So if you're not showing up on the search results page, you're missing out on a huge untapped potential of all these customers who literally are typing your products into the search bar wanting to purchase. Welcome to the journey. I'm Neely and I'm Morgan and today we're going over the beginner's guide to SEO. All right, other than being a super cool acronym, what is SEO? So SEO stands for Search Engine Optimization. Search Engine Optimization is the work that goes into your website. So it's actual work that you have to do to prove to Google and other search engines that you're the most relevant answer and the most trusted for searches relating to your products or business. So those two things, relevance and trust is what Google's looking for to determine which websites it should rank on the first page. And so when I say Google, just so you know, I'm going to be using that interchangeably for all search engines because 167 billion searches happen on Google a month. That's a ton. Most searches happen on Google, right? Right. So I'm just going to use Google interchangeably. I mean, it is the 167 billion pound gorilla in the room. So we're just going to go. I'm scared. All right. So SEO, like why is it important? Why should we invest our time, energy and money into it? So search engines, they're the new yellow pages. This is where people go to find answers. Billions upon billions of searches are happening each month, and many of those are for your products and services. So if you're not showing up on the search results page, you're missing out on a huge untapped potential of all these customers who literally are typing your products into the search bar wanting to purchase. 88% of people research before they buy and they're, where do they research? Google. So you need to just, it's just plain and simple. You need to be there. So instead of me telling you, let me just show you, let's go check out a search result right now. Cool. Let's do it. All right. So we're going to break down the different pieces of SEO by going to the search results page itself. So let's dive into it. So let's go to Google.com and let's an example business that we should look into. Let's try lawyers. Lawyer.  Something like that. Yeah, Phoenix, Arizona. You need a lawyer now. So lawyer, Phoenix, Arizona. So what I just typed into the search bar is known as the search query. And this is a phrase or a question that you are looking for answers for. This can contain your keywords. For example, lawyer is a keyword and Phoenix, Arizona is probably a keyword. So now let's look at the three different pieces of the search engine results page, also known as the SERP. Okay. So these first two sections right here, these are the ads, paid ads. And normally you can tell because they have a little ad flag right there. So you can see there are two ads here. And then if we scroll down to the next section, this is the local map listing sections. So these are local businesses only. So if you serve a national audience or you don't have a physical location that you serve, then you aren't going to show here. The way that you appear here is you have to have great SEO on your website. And you also have to have an optimized Google My Business profile. And you can see that only a few businesses appear here. So there's usually three. This is known as the local three pack. And then occasionally there'll be an ad. So this is an example of someone who's paying to appear in the local listings. And then these three below it are the ones that are naturally organically showing up here, which Google has deemed for Phoenix, Arizona. These are the best three. You can click on more places. And that's going to bring you a wider map of all the different local lawyers. So you can see quite a few. And then you can dig into their Google My Business profile from there. So here's an example of one. So the next and last piece at the bottom, these are the organic results. This is where you want to be because unlike the paid ads, you have to pay to play for those. So once your ad budget is out, poof, you're gone. You're no longer there.  And then you're going to stay here for a long, long time as long as you continue to show Google that you're better than your competition. And people love these. A lot of people, while ads are effective, we're kind of trained to just skip over the ads and go straight down to the organic results. And so so many people will just hop down right here and they'll click and find their lawyer.  And I want to talk about keywords and keyword competitiveness, because keywords are things which we'll be talking about. You need to put all across your website. It's these search terms that people are looking for. And so you need to make sure that you have that on your website as well. However, some are much more competitive than others. So if you look at lawyer Phoenix, Arizona, there's about 32 million results. It's pretty broad. Phoenix is a pretty big city. If we change it to something that's less competitive, let's say a dog grooming dog groomer Phoenix, Arizona, only 2.3 million results. So clearly less competitive business. So there's not as much competition there, which is great if you're a dog groomer, because that means you have a, if you're doing the right SEO, it's going to be easier to appear on the first page for that search term. Unlike lawyers where they put a lot of money into advertising, it's a very, very, very competitive space. There are people always fighting for those top spots. Should we only put short keywords? Is there anything else we can use? So initially, no. With Google, you need to start small with their called long tail keywords. So they're, they're keywords with three, four, five, six words altogether, because you need to prove your authority in the small, less competitive spaces before Google is going to realize that you should be ranking for these more broad terms. So for this example, if I'm a dog groomer, let's say I specialize in poodle grooming. So we're going to change it to poodle groomer Phoenix, Arizona. And you can see the competitiveness. There's only 300,000 search results. So this is great because there's not as many people who put poodle grooming on their websites. And so for me, this is a great opportunity for me to start building that authority with Google. So remember, if I'm a dog groomer and we go to my website and there's absolutely nothing about dog grooming, it's just my name, my phone number, and maybe a photo, Google's going to look at that and think, this doesn't talk anything about relevant. Yeah, it's not relevant. So this person must not be great for this keyword. They're probably not a dog groomer at all. So our job is to go and make sure that all the content on our website is relevant to those keywords. All right, so you're telling me all I need to do is update just a little bit of content on my website? Not exactly. So remember that we're doing this not only for our users, so they have information, but for Google. Okay. So and Google likes our websites to be structured in a very particular way, right? Ultimately, it's a robot that's scanning the back end of our website. So the back end data of the website, Google wants to make sure that we have it formatted in a way that it can easily read and know what our website's about. So these are things like our H1 tag, our metadata, meta descriptions, which I'm going to go into right now to show you where this is. Awesome. Let's see it. So for, since we're here on this poodle grooming website, let's go to this one, Puff and Fluff Grooming and Pet Sitting. I'm all about rhyming. It's a nice looking website, has great colors, great branding, but the problem is Google doesn't see any of that. This is what they see. Boom. That's gross. That's not that pretty. And end users, your customers, if this was your way that your website was presented, they would get nothing from this. However, this is exactly what Google looks at when they're wanting to rank a website. All right. So you're telling me that I have to know how to code to do that? Not necessarily because modern day website builders already have this built in here. You can see with this website, they're actually using a plugin for WordPress called all in one SEO where you just put it in and it just makes it super easy for you as a non-technical user to update all of these SEO elements, which is awesome. So as part of this, you need to have your meta title. So this is basically the title of each part of your website that when you go back to the search engine results page, this is what will show up. So for this example, they set their meta title for Puff and Fluff Grooming and Pet City. And then you can also see right here, the meta description, they get to choose what that is. All right. So that's the basics of SEO, the search engine results page, everything on your website. We just talked about everything on site that you need to do to your website. So now let's talk about the things off site. That shows Google that you're the most trusted answer for search results. All right. So explain trust a little bit more for us. Yeah. So I have an analogy. So let's say that you get a call one day and it's from a fifth grader and the fifth grader says, Hey, Morgan is the best basketball player in the entire world. Are you going to believe him? Probably not. I think you paid him. Right. All right. Now, what if Kobe Bryant, LeBron James and Michael Jordan called you up and said, Hey, got the scoop on this new player, Morgan. She is the best basketball player in the entire world. What would you say to that? Would you believe him? Oh, absolutely. Yeah. They have authority. They have authority. So you will, you will trust their opinion. And it's the same thing with Google. The way that Google can tell if your website, if it should trust your website, because again, we could toot our own horn all day long. And we see this all the time. People say, best dog groomer in Phoenix, Arizona, right? Like people love to toot their own horn, but with Google, it needs that authority from other people. And that's where backlinks come in. And so backlinks are links on other websites that point back to your website. And Google uses this as an indicator to see, okay, this is actually a really good website. Other people are talking about it. Now, with backlinks, it's quality over quantity.  Google's not going to like that. It wants really high quality. The Michael Jordan's. What is one thing they can do right now? The biggest thing that you can do that will give you so much bang for your buck is to put content on your website, especially content that has your keywords. To determine those keywords, you should probably, what are the products and services that you offer? Or what are the products and services that you want your customers to know about? For example, using the dog groomer in Phoenix, Arizona, maybe is there certain types of grooming that you do that you're really well known for? Let's say you're the best darn toy poodle groomer, this side of the Mississippi. You should have a separate page with content on it about that specific service that you offer. So that's what I recommend. Go make sure your page just has tons of content so that way when users and ultimately Google look at it, they know exactly what you're about and then Google will start ranking you. All right guys, I hope you found this beginner's guide to SEO helpful and that these are actionable things that you could start doing now so that way your customers can start finding your business online. If you're going to get started and you found this helpful, let us know in the comments below what was the number one thing you learned about SEO today. Awesome and make sure you like this video, subscribe to the channel and if you want to see these videos first, ring that bell, but this has been The Journey, signing off.


