 That's the last time I'm going to have to do that this semester. All right, so I have a lot of stuff I want to cover today, so I'm going to get started right away. There are no announcements. There's no prequels. Hopefully, there's a short video I want to show you at the end that I hope kind of captures the enthusiasm that I have for teaching, but also for physics. It's not the outtakes thing that's coming. That's like a 11-minute movie, all right? So this will be a two-minute thing at the end. But I got to get to it, all right? So today, I'm going to tell you a little bit. We're going to take a broad and shallow dive into a wide number of topics. And where it's possible for me to do so, I will touch on introductory physics concepts that kind of set the stage for trying out these things. So believe it or not, we're more powerful at this stage than you think you are. You can understand a lot more about the universe than you think you can. And you can also get yourself into a lot of trouble because you don't know everything. So it's a great time, all right? This is a great time for trying and failing, all right? So today, I'm going to tell you a little bit about deep learning and the dark cosmos. I'm actually going to do them in the reverse order of the title. I'm going to set the stage for the deep learning problem that physicists are wrestling with right now. But first, let me put this course in a bigger picture. So introductory mechanics can often feel like an extremely dry subject. And I've tried to avoid making it as dry as it could be this semester, but it's impossible to take some of this material and really spice it up. Nonetheless, we've covered a lot of concepts that are the building blocks of far more advanced investigations. And like I said, believe it or not, you actually have a lot more basic tools in your toolkit right now for going a lot further than it may be obvious that you have. All right, so what are some of the concepts we've done this semester? Broadly speaking, we've covered different kinds of motion, linear motion, rotational motion. We've looked at forces which change the state of motion of matter. So we've looked at conservative forces that have an associated potential energy. And we've looked at non-conservative forces like drag and friction. We've looked at the work concept force applied over a distance, giving you a quantity of energy, energy of motion, the momentum concepts, and then the special case of a time-repeating motion of some kind, an oscillation. So we've mixed up time and space there. And we've looked at a very specific conservative force gravitation. And gravitation is going to come in handy for a lot of the stuff that I talk about today, but also rotation and energy conservation and so forth. These are repetitive themes that show up in investigating the natural world all the time. Now, big picture, apart from Newton's laws of motion, we sort of have three laws of conservation of quantities that we can apply in a closed and isolated system. And when they aren't conserved, it tells us something about the nature of the system. So you can flip the problem around and say, if something's not conserved, I now know something about the system I'm studying. Total energy, linear momentum, and angular momentum in a closed and isolated system are all conserved quantities. And you can take huge advantage of this to understand the universe. And I'll show you some of that today. I'm not going to go through all of this, but I thought it would be nice to put this in the deck of slides for this class today. The next thing many of you are going to go study is electricity and magnetism, the building blocks for applying this new force, electricity, and its cousin force, magnetism. The building blocks are linear in rotational motion. Electricity and magnetism represent another kind of conservative force. They have an associated potential energy. Work, energy, momentum, all these concepts will be exercised almost immediately as if you should already know them when you get to second semester physics. Hint, hint. Now, we don't usually get to cover this in introductory physics, but heat energy is another kind of energy. It's really a kinetic energy associated with the motion of the constituents of matter. So everything in this room, as far as we know, is made from atoms. I'll come back to that theme later. Those atoms are not sitting still, even if the object looks like it is. That table doesn't look like it's moving. But the atoms that make up this table, the carbon oxygen, nitrogen, and so forth that's in the materials here, they're jittering wildly because they're smacking into one another because air molecules are smacking into the surface. That energy gets transmitted through the system. That's what we call heat. The reason when you touch a hot stove or a cold ice cube that it burns or hurts your finger is because your body has sense mechanisms in it to tell you when there's too much kinetic energy going into the cells in your body and the nerves in your body send a warning signal to your brain that this is going to cause long-term permanent damage. Quantum mechanics, which is a broader subject than introductory mechanics, technically everything we've done this semester is included in quantum mechanics. But quantum mechanics goes further and allows you to describe the very small. But it also requires you to have taken electromagnetism and special relativity, which you learn in third semester physics. If you want to understand the humble atom, you need all of this stuff. You can't get away understanding the atom in any reasonable sense without having these foundations. Electricity and magnetism, motion, forces, oscillations. It's all packed into the atom. So no wonder it took us as a species so long to understand the building blocks of nature. If you want to build new materials, you probably want to look at solid state physics or material science. But there again, you need to have a good working knowledge of the atom, which requires a foundation for lots of other stuff. Want to understand how a transistor or a diode or any semiconductor works? It's quantum mechanics. You're forced to learn something about quantum mechanics to understand those. Like non-conservative forces, you'll love fluid mechanics. The Navier-Stokes equation will reduce you to weeping in about three seconds. It looks deceptively simple. It is almost impossible to solve without a computer. So it's fun. If you think gravity is hard, just wait till moving through syrup. Moving through syrup or water or air, that's really difficult. Now these are just some examples of where you can apply the little nuggets of information, the little building blocks we've laid down this semester. I have totally skipped the math that you need that goes along with all this, like vector calculus, differential equations, linear algebra, group theory, complex analysis. But normally, those are prereqs for these courses. So you'd know that in advance. So I've talked about atoms. Let's put atoms in a wider context, the context of matter itself. So the theme of the next section of the lecture is seeing matter. And I want to get you thinking more broadly about what it means to see something. So physics is not about sliding things down and incline. It's not about rolling things. It's not about throwing things. Those are all simple activities that we can use to understand motion forces and conserved quantities and so forth. They're little laboratories. But that's not what I spend my day doing. I don't go home to my laboratory in Europe or whatever and play with masses hanging on a pulley. That's not what a physicist does. What a physicist does is tries to ask questions about the nature of the universe and then try to conduct experiments or mathematical investigations to answer those questions. And these are not small questions. They may seem simple at first, but they often have profound implications for the nature of reality. So all great investigations in science in general begin with one simple question. Usually something like, huh, I wonder why that happens. And then you spend 50 years trying to answer the question. I'm not kidding. That happens. So let's ask a simple question. And let's see where that simple question leads. Now this is the kind of question that maybe you asked when you were five years old or seven years old or something. All right, basically, what makes up stuff? What's stuff made of? That's it. We can make it sound a little less childish by asking, what are the building blocks of the universe? But really, if you boil it down to the question a four-year-old might ask you, it's, what's that made of? What's in that? I once sat on a plane next to a couple of kids and then the flight attendant asked if I would supervise them because they were flying without parents for the plane ride. And they got a cup of water and one of them turned to be and said, what's in this? What's this made of? Like, what is water? And I'm like, yes, this is great. I can be useful, OK? So then I got to talk about atoms, right? That was kind of fun. All right, so I like to think of the universe, I hope. I hope the universe can be understood in the same way that something made out of Legos can be understood. When you see these amazing sculptures that people make out of Lego bricks, they're really incredible, right? I mean, these things look totally life-like sometimes or extremely intricate that can have moving parts. They can look really complicated. But when you boil it down, they're really made of a bunch of sort of fundamental shapes that click together in various ways. So the different shapes and colors of the building blocks and the way that they fit together are what physicists call forces or interactions, forces we've matter into reality. That's a modern understanding of how things work, OK? So let's take a look at the universe from this sort of perspective. Can we answer this question, what are the building blocks of the universe? All right, so how many of you have seen this before? OK, all right, so a few, right? So OK, if you're going to be an electrical engineer, you might want to familiarize yourself with this. These are silicon wafers. Silicon is a semiconducting material that's largely at the heart of most modern electronics