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2:46>> Okay, so for our first story, we are going to go into the world of string theory in a paper out in nature published on January 6th. Paper is about nature's hidden blueprint. How physical networks follow string theory mathematics. Scientists have discovered that biological networks from brains to blood vessels violate simple wiring rules. >> Yeah. >> And instead follow complex surface minimization patterns predicted by string theory. >> Yeah. >> Really good at predictions. Uh this one's out of uh Wrenchler Polytenic Northwestern, the University of Chicago and Northeastern. So a nice Marvel
3:28compilation. >> Yeah. Um, and the the idea is >> that they can now reveal how surface optimizations shape the architectural architecture of physical networks impacting both the brain and our vascular system. This is fascinating. >> It's it's really cool because it's not just the brain and vascule. It's all over biology. If you look at like mycelia and fungal networks, this has something to say about that. If you look at how trees branch out into patterns, it this has something to say about that. And you know, we've been trying to figure out the mathematics behind how these physical networks branch out. And
4:10the unlikely savior came in the form of string theory. And it's really wild because it's all over it's all over the news because you know string theory has kind of a a bad rep given that it doesn't predict anything at least in terms of the fundamental physics that it promised to predict. But it's kind of cool that you know this mathematical physics approach is now being used for biological problems. And one of the reasons why I really loved this story is, you know, I'm a biohysicist by training and there's so many examples of the mathematics of physics being used for something totally different being applied to
4:52biology. You know if you look at hotfield networks and associative memory in the brain that uses the mathematics of Ising models that was being developed to describe magnetization or if you look at the reormalization group which is being used for phase transitions or deep quantum field theory that's being used to describe the stling flocks and how they do murmmorations in the sky. So, it just it's one of these really cool examples of how mathematical physics research for something totally different can be applied to biology. And we're just discovering how life is so clever, you know,
5:32>> and this sort of translational translational nature of the frameworks of of physics being applied in other spaces. >> Yeah. Yeah. Yeah. And I I think I think that's just that's just really cool. There's there's a there's a neat line between the mathematics when we go really deep down, you know, I I think that's really cool. So, the core subject has to do with networks. Okay, networks are basically things and then those things have relationships. And usually when we talk about networks, what we use is graph theory. Okay, one of the famous networks that we all use every day is the internet, right? There's links from one page to another page. That's the
6:13relationship. And the things the nodes of these networks are web pages. and the very famous page rank algorithm that was developed by Larry Page um out of a Stanford PhD thesis that became the bedrock of Google, a trillion dollar company now realized that what they could do is use the mathematics of graph theory to understand relationships on the internet and then rank pages based on their connectivity rather than you know some naive approach that if you remember ask Jeieves >> you know we're old enough to remember ask >> we are we are old enough >> or like the Yahoo search they weren't as good because they weren't realizing this
6:54underlying graph structure Google was good because it was ranking pages with the attitude that the graph structure of the internet is what's important >> and this ended up being confirmed to be true not only by the fact that arguably the best business model ever invented in humanity with the best margins >> is Google and that same concept then ultimately got applied to social graphs. >> Yeah. >> In the rise of social media, Zuckerberg being the first to apply the same concept. >> Yeah. >> Uh but in the context of social networking which then became social media. >> Yes. Exactly. And all of these things at the end of the day there are graphs.