to be speaking to so many people who are interested in both geometry and gravity, and not just one of them. So I'll try to take both perspectives. I should say first, though, that I'm a mathematician by training mostly. So my perspective will be mostly mathematical, but I'll try to give the physical intuition behind the notions as well as well as I can. The topic I'll be speaking about sounds rather old. If you look at the second, these are the main references. I wrote them down already. So if you look at the overview book is from 1996, and then the next overview article is celebrating four decades of black hole uniqueness theorems. So they're an old topic. However, recently, there have been many interesting generalizations and also different methods of proofs. Some of them I will mention at the end. So it's, again, a hot topic. So I thought it would be a good topic. So there are rather basic things you can say, but it's also current. And you can do research right away at the end of the lecture series if you like. Of course, these are not the only references I'll use. Most other references I will use, if they're about older stuff, are in there. So I'll just mention names and years. If I mention references that are not in either of these works, I will, in fact, write them down properly along the way. I will also produce lecture notes eventually, but I just had a small baby, so please allow this to take for a while. So this is the plan of the class. In lecture one, which is today, we will talk about static space times and introduce all the important notions, important being defined as we will need them in the course of the lectures, not they're important generally, or not things we don't talk about are not important. So this is a very brief introduction. Then in lecture two, we will talk about static vacuum black hole uniqueness. And then in lecture three, we will again talk about static vacuum black hole uniqueness, but looking at different types of proofs. And then in lecture four, we're gonna talk about generalizations in particular to higher dimensions and to photon surfaces. And I don't expect anybody to know what a photon surface is by now. I'll explain that in the last lecture. So that's the plan. And I presume you've already seen the Schwarzschild space time many times probably in every lecture. So I decided I'll write it down once so that you get used to my notation and then I'm using it as an example, but I embed it into a larger class of examples. So those who are very familiar with Schwarzschild don't get bored and maybe learn something new. If you're not very familiar, just always imagine the example I'm tracking through to be just Schwarzschild, okay? So Schwarzschild space time can be written as the Lorentzian metric ds squared of the form minus a function n squared dt squared plus one over n squared dr squared plus r squared d omega squared on the manifold are containing the time coordinate t cross some interval maximum of zero to m infinity cross s2 and this contains the radial variable r and this d omega squared is the canonical metric on s2 with the function n being a function only of the radial coordinate r given by the square root of one minus two m over r and m in r is the mass, okay? So this you've probably seen a lot, but I've written it in a general form and we're now going to look at space times which have this form for various different functions of n. But let's first recall that the Schwarzschild space time models a vacuum space time in four dimensions exterior region of a black hole as you've probably heard and it's of course spherically symmetric and I wouldn't be talking about it if it wouldn't be static. Static by now for us only intuitively means that nothing moves. We'll define it more properly later. Pardon? In the bracket the max of zero and two m, okay? Because you need the square root to be well defined. So you can't have r less than zero or zero and you need two m. You need it to be larger than two m if two m is positive and this is an infinity. So if m is positive this is the exterior region of a black hole, if m is zero this is a weird way of writing Euclidean, Minkowski space time and if m is negative this is weird altogether but it's still a well-defined space time. It's a special case of the Kerr family that I'm sure you've seen if you pick the angular parameter a equals zero. That's most I'm going to say that if m is bigger than zero then the black hole horizon is at r equals two m. So that's the threshold where this function becomes a zero and notice immediately that r equals two m is not inside the manifold. So it's on the boundary of this manifold because this is an open interval. That's important because we want this function here to be positive, okay? We'll see this occurring again and again. Okay and we will encounter metrics of this form more generally and I'll give you some examples but before I give you examples let me fix notation or conventions and say that we have the gravitational constant and the speed of light set equal to one which I think probably most lectures are doing here. More examples of this form orders called the Schwarzschild space times in higher dimensions or sometimes called the Tangerlini space times or sometimes called Schwarzschild Tangerlini and are equal to three. We can write the function in of r as the square root of one minus two m over r to the power n minus two. This is also positive, bigger than zero and bigger than the one over n minus two root of two m depending if m is positive and this in fact is just a natural generalization of the Schwarzschild space times to higher dimensions. It's also vacuum. It also has a black hole at this threshold if m is positive, yeah.  There is also a metric in the literature that sometimes has the name pseudo Schwarzschild and we're not gonna talk about very much but I want to mention it because it has confused some of my students enormously which is for n equals two so that's three space time dimensions n is always the spatial dimension for me that's three space time dimensions and you take n of r is exactly as in the three dimensional case of course this is positive for the zero and two m so this gives you a legitimate space time however the space time is not vacuum it doesn't satisfy the dominant energy condition if you heard about that it has no, besides looking exactly like three plus one dimensional Schwarzschild it has no physical relevance within general relativity I don't know about other theories okay not vacuum I'll talk about it a little in the last class so what it does do it is accept being vacuum and not being asymptotically flat that's something we'll talk about later as well it has all the properties of a Schwarzschild black hole so if m is positive it has a black hole horizon just in the same way yes yes yeah that's a very good observation so if I wanted to use this formula it would be a typo right the power off oh here oh yeah right thanks sorry I thought you meant the power here and so the power here is actually really what's written down because you can't use this power in plug-in n equals two so this metric otherwise is exactly like Schwarzschild it has a black hole horizon it's fairly symmetric and it has nice properties but it doesn't satisfy the vacuum Einstein equations and it's not asymptotically flat so another space-time you might have come across that has this form is the Reisner Nordstrom electrically charged space-time very briefly touched on that in the last class and in that space-time there's a mass m and a charge q think of an electric charge and then the function n can be written as one minus two m over r plus q squared over r squared also positive for suitable r this is again n equals three and there's a higher dimensional analog of this as well and then there are lots of other examples and one relating to the class you're following on the ADS CFT correspondence is a metric called the ADS Schwarzschild or the Kotler metric I won't write it down because it requires to put too much notation I just write it's name down and they also exist in all dimensions bigger than or equal to three so this is a huge class of examples and if you don't put any partial differential equations imposing any Einstein equations imposing matter and all of them are static it's fairly symmetric and have other nice properties that we'll discuss in a second so they'll all be examples for the static space times we may be talking about, we will be talking about later so properties they're static and we will define later what this means obviously it's very symmetric if n goes to zero as r goes to the r star of r in r star infinity which I hope is suggested enough to be self-explanatory in a suitably regular way then there is a black hole horizon at r star and we will define that later as well the asymptotic behavior and you've heard a lot about that I presume in Rick Shane's lecture can be specified just by specifying the asymptotics of this function in because n is the only free function in this metric so that's why they're good toy models so if r goes to infinity we can prescribe this is a question mark what n does for example if we want to be asymptotic to Minkowski we want n to go to one because if we plug in the function n equals one we get the Minkowski space time if we want the manifold and the space time to be asymptotic to the Schwarzschild space time we will request that it asymptotically behaves like the Schwarzschild space time so this function in as r goes to infinity plus lower order terms that we need to be precise how fast they decay and I will not precise on this except in the statement of theorems if we wanted to say we are asymptotically anti-decider like in the last example I didn't even write down we would impose other asymptotic conditions on this function in okay another property they have is that the spatial part being defined as one on n squared d r squared that's r squared d omega squared is the same for every t it doesn't depend on t that's one of the consequences of being static it's t independent and also the second fundamental so g of t is the same g for all t the second fundamental form which I don't know by k of t is zero for all t which we will call time symmetric rick shane may have mentioned that I'll draw a sketch in a second here's a sketch here's time and then for each t set t equals constant in this manifold that I just erased looks exactly the same from its intrinsic geometry perspective and looks completely flat from exterior perspective which is why I'm drawing planes of course intrinsically they're not flat but there's not enough room in the platform to indicate that okay and if you look at the Einstein equation that you've seen many times I presume so