Hello, and thank you for joining me today. For today's Wednesday webinar, we are going to take a look at one of my favorite Google tools, Google Keep. I am Tina Souser. I'm a technology integrationist here at ESU 8, and I'm very excited to bring you or to talk a little bit more about this tool today. So first of all, let's talk a little bit about what is Google Keep? Google Keep has actually been very simply labeled as a note-taking app, but it is so, so much more than that. It was launched by Google back in 2013, and when it was first launched, I barely paid much attention to it, actually. And so very few people really grabbed onto it to get started. But as I have taken my journey this year through Google Keep, I find myself using it more and more and more. And find lots of uses for it in the classroom setting and my professional career. So if you would like to follow along interactively, first, you can either load the app on your mobile device. Any mobile device, if you're on a Chromebook or web-based, you can go to keep.google.com. And I would create a note that is labeled either practice or training, anything like that. And you can follow along as we go through the features of Google Keep using your practice note. So I'm going to get out of this screen. And I'm going to go into my Google Keep. And as I mentioned, please note that I have been using Google Keep for quite a while now, so I have a lot of stuff in here. But a couple things about the platform itself. Within Google Keep, on the left-hand side, you will have the opportunity to make all these different labels just like you would anything else digitally, whether it's in Google Drive or on your desktop, any of those things. But you can make these labels in order to organize your different lists. Now, you can also have this. This is actually an extension. This is called category tabs. If you go to the Google Play Store, you can get category tabs for Google Keep. And you can then organize them by color. And you can simply click through the colors as another organizational platform if you so choose. Again, you won't see this when you first load Keep, but you can get that as an extension. So as I mentioned, we have a lot of different tools and features in Google Keep. So when you first land in Google Keep, you're going to get just the basic notes. And so in a note, first of all, you can give it a label. And then you have the place in which you can start taking your notes. Now, there are two different types of notes. You can just take a regular note, or you could make checkboxes, which then become a list. Things such as if you have a grocery list, or if you're working on a project or a collaborative project together, you can have a list of items that way. And it will give you the checkboxes as you see down here below. You can also, we're going to talk through some of these features in the notes here, but those are the two types. So some of the features in our notes include the reminders. Now, the reminders option in our notes, first of all, you can set a reminder based on date or time. They have some general ones set up for you, or you could pick a date and time. So let's say, for instance, I want to be reminded tomorrow at, we'll say, 8.30 in the morning. So I'm going to pick custom. And I'm going to say, I want a reminder at 8.30 AM. I can select it to repeat daily, annually, whatever I want. And then I can save that reminder. Now, if I go back, I can also pick a reminder based on place. So let's say, when I go to Target the next time in Norfolk, I want to make sure that I remember to pick up some diapers. So I'm going to type in Target Norfolk Nebraska. So when I click that and I save, the next time I arrive at Target in Norfolk, I'm going to get a pop-up reminder on my mobile device as long as I have it with me, of course. That's going to say, you need to remember to pick up diapers when you're here. And so then I could also, as a piece of that, I've also added clippings of coupons that I have with the code, excuse me, with a barcode on it. So when I get to Target, I can just use my keep note as the coupon. So just be aware that you can do that as well. So the reminders are a very, very, very powerful tool. Another way that I've used these reminders at work is because we travel so many different places for work, there are certain things that I need to make sure that I take with me. And so I will set a location reminder that when I arrive at work that next day, I need to make sure I pick up these five things before I head out for the school. Another very important feature of Google Keep Notes is the fact that you can add collaborators simply by adding their email address and then click Save. And then this note now becomes a collaborative note between you and this other person. One way that I use that personally is my husband and I, when we go grocery shopping, seeing that we have three small kids, we tend to separate. And so if I create my grocery list as a checkbox list, when he picks something up and he's in a different part of the store, he will checkmark that. And so then I know what he's done and what I still need to do yet. And we're still in the same, and then we come home with what we need and not so much duplicates, which is a great feature. The other way that I see this working, and I've seen this work in classrooms, is on projects where kids are working together or collaborating together and they have a to-do list. The kids can use this collaborative feature to check off stuff that is done. But the cool thing about this is in a checkbox list, when something is checked off, it doesn't go away. It pops down here to the bottom. So if you find that you have a partner who says they have something done, but you may talk in, or as a teacher, you might say, well, I don't think this is really done. You can uncheck it and then it pops it back into the list. And I really love that feature about Google Keep. So, and as you notice, my practice note went away because I did not add a color or a label to my note. So if I come back up here and I find that note, if I search for practice, is what I named it in the title, and I search, come back here to notes. Now if I label that, if I search for practice within my notes, I should be able to see that here it is. So now what I wanna go back and do, one of the other features of this is of course, all my other ones I labeled with that blue color. And then I also had them in my keep on, keep it on folder. So I'm gonna come back here and I'm gonna add that label to this note. And once I've done that, then I could come back here and I could click on the keep on, keep it on label. And I could get all of those notes, including that practice that I just labeled with that. Or since I have this extension, I could click on my dark blue and I'm still gonna get those labels as well. So that's a couple of the features so far, but I'm gonna go back into my practice note here. And I'm gonna find the one. Another feature of this is of a note is that I have all, I have image, I can add any type of image that I want. So I can go out and I can grab one off of my desktop or wherever I have it saved. Excuse my image. And I can pull that right into my note. And so if I have an image and then I can take notes below here on that image, or here's another really cool feature, I can come into these three check boxes and I can say, see how I have text up here? I want to grab the image from that text. And then I can go back in here and I can change the text or add to the text or anything that I wanna do based on the text that was actually in that image. And so that's the grab, grab image text. And so it'll take whatever text you find in here and it'll transcribe it down into a note. So that's another really cool feature. This is an archive button. You can archive your notes if you wanna store them or get them out of your way. In these three dots, there's the option to delete the note. You can change or add labels, you can add a drawing. You can make a copy of this exact note. You can change to check boxes. And down here, this copy to Google Docs. This is another great feature of Google Keep. So if I click on that, it's gonna copy this information into a Google document. So if I say, once it's copied, if I say, okay, I wanna open that document, what it does is it not only brings in the text from that, but it also brings in the image from that note. So what I'm using this before is I started using Google Keep to take notes at different conferences that I went to and sometimes they got to be a little bit big. The notes got to be larger and larger. And so then I pull that into a Google document instead. So then I could go back in and add whatever I wanted to add. So that brings me into another feature of Google Keep. When you are in a Google document, you can open your Google Keep over here to the side as long as you're logged in. And you could take, so say for instance, if you gave the kids a document that they were supposed to read through, they could pull up Google Keep and take notes on that document. Or if the kids are collaborating on a project and they have a checklist over here, the kids could be in the same document and have the same checklist here and be checking off the stuff as they work on it. And that's a powerful feature because not only are the kids collaboratively working in the document itself, they're also seeing things getting checked off on the checkbox, whether they're not even in the same room or in the same house per se as they're working on it. So that's another great feature of Google Docs. Now, if the kids are working on another collaborative project but they have their own Google Keep notes that they've taken, they can take those notes and bring them over into the collaborative document that they have. So they don't have to necessarily share the Keep notes if they don't want, but they could take their notes, and I'm gonna find one here. And they can pull them over into what they're working on in here. So as you see, I got another document and I pulled it over or another Google Keep and I pulled it over into the same document. And again, we have the text and we have the checkboxes here and they come in like that into a Google document. So that's another very valuable feature of Google Docs and that was something that was just added recently to the list of Google Keep tools in the Google Suite. One other thing that I wanna show you is that when you bring in an image in Google Keep, you can annotate over top of those images. And so I'm gonna get back to my notes over here. So this is an image that I brought into Google Docs and see how I've annotated on top of that image. Say for instance, like you're using a map or you're using something that you really wanna pinpoint some in an image. If you pull the image into a Google Keep note and then you double click on it, you will have the option up here to go in to annotate over top of that image and then you have all your drawing tools right up here. So you can draw over top of those images right in Google Keep. Now, one feature that is in Google Keep Mobile, like the mobile app, is that you can take voice notes on the mobile app and when you take those voice notes, it will again transcribe those voice notes into text. So if you're in a hurry and you need to take a note or set a reminder or something like that, you can transcribe it or you can use your voice notes to leave a voice and then transcribe that voice or that audio into text when you get to a location where you can pull it up in here. So that's another great feature of Google Keep. Now, I wanna jump back into my presentation because there are so many uses for Google Keep, not only professionally, but also within the school. And so I wanted to bring some of these or highlight some of these for you and I'm sure that you'll come up with many of your own. But obviously, to-do list, you can set a to-do list and then in the Google Keep, there is the pen tab. So if you wanna prioritize something that you need to do that day, if you click on the pen tab in Google Keep, it will pin those to the top. So if I wanna say, I wanna use this first, if I pin it, it's gonna bring that to the top and then I can organize those once those are pinned. I can say, okay, I need to do this first. So if I drag them around, I can organize them and then they'll be at the top and then you kinda have your rest of your to-do list under here and that's just that pen tab. So you can also, obviously, we talked about this a lot about taking notes, especially if you're collaborating with your peers or colleagues. A lot of times you don't have time to get together to collaborate and so you can do that right in Google Keep grocery list. We talked a little bit about that earlier. Reminders by location. You can store your thoughts and ideas. A lot of times when I'm listening to a podcast or I'm watching videos, I wanna jot down some ideas real fast because I usually do that when I'm running and so if I use the Google Keep and I record audio notes that are things that I wanna remind it of to do, I can then, once I'm done with those audio notes, I can transcribe those into text and have those as a to-do list. Create lists of common comments for grading. I love this one. This one is from Matt Miller. He said that when he was teaching, he would take common terms that he would use on grading papers and then all he would have to do is drag them over onto the paper from the Google Keep note. I thought that was a great way to save time as a teacher. Again, transcribe printed notes to text. If you have a PDF or something and you need to grab some of that text, if you pull that in as an image, you can transcribe that text. Group planning or collaborative checklist. Again, we talked a lot about that when we were looking at pulling that into Google Docs and talking about how you can invite collaborators. Mill planning with recipe links and images. That was one that was shared with me. I'm not very good at cooking or baking, but I thought that would be a great way for you to use Google Keep in your personal organization. Now, the classroom use, I just listed a few of them, but there are so many ways. Obviously, if you have shared group tasks or shared things to do, that Google Keep collaborative note is wonderful. I love the idea of using Google Keep or having students use Google Keep to track their own progress and their own goals. How are you doing? And that could also be a quick exit tool to use just a quick note and have them share that with you. It's a great journaling tool. If you find a picture or have an image and you want your kids to journal about it, you could share that, keep note with them and have them journal underneath or they could find one of their own and journal underneath and share that back with you. Peer or self-reflective process. You could use those Google Keep notes to do the I know, I think, I wonder and have them give each other constructive feedback and how to use it to create more powerful presentations and things like that. You use it as a brainstorming tool. I love the drawing feature because you can use that to brainstorm your different ideas and then you could pull it in and into a keep note of that drawing and then you could use that to work with a group of people on brainstorming tasks and things like that. A research tool. I've actually seen this used as a research tool before in a high school classroom and it was a wonderful way for kids to kind of create their own notes and then pull all the stuff together within the same or shared Google Slides because you do have access to this keep notes in the Google Slides as well. And there is an example on here for flash card reminders. If I click on this, sorry, let me go to this, sorry about that. Let me get to that, back to that. There is a link where you could use Google Keep as flash cards and how to use Google Keep to practice different skills and things like that. And so that link is in these slides and I gave you the bit lead to these slides at the beginning of the presentation. If you have any questions on using Google Keep or how to use Google Keep, feel free to contact me, Tina.Souser at esu8.org. Thanks for listening.