7:34They're vertices. In the case of social networks, there would be individual profiles and then a connection would be like a friendship between the two. Right? Now when it comes to physical networks, physical networks are embedded in 3D space. I'm talking about the brain which has neurons connecting from one to another. But this isn't isn't some abstract link. There's a little physical connection of a syninnapse between a neuron A connecting to a neuron B. Right? If you look at vascule, that's blood vessels that are physically connecting. And all of these physical networks are constrained by 3D geometry, right? They're constrained by thickness. How much room do I have to move in the brain, in the body? And it's not just
8:15these like 1D abstract links. So Ramoni Kahal in 1899, he's one of the pioneers of neuroscience. He's the first guy to um establish the neuron doctrine, which is the idea that the nervous system is made out of tiny individual cells called neurons that connect to each other and it's not just one giant network. And he prov he proposed a neuron morphology that's driven by minimizing wire volume. These are some great drawings that he drew. He was an artist and he could literally trace out using these incredible techniques where he would stain individual neurons and he could trace out how these neurons connected to one another and you could
8:55recreate things like the hippocampus, things like the optic nerve. >> That's incredible. >> And a lot of what he found even back then is true today. like he in the hippocampus for example he figured out that there's this cell layer called CA1 and it gets input from the dentate which is another part of the hippocampus and another part of the hippocampus called CA3 and so on and so forth. It's a he he was an incredible scientist and he proposed that the way that these biological networks um figure out where to go and what connections to make is by minimizing wire volume, which basically turns into what's the minimum distance between two points. Like if I want to connect this point and this point, I
9:35just want to figure out what the minimum distance is. >> So you're saying the shortest distance between two points is a straight line. >> Yes. And that's exactly what what he figured out that biology would >> at some point figure out like evolution would optimize for this right um he wasn't the only one in 1926 there was Murray who established Murray's law which governs vascular branching in the blood and he figured out that you know you can minimize work that the body has to do by doing this minimum distance kind of thing right where using that heristic what you can do is say with this network architecture, the blood can maintain the blood volume, but
10:18at the same time, it does the least amount of work to get over the friction of pushing fluid through my blood vasculature. >> It's it's sort of like an optimiz biological optimization. >> Yes, exactly. And he's like he's like the the the simplest optimization of finding the shortest link between two nodes that actually works. >> Okay. Mhm. >> So it was an old paradigm and in graph theory, this is effectively what's called the Steiner tree problem. Okay. If you've got a graph of points in uklidian space, these are the blue points in this photo. Then if I want to connect them with edges such that the sum of all the edges is smallest. So
10:59it's the it's the most optimized graph that minimizes the distance between all these edges. Then what I can do is introduce little points called Steiner points in between the vertices that I want to attach. Okay. And there's a certain rule that all of these Steiner points follow. Okay. If I basically if I want to have an algorithm that makes a graph such that all of the edges are least distance. Okay, then there's two things that we notice. Okay, first is that all branching points have only three nodes. They're called bifurcations, meaning one path is going to lead out to two. There's never one
11:39path leading out to three >> because one path leading out to three, you could actually decompose that into one path leading out to two and then this branch leads out to two. >> It's it's suboptimal to have three >> coming out of out of a single node. >> Yeah. The a fork is always two. >> It's right. >> A fork in the road is always two. There's never three paths out of a out of out of an input. Okay. So that's the first thing that's just a mathematical truth if you want to solve the Steiner tree problem. Okay. >> Okay. The second point is all of these >> intersections happen at 120°. >> Okay. And that kind of makes sense because if you've got three paths coming out, a circle is 360°. 360 / 3 is 120,
12:22right? So that it all like kind of makes sense. Okay. >> The problem is if you look at empirical data from biology, this is not true. Okay. In recent times, we've done incredible work mapping out the 3D morphology of biological networks. This right here is a neuron from the human conneto project. They've mapped out a human neuron. And what you can see is violations of that stiner tree. Yes, you've got triurcation. So, a single path leading out to three. And you've also got these orthogonal connections where the angle is not 120 but 90 degrees. >> So it it is structurally it appears to be suboptimal. Yeah.
