with questions as I lecture. If there's anything that doesn't make sense, just go ahead and ask. It's quite possible if it doesn't make sense, it's because of jet lag. So ask me, and I'll try to explain it better. So I'm going to give four lectures in a series. And I decided to do something a little bit unconventional. So instead of giving all four lectures on the details of inflation and how to calculate quantum perturbations and so forth, I'm going to condense that material down into the first two. And then in the last two lectures, I'm going to tell you what are some of the problems with inflation, what are some of the controversial aspects of it, and how does it fit into the bigger picture of theoretical physics, string theory, cosmology, and so forth. So if you want, the first two lectures will be about how to do research on inflation. The last two lectures will be about what to do research on. What are the interesting questions? So a little bit more precisely, in lecture one, I'll review cosmology. And I'll describe the problems which led Alan Guth and others to propose inflation in the first place. So that will be today and possibly later today, depending on, well, this would be the first lecture of the lecture now. And this lecture will possibly be later today, depending on Vitor's success in arriving. So in the second lecture, I'll describe how fluctuations emerge during inflation and eventually lead to structure. So when people say structure and cosmology, we mean galaxies, stars, galaxies, clusters of galaxies, the interesting stuff. And then in lecture three, which will be on Friday, I think three and four will both be on Friday, if I'm not wrong. So in lecture three, I'll talk about some controversies and challenges for inflation. And in lecture four, about the big picture, which for me means the strength theory, the landscape, and how inflation fits into that. Any questions so far? So let me ask you this. How many of you have followed a course in general relativity? And how many of you have not? Well, I won't assume much knowledge of that, but I will use a little. All right, so let's start off with a definition of what is cosmology. So cosmology, it's the study of the universe on the largest scales in space and in time. So this means what was the origin of the universe? What's the fate of the universe? And what's its large-scale structure? And if we want to understand the answers to these questions, what was the origin and fate of the universe? What's its large-scale structure? Inflation affects all of these very strongly. So it plays a key role in determining the answers to all of these questions. Now, we believe that the universe on these large scales is described by general relativity, hence my question. So in general relativity, as almost all of you know, one tries to solve Einstein's equations, which take this form. Now, throughout these lectures, I'm going to use units where h bar is equal to c is equal to 1. So if you want to restore the units, you just need to analyze the dimensions of the quantities you're looking at and multiply by the right number of powers of h bar and c to get the dimensions right. And there's always a unique way to do that. So you don't lose anything except when you save some chalk in doing this. And g here is Newton's constant. It sets the strength of gravity. If g equals 0, there's no gravity. T mu nu is the stress energy tensor. And g mu nu is the Einstein tensor, which can be written like this. So r mu nu is the Ricci curvature. And it's a function of g and its derivatives. r is the Ricci scalar, the trace of r, where trace means you can track the indices with g mu nu and then sum. And again, throughout these lectures, I'll use the standard Einstein summation convention. So if there's an index repeated, this is supposed to say mu nu. Let me write it a little bit better. If you see a repeated index, then it's summed over. And I won't write the sum. And g itself is a function of the coordinates x mu. Now, so g mu nu is the metric on some manifold. And I'll only be interested in four dimensional space time in these lectures. So g mu nu is a metric on some four dimensional manifold m. And because we're talking about cosmology, so we need to include both time and space. And so g has signature 1 comma 3. OK, so this means one direction, and that'll be time, has signature plus. And three directions, which will be space, have signature minus. This is a convention. You could choose it to be 3 comma 1 instead. And it makes no difference, except for some minus signs and various equations. But this way, if you want. Distances in time are real, and distances in space are imaginary. Anyway, that's the convention. And so this is described as, people say it's a Lorentzian signature, because it's the same signature as Lorentzian spacetime and Kasky spacetime. And it's pseudo-Riemannian is the term that mathematicians use. A Riemannian manifold would have 0 comma 4 or 4 comma 0. Anyway, so it's a spacetime. And more importantly, we have to be able to write it as a line times some three dimensional Riemannian manifold. OK, so this is time, and this is space. If we can't do that, it's not a cosmology. That's my definition of cosmology. So this M3 is some Riemannian 3 manifold. So it's Euclidean signature. And it has some fixed topology, which cannot change. It's slightly bigger. OK, all right, I'll write it larger. There's a theorem. This is a theorem in classical general relativity. So it's probably not true in quantum version. But in classical general relativity, there's a theorem it's due to Gerrach in the 70s. It's called the splitting theorem, which says that, first of all, whenever you have a Cauchy problem, so whenever you have a well-defined initial value surface that you can evolve forward and backward in time, the spacetime must split like this. And secondly, the topology of this spatial part can never change. It's basically because you can take the data on some initial time slice, and then you can evolve it forward. If the topology changed, there would be some kind of singularity. It would be impossible to evolve forward or back. So the proof is really that simple, just that you can apply a time evolution operator and evolve back to that initial surface. And that doesn't change the topology. So that's a good question. So there's a famous class of examples, which are what you learn first when you study this topic, which are the so-called Friedman, Robertson, Walker, or sometimes Lumetra gets added, cosmologies. And these are cosmologies where one makes a very special and restrictive assumption that, let's just say, space has two properties. It's homogeneous and it's isotropic. So the motivation for making these assumptions is that they are nearly true in our universe at the largest scales we can observe. And I'll come back to that quite a bit later. So when we look on the largest scales we can see today, we see a universe which is nearly homogeneous and isotropic. What's the meaning of these terms? Homogeneous means the universe is the same at every point. And isotropic means it's the same in all directions. It's spherically symmetric. At first sight, you might think these are redundant with each other, but they're not. For instance, imagine you had a universe which is full of an electric field that's always pointing in some particular direction and has constant amplitude. So that would be homogeneous. At every point, it's the same, but not isotropic, because this electric field chooses a direction. Conversely, you could have a universe which is spherically symmetric around some point, like where we are. But where the density or some other quantity varies with radius, that would be isotropic, at least at that point, but it would not be homogeneous. So these are two distinct features. In fact, it's rather difficult to test this one because after all, we're sitting at one point and we don't really have access to a full volume. We have access to our sky, which is telling us more about isotropy than it is about homogeneity. However, it would be rather unreasonable to believe that the universe is spherically symmetric and centered on us. And so the fact that it looks isotropic from our vantage point is a pretty good reason to believe that it's also homogeneous. And in fact, there are some tests of homogeneity that go beyond isotropy. Which, if we have time, we can discuss. That the curvature can change? Yes. That's right. Yeah, good. Yeah, so fixing the topology of a three-manifold, it has a pretty weak effect on the curvature. So for example, if M3 is a sphere, a three-dimensional sphere, then for any function on a sphere, there exists a metric for which that's the curvature. So absolutely anything can be the curvature of a metric on S3. It can be positive everywhere. It can be negative everywhere. It can be positive someplace is negative. So the topology doesn't have a very strong effect on the curvature. But it does have some effects. I'll actually come back to this in one of the last lectures. But that's right. So fixing the topology certainly doesn't fix the metric. It also doesn't fix the Ricci scalar or the Ricci tensor. But it does have some implications. And one of those implications is that there are actually only four possibilities for which it's possible for space to be homogeneous and isotropic. People often say there are three, because they forget one. There are four. So if we want to make this assumption, M3 should be an element of the set S, where S is four manifolds. So there's S3, the three sphere. Where should I put the three? I'll put it here. There's a manifold, which is the one people forget. S3 mod Z2, there's R3, and there's H3. So what are these? S3 is a hypersphere. It's a three-dimensional analog of a sphere. So it has finite volume. And if you move in any direction, you'll come back to where you started after a while. It has no non-contractable, sorry, all loops are contractable on S3, just like they are on S2. S3 mod Z2, this is also known as RP3. It looks just like S3 locally. It's also compact, finite volume. But it has some non-contractable loops in it. And you can think of this as S3, where you identify antipodal points. So if you go halfway around the world, you're back to where you started, instead of having to go the whole way around. R3, that's just Euclidean three-dimensional space. The usual standard, flat, three-dimensional space that you're used to. And H3 is hyperbolic space. So this one, of course, has infinite volume. So does this one. Hyperbolic space is a space in which areas and volumes grow the same way, at least for spheres that are larger than a certain size. If you're familiar with the Poincare disk or the Lobachevsky plane, or I think it has another name, those are two-dimensional hyperbolic spaces. This is three-dimensional hyperbolic space. Anyway, these are the four topologies that M3 could have if it's going to be homogeneous and isotropic.  