of these little units.

Then The other question is, you know, would he even think to ask the question if pixels were obvious in the universe, you wouldn't ask why is the universe pixelated? It would just be one of the basic assumptions that you accept day to day, you know, And that's one of the things I find fascinating about physics is that we keep unraveling basic assumptions about the universe that we didn't even really think to question, you know, questions like is time the same for everybody? Right? Of course? We used to think, of course, it was like time is time, and a clock here and a clock there are the same, And now we know it's not. Time is relative and depends on your speed and all sorts of weird stuff. So physics is helping us peel back the universe and figure out where our perceptions have led to biases in the way we view the universe. And so that's why this space pixelization is just another one on the list. It might be eventually physics shows us that space is different than the way we always imagined, you know, that's made up of these little units.

So I think what you're saying is that as far as we know, we look at the world around us and the complexity of it, it's such that we're pretty sure that it's not pixelated up to a certain scale, which is ten to the minus twenty.

So I think what you're saying is that as far as we know, we look at the world around us and the complexity of it, it's such that we're pretty sure that it's not pixelated up to a certain scale, which is ten to the minus twenty.

Yeah, we certainly do. And if we were close to the pixel scale, it would limit how much complexity we could have in our universe. Right, if if the pixels were a centimeter across, then our one meter scale life couldn't be very complex at all, right, right, Like what kind of interesting thing could you build out of actual real size legos? Right, it can't make a machine that's very complicated, right, You know.

Yeah, we certainly do. And if we were close to the pixel scale, it would limit how much complexity we could have in our universe. Right, if if the pixels were a centimeter across, then our one meter scale life couldn't be very complex at all, right, right, Like what kind of interesting thing could you build out of actual real size legos? Right, it can't make a machine that's very complicated, right, You know.

You want to see these rich effects that you see when you puke the world around you.

You want to see these rich effects that you see when you puke the world around you.

Yeah, yeah, okay.

Yeah, yeah, okay.

So what makes scientists even think that the universe could be pixelated?

So what makes scientists even think that the universe could be pixelated?

I think they were just hanging out in the sevenies and smoking too much weed and they were like, it was man.

I think they were just hanging out in the sevenies and smoking too much weed and they were like, it was man.

Playing media games.

Playing media games.

No, it's not like it. Some people might think, Oh, it comes from the idea that the universe is a simulation, and if it's a simulation, then of course it's pixelated, because computers in the outside the universe are pixelated. No, it comes from a deeper place. It comes from noticing that quantum mechanics seems to work really well.

No, it's not like it. Some people might think, Oh, it comes from the idea that the universe is a simulation, and if it's a simulation, then of course it's pixelated, because computers in the outside the universe are pixelated. No, it comes from a deeper place. It comes from noticing that quantum mechanics seems to work really well.

Right.

Right.

Quantum mechanics has described everything we know except for gravity, and it seems to be a fundamental description of the universe that everything is quantized. You know, packets of light, for example, can't have an arbitrary amount of energy. They can only have certain units of energy. Matter itself is made out of particles, which are little quantized bits of stuff. Right, So it seems like, for a reason we don't understand, the universe is quantized, and quantized of course just means little units of stuff, and so it's very natural to imagine that space also might be quantized, that space also, instead of being infinitely divisible, might also be made out of pieces. Because the universe seems to like quantum mechanics.

Quantum mechanics has described everything we know except for gravity, and it seems to be a fundamental description of the universe that everything is quantized. You know, packets of light, for example, can't have an arbitrary amount of energy. They can only have certain units of energy. Matter itself is made out of particles, which are little quantized bits of stuff. Right, So it seems like, for a reason we don't understand, the universe is quantized, and quantized of course just means little units of stuff, and so it's very natural to imagine that space also might be quantized, that space also, instead of being infinitely divisible, might also be made out of pieces. Because the universe seems to like quantum mechanics.

So you're saying that, like the stuff that we see around us does have smallest bits, like there is a lego piece of matter. Yeah, you can't split an electron really, like you can't have half an electron or a quarter of electron. So maybe that says something about the universe as a whole, like maybe everything is just kind of blocking.

