Should I spin this one, learn the marché. Okay, thank you everyone. So for this last lecture, we'll start by giving you references. So here I mentioned two books to learn about the theory of free probability. There is the first one, which is very abstract, and you can pick a lot of materials independently in different chapters on it. I love this book, but there is not a lot of connection with random matrices that you will find in a second book. So Spicer is a contributor of two of these two books, so it is there is really a good continuation. So here you will find a lot of methods, the method of subordination amalgamation, a lot of things that are useful if you really want to compute spectra with your computer, in particular. So the things that you won't find specifically there are there it will be the theory, the combinatorics, if you like it. About what is more specific to what I told you during this lecture is the theory of traffic that I have written a monograph about the subject. So here there is a first introduction it's called traffic distribution and independence. It's the first volume. And then there's a second volume with two other authors, Cébron and Aguist, that you can read to go further into other aspects. But for the content of this lecture today I will talk about freeness over the diagonal. On this connection with traffic independence is made in an article with several authors, which is the team of traffic guys. Benson, I am Cébron and Aguist and Frank Gabriel. So it's a short article where there is not a lot of theory about traffic. We focus on this result of matrices showing numerical applications of how it works. And then the continuation of this aspect of this relationship, we develop it with Jeremy Bigot for the question of finding the spectrum of variance profile matrices and finding the outliers. For covariance matrices or for ambition matrices. So here again, it will be more about the numerics and release mathematical aspects of matrices rather than traffic themselves. Okay. So do you have questions about the last lecture? If not, let me just remember what we did in a second section. I was starting talking about this weird ensembles for which we need more techniques than the ones that free probability offers. So I gave a proof which was a bit technical that shows a convergence of traces for products of permutation invariant matrices. It involves a lot of techniques including graphs. So as you can feel the price you have to pay is investment you have to pay to understand this is quite high. We won't focus really on this, on this aspect we will try to move this complicated combinatorial results into something which is analytic. And especially yesterday with Mark Potter, you discovered that for the classical cases of Gaussian matrices, there exists fixed point equations called the subordination property in the case of the sum, involving the S-transform, S-transform, T-transform, all these voicoles could transform that voicoles could define 40 years ago, and that we use intensively today to compute spectrum. What we will do today after remark and balance profile matrices is to turn this analytical theory to a higher level, which is the level over the diagonal, a theory that also has been constructed by voicoles could 40 years but that has been applied recently for this weird ensembles. So the equation you have met of the subordination property this fixed point equation will meet the same equation but for slightly different objects. And changing a little bit this definition will change the algorithm somehow, it will be more consuming in terms of computational resources, but it will give a good solution computing spectra of this weird ensembles. Okay, so this is the program and let's start. I have to talk about the second kind of weird ensemble I want to consider it will be quite short and just to show you that the tools that we introduce with the trace of test graphs turns out this problem very easily from the moment point of view. It doesn't tells that we will have, obviously a nice solution to an analytic solution to compute the spectra but at the level of combinatorics and moments, this is quite trivial. Let me be more explicit. Assume that we are given a matrix HN that can be written as a Nadamard product a naturalized product of two matrices, but these two matrices does not play a symmetric role. One matrix is like your favorite random matrix you're studying the spectrum, like a GUI matrix or a Bernoulli matrix if you need sparsity. On the other guy, I will call it gamma n, and I'm doing the entry range product. These guys is a variance profile or just a profile function. Let's say your deterministic function. Once you take a shape like this, and you decide that you put zero here on the one here. Okay. So what you're doing is you're taking your matrix and you're erasing your taking your random matrix. And if you do this enterprise product, you're erasing a part of the matrix. We assume that this variance profile is macroscopic. Should I start again? Okay. We assume that this guy is macroscopic example. And it is not a restricted to this example but let's look at this. We fix a function f, a measurable function from zero one square to, let's say, see. And we set gamma n, it will be a n by n matrix with entry a j is this function that we sample at the point i over n j over. Okay. So I draw this picture you can model this by a function, the indicator function of an ensemble on the square. And then you just discretize your matrix and take this value. Of course, because there is this discretization we will assume that this function is at least continuous by path. If you have a measurable function there is a way to invent a relevant profile, where we not taking a point wise as a value because it doesn't make really sense for miserable function but let's look at this. Okay. You can also take a variance profile gamma n, which will be a random matrix. Another example will be to take gamma and random. It will be independent of XN. And for instance, is one with probability alpha and zero otherwise. So you just destroying randomly the entries of your matrix. So just let me write something which will be just a little lemon that will end the section that tells us how to understand the moments of HN in terms of XN on gamma n. Remember that we define the trace of a test graph. And if you don't care about all the test graph you can focus on these simple cycles. This is just a way to encode the moment. If you take something more general than moments like add them up more products, you see that you can cook the good test graph to do that. But even for tea which is a cycle this is interesting to have this approach. Let me maybe recall the definition of this guy. This is a morning we need to refresh a little bit of what we had seen before. This is a single matrix, let's say, what does that mean. So it says it's represent an expectation of a normalized trace, but it's a bit more general. If you have an arbitrary graph like this, you have the set of vertices for which for each vertex to choose an index, your test graph on code matrices and the ages. You have a single matrix. So you, you put the same matrix on each edge. Okay. And then given this indices, you make the product of the matrix entries that correspond to each edge, which is represented like this in a short way. This is a sample on this mean fire of the value fire. Okay. Traffic theory tells you that there is a decomposition of this quantity as a finite sum. And this finite sum is organized. The partition, the partitions of the vertex set on there. Another functional called the injective trace