Is our universe a fractal? How do we test this? Are there any places in the universe that look like fractals? I discuss these questions and more in today’s Ask a Spaceman!
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How do you take the measure of the universe? Let's all dig in and celebrate that wonderful question that here we are little humans who just learned how to write only a few 1000 years ago on a on a random little ball of dirt and orbiting a random old star that you wouldn't be able to pick out from a crowd. And we're sitting here discussing measuring the universe whenever I need a reminder of just how awesome science is and why I love this stuff. I think of questions like that, and it's easy enough to measure, say, the width of the universe, which we talked about last episode. And while this episode isn't exactly a sequel, you can think of it as a spiritual successor where we're asking not the size of the universe but its structure. It's arrangement, it's contents and and we've covered the large scale structure of the universe before. But this is going to go in a very different direction. It's going to go in a fractal dimension, you see, back in the olden times, like, you know, 40 years ago, we didn't really know all that much about the structure of the universe.
We had some survey, some rudimentary surveys, some maps of the universe around us, and from those very, very rudimentary maps we knew of Galaxies and we knew of clusters of Galaxies. And that was pretty much it. So either you had clusters, which were these massive cities a million light years across containing 1000 or more Galaxies. Or you just had Galaxies scattered around randomly, something we called field Galaxies. You had cluster Galaxies and field Galaxies and that was it. We didn't even have any hints of anything larger. Anything bigger? I mean, yeah, Yeah, way far away. We had the quasars, these objects, that at first we thought were stars, but kind of weird and then turned out to be just Galaxies that were super loud in the radio spectrum. And those were only very, very far away, which means that they were only a feature of the very, very young universe. And so our present day universe didn't have a lot of structure.
There was random clusters floating around, and then in between them, there were random Galaxies floating around, and that was it. We had assumed that the universe was largely pretty boring there were clusters here and there. There was a bunch of space between them. There are some quasars way out there, but they were also pretty random. It was just boring and random and boring and random. And there's just nothing interesting or unique in any way, which is exactly what we wanted. I see in cosmology the study of the universe. When we're trying to come up with our mathematical descriptions and models and theories and and just begin to wrap our heads around this massive question of how to take the measure of the universe, you need to start with something you need some ground assumptions. You need some principles, some statements that you are going to assume to be true just so you can make headway in the mathematics and the mathematics here.
To describe the universe is Einstein's general theory of relativity, which is a massive beast of 10 complicated equations that are all interconnected and to find solutions in general relativity. If you wanted this theory to apply to the universe and give you useful information, you need to make some starting assumptions to kind of knock down that those 10 equations into something easier to handle. And so in cosmology, we assume something and continue to assume something called the cosmological principle. How handy is that name? It assumes two things. And again, these are assumptions. These are starting guesses to make the math easier. Yes, we will go test our assumptions because we are very good scientists. But we'll we'll get to that. The two assumptions are that the universe is isotropic and homogenous now, isotropic. We're not going to talk about too much in this episode. But it means if you look in a random direction like look straight up and you look at sufficiently large distances like I don't know millions of light years, you'll see you know, Galaxies and nothing and Galaxies and more nothing.
And if you look in another random direction, you'll see Galaxies and nothing and more Galaxies and more nothing. And the universe in one direction looks pretty much like the universe in any other random direction on sufficiently big scales. OK, that's isotropic. The other thing is homogenous, homogenous means if you take a random patch of the universe like a box and you draw the the box and you measure everything inside you measure all the Galaxies and all the nothing. There's not a lot of choices here in the universe. And and then you take another box of the same size but another random patch of the universe. And you look at its contents, the homogeneity principle or the homogenous part of the cosmological principle says that it's gonna be pretty much the same thing. Yeah, I mean, there will be a different arrangement, a different pattern. But like say, the average number of Galaxies is is gonna be pretty much the same. The average mass of Galaxies is gonna be pretty much the same. The average distance between Galaxies is gonna be pretty much the same.
It's homogenous now. Obviously, you need to get to really, really big scales before you can measure this homogeneity. Because if you were to draw a box containing your body and then a box right next to it, not containing your body, that's not very homogenous. Your your room is not homogenous. The earth is not homogenous. The solar system, even our parts of our own Milky Way galaxy, are not homogenous. But the thinking is like once you reach a certain scale, once you draw a big enough box. The universe looks pretty much the same from box to box, and our early observations of the greater universe reflected that, like, you know, clusters, Galaxies, whatever it all looks pretty much the same. But in the 19 eighties, we started to wake up. We started to discover the cosmic Web, and it was really in the early 19 eighties, really going to the mid to later 19 eighties that we were finally able to have enough sophistication.