because of its ability to conduct sometimes and not others, thus the word semiconductor. Now, the reason it does that is quantum mechanical in nature, and it takes some effort to understand it. But that silicon, you can look at it, you can appreciate it, all right? So this is a 12-inch polished silicon wafer that might be used in computer chip manufacturing. In fact, I suspect that's exactly where these wafers come from. These wafers are often grown in what are called boules. So they are long, single crystals of silicon that are then sliced very thinly and polished. And then you can imprint on them circuitry, slice them up and make computer chips out of them, OK? And one of the things that industry tries to do is maximize the usage of the wafer. A circle is not optimal for cutting into squares, so people get very creative. So there's a small wafer, there's a big wafer. But fine, what is this? What is silicon? Now, how many of you have seen an atom before? Good. OK, so this is not a computer-generated image on the right-hand side. This is using a technology known as a scanning tunneling microscope. You need quantum mechanics to understand how that works. But just accept for a moment that it's an extremely powerful microscope. Capable of seeing things on the subangstrom scale. Angstroms are 10 to the minus 10 meters, which is roughly the size of an atom. These are silicon atoms arranged in what are known as a crystal lattice, a repetitive structure. In this case, it's six atoms in these little rings. And these structures repeat themselves. If you understand that ring of silicon atoms, you can repeat it over and over and over again and build the material in your mind. You don't need to understand the whole material. You just need to understand that ring and how it interconnects with the rings next to it. If you can do that, you can fully predict the properties of a material, at least grossly speaking. Understanding structures like this and materials will predict the color of the material, the thermal properties of the material, the conductive properties of the material, all from the structure and arrangement of atoms and the electrons in those atoms. Now, what do you notice in this picture? This picture of silicon atoms, a beautiful, repetitive crystal lattice. What do you notice? Anything interesting, John? There's an imperfection. Look at that. I'll come back to the theme of neural nets and pattern recognition in a bit, but our brains are highly attuned to look for patterns. And there's something wrong. There, right there. There's an imperfection in the crystal lattice, a missing atom. You can see a single missing atom. Again, 10 to the minus 10 meters in scale. Now, you might be wondering, well, this is a pretty crappy camera. Look how fuzzy those atoms are, right? They're not fuzzy because the camera is crappy. They're fuzzy because nature is fuzzy at this scale. There's no one place where a silicon atom is and is not. It's spread out in space. And when you look for it by shooting a photon or an electron at it, you'll find it in one place one moment. And a moment later, you'll find it in another place. That fuzziness is what is considered often the weirdness of quantum mechanics. But once you understand that everything at this scale is wave behavior, it's not that weird. If you've ever been to a big lake where there are wind waves or the ocean where there are very strong, nice waves, and somebody says, hey, where's that wave? Well, there's no one answer to that question. It's sort of mostly here at the crest, but it's partially here over as we approach the trough. And it's also partially back here and the trough behind it. There's no one answer to that question. I can tell you the frequency of the wave. I can tell you the length of the wave. But I can't tell you where the wave is. And that's the same problem atoms give us. They're not in one place at one time. If we know where they are, we don't know how fast they're moving. If we know how fast they're moving, we can't figure out where they are. This is something you would learn in third semester physics and quantum mechanics. But that fuzziness is not the limitation of the camera. It's the reality of nature's uncertainty at this small scale. So I want you to think about atoms. And I want you to think about atomic matter. That's the stuff in principle that's in this room right now. You're made of it. I made of it. Everything in this room, as far as we know, is made of atomic matter. So let me ask you a question. How do we know that matter is here at all? Simple question. I know, right? Oh my god, existential crisis. One slide, 10. Existential crisis. How do we know that matter is here at all? How do you know that there's stuff in this room? Give me a simple answer. How do you know there's stuff in this room? Marilyn? OK, in what sense? You interacted with it. So what do you mean by that? I can touch it and see it and stuff. OK, so you can touch it, right? You can touch it. You can see it. So how do we see things? Oh, I'm not proving it's there. I'm just saying, how do we know it's there? How do we know anything is here at all? All right? Is it a philosophy? No. No, philosophers want you to think that, but then we do experiments and actually test things. So is that on camera? Good. Yeah, awesome. Take that, Dan Hooper, a colleague of mine teaching a philosophy of science class. OK, all right. So touch, sight. What do those things rely on? What is sight? Light reflecting off of things. Ding. OK, right. So light is being generated by the gas with a high voltage across it in these tubes. That light is diffusing throughout the room. It's scattering off of surfaces. It's getting into our eyes, which are really, really kind of fickle optical cameras. And then it's being transmitted as an electrical signal to our brain. And it's being interpreted by what we call sight. But light, fundamentally, is one way that we know about matter. Touch, as I've mentioned a few times before, touches an aspect of the behavior of light. It's electromagnetism. It's electrons in my hand repelled by the electrons in the surface of the table. Fundamentally, that is also a photon or light-related behavior. That's something you would learn in second semester and third semester physics. Now how else do we know that matter is there? Light. We've used up light. That's touch. That's sight. We've used up that stuff. How else do we know that matter exists? What else does matter do to matter? But through what force? So reactions require a force, some kind of transmission of information from one piece of matter to another. So light is one way to do that. Light is a photon emitted from an atom here, going into the matter in my eye. How else? Gravity, right? The moon goes around the earth, right? We've studied gravity. We've looked at the law of gravitation. What's in the law of gravitation? Mass. Some kind of gravitational mass. So there are two ways that we have established. There are other ways. But these are two big ones, especially if you want to do astronomy, where you can't actually go out to stars and touch them. You have to look at them. You have to look at how they move and infer from that what gravity is doing to them. So there are basically two ways we know how to see matter at great distances, especially. And that's why I bring this up, because I'm going to come back to it. Atomic matter absorbs light and emits light. And in fact, as I'll demonstrate here, so these tubes contain elemental gases, so elements, atomic elements. And if you run a current through them, they look extremely different, right? This is neon. This is argon. You wouldn't confuse these two things for each other. And that's because the light emitted by different atoms and the light absorbed by atoms has a pattern to it. That pattern is quantum mechanical in nature. Again, see the theme here. Quantum mechanics tells us why neon emits certain wavelengths of light more prevalently, why argon emits different wavelengths of light. This is more red. This is more purple. So atoms have thumbprints or DNA, and that's encoded in the way they absorb and emit light. So that's very different. Now, in addition, when things have different masses, they gravitate differently. Now, gravity doesn't have a big effect at all on the atomic scale. Run the numbers and see. Two atoms that are near each other barely interact with each other through gravity, but the strength of their electromagnetic interaction is vastly huge. And because we can't switch off electromagnetism, it's tough to get rid of it and just study gravity at the small scale. But on the big scale, gravity influences the motion of atomic matter. It's matter influencing other matter. So we have two ways that we can infer that matter or mass is present. We can look at the light that's being emitted from a distant object, but we can also watch how it moves in the gravitational field of another object. And from those two things, we can infer mass. And for a couple of centuries, human beings experimenting with atomic matter worked up ways to quantify the amount of mass in something based on light and based on gravity. So let's take a moment and reflect on where we are in the cosmos, because we have to go big in order to understand why we think that there's a whole bunch of unseen matter in the universe. So what's our place in the cosmos? Well, we live on a planet called Earth, which currently is our home planet. We live in a solar system with other planets and many interesting moons. And we're centered on a middle-aged yellow star, which you could call soul. It often gets called that in many writing applications. Our sun is about halfway through its life. So it's got about 5 billion years left to go before it enters the first phase of dying. We are a part of a much larger system of stars known as the Milky Way Galaxy. We, our system, the solar system, orbits the center of our galaxy once every 250 million years. And for those of you that have only ever known the glow of city lights or urban landscapes, this is the rest of the Milky Way as we look in toward the center. So this is viewed from the Atacama Desert in the southern hemisphere. You can only see the center of the Milky Way from the southern hemisphere of the Earth. It's not visible from