So you're saying that, like the stuff that we see around us does have smallest bits, like there is a lego piece of matter. Yeah, you can't split an electron really, like you can't have half an electron or a quarter of electron. So maybe that says something about the universe as a whole, like maybe everything is just kind of blocking.

That's right, it would make sense, it would it would feel natural, and it would feel coherent with what we think about modern physics if space was also quantized. And then there's you know, there's some technical reasons, like there are some theories of physics which just don't work if you get small enough. What do you mean, you know, some theories of quantum mechanics and the way it describes interactions below a certain distance that you just start to get infinities. Like you you know, how does the theory of physics work? Well, it's a it's something that predicts an experiment, right, say, I think this is going to happen. What is my theory of electromagnetism tell me? And so you can do some calculation. It tells you, oh, the electron is going to turn left and go at this angle. But sometimes the theories break and they give you numbers that make no sense, like oh, the electron is going to turn and it's going to go to infinite angle or have infinite energy. So there's some theories and it's a bit too technical to get into that break down at really really small scales. Wow, and they just start to give infinities. And so some of those problems are solved if you have a smallest distance, because then you don't have to go to those smallest scales right right, And this especially is a problem when people try to describe gravity using quantum mechanics. It comes up with all sorts of crazy problems and one solution to that is to say, well, what if this is the shortest distance, then we don't have to think about doing these calculations down to infinitely small distances.

That's right, it would make sense, it would it would feel natural, and it would feel coherent with what we think about modern physics if space was also quantized. And then there's you know, there's some technical reasons, like there are some theories of physics which just don't work if you get small enough. What do you mean, you know, some theories of quantum mechanics and the way it describes interactions below a certain distance that you just start to get infinities. Like you you know, how does the theory of physics work? Well, it's a it's something that predicts an experiment, right, say, I think this is going to happen. What is my theory of electromagnetism tell me? And so you can do some calculation. It tells you, oh, the electron is going to turn left and go at this angle. But sometimes the theories break and they give you numbers that make no sense, like oh, the electron is going to turn and it's going to go to infinite angle or have infinite energy. So there's some theories and it's a bit too technical to get into that break down at really really small scales. Wow, and they just start to give infinities. And so some of those problems are solved if you have a smallest distance, because then you don't have to go to those smallest scales right right, And this especially is a problem when people try to describe gravity using quantum mechanics. It comes up with all sorts of crazy problems and one solution to that is to say, well, what if this is the shortest distance, then we don't have to think about doing these calculations down to infinitely small distances.

Right, So nothing can happen at such a small scale. So in theory, the theory doesn't break down. It's just nothing can happen at that scale, So why even worry about it.

Right, So nothing can happen at such a small scale. So in theory, the theory doesn't break down. It's just nothing can happen at that scale, So why even worry about it.

Yeah, it's like a clue. It's saying, oh, this theory doesn't work. It can't describe universe where there's infinitely small distances. Then the idea is, well, maybe the theory is wrong, or maybe the universe doesn't have infinitely small distances, in which case the theory works.

Yeah, it's like a clue. It's saying, oh, this theory doesn't work. It can't describe universe where there's infinitely small distances. Then the idea is, well, maybe the theory is wrong, or maybe the universe doesn't have infinitely small distances, in which case the theory works.

Right.

Right.

There's lots of fun ways to make theory work, and one of them is just to imagine that the places where it breaks are the places where it's not physical, where it's not actually describing what's happening.

There's lots of fun ways to make theory work, and one of them is just to imagine that the places where it breaks are the places where it's not physical, where it's not actually describing what's happening.

Well, this is a perfect point to take a break.

Well, this is a perfect point to take a break.

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Well, this is interesting, so there's apparently a number that physicists think might be the pixel of the universe. Like there's like a concrete number they think might tell you what the pixelation the resolution of the universe.

Well, this is interesting, so there's apparently a number that physicists think might be the pixel of the universe. Like there's like a concrete number they think might tell you what the pixelation the resolution of the universe.

Is, right a little bit, I mean, I think that's overstating it. There is a number which we think might have something to do with the pixelization of the universe. So the argument is pretty weak. All right, I'll walk you through it, but you'll be unimpressed at how starting the argument is. All right, just trying to manage your expectations a little.