denoted with this little nut. Apply on what is called the quotient graph of tea obtained by identifying vertices in the same block of pie. Okay, good. And this guy has actually very good properties when you compute it for classical model of matrices. The limit of this guy is either zero, either something non zero when he has a specific geometric or combinatorial form like being a double tree being a cactus depending on the model. Okay, so it's quite nice and it's also quite nice to see what is traffic independence because the formula is a product when it's zero. Okay. And what about variance profile. It will be quite trivial. In presence of permutation environment matrices. Maybe I should add one. Another definition that we involved that was involved in the proof two days ago. I called it a delta and zero. It's just a different normalization of this two and zero let me write explicitly the definition. It's the expectation of the product, the same product here. So I put five of it as a shortcut. Is it okay online. No one day. No one day. And here there is a fight. And for fight is a given injective map. So let's put a tip I to be consistent we are talking about this guy injective. So if a chain is permutation variant, when you're summing over five injective, the expectation you're not to the, you have an equity which does not depend on fire and so we just see that this guy is just a normalization of this guy right. And this guy is just a product of matrix entries. The expectation of a product of matrix. Okay. Let me change course to gamma n times X n. Assume that the matrices are independent. X n is permutation environment. Assume that the entries are boondi or boondi moments or assume that the quantities I'm going to write makes sense. This content is then. If you want to compute the injective trace of a chain, and you want to do that if you use this formalism as you see because of this formula. It is quite simple. It is what I call the injective density because it's a small quantity on the violence profile time, the injective trace of the original matrix and of course I forget something doesn't make sense. It's not for any test graph, or let's say any question graph if you start from the computation like this. Sorry for some mistake. So you fix a graph you want to compute the injective trace in the matrix of interest, HN. Actually, it is just a product of the injective density of the test graph in the violence profile. The injective trace of this test graph in the permutation environment matrix conclusion is that again, we have a simple formula which just involves a product. Why this is true. Let's look at the definition of this guy. Let me not write everything. We look at the definition of this guy. Let's look at the expectation I can, as before, do it here. But here, HN is the entry-wise product of a gamma N under XN. Okay, so I can just write this product as the product of gamma N of phi of E times XN of phi of E. I can also write a product of this times a product of this. Then I assume that the two matrices are independent. So I can just split my expectation product of XN of phi of E. But XN is permutation invariant. So it does not depend on phi. So this phi and this phi, you can put phi tilde, which is another injective map fixed where I am. Oh, I start from the expression of the trace. I should have a start from the beginning, working on the injective trace of the quotient graph. Sorry, it's injective. And here it's quotient graph.  This is just because you have just you're considering the expectation of products and entries. And of course, you can factorize that where phi tilde is any injective guy, not especially this guy. So you can put this outside. Okay, and you can rearrange, of course, you have the sum on this guy, but Okay, maybe I should. I did not, I define this for permutation invariant model, but I should say that when you have your variance profile, I was confused about this definition is not exactly this. When the matrix is not. So this works for XN. Yes, there is a summation, but I will write something different than the summation, it will be the same. But I will say that it is the same quantity like this, but where phi is a random injective map uniform. So it's just a replacement of the sum, random uniform, but being random uniform you know it's just doing a sum normalizing well by dividing by the number of elements, but if you balance this is what you get from the other term, you will get this formula. Okay, which the conclusion is that if you want to understand advanced profile matrix from the point of view of the injective trace, you will have something which is quite immediate to factorize. It doesn't mean that your distribution is easy to compute, because first this method allows you to compute moments, which is just one way to understand the distribution which is quite obscure quite algebraic. And this moment will be, you will have a summation, because you want to compute a moment by you have the sum over the partition of terms that factorize. So from the combinatorics point of view it is easy but it doesn't tells you that you will have a nice spectrum and a nice method to compute. Okay. So in the context of asymptotic traffic independence I want to go back to the techniques of that. It means that if you have a family of independent families of permutation matrices as two days ago. But for each matrix, you put the variance profile. The formula that I show you involving the graph of color right components. It's called, but with the pre factor. We will have we will factorize some terms due to the variance profile. So the phenomenon that the, the structure of three of trees rules the asymptotic of the moments of the injective moments, still be true. But just, you will have a factor, which depends on your variance profile. Again, I'm not going to the details about this but it is important just to see that it doesn't really modify what happened in this topic in this context. The computation we were able to do for pure permutation in round matrices is still valid when we put the variance profile. Just notice that if you have a permutation balance matrix, and you put the variance profile you no longer have a permutation in that matrix. Imagine you your violence profile is like this. Of course, you, you are breaking this. You're breaking the permutation in advance, but you're not breaking the method. Okay. Yes. No, no, no, no, no is sorry for not being very precise about this is a matrix. If, if a matrix is permutation invariant, this delta n zero is just this expectation for a chosen five. If not, you must some over all five and divide by the number of injective map, which is equivalent to take your random uniform injective map. Okay, but what is always true. If you take this more general definition is that the injective trace in a graph, let me put it by is always just the relation between these two quantities is always just a question of normalization. And this is always true. So we computed is n factorial over n minus V by. So this is always true. This is why I call it is injective trace and the injective density because it's just normalization. Is it answering your question. No, no, it's any matrix. If it is not permutation invariant, the definition of these dead ties and zero must be this one. You must average on all your matrix. If it is permutation invariant by just choosing in your matrix if you have a test graph of size three, you will have just to consider a sum matrix of type of size three, you compute your expectation involving this little part of your matrix computing this but permutation invariance tells you that actually