Where our telescopes were powerful enough could be operated for long enough time so we could do wide scans of the sky. We could see fainter and dimmer objects so we could push further in distance and then also within that same distance, we can collect more and more Galaxies. We can see a lot of the smaller ones and dimmer ones, and it wasn't just random clusters and random Galaxies all floating around. There was a structure there, that structure we call, appropriately enough, the large scale structure of the universe. It's also known as the cosmic Web. What we saw as the clusters were just one part of a much larger framework. The clusters were these very dense knots and strung between these clusters were the filaments, these ropes of Galaxies like like millions or tens of millions of light years long. And then there were giant walls of Galaxies like Imagine a giant wall made of Galaxies.
So we see that. And then there are these vast empty regions of the cosmic void. So there's like almost nothing at all. Cosmic Web is gigantic. It is the largest pattern found in nature. It's why we didn't see it until the 19 eighties because we didn't have the telescopes powerful enough to pick it out. If we're just looking locally, we just see one tiny little corner. You don't reveal the grandness of the cosmic Web, but the cosmic Web isn't homogenous at all. It's different, and it's different all over the place. We were sold a homogeneous universe, and when we opened up the box, we got a cosmic web. If I draw a box around a cluster, it looks very, very different than if I draw a box around a cosmic void. What's going on? Enter Benoit Mandelbrot. First we have to get the pronunciation of his name out of the way. I grew up saying, Benoit, you know, because I had some level of sophistication. Mandelbrot, I would say Benoit Mandelbrot. And but then, after I learned a little bit of French, I thought maybe it was Benoit Mandel, bro. And like, Hey, Mandel, bro, you're my bro, bro. But then I found a clip of him saying his own name, and he very much surprised me with Benoit Mandelbrot.
Or it's more like Mandelbrot. Anyway, I'm 90% sure I will spend the rest of this episode butchering his name at every possibility. So a I apologize in advance for everything I just said. And B, we're just gonna call him Benoit like we're good buddies or something. Anyway, Benoit didn't invent the concept of fractals, but he did invent the name and he did go to town with him. And we can thank him for our present understanding of fractals and its growth as an entire field of mathematics, which is super awesome. Benoit really is the father of modern fractals. We had been studying fractal like things for ages, of course, but Benoit was the guy who did it and did it in a big way. In a very mathematical way up, right? So what is a fractal? Turns out it's frustratingly hard to define. Benoit even switched definitions a few times in his life. But we can give some examples. So, for example, if you take a snowflake little pretty stuff like and you zoom in on a part of it, it looks like a snowflake. And then you zoom in on a part of that, and then it looks like a snowflake.
And then you zoom in on part of that and it looks like a snowflake. Or if you look at a tree and then you zoom in on the branches of the tree, it looks like a miniature tree with its own branches. And then you zoom in on one of those branches and it looks like an even smaller tree with its own branches, and you zoom in again or or a coastline. If you look at a coastline, it looks like a coastline. You zoom in on a part of the coastline and it looks like a coastline, and you zoom in on a part of that. It looks like a coastline. If I didn't give you the scale and I appropriately massage the images. You wouldn't be able to tell me how far we were zoomed in on a coastline or a tree or a snowflake. And this is one of the key properties of a fractal is that it's self similar. It looks like itself whether you zoom in or zoom out. The word fractal itself comes from the Latin word for broken, and you can think of a fractal as a fractured dimension. So there's this famous example of the Koch Snowflake. Uh, if you take a line and then you draw, you take the middle of the line and see you turn that into like a little upward pointing triangle.
And then on the two sides of that triangle, you draw two more triangles right in the middle, and then you go into those sides of those smaller triangles and draw two smaller ones, and then you zoom in and keep drawing. You keep drawing and you keep drawing and keep drawing. You can do this mathematically. You can define it to infinity, and it kind of looks like a snowflake. In one sense, it's it's just a line. You're just taking one pen and drawing all this and and lines are one dimensional, right? But the length of a kosh snowflake is infinite because there's always another corner. You have to turn because these iterations go down to infinity. And so if you start at one end of the Kosh snowflake, you will never reach the other end because you're always turning. That's not very line like because lines have length. But it's also not a square, which is two dimensional, like it's definitely not a square. So a Koch snowflake has a dimension somewhere between one and two. It's not quite one dimensional, but it's also not quite two dimensional. Its dimension is fractured, a fractured dimension.