13:03>> From an efficiency perspective. >> Yes. And if you were to actually calculate the minimum Steiner tree and then add up the lengths of all of these guys, the length the total length is about 25% more than what the minimum would be. So it's requiring more surface area to have the output that equivalent to the optimal version. >> Yeah. Yeah. Well, you're jumping the gun here a little bit because >> it's requiring more length. >> Okay. >> Right. >> I >> like the length is what is what is what is not optimal. >> I understand. >> You see what I'm saying? >> We're separating different degrees of measurement because they have different implications. >> Exactly. And and the older paradigm was
13:45that I want to minimize length. But you got there by saying, well, what if I want to minimize surface area instead? Now, let's think about it. Why would I want to minimize surface area? If I'm a living being, why would I want to minimize surface area rather than length? Well, the reason is surface area is the actual thing that requires material. Ah, you know, I need a cell membrane and that cell membrane is the thing that I want the least of. [clears throat] >> Doesn't really matter what the length is. >> Right. >> Right. Because if I can if I can minimize surface area but have a longer length maybe that's fine because I'm using less material. >> Okay. >> And that is the insight of this new
14:25paper. >> Interesting. Okay. >> Okay. The new papers introduces the fact that maybe if we minimize surface area then we can replicate biological networks. And what's really cool is they introduce an exact mathematical ma mapping between this local network design of minimizing surface area and the highdimensional fineman diagrams that we see in string theory. Okay, that's the key insight. The key insight is string theorists have been worried about this problem for like 30 years. >> Mhm. And if we can just borrow all their mathematics >> and apply it >> here >> instead of in an abstract space in a in a measurable space >> then then all of a sudden we've got a
15:06heristic a mathematical heristic that solves for why biology is doing this. >> It's it's a language to interpret the observations of biology where we don't necessarily have a coherent cohesive like language to describe it mathematically currently. >> Yeah. Currently but now maybe we do right that's the idea. Yes. So let's think about this a little bit more in detail. Okay, biological networks are 3D manifolds, right? There are these 2D structures embedded in 3D. So you've got tubes bounded by membranes, bounded by endothelium, things like that. And what we want to do, the optimization is to find the minimal surface. This is what's called a plateau problem. And physical
15:46structures do this all the time. Here you see a bubble in between two rings. Mhm. >> That bubble naturally is going to minimize the surface area of the bubble because of surface tension. >> So we sort of see this concaveesque uh cuz a bubble when you say bubble it's >> it's a spherical thing. But imagine now two rings like the bubble generators, right? And they're right next to each other. You get this sort of concave surface. >> Yeah. Right. >> Cuz it's trying to minimize >> Yeah. the surface area. And this is a a natural example of property I mean the reason why a bubble is spherical is because a sphere minimizes surface area right so the same mathematics maybe we can use for this right and the other
16:28constraint is that the surface curvature has to be continuous so you can't have like kinks you can't have like singularities like little points like you know you want a smooth surface everywhere >> you want a nice smooth bald head. Yeah. Yeah. Yeah. Yeah. Yeah. [laughter] And so with that in mind, let's now do a little bit of string theory. Okay. >> A deep dive into string theory. >> Okay. The infamous uh physics theory that is supposed to solve everything. Okay. >> Yes. >> And just to briefly before we dive in, Yeah. is the is the is this the idea that it's meant to be a theory of everything or unifying classical and quantum or or No, that's
17:09like a different concept. >> No. No, no, no. This is the same theory and it's it's unifying um general relativity and quantum. >> I'm sorry. Okay. Yes. >> Yeah. Yeah. But it is that is exactly what we're talking about. This is the thing of Ed Whitten fame and um who's that guy who goes on Joe Rogan >> and talks trash all the time. [laughter] >> I know. >> Weinstein, Eric Weinstein, I believe his name is the geome geometric unity. >> Geometric unity. So So string theory is purporting to do the following, which is unify quantum mechanics. Yes. With general relativity, right? And in quantum mechanics the the best picture that my favorite picture is Fineman's picture which has to do with the particle picture but the field picture of quantum mechanics. Okay. The way we
17:51understand the interaction between particles in quantum mechanics is that they exchange virtual particles. So here what we see is an electron that's being deflected by an electron. You know electrons repel each other. That's the classical picture, right? Electrons have negative charge so they don't like to be next to each other. In the quantum picture, the reason why they don't want to be next to each other and the reason why they get deflected in opposite directions is because they're exchanging a virtual photon. Okay? And that's what you're seeing in that Fineman diagram. An electron is coming from the left and electron is coming from the right and they're exchanging a virtual photon and that's how the momentum gets transferred from one to another. >> Copy. Okay. So that's the Fineman picture, right? In string theory,