this is the same thing as if you were doing this computation in all the matrices. Let me comment a little bit this, how do we compute that. Imagine you have such a test graph. You choose uniformly at random. You choose the matrices. So you choose. Okay, I'm going to be confused. So, a jk. So what does that mean, you choose a j choose a choose a k uniformly at random. It will give you the matrix entries somewhere. So you compute the product of this random variables. Okay, for a given a jk, you're just choosing three entries, but then you average over all the matrix, picking a lot of information on the matrix. Here, this is the same object. The test graph is a test graph and then you can take the question to the test graph you will get a test graph. Just the point is that usually you start computing a moment, then you model in your tea. And the first step is to write as a sum of question graphs. So the question appears as an expansion of a trace, but you can start with a test graph with repetition there. There is no repetition there there will be repetition there, but the nature of the object is the same on the right hand side on the left hand side in general. Of course I start by considering very specific object 30, like the cycles or the double cycles like this, but it was just a choice for the presentation. So this is just a way to pick information on your matrix.  So this was just to mention that this science profile matrices can be handled with this injective place. So let's stop talking about this injective stuff and combinatorial aspect on the start again with the classical theory of free probability at the level of amalgamation, which is a kind of analog of conditional expectation and introduce the notion of freeness over the day ago. Okay, so I recall you that an uncommitative probability space is the data of a couple. a phi, where a is an algebra phi is a linear map, playing the role of the expectation. You can also consider a star. If you want to do things properly but it will want to be mandatory for the presentation today. So I will introduce what is a conditional expectation in terms of this non primitive language. So this definition of freeness respective to this computational expectation. But for the moment I did not give you the definition of freeness just for fine. So I will start by giving this definition and then adapt it at the level of the conditional expectation, or maybe you will be surprised by the definition of freeness because it's not very similar to the definition of independence so we will take time. So, so you can see there a one a L, which are sub algebras of a classical theory you define the independence of sigma fields, right. And random variables are independent is a sigma fields they generate are independent. This is the same. We define the thing for algebras and different families of non commutative random variable will be free. And the algebras generate are free. So let's talk about this algebra. We say that they are free. And in the classical basic sense of very cool, let's go. And if we have this property. For all integer and for all indices L1 L2 up to LN. So indices that appear that choose one or another algebra. So the first algebra is not the second one. And the second algebra is not the third one but the third one may be the first one. We say that we take an alternating sequence of indices. So this guy, I told you there, they correspond to algebra so they are indices in L. So this algebra in this step, you consider an element in this algebra for all a one in the first algebra a L in the last algebra. But these guys, these n variables are sent to rate. j is zero for all j. Then the product of this variable and because it's non commutative, you must specify another is something. Is there any mistake or. I think it was on in words, we say that an alternating. Alternating, alternating refers to this property products of centred elements. So these guys are my centred elements are sent to my product as expectation zero. So one of the product is the product of the expectation, but the alternating product of centred elements is sent to it. That's it. And if it is the first time you discover what is finesse you should be a bit confused. But remember how you were confused the first time we define in classical independence in little school. It's the same thing. Why this is a good universal rule should be developed in a proper lecture. So if I want to compute a moment with that. It's not obvious maybe I should mention that. Let's say that I take different elements in a one a l and I want to compute the expectation of their product. If I'm not in the situation where it is an alternative product I must work on this formula because they have no no direct rule about that. For an arbitrary guy in the algebra generated by this guy, I can assume that by linearity. It is a product. I can organize my term in such a way I have alternating products. So that we have this property. If you take a monomial, which is a product of element of this, you can just organize a product to regroup the guy in the same algebra. Okay, and then write it like this. If I'm able to compute the expectation of a for any guy of this form by linearity, I'm able to compute five on the algebra generated by this guy. This is knowing the joint law of this element of this algebra. Okay, this whole doesn't tell me directly to this guy because I cannot assume in general that my guy are sent to write. How can I do to compute five of a. I artificially, I start writing the quantity that is involved here by removing for each terms the expectation on this expression is by stop it. Obviously it's not correct because I modify it. So I expand these terms to have a nice expression plus other terms. This guy is actually. So this guy is fire of these guys times the second guys times the other guy, we have this term, this is the one we know. So the other term are the one we obtained by removing all the other expansions, like if I choose first to factorize minus five of a on an arbitrary way the other one is to be another time that I will have to remove. Okay. Then, this guy is zero by fitness, because I'm just made things in such a way as an alternative product of alternative of central elements. And then, by addiction, I do the same trick to compute my terms here. It can be a long process, of course, because it is by induction, and it explains that computing moments in non commutative probability needs some some techniques because there is no direct method. Okay. Okay, so now we can consider what is a conditional expectation. Yes. This is the moment approach. In classical probability, you know you can use the expectation or the characteristic function which has very nice properties. Then, I'm not really mentioned it but there is the cumulant approach, which involves the subject mentioned by Jean, which has a non crossing partitions, and which is related to the Schringer days and formula we have proved for Gaussian matrices in the first Okay, so there is another way to translate what is a fitness and based on these objects, it will require an hour or more to develop this. Okay, so let's skip that and talk about fitness over there. So now we are considering a space which is a little bit richer. We now assume that we have an operator valued probability space that is a triple a B and delta where B is a sub algebra of a and delta is a linear map from a to B. We assume that it is a non commutative conditional expectation in the following sense that should be that should. Okay, let's look at this. The delta of B one a B two is B one delta a B two for all a in a and little bees in B. So