For instance, you could take R3 and make it into a torus by just identifying some directions. So you could have a three-dimensional torus, T3. But this can never be isotropic. And to convince yourself of that, imagine a two-dimensional torus. So you can draw a two-dimensional torus by taking a plane and then identifying this line with this line and this line with this line. So the identification is straight across. So these two points are the same. These two points are the same. And also these two points are the same. And these two are the same.    And when your bullets exit here, they reappear here. They exit there. They reappear there. So they wrap around. That's a game played on the surface of a torus. OK, that's a torus. And if you stare at this picture, you can see that it's not isotropic. Because if I start from here and I shoot a bullet in that direction, it comes back and hits me after however long it takes to travel that distance. And that might be the same as this direction if it's a square torus. But if I shoot it along a diagonal, it may or may not hit me. But if it does, it'll take longer. Or it may not hit me at all. It may miss me. So different directions are not equivalent. And it's impossible to put a metric on the space that fixes that. It's just intrinsically not isotropic. So that's why there are only these four possibilities. And again, everybody tends to forget RP3 and say there are just these three. This is referred to as a closed universe, open, flat. Good. Now, it's important to say, and this was what the question was asking, that even if the universe has one of these topologies, it does not mean that it's homogeneous and isotropic. So the implication goes the other way. If it's going to be homogeneous and isotropic, it has to be a member of the set. But being a member of the set does not guarantee that it's homogeneous and isotropic. Because you can always put some matter in. Let's say you have your spherical universe. You can always have matter be concentrated in one place more than it is in another. And if you do that, the metric will respond because of Einstein's equations. And so the metric itself will not be homogeneous. There will be more matter in one place than another. OK. And another thing to say is that if the topology is not one of these, you can still be very close to homogeneous and isotropic. Because you can just make the universe very, very, very large so that, for instance, you'll never see this wrapping around phenomenon because it'll take too long. And in that case, you won't be able to distinguish this torus from just flat space. So it's not really motivated observationally to assume that the topology is one of these. Because you can always assume the universe is big enough that you won't notice the anisotropy induced by this other topology. Anyway, so that's FRW cosmology. And in fact, what does inflation do? So I'm going to come back to this in just a few minutes. But what inflation does is it blows the universe up and makes it really large, so large that all these effects of the topology can easily be far beyond our horizon and not observable. So inflation is a way of being sure that you don't care about the topology. Once it happens, if it lasts long enough, at least, it makes the universe so large that you'll never be able to measure the topology. And it simply won't matter what it is. Everything will look flat. But for now, let's assume the topology is one of these. So the universe is homogeneous and isotropic. And let's write the metric that goes along with that. OK, so three possible spatial metrics here, all of which are homogeneous and isotropic. One of them corresponds to the closed cases, one to flat and one to open. So k is an integer that's plus 1, minus 1, or 0. And d omega 2 squared, that's the metric on a two-sphere. So it takes this form. It's the standard round metric on a two-sphere. Now, to see that this metric actually describes what I said it did, let's take the case k equals plus 1. Then if I define a new coordinate psi as the inverse sine of r, then you can see this is going to become sine squared. And this simply becomes deep psi squared. So we just get this metric. And that is the metric on a three-sphere. Sorry, ask it again. Is it a square, did you say? Yeah, it's a square. D-sigma, the three? This one. Sorry, sorry, that's a square. Sorry, yes. Thank you. And this is also. OK, yeah. So this is the metric on a three-sphere. It looks just like the metric on a two-sphere, except while this d phi squared is replaced by d omega 2 squared. And notice that the range of r is from 0, the range of psi rather is from 0 to pi. Now, if k is equal to minus 1, then we can define sinh of psi equal to r. And this becomes a plus. And the metric becomes hyperbolic sine. So now you can see this fact that I mentioned that areas and volumes grow the same at large psi, psi bigger than about 1. Maybe you can see. So this grows exponentially with psi for large psi. So the size of the two spheres here grows very rapidly as psi increases. So that's hyperbolic space. And of course, for k equals 0, we don't have to do anything. This is just flat space. All right, so those are the three spatial topologies for homogeneous and isotropic cosmology. Now, I should have said this metric is a three-sphere with radius 1. Can people see the bottom of the board? Can anyone not see the bottom? So this is a three-sphere with radius 1. So when we multiply it by a, let's say with k equals plus 1, this is a three-sphere with radius a, a of t. You just make it bigger by a factor of a. It's a not a squared because this is ds squared. It's a distance squared. Now, that means that we can think of this metric as describing a space, which in that case is a three-sphere, which expands as time passes. So it's an expanding universe. Well, I shouldn't say it necessarily expands. It's size changes. We'll see in a moment that, well, typically it expands. And that in fact, it will be almost impossible to have a of t constant. But in any case, it's size changes with time. Let's just put it like that. Now, you might wonder if k is equal to 0, you already have an infinite volume flat space. What does it mean for that to expand? It's a question we're thinking about. It might become a little more clear in a few minutes. It does mean something. But in a way, it's convenient to think about this closed compact universe. It's a little bit easier to picture. And you can always make it so large that you can't distinguish it from flat space. So that's, I think, if you find that confusing, you can always imagine that the universe is closed. And so it's really a finite volume thing that's growing with time. So now if I take this metric, and by the way, you should convince yourself that this metric suffices to describe a cosmology where the space is homogenous and isotropic. It's not very difficult. If you take this metric and you plug it back into Einstein's equations, which are way over there, the result is pretty simple. It has to be because there's only one function in the metric. There's only this a of t. And what you find are two equations, one that depends on the first derivative of a. And another one, which depends on the second derivative of a. So t. OK, so t mu nu is a diagonal matrix. It has to be diagonal because any off diagonal component would indicate some kind of anisotropy. If these components here were non-zero, so maybe I should remind you that the 0,0 component of t is the energy density. The space-based components are pressures. These components here, along the top row, t is a symmetric matrix, so it's the same down here. These represent flows of energy. If you have a flow of energy, the universe is not isotropic because the flow is pointing in a particular direction. If you want, this is like a spatial vector. And you can't have any spatial vector non-zero if the universe is isotropic. Similarly, these represent anisotropies as well. And the diagonal elements have to be equal because otherwise there would be some, again, anisotropic component, something that selects out the different directions. So the spatial part of t has to be proportional to the identity matrix. That's the only rotationally invariant three tensor. OK, so t mu nu must take this form. And so we just have a row and a p. And this is how they appear in these equations. Dot means derivative with respect to time. And what else? This is the 0, 0 component of Einstein's equations. And this comes from the space-based component. Remember, there's many of Einstein's equations because there's a mu nu index here. But in this case, they reduce to just these two. Now, with some algebra, we can combine these two equations and write