the Ricci of ds squared minus one half the scalar curvature of ds squared times ds squared is 8 pi t where t is the energy momentum tensor reduces to ODE's for so to ordinary differential equations for the function n and the components of the energy momentum because everything only depends on the variable r that's why they become ordinary differential equations instead of partial differential equations because of the spherical symmetry and the statisticity and so if you want to do exercises then you exercise one could be compute those ODE's just to get more familiar with this class of examples there's one more property that I want to discuss because it will be very important in one of the or several of the proofs of static black hole uniqueness and that is conformal flatness okay this is a confusing topic I'll write down the form of the metric again just so you can see it so of course unless this is Minkowski space this is not flat it's also not conformally flat in general or actually in very few cases it will be conformally flat if you don't know what the notion of conformal flatness means please look it up as another exercise I'll just give intuitive explanation and it's very well explained on Wikipedia so conformal transformations and conformal flatness so intuitively what it means that two space times or two other Romanian manifolds are conformally related or can be conformally transformed into each other it means that at each point if you pick two vectors in the tangent space and put them into the other manifold with the diffeomorphism the angle remains the same and isometry would also imply that the length of both vectors stay the same for conformal transformation we only require that the angle remains the same and this conformal flatness then means you're conformal to flat space or flat space time depending on context where flat space time would be Minkowski and flat space would be Euclidean space of the corresponding dimension okay so what I'm going to write now is that these metrics typically are what is called spatially conformally flat which means that the metric g which is the spatial metric here on any of these fixed slices can be written as a function phi to the power four over n minus two that's the dimensional convention and of course we need to stay away from two to write this down even times the Euclidean metric so delta is my Euclidean metric phi is a function is a function on say t equals zero so they're conformally flat but only at each instant of time so each of these extrinsically flat intrinsically curved time slices is intrinsically conformally flat it's curved but it's conformally flat so the angles are such that it could be flat the lengths could be different and this is true for schwarzschild this is true for schwarzschild in higher dimensions and I'll write down some details in a second and I'll say it again because it happens so frequently this is not to be confused with the whole space time being conformal to Minkowski space time because then there wouldn't be the causality theory for Minkowski and for these space times would be exactly the same and this would be very boring just the spatial slices example schwarzschild M bigger than zero and n equals three we can write the metric either as we've done before as one minus two m over r d r squared plus r squared d omega squared or one plus m over two s to the power four delta or if we spell out the Euclidean metric in spherical polar coordinates ds squared plus s squared omega we're here we needed that r is bigger than two m and here we need that s is bigger than m over two to correspond to the same region and the coordinate transformation reads r is one plus m over two s squared s as you can see if you compare the coefficients of d omega squared so we've never seen this way of writing schwarzschild in different coordinates the angular coordinates say the same just the radial coordinates transforms because we wanted to preserve the angles anyway yeah if you've never seen this I recommend you to do this computation once to believe this that would be exercise three verify if you have seen this and you're curious you could try to come up with what needs to be here in higher dimensional schwarzschild if you have seen this way of writing schwarzschild the spatial part of schwarzschild you've probably seen it with a variable called r here as well which creates also a lot of mistakes in the literature so I'll try to be super consistent and if I write it this way I'll always try to call the radius s okay in these coordinates they're called schwarzschild coordinates because they are the coordinates in which this was originally discovered by schwarzschild so schwarzschild coordinates and on this side the coordinates are called isotropic coordinates because they make the metric look isotropic and again this only applies to the spatial part of the metric okay you can do the same thing for positive mass higher dimensional schwarzschild of course you can do it in all dimensions bigger than or equal to three also for zero m but then nothing happens for negative m you can also do it in a neighborhood of infinity but not all the way down to r equals zero because your transformation breaks down at some point the fee in this formula will start being negative and then this makes no sense okay so in that's why I'm saying here that they typically are spatially conformally flat meaning a lot of them are locally conformally flat spatially conformally flat near infinity and then again on regions but they can be lines of r where they're not okay also Reisner Nordstrom has this property of being spatially conformally flat with a nice transformation globally if the mass and the charge satisfies suitable conditions called sub-extremality then otherwise the regions of Reisner Nordstrom and higher dimensional Reisner Nordstrom will be spatially conformally flat same for ADS schwarzschild it will be a spatially conformally ADS so this is important and one more important thing here is this threshold and it'll get a little color while here the radius threshold two m needs to be there because otherwise the formula stopped making sense this cut off here at m over two doesn't need to be there at all in order for this formula to make sense and in fact we can just allow s bigger than zero and say this gives a well-defined smooth metric spatial metric for s bigger than zero so on either whatever you want r3 without the origin or zero infinity cross s2 whichever way you prefer to write it okay so this way of writing the schwarzschild spatial slice metric allows you to extend the spatial slice beyond where we can look before and then the surface the two surface in this three space time in this three space sitting here any two surface sitting inside here can actually um... sorry what did I want to say so I can extend through this threshold and speak of this in a regular way just in the sense that I listed before that if you take n to zero is suitably regular way now here in these coordinates it's hard to say whether I can take n which was the square root of this to zero in a suitably regular way but if I change to these isotropic coordinates then the surface which used to be called r equals 2m as the boundary of my spatial slice is now the surface s equals m over 2 which is a perfectly regular surface in this manifold okay and I'll draw a picture so if your usual schwarzschild spatial slice equals zero schwarzschild looks like this where r to infinity is here and r 2 2m is this boundary which is the horizon which is why everything goes in there vertically then in the s coordinates actually what happens is I have two copies of this and then this corresponds to s m over 2 this corresponds to s to infinity so this is s bigger m over 2 and this is s bigger than zero and less than m over 2 and this is s going to zero okay so now I have two copies of a spatial slice of schwarzschild glued together completely smooth through this t equals zero section of the horizon and the whole thing is conformally flat as you can see by this formula okay so now in the spatial slice there is no singularity anymore at all in these coordinates of course the singularity is still there in the spacetime I'm not going to talk about that otherwise I wouldn't be boring again but in the spatial slice it's gone and you can do the same thing with suitable choices so in higher dimensions for m positive in schwarzschild for what is called sub-extremal horizon or Nordstrom so suitable condition between the charge and the mass and also in higher dimensions and for ADS and ADS schwarzschild you can do something similar but not precisely that and what you can see in this picture and which is actually true fully and can be proven rigorously is that this double is geodesically complete okay spatially geodesically complete this is just the t equals zero slice I'll write that over there and the other thing I want to write down excuse me is that it's reflection symmetric through the surface S equals m over 2 so if you look at this picture I already tried to suggest it in this picture you can take something along the lines of an inversion in the sphere in the sphere or something like S going to 1 over S but you need to be a little bit more clever than this to take the upper part to the lower part and vice versa which is why this is a totally geodesic hyper surface so this is then totally geodesic and if you don't know exactly what this term means it means it also has vanishing extrinsic curvature in this curvature I'm going to denote by H in particular it's minimal this is something you've probably seen in Rick's lecture so the mean curvature is zero this is mostly to fix notation and also what we've seen is that n of S m over 2 is zero so if you're very listening very carefully you notice that n was a function of r and not of S and S is now a new coordinate so I'll write a little twiddle over there meaning the same function written in a different coordinate variable okay so it's a different formula but it's the same function and we won't need the explicit form that it will be zero there okay so much for this class of examples that you can have at the back of your mind now that we introduce general static metrics before I go there though is under any questions yes maybe I should write that that way that's a good way of saying it n r of S and S equals m over 2 thank you so here comes the definition definition one the spacetime r cross mn ds squared i.e. a Lorentzian manifold which is time orientable mn is orientable and connected hello is unless I say something else all manifolds will be connected in this in this lecture the spacetime of this form r cross mn with a metric ds squared is called standard static and most people