what is the classical definition of the conditional expectation, you have the expectation of a product of XY conditionally on X, and you can factorize one of these variable. And you which go outside the filter here it is non commutative. So you do the same thing but on two sides. Okay, it looks just formal, but it works very well. Is it clear. Which example we will consider of non commutative probability space operator valued will take. So for the general for the algebra we take matrices or random matrices but let me write the deterministic setting for B and we will take the diagonal matrices. What I call the again of C on for delta we take the linear map that given a matrix a associate the diagonal matrix of the diagonal element of a. Okay. There are other structure on matrices which are very interesting and useful in practice with today for this weird ensemble this is the one we want to consider. Okay, so just a definition a bit abstract of a structure, but we can adapt the notion of finesse. And we say that sub algebras of this guy a are free over over B, or free with amalgamation over B but I prefer the shortcut. Even if I have these properties where no, I take my family is a J in the algebra generated by the good algebra I want as before, but also I include B, the operators I play the role of scholars, such that they are centered but not for the complex for the combiner for the conditional expectation. Then the conditional expectation of the product is zero. What is important to understand is that formally, and for, let's write it there because it is where it is important. And we replace the following replacement, we replace the complex numbers by diagonal matrices, and we replace the normalized trace by this diagonal operator. And if you make this translation at this level. So I have written with a file instead of the normalized trace, because the asymptotic finesse is just asymptotic I need the limit. But if you made the replacement you see that it is a is defined finesse with amalgamation. Just by replacing here. We add to the complex numbers. And by replacing the trace by the delta. So the diagonal is zero. Absolutely, which is weird why is it's interesting but it works so give you algorithm at the end so you don't be so picky. Okay. Okay, so it's almost the end. This part was quite technical and I think that if I come back to that to justify to justify that the relation it will be painful for everyone. Just let me sketch a proof that traffic independence implies finesse over the diagonal. And then I will answer your question if you have a moment. I hope that if I have permutation in one matrices I have this relation during this assumption. What we know is a technique to compute the trace of a product that involves this complicated graph of component, component or connected components. Right. Okay, let's try to imagine what happened. Take an expression like this. It is a moment. This is a product that I represent with a cycle like this. And I have several colors let's say we have two families and so talk to colors. If I find this. Okay. So these represent a group of ages in an algebra, a group of ages in the other algebra, and so on. We were considering matrices a one on a two remember. So let's say it is a poor of a one, a poor of a two and so on. So if we want to compute the trace of a poor. Let me just sketch the proof that this fire is zero it's not it's not showing that the delta zero but it will be it will contain all the ingredients. So let's, if we want to compute the fire we compute the total this guy, and we knew that it is a sum of a pie of the injective trace on here. So, up to a small error the indicator function of an event, which is that the quotient graph has a street a tree structure, the graph of color right component is a tree, but it's all pulled by trees, pulled by trees. Okay, let me not be more specific. So if, instead of just taking the trace of a product, I take the trace of products where I remove the diagonal. Let's call the V1 V2 V3 and so on this vertices as a junction between two segments like this, removing the delta. And considering not only a product, but it will be a linear combination, which should be complicated. In general, because as I told you we compute things for moments and so if you have a polynomial you should go for every monomial and have a linear combination should be more complicated. But because you remove the diagonal, it turns out that it actually simplified this formula. This is an equality. You have the same equality but we have a restriction. It won't be the sum for all permutation, but all permutation such that two adjacent vertices are never identified partition. And again, we have not just a monomial but a linear combination, but by some good properties, this actually simplify things instead of complicifying it. Okay, but now if you have a tree, a tree has branches and it has leaves. Okay, this is a very simple. So we should check on the combinatorics, but for the graph structure of tree. It means that if I take a branch of this to get a quotient, which give whose graph of color right component is a tree. We can see that at some point, I must identify one, one, one VI with one VI plus one. Because you just graph of color and component make I'm making an arbitrary graph sub graph like this, and I have a graph structure tree structure. So this condition of being a tree for the level of the graph of correct component is incompatible with the condition we add by removing the data. Okay, this is a sketch of proof. So just try to convince you that five zero. And once you have this technique, you can prove that at some point, and some level, actually the diagonal is zero, not only the trace but any, all the entries. Okay, so this is the end of the first part of the lecture if I'm correct, we have a short break. And just later we'll see a question we forget about these combinatorics and turn this formal notion of freedom servers diagonal into something analytic. Thank you. And you have questions or you can probably answer it right now. Yes. What does that mean. So the question is to specify what does that mean this right. A J. Also, let's say that assumes that AJ is just the algebra generated by a single element. Just to simplify what means being in the algebra generated by a and B, it means that being of the form B zero a B one a B and a B and plus one. B zero B and plus one and for some end on your complex if I because B is non commuting with a. If B is just the algebra of complex numbers, you can just factorize all the B and say it is will be proportional to a board. So you have to have to complete some of these issues. And so you have to to be too unsure that you, you're taking an element of this form or linear combination maybe such that the diagonal of these guys you will. Of course I'm saying diagonal but in the abstract setting it's not good diagonal its just you must find a way to approximate diagonal matrices which is tricky and technical I'm avoiding a lot of or is it more clear other questions okay if not let's have a break thank you other question nine maybe i don't think so


The main factors related to error are the presence of homopolymers, position in the sequence, size of the sequence and spatial localization in BT plates for insertion and eletion errors. No single variable can account for the error rate distribution, but most of the variation is explained by the combination of all seven variables. The pattern identified here calls for the use of internal controls and error-correcting base callers. This article was authored by Miloza Tibor, Ferreira Stephanie, Technicolas, and others.