where we are now. But you can see the trailing arms of the Milky Way in the northern hemisphere. That's visible. The center is visible from only the south, though. So we are about 25,000 years traveling at the speed of light from the center of the galaxy. That means if we could travel at the speed of light, it would still take us 25,000 years to get there. That also means that any light you see from the center of the galaxy left that place in our galaxy 25,000 years ago before what we consider modern human civilizations even existed. So we're not seeing the center of the galaxy as it exists now. We're seeing it today as it existed 25,000 years ago. And it takes us about 250 million years to make one revolution around the center of the galaxy. The Milky Way itself is home to something at the level of 100 billion stars. It's hard to pin that down exactly because we're right in the middle of it and it's hard to count all the stars. But astronomers have refined that measurement over decades and it's something at the level of 100 billion stars. Now the Milky Way is not alone. It's an island of stars in a great sea of islands. The Milky Way is part of something known as the Virgo supercluster of galaxies. That supercluster is 100 million years at the speed of light across. And the visible universe, the stuff that we should be able to see by looking further and further out in space, is roughly about 93 billion light years in size. We are really tiny. But I like the cleverness of our species because I think we can learn a lot by looking out at the cosmos from our little vantage point here in the suburb of the Milky Way galaxy. We're kind of out in the suburbs of our own galaxy. We're not in the city center. We're out in the winds. We're looking in toward the center where that bright cluster of stars is. By the way, that black band you see there, it's not that there's stuff missing there. It's that there's dust in the way. That's just molecular dust that gets in the way of the visible light. We can see through it in other wavelengths of light, though. We do that. So that gives us a sense of our place in the cosmos. And what's neat about galaxies is that they are essentially laboratories for studying matter. So you can use light to study galaxies, and you can use gravity to study galaxies. So we've looked at what a galaxy is. It's just a big collection of stars, gravity rules in galaxies. So it's gravity that keeps this big swirling mass of stars together. I'll show you some external pictures of galaxies in a moment. They're not our galaxy. We can't see our galaxy from outside. But we can look at others nearby and get really nice pictures of them. In fact, the closest galaxy to us, the Andromeda galaxy, it's far away, but it's huge. It actually has more stars than the Milky Way. And it's about the size. If you hold your thumb up to the sky at night, it's about the size of your thumb in the sky. But it's so far away that it's trillion stars are too faint to see with the unaided eye. You need a telescope, and you need to do a long exposure with a camera to see it. But if you can do that, it's the size of the moon in the sky. It's just that we can't normally see it, because the light from all those trillion stars is just too faint. It's traveled too far. It's too faint by the time it gets to our eyes here. But you can't observe it. There are some good times of the year to observe the Andromeda galaxy. And even with a modest telescope and patience, you can see it. Now, observational evidence tells us that stars and gas are all made from the same atoms we find on Earth. When we look at the light that comes from other stars or other galaxies, we see that thumb print from the atomic structure of the atoms we see here on Earth. We see hydrogen. We see helium. We see carbon. We see oxygen. We see nitrogen, iron, nickel. We see all of those things out there, and all based on the way that their light is structured when the light gets to us. So as far as we can tell, all the stuff we can see with light really is the same stuff we find here on Earth. It's just spread out over the cosmos, and some of it clumps into galaxies in the form of stars and gas. Now, if atomic matter is the primary component of matter in a galaxy, in other words, if everything you can see in the picture of the Milky Way is maps directly onto all the mass in the Milky Way, then the amount of light emitting matter enclosed, say, by the orbit of our own sun is we make a 250 million year journey around the center of our galaxy that the velocity of our sun should tell us something about all the mass that's enclosed inside. Our kinetic energy is related to our gravitational potential energy as we circle the galaxy, conservation of energy. So we should be able to use our velocity or the velocity of stars in general to tell us, using gravity, what the amount of mass is inside the orbit. So light could be one way to do it. Gravity is another. So we have two independent ways of measuring mass in something the size of a galaxy. That's awesome. Scientists love having two different methods of trying to measure the same number. It's a cross check. If you've really understood the universe, those methods should intersect at the same point. But if they don't agree, it means you don't understand the universe and you need to work harder. So if they don't agree, we have an interesting puzzle on our hands. You don't give up. Yeah, that's failure. But you learn from it. If an idea fails, have a better idea. So here's a picture of a galaxy. This was taken with the Hubble Space Telescope. It has the uninteresting name of NGC4414. But it's a really beautiful example of a spiral galaxy. And we think the Milky Way looks like this. There's a lot of astronomical measurement effort going on to try to map the shape of the Milky Way from our little vantage point in the suburbs. It's like mapping the Metroplex by being out in something like what, Irving or Southlake, for instance. I'm assuming that's where you're from. It's like Southlake. And then just looking around the Metroplex and trying to figure out how the Metroplex is shaped. Fort Worth is like a satellite galaxy for Dallas. I mean, the analogies actually work really well. But we're observing. We're stuck in our suburb. There is no transit system to the center of the Milky Way. There's no transit system outside the Milky Way. We kind of have to look around and go, all right, let's see if we can figure out how the city is laid out. That's a tough thing to do. So we have galaxies. They're swirling, orbiting masses of stars. Those bright points, they're not individual stars. They're probably groups of stars. There's a group of stars around us. Vega is one of them, for instance. Arcturus is another one. There's all kinds of stars. When you look out, the really bright objects you can see first, if they're not planets, they're stars in our interstellar neighborhood. So they're all within about 80, 100 light years of us, something like that. But they're far away. So let's consider some star in some galaxy, and it has a mass, m star, not very creative. So maybe it's our star. Maybe this is the Milky Way, and we're kind of here in the suburbs, and we're making this swirling journey every 250 million years. Now astronomers have developed these really nice techniques. They don't have to wait 250 million years to see how fast a star is moving. They can look at the light being emitted from it now, and using the properties of the light, they can tell you how fast it's moving. So that's a really neat technique. So we can actually look at other galaxies, and we can measure the speeds of stars as they orbit the galaxy, even in very short times. So that orbit will enclose the mass inside of the orbit. So if we imagine speeding up time, and we're orbiting and orbiting and orbiting, the mass inside of that orbit is what does all the gravitating. So Newton's law of gravity tells us the potential energy that a star has relative to the center of mass of the galaxy, which is roughly there. So that's an equation that we should be able to write down at this point in the course. The potential energy from gravity of a star is the negative of Newton's constant times the mass enclosed in the orbit of the star times the mass of the star divided by the radius of the orbit, gravitational potential energy, gmm over r, with a minus sign in front of it. Now the star will also have kinetic energy. It's moving as it goes around. It's rotational motion. And that kinetic energy is 1 half times the mass of the star times its velocity squared. Nothing exciting going on there. It's just 1 half mv squared. So stars swirling around a galaxy have kinetic energy. They have gravitational potential energy. And we can relate the two of them. We can use conservation of energy to relate them. Now I don't want to get into the details of this, but for a big system like this where you have a gas of stars, and all those stars are moving under the influence of mutual gravitational attraction, you can't just blindly write down that kinetic energy equals potential energy. It's not quite that simple. But there is a theorem that you can work out called the virial theorem. And the virial theorem says that the average kinetic energy of a star is equal to the negative of 1 half of its average potential energy. So it's a bit more complicated than just like Earth rotating around and then you're standing on the Earth and you're being pulled down by the Earth. It's a bit more complicated than that because you're not a gas, the Earth is not a gas. But galaxies are like gases of stars. So those stars are point masses on something the scale of a galaxy. All right, so if we plug in all the equations, the average kinetic energy of the star is 1 half times the mass of the star times its average speed squared. The negative of the potential energy is 1 half g m enclosed m star over the average radius. Then we can rearrange this and solve for the velocity. And what we find out is if we can use astronomy to measure the speed of a star, v, and the radius of its orbit, r, then we can figure out how much mass is enclosed by that orbit. It's a simple equation. So measure v, measure r, calculate the mass enclosed, and see if it follows what the light is telling you. Does the light give