never use the additional term standard but still use this definition if ds squared can be written as just connected doesn't matter just not several pieces ds squared is minus n squared dt squared plus a metric g where t is the variable in r n from mn to r and positive is a function called the lef's function and g is a Romanian metric on mn so we have this product manifold r cross mn r is the time coordinate and mn is the spatial manifold as before and now we have a term here that looks exactly like before but our spatial metric g can be different from spherical symmetric and n also doesn't only depend on some radial coordinate but can depend on the whole spatial coordinate set but of course we still want n to be positive and now g is a Romanian metric meaning it's also time-independent and n is also time-independent they're just on mn they don't depend on t that's what's called standard static and of course all the examples we've looked at before are of this form and i want n bigger or equal to three why is this called standard static let's make a few remarks so first of all dt is a time-like killing vector field in the spacetime and in fact if you were wondering what the physical meaning is of n it's the length of dt with respect to the Lorentzian metric if you draw the picture then dt is a field here and also and this is a more tricky condition to write down the orthogonal complement of this field dt is for venues integrable that's how the mathematicians would say it the physicists would say and this actually means the same thing dt is hypersurface orthogonal which in formulas means dt index alpha the covariant derivative in the spacetime beta index gamma anticommute so this is the vector field dt index alpha covariant derivative in the direction of coordinate beta take again of the vector field dt in coordinate gamma and cyclic anti permutation so what it really means if you know nothing about these things is it means that there is a right angle here so i can have surfaces of constant time and the vector field dt is perpendicular to them everywhere if you think about Kerr this cannot be done in Kerr there's no time function on Kerr that does this the dt in Kerr is a time like healing vector field at least far out the way from the black hole but this is not for venues integrable or in other words this is non-zero so the vector field is not perpendicular to the t equals constant slices and typically the statisticity is defined to be static is defined as just this and this not what i wrote this implies that locally it has this form so let's call this form three i forgot a number two on the equation for the conformal transformation of Schwarzschild if you want to add that to your notes so i can refer to that later so locally it has to be of the form ds squared has to be of the form but what we're assuming is that this is globally true that's why it's called standard static typically people are very sloppy and use these two notions interchangeably even though they mean global and they would mean standard static but they don't say it so be careful when you read the literature there also we can alternatively represent the standard static space-time as the system which has just the remanian manifold m and g and the function in and such things are called static systems so then let's have definition two we want to talk about black hole uniqueness so we need to say what a black hole is in this context then m and g and your static system and then if n minus one sits in m and in in the boundary of m and as a comp is a closed surface so compact surface and so maybe you're confused surface in if any close three it's a surface otherwise it's a hyper surface but I'll be sloppy and has and is tricked in to the surface equal zero where we implicitly presuming that and extends to the boundary I'll give an explanation of this in a second we call it a killing horizon or the cross section of a killing horizon the why this the laps function in was the length of the killing vector field so if and zero the killing vector field is at least now or even possibly zero on the surface this which is why it's a surface characterized by the killing vector field the surface cannot be inside the manifold but has to sit in the boundary because we said the function and has to be positive in the manifold so then it can only be zero on the boundary and not inside because it's positive yes no so so if you think about short yield and you have your usual short yield on which and is positive it will be zero on on the horizon so the horizon is not part of this static system okay and then the horizon will be this exactly the surface sigma n minus one which sits in the boundary of your special slice of short yield at the quad that the T equals your slice of the killing horizon in the usual sense okay and then the mean curvature age of sigma n minus one in mn union with the boundary is zero so if it's a minimal surface which I'm sure Rick Shane discussed it's a horizon and if you've heard about marginally outer trapped surfaces or mots this is exactly a mots here because the second fundamental form of the slice in the space time vanishes so the part coming in a mots from the second fundamental form is not there if you've never heard about this ignore the comment and we will say and say sigma n minus one is a static horizon and extended to n minus one is zero and age is zero so both conditions hold true and we will call it a static horizon it's there a question does everybody yes does it depend on the coordinates in which I define my metric no yes if a coordinate if a time function T exists that you can write it like this there is no assumption on spatial coordinates just on the time court court yes in some sense you may be afraid that these conditions are a little bit redundant and if you assume Einstein equations with pseudomilm matter fields in some scenarios if you have vanishing laps function you get mean curvature vanishing for free or vice versa but it depends on the matter okay so in general it's not redundant and of course in order to even say that age is zero here I need to extend the geometry of the manifold and then to its boundary assuming g extends sigma n minus one as well so what does this mean again in the short you context let me draw again this picture so this is our men with metric and laps function from short shield then on this surface it's a minimal surface h equals zero and the laps function vanishes but the surface let me repeat is not part of the space which is why it's the boundary of the space once we doubled it this is a nice smooth judezically complete manifold however the laps function of course still vanishes on this surface so this surface cannot be part of the standard static space time because we requested that and the positive and even worse well and his positive here you reflect and down here and will be negative here necessarily okay and then equals zero in this so only the upper part of this is a standard static system those of you who know what this means this is the special section of the domain of out of communications okay inside here you're inside the whole in the special section of being inside the whole so only here you're in the stat in the static system this is a little bit complicated to to speak about that's why i'm making sure everybody understands this in the short example so let me say once more in the in the part above and not including the boundary here not including the minimal surface we are a standard static system if we add the time direction and the laps function incorrectly to have a space time on the boundary we are have a horizon because we can smoothly extend both the metric and the laughs function through here however the whole thing will not be the special slice of the standard static system and is zero here and negative here so if you want to do another example but in my book a little another exercise number four verify are equals two m and i'm writing a quotation marks because this is not part of the system is a static black hole closed and all i'm assuming it's closed i'm assuming it's closed and smooth and everything but the part of the boundary and then if the laughs function and assume the laughs function extends smoothly and the metric extends smoothly and then these conditions and uh... and a horizon in the sense of initial data sets now comes a definition you may have seen in a similar form in rick shane's lecture deciding on uh... defining the asymptotics the static system and three g and and then yeah let's do it in three dimensions here it's easier now we can do it then and and bigger equal to three is called asymptotically short shielding were also asymptotically isotropic if there exists the number m and r if m and can be written as a compact set in the disjoint union with the manifold e and which is called an end such that e and if your morphic are and outside some close ball the idea look like one plus over two as forward to the four over n minus two delta ij plus lower order and n looks like one minus power missing as n minus two n minus two plus lower order terms ss goes to infinity i presume you've seen asymptotic flatness in rick's lectures so asymptotic flatness of course here you just write delta ij and lower order terms and lower order in rick shane's lecture lower than even this so this is in particular asymptotically flat with very very vigorously prescribed asymptotics and of course to make this precise i would need to say what i mean by lower order sorry yes disjoint union so there's a compact set and an end that and they don't have any intersection and so of course i would need to make precise what i mean by lower order okay but i won't because it won't matter too much i will write it in the theorem and in particular keep in mind that lower order terms also means derivatives have prescribed behavior so that the first partial derivatives of this also have look like the first partial derivatives of this plus terms of lower order and and second ones as well and depending on context third and fourth ones as well possibly okay so lower order terms can include derivatives and you will find this in the literature mostly under the name of asymptotic short being asymptotic to schwarzschild or asymptotically schwarzschildian however i wrote it in as variables because it really looks like the isotropic version of schwarzschild and this is not equivalent to being asymptotic to the schwarzschild space time and schwarzschild coordinates and this order of lower order that we will be talking about you can perform the same change of coordinates of course to transform one into the other but then you will have a different different morphism here so be careful it's really should be called