Is, right a little bit, I mean, I think that's overstating it. There is a number which we think might have something to do with the pixelization of the universe. So the argument is pretty weak. All right, I'll walk you through it, but you'll be unimpressed at how starting the argument is. All right, just trying to manage your expectations a little.

Bit, right, all right, I'll make them pixel size.

Bit, right, all right, I'll make them pixel size.

There you go, Yeah, I go for one unit of expectation. Here's the argument. The argument is, we've noticed there are some fundamental constants in the universe, like the speed of light, and that has units meters per second, right, And that's just a number and we measure it, and it's a parameter of the universe. We don't know why it's this and why it's that, and we of course we have a whole podcast episode about that, but it is a number. And there are other units we've noticed, like the strength of gravity. Right, it's called big G. The gravitational constant appears in Newton's formula, and you know in the Plank constant, the one that appears in quantum mechanics that tells you how well you can know two numbers at the same time. So there's all these basic units that we've measured and we've discovered, and we think they reveal something about the universe. We think they tell us something about why the universe is this way not that way, And we don't know where they come from.

There you go, Yeah, I go for one unit of expectation. Here's the argument. The argument is, we've noticed there are some fundamental constants in the universe, like the speed of light, and that has units meters per second, right, And that's just a number and we measure it, and it's a parameter of the universe. We don't know why it's this and why it's that, and we of course we have a whole podcast episode about that, but it is a number. And there are other units we've noticed, like the strength of gravity. Right, it's called big G. The gravitational constant appears in Newton's formula, and you know in the Plank constant, the one that appears in quantum mechanics that tells you how well you can know two numbers at the same time. So there's all these basic units that we've measured and we've discovered, and we think they reveal something about the universe. We think they tell us something about why the universe is this way not that way, And we don't know where they come from.

Of like the pie or you know, just the number that exists in the universe.

Of like the pie or you know, just the number that exists in the universe.

Yeah, well pi is and especially fascinating one because it's unit lists, right, so it's pure in some sense. But these numbers have units, you know, they're like jewels per second or meters per second or whatever. Okay, and so we think they tell us something about why the universe is this size or has this or you can go this fast, or you know.

Yeah, well pi is and especially fascinating one because it's unit lists, right, so it's pure in some sense. But these numbers have units, you know, they're like jewels per second or meters per second or whatever. Okay, and so we think they tell us something about why the universe is this size or has this or you can go this fast, or you know.

It's some sort of like ratio between two things.

It's some sort of like ratio between two things.

Yes exactly. They fix the relationship between things, like the speed of light fixes the relationship between distance and time. Right, it's meters per second, So.

Yes exactly. They fix the relationship between things, like the speed of light fixes the relationship between distance and time. Right, it's meters per second, So.

I see that the speed of light is like a universal physics number, Yes exactly. And so there's other numbers like these in physics theories.

I see that the speed of light is like a universal physics number, Yes exactly. And so there's other numbers like these in physics theories.

Yeah, there's a few that we've discovered along the way, and we think they're deep and fundamental, and you know, some future theory of physics might reveal why they are the way they are. But currently they're just numbers, and we imagine that they could have been set to something else, and that's a whole other discussion. Here's the thing you can do, though, is that you can manipulate these numbers. You can multiply them by each other until you get a number that has units of distance. So you multiply the plank's constant and you have the gravitational constant the speed of light squared. You can cancel out all the units until you get a number that has just units of distance. Okay, so what is that number. Well, they call it the plank length because it has planks constant in it, and it's a number. And the number is ten to the minus thirty five meters. That's zero point thirty five zeros and then a one. So that's a tiny, tiny number. And because it comes from these simple basic units, we imagine it has special meaning. We imagine that it's a clue that it tells us something about the way the universe works. And because it's just units of distance, we like to think that it tells us something about the fundamental nature of distance in the universe, now does it. I mean, who knows. It's just a bunch of numbers. We multiply it together, you know, and we thought those numbers were important, but maybe they're not.