Is it on or off? Can we turn it up a little bit? But it's very the highest level. OK, apparently this is the highest level, so I should speak up a bit. Good morning, everyone. We start by Ichiro's lecture on CMB. OK, thanks. Is this the song? Yeah, can you hear me? Good. Welcome back. So let's continue on the CMB. We remind you the power spectrum. So you do the spherical harmonic transformation of the sky. You decompose sky into hot, cold, hot, cold, that equals two, things like that. Coefficients depend on the coordinates, whether you pick the galactic north pole as the origin of the polar coordinate, or ecliptic coordinate, or solar coordinate, right? But so ALM values change with coordinates, but the squared amplitude averaged over m would not depend on the coordinates. So it's a rotationally invariant quantity that's super convenient. Moreover, this gives you the measure of the amplitude of the temperature power spectrum, temperature on a solar piece, because it's a variance. And indeed, you calculate the variance of the CMB, namely, you square the temperature fluctuation value at the given position. You average over the old sky. You can relate that to the sum of power spectrum multiplied by 2L plus 1. And per logarithmic interval, let's say, per logarithmic L, you multiply the whole thing by L, then this L times 2L plus 1 times CL divided by 4 pi measures the amplitude in terms of Kelvin squared, the amplitude of fluctuation that's available at the given angular scale. I remember that the L is approximately, not exactly, related to the angular scale, angular separation in the sky that's pi over theta. That's exact for L equals m. It's approximate for other m's. So that's the central quantity that we're interested in. And it's observable. So that's the measurements from the Kobi in 1996. This is a four-year results. And the first thing you find that there are significant detection of these data points above zero. So this gave the Kobi team the Nobel Prize, first discovery of the aerosol entropy in the cosmic micro background. Second thing that got people excited is that it's more or less independent of L's. So it's so-called scale invariant spectrum. And this is a prediction of inflation that will be the subject of the lecture next week. So these measurements should be related to the three-dimensional power of the gravitational potential phi at the last of scattering. So let's figure out the relationship. But it's consistently scaling invariant. There's no obvious scale dependence. It doesn't go like that, it doesn't go like that. So let's remember gravitational anisotropy for adiabatic inertia condition. Delta T over T is equal to 1 third of phi. Phi is negative in over-dense region, so you will have a cold spot in over-dense region. That's what we learned yesterday.  Then you get this complicated formula. You have a three-dimensional Fourier coefficient of phi. Times spherical best-seller function that people hate. This will give you the projection from k-space to L-space. And we learned using flat-scapric emission, what this actually means. Geometrically, I'll get there later as a reminder. So all you need to now do is to just square this, right? That's the definition of CL, and that's the result. And this relates what we observe as seesaw else to the product of gravitational potentials that are actually out there at L-scattering surface. In other words, we live in our universe and we have our own L-scattering surface. But if you go to, let's say, galaxy in the future or galaxy somewhere else out there, they have different L-scattering surface, so they will see different potentials. Are we interested in knowing really what the gravitational potential in our universe is? Answer is probably yes. But if you wanted to compare that measurement to the theoretical prediction, then you are in trouble. Because theoretical predictions don't really tell you what exactly fluctuations are created in the given particular point. And in fact, this is a fascinating thing because, for example, Einstein didn't, although he was one of the founding fathers of quantum theory, he disliked it. And he famously said, God does not play dice with the universe. Namely, quantum mechanics is a random process and he didn't like it. Probabilistic approach is something he didn't like. But as you learn next week by the professor Clemens' lecture on inflation, now we think that the initial condition of fluctuations came from quantum processes. Indeed, God loved playing dice with the universe. Basically, they were like, OK, here, this position, throw dice, OK, under dense region. There, throw dice, OK, over dense region. Good. OK, if the initial conditions were like that, there's no way you can predict this value at the given position in the space. So what do you do? You instead take the ensemble average. Assuming some probability distribution of phi, let's say Gaussian, you take the average of this. Then you have the, let's say, you take the average of the product of the phi. Let's write this. Now that's called power spectrum, three-dimensional power spectrum of phi. But let's try to understand this better. It's always useful to go to real space. So we inverse Fourier transform this phi to this real space phi, OK, just a Fourier transform. And this average of the phi at the two different locations separated by position r is two-point correlation function in the configuration space. Now, this quantity depends on x location in the universe and separation from it. If you assume universe does not have a preferred location, all the locations are equal in the universe. There's no center of the universe. There's no preferred location. Then this quantity should not depend on x. The major correlation functions there, correlation functions there, correlation functions there, they should all be statistical equivalent. If you assume that, you can integrate over x, disregarding this.  So this statistical homogeneity requires that this correlation function in Fourier space is zero if wave vectors are different. This is purely the consequence of statistical homogeneity. And we now define, OK, now that's fine. But still this quantity still depends upon the direction of q. Now let's further assume that this quantity does not depend on the orientation of the separation. You measure correlation function this way, you measure correlation function that way, or that way, it shouldn't matter. This is something you should test, however. You should remember, all of you remember that. I'm pretending that this is true without testing it. But trust me, we have tested statistical homogeneity, statistical isotropy using the data as well. And all the data that we have today are consistent with the notion that the correlation functions are invariant under rotation or positions. Once you assume that, then this thing here does not depend on the direction of q anymore. Depends only on the magnitude of q. This is what we call the power spectral. So this relationship is a generic relationship for statistically homogenous and isotropic fluctuation fields. So this is what we can predict theoretically. So now we have this nice relationship between the ensemble average of power spectrum we see to the ensemble average of the power spectrum of the gravitational potential. But once again, this involves this nasty Bessel function that everybody hates. So let's do the same thing in a flat sky. And you relate this power spectrum to the power spectrum. But now it's apparent that this is the perpendicular part of the wave number which is exactly equal to L over RL. So let's remind ourselves what this actually means. So you have the gravitational potential that's going up to the z direction. In the x direction, you have the cube perpendicular, that's perpendicular to the line of sight. This is where half wavelengths can be related to theta in a straightforward way. Distance to this, the surface is RL. Angle is given by just geometry. So this will give you L equals Q RL. But here, that's not the case. Angle is broader, greater, or L is smaller. So that's reflected the fact that this thing corresponds to that here, this part. And then the whole thing, which is greater always than this thing, corresponds to this. Is that clear? So we have a nice geometrical relationship. Good. OK, now let's plug in theoretical expectation for P here. Inflation predicts that this P is a power law with some power index n. And for historical reasons, we parameterize this P as Q to the n minus 4. When n equals 1 is scaling variant. And I'll show you how that works. So let's plug this into this formula here. And you get CL of zaxolife, which is proportional to L to n minus 1 power. And it's 1 over L squared here. So you multiply both sides by L squared. L squared CL, that's the variance. Remember, that's the variance of the temperature at the given scale. Is L to n minus 1 power? When n is 1, it's independent of L. This is what we call scaling variant spectrum. And inflation predicts n that's close to but not exactly equal to 1. And finding this n less than, and more of our many inflation models predict n is less than 1. Finding n less than 1 has been the dream of a cosmologist for many years. And WNAP team achieved this in the late 2012. And Planck team confirmed this result in four months later. So, right? We're very proud of this. So I have to say this. Finding this has been really the dream. If you take n, n equals 1, then you get this formula. And in fact, if you use the flat to sky formula here, you get 1 over L squared. But you plug this into this formula, and you can integrate also analytically, and you get plus 1 here. Otherwise, it's identical. So the difference between full sky and flat sky is just plus 1. So the nasty vessel function gives you plus 1. Of course, flat to sky works only when L is much greater than 1, so everything is consistent. n is 1 plus 2 plus 1 is 0.3. That was what the code is all. It's consistent with scale invariance. Therefore, people are very excited. Now you go to WNAP. What? It's not parallel, right? And Planck, it's not this. Any parallel wouldn't fit the data. Why? Because what you see here is not gravitational effect. It's a hydrodynamics effect, OK? It's a sound wave. It's not just relativity anymore. It's general relativity anymore. So does everybody know what this is? This is called miso soup. It's a signature Japanese soup. It's made of soy bean paste. And this is something called tofu that's also made of soy bean. So as you can see, Japanese people love soy beans. This soup is not transparent. It's opaque, just like CNB. And when universe is hot and dense, and everything is ionized, photons constantly scatter with electrons. The universe is opaque. And this system, as I show you later, this system behaves as a fluid. Photons are not fluid. Photons freely propagate. But if photons scatter with electrons, they cannot freely propagate. Hence, they behave like a soup. And now he throws tofu into the miso soup. It creates ripples. But how exactly these ripples are created? And moreover, how fast they damp depends on the composition. How much miso do you have? So perhaps it's really like a miso soup. And this is a viscous fluid in which the amplitude of sound waves damps at the shorter wavelength. Analogy to miso soup really works, and I love it. And usually, when I give this kind of lecture at the different countries, I try to find a soup that, in that country, that also works. But I never found one. Potato soup in Germany is too viscous. And if you put potato in, nothing happens. So miso soup