asymptotically isotropically schwarzschild or something like this and i'm going to call it asymptotically isotropic throughout so i'm going to go where is green i'm going to call it asymptotically isotropic of course rick shane has introduced the ADM mass and maybe some of you have already been wondering at least in three dimensions does this M have anything to do with the ADM mass and yes n equals three M is nothing else but the ADM mass of this G in high dimensions two if you know of higher dimensional notions of ADM mass and in particular this means that it's unique you cannot have the same static system having two different mass parameters for different different morphisms and have these expansions it's an invariant not important and we're going to call it of course the mass of the system so the last thing i want to talk about today is look at what happens to the Einstein equations and the Einstein equations of course are an equation for general space-time with matter field and if i specify the matter then it becomes like a clear equation for example if i say it's vacuum the energy momentum tensor vanishes then it's an equation which equals zero so if i have this equation which equals zero and i have a space-time of the form where the metric is of the form minus n squared dt squared plus this three metric G or n metric, the Romanian metric G i can plug in this formula and simplify the equations so in vacuum plugging in this into Einstein and did the Einstein equations we obtain the following system the Hessian of n equals n times the Ritchie where this is with the Hessian with respect to G and this is the Ritchie with respect to G and the scalar curvature with respect to G vanishes these are the equations that remain scale or flat and the Hessian of the lapse is the lapse times the Ritchie now there are a couple of nice things about this this equation doesn't involve the lapse at all and this equation is linear in the lapse this will be useful later and together if you trace the first equation the Laplacian with respect to G or n vanishes automatically so n is harmonic necessarily as a consequence if you trace this it says Laplacian of n is n times scalar curvature, scalar curvature is zero so Laplacian of n is zero so n is harmonic so the last homework exercise for people who want to do homework will be exercise five verify this and of course if you choose another matter model then vacuum say electro vacuum or something else a fluid you will get other equations they will keep the property though that they're all linear in n so thanks for today and I'm taking questions


Welcome back to the School of Calisthenics. We've got great videos for you looking at a back lever basics. The back lever was actually the first thing that me and Tim both did and got us hooked in calisthenics right at the start. Now it looks quite complex, but actually it's far more achievable than you may think. A lot of people ask us, prefer a back lever, how do you even get into that position in the first place? That's a fairly easy bit and we're going to show you that. And the second bit we're going to show you is once you're in that position, how do you create tension? To do one of the easiest gravity defying moves in calisthenics. So the first point of a back lever is being able to skin the cat. That's going to help us to take the shoulder through the range of movement and get the hips in a position where we can start to create some tension. Jacko's going to give us a quick demonstration. We're using the rings here so he's going to do an active hang to start off with. So what that means is setting the shoulder blades in is going to try and pull them down. You can see the shoulders move away from the ears. What that does is create stability across the shoulder from which he can now start to move the rest of his body. If he sits in a dead hang, it's really difficult for us to actually create enough tension to get around. So from this position, he pulls himself up. This might feel when you get to this stage that, right, I'm doing it, I'm all the way around. You've got to keep going until you can get those feet pretty much close to the floor. But what you're looking for is if you get this full-range rotation, which enables us to get a back flat, and then we can build on for the back lever. When you're starting to build a bit of confidence for the skin the cat, you might want to have a bit of a kick up to support you to get through because some of the pulling strength can be a little bit tricky while you're first learning. So you can see, give yourself a little bit of a nudge.  It looks hard, but it's actually pretty comfortable. It gets a bit more difficult when you go backwards. You can see here that Jaco's pointing his palms to the ceiling, rotating the shoulder inwards when the first learning is a back lever, and he comes through into this position. And if he's strong enough, he can either pull himself back through or just pop his feet on the floor and walk back out of it and let go. The two different ways for the back lever. You will see people doing a back lever with the palms down. We wanted to learn at the beginning with the palms up. What it does is it screws the shoulder into a nice stable position, makes it a much more safe position to achieve as we're beginning our back lever journey. The rings gives a really comfortable starting point because you can put them quite close to the floor whilst you build the confidence. When you get to that point and you're happy with your skin the cat, you can take it onto the bar, exactly the same position, overhand grip and then Jaco is going to go, you'll see him really in this position, he goes to active hanging position, pulls himself through, a bit of hip and lower body flexibility to get their feet between their hands. He pulls himself around and actually this German hanging position is the end of our skin the cat. But it just shows we've got full range of movement. You can see there with the palms still facing towards the ceiling when he's in that rotated position, it screws the shoulder in nice and tight. It can come back through and complete the rep. Skin the cat then taught you how to get around and start again into some of these positions to build up your back lever. Next part though, and this is where the magic really starts to happen, is in the movement patterning exercise, the walk back lever that we like to call where we're starting to link muscles together in this chain to be able to activate them correctly so that they will actually hold you in this position. We're going to do it nice and easy with the feet on the floor. So Tim walks himself forward, he's got the rings, he turns them outwards so that his palm is facing up to the ceiling just like in the skin the cat. And then he can just rest slack in this position. The further his feet are back the harder this is so you can make it easier or harder for you. But just start nice and easy. All we're trying to do is get the right activation pattern. So first thing he does is he squeezes his bum on and pushes the hips forward. He then locks his rib cage down, he's ab tight like he's ready to take a punch. The shoulders then he's trying to pack them in tight into the socket. And then he's also trying to squeeze his bicep to his side to almost pinch my hand in there. Whilst he maintains all of that to keep that alignment the shoulder in a nice stable position. The next bit is the strength to be able to pull hand down towards the hip to leverage himself up. And as you see that he moved up, he stays in one nice straight line bum on, core on, shoulders packed in tight, squeezing bicep to his side and then he's pausing at the top to maintain that tension. It's this position here driving the hand down towards the hip shortening that angle that the shoulder is making with the body is where you have to be strong to hold the back lever. And you're going to be able to hold it for real is when you've built up enough of that strength and whether you're actually strong enough through there to hold it. But before you can be strong in this position we need to learn and teach the brain how to actually activate in that whole pattern in one complete movement. So that exercise is brilliant for that with your feet on the floor and that is one to get in your program. So that's the end of the first lesson on back lever basics. We've shown you how to get into a position and then also how to start to create tension through the chain which is going to support your body weight when you've got your feet off the ground. One of the reasons why this is so easy to learn is you've got a bit of strength training background and why it was the first movement that we learned is actually you've got the basic strength to be able to do it. The real key is being able to start to teach the brain to activate the right muscle patterns together at the same time. And when we do that, sometimes at workshops people do it right in front of you for the very first time because they are as strong as they just haven't got that activation exercise. So if that's you, you might be well on your way to be able to get there. If you need a little bit of my help and you want a natural guide to follow we've got our back lever training guide on the website so you can always check that out but we've got some more content for this back lever coming for you in the coming weeks. So keep your eyes out for lesson number two until then class dismissed.