the following, that rho dot is minus 3h rho plus p. And that equation follows directly from the definition of rho and p, and then conservation of energy. It actually just says, well, it says that p is minus dE by dV. So dE is minus p dV. That means dE by dT is minus p dV by dT. And E is rho times a cubed, or at least it's proportional to that. So take our spherical universe. The volume is proportional to a cubed multiplied by rho. And that's the energy. So that's E. V is proportional to a cubed with the same proportionality factor. And now, if you just plug this in, you'll get this equation here. So the two Einstein's equations together enforce conservation of energy and momentum. Another thing to notice is this h, a dot over a. Note that it has units of 1 over time, which is 1 over distance since we said c equal to 1. OK, good. Now, what do these equations tell us? Well, among other things, they tell us that it's very hard for the universe to be static. If you want a dot equal to 0, you need h to be 0. So this has to vanish. And so that's a very particular condition on rho. And then if you want it to remain static, you need a double dot equal to 0. So you need rho plus 3p to vanish. So you can arrange this to happen. Rho generally is positive. So we need k to be plus 1 in order to satisfy that. But then we also need p less than 0, which is strange. You can do this if, for instance, the universe is closed and rho consists of two components, ordinary matter and something called dark energy, which has the property, or let's say vacuum energy, which has the property that p, p vacuum, is minus rho. So if I choose rho vacuum to be positive, p is negative. And then it's possible to make this happen. So there does exist a static solution to these equations. But it's extremely unstable. If I add just a little bit of rho, then this a dot will become positive and the universe will start to expand. If I decrease rho by just a little bit, a dot will be negative and it'll start to collapse. And that's only in the homogeneous case. So the homogeneous case is akin to this. It's like balancing a ball on the very top of an upside down parabola. Just the slightest perturbation will make it fall. If you allow inhomogeneities, it's even more unstable because inhomogeneities tend to grow and invalidate this whole analysis. So it's pretty much impossible to have a static solution to these equations. Cosmology must be time dependent. By the way, you all know the famous story that Einstein invented the cosmological constant so that he could find a static solution because he needed something like this to find it. He didn't notice that it was unstable. OK. Good. Now another thing to say about this. Ordinary matter and radiation have rho and p positive, or at least non-negative. So this means if that's the only thing in the universe that a double dot is less than 0. So if you have a universe that's expanding a dot greater than 0, its expansion will be slowing down. And this is completely what you would expect. Gravity is an attractive force. You have a bunch of stuff in the universe which is flying apart. That's what it means for the universe to be expanding. That stuff is attracting itself. And so its expansion is slowing down. Just like if you throw a rock in the air, its velocity, well, its speed decreases because it's attracted back towards the ground. So a double dot is negative. And what this implies is that the universe has a finite age, which was a shocking realization back in the day. So if we have a dot positive, so here's, I'm plotting a versus t, a dot is positive, and a double dot is negative. It's curving down. That's what it would be if a double dot were 0. So it hits this axis at some finite time, which we can call t equals 0. And at that moment, a is 0. The universe has 0 volume. That's a singularity because if we were to compute the curvatures, we would find that they depend on time. And they depend on inverse powers of a. So they blow up when a goes to 0. When a curvature blows up in general relativity, you can no longer trust Einstein's equations. So you expect that Einstein's equations will be modified by something. So we don't really believe that we can trust this analysis all the way down to t equals 0 at this singularity. But if we do trust it, well, it tells us that there's this point where the volume vanishes. OK, and this is, of course, called the Big Bang. That term was coined by Fred Hoyle, who was an eminent cosmologist. He made major contributions, very important contributions. But he hated this whole idea of an expanding universe. He fervently believed that the universe should be static. And he believed that to the point that he went on a kind of publicity tour where he would give public lectures ridiculing the idea that the universe could be expanding. And he made up this term just to make fun of this idea. He was more and more sort of ostracized by his contemporary physicists. But he became quite famous. He wrote books. So if you see people going around ridiculing ideas in modern cosmology, eminent cosmologists doing that, you might remember this story. It's an interesting cautionary tale. Anyway. OK, so that's the Big Bang. So now, to help us solve these equations, let's take this continuity equation that's written over there. And let me make an assumption that the equation of state p over rho is constant in time. If I make this assumption, then I can rewrite this equation like this just by dividing by rho. This is delog rho by dt, delog a by dt. So I can immediately integrate this and get that rho is some constant times a to the power minus 3 1 plus w. So now let me do some cases. w equals 0. So this means p equals 0. And this is usually called dust or pressureless dust.  They don't exert any pressure on the walls of the container because they're not moving. So with this value of w, we find that rho scales as a to the minus 3. w equals 1 3rd gives us rho scales as a to the minus 4. That's the equation of state of a gas of photons, of radiation. So this you can understand, this a to the minus 3. It's very simple. You have some number of massive particles. And a cubed is the volume. So if the number is conserved, then rho will decrease like 1 over volume. Rho is n over v, where particles divided by volume. Similarly, this a to the minus 4 you can understand because if you think of a gas of photons, the number is conserved as the space expands. So the number density goes like 1 over a cubed. But each photon red shifts as the space stretches. So the wavelength of each photon increases like a. And that means its energy goes down like 1 over a. So each particle loses energy as the space expands. So there's an extra factor of a. And finally, if we choose w equals minus 1, so this is p equals minus rho, then we get rho is proportional to a to the 0. It's constant. So w equals minus 1 is what's called vacuum energy because it's an energy density associated to each cubic centimeter of vacuum. It doesn't change as a expands. So the total energy is increasing if rho is positive as the universe grows because its volume is growing. The energy density is remaining constant. So that's a very weird form of energy. Good. What about h? Oh, yeah. Yeah, w bigger than 1 is perhaps possible, but it's pretty weird. So let's see. If we plug it in here, it just means it doesn't look odd here if we just tell you that a red shifts very, very rapidly. But it's a very stiff equation of state. There's sort of more pressure than energy when you include the C's. So there's no ordinary form of stuff that has that equation of state. But whether it's really inconsistent, it's not entirely clear, I would say. The speed of sound is often related to w. So naively, at least, w bigger than 1 would give you a speed of sound that's greater than 1. And that means faster than light, hm? Is that perfect? Yeah, exactly. So it depends. It's really dp by d rho that matters. That's right. So if it's a perfect fluid, it would have speed of sound that's greater than 1, and that's certainly problematic. But there might be some other stuff that has speed of sound less than or equal to 1 and still effectively has p greater than rho. OK. Now, in our real universe, we don't have just one type of stuff. We have matter, which is non-relativistic and effectively pressureless. We have radiation. And it seems we have vacuum energy. So the actual universe contains all these components, which means, oh, I should do one other thing. Sorry. I should solve for a as a function of time before I say that. So we have that h squared. Let's take a to be t to the d. So then h, which is a dot of r, is d over t. So h squared. And now, if I plug in these scalings for rho, I have some constant a to the minus 3 1 plus w. And so if I invert this and solve for a, I find that a is proportional to t to the 2 over 3 1 plus w. So in the case w equals 0, we have a is proportional to t to the t thirds. Here, we have a is proportional to t to the 1 half. And here, it looks like we have t to the infinity. Well, actually, what we get is e to the t times some constant h. t to the infinity is sort of like an exponential, just like t to the 0 is like a log. OK, so those are the scalings. That's how the universe grows, if it's filled with a fluid or filled with a substance that has these different values of w. Notice that for both matter and radiation, it's t to a power less than 1. That means a double dot is negative. So the universe is expanding but slowing down. But for vacuum energy, it's e to the th a double dot is positive h squared. And so the universe is accelerating. It's expanding more and more rapidly. Yeah, yeah, I forgot to say. Yeah, so everything I've written on the board is valid. Well, everything I've written on the board is valid with k equals 0. Some things are valid also with k not