Fractal now fractals can be defined mathematically, and fractals are everywhere. And but But the fractals that we find in nature aren't perfect. They're they are self similar and can be described with the mathematical language of fractals, but only in a certain set of scales, like a tree. For example, if you zoom out too far, you get the forest, which doesn't look like a tree. And if you zoom in too far, you get like cellulose and chlorophyll, which doesn't look like a tree. So it's only in a certain limit. It says scales that you get this fractal like nature. But that said, these kind of self similar repeating patterns, fractal like patterns are found everywhere they you know, there's snowflakes and trees and coastlines. There's also clouds mountains, river deltas, broccoli, patreon dot com slash PM Sutter to keep supporting the show. Blood, vessels, flowers, lightning, seashells, stalagmites and stalactites. There are fractals everywhere, and one of Benoit's most amazing accomplishments besides giving us a firm mathematical grounding of fractal, was to point out all the self similar structures found in nature.
And maybe, you know, if fractals are everywhere, maybe everywhere is a fractal. Maybe we live in a fractal. Maybe the universe is a fractal. This was Benoit's guess. He modified the cosmological principle, not focusing on isotropy or homogeneity, but instead focusing on self similarity, he said. Maybe, especially as we look at this cosmic web that's starting to appear in our surveys. Maybe the universe is self similar. Maybe the universe looks pretty much the same, regardless of viewpoint and regardless of scale, that you can zoom in and out of the cosmic Web and you'll just get more cosmic Web. So let like when we see the cosmic Web in our surveys, with its intricate lattice work of clusters and filaments and voids, it's just like Step one in the fractal universe. If we zoomed out, we would see our chunk of this cosmic Web is just a tiny piece of a larger super cosmic web.
And if we zoomed out further, then that would be a tiny piece of an even larger uber cosmic web. And so on, with all the voids getting voider and all the clusters getting cluster and all the filaments getting filament. Maybe what we are seeing as the cosmic Web was just the beginning of a much larger nested set of structures. Unfortunately, I have to be a little careful in this episode because the word fractal has become the ultimate F word in cosmology. Because while it was a good guess for a while, I mean as good as guess is any about, like, how is matter in our universe? Structured and arranged eventually, I'm spoiler alert. The data caught up and showed that it was wrong. We we do not live in a fractal universe, but Benoit continued to hold on to it and several, Uh, shall we say, uh, fringe scientists continued to work on it as well. And there's still some like a deep minority, like three people in cosmology who are claiming that we live in a fractal universe.
And Benoit himself, like, hung on to this concept, and that made it. That gave it a really bad reputation. And I'll explain the date. I'll explain why we don't think we live in a fractal universe. But then I'm also gonna show how maybe it's a little bit undeserved because there are parts of the universe that can be described by a fractal. But let's let's get into that first. The evidence. It's easy conceptually to disprove the fractal universe idea. You just find the homogeneity scale. If you can zoom out far enough and you just keep getting larger and larger versions of the cosmic Web, then you might be tempted to think we live in a fractal universe. But if you zoom out to a certain scale and then you can start drawing boxes that are big enough, and then the boxes in these random patches of the universe look pretty much the same, and you don't get larger cosmic webs. You just get the cosmic Web, and it just peters out, and it does start to look homogenous and all blend together. Well, then, that just shows that the universe is in a fractal. And that homogeneity scale isn't like a scale you use to weigh yourself.
It's the size of the box you need before one box looks pretty much like any other box. It's obviously bigger than a solar system or a galaxy or a galaxy cluster and larger than our local patch of the cosmic web, and it took us a few decades to find it. And what's connected to that is, once we realize that our universe has this beautiful, complex cosmic web, we started to come up with theories and ideas of how the cosmic Web formed. And then those theories would predict where we should find the homogeneity scale. So we became very, very interested in measuring the homogeneity universe and finding the scale one, because it's part of our cosmological principle, part of our ground based assumptions. And like good scientists everywhere, we don't just test our hypotheses. We also test our assumptions and also it a certain number for the homogeneity scale became a prediction of our theories of the formation of structure.