Yeah, there's a few that we've discovered along the way, and we think they're deep and fundamental, and you know, some future theory of physics might reveal why they are the way they are. But currently they're just numbers, and we imagine that they could have been set to something else, and that's a whole other discussion. Here's the thing you can do, though, is that you can manipulate these numbers. You can multiply them by each other until you get a number that has units of distance. So you multiply the plank's constant and you have the gravitational constant the speed of light squared. You can cancel out all the units until you get a number that has just units of distance. Okay, so what is that number. Well, they call it the plank length because it has planks constant in it, and it's a number. And the number is ten to the minus thirty five meters. That's zero point thirty five zeros and then a one. So that's a tiny, tiny number. And because it comes from these simple basic units, we imagine it has special meaning. We imagine that it's a clue that it tells us something about the way the universe works. And because it's just units of distance, we like to think that it tells us something about the fundamental nature of distance in the universe, now does it. I mean, who knows. It's just a bunch of numbers. We multiply it together, you know, and we thought those numbers were important, but maybe they're not.

It's kind of like if you take the smallest things and the fastest things, you know, you know, like the smallest bit of matter and the going up the fastest possible speed, and you know what would be the smallest distance that it could go. That's kind of what it is to mix all of these numbers together.

It's kind of like if you take the smallest things and the fastest things, you know, you know, like the smallest bit of matter and the going up the fastest possible speed, and you know what would be the smallest distance that it could go. That's kind of what it is to mix all of these numbers together.

Right, Yeah, it's not that much smarter an argument than that.

Right, Yeah, it's not that much smarter an argument than that.

Great I feelt like that was an insult.

Great I feelt like that was an insult.

I don't say that to insult physics, right, Like, it's not a great argument. But it's the first thing you do, right. It's unit analysis saying, well, if we have no clue, what can we do, Well, let's combine these numbers and maybe that'll give us a clue. So it's not no physicist or out there saying this is definitely the fundamental unit of distance. It just says if there is one, it might be around this number. I mean, to within a factor of one hundred or a thousand would be pretty still a pretty good clue, right.

I don't say that to insult physics, right, Like, it's not a great argument. But it's the first thing you do, right. It's unit analysis saying, well, if we have no clue, what can we do, Well, let's combine these numbers and maybe that'll give us a clue. So it's not no physicist or out there saying this is definitely the fundamental unit of distance. It just says if there is one, it might be around this number. I mean, to within a factor of one hundred or a thousand would be pretty still a pretty good clue, right.

Ten to the negative thirty five, which sounds really small.

Ten to the negative thirty five, which sounds really small.

It is really small.

It is really small.

It is really small, but it's not small compared to infinity, do you know what I mean? Like the number Pi. You can take decimals out to thirty five thirty five hundred thirty five million decimals. Yeah, but you're saying maybe the universe only goes up to thirty five that's.

It is really small, but it's not small compared to infinity, do you know what I mean? Like the number Pi. You can take decimals out to thirty five thirty five hundred thirty five million decimals. Yeah, but you're saying maybe the universe only goes up to thirty five that's.

Most Yeah, that's right. It's a lot bigger than you know, ten to the minus one hundred, or ten to the minus one thousand, or ten of the minus ten thousand, Right, these are much much smaller numbers. The thing is, it's also much smaller than the thing we've seen. Remember we studied space down to about ten to the minus twenty, So that means that we are a factor ten to the fifteen away from seeing these pixels, if in fact they exist, and if they are at that scale.

Most Yeah, that's right. It's a lot bigger than you know, ten to the minus one hundred, or ten to the minus one thousand, or ten of the minus ten thousand, Right, these are much much smaller numbers. The thing is, it's also much smaller than the thing we've seen. Remember we studied space down to about ten to the minus twenty, So that means that we are a factor ten to the fifteen away from seeing these pixels, if in fact they exist, and if they are at that scale.

Wow.

Wow.

Yeah, I mean for a sense of scale, like the solar system is ten to the fifteen meters across I believe, so you could only see things, you know, down to ten of the fifteen meters, you'd be missing a lot of interesting detail, Like you'd miss Earth and life and planets and stuff and us.

Yeah, I mean for a sense of scale, like the solar system is ten to the fifteen meters across I believe, so you could only see things, you know, down to ten of the fifteen meters, you'd be missing a lot of interesting detail, Like you'd miss Earth and life and planets and stuff and us.

What a tragedy, I know.

What a tragedy, I know.

How could you study the universe without seeing the most important and best looking to dudes in it? Right?

How could you study the universe without seeing the most important and best looking to dudes in it? Right?