equal to 0, but yeah. Here, I've ignored the k over a squared term, just for simplicity. We know in the universe we live in that this k over a squared term is much smaller than the row term, at least today. And it was therefore much smaller, and I'll come back to this in a moment, going all the way back into the past, except possibly in the very early universe. So it's pretty good approximation to ignore it in our universe. And I'll do that in some things I'm saying just for simplicity. Anyway, so our universe contains a bunch of things, not just one type of stuff. And so the actual dependence of A on T is much more complicated, not much more, but it's more complicated than this. But it's easy to work out. If the right-hand side of this equation contains a sum of terms like this, it's not difficult to solve. And what you find is that as the universe expands, it goes through various phases. So this here has the most negative power of A. These are the three components. This has the most negative power of A. So the smaller the universe is, the more important this term is. As the universe gets smaller, radiation gets denser, like matter, but also each photon gains energy. So this dominates the early universe to expect them to be radiation-dominated and to grow like T to the 1 half. At a certain point, radiation red shifts past where matter is, so if there's some radiation and some matter, at a certain point, matter will come to dominate. And from then on, the universe will grow like T to the 2 thirds until if there's any dark energy or vacuum energy, that comes to dominate. And then it will grow exponentially. And in the history of our universe that we know of, well, those three periods, we know very well. There was a period of radiation domination, then a period of matter domination, and now we live in a period of what seems to be vacuum energy domination. Hello, what time do I finish? OK. OK, good. So any questions on this? It's pretty strong. It's not true for just about anything in detail. So for example, if you have some massive particles which are moving relativistically because they're hot, then their W is not 0. It's more like a third. And then as they cool, they start to behave as pressureless dust. So if you really want to do this properly, you should take all that into account. But it's not very difficult to do for most forms of matter and radiation. But it does make the solutions more complicated than this. OK, so very good. So let's talk about causality. In general relativity, light is affected by gravity and it moves at finite speed. So let's work out how a ray of light or any massless particle would propagate in this metric. So again, I'll take k equals 0. Actually, let's write it in spherical coordinates. And let's consider a radial light ray. So a null, a light particle follows a null geodesic, assuming it doesn't scatter off of anything. A null geodesic has ds squared equals 0, 0 proper length. So this means that dt is plus or minus a dr for radial geodesic. If I integrate both sides of this, divided by a, and integrate both sides of this equation, I find that delta r is the integral dt over a. So this is the distance in these coordinates that light moves. If I integrate it from 0 up to some time t, it's the distance that light moved from the big bang up until some time. So for instance, suppose the universe was radiation dominated all the time. So if a is t to the 1 half, then when you integrate this, you'll get something like that. And so what you see is that this distance grows with time. And it's finite crucially. There was a question. Can you raise your hand? Sorry, I'm having trouble seeing. Ah, there you are, yeah. t times h over here. Yeah, you're asking about this equation, maybe? Or this one? Here. Yeah. Good. So h in this equation is 8 pi g over 3 times rho lambda. OK, so this is the energy density of the vacuum times this constant. That's what h is. And if I plug in a to the left-hand side, take two derivatives, and then divide by a, then it satisfies this equation. Is that clear? Yeah, this is not true for W not equal to minus 1. Yeah, no indeed. And in fact, it's very important that it's different when W is minus 1. That's the whole point. We'll get there in a minute. Thanks for pointing that out. OK, so assuming radiation domination for the moment, we find that light travels this distance after a time t. Now, notice that this coordinate r, it's the thing that's multiplied by a. So if I did k equals plus 1, this would be a sphere of radius 1. So you can think of this coordinate r as kind of like some tick marks on the universe. And as the universe expands or shrinks, tick marks remain in the same positions. OK, so delta r is some distance like this, about the same distance here. So this coordinate r here, or this distance delta r, is called a co-moving distance. Co-moving, co-moving. It's not a physical distance. It doesn't change. It's the same delta r in these two pictures. It doesn't change as a grows. a times delta r is a physical distance. It's the distance you would measure with a meter stick or something. OK, so this is the co-moving distance that light can travel after time t. Now, what does it mean? Well, it means that, again, imagine the universe was a sphere. You might complain that I neglected the k over a squared term when I calculated this. That's true. But never mind that for the moment. Imagine the universe is a sphere. If we get to large enough t, this delta r will reach pi, which would mean that the light has traveled half way around, or it'll reach 2 pi. Eventually, it'll travel all the way around. So in a universe which is decelerating, if you wait long enough, light will have propagated everywhere around the whole universe. Or if it's an infinite volume universe, it will propagate an arbitrarily large distance. So what does this mean? Well, it means that more and more of the universe gets connected to itself. So imagine that the universe, when it was born, was not in thermal equilibrium. Suppose it was hotter in one part and colder in another part. For two regions to come into equilibrium, so let's say this is hot over here, cold over here. For two regions to come into equilibrium, there has to be an exchange of energy. There has to be time for particles to propagate from one region to the other. So that can only happen at a sufficiently late time. Now, hold that thought. Another comment about H. If I take the physical, this is, by the way, it's called the particle horizon. So this is called the delta R. It's called the particle horizon.  So it's 2t. And that is 1 over H. So 1 over H is two things. First of all, it's the age of the universe, or well, twice the age of the universe in this case. And it's also the distance, the physical distance, that light can travel from the Big Bang until now. So it defines two things, the size of the universe. The size of the universe that's affected by one point. And also it's age, roughly. It's a factor of two. All right. So now let me explain the horizon problem, cosmology. So let's suppose that the universe was radiation-dominated all along. So let's just ignore matter and dark energy. Putting them in would change a few numbers a little bit, but otherwise it would have very little effect on this discussion. So here is t equals 0. This is a singularity, so let's make it spiky. And here is today. Today is usually denoted t sub 0. So if you consider yourself sitting at some point today and you ask, what parts of the universe can you see? We can draw some lines back towards the Big Bang. These wouldn't really be straight in these coordinates. It's t to the 1 half, so they should have some curvature. But we draw them back to this t equals 0 surface. And what we can see today, in principle, at least, is all the stuff in this region of the universe. So there's some delta r here. That's the co-moving distance that light traveled. So it traveled from here to here, traveled delta r. On the other hand, let's consider some very early time. Let's call it t initial. So this region here has access only to this part of the initial conditions. And this region here has access only to this part of the universe and so forth. Delta r is much smaller back then. So what you see is that the state of the universe at this early time is affected by many disconnected pieces. It splits apart into many disconnected volumes, which have not had time to communicate to each other. So imagine we can measure the temperature of the universe at this time. Would we expect it to be the same everywhere along here? It depends on what you believe about the initial conditions. But if there was any inhomogeneity in the initial conditions, if there was any variation in temperature or density in the early universe, it wouldn't have had time to thermalize. Because this region and this region and this region, they never talked to each other. They're completely disconnected causally at this point. And in fact, in cosmology, we can do precisely this. We can look back and we can measure the temperature using the cosmic microwave background of the universe at an early time. And what we see is that the temperature is almost exactly the same. It only varies by one part in 100,000. It probably varies by less than the temperature in this room. Why would we or would not? Why would we? I'm not sure what to expect. So no one really knows what the initial conditions should have been. And indeed, when we come back to the sort of controversies about inflation, this is one of them that we'll discuss. But well, it would be odd if the initial conditions were almost perfect but not quite perfect homogeneity. So what we're going to learn is that inflation provides a mechanism that essentially, no matter what the initial conditions were, produces a universe that looks just like the one we see. So without