Mr. Speaker, I'm just sorry we got sidetracked by the little theater a few moments ago. It was about shaping up with a kind of contest that I was looking forward to. I was from the time I heard the presentation of the member of the Fort North. I said to myself, well, it looks like we're going to be shaping up an interesting debate and contest. But the theater that we saw a while ago, I'm flutating that. However, Mr. Speaker, I think it is very important to put the amendment in context. Because anybody listening to the presentations we have had would somehow believe that St. Jude could have raised money at any time. But the major problem with the legislation that there was no provision for guarantee, which is not really correct, actually. But I remember these provisions very clearly. The trouble sometimes is that when you see you have amending legislation, you often don't refer to what the actual act says, what you're amending. So that you contrast what is in the legislation and what the amendment is actually saying. The original section 20 does in fact make provision if the government, the Minister of Finance, so decides to get a guarantee for a loan. It says in the original section 20 that the Minister of Finance made it set whatever terms and conditions for any money that is raised by St. Jude. Because in the original conception of St. Jude, the thinking was that St. Jude would have been capitalized, including, of course, making available to St. Jude the land on which the original St. Jude was constructed. So that it would have had a very independent or semi-independent existence. So, for example, if he decided that it would want to mortgage two acres or a acre of that land to raise the money, it could have done so. And it may have been possible for a bank to say, well, listen, since we are getting the land as a security, then there's no need to go to Parliament to get Parliament to approve such lending. We get a guarantee. That was the objective. Of course, all of that went up in smoke because of what happened with that historic fire and subsequent problems. So it was not essentially correct to think that a guarantee was not necessary. Under the old section 20, it was for the Minister of Finance to set the terms and conditions and it was for the Minister of Finance to say, listen, well, I'm agreeing that you need a loan, but I'm not letting you go and get that loan unless we go to Parliament to get a guarantee. That's what it meant. What this does, this amendment does, however, is to say that in all circumstances you need a guarantee, so the Minister of Finance has to come. Now, of course, why would you do this? Simple. You now have a public finance management act that compels you to do things like this. Because other than the terms of the new public finance management act where you are required to provide that guarantees for the slightest amount of money you borrow, then you have to come and do it. So the larger imperative is that act because you would run afoul of it. So the reality is that the government has been obedient to this new public finance, this new minister called the Public Finance Management Act that is insisting on this. But it is incorrect to suggest or to imply that somehow there was a deficiency that would not have allowed St. Jude's Bowl to go to Parliament. But of course, these things are strange. When the government takes the step to do this, quite correctly in obedience to its Public Finance Management Act, then when we in this world of guarantees, we can't be lukewarm to insist to get a guarantee so that you can get an overdraft to pay staff at St. Jude. But all the loans that were raised for persons to build the new hospital and conduct other work, those can stay at large, those have to be brought here too. I've always said repeatedly that you can't go and give loans or allow investment by direct purchase orders and they don't come here because it is a liability on the government. So I'm hoping that the day will come when all the money that was made available to fresh start will reach the floor of this house for full debate. And I'm thinking that perhaps this is just a tip of the iceberg for that debate to commence because if fresh start expects to be paid for the work that it has done in constructing that boxing view for, then it has to be legitimized and there has to be a debate in this house over how it got that money, how it was possible for the Ministry of Infrastructure to have estimated No, no, no, no, Ministry of Infrastructure to have estimated that preparing a site would cost 3 million and the Ministry of Economic Development allowed a contract for 9 million. And I raised this in this house when I was in opposition and I sought an explanation at the time. So, Mr. Speaker, I'm just saying that we have to, yes, we have to bring the thing to its natural conclusion that if you're going to ask and do it together, I guarantee to raise money from the bank so that you can pay staff and deal with overdraft to legitimize that. No problem. But look for my part, from my point of view, Section 20, as it was, could have done the job. But in the circumstances, as I said, you have a new public finance management back, you have no choice but to come to Parliament and do this because it is compelling you to do this. But at the same time you're doing all of those things that you did with St. Jude, we have to make sure we come full circle and that the monies that were made available by direct purchase to do the construction, etc. I hope that they come to Parliament as well so that we can cast judgment and cast opinion on these matters. Because I have always stayed in my position very frankly. If you see ever you come to a situation that you have fiscal difficulty, the first thing that the government will have to do is to decide whether it is paid any of those bills, any of those monies, any of those investments by direct purchase, by contracts of direct purchase. Because they are not secured by Parliament as a solution. I have always said so, that has always been my position on these matters. As I said, Mr Speaker, I am not here to repudiate what I have believed before and what I have said before. I will honor those things unless I have compelling reason to change. And nothing has made me change. So I am suggesting and making clear that if you are going to be acting in obedience to do this, then I would want very soon sometime in Parliament so that we can open a can of worm zones and for all, that we have a full debate on the monies that were made available to construct the box in view of thought. That is an eyesore, that is a problem for the people of view of thought and that has to be resolved. We need a very full debate, Mr Speaker. I am not going to waste too much energy on this because as I have said, Mr Speaker, it is very clear what this is all about. Not that it could not have been done before, but of course you do have to be here in obedience to the legislation you passed. So that is it. But the addendum to that, time to have this debate on the financing of that box in view of thought, how it happened, who made your money available, how much money. Let us get to the root of this matter and a public debate is vital and necessary. I thank you, Mr Speaker.


The current study found that women experience higher levels of anxiety than men, and men are more likely to use problem-focused coping strategies compared to women. Additionally, the study showed that any level of anxiety increases the risk of hopelessness, and problem-focused coping strategies have a negative effect on hopelessness. These findings suggest that it is important to provide people with pre-prepared mental health protocols during a crisis and to focus on problem-focused coping strategies, particularly among women. This article was authored by Kodemirad Momini, Yaya Salimi, Muhammad Rezumaj Subi, and others.


Happy holidays.  Good morning. Look, I got on this big-ass bunnet This is that bunnet by red by kiss that they sent me y'all look. Um, I Guess cuz yesterday was the day after you know The holidays and a bunch of stuff that it was the day after Christmas I got bombarded with all bombarded Y'all got attacked by all these emails coming in after my email So look, I'm hating on other youtubers y'all I'm about to call you says angel. Nancy. Naps. She's did her last video video as it pertains to Her hair regiment her hair journey. So she finally made it to wasteland. I Thought you were wasting like a couple of years ago No, that was busby busby was a busby was actually at was like two years ago. Um, I Think she was but I thought angel was too. But anyway So she's going a different direction on her channel angel is a aka medzi naps and I know a couple of y'all are subscribed to her But I was looking at it jealous cuz I'm like what the hell? I'm pretty sure I can get to wasteland by the end of next year Especially since I won't be using a lot of new products I'm gonna try to minimize my heat use usage and yeah, I'll just keep my hair leave my hair alone Hey, you guys so today. I'm gonna be making crock pot turkey chili I just don't have a lot of time today to cook. I love to cook don't have the time So I'm throwing everything in the crock pot. So we're gonna be having Quite a bit of ingredients. I'm gonna take my time to go through them By the way, I'm using what I have in my pantry. I typically keep a lot of the stuff just on hand So here we go. We have kidney beans black beans Mexican style stewed tomatoes dice tomatoes beef bullion garlic bell pepper Onions jalapenos a package of seasonings Corn in the back ground turkey as for our seasonings. We have garlic powder onion powder black pepper salt Red pepper flakes oregano. I don't have cumin. I typically would add that so what I'm gonna do you guys is brown My excuse me a salty my veggies on top of the stove Brown my turkey and then throw that along with everything else with the exception of The beans and corn throw everything in the crock pot two hours after two hours at my beans and corn I'm also thinking I may just add I'm gonna add some tomato paste and tomato sauce a new duffel bag came For a trip in a couple more weeks to Texas. I'm buying our tickets next week y'all these tickets are ridiculous ticket prices range from five fifty to almost eight hundred dollars, so I I hate to come in kind of late, but we're gonna come in Not really late. We're gonna be flying in six o'clock at night. We're getting here six The reason why it seems like this is because it's getting darker later here early here in Phoenix So by five o'clock it's been getting dark JB showing you so this is a good size. I mean we're only there Thirsty through Sunday Four days I could fit four days of clothes in here Hey, you guys it is this girl this vlogmas. I'm breaking all the rules basically Vlogmas is different. It depends on what you want to do. You know the whole Point of it is to vlog during December some people vlog up until Christmas some people vlog the entire month of December Some people may do one week It just depends on the person So for me personally, this will be my last day since I started late I wanted to give y'all a lot so this will be basically 20 blogs and one month. I think that's pretty dang on good Excuse me. I Haven't added to your problem I'm change. I'm trying to It started to manifest yesterday. I got a lot of emails today after And I told y'all this the day after Christmas I'm having to redo a video It's got me a little bit bit attitude, but it's okay. I got some feedback from another youtuber Thank you girl. I really do appreciate that. I know she sometimes watches my vlogs. I Told y'all I'm open to Critical criticism. Is that how you say it? Yeah, I'm tired. I'm not tired, but mentally I'm wrapped up girl so this morning I am Doing a brain dump Basically jotting down all my ideas for 2020 for YouTube videos you guys I've already communicated this and My changes to my channel video, which by the way that video got very low hits So if you didn't watch it, don't be surprised. Don't be asking me why I'm not reviewing mo nose hair stuff No, when I told you it's going down the content is going down. I mean I can't remember exactly what I said in that video, but it'll be three to four videos a Month as opposed to a week. I think I mentioned that so anyway I already have my idea of staying on as far as hair related videos And I'm just capturing all of that all these brain dump sheets that I got from Alexis. She's in her trench coat. She is a Productive planner Content creator, I absolutely love her right of my alley Also, I am planning my hour trip to Texas. I will be vlogging that because that will be lit That would be a two-part blog too My mother is celebrating 60 years on this earth and We are going to our birthday party y'all when my parents do parties They do my family in general When they do get together some parties they do a big they are all extroverts um I mean some clearly some of them, you know mixed personalities, but overall They like people Sorry, y'all. It's dry here. It's my throat. It's dry So yeah, my mama spent a good change on this party. I know she did And the theme is going to be Paris a Paris theme. Oh la la the color will be blue A navy blue. Yeah, they do it like that. Yeah um And it's a big family My mom was the youngest of 13. My dad is the middle of 10 And all they butts will be their cousins or in the hundreds. Yeah, so it's a big family. Um, I'm excited though She asked my sister and I to emcee the event my sister's going to do it.  