That number, by the way, is around 100 million parsec or like 320 million light years. That was the number that was predicted from our theories of the structure formation of the universe, of where things should peter out and become Hama. You know, it's very, very rough. But in that ballpark, and if we couldn't find it, well then that would mean our understanding of structure formation is incomplete or wrong. And we maybe we have to give up one of these fundamental assumptions about the universe. But it took us a long time because 320 million light years is really, really big folks. It's huge and you can't just get one. You need a bunch of random patches of the universe this size so you can all do. You can do some statistics and compare them all against each other, so you need like a survey volume like a billion light years across just to get started. And it's also very, very difficult because the further back we go in our galaxy surveys, the further and further you go in space, the deeper you go in time and the universe is evolving with time.
So it's not like we have a snapshot of the universe, as as it is today in the present, right now at this instant. And we can test this homogeneity scale instead because the universe is evolving because the cosmic Web changes with time. This homogeneity scale is also gonna change with time. So when we push back further with our surveys, we have to look for a different scale, a different number. And we can't compare a galaxy like 6 billion light years away to a galaxy today because they come from different epochs of our universe. It's complicated, but we did it because we have big, giant galaxy surveys that are big enough to, like, take a certain range of distances. So we know all the Galaxies are pretty much from the same epoch, and then measure a homogeneity scale there and we get it. We got it. We did it 100 million parsec 320 million light years. Yeah, plus or minus, like 50 million light years. We're not gonna be super precise about this. That's how big of a box you need before all the boxes look pretty much the same.
Like the the cosmic web you get in each box is gonna look different, like there will be a different pattern of voids, a different arrangement of clusters. The filaments will go in different directions, but the statistics will be the same. So, like the average number of Galaxies, the average size of the voids, the average length of the filaments, all that will be roughly the same or statistically the same. So fractal cosmology is dead. Or is it? Here's the thing, folks. We know that all the fractals found in nature aren't true fractals. They don't extend to infinity in scale, either big or small. The real definition of fractal has this infinite range component. You can define it mathematically, but but like nothing in the universe does that. But lots of things in the universe can be self similar for a limited set of scales, and they may not be described simply with a simple fractal equation, but still have the essence of practicality. I made up that word and I like it like if I look at a tree, there's probably not a simple fractal expression that describes the branching of that tree.
But I can still analyze it using fractal language and get some cool understanding of the tree shape using my language or fractals, even if I don't have a simple single equation that describes it. So I can't say that fractal cosmology is still alive because fractal cosmology is a very specific thing, starting with Benoit's first guess, that says that all large structures in the universe can be described by a fractal, and they can't. It's dead. And it's not just because of finding the homogeneity scale, but because the cosmic Web itself doesn't look like a fractal. It just looks like a cosmic Web. Mostly, you see, there are places within the universe within the cosmic Web that do have self similar features. So even though the cosmic Web as a whole is just clusters, filaments, walls, voids done, move on. There are parts within the cosmic web that do have self similar features.
For example, when you look at a cluster of Galaxies, most of the mass of that cluster is in the form of invisible dark matter. It's a big ball of dark matter that we call a halo that provides all the gravitational glue for all the little Galaxies. That giant ball that's a million light years across or more made of dark matter that Halo has high density pockets inside of it, like it has some average density. And then there's like sub halos or sub balls inside of it. These contain the Galaxies, so each individual galaxy gets its own halo. That's pretty high density, and then the galaxy cluster contains them, and that has its own halo. And then we can explore in computer simulations the dark matter structure of a galaxy cluster. And there are halos and sub halos and sub sub halos. There's this nested structure, and one of the biggest things we realized was that the density of these halos, the relationship between the distance you are from the center of a halo and the local density of dark matter that you'll encounter all follow a similar relationship.
So not only do the dark matter halos of our universe have this nested structure, but a halo, a dark matter halo around a galaxy. An individual galaxy looks like a scaled down version of the dark matter halo around a galaxy cluster, a much larger one. So if you take the dark matter halo around a galaxy cluster and just squish it down to fit the size of a galaxy, you'll get a good description of the dark matter halo around the single galaxy. So that's more than just nested structure. That's a self similar structure. You can do this with the halos with the clusters, the big, high density regions of the universe. You can also do it with the empty patches. You can look at a cosmic void where there's hardly anything, but you can do a deep, deep, deep scan of it with galaxy surveys, and you'll find very dim dwarf Galaxies. And those Galaxies that inhabit the void aren't scattered around randomly. They follow their own faint, dim, effervescent, barely there cosmic web with little mini faint filaments, little mini faint clusters, little mini faint sub voids.