inflation, you'd have to assume that the initial conditions are exactly right to produce what we see. You wouldn't have any mechanism to explain it. But we'll come back to this quite a bit. So that's what it sounds like. But when you work at the math, that's not what you find. So let's not actually go to the Big Bang. Let's go to this early time because the Big Bang is a singularity, so it's a little hard to talk about. So then the universe is not really a point. It has finite size. And what we can see is that these regions can't talk to each other until a much later time. So for example, this guy and this guy can only communicate way up there. So if we go all the way back to the Big Bang, it is confusing. It's a singularity. It has zero volume. It's hard to know what to say. But we probably shouldn't do that anyway. We should go back to some very early time, but not quite all the way back. Yeah? No, I mean, I wouldn't expect any of the equations I wrote to be valid literally at t equals 0. In particular, general relativity is almost certainly not valid. So we know from quantum mechanics that there should be large corrections to it before a certain time. So yeah, I wouldn't trust it at t equals 0. But I would trust it at some early time here. So at least there's no reason not to. OK, good. So how many in this picture, it looks like about n and r10, but how many of these volumes are actually there? Well, of course, it depends on what we choose for t initial. So let's choose the Planck time, which is 10 to the minus 43 seconds. The motivation for choosing that is that we certainly can't trust these equations before that. So that's as far back as we can go. The Planck time is the time when, well, the energy density of the universe will be of order of the Planck density. It's the time when large corrections to general relativity certainly kick in. So we certainly can't trust GR before this time. If we go back to that time, then we said that the particle horizon grows like t to the 1 half. So delta r of t0 divided by delta r of t Planck is the age of the universe today. Anybody know what it is in seconds? You can remember it like this. It's 10 to the 10 years, roughly 10 billion years. 10 to the 10. And a year is pi times 10 to the 7 seconds. So it's about 10 to the 17 seconds. OK, so 10 to the 17 seconds divided by 10 to the minus 43 to the 1 half. So this gives us about 10 to the 30. That's linear scale. If we want to know how many volumes are in there, then I should cube this. So there's about 10 to the 90 causal volumes, or Hubble volumes, let's just say, inside this code here. Remember, this is really three dimensional also. OK, so there's about 10 to the 90 different regions in there. Actually, if you include matter and dark energy, you get more like 10 to the 80. But it's a very big number. So why do they look all the same? There's another problem, which we're going to see is very closely related, called the flatness problem. 10 to the minus 43 seconds. Sorry, I'll try to write bigger. OK, let's talk about the flatness problem. So let me put the curvature term back in. So we have h squared. And now it's convenient to take this equation and divide both sides by h squared. And this is called omega total. This is called omega k.  Not that omega k is negative when k is positive. That's some annoying convention. But anyway, it looks like this.  And by the way, this omega total contains all the rows. So it's got row matter, row radiation, row lambda, if there is one. We know from observation that this can be no bigger than about 10 to the minus 2. That's why I said we can ignore it. In the universe today, this term is at most about 1%, about 10 to the minus 2. So now let's go back. That's today. So let's go back to this time t plank and see what happens. What happens to omega k? Well, it scales like 1 over h a squared. And for radiation domination, a is t to the 1 half, h is 1 over t. So this goes as t. So if I go back, excuse me, if I go back, and I evaluate omega k at t equals t plank, it's about 10 to the minus 60, which is certainly a small number. Now, what does that mean physically? Well, there's a nice way to think about omega k. So if I write a h as a divided by 1 over h, can't stop me from doing that. So this here, this is the radius of the Hubble volume. It's effectively the size of the universe, the physical size of the universe that you can see. And this is the radius of the whole universe. It's the radius of curvature. Remember, in the closed universe, a was literally the radius of that sphere. So this is the ratio, a h, is the ratio of the radius of the universe divided by the Hubble length, divided by the part you can see. So if you want, it's the size of the universe divided by the size of the observable universe. OK, now a h is 1 over the square root of omega k. So the fact that observation tells us that omega k is less than 10 to the minus 2 tells us that a h is greater than about 10. OK, so what we know today is that if the universe has a curvature, if it's a sphere, the radius of that sphere is about 10 times bigger than the observable universe, than our Hubble volume today. 10, because it's the square root, it's 1 over the square root of omega k. And now, if we go back to this time, t-plank, it tells us that the radius of the universe back then, so this is a h today, if we go back to t-plank, then it would be about 10 to the 30, square root of 1 over 10 to the minus 60. So we would say that the size of the universe back then was 10 to the 30 times in linear scale, the Hubble length back then. Or if you cube it to get a volume, you would get 10 to the 90 Hubble volumes per universe. OK, so it says that the universe back then was much, much, much bigger than this causal size. So there's another way of looking at this flatness problem. So how did it get so big? How did it get so flat? And again, you can say this either way. You can say, what set this number to be so tiny, this omega k back at this early time, to be so tiny? Or if you're looking at this way, it says, what says that the total size of the universe, which is at least this big, is so much bigger than the characteristic scale at that time, than the Hubble length at that time? OK, so these are two ways of saying the same thing. And these problems are very closely related. I mean, you'll notice it's exactly the same number, or pretty close anyway. What it really says is that without inflation, the universe had to be very, very flat and very, very homogeneous on scales much longer than c times t, where t is its age, much longer than the light crossing time of the universe, the distance light could travel back then. OK, so I should finish. And unless there's any last questions? Yeah, thank you. Yeah, that's true. I cheated a little bit. Yeah, so when I derived the scaling of a, I assumed k was 0, and now I'm taking it not to be 0. Right, so the only time that will matter is when this term becomes large compared to this term. In other words, if we keep this term, but it's small compared to rho, it won't change very much the solution we found for a. So it'll be pretty close to t to the 1 half.  So in the late universe, this t to the 1 half is not correct anymore, and there's a slightly different solution. But in the early universe, it doesn't matter. And since the universe today has this small compared to this, it really doesn't matter much. But you're right, we could do a more careful job where we take both terms into account. It wouldn't change anything. This number wouldn't change at all. Not this one, but this one, just because it's completely irrelevant in the early universe. But yeah, thanks for the question. Yeah, oh, yeah, that's a good question. I would say, yes, there is a difference. They enter Einstein's, yeah, the question was if there's a difference between vacuum energy and cosmological constant. So Einstein added a term, I erased it, but he thought of it as a term on the left-hand side of his equation, so part of the geometric, you know, part of the curvatures, which was lambda times T mu nu. And so that was the cosmological constant. If you shift that term over to the right, then it looks like it's part of T mu nu. Of course, it's the same. So in that sense, they're identical. However, vacuum energy is not necessarily fixed forever. It's something that can change. For instance, you might have multiple vacua in a theory, multiple stable phases, which have different vacuum energy. So you can have theories with multiple possible values of the vacuum energy. But strictly speaking, there's only one cosmological constant. So they're not exactly the same, but as long as vacuum energy doesn't change, they play exactly the same role in the equation. OK, so I think we have a coffee break. If anybody has more questions, you can talk to me then. So thank you.


We had a high-end audio brand making an assistive device and a medical company putting out high-end audio. What's going on here, Patrick? Recent changers and over-the-counter hearing aids and my favorite dead horse to beat industry consolidation. So there's a lot going on in this area and a lot of companies are like, wait a minute, there's money here. Actually, there's a company called Nura. They're an Australian audio company. And they did this wild thing where they bounce sound in your ears and they measured autoacoustic responses, essentially some sounds that your ear gives back in response to these particular pulses that are sent into it. This is legit. It sounds really audiophile-hinky, but it's actual legit science. I've experienced them. They do a fantastic job tuning their headphones for your ears. I've used the over-ear ones. I suspect that's a step towards Massimo doing their own over-the-counter hearing aid system. That's complete speculation on my part. Please don't sue me.