you the same story that gravity gives you? So people have done this. Now galaxies are a teeny bit more complicated than I've just described. There's that bright core of stars, the galactic core, which here is about a third of the total galaxy that you can see. Down in the galactic core, things get a little crowded. It's just like downtown Dallas. Traffic gets pretty dense. Cars aren't moving freely in downtown Dallas. They're slaves to what the cars around them are doing. So I'm in a traffic gym. The car in front of me moves. I move. Ha, car moves. I move. And that's my typical morning, right? That's what stars in the galactic center are forced to do. They're not isolated from each other as much as they are out here in the suburbs. So in the galactic center, those swirling stars are more like a gaseous planet. And as you move out from the galactic center, stars should go faster. But then when you get out to the edge of the core, then you hit the big gas of stars. And then the velocity of the star falls as the square root of 1 over the radius of the orbit. So mathematicians and astronomers and astrophysicists have worked out all these predictions over decades based on modeling galaxies and so forth. There's whole papers on this stuff if you want to deep, deep dive. But let's take a look at what these should look like. No, it's not, because this is not a rigid body. This is more like a swirl of water. The water on the outside of the whirlpool is not moving at the same speed as the water in the center. Over time, well, okay, so galaxies could collapse if there's enough mass to pull the suburbs in and collapse the whole thing. But that seems to take longer than other things happening, which is usually that the stars die out, star formation stops in the galaxy, and then the galaxies kind of age and fade. So it takes a really long time for a galaxy to collapse, for instance. Often what happens is galaxies actually collide with each other. I mean, that's happened many times in the history of the universe. The galaxies are pretty far apart, but many of them have collided with each other. So it's really complicated. It's a mess out there. In fact, the Milky Way is going to collide with the Andromeda galaxy. And I forget how many billion years. But there will come a time where the Andromeda galaxy will fill the night sky if this planet lives long enough. Now, when we collide, not much is going to happen. There's a big gap between stars and galaxies. And so we don't really expect to hit anything. But I don't think our star will be around at that point anyway. So let's take a look at prediction versus reality. So the prediction of the speeds of stars is that they should rise in the galactic core, hit some maximum. And then because we see from the light that there's not a lot of mass out here, right? There's not a lot of luminous matter out here in the suburbs, kind of where we are in the Milky Way. Then the speed drops more and more and more as 1 over the square root of r. And that's again because you're not enclosing so much mass out here. That's most of the mass from the light. There's not a lot more mass to enclose here versus here versus here versus here. And this velocity has to fall off. If a star is going to remain as part of this galaxy, it can't move too fast. It's a balancing of centripetal force and your linear speed. If you go too fast, you'll leave the orbit of the galaxy. But here's what's observed. Indeed, stars in the center of galaxies move faster and faster. And then they just kind of keep going. They don't drop in speed. In fact, our own sun is moving around the Milky Way faster than it should be able to. We shouldn't be bound to the Milky Way. We shouldn't have made orbits around the Milky Way so far. We should have been flung into intergalactic space. We shouldn't even be here. So if this is correct, the Earth should not be bound to the Milky Way. But it is. Lots of stars shouldn't be bound to the Milky Way. But they are. So gravity is telling us one story. Light is telling us a different story. And I'll come back to that in a moment. This is an animation showing you what galaxies with these different rotation velocities would have. On the left is a galaxy swirling in a way consistent with the expectation from luminous matter. So you'll notice that stuff out here in the suburbs, and this kind of goes to your question before, right? The stuff in the core is swirling really fast. The stuff in the suburbs in the prediction is not swirling that fast. And so you get this kind of whirlpool effect in the galaxy. But this is what a real galaxy. In fact, every galaxy we've been able to measure this stuff in basically does this with a few exceptions. And they're interesting. And you can ask me about them at the end if you want to. This is the case where the stars out in the galactic suburbs are moving almost as fast as the ones in the core. This shouldn't be possible with just the visible mass that we see. That's interesting. So we have a failure. We have a failure that we can learn from. So the life from stars and gas tells us one story. It tells us that atomic matter in the form of stars and gas clumps mostly close to the galactic center, but less densely out in the galactic suburbs. We would predict then that stars shouldn't be moving that fast out in the galactic suburbs. But the motion of the stars tells us a different story based on gravity. And that is that indeed there's a dense core in the galaxy and it's true that stars move faster and faster and faster in the core. But when you get to the suburbs, they're still moving real fast. Those curves flatten out and they shouldn't. They should fall off down towards zero speed. So the tension here is that light emitting atomic matter and light absorbing atomic matter appears not to have much to do with the mass of a galaxy. In fact, the evidence right now is that galaxies are dominated by an unseen, non-luminous form of matter, which I'll come back to in a bit. Not only the galaxies, but the whole universe. This is something that we've only really known for about 15 to 20 years at this point. Now, pioneers in the field did work decades ago, but nobody took their work too seriously until there was a convergence of many lines of evidence. So this is Vera Rubin and this is Kent Ford. And they're considered pioneers in modern stellar velocity measurements in astronomy. Vera Rubin died before she could receive the Nobel Prize. Kent Ford is very old, but he's still alive. So it's another one of these losses to the field that nobody bothered to nominate. Or if they did, the Nobel committee didn't bother to pick these two for having made a really incredible measurement that stars are moving far faster than they should be. And this implies an unseen, non-luminous form of matter in the universe. So these are just two of many players in this story. Another one is Fritz Zwicky. You can ask me about him later. He was an interesting character. All right, so there are two broad hypotheses about what's going on. That there's a new kind of matter in the universe we didn't know about until very recently. It's been labeled dark matter because it doesn't absorb light and it doesn't emit light. Now, that doesn't mean it isn't some kind of cool atomic matter with its own set of forces that hold it together. We just literally have no idea what it is. As far as we know, the only thing we can say definitively if there really is dark matter in the universe is that it definitely influences normal matter through gravity. That's about all we know. There's a dark matter-like thing out there. It definitely influences other matter through gravity. Okay, that's about it. And so the dark also suggests our level of ignorance about this. We just don't have any light to shine on this question. But we're working hard, thank you. We're working really hard on this. She gets regular paychecks to laugh at my jokes, yeah. All right, so now the other possibility, or both of these could be true, is that the gravitational force that normally we think of as falling off is one over R squared, Newton's law of gravity, doesn't. That maybe we've gotten it wrong at the largest scales in the universe. Maybe gravity is one over R to the two plus a tiny number when you get to things the size of galaxies. This is known as the modified gravity hypothesis. This is an active and ongoing scientific debate. And by scientific debate, what I mean is people are working really hard to prove or disprove these ideas. And there's no killer measurement yet. There are some measurements that put nails in the coffin of some of these ideas, and I'll comment on that in a moment. But nobody has said definitively it's dark matter or it's modified gravity. In fact, it could be both. There's nothing to say, or it could be neither. And maybe we just lack the imagination to solve this problem, okay? So while neither of the above are definitively known to be the correct description, the dark matter hypothesis is generally favored, although this could be a bias in the community, over the modified gravity hypothesis. But there's a decent reason for this, at least. As I mentioned, we have lots of intersecting lines of evidence, and they intersect very nicely on the dark matter hypothesis. A new kind of non-luminous matter explains things we've seen in the light left over from the formation of the cosmos, the rotation of galaxies, the motion of clusters of galaxies, the large-scale structure of the universe, the motion of objects in the vicinity of our own Milky Way. A new kind of matter fits all of that really nicely. Modifying gravity solves some of those problems, but it fails to solve others. And when you try to make it solve all of them, it sort of pops out over here with a new problem. That doesn't mean it's not the right explanation. It just means there's more work to be done on that idea. The fact of the matter is, is that to date, we have not observed a non-luminous form of matter we don't already know about. There is some that exists in the universe that neither absorbs nor emits light, but we've accounted for that in the universe, and it's not enough. This stuff is really beyond what we know. And nobody has definitively shown a test of the law of gravity that fails one over r squared. And believe me, people