Okay, this is a video response for Chad and Chris over at hppodcraft.com their latest episode they talked about a story by Clark Ashton Smith called Hunters from Beyond or something like that and they were laughing at this cover painting from the magazine where the story appeared and I have to admit when I first saw it when they posted it on Facebook I laughed at it too I was like is this for real is this I thought maybe it was a joke that somebody had had photo shopped up but anyway I wanted to I wanted to address what they said during their episode about how they thought that the artist didn't know what he was doing or he didn't care or that he misunderstood some of the vocabulary that was used to describe this monster speaking as a contract artist myself I can pretty much guarantee you that the artist had not read the story he was going by what someone told him to paint and he had to do it in a couple of hours it was due at the printer that day or the next day these cartoonists and painters that were working for magazines at the time they were just like the writers they were working for pennies they were doing the best they could with what little they had they weren't being told enough about what they were doing back in the early days of the sci-fi channel Harlan Ellison had his own show where he would sit in front of a video camera and rant about some science fiction related subject and one day he started by saying that he used to think that artists were complete idiots or at least completely incompetent because back in the day he would write a story about say a robot and it would be bought by a astounding magazine or something and when the magazine hit the shelves he would pick it up and the cover painting would have a robot on it but it would look nothing like what he described in his story nothing at all and it would be chasing a girl or something which didn't happen in the story and this happened repeatedly and over the years he was thinking these artists are breaking me down they're either completely stupid or they don't care or they're deliberately disrespecting me and many years later he talked to one of these artists who used to do these cover paintings and he asked him what the deal was and the guy said I never read your stories you think I actually got to read these stories before they were published no I would get a phone call from the editor and he was said I need a robot painting tomorrow and I would say well what's it supposed to look like and he would just say just paint a robot damn it click that's the way it was done and that's the way it's still done not only did these artists not know what was in the stories for the pictures they were painting they didn't even know which stories these paintings were for they had to crank out paintings they had to crank them out every day they had to go by what little they were told which is usually nothing paint a robot this library monster in this cover you were talking about here it actually looks kind of like what Smith was trying to describe so I'll tell you how this conversation went this artist got a call from the publisher who said I need a I need a cover painting today and he says well what's it supposed to look like and the guy says it's a guy in a library looking at a monster go paint and the guy says wait a minute what does this monster look like and the publisher says ah you artist in your details is it has like a baboon skull for a head and a puffy snake body just paint it we go to print tomorrow go I mean do you really think that these editors and publishers back in the day sitting behind their desks in their CD New York offices with their tie undone chain smoking with a bottle of bourbon with piles and piles of unpublished typewritten manuscripts on the disc you really think these guys were going the extra mile to make sure that every artist got a preview copy of these as yet unpublished stories that that no I mean today writers and artists have an opportunity to contact each other and cross pollinate and and produce some kind of some kind of thing that resembles what both want but that doesn't even happen today I mean look at the covers of magazines and books that are even being published today it'll just be a painting of a spaceship exploding in front of a planet has got nothing to do with any story that's in the book they need paintings they need them in time to go the printer and they need them now when you stop and think about it realistically for a second you'll realize how naive is the idea that the artist is supposed to know what the what the writer had in mind much less what the writer even wrote so yeah don't blame the artist if you want to get a better idea of what creative contract work is like there's a tumbler and a Twitter called clients from hell follow that you'll see stories of what contract artists and designers go through every day and you and you'll learn to be more realistic about your expectations so Chad and Chris I love the show I've been listening to it from the beginning and I'm looking forward to next week bye you can support 30 second sci-fi and my other projects by becoming a patron there is a link in the description below and visit the 30 second sci-fi tumbler that's my headquarters in addition to my videos I publish links and updates there every day


Now that the naming is finally settled, it's time we talked about Flatmap. Flatmap is the newest of the functional array methods, and browsers are just implementing it. But I expect it won't be long until it's available in stable releases. So let's get an early look at this new gem. Flatmap is similar to map in so far that it applies a function to every element in the array. However, if this function returns an array itself, each element of that array will be an element of the resulting array. That means that flat mapping an array can result in a new array with more elements than you started with. So for example, let's say you want to show your user the name of the items they ordered in the past, but your database only has a list of orders each containing potentially multiple items. Flatmap comes to the rescue. We use map to pick the names of the items from every order and Flatmap takes care of flattening all of this into one big list of item names. Quite handy and concise, isn't it? So if you found this interesting, I did some more videos on functional array methods. So if you haven't seen those, you should go back and watch them now. And if you want to stay up to date with the most recent supercharged, you should subscribe to this channel.