this is going to be in the final exam okay? This is likable science today. We're going to talk to a real-life dissertation defender person at UH in southwest as an ocean oceanography student who just finished her the defense of her dissertation about the logic ecology. Jessica Perleman, thank you so much for joining us today Jesse. Thank you for having me, glad to be here.  There you go yeah it feels really good to be on this side of everything five years is a long time but certainly worth it all. That's great so what was the five years like can you talk about the coursework you had to take and the research you had to do to get through it? Yeah so part of the oceanography department at UH I have to say I really didn't have a strong background in oceanography whatsoever and so taking all the courses was shedding a lot of light on entirely new topics for me so we you know in this program take the the whole suite of courses to familiarize yourself with not only the area of oceanography that you might be focused on but also kind of all the areas so that you can have a general understanding of of all the different topics that people might be focused on so that's physical oceanography chemical oceanography my area focused biological oceanography so just trying to trying to get a good understanding of you know what what this field is all about and then with UH it was about two years of coursework so a lot of focus on really learning the basics as you're developing your dissertation research and trying to figure out what specifically within all that suite of information that you're learning that you want to focus on and want to study. You must see you know a square foot of ocean as a different a different thing than than regular people see it you must see into that square foot and see all these things happening all these animals and microbes and what have you jumping up and down you're not like regular people anymore are you? No I guess it's like you know I hear people say if they study film you can ever just watch a movie again for what it is you always you're always looking deeper so yeah every time I get a chance to get in the water it's you know what am I seeing what what cool critters are in the water and where are they coming from and how am I disturbing them? Yeah right right right and so you must also have a feeling about how very precious the ocean is and how very fragile the ecosystem is I mean how do you feel about that after five years of a PhD? Absolutely yeah I think understanding a lot more about how ocean ecosystems operate and now understanding a lot more about the pressures and the potential threats to that natural state of operation it's it's concerning it's you know there's there's a lot of changes happening there's a lot of potential you know industries and and changes that might happen so one of the areas that I focused on a lot was a developing deep sea mining industry and so I guess in the back of my head throughout the last five years it's always been that question of you know what's going to happen to these precious ecosystems and you know we had a show but we had a show about that and it was one of the most interesting shows in oceanography that we've ever had it was about manganese nodules and about how this you know this industry is waiting on the sidelines that pounce on all the ocean floors in the world and mine these manganese and other and other you know other materials as well but how do you feel about that because I mean there are people who will make a lot of money doing it and what does it take to protect them and what is it you know what will you know wholesale manganese nodule mining do to the world? Those are all really great questions and ones that I've tried to grapple with for the last five years. It is a rapidly emerging industry and there's a lot of increasing demand for the kinds of metals that they want to mine from the deep sea floor so I think interestingly you know these manganese nodules aren't mind the same way that a lot of land-based minerals are mined and they're not drilled for in the way that you think that oil mining or oil drilling might happen. These nodules are sitting kind of just in dense fields in some areas on on the deep sea floor in parts of the ocean so one area in particular is this massive massive area between Hawaii and Mexico that spans about the width of the continental US and I think that's one of the the primary targets for this industry and you know they're figuring out the engineering details of how to physically lift all these nodules several miles up from the sea floor all the way to the surface and as scientists you know we're trying to ask the questions well what you know what harm is this going to have to the ecosystem how can we mitigate that harm and and even more basic questions of wait what even lives in these ecosystems these are areas that really haven't been studied all that much how you know how can we assess what kind of changes or you know threats might be occurring in these waters if we don't even know from a baseline standpoint what's there and and how they behave so yeah it's interesting to see this develop you know I'm I'm curious to see how quickly if at all this this industry really picks up then how it might compete with or rival or kind of add to the existing land-based mining for some of these minerals that are quite important yeah I mean manganese is only one of them there are a number of them and they could become you know in the 21st century really valuable at the same time the law of the sea is not all that well developed and it's not clear that the law you know say protects them or limits the people who would like to mine them and so you have the science moving on the one side you have industry moving on the other side and you have arguably the law of the sea moving you know to try to mediate between those things and of course concerns about the ecology in general right why did you go into this Jessica I mean and you know it sounds complicated and certainly five years is a biblical period of time so why did you why did you do this did you have some fascination you know with the ocean yeah absolutely I actually grew up nowhere near the ocean I grew up along Lake Michigan which you know seems like a freshwater ocean to some and so I think that maybe that distance from really ever being near the ocean is what drew me to really wanting to study it and to understand more about the animals that live there and and how they live and how they persist and research was always something that I really enjoyed as an undergraduate student having you know having the opportunity to work in different laboratory spaces and dabble in a little bit of research here and there and really feel like this is this is cool I didn't know you could do research as a career and I could ask questions for a living and try to answer them for a living and so you know some of those more basic reasons definitely led me into choosing to pursue you know a degree in oceanography and you know ending up out here perhaps a little bit by happenstance but I really wouldn't change it for the world I think falling into the areas of study that I have and getting to collaborate with folks at UH that I've been able to to do over the last five years has been just an immense undertaking and privilege for me so you know the difference between us is you get to ask questions and satisfy your curiosity for a living and they pay you for that I get to ask questions and they don't pay me for that there's a difference but we can be equally curious you know so when you look at it from the shores of Lake Michigan and you looked you know around the country and the world for that matter because this is you know global science for sure um what attracted you to UH what attracted you to SOAS um I have to say I um when I first found out about SOAS and the programs here and had the opportunity to to chat with and have some discussions with faculty it struck me that this was a place that was ripe with opportunities and you know getting getting to hear about the active research going on here and the importance of some of that research really I think that's what led me to feel like this was this was an area that I would like to study and this is a place that I would like to pursue this degree and um you know and I guess five years ago and I first had a chance to to talk with my my former PhD advisor about the kinds of projects that um that that particular lab was interested in and studying and the areas that I could come in and you know enhance that research and develop my own research um it just seemed like a really great learning environment with a lot of really great people um and I I'm about to took the risk and you can and you stay in touch with them through the whole period they're right there in Manoa and there's some of them doing long-term research projects and I'm thinking of Dave Carl you know the National Academy of Science who who um you know has um have been working on projects that go decades and decades and decades did you have to go out in the ocean did you have to do dive did you have to take those UH ships around and and drop instruments tell us about that yeah quite a bit actually um for a good part of my research um involved going out on two very long cruises um out into the middle of this area that I was just talking about that's that's being targeted for mining so it was you know a five or six day steam from the nearest port just to get out there and being out on these ships for 45 or 50 days at a time um dropping all sorts of instruments into the water and trying to assess the general ecosystem baseline if you have it just what's going on in these areas that really haven't been studied all that much and in terms of what we dropped in the water we dropped a lot of different instruments to measure different properties of water so um instruments to measure temperature and salinity um and productivity and oxygen um you know different variables that might affect the animals that um you know I personally was more interested in studying um we were able to tow really big nets behind ships to collect a lot of the small fish and crustaceans and squid um that we were aiming to study you don't eat them or anything no they uh they don't smell so great all the time when they come up but probably not as tasty as if fish you might be more used to eating okay um but yeah just you know a lot of fun being able to dabble in in different aspects of oceanography being out at sea collecting different um yeah different measurements different animals um one of the collections I was able to do quite a bit was acoustic data collection so kind of sending sound waves down into the water to reflect off animals and get a sense of where they are in the water column and how they're behaving um and so that was a lot of fun to try to use this tool that would allow us to sample a lot more space um and for a lot longer time than just being out there on a ship in the middle of the ocean uh yeah well I want to I want to drill down on that it's not it's not a pun I want to drill down on water column I want to drill down on pelagic and when I first saw the title of your phd which was um let me let me read this so I know what I'm saying it's uh oceanographic influences on pelagic ecology acoustics and combined sampling approaches I I don't know if you can put that to music actually you have to really work at it first thing I said pelagic is this some sort of skin disease a skin condition because if I watch mb and mbc long enough I'll find 10 modern high-tech cutting-edge drugs that will help me with my pelagic skin condition but it's not that at all is it what does pelagic mean not quite um pelagic means open ocean so um if you think about different habitats in the ocean you might think of coral reefs or um habitats at a right offshore that you can see just you know from hopping in the water when you think about pelagic it's when you move further offshore and suddenly the water gets quite a bit deeper and you have these increasing expansive expansive volumes of of water that have no no boundaries in the horizontal and might be further and further away from the seafloor um that's what we're referring to when we say pelagic so it's just