look for this. So this is active. This is a frontier of human knowledge. There are no answers here yet. But some of you could help us to figure out the answers to these questions. So how could we hunt for dark matter? I'm going to focus the rest of this lecture on dark matter itself. How can we hunt for dark matter? It's a non-luminous form of matter. You can't literally shoot light at it and see it. We take for granted how easy it is to see atomic matter. But what happens when light is not an option? What happens when electromagnetism is not an option? Now you have a challenge on your hands. All we know is that they interact by gravity. That's it. It could be that there are other forces of nature that are new, part of dark matter. But if they're there, they're extremely weak, or we would have seen this stuff already, perhaps. So how do we hunt for this? I don't want to go into the details of this picture. I just want to paint for you how crazy active an area of investigation this is, both from mathematical physics and from experimental physics. This is one of the things that, for instance, the US is spending a lot of money as a nation, scientifically trying to address, with a suite of three large experiments over the next decade, with plans to build even larger ones over the next 50 years. So this is not a one-year plan, a two-year plan. The scientific community and the funding agencies in the United States, Department of Energy, National Science Foundation, NASA, and so forth, they have made a real long-term investment in building, operating, and taking data with these experiments to answer this question. Mathematical physicists have been busy trying to come up with all kinds of neat mathematical ideas to make predictions about what the properties of dark matter might be so that we can target those properties with experiments. So we're building experiments as experimentalists to try to look for some non-luminous form of matter. The mathematical physicists are trying to say, oh, well, if the universe is this old and it was present at this time, and it's in this amount now, then it probably has this mass and maybe these other properties, and you should go look for this. So it's a very active back and forth right now. This is just to note that mathematical physicists are very clever. And just to calibrate you on this scale, this is a scale of mass, although it's in funny units. It's not in kilograms. You learn in modern physics, the third semester physics course, that mass, energy, and momentum can all be described by the same units. Particle physicists take advantage of that. And as a result of that, the mass of the proton, for instance, is 1 billion electron volts. 1 billion electron volts is the mass of the proton. Mathematical physicists have proposed explanations for dark matter that go from zeta electron volts. Look that up. That's a really tiny number. All the way up to 30 times the mass of our own sun in the form of black holes. So this spans, well, they didn't even bother to include the full scale. This spans so many orders of magnitude that this is a really tough problem. The problem is we don't know what the mass of a dark matter particle is supposed to be. So we have to cast a really wide net to try to find it. So I'm going to show you some of the net today. And the net I'm going to show you today basically spans this region right here. That's it. Three orders of magnitude on this huge scale. But I promise you there are experiments all over the world that are trying to cover as much of this as they can. Very active right now. You get involved in this. You're operating at the frontier of human knowledge. OK, so we've seen the gravitational effects of dark matter, not just in the things I've shown you, but in other things as well. There's evidence, for instance, that similarly affects our own Milky Way. Our star is moving too fast around the center of the galaxy to have been bound there only by the luminous matter in the Milky Way. So there should be dark matter right now in this room. And in fact, if you put your hand out based on some of those theoretical predictions, there are dozens or hundreds of dark matter particles passing through your hands right now. But the joke we like to tell is that you're not that important. Most of the universe can't even be bothered to interact with you. That's pretty, what, emo? Is that what I'm going to say? I guess that's pretty emo. It's dark, right? This is how little you matter. Most of the universe can't be bothered. Dark matter does not even know we're here. Dark matter does not even know we're here. So how do we make something that doesn't interact by these stronger forces like electromagnetism? How do we trap them? How do we trap those dark matter particles that should be right here in this room right now? All right, so there's three ways that people try to detect dark matter. And they boil down to these three techniques. Shake it, break it, or make it. I knew I'd get any in response out of that. OK, so here are the techniques. Shake it. What do I mean by that? Well, if there are really dark matter particles from the cosmos in this room right now, put a really dense target in the room, put as many atoms into a volume as you can, and hope that one of those dark matter particles will hit one of those atoms somehow, because we don't know how they interact besides gravity. So make a target, wait for dark matter to hit it. When it shakes the target, get information out of the target, and say an interaction happened, it was dark matter or it wasn't dark matter. There's a lot of things that interact with targets. Natural radioactivity is a real problem for this. I'll come back to that in a bit. You could break it. You can look for places in the cosmos where over the 13.78 billion years of the universe, dark matter has clumped over that time from gravity. Centers of galaxies are a good candidate. Those are really dense clumps of matter. They're probably a very dense clumps of dark matter there as well, and in fact, we're observing the center of our own galaxy for evidence that dark matter particles are interacting with each other, or maybe even decaying like unstable radioactive elements over a billion years. So every now and then, one dark matter particle might decay, we might see something from that. That's break it, or you can make it. Do things the old fashioned way. Make it yourself in a factory. You built yourself in your backyard. So the way we do that is we take normal matter, protons, for instance, which is what I use. We smash the protons together over and over and over again, hundreds of millions of times a second, and we try to look for evidence that dark matter has been created in those interactions. We take advantage of something you learn in third semester physics, that mass and energy are the same thing. If you put energy in, you can get a commensurate amount of mass out, and the relationship is E equals mc squared, one of the most famous equations in the history of physics. I did not pay her to ask this. How do we know we've made dark matter? We'll talk about that in just a moment. So let's look at shake it for a second. So again, you take an atom, and then a whole bunch of other atoms, and you put them in a target, and you hope that dark matter will strike one of the atoms, kick it out of where it was. This costs energy, and then you'll get light ionizations or electricity sound. You can get the whole mass of atoms vibrating when this happens, and you can try to read that out. You can try to be clever and say, well, that's more consistent with what we expect a dark matter particle to do, and that looks more like a gamma ray that did that. We know about gamma rays. They're boring. So this is banked on the fact that there's some interaction between dark matter and normal matter that isn't just gravity, but we don't know that that's true. We might luck out on that one. So here's one experiment. Part of it is being done here at SMU. So Dr. Jody Cooley is the lead principle investigator here at SMU for the super CDMS experiment. CDMS stands for cryogenic, ultra cold, dark matter search, CDMS, cryogenic dark matter search. I wanna show you the technology here. This is a hockey puck sized single crystal of germanium. So it is a single crystal lattice. It is essentially unbroken across the volume of that entire hockey puck shaped piece of germanium. So it looks a lot like that silicon wafer we had before. It's got that gray black color to it. And it's patterned. You can kind of see that more pattern in the picture. Those are lots and lots of little sensors that have been photolithographically etched. The same technique that's used to make computer chips on the surface. These are each custom built. This is not stamped out of a factory. Nobody needs this in a PC. Nobody needs this in a Mac, sorry Ian. Okay, all right. So these have to be custom built. These have to be custom built. So there are facilities across the United States that are devoted to just building these experiments. Now I don't wanna talk too much about the next experiment, but they use a big tank of liquid xenon. And they make that the target. And again, they try to get light and other things out of it when dark matter collides. You're gonna see a lot. If you go look at dark matter search pages, you're gonna find a lot of pictures of people in bunny suits. All right, bunny suits are clean room suits. You glove up, you're covered up. You put a hair net on. You have to work on a sticky mat before you go into the clean room to take the dust off your shoes. If you get a thumbprint on one of these detectors, the oils in your finger contain so many radioactive contaminants compared to the sensitivity of this instrument that you've just effectively rendered the instrument useless. You will blind it with radioactive potassium decays. You are a huge source of background for dark matter searches. And that's why you glove up and don't touch these things, okay? By the way, this is the xenon here. You see that tank is roughly the size of a person. But the room it's in is huge because you have to shield these experiments from all the ambient radiation that's constantly raining down on them just from stuff we discovered 100 years ago. So uranium, radon, cosmic rays that