works, always. The cosmic background radiation is the wall at the edge of the visible universe that we cannot see directly the further past beyond this wall. But these temperature fluctuations may tell us what happened in the further past. The conditions beyond the wall of the cosmic background radiation could be thought of as a liquid with high temperature and high density. You could say it was like a hot soup. Something happened behind this wall that made waves, which can be seen in the fluctuations in the cosmic background radiation. There must have been a grand sound that shook the universe. We're in a great deal about the universe if we can extract this cosmic sound. The origin of the sound would be the moment of the birth of the universe. Yeah, so you put some initial condition, sound waves propagate. And that's what we're going to study. When do sound waves become important? When, in other words, when does the Zaks-Woffel effect formula, gravitational only, will break down? Key to the answer is the sound crossing time. Let's say your sound waves with some sound speed, you integrate over time to get the distance that's traveled by sound waves. If your length scale or angular scales becomes comparable to or smaller than the sound of crossing time, you cannot ignore pressure, hence sound waves anymore. So as the warm-up, let's look at the horizon, namely the distance that's traveled by photon. From time 0 to some time t, you integrate the geodesic, the shortest distance that's traveled by photon. That would be the four-dimensional spacetime distance. And you set that equal to 0. That can relate then radial coordinate, in Cartesian coordinate, sorry, spherical coordinate, to the time coordinate. You integrate, then you get this as the answer. That's the distance that's traveled by photon. You now replace speed of light with a time-dependent speed of sound. This would be the sound horizon. And sound waves cannot be ignored if wave number times sound horizon rs is greater than 1. That's a criterion I'm going to use. Let's calculate the sound speed. And something neat happens, by the way. So I'm going to give you sort of physical argument why sound speed should be a certain way. And then later you discover that this automatically comes out after playing with a couple of equations. So that's very nice. In fact, I'm doing this only to understand the equations that come later. So let's begin. By definition, sound waves is the wave whose restoring force is pressure. You perturb some medium, then pressure tries to push you back, then oscillates, and this thing propagates. As a result, what you need to calculate is the response of the pressure given the density perturbation. There was a p over the rho. This has a unit of velocity squared. So this will be the definition of the sound speed squared. Now we are talking about a system that consists of variance and photons. Ignore dark matter, because they do not scatter photons. They do not participate in sound speed. Or neutrinos, let's ignore those. We just consider photon and variance. Maybe I should say also, now variance, what do you mean by variance? Protons and helium nuclei. Do they scatter light? They actually do. But not very efficient. But electrons scatter photons very efficiently by Thomson scattering. Electrons also scatter protons and helium nuclei very efficiently by Coulomb scattering. So by using electrons as a catalyst, photons and variance are tightly coupled. So that's what I mean by photons interacting with variance. Energy density has both photons and variance, but pressure, the baryonic pressure is not zero, but it's much smaller than the photon pressure. Photons has an enormous pressure. It's actually one-third of the energy density in the photon. That's enormous. Sound speed of the baryons would be smaller. That's in fact what we're going to calculate. All right, now we have this idea of a relationship, okay? So as a reminder, what is the idea of a take? The ratio of the number of densities in photons and variance is independent of space. Now you can relate number density of photons to energy density photons in this way. And number density perturbation in baryons is the same as mass density perturbation or energy density perturbation. That's the relationship, that's the idea of a relationship. And you plug this into this formula, you discover that the sound speed is one over square root of three times this factor R that depends upon the ratio of the baryon energy density and photon energy density. And this is neat, okay? So relativistic fluids. Once again, relativistic particles are not actually fluid, but if they are coupled to matter particles and still, but still behave like relativistic system, equation of state is the sound speed is one over square root of three times speed of light. But this system that consists of baryons and photons has a reduced sound speed, okay? So in a way, it's a dirtier system. Your pure relativistic fluid has a sound speed of one over square root of three times three light. You put dirt in it, baryons, dirt. That's sound speed will be reduced. And this automatic kind of comes out later, which is very neat. So let's take a note of this relationship. It's about one. And, but this is the baryon density which goes like one over volume. So it's one over scale factor cubed, one over A cubed. Photon density loses energy as the universe expands. So this goes like one over volume over A. So it's one over A to the force power. So this ratio actually grows with A, which means this ratio of unity at the epoch of lots of scattering, but this would be very small quantity in the earlier universe. In the radiation dominated universe, this quantity is negligible. And we're gonna use that later. And once again, my slides are available online. And in fact, if you go to the school website, my slides are already uploaded there in the program as well. So you don't have to take, you don't have to write everything. Don't waste your time. Just write directly on the slides or just take a memo, small memo, and then compare to the slides later. So I can not calculate, given that I know the R, I know the sound speed and hence I can calculate the sound horizon. And that's 145.3 megaparsec. And if you plug this into this formula here, so q R s greater than one would be the region where sound speed wouldn't be ignored. L is roughly speaking q times R L from geometry. Then L should be greater than 100. So if you go to L that's greater than 100, for sure you cannot ignore the sound waves. So let's look closer, look at creation of sound waves. Usually if you read textbooks, you have to deal with Boltzmann equation. And many people just give up there because it's so complicated and it's not intuitive. So I'm not gonna use Boltzmann equation, okay? If you wanted to play the Boltzmann equation, read Weinberg's textbook and I'm going to tell you how it actually works physically. There are four things you have to use. One is every physicist's friend conservation equations. Energy conservation, momentum conservation, okay? You have to obey those always. Then you need to relate pressure to density. This is something called equation of state. You have to specify that otherwise equations do not close. You need to also relate how energy density is related to the gravitational potential. In a non relativistic limit, that would be the Newton's equation, the Poisson equation. We use a general relativistic version of it, namely Einstein's equation, relating potential to density. Then you also need to know the viscosity. Remember miso soup, you drop tofu in it, repose them. You somehow have to take into account the fact that it's a viscous fluid, not the perfect fluid. You need to know four of those things.  This looks complicated, but once you understand it, it's no longer complicated, okay? And what did I do here? So you learned yesterday the conservation of stress energy tensor, this T mu nu derivative of that will give you conservation equations. This is the conservation equation, one of the conservation equations you can derive from this T mu nu, stress energy tensor, but this has a very nice physics understanding too, so let me walk you through. First of all, this alpha here is the element. It can be variance, can be photons, can be neutrinos, can be dark matter. If you sum over all elements, then right-hand side should always be zero because energy has to be conserved. If there is no energy transfer between elements, then you can drop this sum and energy density will be conserved separately for photons and variance and dark matter neutrinos. That's indeed the case for my lecture, so let's take that for granted, okay? And if you apply this to the homogeneous equation, homogeneous background, not perturbations, you get this thing here, that which you actually have seen from Professor Sheth lecture yesterday, this will be the conservation equation in the homogeneous background. This tells you how energy density changes. If you plug in, for example, p equals zero, that would be for the matter density, then rho goes like one over a cubed because you have here three a dot over a here. If you have relativistic fluid like photons, p will be one-third of rho, hence this would be four-third of rho. You multiply by three, you get four a dot over a times rho, so rho goes like one over a to the four, right? So that's what we already used previously. Now you perturb it, and first thing you see, I hope you agree it's just a delta rho, perturbation rho, this bit is that, okay? That's fine. This is viscosity. This viscosity is here because this pressure is the diagonal element of the stress energy tensor, and there's a correction to the diagonal element of the stress energy tensor from viscosity too. That's why you have viscosity right there. And there's a special gradient because of just how I define the viscosity here. This will be the second derivative of the pi. This will be, if you like, potential for viscosity. This delta u is a velocity potential. Spatial gradient of the velocity potential will be velocity, okay? Let's understand one by one. This, where does that come from? So this is actually the same effect as that one. Go back, right? You have A here, but as I told you when I was describing gravitational and isotropic piece, A has to be corrected by perturbation because the spatial part of the perturbation, spatial part of the metric has this e to the minus two psi here. There's a curvature perturbation. Four tons, we'll see the local scale factor that's including also e to the minus psi. And this is just that. If you have this, you have to have that too. That's it, okay? This one, if you are familiar with this conservation of the mass in the non-expanding medium, that's that, okay? What does that mean? When velocity is going away, if you have a sphere and velocity is going away, there's a velocity divergence that's positive, density goes down, right? Of course, because particles are escaping from the sphere. If particles are coming into the sphere, velocity divergence will be negative. Therefore, you get an enhancement in the density. That's what that is, and that's exactly the same. Once again, delta u is a velocity potential, so gradient of this is the velocity, and you have additional spatial derivative, that's the divergence. You have rho plus p instead of rho here, because in general relativity, pressure also contributes to inertia. In fact, it's an interesting thing. Let's say you have one gram of matter and one gram of photon, okay? U to conversion equals mc squared convert energy to