the kind of the whole water column nowhere near shore nowhere near the seafloor you know I was talking before about that you know one foot square of water but you're not putting your arms around that you're putting your arms around the whole thing and actually it's it's beautiful to think of it that way isn't it when you're putting your scientific arms around the whole enchilada you know it's it really it really is a beautiful experience so it is yeah a lot to take in yeah why that why did why did you turn in that direction I imagine you had a meeting with one of your former advisors because right now they're all former advisors former advisors and former committee members hi guys you can call them by their names everything so yes so you sat down with somebody and and and he said Jessica you know what about doing ocean our oceanographic influences on pelagic ecology is that what happened or did you wake up at two in the morning and decided uh maybe somewhere in between it was maybe more a year or two of taking all the questions buzzing around and trying to fit them together into a coherent story of several chapters so with a dissertation you have you know three or more chapters of of different projects and trying to fit them all into a topic or a category hence the very long name of of a dissertation as you have found out yeah but I I think a lot of the questions that I was interested in and that my lab was focused on fell into this this really large habitat the pelagic ocean and part of the reason for that is there's just not been a whole lot of focus on studying some of these habitats as you can imagine they're they're quite hard to get to you know takes several days just to steam there in a ship they're a bit out of sight and out of mind for a lot of people and and you know the amount of money and time and you know resources that it takes to get out there makes them quite difficult to study and so being able to contribute research in an area that certainly needs it and is certainly important to study but has perhaps been a bit neglected overall I found to be a good reason to pursue it oh yeah well so um let's talk about influences on pelagic ecology you you wanted to identify them you wanted to measure them what are the influences on I know we only have a few minutes but but what did you find what are the ones that count yes that is a great question so I was interested at different scales of influence and so thinking at the scale of this whole massive region that I've mentioned before you know what what oceanographically drives the behaviors of some of the animals that live in this really big region and at that really broad level I found that one of the biggest drivers is something called an oxygen minimum zone and that's a really big feature in this region and it's basically an area of the water column that has really really really low oxygen and so it's as you can imagine quite hard for a lot of animals to live there because it's just not enough oxygen and so while you do have some animals especially adapted to living there it drives the behaviors of a lot of you know different communities living in that area maybe makes them live at shallower depths so they are not you know migrating too deep into these really low oxygen waters so at a really broad scale we found that that was an important oceanographic influence and at smaller scales um one of the things we found really important was what we call mesoscale features or or features that are on the scale of just a couple you know 10 to 100 kilometers and that includes features such as eddies and eddies you can think of as these these water masses propagating across this big region rotating bodies of water that have their own unique properties to them and can affect you know a particular area for a finite period of time perhaps a week or a month and we found that a lot of animals are actually responding to the passage of these eddies coming through this region at smaller spatial and smaller time scales so in a in a broader context putting this into something like deep sea mining that we were just talking about if you really want to understand how mining might be affecting this ecosystem or changing the behaviors of these animals you have to understand that the natural scales of variability and their behavior and so that was what what we were aiming to do wow that really really sounds really interesting and when you think about you know the different areas in the world and how it might be different from one to the other and how it might have participated or influenced the the evolution of the animals that are in the water calm you know I'm sure that when you go and look at them today in a snapshot kind of way you have to think about where they've been for the last hundred thousand years and how they have evolved and therefore how the oceans have changed for them in the last time wow that's pretty exciting and how they might change in the future right yeah yeah wow exciting so okay so how long is it to take you to write the dissertation you know it's a threatening word for anybody who hasn't done it in fact I would say it's a threatening word for everybody who who has done it yeah the the feelings it brings up are are always going to be there uh for me I I kind of spread it out across the whole process so I I never had to sit down for months and months at the end just to just to write it all I kind of took it one project at a time did all of the you know the research collected the data did the analysis wrote up a chapter moved on to the next maybe worked a little bit on the other projects here and there but definitely spread it out over probably about two and a half or three years um is that is that common is that difficult I yeah I think there's a mix I think part of it just depends on on how things work out and how your data collection and and research flow just just turns out um and I was fortunate that it that it turned out in a way that allowed me to just progress through each of these chapters in a in a more fluid way I think then trying to cram at the end and just put it all together so so are you expected to send drafts to your advisors um and and connect the dots with them and get some ideas about where to go next on this is is it a sort of an exchange of ideas is a collaborative effort in that way absolutely yeah it's very collaborative uh between you and your committee and you and your co-authors um you know I say me here but certainly none of this was done alone and and all of the ideas and analysis and research have had you know lots of exchange among um all of the people involved and um you know yeah there everything that goes into a dissertation is it is a team effort but at the end of the day it is you know you as a PhD student who who has to really do the branch of the work and put it all together and connect all the dots um obviously getting input along the way and it's your signature you're at the end of the day you're the one who wrote it and you're the one who has to stand by and defend it you know yes exactly that is why they call it a defense yes well I'm interested in that I mean I went to law school and we had defense in law school so you know my my impression though is that when you finish a degree like this and you focus on Bellagic ecology and and the instrumentation and so forth um that is actually a narrow aspect of the work you have done because in the process you have learned about all kinds of alternative and additional things about the way animals work the way the oxygen works the way the sea swells and eddies work um and so you're you're only covering putting it this way you're only covering a small amount of what you've learned and you have learned lots more than what you write about am I right yes you're 100 correct it at the end of the day it feels like you've done a lot more work than you're really able to kind of put in in the booklet at the end of the day and even less so that you're able to present in a you know 45 minute defense at the end of it all so everything you learn along the way all of the you know the methods and the tools and the different topics some that you might you know go down one route and decide you know that's not working or you know you don't want to pursue that and there's a lot of trial and error that nobody sees at the end of the day it's just the finished dissertation so how long is it what six seven thousand pages what oh a couple hundred pages that might take a bit more than five years how many chapters uh mine is about five chapters there's three data chapters and then a introduction chapter and a conclusion chapter and I think that's maybe the the standard length okay and the the English has to be perfect um that I know that from talking to people who've taken phc's they really have to be careful about every word and you know the grammar the the punctuation all that uh what about the footnotes um is it loaded with footnotes you have a separate bibliography of footnotes uh definitely a lot of appendices and supplementary information and and a ton and tons and tons and tons of references you know you pull thoughts and ideas and comparisons from a lot of different published work and um yeah there there's a lot more than just the actual research that goes into it so what are the footfalls you want to avoid in writing and dissertation I mean I suppose you you don't want to misquote uh a source or reference an authority um you don't want to come to the wrong conclusion uh about you know how to how to put it all together what else I mean when what what are the things you're trying to steer clear of yeah that's a great question and part of the reason um that it's nice to have a committee to you know to go through everything with and make sure that you are making the right conclusions or at least that everybody's in agreement uh on those conclusions um I think when you you know if you go to publish those individual chapters and journals um you have this whole peer review process and so you actually have people completely external to what you've been working on that might come in and and have you know a lot of gripes perhaps with what you've written that neither you or your co-authors or committee may have had and so um there's a lot of uh not really knowing what you know whether what you've written is um incorrect in the eyes of somebody else until you go through that process and um certainly also maybe you're realizing mistakes that you and your committee who have been looking at the same work for several years now might have missed so you definitely want to go into that review process trying to make sure you've dotted all your eyes and crossed all your t's but um at the end of the day there's there's some amount of just not knowing until you until you go through that process yeah but you know when you when you say peer review and you say well these people have to agree um that your work is right that your conclusions are right and defendable and so forth don't you have the risk of somebody out there in the scientific community going to say Jessica you're all wet isn't that possible absolutely and you know to some extent nobody's ever right and you know we're all wrong to some extent and I think there's a there's a uh a skill to the way that you write a scientific publication because it is really difficult to say with absolute certainty what you found and what your conclusions are are you know are what they are and so there's um there's definitely a certain way of writing that leaves room for error that leaves you know a lot of your conclusions might be suggestions for example because you you know at the end of the day you really might not be able to prove with absolute certainty what you are trying to stay and I I think there's rarely a circumstance where you are truly able to prove something as 100 percent fact but the idea is that you are advancing science that's the mission isn't it you're making a material contribution to the state of science in this area isn't that what it is it is yeah that's correct and you know you you do as much as you can and um you know try to put that information out into the world to be used to be you know put into management or you know just to kind of expand the basic knowledge of the field that