18:33there's no longer anything called particles. Instead, all of our fundamental particles, all of our fundamental fields are made out of one-dimensional strings. So, you can imagine a rubber band that's one-dimensional. It's a line. And that line oscillates in multiple dimensions. Okay? Just like a guitar string can oscillate, you know, this way or into the guitar and out of the guitar. So, that's two dimensions that it's oscillating. A string can oscillate in multiple dimensions. Sometimes 10, sometimes 12, depending on what theory is your favorite. Okay? And and the idea here is that in this diagram we see starting from matter all the way at the top as you break down to smaller scales molecule, atom, neutron, strings are
19:13smaller than that are the are the most are in this theory are the most fundamental atomic unit of physical reality. >> And they're the same. The beauty of string theory is that it's all just one string, but the way that it oscillates in all these different dimensions make it an electron or a photon or a up cork or a down quirk, things like that. So, it's this nice like unified principle, right? That actually there's no such thing as all these different fields and all these different particles. There's only one fundamental thing and that is the one-dimensional string and the way that it moves around in these 10 dimensions gives it the properties of an electron or up quark or a down quirk and all these things. So it's it's a nice
19:54like mathematical unified picture. >> That's interesting. um it just hasn't found any like realworld physics use cases because in order to prove whether these strings exist you need to go down to the fundamental scale like the plank scale of really tiny length really tiny time um the energy is massive 10 the 19 um giga electron volts which you know the LHC only has 10 the 4 gig electron volts so we're trying to do 10 the 15 on top of what the LHC at CERN is doing >> the the Large Hadron Collider for those who might not know. >> That's right. Yeah, the LHC is the large hydron collider. So, we need a we need a LHC the size of the galaxy in order to
20:34probe these limits. >> And so, the the the point being like this is very largely theoretical because as of yet there's been no way to experimentally play with these theories. >> Exactly. Yeah. Exactly. And it's been a really cool mathematics exercise on its own. If you were to just look at the mathematics, it's amazing. It's won Fields medals. Ed Whitten won the Fields Medal for his work in string theory. He's never going to win the physics Nobel Prize. >> Okay? Because to win the physics Nobel Prize, there has to be some experimental grounding for whatever thing you do. But the Fields Medal is pretty nice. [laughter] So, I don't think he's like too worried about it.
21:14>> He didn't win the Oscar, but he got the Golden Globe. Oh, no. >> Yeah. Yeah. Yeah. Exactly. Even though I mean well I think you're gonna piss off some mathematicians in the audience who are gonna bad analogy analogy do not come in my comments. Maybe like something closer is like he won finals MV MVP but not league MVP. >> Yeah. Yeah. That's maybe a better >> Yeah. Yeah. No one please stay out of my comments. [laughter] >> Yeah. But um so in string theory you know we had that original Fineman diagram which was looking at the interaction between particles. So in string theories what you can do is you can turn a Fineman diagram into something called a world sheet. Okay. So
21:56on the left we have that same Fineman diagram and on the right you have strings that are merging together and they're interacting in this world sheet which is like how they're going through spaceime and all these dimensions and then they come out. >> And that is the key here. the world sheet >> that world sheet is the key here because it turns out that that smooth merging of those 2D world sheets those 2D string world sheets because when they merge they have to obey um smoothness there can't be any kinks in this world sheet because that's unphysical and they also have to minimize the surface area in this
22:37>> world sheet in this [clears throat] in this you know space whatever they're moving in and that is topologically identical ical to the smooth merging of biological tubes in 3D space. >> Yes, >> that's the key insight. >> Okay. Yes. >> Okay. >> Yes. Yes. >> That is the key insight. And the equivalence is pretty stark. They they lay it out in their paper. >> You know, on the right hand side, they've got that fman diagram and and the world sheet. >> Yes. >> And on the left, what they're showing is if you've got these physical networks, they're going to start obeying the same physics of those world sheets. Right. That's the that's the key thing. The string cross-section is now our biological tube cross-section. >> The time evolution for strings, like how
23:19I go from past to future. For us, it's just, oh, I'm just like moving along the tube. >> Okay, so it's another spatial dimension. >> My 2D world sheet is my biological membrane now. And then the tension, the string tension, which is something that is used in string theory to figure out like you know how tense sort of the strings are in in a loose sense that becomes the metabolic cost of surface area. >> Yes. >> Oh, that's so that's really okay. I I I'm tracking because I I think what's what's what's fascinating is we've basically there's been a mathematical structure that has been very millions and millions of dollars has been spent on Yes. in string theory to
24:00really hone in on this mathematical framework and language to communicate a conceptual idea. >> Yes. that when we look at these physical manifolds in like biology, >> that math that we've spent millions of dollars on almost is a perfect and you can see from these images almost a perfect map onto our observed >> biological structures that effectively take the same shape to respond to a similar math framework. >> Exactly. Exactly. That's the idea. And what they're doing is they're they're trying to basically do the math of string theory which is this Namboo Goto action. It's an action that measures the area of the world sheet, which is the total cost, right? And the equation is