are raining down on earth, they'll all ruin a dark matter search. Now, to come back to Fatima's question here, how is it that you can make it and know you've made it? Well, ideally what you would do is you would have evidence that you saw something non-luminous, something that doesn't interact like normal matter, and then you would pin down its properties and have other experiments go and look for it. So you need multi-experiment confirmation. Nothing in science can be decided from a single measurement. That measurement could be unreliable or it could have been biased. So you need multiple experiments to all say, oh yeah, okay, we confirm in our own way that there's something there. This is how reliable discoveries get made. So this is a picture of the kinds of images that are taken by my experiment. My experiment is called ATLAS, okay? It is an eight-story tall, 50-yard long, 150-megapixel camera, custom-built. It has to last about 30 to 40 years. There's only one of these in the world. It's the largest multipurpose subatomic particle detector ever built for a collider experiment. And it can take about 40 million pictures per second. It can't keep 40 million pictures per second. That's one of the problems we face. But it can actively try to take them and then make decisions about what to keep and what to throw out, okay? So this is an image of a proton, a single proton-proton collision that is occurring at my experiment, the Large Hadron Collider using the ATLAS camera, the ATLAS experiment, okay? I'll come back to this picture in a moment. Now, believe it or not, you already have some of the guiding principles needed for looking for evidence of a non-luminous, non-interacting, non-electromagnetically interacting form of matter at a particle collider, okay? Here are the driving principles you already have in hand. One, whatever energy goes into the proton-proton collision comes out of the proton-proton collision, conservation of energy. It's a closed and isolated system, okay? Momentum is conserved. Whatever momentum the protons had in the initial state comes out in the final state, regardless of what gets made in the final state. Total momentum n equals total momentum out. And what's really nice about the design of these collider experiments is that the protons all travel on one coordinate axis, essentially along a straight line. And we call that the z-axis by convention in these experiments. So proton goes in negative z, proton goes in positive z, they smash together. There is no momentum in the x or y directions. And because momentum has to be individually conserved in x, y, and z, you know something quite powerful. That there must be a net zero momentum in the plane transverse to the z-axis. There should be no net momentum in x and y. It should be zero in, zero out in the plane transverse to the z-axis. And, otherwise we would have seen it, dark matter should have very small, almost zero interactions with normal matter. In other words, we might make it occasionally through proton-proton collisions, but the chance of making it and then additionally having it actually interact with our camera is zero. Just making it is a rare thing. Getting it to actually hit our detector so that it makes a pixel light up, that's probably not gonna happen. So we don't expect to see dark matter leaving traces of itself directly in our camera even if we make it. So again, how are we gonna know that we've seen something we can't see? Let's take a look at this picture again. Take the principles I just laid out. Total energy has to be conserved, total momentum has to be conserved, and especially total momentum in the plane transverse to the collision has to be conserved. So this is a three-dimensional image. We're seeing all three axes of the collider here. This is the z-axis. That's where all the action happens at the center. And then we've got x and y in planes transverse to that. This is just the x, y plane. So this is just the plane that's perpendicular to z. The beam goes into the page and out of the page in that view. So this is just a small image of this three-dimensional image but projected into two dimensions. What observations do you make based on the principles of conservation of energy and conservation of momentum about this proton-proton collision? Anything? Any ideas? Say that again? Okay, right, so we kinda know how much energy goes in so this stuff here is from our energy-measuring device known as a calorimeter. So these blobs are proportional to the amount of energy deposited in our detector. Yeah, so we could add up those blobs and see if that adds up to what we expect. What else? Yeah, that's good. Energy conservation. Okay, so we used up energy conservation. What else could we do? Well, let me lead you. Let me lead you a little bit. Momentum in the plane transverse to the beams has to be conserved. Does momentum look like it's conserved in this plane or not? Okay, Austin, you're like, no, no, no, no. Am I leading you too much? So what do you think? Why do you think momentum isn't? You shook your head. So why do you think momentum's not conserved in that plane? Okay, yeah, so these things here, these are electrically charged particles. Are they balanced in space? Are there more of them in one direction than another? Yeah, I think there is. Yeah, this is more densely clumped and look, there's a ton of energy up on this side but no commensurate deposit of energy down here. Those are all little deposits. They won't add up to those big towers right there. So there's a big imbalance in this event. And because we know that momentum has to sum to zero in the transverse plane, and in this one, if you add it up, it doesn't, we can infer where the unseen matter is traveling. So Austin, where do you think the unseen matter is going in this picture? So the seen matter seems to be going that way, right? Opposite direction, good. That's how you conserve momentum. If you see a bunch of stuff go this way and you know the sum has to be zero, the rest of it has to go that way. And in fact, there it is. That's what the computer decided was the best trajectory for the unseen matter in this collision. This is a candidate event in what is known as a monoget search. There should be two jets in these events. That's a jet, but there's no jet over here. It's blank in the detector. That suggests something heavy and invisible was recoiling against what we can see. So it's the same way we use gravity to detect unseen things like black holes. If you see a star whipping around in a circle like this, but there's no star in the middle, that's a good evidence for a black hole, something you can't actually see. In fact, that's how the first black hole was detected. Same principle here, but not using gravity using momentum conservation. So this is how you could look for dark matter at a collider experiment, even though you can't see the dark matter directly, you can see everything else that's been produced and infer that something unseen traveled here. Now you can't just do it from one event, you can't just do it from a thousand events. You need a lot of events in order to get these questions answered. And that leads in nicely to the next issue here. And that's the fact that we operate about eight to nine months a year in three-year blocks with a two-year gap in between for upgrades. We're in an operating period right now. I'm one of the people that runs operations for part of the Atlas detector, which is why I'm... Well, they're not done. Oh no, the lecture's not over. No, no, no, no, everyone could put your books down, we're good, right? I have a very tiny middle management role, so let's not get too excited about it. I'm basically middle management. No offense, Atlas, okay. So we have a challenge in our hands, and that is we cannot keep, we can't keep 40 million events per second, 86,400 seconds a day, is that right? Did I get that right, yes? Pi times 10 to the seven seconds roughly a year. We can't do that. There isn't enough disk space on the planet to store all that information. And even once we throw out a bunch of stuff, we still have a ton of data to sift through. This sounds like a big data problem, which is the buzzword that everyone's latched onto. We've had a big data problem since the 1990s. The rest of the world seems to have caught up to that problem now, okay? Now, I'm not gonna actually show this movie. I'm just gonna... That's basically what I told you before about the Atlas experiment, okay? This stuff collides. The Atlas camera takes a picture of it. We ship a ton of data off the Atlas image. People working in the Optoelectronics Lab are working to speed up the rate at which that data can come off of the detector itself starting in the mid-2020s, okay? So we have to start now to make that happen in the future. But one of the ways that we can use this data and mine it to see if we can find evidence of dark matter in our data is using what's called deep learning, okay? So I'll close out this lecture with a brief overview of deep learning and I'll touch on some of the physics of deep learning. So let me begin with some basic definitions because there's a lot of buzzwords out there and people mingle them together and they shouldn't be commingled in the same way. Machine learning, deep learning, neural networks, they don't all mean the same thing. So let me give you some definitions first. Machine learning, that's a buzzword that you hear a lot. Oh, we're using machine learning to do self-driving cars. What does that mean, okay? It's a generic term. Basically, this is a very specific field of computer science. So it's actually a field of computer science. It's not just, you know, a bunch of stuff. And it specifically employs statistical techniques, quite advanced ones, to give computer systems the ability to improve over time their ability to execute a task or set of tasks, okay? So for instance, what may be a task is we wanna separate promising dark matter containing proton-proton collisions from junk. The stuff that we knew about 50 years ago that we don't care about anymore, but it's trying to fake dark matter in our experiment just randomly, okay? Can we train a machine to do that? That's a good question. We've been trying to do that and have been successful at that in many ways for decades now