They have a close relationship discovering natural is a natural her youtuber out in texas Nigerian woman beautiful family. She's so funny to me y'all I envy that my sister only have one sibling my sister. We are not close at all There's no bad blood. There's no bad beef. We're just not close. We are extremely different personalities to the point to where When people have met her, um When I was in college, they were like, that's your sister. I'm like, yeah, I love her My sister She's what you call hood country That's that's what I call her hood country. So anyway, y'all Planting the trip to texas. We will be going the first week second week of february We will be staying in urban my parents live in east texas. Y'all know this The east texas is huge texas is huge We are about 40 minutes away from street port louisiana Long view close to tyler keogh or marshal our rather just especially since jb is going It's just us by herself. I would rather just be you know, I'm very familiar with dalas even though the dangled tall ways when we were there earlier this year Y'all have gone crazy with those tall ways girl girl chocolate cap coin. You need to come pick me up from the airport Look, I'm gonna assign some of my subscribers to pick us up from the airport You need to pick us up from the airport I need another person to drive us to east texas No If I wanted to I could have my family to do all that but I don't like to depend on people y'all This is my personality. I've been this way since I was 17 I don't think ever My husband unfortunately cannot come with us because he's using all of his vacation for JB's birthday y'all Why didn't y'all tell me JB's birthday was coming? JB's birthday is coming up and like three more weeks So we we don't do Big parties or anything. First of all, I am paranoid and afraid that if we do something either I know that kids will show up, but I'm just paranoid. So I Instead I do little get-togethers at our house Last year we Did a hotel We stayed there. We had such a good time And we went out to eat and I made him a little cake and invited friends over. I think I'm gonna do that this year Yeah, I'm going to Make a cake. He wants a super mario theme. He wants a coconut cake I hope you bring an allergic to coconut because that's what we do it All right, you guys I yeah plenty my I'm a planner. So I use extra Notebook paper For my happy planner. I used to happy planner you guys Um to help plan my trips. So I have stickers here. I have my to-do list I have a packing list and I've already started Um, I have a note list for flights here I haven't booked my flight but one of the things that I started to do, you know, one of the Unfortunate things as african-american So people of color in general is that we haven't had good examples Um as far as being financially fit health physically fit. We ain't gonna talk about that So we've had to either learn from our own mistakes or our parents mistakes Other cultures have either had examples in their life. Um, they've had a nest egg They haven't had the necessarily and this is not all okay. Um, this is not everyone Let's just be clear of that, but they haven't had the Uh, they've had generational wealth. We haven't had that You know, we haven't he'll we just got out of quote-unquote slavery. Some of us are still in it But you know, we haven't had that so I've had to learn. Um, and I've learned from my from my um My white older friends or my white friends So one of the things I've learned as an adult is that if you can pay for it upfront do it Don't get um caught up in pink girl black people will be thought I'm gonna save up my money and get it when I have my money saved up Or I'm gonna, you know, I'm gonna make payments on it My husband for the first his first few vehicles. He paid for them in cash Or if he has at least a vehicle he'll pay it under the long requirement. He'll pay it off really fast. Um so For this trip I learned to uh, I have my credit cards, but to use the point system Um, and my neighbors who are from paris, texas, they're like, oh, yeah Well, we what we tend to do is we use our credit card To pay um mumbling. We'll get a credit card that has a good interest And one that gives us rewards and we'll use that that one credit card specifically for traveling And that's what I learned to do the course of the past five years or so So I have my one credit card that I use I treat it as like a monthly bill, of course I use that for Traveling but I also use it for gas to keep the points accumulated and then I'll pay it off double What the the requirement payment monthly payment is okay? So I was able to get my car for this trip Just using those lessons again from other people because girl I didn't learn anything from my parents that way Seriously, I'm just being honest So I was able to get my car for the texas truck using my points that I already had accumulated over the over the year.  I'm not okay. If I pay for my Dallas at least my Dallas hotels If I pay for those now, I say 75 dollars Done, so I'm gonna pay for those hotels get the tickets in advance um Yeah, so it's hard, you know having to learn things on your own and make mistakes Yeah Look at that No, you can't put it back Look at that It did it at the crossing that's very weird Yeah, we just got a lot out of the library And you saw that my glasses are dirty. Um, you saw that the train that we were on derails out of all the years We've been arriving that train and we've been going to this train park for almost two and a half three years We've never seen the train derail before. Um, so y'all I'm almost done. Okay, baby YouTube hold on. Let me clean my glasses and come back on cam Honestly, I think I made it a little bit worse, but we're gonna do youtube straight hat me panicking I when I upload a video, I try to check my messages at least for the first 24 hours y'all I don't I have some a couple of videos that have high numbers So I don't have time to be checking comments on those old videos, but at least for my new ones I do So I'm in the library, right? And I'm checking and all of a sudden I see vlog number 17 And we're on vlog number 19. So I see vlog number 17 13 12 5 And some random hair vlog from earlier this year. I mean hair videos. So I'm like am I in a history Don't do that, baby. Am I looking at a history? Am I looking at a playlist? No, I sorted it by newest newest videos only eight videos appeared I'm like, what? I get out of it. I get out of it because I'm not panicking yet because I'm like, this is just something going on, right? I get out of it. I close it. I open it back up saying thing eight videos I'm like, okay, calm down. I type in my name vlogmas Five videos show up. It should be about 19. Right five videos show up. I'm like, okay, Vivian I look at my history. I click on a video that wasn't listed on my view. I was able to view it I'm like, okay, so the videos are there So something's going on in the background to why my videos aren't appearing So then I go to my community tab not available Not available Y'all I freaked out changed my password did everything Yeah, got JB out the library rushed over here to the fries check my account again. Everything's there YouTube got Like literally almost nearly 90% of my stuff had disappeared for like 15 20 minutes. I'm sure none of y'all noticed it But still that's dangerous We gotta go


If you're wanting to get into classic sci-fi authors, this is exactly the kind of thing that you should be looking for. A vintage anthology of stories written by some of the biggest names in science fiction and edited by one of the biggest names in science fiction. This particular one is edited by Arthur C. Clarke. Isaac Asimov and Robert Silverberg made countless numbers of anthologies collecting stories by their compatriots that they appreciated and they're some of the best things ever put together. This collection has some great stories in it. A lot of them I had already read and they're classics here I'll show you. In this particular collection, Clarke used the gimmick of dividing the stories into scientific specialties like mathematics and meteorology. The first one here, he built a crooked house by Robert Highland, is a classic about the fourth dimension and hypercubes. The artifact business by Robert Silverberg, speaking of Silverberg, is not one that I was familiar with but I enjoyed it a great deal. Grandpa by James H. Schmitz was one that I had read before and I'd forgotten that I had read it but I remembered as I went along. Not a great story as it goes along but a great ending. The Little Black Bag by Cyril Cornbluth about medicine in the future and social commentary about specialized education. Exactly the kind of thing you would expect from Cornbluth. And The Potters of First by Jack Vance. Again, not a story I read before but fantastic. So yeah, this is a perfect example of the kind of thing I recommend if you're wanting to learn about classic sci-fi authors. Please remember to press that like button, it helps my videos get seen. And then subscribe so you can come back next time. I do science fiction book, TV and movie reviews all the time. And please consider becoming a patron, there's a link in the description below.