mass. In terms of inertia, in terms of momentum, one gram of photon has twice, not twice, this one third, right? So p is one third of rho, so four third of rho, okay? So one gram of photon has four third gram of momentum, equivalent momentum for matter, doesn't make sense, it has more momentum because of pressure here. Momentum conservation, this looks a bit complicated, but it's actually even simpler than mass conservation. This simply tells you that if you have a moving particles, they slow down in the absence of external force in expanding universe. Your velocity, matter particles are going with some velocity, that velocity goes down by one over a, cosmological latitude, it's just that, okay? This, now remember that the delta U is actually, once again, velocity potential. Velocity is a gradient of that. If you apply gradient everywhere, this is the gradient of the potential. So this is Newtonian force. Just, you know, the force gives the kick to the fluid. Gradient of the pressure part of the pressure gradient force. Right? This is just gradient of anisotopic stress, gradient of viscosity that also gives you the force. So this is really the same as any other fluid equations you might have learned in the physics courses. Just you apply this to, apply this to expanding background and generativity so that you pick up extra P pressure in the momentum. Yes? So yeah, let me repeat then. This is the velocity potential. Velocity is the gradient of that. So if you apply gradient in both sides, you get velocity dot in the potential gradient and pressure gradient. Yeah? Equation of say. So so far we have this evolution of density, evolution of pressure, but it's somehow you still need to relate P to rho, okay? Oh, and another important thing. Here again, only when you add all the elements in the universe, right down side of this equation is zero. So total momentum is conserved. But for individually, however, unlike for energy conservation equation, photons and variance exchange momentum by Thomson scattering. So you cannot apply this formula individually. You need to add momentum exchange between photons and variance for individual things and we'll do that later. All right, equation of state. So let's take the pressure of variance and dark matter to be zero. It's a very good approximation for cosmology on a large scales. Both pressure perturbation and mean pressure would be zero for variance and dark matter. For the mean pressure, relativistic fluid have the equation of state of one third. So P is rho background one third, P rho background one third.  You have to correct the pressure by viscosity too. So that's the relationship where does that come from. So this for advanced participants who studied generativity before. Definition of the, let's see. So any relativistic fluids have the trace of stress energy tensor that vanishes. Any relativistic particles have zero trace for source energy tensor. And if you plug in, the T00 would be density and trace at Tij would be pressure and sort of stress by definition. So you take the trace of that, you pick up three because each diagonal element of T contains one piece or sum of it, you have three. They have a derivative of Tij would be two derivative of phi. You sum over i and you get two derivative becomes Laplacian, that's why you have this. So this is basically the consequence of the fact that these two things are relativistic. Just a small remark, it's not very important, but to get the right answers, you need to do this. So I said this already. In the standard Cosmos scenario, energy densities are conserved separately, but momentum densities are not conserved separately, especially photons and variance. Let's simplify the equations and now we go to Fourier space, yes? Angular momentum. Yeah, so angular momentum is a vector perturbation. Right, it's like a, it's like a vorticity, okay? Scalar perturbations do not have angular momentum because velocity can be written as spatial gradient of a scalar function. So in fact, that's an excellent point. This is a velocity potential. We said velocity can be written as derivative of this scalar function. Angular momentum cannot be written that way because this has zero curl, right? Very good question. For scalar perturbations, we don't have angular momentum. So let's rewrite this conservation equation of energy in a compact form like this and go to Fourier space of the Laplacian becomes minus q square for photon, for variance. This is momentum for photons, momentum for variance and variance do not have velocity, the pressure gradient, so this is zero and it doesn't have an assortment stress either. This is zero. That's why this and that look like that. And the difference here has to do with the cosmological redshift difference of the variance and photons. Here is the momentum exchange. Let's understand this. Sigma t is a Thomson-Scattern cross-section and it is a number density of electrons. So in the absence of Thomson-Scattering, right-onside is zero as expected. If there's no free electrons, right-onside is zero also. Very nice. And of course, you can understand this. If velocity of variance is faster than velocity of photon fluid, we want to accelerate. Photons want to accelerate to catch up with variance velocity. If variance are going slower than photons, then photon velocity wants to go down to sort of catch up with the variance. Just a consequence of momentum conservation, momentum exchange, variance and photon want to go at the same speed. That's all that is. Okay, good, and you have R here because you need to make sure that total momentum is conserved. So you multiply both sides by R and sum the left-onside, you get zero here, right-onside, because total momentum has to be conserved. Is that clear? So far, all we have done was to write down energy conservation momentum conservation equations, okay? That's all we have done. What about photon viscosity? So we haven't talked about that. To get this, you actually need to solve both migrations, which you are not gonna do. Instead, we rely on the knowledge of the fluid dynamics, okay? But I repeat, photons are not the fluid, okay? They free stream. Neutronals are not the fluid, they're free stream. Only when they are coupled to electrons and electrons prevent them from moving straight, they behave like a fluid. But this coupling is not perfect. If this coupling is very, very tight, then you don't have viscosity. It's a perfect fluid. But when photons and electron velocities displace from each other, they no longer behave like a perfect fluid and you have a viscosity. And when photons and electrons are not coupled at all, you don't have a fluid. So forget viscosity, forget everything. It's not a fluid. It doesn't even make sense to talk about viscosity here, okay? All right, but frequent scattering photons variance will give you photon variance fluid, effective fluid, single effective fluid with a viscosity, also known as a miso soup. Here is a miso soup, okay? Variants are miso. Let's solve this equation. Let's do the tight coupling approximation. Namely, two velocities are basically the same, okay? So when you have, this d is some dimensionless variable that you don't have to worry about. It's one over sigma t times Na. So in the limit of very, very tight coupling, Na is very large, this difference goes to zero. So we're going to take the limit in which sigma t and Na is go to infinity. Then you can take this, you have to do these two equations. You eliminate d, then you get this equation here, okay? Good. Now I still have velocity here. I'm going to use energy conservation, energy conservation to replace photon velocity with the derivative of the energy density. It's a sound wave equation, okay? Why is that? You have the second time derivative of density. You have a second time spatial derivative, it's q square here, of the density, times sound velocity square. That's wave equation. It looks a bit complicated simply because you have the a here and there, and you have gravitational potential here, but it's a sound wave. If you see them now, if you now take the limit in which, oh, by the way, let's see. Let me, good, yeah, okay. So this once again, this is what we got from tight coupling in momentum. This is what we get after replacing this with the photon density using energy conservation. And you get some complicated thing. And you have here the term that has q square source, Laplacian, times density divided by three times one plus r, okay? All we did was to combine energy conservation for protons and variance, a momentum conservation for protons and variance. We have now single equation that describes photon density perturbation with reduced sound speed. Remember that the photon fluid has a sound speed of one over three square root. Here we have one plus r, automatically. And this is exactly what we got from the heuristic argument using the Cs square equal to delta p over delta rho, right? Conservation equations know about that. We automatically get that. And then now we take the limit in which, which is goes like a, and phi, which also evolves in the cosmological time scale, psi, which is basically same as phi, and r, yeah, and a, also evolves like a cosmological scale. We're gonna ignore evolution a or phi or psi compared to the frequency of our perturbations. Q is much greater than the change of the time, change of the time scale of the change of these other variables. Then we can simplify the equation, and that's really the wave equation. Solution is cosine sine. And we have some displacement due to phi gravitational displacement times r. This is the ratio of the baryon density and this becomes important later, but let's ignore this. Let's sort of appreciate, you know? It's a sound wave. You have coefficients a and b which need to be determined by initial conditions. You don't know what these are a priori, okay? If you impose adiabatic initial condition, certain values of a and b are chosen. But you don't know these are a priori. You need to determine them from observations, okay? So photons are not fluid, but tons of scattering makes them like a fluid, the photon baryon fluid, or it's miso soup. Reduce the sound speed, emerges automatically, it's really beautiful. Now, delta rho over four rho is in fact equal to delta t over t, temperature, and that sort of thing, because rho photon goes like t to the four. So delta rho over rho is four times delta t over t. So delta t over t would be equal to delta rho over rho over four. Remember that at the Lasker scattering, there's a delta t over t, but what we observe is the red shifted one. So delta t over t plus phi is what we observe. This is what we observe. We observe the sound speed, sound waves. RS is the sound horizon at the Lasker scattering surface. So when I was a graduate student at the Princeton University in year 2000, this is what we've got, okay? It's a sound wave already here. Very, very exciting moment. And if you change baryon density, peak changes. Why? How? We're gonna learn that tomorrow, okay? We learn more than necessary how the past problem depends on cosmological parameters tomorrow. So be prepared for that. But it's good to sort of step back and think about what we have done. Some initial conditions drop stones, okay? Then sound waves are emerging with reduced sound speed, and that's what we observe. But what are the stones, okay? I mean, who dropped them, first of all? The answer is actually nobody dropped them. They quantum mechanically emerged, right? That's the stone. You're gonna learn that next week. Another concept you have to