as a community. Artificial neural nets, all right? So this is another neural networks or artificial neural networks, another buzzword. This is a subclass of machine learning. So machine learning incorporates support vector machines, boosted decision trees, lots and lots of things. Neural networks are one way to machine learn, essentially. They're mathematical or computational algorithms that mimic only the most basic functionality of the wetware that you and I all have in our heads, whereas you'll see cats have in their heads, okay? In fact, I think it's funny that the revolution in self-driving cars is driven by the information that it's driven by. You'll see in a moment, okay? But basically the idea is you have a mechanism here that can pass information through, make a decision, and then based on the accuracy of the decision, learn from its mistakes. That's essentially what a neural net does. You want it in A on exam three, but you got a C. So the lesson is, what do I have to do better to get closer to my target goal? Welcome to the world of neural nets. You're a neural net, okay? Now what is deep learning? Now deep learning is a subclass of neural networks where the density of information that can be stored in these neural networks is insanely high. 20 years ago, we simply didn't have the computational power to do really powerful neural networks. I played with toy neural networks as a graduate student. I even developed some neat tech for particle physics using neural networks in the late 90s and early 2000s. But it really wasn't until the revolution in gaming systems and graphical processing units, GPUs, that we had the horsepower necessary to do what is known as deep learning or deep neural nets where the density of information stored in the network is insanely high and computationally expensive, although that's gotten really easy with graphical processing units. In deep learning, algorithms are really learning to represent the data in a mathematical way. They're not just trying to accomplish tasks. They're trying to understand what does this data mean? What are the representations of data, high level functions that tell me what the data is really doing, how this variable relates to that variable and when one predicts another and when it doesn't? That's what these deep neural networks are really doing and they're very effective at it and nobody really understands why. And I'll come back to that. And then there's artificial intelligence and in the context of computer science, this is the development of systems that learn about their own environment and they take actions to maximize the possibility of achieving goals. Again, think of a self-driving car. I want to get from home to work and I don't want to die. The self-driving car is designed to try to do that as safely and legally as possible, okay? But as I've chatted with a few of you, the problems of self-driving cars are not the driving part anymore. They're the ethical and moral driving decisions that cars' neural nets are going to have to take. Do I swerve and hit those school kids in the crossing, where the crossing guard is in the crosswalk, there we go. Or do I swerve the other way and save the kids and kill the passengers? These are the decisions the self-driving cars are gonna have to make at some point and nobody wants to program those decisions and because nobody wants to get sued, all right? So deep artificial neural networks are at the heart of most AI, that's the buzzword, AI applications today and I'm gonna focus briefly on using these to improve searches for dark matter at the Large Hadron Collider. Okay, so where does this stuff come from? You're gonna love this. So much of what we know about the operations of these deep, natural, biological neural networks comes from the experiments of a 20-year-ish, 25-year collaboration between David Hubel and Torsten Wiesel. So the famous Hubel and Wiesel experiments that rolls off the tongue. They got the Nobel Prize in the 1980s for their work in physiology or medicine. This is remarkable work. Some of you are gonna cringe at this. I'm a cat lover, so I'm gonna cringe a little bit at this too. But nonetheless, when you understand where self-driving cars come from, you're gonna laugh, all right? Here's where self-driving cars come from. They were trying to understand how the visual cortex, the system of the brain responsible for processing light information into decision-making worked and their model was a cat and by model I mean they used a cat, okay? They anesthetized the cat and they stuck a microelectrode into individual neural cells in the visual cortex and they measured what the cat's brain did when presented with certain visual stimuli. So let me show you a movie, just 30 seconds of what this looks like. So they're just taking a light bar and they're passing it in front of the cat's eye. So they go this way, nothing. That way, maybe a little activity in the brain. Clicking is the electrical signal. That's the electrical signal from the cells in the visual cortex, just a little clump of simple cells in the visual cortex. Less activity, almost no activity. When it goes horizontal, there's almost no activity, but when it goes diagonal, lots of activity. What they learned is that the brain of the cat is essentially arranged as a collection of simple cells that get a little bit of information about the visual stimuli. Hooked into a bunch of complex cells that combine that information. So there's a clump of complex cells that take in information about the orientation of the light and they get excited. They fire off electrical signals when the light is diagonal at 45 degrees to the right, but not when it's to the left, not when it's horizontal, not when it's vertical. But there's another clump of cells that gets excited when the horizontal lines are shown, the vertical lines are shown. And then together the cat can figure out that's a corner of a table. It's a horizontal line meeting a vertical line. This is essentially how your visual cortex processes information. I know that that's a table because it's a combination of horizontal and diagonal lines and curved surfaces, and I have little clumps of complex cells that are designed to see horizontal lines and of different contrast and color. Careful experiments, albeit unpleasant for the cat, I have no doubt, revealed how the brain's visual cortex system is wired up. This inspired the development of the mathematics of neural networks and eventually the computation of neural networks, and this is the origin story of self-driving cars, the cat's visual cortex. That's it, okay? So, yeah, and soon cats will be driving cars, it'll be horrible, right? The end of the world is nigh at that point, so. Okay, so here's a cat, that's my cat in fact, that's one of my cats, okay? Yeah, all right? Yes, all right, so you can, so you look at that, right? You look at that and you know right away, that's a cat, even though it's quite pixelated, right? It's a grainy image, I actually took the photo of a cat and I made it grainy on purpose. I took information out of the picture, and yet, your brain is still capable of looking at that and going, that's a cat. Because the pixels together, all those little minimum units of color and intensity, they all together form in your brain the trigger of cat, okay? So, most of the time when you do image searches or word translations on the internet now, that's not a for loop. Oh, the person wants cat images, so I will go pixel by pixel and I will see if this is a cat image, that's not how it works. Artificial intelligence, deep neural nets are used to do image recognition on the internet. If you say, oh, I like that picture, I want pictures like that picture, or oh, I like this painter's paintings, give me other painter's paintings like this. Deep neural nets are making those decisions now for you, okay? They're very good at it, in fact in many cases they're better than people. So, there are many basic mathematical ideas behind neural networks. There are input variables. Every pixel in this image has intensity, color, and location. And all of those things together carry information about the cat in total. No one pixel tells you there's a cat, but all together, their orientation and space, their brightness, their color, that tells you that they're a cat. So, we need to have inputs. How can we make an algorithm learn that that collection of dots with those brightnesses and colors is a cat? Well, for that we need functions. So, we need to take the inputs, and we need to process them through functions. And in neural nets, the functions are highly nonlinear. A little bit of stimulus won't give a proportional response from the function. More stimulus doesn't double the response. You can put in more and more and more. And finally, there's a threshold in the function where, boom, the stimulus happens and out goes a number from the function. Nonlinear function response is a key to neural network functioning. And not just that, but weighting those functions. So, the weights, how much you weight one neuron's output is really crucial to all of this. You have to update learning. It's not enough to put a bunch of inputs in and get a bunch of numbers out. At the end, you're gonna get a score. One, cat-like, zero, not cat-like. All right, well, that is a very cat-like picture. In fact, I know that's a cat. I made the picture, right? If I train a neural net and say, tell me if that's a cat. And it gives me a number like 0.1, not really a cat. I go, no, wrong. I know that's a cat picture. Do better, okay? So I wanna get an A in this class, but I gotta see, well, bad. All right, if you want an A, you need to get closer to an A, all right? Okay, so it's the same process. Now you need to update your learning. So it's not enough to be like, the neural net gets a 0.1, okay? The neuron gets a 0.1, that's not a cat, bad, jab, neural net, try again. Next time, no, no, no, no. You take that information and you update the neural net so it does better next time. What you do is you minimize the derivative of some output measure of quality with respect to those weights on those functions. You need derivatives to train a neural net because you have to minimize the derivative across the entire neural net. That's fun. And then you need trading