Sports are fun. I crave the competition, the adrenaline, and the challenge. In high school, I made some of my best friends through football. Sports could be hard at times, even painful. But my teammates and I shared that challenge and shared that pain. And we had a common goal. And of course, sports are a common culture. They cut across age, race, economic status. When a kid turns on the TV, he or she sees athletes, not mathematicians. They see how desirable it is to be an NFL player or an NBA star, or even a relatively mediocre, unpaid college point guard with a future as a plumber. They don't see the part about the plumber, but if you have any athletic talent when you're a kid, people will encourage you. I had coaches in my ear motivating me to do just one more rep in the weight room when I thought I couldn't do any more. I had the example of so many athletes and teammates next to me putting it on the line. Strangers would come up to me and encourage me. They would literally cheer for me. Strangers. And I'm not talking about my time in the NFL. I'm talking about high school. Needless to say, I didn't have math teachers who were coaxing one more problem out of me. They weren't calling the Princeton Math Department and telling them to recruit me the way my high school football coach was calling the Alabama football team. I didn't have any public mathematicians to inspire me or for me to want to emulate. I didn't even know what a mathematician did when I was a kid. I believe it's up to all of us to encourage young people to pursue mathematics, whether as a career or as a tool in whatever they're passionate in, or even as a source of pleasure the way puzzles are for me. It's my goal, even I believe my responsibility, to try to help others see how fascinating, rewarding, and even fun mathematics can be. I want us to put an end to the idea that anyone can say casually that math isn't for me. Math should be in some respect for everyone. We don't, as a society, tolerate illiteracy. We shouldn't accept math illiteracy either. Beyond that, I believe we should identify those who are interested in math, encourage them, and give them opportunities to push themselves and excel, much in the same way people routinely do for young athletes. I wish that when I were in high school, I had mathematicians to look up to and inspire. How can we motivate young people to become interested in math? There will always be kids who know from an early age that that is what they love, who dream of winning the math Olympiad, not a gold medal at the Olympics. But that only describes a few. I'll bet there are a whole lot more kids, just like me, who weren't even aware of their aptitude and interest, who weren't being challenged, who didn't even know that mathematics is a field that you can do things in. How do we reach them? How do we show them that math isn't just homework, that it isn't just drudgery? The National Museum of Mathematics is an important part of this effort. Their emphasis on interactive exhibitions, collaborative projects, and surprising solutions can instill a sense of wonder and excitement about mathematics. They can help instill a sense of satisfaction when a hard problem or puzzle is solved. I know no better feeling than that sense of satisfaction. It's not unlike winning a game. Only the game couldn't be more important. It's the game of determining what holds true. Thank you again to the National Museum of Mathematics, and most importantly, thank you to all of you. When a child looks at the Museum of Math, they see interesting and challenging exhibits and games, and a glimpse of the fascinating mathematics that underpins them. When I look at the Museum, I see something different. I see a community of people who know in their hearts that math matters, and who have made it a part of their life's mission to promote mathematics and inspire the next generation of young thinkers. And it warms my heart. For that, I thank you.


Our first speaker of the day in the developer and designer track, that's track two here is David Zimmerman. David has been consulting companies on their SEO strategies and tactics for over 15 years. He's helped everyone from publicly traded companies to mom-and-pop businesses. Eight years ago, David started his own internet marketing company in Charlotteville, North Carolina, Reliable Acorn, LLC. Recently, he launched curiousants.com to share what he's learned about SEO best practices with others. And today's talk, things well-meaning developers do to hurt SEO in 2023. So everybody give a warm welcome to David. Anyhow, everybody, I'm glad you're here today and glad I get to speak early because then you're excited and awake. And then later in the afternoon, we'll all be having a little food coma after lunch. So glad you're here. So this is really a talk and trying to talk to developers.  But I want us to have and find a common ground today, which is ultimately you may never want to do SEO for your clients. But I know you want to deliver a better product to your clients. A website that is set up to be findable, indexable, servable by the search engines, right? This is what we want. And the whole purpose of this talk today is to help you as a developer to know what you can do to deliver a better product to your clients that's more ready for SEO. So when we talk about SEO, I do always need to take a moment and define it because I find that at this point, everybody's LinkedIn profile says they do SEO. Every CMS promises SEO. Every email platform promises SEO. Everybody says SEO, but so we need to point out what are we talking about here? And I just want to define SEO as helping customers find what you have to offer. That's SEO. Your customers are looking for what you've got. And if we do SEO, we're helping connect customers to what you have to offer via your website. That's really what we are. But I think we need to take a moment and talk about what SEO is not also to clear it on the same page. SEO is not all web marketing. There are many ways to market a business online. But SEO is just one of them. You know, sometimes a client will say, Hey, David, would you SEO my email for me? No. Because that's a different form of marketing, right? Search is demand driven. If people are looking for what you have to offer, search is an excellent marketing channel. If people don't know what you have to offer, what you offer is so first to market that people don't know you solved the problem that they have yet. That's great. Congratulations. But search isn't your play, right? Search responds to customer demand. It doesn't create demand for a product. So SEO is one way to market a website, but it is not all web marketing. Second of all, and it kind of hurts me to say this a little bit, as much as I love SEO, it's not for everybody, right? Again, SEO responds to products demand. If people are looking for your service, SEO can help them find you. But if people don't know it exists yet, you've got such a unique angle to your product or service. You need to consider SEO, but that's probably not the way you're going to grow your business. Also amongst commodities, SEO can be really, really hard. If you're offering something that's just like everybody else has to offer, oh, SEO is going to be a hard play. You need to take additional steps in your marketing funnel to make sure people not only know what you have, but know how it's different, right? So we just need to understand SEO isn't necessarily for every business. This really frustrates me. So many people say SEO is just really about knowing the secret sauce.  If you use this tool and you install my plug-in and I'll put the keywords in the keyword tag, you've done SEO.  