And once again, you can explore in numerical simulation. With computer work, you can explore the dark matter structure of a void of what's happening to the dark matter, and you'll see voids and there are sub voids in it, and then you zoom into those sub voids and you'll get tinier voids, sub sub voids and then sub sub sub voids sub sub sub sub sub sub voids. And just like with the Halos, there's a self similar structure. This is actually something I worked on myself. Well, not myself myself, but there was. I was part of a team we were all working on together, but we discovered a self similar universal structure to voices, so they're not just nested. They're also self similar. A tiny void, a sub sub sub void just looks like a scaled down version of a big void, and vice versa. If you take a big void and squeeze it down, you get a good description of a smaller void of one of its sub voids. It's It's a fractal like structure. Obviously, these fractals don't exist at all scales because eventually, if you get too small, you get down to like, absolutely nothing inside of a void, or you get inside of a galaxy inside of a cluster and bigger at the homogeneity scale.
All fractal stuff breaks down because you're just at the homogeneity scale and you just get bla cosmic web all over the place. But in that range of scales between about, uh, roughly 10 million light years to 300 million light years in that range. Roughly, you get these self similar structures, which is pretty cool and very fractal like. And maybe there's another fractal structure operating at scales even bigger than the universe. We get this idea through our concept of inflation. You remember inflation. That was fun. It's this hypothetical idea that we largely suspect is true, based on the available evidence that when our universe was incredibly young, it expanded really, really quickly in a very short amount of time. Like I'm talking a billionth of a billionth of a billionth of a billionth of a second, and in that time the universe expanding by a factor of like 10 to the 52 or something gigantic like that. We don't know what powered inflation. We don't know what caused inflation.
We don't know why inflation stopped. We don't know a lot about inflation, but we're pretty sure that the event happened. There's one version and and inflation because it's an idea of a concept of an event. We have a lot of different theories about what caused inflation or powered inflation, what drove inflation. There's one family of inflation theories called eternal inflation in the eternal inflation idea. And I talked about this more in the episode I did on the multiverse, So feel free to listen to that again if you want. But in this idea, inflation never ends. Instead of just being a one and done kind of thing. There's always inflation happening all over the universe, and what we see is our little pockets, our little big bang with our little cosmic web. And it's so cute. It's just one little bit of the universe that we inhabit. But outside the bounds of the observable universe, inflation is still happening, and the little universes are percolating all over the place.
They are very distantly separated from us. And then someday, in our distant future, there'll be random parts of our universe that will begin to initiate their own inflation events. So our universe in the distant future will contain a sub universe, and we, in fact, in our universe, might be a sub universe of an of an even larger universe. And then that sub universe, a long time from now, will get so large that it will start to spawn its own inflation events inside of it. Each one of these sub universes are spatially separated from each other, so you can't jump from universe to universe. Sorry, and it's like a fractal You you start with some set of universes and you zoom into one universe and you see that there's actually a bunch of sub universes and you can zoom into one of those and there's a sub universe and zoom in so eternal inflation, like looks like a fractal, a fractal made of entire universes, which is really trippy to think about is eternally inflation true?
We don't know. We have no way to test it right now. We're pretty sure, like I said, that something like inflation happened, but we don't know, uh, what exactly it happened. We don't know if which family of ideas is more correct or the others. We don't know what drove it, why it stopped or really anything about it, except that it probably happened. So if eternal inflation is true, then yes, our universe is a fractal at very, very large scales and Benoit's revenge, but we don't know if it's true or correct. So do we live in a fractal universe? No, not really. Except yes, sort of in in in a way, like fractals themselves. It's kind of hard to define thank you to N DS Bob a. Martin N for the questions that led to today's episode and thank you to all my dear, wonderful patreon contributors, especially the top ones. This is patreon dot com slash PM Sutter to keep the show going Matthew K, Justin Z, Justin G, Kevin O, Duncan M, Coy D, Barbara Kay Dude, Robert M, Nate H, Andrew F, Chris Cameron, NAA Aone, Tom B, Scott M and Rob H is your contributions that seriously keep this show going.
I can't thank you enough. I'm humble every month by all of your generous support and by all of your amazing questions. That's ask us spaceman at gmail dot com, or ask us spaceman dot com for all the old episodes hit me up on social media. I'm at Paul Matts Sutter on all channels like the show share on iTunes or however you consume podcasts. Recommend it. I really do appreciate it, and I'll see you next time for more complete knowledge of time and space