the journey to the Axiom of Exceptionlessness. There's a certain arbitrariness in choosing where to start any story. So I am starting with Marcus Zuerius von Boxhorn who lived from 1619 to 1653 and he's at least as reasonable a starting point as anyone. He proposed that Dutch, Greek, Latin, Persian, German, Slavic, Celtic and Baltic languages all descend from a common source and very importantly he thought that this common source was not Hebrew. At his time following biblical traditions there was a tendency to try to derive living languages from other living languages in particular from Hebrew. So in instead proposing that living languages descended from something else from a language which is no longer around he anticipated the reconstruction of proto-languages and also his choice of related languages is correct by our standards today in terms of isolating the Indo-European languages as opposed to other languages. So the next stop in our journey is Gottrib Wilhelm von Leibniz, 1646 to 1716. He's famous for many reasons including being together with Newton, one of the joint founders of Calculus. So he divided the languages of Europe into three groups depending on their work for God. You see Germanic has words for God to start with a G, Slavic words for God to start with a B and Romance words for God to start with a D. For our purposes what's important about his contribution is that he correctly identified Indo-European subgroups using some explicit criterion. Now the fact that this particular criterion got him the right answer I think was to some extent just luck but it also shows that sometimes the signal is just so strong that even using a method that would now be considered quite coarse can lead to the right answer. In other words spotting these three language families was relatively easy. So now moving on to William Jones. So William Jones is where many people begin the story of historical linguistics. He was a judge in India, a polyglot. As someone knowing Greek and Latin when he learned Sanskrit he was really struck by how similar it was to Greek and Latin and Greek and Latin and how beautiful and well-structured it is as a language. Something that I think anyone who has studied those three languages can only agree with. So he really drew attention to Sanskrit and it turns out that knowledge of Sanskrit makes the study of Indo-European much easier. So now I will just give some evidence for that. So here we're looking at Latin, Greek and Sanskrit verbs in particular the verb to bear or to carry. So I'll just read this paradigm out loud. So first person singular, pharaoh in Latin, pharaoh in Greek of course originally it would have been pronounced and then in Sanskrit. So then second person singular, phares, then third singular, and just notice the s in the second singular, the t in the third singular in both Latin and Sanskrit. The long vowel in Greek pharaoh cognate with the long vowel in Sanskrit, barami. So there are just many similarities in these paradigms. I won't talk through the other two numbers. Anyone who had learned these three languages would be naturally inclined to compare their structure and it turns out that Sanskrit provides a nice model for exploring the structure of Greek and Latin and this research agenda of using Sanskrit as a sort of key for analyzing the comparative morphology of other Indo-European languages was taken up by Franz Bopp, 1791 to 1867. So he systematically studied the comparative morphology of Indo-European languages and can really be I think considered the founder of comparative and historical linguistics. So now the next stop in our journey is Rasmus Rask, who lived from 1787 to 1832, so quite a short life, and he discovered what later came to be called Grim's Law and showed also that a Vestin was an Indo-European language, a Vestin the sacred language of the Zoroastrian religion. So now I'd like to present Grim's Law. So I'll put it together a piece at a time sort of starting from some specific components and then moving towards a more general statement. So to start with Indo-European P becomes dramatic F. I use Sanskrit and Latin, which come from quite different parts of Indo-European to exhibit this. So we have Pittar in Sanskrit, Pater in Latin, Father in English, Pada in Sanskrit, Pez in the nominative and Pettis in the genitive in Latin, and then Foot in English, Pisces in Latin, Fish in English, Purna in Sanskrit, Plenus in Latin, and Pole in English. So pretty good evidence that a P becomes an F in Germanic. Next, an Indo-European T becomes a Germanic Th, written with Theta in the IPA. So we have Tri in Sanskrit, Trares in Latin, and Tri in English, Thvam in Sanskrit, Tu in Latin, Thao in English, Tut in Sanskrit, That in English. So again, pretty good evidence that Indo-European T becomes a Germanic Th. Indo-European K becomes a Germanic Ha, pronounced Ha in English. So we have Kefale in Greek, Kaput in Latin, where the letter C makes the K sound, and Head in English, Kardia in Greek, Kors in the nominative and Kordis in the genitive in Latin and Heart in English, Kouon in Greek, Kanus in Latin and Hound in English. So that's the evidence for K turning into Ha. And now we see P changes into Fa, T changes into Tha, K changes into Ha. So altogether, we have voiceless stops becoming fricatives. Now I move a bit faster, only give one example for each specific change, and then move to these more general switches of manner of articulation. So we had stops becoming fricative, now we have voice stops becoming de-voiced. So B becomes P, for instance, Latin labium becomes English lip, D becomes T, so Sanskrit doshan, Latin dekem, we get English ken, G becomes K, Latin gelu gives us English cold. So those examples show that voice stops become de-voiced. And then we have murmured stops becoming voiced. I give Greek here, but in Greek the murmur stops were de-voiced. B becomes B, for instance, Barati in Sanskrit, Pero in Greek, and Bear in English. D becomes D, Madhu in Sanskrit, Methu in Greek, both meaning honey, and then Mead, alcoholic beverage made from honey in English. G-H, so G becomes G, Stignoti in Sanskrit, Steakene in Greek, and German Steigen, which means to climb or yeah climb step up. So putting these three sort of overall changes together, we have de becoming de, de becoming te, te becoming the. So murmur stops becoming voiced, voice stops becoming voicestops, voice stops becoming fricatives. It's as if each manner of articulation moved one over in some game of musical chairs. So that's a generalization that's extremely broad and takes in a lot of details about the development of Germanic. And now with Grims law in place, we have a tool whereby we can weed out promising but false proposals. So if you just prima facia look at English have, is it cognate with Latin Habeo? Meaning exactly the same thing. They look so similar, must be related, right? But no, English H comes from K as we've seen, whereas Latin H comes from a G-H. So they can't be cognate. And instead, Habeo is cognate with English give. And English have is cognate with Latin Capere. I think that's a nice result, right? We have a generalization. And then if we believe our generalization, we can use that generalization productively. But there are some exceptions to Grims law and that's what we'll look at next. So Carl Lautner, 1834 to 1873, who I so far have been unable to find a picture of. And if you have one, please let me know and send it to me. In an article in 1862, he catalogued all of the known exceptions to Grims law. And one point I want to make in this presentation is what a service to science that is. In the rat race of academia, there can be too much emphasis on trying to produce new results or use new methods. Well, here is a guy who just systematically collected evidence in a tidy way. And that is not an activity that gets a lot of glory, but is enormously beneficial to the progress of science. So two of his readers were then able to find patterns in these exceptions. So one was Herman Grasman, 1809 to 1877. So he solved one of the classes of exceptions to Grims law and then is also known as a great mathematician. So here is Grasman's law. First, let's look at the exceptions. So we have Grbnati in Sanskrit, cognate with grab in English. Now, the problem here is the G in Sanskrit corresponding to a G in English. We should have a G H in Sanskrit corresponding to a G in English. And then in another example, we have Bodati, cognate with Pothomai in Greek and Bid in English. And here the B in English should have a BH as its cognate in Sanskrit. So Grasman's proposal is that both in Sanskrit and Greek independently, if you had aspiration on either side of a vowel, the aspiration was lost from the consonant before the vowel. So we have Grab becoming Grab. So the G diasporating. And then Bod becomes Bod. So the B diasporating. Just to make clear, this hypothesizes that in Indo-European, everything works, right? So Indo-European had G H R BH. And then that gave us the G in Sanskrit through Grasman's law and the G in English through Grim's law. And similarly, Indo-European had something like BH U DH. And then that becomes BU DH in Sanskrit through Grasman's law. And it becomes B in English through Grim's law. There were still a few exceptions left for Carl Werner to solve. So Carl Werner was 1846 to 1896. And in an article in 1877, he solved the remaining exceptions. So Werner's law is is tricky. And it's easiest to remember using these two kinship terms. So the regular development we have is Brata in Sanskrit, Brothar in Gothic and Brother in English. Now English actually collapses the distinction that Gothic maintains. So that's why we have to turn to Gothic for the Germanic forms here. We're looking at the medial. So we have a T in Sanskrit becoming a Th in Gothic. But then in the word for father, the T in Sanskrit becomes a D in Gothic. Now what Werner noticed was that the placement of the accent was different in these two cases. So in the word for brother, the accent in Sanskrit is before the T. And then in the word for father, the accent in Sanskrit is after the T. So we can generalize that Grim's law does not apply in stops that come after unaccented syllables. Now I'll just point out that Werner's law explains what's called Gramartische Wechsel in Germanic. And I and this phenomenon is extremely marginal in English. It's really, really marginal. There are only these two examples. But I give them was and were, is and are. So you want to know what is this S in the singular, R in the plural, alternation about, we'll just notice that it's predicted by the placement of the accent in Sanskrit. So we get S changing into R when the S follows an unaccented syllable. So Werner's law is extremely impressive because it's connecting the development of constants in Germanic with the placement of accent in Sanskrit. So Werner's achievement in solving the remaining exceptions to Grim's law was extremely impressive. And two people who were impressed were Karl Brugman, 1849 to 1919, and Hermann Osthoff, 1847 to 1909. And then they founded a school of thought called the Neo-Gramarians, where they said that this result, namely, that a sound change has no exceptions is just how sound change works. So that is called the Neo-Gramarian hypothesis. Although it's probably more accurate to call it the Neo-Gramarian axiom, because it creates a research program where if we find exceptions, we have to explain them. So this axiom is that sound change is phonetically conditioned and admits of no exception. Now, apparent exceptions then can either be explained by more sound change, more refined conditions to sound change, by borrowing or by analogical developments. And I won't talk about barring or analogical developments today. Instead, we will rest content that we have completed our journey towards this Neo-Gramarian axiom.