know. Professor Schach sort of said that yesterday, but it's so important that I have to repeat it, okay? It's a tricky concept, but bear with me. Okay, suppose that you have fluctuations at all wavelengths. Inside the Hubble lengths, horizon, inside the horizon, or outside. Let's not ask how these super horizon fluctuations are generated. Let's ignore how that happened, because it sounds so counterintuitive. But next week, Professor Klever will tell you how that happened. As the universe expands, Hubble lengths, or how the horizon grows, faster than stretching of wavelengths. So you can see more and more, longer and longer wavelength perturbations. Well, it's like you get confused. But let me just say, let me rephrase this in some trivial manner, okay? It's just that as you wait more, you can see more of the universe. That's all, okay? The perturbation outside of our horizon now, you wait longer, you see more, more, more, right? But from fluctuations point of view, super horizon fluctuations now enter the horizon. Okay, that's a jargon, and that's a diagram. So let's take some physical lengths of given fluctuation. Let's say, this will be the fluctuation, whose wavelength is 10 gigaparsec today. This is today, okay? And fluctuations are stretched linearly by scale factor. Scale factor doubles, length doubles. But our horizon grows faster than scale factor. So if you wait more, this one megaparsec fluctuation enter the horizon here during radiation error. This is the time when matter and radiation have equal densities. These perturbations enter during the radiation error. This enters later. This entered at the radiation matter equality. That will be 100 megaparsec today. This entered, oh, sorry, what did I say? I can't read this. This is 100, that's 100 megaparsec, yes, that's right, yeah, and so forth, okay? And this fluctuation enter the horizon during matter error. Now, what do they do? Let's see, yeah. This is like you have a miso soup. And fluctuations enter into miso soup, okay? And create ripples. If fluctuations are outside the horizon, they cannot do anything to sound because that's much greater than sound crossing, sound crossing, sound horizon, okay? This is a photon horizon, so it's even bigger. So you have a situation where you have the cosmological fluid as time goes by, new fluctuations just keep coming in and perturb.  This is like an orchestra. They are synchronized because they come in at a constant rate, one person comes in, bam, another person comes in, bam, bam, bam, and they're all synchronized because they're coming in a constant rate, yeah? Does that make sense? This is a picture you need to have in your mind. Part of the picture is coming inside the horizon, complicated, but just think about the drum, coming, bam, bam, bam, bam. Then when, you know, on super-horizon scales, only gravity is important, but in sub-horizon, but super-sound-horizon scale, so it's greater than sound-horizon, but less than the photon horizon. Then still gravity is important, but the evolution is similar to Newtonian, and sub-horizon scales hide all dynamics is important, so when people come in and say, bam, sound waves are propagated, that's the picture, okay? So, which fluctuation entered the horizon before the meta-radiation equality? The answer is, in terms of key value, that's 0.01, mega-parsec inverse. Well, in terms of the L, it's 140. So, basically all of these peaks correspond to the fluctuation that entered the horizon during the radiation era. These are, bam, during the radiation era. Okay. Now, why do you see these oscillations? This fluctuation entered the horizon before, oscillates, and ends up being here at the Lusso-Scatani surface. This fluctuation entered the horizon later, bam, oscillates, and ends up being here. Reason why this is different from that is that this fluctuation entered the horizon earlier, so it had more time to oscillate, right? So these are all patterns, you know? Doesn't make sense? Okay. So what determines the location of peak heights? Does the sound web solution explain it? Let's take a closer look. So this is a high frequency solution when you are deep inside the horizon. Q is much greater than A times H. And, let's see. So very roughly speaking, Q is L over RL, okay? Using this geometrical relationship, we encounter this a few times. Left-hand side squared would be the power spectrum, okay? What about A and B? For idea of the condition, in fact, A is much greater than B, so let's take that for granted. We will show that later, okay? So let's take cosine. Square this. Then, and Q is L over RL. Therefore, L, peak locations would be given by this QRS. When QRS is pi, you get the large value. Remember, we're squaring it, okay? So pi at RL divided by RS times one, two, three would give you the peak locations, yeah? So it would be 300 times one, two, three, four, five. Let's compare this to what we observed. That's a prediction, that's actual peak location, and they do not match. If you actually heard lectures on C and B of a similar kind before, you might be surprised, because you should have heard that this is exactly the same as peak locations. That's not correct, okay? Lecturers said that because they probably didn't have time to explain it. I have time, so I'll tell you why they are different, okay? This simply comes from the fact that you are not really in the high frequency regime here. This deviation from high frequency actually gives you the mixture of cosine and sine. Adiabatic solution selects cosine only in the very, very high frequency regime. If it's not very high frequency, there's a mixture. That's the reason. So let's take a better solution. And let's go to the radiation-dominated error. So this is the original equation without any approximation except tight coupling. In the radiation error, R is much less than one, so we can ignore R here, okay? We can ignore R, but we don't even know anything else. Let's also change the independent variable from the time to phase given by QRS, because we know that there will be a sound wave solution whose argument is QRS. So let's use that as an independent variable instead of T. It's just a matter of convenience. Then this equation simplifies greatly to that. Looks like we can solve this. This X here is a delta rho gamma over four rho gamma minus psi, that's argument here, okay? And also taking the approximation that psi is equal to five. Which is not exactly right, but it's good enough for getting the understanding, all right? Looks like we can solve this. Indeed, you can solve that. That's the solution. So cosine, sine, but then you have the term that's coming from the evolution, time evolution of phi and sine, okay? That's the solution. Or if you go back to, let's say, high school math class learning trigonometry, you can combine cosine and sine to have, sorry, no, I didn't use trigonometry yet. I just, sorry, no, I didn't use.  If you do that, I can basically let it be absorbed by first two terms, just change the coefficients, and you get that, okay? So delta A is like that, delta B is like that, okay? So now we have cosine and sine. Now, in order to get phi and sine, we need to relate these things to perturbations of the density. Now we have to ask Einstein to help us. Einstein's equations look like that. And remember that Poisson equation in Newtonian limit didn't have this term. Why? Because in Newtonian gravity, momentum does not contribute to gravity. But with generativity, it does. And momentum also contributes to gravitation potential. That's why you have this correction. And you have all the other things. For example, this phi and psi are not exactly equal due to viscosity.  But neutrinals are not fluid. So neutrino will make phi and psi different. We'll come back to this later. But for now, let's ignore this. And the phi is equal to psi, just to simplify, okay? Now if you use this equation, then the equation we had before becomes something like this, even simplify further, okay? With this, it gives you that. This is a non-adiapatic pressure. This is where initial conditions come in. If you have an adiabatic initial condition, this is zero. So let's ignore this. Then this is a solution. For adiabatic initial condition, gravitation potential during radiation error is a constant in low frequency limit. So in a longer wavelength limit, gravitation potential is constant. But if you go to high frequency, shorter wavelength, gravitation potential decays. Why is that? It's simply because there are many, many explanations you can do. One way to think about that is that we have density perturbations. They try to cluster, but the universe expands also. So there's a competition as Professor said yesterday. If the expansion rate is faster than the gravitation on collapse time scale, you cannot grow. There will be explanation why matter density perturbations cannot grow during the radiation error. But here, the energy density perturbations are dominated by photons, so you cannot use the analogy. Instead, what happens here is that the photon density perturbations don't collapse. They oscillate, but they do not collapse, because they have too much pressure. Therefore, universe expansion simply let the potential decay. That's what happens inside the horizon. You can actually derive this relationship, although we have done something complicated. You can intuitively understand that by, because we are deeply inside the horizon, you can suddenly use Newtonian Poisson equation, except that you have to take into account the fact that the delta over rho oscillates, doesn't collapse. Delta over rho times rho. Rho goes like one over eight to the four, so a squared, one over eight to the four is one over a squared, that's what you get. Inside the horizon, gravitation potential decays. What is this data? So let's define this data here, which I secretly put in here. This is the initial condition. It's even better, it's a conserved quantity. And you probably encountered this data many times next week, so let me give you some preparation for that. Gravitational potential is independent of time during radiation error in the super horizon scales. Similarly, gravitation potential is independent of time in super horizon scales during MATA error, but it changes the value from radiation error to MATA error. So it's not the conserved quantity. This data is conserved regardless of content of the universe. It doesn't matter if MATA dominated, it doesn't matter if radiation dominated. Let's get that from this energy conservation equation we already written down. Except we are ignoring the pressure, we are ignoring spatial derivative coming from velocity, okay? There's no velocity term here. We're taking the super horizon limit. Q is much smaller than H. And once we say adiabatic initial condition, which means pressure, so adiabatic initial condition, I said energy density ratios is independent of a space position. Actually, you can also show equivalently that adiabatic initial condition means that the pressure is the only function of rho, okay? Pressure is the assault function of energy density. If you do that, then you can integrate this equation once to get this. There's no time derivative because we integrate it. And this is the integration constant, which depends only on X. This is the conserved quantity. And for adiabatic initial condition, this delta alpha is independent of species. So everybody, all the elements, volume, photon, neutrino, dark matter, they all share the same value for this combination. That's the initial condition. And it's conserved. It's a very convenient