And that led to this because then that's the secret sauce to now SEO. Why are we trying to find whatever the secret thing is? Like SEO done right, it's just good marketing. It's not finding some secret that maybe possibly works for a week or two into Google and their immensely powerful web computing resources figures out you're trying to cheat the system and change the algorithm again, right? Are we chasing an algorithm or are we trying to market and promote what we have to offer? Don't think of good SEO as trying to trick Google. And this, this is where I step on developers' toes a little bit. So that's not a great way to start the talk. SEO is not set it and forget it. It's not the showtime or tisry chicken thing. Okay, thank you. A lot of reference here. You know, we can't just like SEO website and walk away, right? As a developer, let's get this out of our nomenclature and our contracts and our promises to our clients. Your clients are going to be disappointed if you deliver an SEO website. And that's the only SEO you've done, right? SEO is done is an ongoing process. It's an ongoing thing not only because Google's algorithm is changing hundreds of times a year, but Google loves new stuff on your website. So you have to keep up with it. You can tell your clients, I'm going to set your website up for SEO success if you decide to do an SEO campaign. But please don't promise that even if you implement all of the recommendations that I say here, your clients' websites are now SEO'd, right? I knew someone who said, I SEO'd the website. I installed Yoast. I think Yoast is a great plug. I use Yoast. I like Yoast. But that's not SEO, right? Or don't even get me started about some rush. All right, so SEO is not set and forget it. And SEO is not dead. I wanted to put like a Monty Python. I'm not quite dead yet picture here, but copyrights and all that. I know we're going to have a huge disruption coming up. Not just in search, but in websites. Thank you, chat, GPT, right? But it's not quite dead yet. SEO is going to look really different. Fact is rank hasn't existed for years. I know there are ranking tools out there that are happy to take a subscription for you and tell you where you rank. But they've been lying to you for years. Rank doesn't really exist. And rank really won't exist when everyone is using language models to answer their questions. So SEO will change. Wordpress will still be very relevant in that world. But I just don't want us to think SEO is dead because chat GPT. It's going to look different. But there's still these things that we're talking about basically are how the search engines and pay attention to Bing, because they're beating Google at that chat and language learning search results, right? Even the Bard engineers are kind of laughing at it is so bad. So pay attention to Microsoft and Bing a little bit more. But just know SEO isn't quite dead yet. So let's talk about SEO. And when I talk and describe SEO, I like to break it down to these four key components. First of all, we've got to measure SEO. This is true not just of SEO. This is true of any web marketing you're doing. The value of marketing on the Internet is that we know it works. We're not buying a billboard and hoping enough people see it and enough people remember the website off the billboard or the phone number and call you and maybe then you get some business, right? We're not sending out hundreds of thousands of pieces of junk mail with the hope we get a customer out of that. Digital marketing is amazingly targeted. And if we can measure it, we can know whether it works and we should keep doing it. Or it doesn't work and we should modify our strategies or stop doing it altogether. But all web marketing, especially SEO is about measuring it. Second SEO is about crawling the website, right? We need to make sure that when Google sends its spiders to our website, they can read it. Now, this is where we're really glad to be WordPress and we're not JavaScript developers freaking out about whether Google can read our framework or not. WordPress does this really well but we need to consider it and we'll talk about some of the problems WordPress has with crawlability coming up. Third, and we finally get to what most people think of when they think of SEO is the content, right? That's the third step of SEO. We're not just optimizing content, whatever that's supposed to mean from day one. We need to make sure things happen before that. And then finally, we have to talk about how other websites reference your site. This is called link building. This is fundamentally what makes the Google search algorithm understand what your website is credible. And so we need to talk about how links affect it when we talk about SEO. And if we do these four things, we're doing SEO. So let's start with the first one, measurement. And that really starts with a good analytics system, right? Now, I have been using Google Analytics for a long time and I still think that's the best platform for you to begin. I know there's a lot of rumors out there that Google Analytics is illegal. Have you heard this? Okay, good, because it's kind of an exaggeration. There's a lot of people out there selling products that are trying to generate fear. Oh, by the way, you got to buy our cookie management plug-in because of fear. Or you got to buy our paid analytics platform because you're going to get into... No, okay, I'm not a lawyer to disappointment of my mother. But be careful about fear tactics when it comes to analytics. Google Analytics has, you know, talking about financial motivations. Google has a massive financial motivation to make sure it complies with laws and is doing a really good job pivoting there. I know GA4, which we have, what, seven days before we have to be on GA4. Which meant we should have done it a year ago. GA4 is different. It is actually better. But we need to install. Now, you're developers. You deliver websites and build them for clients potentially. Some of you are saying, you know what, David, Google Analytics is out of the scope of what I do. I'm not going to do it. In fact, my clients don't even want it. But I'm here to tell you it is worth your time to install it on your client's sites because if your client's sites succeed, they are going to thank you when you've been collecting that data for them. When they come back to you three to five years ahead into your website refresh, you have data showing them not just how many people found their website. So now your website's no longer a cost of doing business. It's sunk cost in their business. Hey, competing today's world, you got to have a website. Oh, I guess I got to pay whatever for a website. No, you can show them the value of their website whether they ever look at Google Analytics or not. So please install Google Analytics. It's easy. The Site Kit plugin from Google makes this real easy. I prefer to do Site Kit in Google Tag Manager because Tag Manager allows you to add and subtract other analytics scripts. You're doing Facebook marketing, you're doing MailChimp. You can add and subtract without monkeying with the code, right? Set that up so your clients, when they decide to do Facebook marketing or messing with the website you've delivered them, adding more plugins and making the site have bloat, set up Site Kit, use Tag Manager. One of the other advantages of Site Kit is it makes it really easy to set up Google Search Console, which is an amazing source of data. I know there are very expensive subscription-based SEO tools out there that are more than happy to take your money for data that you never look at. Might as well get it for free from Google and straight from the source, right? Google Search Console has so many actionable insights, but you as a developer, even if you're not doing an SEO campaign for them, you know you still get that call when someone has a problem on their website. Why am I not finding it?  