you're studying so um you know inherent in all of this is that when you finish a paper like this and you go through the the process um you get published right uh so where is this going to be is it going to be in the the food section of the star advertiser if it could be on civil bead or maybe pacific business news where will i be able to find your work uh well you can find the whole dissertation on the pro quest website um they published uh entire dissertations and then each of the individual chapters will be published uh in different uh oceanographic journals so yeah a handful of different journals that i can certainly share the links with but um okay well that's great so now what about tuning it up you know so you've you've done it you defended it you got through um you're going to get your phd soon enough you're going to get published on these various sites i was only kidding about the star advertiser if we saw if we saw your dissertation dissertation on the star advertiser i for one would need smelling salts um but but what about tuning it up you know what about you stumble into something six months down the road a year down the road and in the course of other work that you do wait a minute you know i want to add something want to change something i want to expand this uh i want to make a uh you know uh um something else about it another paper or an expansion of the existence what about that does that happen yeah i i think that's more common than not uh especially when you become such an expert in in whatever area of expertise that you've spent the past five or more years studying i think you do relate a lot of what you do down the line your future research back to what you know so well from that dissertation work and i think a lot of new ideas for projects and a lot of expansion of the work that you might have done during a phd into your future research is is probably more common than not and i'm excited to try to answer some of the questions that we weren't able to answer along the way just in in the five years that i had to uh to conduct all the science that i did during my phd and so i i think that's something to look forward to so uh you were telling me before the show that you've got a job out of all of this and you will be paid for your curiosity and it's a research job my right it is yes it's a continuation of the academic experience except you this time you know you get paid for your time um and your product and so what what is that job what is it going to be like and and let me go further and say how do you see your career unfolding you know in in a logic ecology um all great questions uh i'm now working at the noah fishery center at fort island so it's the pacific island fishery science center and i'm able to take a lot of the skills and tools i learned during my phd to answer some similar questions and some slightly different questions uh particularly about some um you know local fish communities or on hawaii and the u.s pacific islands and trying to understand um you know what what are the oceanographic influences on on some of these different communities of animals and then also continue expanding those questions into the pelagic uh you know everything is connected so a lot of a lot of what happens to near shore communities has uh you know influences or is influenced by what's happening to offshore pelagic communities and so trying to couple and better understand the interactions between you know what's happening close to shore and what's happening offshore is it's definitely an interest moving forward and um hopefully something that my career will allow me to continue to pursue and ask questions about for the next uh hopefully foreseeable future 100 years or so yeah so what about these uh former committee members and former advisors you know the ones you now call by their first names uh would you have contact with them would you have uh you know either formal or schmooze contact with them going forward certainly yeah i think um you know one of the nice things about being able to work with the committee for so many years is you build up a a network of people who are experts in the various topics that you're also interested in and so having having a rapport with them already and having collaborated with them already makes it a lot easier um you know to both collaborate and continue interacting with them in the future whatever future projects come up and and just you know interesting topics in oceanography that you want to discuss with people that you've been able to discuss for the last five years or so um i look forward to keeping those connections oh yeah that's great you know and and of course uh i'm sure in the last five years you've had contact with other people doing other research and other institutions uh in the u.s and elsewhere and um so part of being a scientist uh wow the people call you scientists and everything i bet they do i'll call you scientists feels very formal so uh you know when you have when you have when you grow this community of people who are you know also into the same area or similar areas of research now you have a a global network and you can send your papers to them they'll send their paper it's just what it's like i mean how much how much connection connectivity do you have now and how much connectivity do you think you'll have going forward uh that's a great question and and i've actually been able to have quite a bit of connectivity uh during my phd um some of the biggest collaborators that i've had are actually folks over in new zealand that i connected with just out of you know curiosity and having questions and you know choosing to reach out to folks and i've found that building connections um through that that uh communal curiosity has been really really rewarding and i think the people that i've had a chance to work with both throughout the u.s and internationally will be people i continue to work with um for years and years and i think that's that's a good precedent for how i'd like to go about expanding that network of of people down the line and into the future yeah and and that's a a measure of your success um the quality of your community is a measure of your success you heard it here on think tech but um let me let me just ask you one more question and i i'm trying to put myself in the room with you when you when you finish a few weeks ago when you finish you know your defense and everything so you have a committee you're in the room um are you sitting or standing and if you're standing you have to stand in attention uh if you're sitting can you have a glass of water with you um and do they sit and how many of them are there and you know what's the attitude in the room what's the the tone uh and tenor of the conversation so i think that varies depending on the committee and and even perhaps the university um for me there is well there's the public defense so that's giving a big presentation to um to the public and uh so that's uh you know a well-prepared presentation and you're standing and walking around and and trying to answer people's questions and then once that completes everyone leaves the room and then you're right it's just you and your committee and it was about an hour and a half of the committee asking me questions and um really more just having a discussion with me about the broader implications of all the research um additional questions that people hadn't thought of previously or or interests and um i have to say it was a lot more uh it was a lot more of a discussion than i had expected it was nothing like the comprehensive exams that you take two or three years into your degree when you're just getting drilled on everything you know about oceanography and it really feels like you're the expert and you're having a conversation with your peers about all of the research that you've done um and you know we were sitting we were standing we were joking and um yeah it was a it was a great atmosphere to be honest it's great and and i have the sense that when you when you are drilling down in that conversation with them on something that you've been focusing on in your research actually you know more than they do it's a good feeling it's a reversal from feeling like you don't know nearly as much as anybody else to actually i do know a bit more about this particular topic at this moment i what a great experience in life i i envy you uh you know your success your achievement and your future it's wonderful to talk to you jessica and uh i hope we meet again and i wish you well in all particulars thank you so much jay i really appreciate you having me and it's been a great chat jessica perlman and and please call her doctor thank you thank you so much for watching think tech hawaii if you like what we do please like us and click the subscribe button on youtube and the follow button on vimeo you can also follow us on facebook instagram twitter and linked in and donate to us at think.kawaii.com mahalo


We wouldn't have a business here if it wasn't for Mid-State. The majority of our employees here have either gone to Mid-State Technical College or North Central Technical College. Martin Machining is a CNC machining job shop. We create tools, fixtures, component parts. Pretty much whatever our customers want us or need us to build for them, we are located in Stevens Point, Wisconsin. Martin Machining was started by my father in 1984, so my father and my mother were the first two employees. After a few years the business, you know, started to expand. So he was a second and third employee that my dad hired for students that were currently going to Mid-State Technical College back then. We've been involved with the machine tool program advisory board for many years now and I think what I'm seeing as we've got more involved in that is they ask us a lot of questions about where do we see industry is going, what new technologies are coming, what are our customers asking for us, what kind of methods, skills are we getting asked to provide for our customers. They've responded by making changes to the program that address the requirements and the needs and the skills that we're seeing and we're really happy about that and think that that's going to help us continue to find employees that have some exposure, have some knowledge about how the things we do work and how they happen. The other way that they've helped us out a lot is that they put a lot of effort in making time to take students out of the classroom and bring them out to our facility. So we'll see at least two times a year both from North Central Technical College and MSTC and RAPIDS. The teachers will bring students on site here and we get a chance to show the students what we do. One thing the Technical College has also been a big supporter of is the heavy metal tour and that takes eighth graders in multiple counties in Central Wisconsin, puts them on buses and takes them out to our facility and several other facilities in our area. So we help sponsor that and so does both MSTC and NTC and we see some tremendous benefits from that. I think it's important to get young people interested and aware of what's going on in manufacturing locally. Our industry manufacturing as a whole has the same issue that a lot of industries do right now. The average age is rapidly approaching that, you know, 55, 60 year old range. There's gonna be a lot of people retiring in the next, you know, 10 to 20 years and we're gonna need to find ways to replace the people that are retiring. Not only just the people but the skill sets that and the knowledge and the experience that they're taking with them. Seventeen of the 22 full-time employees we have are technical school graduates. All of them work and live in Central Wisconsin. We work with people here, we employ people here and as our business is growing, our employees are starting to grow their families here. They've helped us see ways that we can connect and give back to our community. They've helped us start creating a vision for what the future of our company is going to be. They really provided us a way to see, okay, hey, if we want to do X with our company, we want to grow to a certain size or we want to take on maybe new customers and new projects, they're helping us see that, okay, it's possible.