quantity. That's why when people working on inflation calculate primordial scatter perturbations, they calculate this quantity with this ambiguity, okay? This is conserved quantity. All right, so this is a solution. So we now got the solution. X is delta rho over rho, four rho minus psi. And that's a solution. And now we have this correction factor delta n delta b here. It's all given by that. And in the low frequency limit, the longer wavelength limit, this goes to zeta. And if you look at it, so this essentially sets this a tilde and b tilde in integration constants. So if you take phi much less than one limit, this survives and this is phi square. But in this low frequency limit, this goes to psi at zeta constant. Doesn't depend on time. Which means that this term should be zero. And this term should be zeta, okay? So this means that the adiabatic solution selects cosine, not the sine, okay? For this combination. Now you're plugging all these things here into equations. Then that's the final answer. So that's the answer. Delta rho over four rho minus psi is zeta minus cosine is a phi plus two over phi sine phi. In the high frequency limit, it's much greater than one. So this is negligible compared to cosine. So it's a pure cosine. But only in the high frequency limit. If phi, so if phi is about unity, that's the scale comparable to sound horizon. Then you have a mixture between phi, cosine and sine. That's why you get shift in a peak position from the naive cosine term and you go to the left. You can trace this basically to the time dependence of gravitational potential. Because during the radiation era, gravitational potential is not constant inside the horizon and this is responsible for this mixture of cosine and sine. Now let's take the viscosity. Let's see. Good. There are two viscosity, one is coming from neutrinos, another is coming from photons. Let's look at the neutrinos. Neutrinos change relationship between phi and sine. That gives you the important effect. So initially, before already, we sort of made phi and sine equal. That's how we solved this equation and got some factors. This is without neutrino, we've seen this already. Once we include neutrinos, then a solution picks up extra terms. And these extra terms do not vanish in the high frequency limit. So this delta B, delta A, pick up non-zero values in high frequency limit. Remember that previously, coefficient of sine phi was one over phi, so it vanishes in high frequency limit. If you add neutrino viscosity, this doesn't vanish anymore. This R nu is an energy density fracture in neutrino. That's 40% of total radiation. So it's not small. It's not a small effect. Now let's do this cosine A plus B is cosine A sine B minus cosine B sine A. I hope I got it right. Then you can absorb this into a phase shift. Amplitude changes also, and phase also changes. So amplitude is reduced due to neutrino effect and phase will be shifted from the case without neutrinos. So these are pretty distinct effects of neutrino viscosity, which you can use to detect cosmic neutrino background fluctuations. Neutronals affect, cosmic neutrino background affect expansion history. By the way, what is cosmic neutrino background? We all know cosmic micro background. You heard enough about it. How many photons are there per cubic centimeter? 410. Neutronals, cosmic neutrino background, they also came from fireball universe. They are 336 neutrinos per cubic centimeter. And I told you that CME photons are most numerous particles in the universe. Neutronals are second most numerous particles in the universe. There are a lot of them. They certainly affect the mean expansion history, but they also fluctuate because they're free stream too. Using this change in amplitude and changing phase shift, we can now detect fluctuations in cosmic neutrino background without ever detecting neutrinos directly. You can see the gravitational effects of neutrinos on the cosmic micro background. Why gravitational? Because the only thing that the neutrino does is to change the relation between phi and psi. That's gravitation. It's a Newton's, it's Einstein's equation of effect. So neutrino viscosity will reduce amplitude of sound waves at large multiples and shift the peak positions over the temperature power spectrum. I'll come back to this tomorrow. And photon viscosity, this will damp the fluctuation but I'm out of time now, so I'll do this tomorrow as well. Okay, I'll stop here. We reconvene at 11.15. Yeah. Coffee break.


Hello, in this lecture, we're going to talk about the process cost system. At the end of this, we will be able to define the process cost system, list the accounts involved related to inventory, journalize the activity related to the production of inventory in the process cost system, support accounting instruction by clicking the link below, giving you a free month membership to all of the content on our website broken out by category further broken out by course, each course then organized in a logical, reasonable fashion, making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files, and more like QuickBooks backup files when applicable. So once again, click the link below for a free month membership to our website and all the content on it. First, let's take a look at our trial balance. We have our trial balance over here. The debits represented with no brackets credits having brackets, debits equal the credits by the debits minus the credits equal and zero. We have the assets and green liabilities in orange or yellow and then the lighter blue or the equity account the darker blue or the income income is here added up to a loss at this point on the books. That's what we have at this time. We will be focusing in on the accounts and the flow of the process through the processing and creation of inventory. Therefore, we'll be looking at the raw materials, which is part of inventory, the work in process part of inventory, then it goes to the finished goods. And then we'll talk about factory overhead. When would we have to use factory overhead? I'm going to put the factory overhead up here on the balance sheet because it will be part of inventory at the end of the day. So we can see them all together up here and we will not be looking at the units of production here. We'll take a look at that later. Here we're going to look at the flow of the inventory through these accounts using journal entries. So first we had the raw materials purchased on credit. So if we had raw materials purchased, we would debit the raw materials inventory. So inventory is going to go up and we're going to credit the accounts payable in this case. We're going to focus in on the general ledger accounts related to inventory. So obviously, there will be a general ledger account for the account payable, but we're not going to list it here. We're just going to list the inventory accounts raw materials going up 68,000 up by 300,000 to 368. That of course matches our trial balance here at 368. The other side went to the accounts payable there. That's our first transaction. Then we have the factory depreciation 50,000. So anytime something says the factory, remember that it's going to be a part of inventory. Now this is what we have to unlearn some things we probably learned in the past because we memorized the depreciation journal entry probably to be debit depreciation expense credit to accumulated depreciation. Now the reason we memorize it that way is because it's the matching principle and we have to debit the expense because we usually used some type of equipment in order to help us generate revenue. That's when we expense something, but just because we had depreciation doesn't necessarily mean that we're using it to generate revenue in that time period. In this case, we are depreciating in order to help generate an asset. That's why we're going to debit factory overhead, not depreciation expense can have to kind of unlearn that or relearn the rules on that to kind of understand that. Then we're going to credit accumulated depreciation. That would be the same as the normal process. So if we look at our general ledger accounts, then we are going to debit the factory overhead. Why is it in factory overhead? Because these are one of those things that we don't know exactly how to allocate it out yet. We're going to put it into factory overhead. We know it needs to be in the raw materials, but we're going to put it into the factory overhead first and then allocate it out using some kind of allocation method. We don't have the accumulated depreciation on the GL account. There would be one, but we're just going to focus on the asset accounts. The credit of course went to accumulated depreciation here. We now have the factory overhead at 50 on the general ledger, which ties out to the trial balance at 50. Then we're going to say factory utilities on account 28,000. So we paid 28,000 for the utilities. You probably automatically think in your head, utilities, how do I record that? Well, debit utilities expense and credit cash, but in this case, we're not using the utilities in order to generate revenue. We're using the utility utilities in order to help us to generate the asset. Therefore, it's going to go to the factory overhead. And because again, we don't know exactly how to allocate it. So we're putting into that bucket of factory overhead, and then we will allocate it to the working process at a later time. We're going to credit the accounts payable. In this case, we're crediting the account. We put the utilities on account. We did it on account. So instead of crediting cash, we put it into accounts payable. Therefore, if we look at our general ledger, here's the 28 going up from 50 to the 78 going up by that 28. And that's 78,000. Now is, is what is in the factory overhead here on the trial balance? Next thing, direct materials use. So direct materials, that's pretty straightforward. If the direct materials are going to be used, it's going to go directly into in this case, work in process. So we know exactly where the direct materials are going, we can account account for that directly. And therefore, we can put it straight into the working process accounts, rather than having to put it into the factory overhead, which will then go into working process with some type of estimate. In that case, we're going to credit the raw materials inventory, it's going to come out of the raw materials inventory. So when we buy it, we put it, you can kind of think of it going in the corner. Then when we start to process something, we take it out and start to use it. That's when it transfers from raw materials to work in process. These are both our inventory type accounts of raw materials going down from the 368 down by the 214.5 to the 153.5. And then the working process is going up from 419 by the 214.5 to the 633.5. And those of course are reflected here on the trial bounce, trial bounce matching the general ledger. Then we have the indirect materials used, indirect materials. So indirect materials are still going to be part of inventory, but we're going to have to put them into factory overhead. Why? Because we don't know exactly where to apply them out again. Therefore, we're going to put them into factory overhead and then apply them to the working process using some type of allocation method. We have the raw materials are going to be credited. So we're taking it out of the raw materials. If we take a look at that transaction, same type of idea. It's coming out of raw materials, but we're going to put it instead of putting in the working