24:41insane. I think I've got a little photo of it. The the equation is it's it's minimizing this integral over all of your possibilities, right? And it's making sure this mathematics is making sure that your stuff is smooth. And it's making sure that if you minimize this giant integral that the surface area of this whole thing is going to be minimal. Okay. The point is this math looks insane. >> Looks like man, >> but >> we've worked on it. >> Yeah. >> Because all of these physicists >> have been working on string theory. So, we've worked on it. So, we don't need to start from scratch. We can just take all of these results and apply it here. Right. And it bakes in the smooth it
25:22bakes in the smoothness >> and all of these mathematical tool kicks toolkits that have been developed can now just be applied directly to the biological problem. So the the point being the biologists don't have to spend years sort of waiting through the dark of discovery around you know finding the four corners of the sandbox on the mathematics. It's a Lego block that already exists. They can just be like oh here are these glasses. Let's look at it over. Oh my god I can see. >> Yeah. >> Yeah. Yeah. It's pretty cool. It's pretty cool. So now let's see how it actually works with biology. Okay. So let's first tackle the bifurcation versus triurcation which is the idea of
26:04a single path going to two according to the old paradigm of Steiner trees. But now what we see is single paths going to three. Why would the new paradigm now that we've borrowed this math from string theory allow triurcations and make that totally chill? >> Yes. >> Okay. The reason for that is because the surface area is what matters, >> right? not the length. Not the length. Right? So the wiring economy of minimum length only matters if your width of the world sheet is really small. And basically if if the thickness of your world sheet the string like the radius of your string is really small
26:45then it becomes a line. >> Yes. >> And then you only have >> bifurcation. There's there's not enough complexity to need bifurcation. But the thicker we make the biological network, the more we might need triurcations. And that's what you see in this paper. That's what they figured out. As we go from from thinner manifolds to thicker manifolds, at some point the the two forks in the road merge to become these >> three forks in the road. >> Road be because as you get thicker, your surface area is increasing over every length of distance.
27:25>> Yeah. >> And so subsequently it's becoming inefficient uh even if you're at the same distance. >> Yes. Exactly. And they actually introduce an order parameter. They call it kai and that controls whether you're going to go for two or three. Okay. If it's really thick compared to the separation distance, that's the thing that matters. >> Ah, yeah. You see? Yeah, that makes sense. >> If it's like if it's really far away, then I could do these Steiner tree approximations. But if my branching is really close compared to my thickness, then I'm going to need to >> do these higher order >> Yes. >> bcations. >> That that makes sense. >> You know what I mean? And that's what this is showing. And you can actually see the prevalence in the biological data. So they got data from the human
28:06conneto project. They got data from fly neurons. They got data from tropical trees. They got data from blood vessels. They got data from coral. It's just a massive amount of data. And what you can see is 15% of the time you do have these triifications. And it depends on that order parameter that I was telling you about. How thin is it versus how thick is it? like how far away is the is the branching versus how thick it is and they can immediately map the biological data and show that the Steiner tree algorithm is wrong. But this new heristic that they have using the string tree using the string three using the string theory mathematics >> yes
28:46>> that's what's closer to the biological data. So the idea is if you have two nodes at some distance apart, the old Steiner model worked if the distance between those two nodes where the branching was happening was >> really far away, >> was really far away. But as those nodes close in distance, um the the the thickness of the the line between those two nodes or or the path and branch between those two nodes as it gets thicker and as it gets closer. >> Again, the the the optimal the the optimization algorithm flips from um optimizing for two bifurcations to now we need we need to start introducing three. >> We need to offload more.
29:27>> Yeah. and keep it's almost like the thicker you are, the shorter you need the distances, the more bifurcate, the more uh out outlets you need for optimal for optimizing for uh efficiency. >> Exactly. And what's really cool to me is that across all of these different bi biological networks, right, we've got neurons, we've got trees, we've got fungi, we've got coral, it's all showing the same strategy. >> There there is an under again going back to what we always talk about there. There's an there is something that is true across all these different types >> that they all are speaking the same mathematical language that the string theorists have been trying to get everyone else to think about for so long. >> And it and it kind of makes sense
30:08because like even though these guys are so evolutionarily distinct, right? You've got plants, fungi, coral, and and the human brain. Even though evolutionarily we're divided by millions, hundreds of millions of years,