data. I just talked about supervised learning. I know that's a cat, what do you think it is? Not a cat, wrong. That's supervised learning, that's what we're doing, okay? All right, I'm doing supervised learning with most of you at this point, all right? So supervised learning, you know the truth. You know that you test the neural net to see what it gets. If it's way off the mark, you update its learning and you tell it to try again. And you have a big training set, you do many epochs over the training set and it gets better and better and better. Algorithm, modern algorithms these days can do image recognition at better than like 99.9% accuracy. It's ridiculous, okay? It's better than humans. So this is what a neural net looks like. You have input variables, they go into functions, those black boxes are nonlinear functions. The output of the functions are then wired into other functions that can take those inputs and combine them and then they spit out outputs which are wired into other functions. That's why it's called the network. The layer of nodes at the beginning is connected to the next layer, is connected to the next layer, is connected to the next layer and these layers don't have to be just single functions. They can be whole n dimensional spaces of functions. That's what's deep about deep learning. And again, we couldn't handle that computationally until GPUs came on the market, okay? So I would encourage you if you wanna play with neural nets and see how to train them, you can go to the TensorFlow playground that Google provides and you can go ahead and you can, it's playground.tensorflow.org I think. Go there right now and play with the neural net. You can get some training data. You can say, look, I wanna separate the blue from the orange and you can build a network that does that better and better and better by adding more neurons, more layers, et cetera. Changing the way it learns, okay? Changing the nonlinear function present in each of those black boxes. The really popular one now is called a relu. That's really popular right now. Nobody's really completely sure why it works. And so let me come to my last point here, okay? You can play around with the neural net and in fact this is what people do. People are playing around with neural nets all the time. But if you ask the question, I have a problem. What's the optimal neural net for my problem? There is no theory of machine learning that can answer that question. It is unsatisfying. What's the optimal neural net that solves your problem? I don't know. Go to TensorFlow and build one and see if you can make one that works really well for your problem. Play around. That's fun, but also gets really tedious because then you have the right programs that automate the playing around because you don't wanna do that all the time manually. You want a computer to play around with the neural nets and find you the optimal one. If we only had a theory of learning, then maybe, maybe, if I knew the problem, I could apply the theory of machine learning and get the right solution to it. We don't have that in hand, but I'll say that there's a lot of momentum in trying to solve that problem and that momentum is coming from several directions. It's coming from statistical scientists, data scientists and mathematical physicists because all of them have aspects of the tools that are likely needed to build the theory of learning. You need statistics to figure out what's gonna happen with this data. You need information theory to take the information present in that data and figure out the optimal way to arrange it or organize it or represent it. You need thermodynamics, ironically, the study of heat energy, which is also the study of the organization of material systems. Highly organized systems, poorly organized systems, they have different properties. Ice is more highly organized than water. When you go from ice to water, you're changing phase. Something profound is happening to the material. You're going from a highly organized state to a very disorganized state, a liquid. What's the science of that? Thermodynamics describes that. Information theory tells you about the risks of compression but also the ability to tease a signal out of a dense field of noise. In fact, information theory was born from simple questions like, if I have a lot of noise and a little signal, how can I pull that signal out of the noise? And Claude Shannon is one of the most famous people in the history of this field. He's the one that started this field, okay? So information theory is born from a single paper he wrote back in the 60s, I think it was. Something 50s or 60s, 40s, 50s, 60s, 40s was the 40s because it was around the time of radio and radar. And there was this big question about how you tease signals out of noise and radio, okay? So there's a lot of renewed interest now across the world in applying these ideas, thermodynamics, statistical science, information theory to try to come up with a better understanding of why neural nets work as well as they do and how to build a better neural net, how to build an optimal neural net from a pure theory of learning. So here's one example of what some people are trying to do for this. So this is Naftali Tishby's work. I met him at a deep learning particle physics conference last summer. Fascinating stuff. I got interested in the thermodynamics of neural nets back in graduate school. Now I wasn't gonna go and do the work. I was just like, oh, that sounds interesting. I mean, I had kind of a pop interest in the ideas. But people like Tishby were in the 80s were writing down statistical and information theories, entropy, order theories of learning and neural nets and systems that now are having renewed interest in them because they may be the basis for actually understanding why these things work as well as they do. And one of the things that's interesting is that Tishby and his students and postdocs, his colleagues have studied the learning process in a neural net. How much information does a layer have about the inputs? How much information does a layer have about the outputs? And so what we're seeing here is the learning process happening represented in information theory. So at the beginning, some layers have almost no information about the input data and they have almost no information about the labeling of the data. What's the truth about the data? What's really in it? And then as they learn, they gather more information about the input data. They gather more information about the output label. What's this data really contain? And then what's really cool about this? They go through a phase transition. So you're packing in information, then you're deep, now you're getting rid of it. You're shedding information. So this is like going from solid to liquid here. And in fact, the mathematics of all this works extremely well for understanding what's going on in here. Now, there's nothing definitive here and you can check out the article here in reference five from Quantum Magazine about his work, because there's been a renewed interest in this. But it's pretty cool stuff. And it ties physics ideas to statistical ideas, information theory, deep learning and data science all in one place. And I think that's just really neat. The hard problems are usually solved at the interfaces of disciplines. But you need strong disciplines to make that work. So to hunt for dark matter, we're trying to bring to bear more deep learning, more artificial neural nets on pictures like this and thousands of others like it that may or may not contain dark matter. The question really is, can we use deep neural nets to really high advantage? Can we make discoveries with these things? And can we rely on what those neural nets tell us? That's a really tough question. Now, many physicists have been studying this. I'll highlight Michaela Paganini's work because she's currently a PhD student on the Atlas experiment at Yale University. But she's been snatched up by Facebook's AI research department. So, yeah, last for the field, congratulations Facebook. Or I don't know, maybe sorry, Michaela. I'm not sure which at this point. But Facebook has a lot of artificial intelligence research going on as you're all aware. And so she's soon to be a postdoc there with their group, right? So you can get a physics PhD, but you don't have to do physics. That's the message I want you to take away from this. So let me make some final comments and then I'm going to show you something at the end here. All right, so dark matter. A convergence of many lines of evidence suggests that there's some kind of unseen non-luminous form of matter. It could be in this room right now. We just haven't figured out how to detect it, assuming it's even there at all. Dozens of physics experiments are racing to figure this out. And if dark matter really readily interacted with normal atomic matter, we should have seen it. So this is a tough problem. In fact, this is one of the hardest problems that any scientific endeavor is facing right now is how do you detect something that, for all we know right now, can't be detected other than gravity? That's a tough problem. And it makes up about 85% of the mass of the universe. So it's important. It shaped the cosmos from its beginnings. We don't know what it is. This is all new for us. Many experiments are taking increasingly dense data sets and deep learning might provide a path forward to understanding what's going on there. And I would point out that deep learning as a subset of machine learning is really constantly being explored to try to improve things, but we don't have a theory of deep learning that tells us the best way to learn and solve a problem. So if you're interested, this is my shameless plug. If you're interested in anything you've heard about this semester, I have some awesome co-authors I wrote a book with. Go buy it, all right? I hope you've enjoyed this semester as much as I have. Teaching is really hard when you have to teach physics over and over again. Now this is my first time teaching this class and I'll teach it a bunch more times, but I really enjoyed working with all of you and I hope you've enjoyed being in this class. Thank you very much for a wonderful semester. I hope you've enjoyed it as much as I have.