process directly, first putting it into factory overhead, factory overhead going from 78,000 up by 68,000 to the 146,000. And we're putting in here instead of work in process, we will allocate it to work in process at a later time. Now you might be asking, what is the difference between indirect materials and direct materials? So again, that the indirect stuff is usually the smaller stuff where we can't track it as easily, or it would be too expensive to track it as specifically. Therefore, we're going to put it into the factory overhead and then allocate it out. All right, then we have the direct labor used. So direct labor, the labor in the actual production of the process, we can track that directly to the process. Therefore, we're going to put it into the working process part of inventory. And we're going to credit the factory payroll. Now, when you think of direct labor, you should be thinking of payroll that we're just processing payroll here. We're cutting out the idea of payroll taxes, not because they wouldn't be there, but because we don't want to complicate things at this point. And so we kind of have our payroll entry, we're going to credit instead of cash, we're crediting, in this case, the payroll payable to show that it is payroll. And instead of debiting payroll expense, like we normally would if we were processing payroll, it's not being used, the wages aren't being used in order to help generate revenue this time period, they're helping to generate the asset of inventory this time period. Therefore, we're debiting working process, the asset account of inventory type, rather than debiting the expense. So here we have it, it's going to go into the working process, working process going from 6.335 up by the 7.82, 1 million 4.135. That 1 million 14.5 is what is currently on the trial balance at this time. Then we have the indirect labor used indirect labor. So same idea. Instead of debiting, we're processing payroll once again, instead of debiting wages expense or some type of expense for the payroll process as we normally would, we are making the assets. But we don't know exactly where to apply it. If we have different departments, we don't know exactly where to put it might be the supervisor or something. Therefore, we're putting it into factory overhead. So we're debiting the factory overhead, and then we'll apply it out to the working process. And then we're going to credit the factory payroll payables, or if we paid cash, it would be too cash, right? If you work problems like this, they often will credit a payable account for a lot of things you might not see a payable account for. Why? Because if I just put cash here, it's not very specific by the journal entry what's been affected. If I put payable for payroll, then we know that this journal entry is related to payroll without a description. All right. So here's the transaction.


Hey Psych2Goers, let's take a second to re-center, find some more comfortable and shake off all of that old energy And let's prepare for our exercise Box breathing is a four-part exercise So you inhale for a count of four and then you hold for a count of four and then you exhale for a count of four And then you hold again for a count of four. So let's begin inhale one two three four hold two three four Now exhale two three four and hold two three We can try something new next time and I'll see you then And please note you can adapt this count to whatever feels most comfortable to you. Bye


So, hello everybody, my name is Angelo, and I work as an embedded systems engineer at Tamsys Corporation. So, I talked to speak about early booth stages. I know these are probably quite well-known arguments that you often find in such kind of talks, but I thought it may be interesting to talk again about this, because sometimes when you are on the over the Linux booth, you are more familiar, but sometimes the early booth stages may be more complex. So, these are some abbreviations I will use. So, this is the roadmap I will try to keep, and it ranges from generic booth concepts through Rombu Loader, and of course, reaching also touching new booth, and touching some hardware troubleshooting, and things like that. So, of course, I am focusing on system on chips. There are the majority of the chips used nowadays. So, of course, they generally offer multiple booth options, because they are full of hardware modules and interfaces built in inside. So, here comes to play the Rombu Loader, so the read-only memory bootloader. That is, of course, a program that is generally not updatable, and it makes the initial initializations and decisions about from what device to boot. So, just after, it comes into play the static RAM, so where to boot the code, of course, this system on chips is inside a static random access memory that is mainly a kind of memory that you will know probably already that doesn't require any refresh cycles, so it's easy to be assessed and used, and it's quite fast, and so on. So, you have generally two chances of execution that are execution in place, and execution of code that has been already copied into static RAM. So, when you have a program that needs to be serially read, generally you have a header with a lot of information inside, and also, of course, the size to read from the Rombu Loader. In some cases, Rombu Loader may miss, so there may be legacy CPUs that are booting directly from a parallel bus, like maybe coal fire stuff or things like that. So, it also runs Linux, but, of course, the boot is more simple. Otherwise, execution in place requires random access. Of course, you have the code that is loaded, and in the code there may be, of course, jumps, so the ability to read from a certain specific address is needed. So, then there are some definitions as Rombu Loader is generally the first program loader, and then there are secondary program loader that is the first binary read, and the next to be executed. Then you find SPL, so, then you may find a tertiary program loader in some specific cases that we will see later. So, as a Linux-oriented boot, we are landing on, of course, 32-bit CPUs, or major, of course, or 64. So, those are supported from Linux. So, you generally need onboard some synchronous dynamic random access memory, so DDR or all the rest, the RAM. And because, of course, you need an appropriate amount of RAM to run the kernel, so, maybe 10 megabytes, 16 megabytes, something like that. So, then, of course, a normal attack memory is needed, and to boot to read, of course, the root file system and all the rest. And an SD card or USB stick may be useful, of course, for development to test the kernel multiple times and be able to have a fast development. So, U-boot is a common choice. Of course, you have several bootloaders. Several choices is not that hard to program a proper bootloader in case, of course, U-boot offers a lot of help, and many of you will know it already. So, you can do a lot of things from U-boot. And, at the end, it is good because it is popular that there is a friendly community and there are regular releases. So, in case you have issues with U-boot, better to try a recent mainline code or the last stable release. So, these are some extremes. So, we can go from a simple boot with just a single binary, uncompressed code and standalone to, of course, at the more recent trust zone secure world boot where you have a lot of blobs involved. So, these are kind of extremes I tried to figure out. A bootloader may be avoided, of course, but this is unusual and not often such flexible, let's say. Okay, this is a common generic boot. This is about normal world and 32-bit systems. And you see that in the first stages there is always this wrong bootloader after a reset that starts to check and evaluate some conditions. So, one condition is initially these bootstraps pins. So, you have generally resistors on the board or you can have some switches that define this bootstrap code. So, the system on chip knows, for example, what is the device selected for the boot. Of course, you may have also fuses that you flash like one-time programming fuses. So, generally, the wrong bootloader checks also those fuses. And finally, the wrong bootloader needs to read the first program from the selected boot device. And, of course, it reads inside a built-in static RAM on chip RAM. And that may be from small size, like 4 kilobytes to sometimes also 512 kilobytes. It depends from the system on chip, of course. You have a lot of scenarios. And then once the first program has been loaded, of course, you need to initialize and if you want to try the DDR, and then you finally can load the Linux into the DDR and jump to it. So, this is just a road schematic. So, these are something about bootstraps pins. It's very simple. So, you have generally resistors. As you can see from the image, there are generally three pads, so you can unsolder and move it eventually. Or there may be switches. Of course, the CPU samples these pins at first result. But just after, you can use the pin for other purposes, like GPIOs or the like. So, we can boot from different memory types. These start to be interesting. So, system architect should define the proper hardware. So, depending if it's needed a fast boot or keeping the cost low. Okay, this is one of the common boot device. It's SPI NOR flash. You will probably, many of you will know it already. I am talking about the standard SPI, so it's a bit simpler. And, of course, for this kind of memory that is often used for your boot or initial boot, you have four wires. So, it's very simple, the connection. You have master input and slave output that needs to be connected to master input slave output. So, it's difficult to make mistake, but still, of course, you can find swapped wires on prototypes. Because sometimes the constructor of the chip is using a different naming. So, he's using DO, DE for the bidirectional lines and sometimes maybe swap it. So, here you have a clock and it's quite easy to troubleshoot to the bug. So, you can check the clock by your oscilloscope if something is red. And, of course, there is a chip select that is a signal that you keep low to select the chip and then you can start the conversation. So, this is a quite common option, this SPI NOR. So, it's used to isolate your boot, generally. And, it is synchronous, of course, it is full duplex, but for the first boot, of course, it is generally used just reading. It's simple to wire. And, of course, these SOIC packages are simple to unsolder in case you have some issue in place of reprogramming through JTAG or something else. So, transfer rate is, of course, clock dependent and, of course, is dependent from the lines, from the data lines, of course. So, this chip is not random access, but when you go to quad and octal, there are a lot of chips that are execution in place enabled. So, you can read the busts of bytes, group of bytes, using, of course, specific commands that are available in quad and octal bus devices. Okay, this is an old new friend. He is the parallel nor. So, who worked with all the CPUs will probably know this very well. So, you have just an address bus and a data bus and some signals to read and to write and to select the chip, of course. So, it's interesting to see that this is a 16-bit words chip that are very common. And the CPU side address one is wired to the address zero because, of course, at each address increment you have to read 16 words, so not a single byte. So, for this reason, the A1 is mapped to A0. So, still on parallel nor they are often used for execution