Like if you were a giant decize of a galaxy and you had an iPhone the size of you know, the Milky Way, and the biggest pixel in it was the size of a solar system, there would be a lot you'd be missing.

Like if you were a giant decize of a galaxy and you had an iPhone the size of you know, the Milky Way, and the biggest pixel in it was the size of a solar system, there would be a lot you'd be missing.

Exactly So between where we've seen at ten of the minus twenty meters and how far things might go at ten of the minus thirty five meters, there could be a huge amount of complexity and richness down there that we're totally ignorant of.

Exactly So between where we've seen at ten of the minus twenty meters and how far things might go at ten of the minus thirty five meters, there could be a huge amount of complexity and richness down there that we're totally ignorant of.

Little tiny pixel people.

Little tiny pixel people.

That's right.

That's right.

I think asking these same questions could be a little pixelated alien going, Mamario, what's good?

I think asking these same questions could be a little pixelated alien going, Mamario, what's good?

Hold on, I don't think i've ever heard your talent accent.

Hold on, I don't think i've ever heard your talent accent.

That's pretty good, and we just lost all of our Italian listeners.

That's pretty good, and we just lost all of our Italian listeners.

That's yeah, Italian listeners, please write in and comment at Jorges accent at Danelinhorge dot com.

That's yeah, Italian listeners, please write in and comment at Jorges accent at Danelinhorge dot com.

Jorgel fans Whole Country dot Com. Okay, well, let's get some perspective here. What what do you think would mean for us and our understanding of ourselves, our universe if we found out that the universe is pixelated?

Jorgel fans Whole Country dot Com. Okay, well, let's get some perspective here. What what do you think would mean for us and our understanding of ourselves, our universe if we found out that the universe is pixelated?

It would be a really deep inside just into the very nature of the universe. You know, to know that number tells you something about the scale at which the universe was built. Right, Everything in the universe happens from its basic elements. So we have fascinating structure, you know, galaxies and superclusters and all that stuff, but all that arises from the interactions of smaller pieces, you know, particles and electrons. Everything is determined by what happens at the smallest scale, right, So everything in the universe comes out of these basic elements. So to learn how big the smallest unit is tells you how the universe was constructed. And in the end, what is science and physics about other than this goal of trying to deprogram the universe or look at the source code or figure out how this thing is organized? And so that would be pretty pretty awesome, but you know, it actually just be a first step.

It would be a really deep inside just into the very nature of the universe. You know, to know that number tells you something about the scale at which the universe was built. Right, Everything in the universe happens from its basic elements. So we have fascinating structure, you know, galaxies and superclusters and all that stuff, but all that arises from the interactions of smaller pieces, you know, particles and electrons. Everything is determined by what happens at the smallest scale, right, So everything in the universe comes out of these basic elements. So to learn how big the smallest unit is tells you how the universe was constructed. And in the end, what is science and physics about other than this goal of trying to deprogram the universe or look at the source code or figure out how this thing is organized? And so that would be pretty pretty awesome, but you know, it actually just be a first step.

Yeah, no's you just made me realize it would really kind of blow your mind to just have this sense that the universe has a structure, right, that it somehow feels built, you know, like there's a scaffolding to the universe.

Yeah, no's you just made me realize it would really kind of blow your mind to just have this sense that the universe has a structure, right, that it somehow feels built, you know, like there's a scaffolding to the universe.

Yeah, like a graph paper, right, yeah, and then you have to ask questions.

Yeah, like a graph paper, right, yeah, and then you have to ask questions.

Like who made that graph paper.

Like who made that graph paper.

And why that size? Right? Why is it ten of the minus thirty five meters and not ten of the minzed five hundred meters or ten of the mized thirty meters? Right? What does that mean? There's like a clue there about the very structure of the universe. Is it a random number and it generated arbitrarily when all the multiverses were created? Or does it give you a clue somehow about something deep about the universe. On the other hand, you know, we talked about like galaxies just being emergent phenomena. Right, They're a really cool thing, but they're just formed out of smaller bits and their complex behavior arises into this thing called a galaxy. A lot of people think these days that space itself could be an emergent phenomenon. Okay, that these pixels of space could be built out of something smaller that are that's not space?