in place. So, the code is very simply read from the CPU and executed immediately. So, it's just a fetch and execute as in the old CPU, as, for example, 1851 or the like. So, where they were reading from EEPROM or Flash chips. And the read operation is quite simple. So, this chip are, of course, random access because you can set on the address bus the exact address that you want to read, so you can jump over the code. And the read procedure, for example, is very simple, so you have to put down the chip select, put down the output enable and then, at this point, of course, you have to configure the states on the CPU because these kind of chips are giving the output after a certain time. So, if you read before, you can find simply garbage. And once the CPU has read the proper time, you can find the data in the database. But the output in this simple way of reading is not very impressive. So, this kind of nor parallel chips are used generally in another way for fast boot. So, you need to configure page mode and also set as cacheable the address range used from the parallel nor. So, this may be done simply setting some bits on proper registers, generally. So, you set the address on the address lines. Chip select and output enable are set low. So, you have a first read delay. But then, you still keep chip select and output enable low and you can increment the address. So, the next word is available much sooner, so in 10 nanoseconds, for example. And the speed is much better. It's near 100 megabyte per second. So, this is an end flash memory, nonvolatile memory, of course. And it's quite different from the other memories we have seen. So, there is a kind of a database, but it's bidirectional. And also, there are two wires. So, you can see CLE and ALE that are used to combine commands for the end. And so, the end flash is more error-prone. It's much faster, of course, writing compared to the nor parallel flash. And it's quite fast for reading. But of course, since it's an error-prone technology, you need a mechanism to error correction mechanism done by software. Then is a very interesting chip. It's very nice to use. It's the EMMC that is mainly like an SD card, but of course, is in the shape or in the package of a chip. And the protocol is very similar. It's very similar to SDIO. More or less. So, you have a clock, a command line and a database that is often of eight lines. And it often works also with DDR so can reach very high speed, like 400 megabytes per second. But of course, this kind of chip requires an initialization time because they have inside a circuit that manages the end-flash that is inside and take care, of course, of everything of error correction and everything. So, you just see this chip as an SD card, you can partition and use it in a very friendly way. But of course, still requires 50 milliseconds before you are able to read data. It is not random access, so you need, of course, to read block by block and shadow the code on the static RAM. These are some other... This is a SD card, of course, maybe used for development. There are often some quite high time because before you can read the data from it. These are some other technologies I have inspected that are available for as a non-volatile boot methods. There may be other, of course, but I couldn't enter for a matter of time also, end of knowledge. So, this is... These are some typical cases of boot. So, you generally have a wrong boot loader, of course, and if you are able, in a non-secure world, you can boot, you boot, you are able to make it fit inside the static RAM, very big static RAM chips, so you can then easily initialize SD RAM, DDR, and boot Linux. Where you cannot make... You boot fit inside the static RAM, at this point, you generally use another mechanism that is a secondary program loader that is smaller and you can make it fit inside the static RAM and it generally then initialize the DR and load if you want the fully boot and then the kernel. But it's more common, you can find that SPL can boot directly the Linux kernel. There is a FICOM mode, sorry for the error. So, this FICOM mode mainly allows to initialize and boot the kernel without passing for the fully boot. You can still exit from SPL, generally typing a key and load the normal new boot so you have the command access and you can manage some operation from there. And, of course, this exit pressing a key needs to be implemented in the board C file. This is a case where you may find TPL, of course, so tertiary program loader. There are specific cases where, for example, on one end you can just read one kilobyte, for example. So, it's not mainly a static RAM limitation but it's a limitation of the size of the code. And then, so you can initialize the DDR later from the TPL, boot you boot and the kernel. Okay, this is an interesting case. I found working on this cold fire quite legacy stuff that mainly everything is... the static RAM is small but has been put in the header a small size of code that is read from the wrong bootloader. And inside this small part of the bootloader is performed the DDR installation. So, you need to check the linker script to put the code in the initial part and then you are able to, of course, load the rest of the binary through proper simple driver and it's just a thing I have found. So, I just mentioned it. This is iMakes, some more iMakes scenario. So, who worked with iMakes chips probably knows this well. So, this kind of system on chips allows you to prepend the boot program with some special operative codes. So, you are able to initialize the DDR, for example, before booting the second program loader. So, you can initialize the DDR and boot a new boot bigger than the static RAM size. Of course, you load it directly into the DDR. And this method is, by the way, not always welcome because several times a training is preferred on the DDR, especially for some special cases where you have edge thermal conditions, stuff like that. So, a training is always better. So, sometime you find still inside the U-boot code a training done later. Then there is also a chance to boot directly the kernel. I just briefly tested it. But it's not really versatile, of course. OK, then some words on trust zone. It's more actual technology. So, now several system on chips already boots from the secure world. So, there are specifications, but there are sometimes different implementations. They are very wide to be covered in this talk. So, you may have an additional core that is managing the boot. You have different boot blobs. And also you may find proprietary blobs that there are a lot of guys actually working to try to keep it open. So, you will find a lot of information in these two links where you can find all the platform supporting this secure world boot. OK, here some common U-boot commands. So, these are very, very well-known commands generally. Common to check the device tree that is generally built with U-boot. And it's very useful to lower the kernel image from the file system. So, it's simple. You can just access the file. And you access the... So, U-boot is offering, of course, a lot of file system support. Then you have common commands for memory display, of course. Common for write effuses. You have... This command is nice, it's on IMX. So, there are cases where you don't have... You don't have access to boot mode switches. So, you can use this B-mode to reboot in a different boot mode. Or if you don't have B-mode built-in because it needs to be configured, of course, in U-boot, you may use some tricks like these directly writing or registers. So, it's kind of tricky way to reboot in a different mode. So, then you have GPIO, of course, commands. So, you can test on prototypes. You can enable some circuit stages. You can see if they work before booting Linux, of course. Then here are commands to access, for example, the SPI nor flash. And, of course, the SPI flash... nor flash needs to be supported. So, you need to define the support for it in U-boot specific board includes. Then I like to use, for example, SPI. It's a command that you can just load the binary to the console. So, it's quite old way, but I find it useful because you don't need to care about the network. And then, of course, you can flash directly the SPI nor. These are most common boot commands. Go for an uncompressed kernel, for example. It's kind of legacy command. Then you have the more common boot M that is loading U images. Then you have boot Z that is loading Z images. And then there is the newer 50-mage way. So, you can load this kind of 50-mage built from a device tree and so on. So, you can boot through 50-mage. Okay, these are some tricks about optimization that I have experienced. So, a good result starts often from the hardware. So, from the components choice mainly. And most of the cases for a fast boot, the nor flash, the nor parallel flash and execution in place is chosen. Of course, you have also, as you have seen, EMMC very fast, but there is a startup time while the parallel nor is ready immediately after reset. So, it's still often chosen as a boot method. Then in your boot, of course, you need to check that the drivers are working in the selected mode. So, you can enable, for example, DDR for EMMC and stuff like that. So, you need to check that everything is really enabled and working. So, then you can, of course, disable console and kind of simple tricks. You can check clock signals, of course, on the boot device, so you are sure that you are reading at the proper speed. And of course, you can measure boot time to GPIOs and oscilloscope. So, you can just put on some pins, some levels so you can see where you are over the boot. And then there are, of course, camel optimizations, that this is quite complex story. These are some tricks to debug. In case you have a prototype, the first boot is not providing any output. So, you can check power supplies. Of course, all the involved chips in the boot needs to have proper power supplies, like 3V and 3V and stuff like that, 1.8V that must be stable. And you need to check, of course, the reset signals. Generally, there is a circuit and the signals may reach different, multiple chips. So, you need to be sure that, of course, one chip is not wrongly reseted before another or things like that. And then, of course, you can check CPU clock sometimes. So, it's often possible. You can check activity on the first boot device. So, you can check the data lines. On the SPI north, if something is read from the wrong boot loader, you need to see some bars. So, also from the size with a good oscilloscope of the data that you see, you can understand in what phase the wrong boot loader is stopping. Of course, often you can find on prototypes and on custom boards errors, even if there are very expensive card systems. There should be signal integrity checks and stuff like that, but sometimes you still may find errors. And, of course, also here you can add some toggling on the GPIOs. OK, this is just a small table I did just to show some famous system on chips. I couldn't go over 64-bit stuff because I work just on MX8, but you can see that quite all of them are offering, for example, execution in place. But not all. So, I mean, if you don't have the generic bus, you cannot boot from a parallel north, of course. And then you see that newer stuff is as a big static RAM, generally a bigger static RAM. And, OK, so that was just a brief comparison. OK, I completed probably quite sooner, so if you have any question, I am happy to try to answer. Thank you very much. Thank you.