Search Console is going to help you because you've installed it already. You've already collected the data. You can then use that to say, oh, and by the way, you probably need to hire someone to do search or something like that, right? But the point is you have the data, you're going to get the questions, have the data to be able to help them. Here's the best secret. Have you heard of a website called Bing? Okay, you're going to hear more about it because they're really winning in this battle. Bing Webmaster Tools. Wow. Don't underestimate this. All you have to do, once you set up Search Console, thank you, Sitekit, making that really easy.  Bing Webmaster Tools is already set up. Bing Webmaster Tools is better than Search Console. You can use Bing Webmaster Tools to optimize for Google, right? But there's a lot of really great tools. There's a crawling tool where you can set it out and say, hey, Bing, see, I even did it. Hey, Bing, crawl my website. Tell me all the errors and it gives you ranked prioritized suggestions to improve it. Like it's a pretty great little tool. Key research in Bing Webmaster Tools is really, really great for a free tool. So please take this time to do it. But don't just set up Google Analytics. Websites are trying to accomplish a goal, right? There is no such thing as a brochure website. I know your clients think they have a brochure website. I know they don't only want to pay for a brochure website, but the website is a tool for them to grow their business. What is the goal of that website to help them grow that business? Make sure you track that in Google Analytics. So you know not just traffic, not just where the traffic come from, but how many people purchased a product, how many people called them, how many people submitted a web form. This is the value. But even beyond that, Google will tell you that. I'm sorry to invoke the Bible here. The quality of a website is a function of the goal of the website. This is in two sources that are really important for everybody to know about. One is, don't make me think, which I'm pretty sure most of you have read, and highly great book if you haven't. And Google's Webmaster Review Guidelines. This is a document. Google will have people going and doing searches and evaluating the quality of those searches. This is a document that basically doesn't give you SEO secrets, but it does tell you what Google thinks should be quality. And in there, one of the most important things it states is the highest quality websites have a clear goal, meaning brochure websites are not high quality, and it's really easy for people to know what the goal of that website is. And that's just a good practice. So deliver a better product to your clients by making sure their website isn't just a traffic generator, isn't just a brochure that maybe someone would find possibly. Show them how it accomplishes a goal that helps them grow their business, build it into their website as you're building it. Frankly, if you don't do it when you're developing a website, I've got to do it and you don't want me monkeying in your website. Now we've got to talk about privacy. This year already there have been three laws passed about website and tracking and privacy, and this assumes you don't do business in Europe or Brazil. And in a week, July 1st, even more laws are coming into effect about website privacy. Pay attention to this because there are laws about collecting data and what you do with that data that you should be aware of. Pay attention to there are a lot of products out there that claim and maybe use a little threats and fear to incentivize you in this. I want you to be aware of this. I also don't want you to be afraid of this, but if you are installing an elix, help your clients out by protecting them with a good privacy system. So the first step of SEO is done. We can measure what's going on. I tell my clients you can try anything you want, but we're always going to measure it, right? But once we've done, set up the measurement, we can then proceed into SEO by trying to make sure Google can crawl. And like I said, WordPress is so good at this, like almost instantly Google can crawl any WordPress site as long as you allow it to do it, right? That little check box has made me so much money in SEO audits, right? Because Google really respects that little check box. A really good buddy is a WordPress developer, and he works really hard to make sure it's set up for SEO. And we launched this website six months later, and we're like, what the heck? And he called me and asked, he's talking with me about it. He's like, oh, no. He knew the first question I was going to ask was, is this unchecked, right? Please. What I would do if I was you as developers, always have a staging server that is password protected in the root. That's the only way to prevent Google from indexing a site besides this check box. But it will prevent you from accidentally leaving it when you migrate it to the live server, right? Or at least, like, launch website, check this check box, right? Like, make sure here, like, it's so funny. We've all done it, but let's just do it. All right, mobile. Google, at this point, is what we're doing, what we call the mobile-first index. In other words, they're evaluating the mobile version of your site when they try to decide whether they're going to serve it and search results. So mobile, in a way, this should change how we develop websites completely. We should shift our thinking of web design development to a mobile-first perspective, right? And there's several reasons for a mobile-first web design philosophy. The basic one is so many people, I know your clients don't think people look on their websites on their phones. Because you have Google Analytics, you can tell them that's not true, right? But Google is looking at the mobile version of your site. But the best reason is, and we'll talk about this in a second, if you start with a mobile-first design, your website inherently is going to be faster. Because you're building up to desktop, rather than displaying stuff and hiding it on mobile. So start from a mobile-first design perspective. And thank you, Google. They have got this really wonderful mobile-friendly test. This mobile-friendly test is super powerful. I know it seems boring. I have a client that uses the JavaScript framework website. This also tests whether Google can even read your website. So if you ever get a client, you want to just make sure Google can actually even look at the site, use the mobile-friendly page. You want it to be mobile-friendly, and yes or no, right? But that's not necessarily a scalable solution, because this is a page-by-page tool, right? And you really can't always run it on every single page. So thankfully you've set up a Google Search Console. And you can look at all your pages. And you can see whether all of your pages are mobile-friendly. And so that brings us to speed. Air quotes. When we talk about, SEOs talk about speed, it really is not the right word. I know everybody likes GT metrics and all this stuff. Google, when it's evaluating websites for speed, doesn't have a stopwatch, right? It is basing your speed on not three, but as of this week, four Webcore Vitals. By next year, they're going to add a fourth Webcore Vital. These Webcore Vitals are not like stopwatches on your website, but specific things that the Googlebot can mention that imply speed. In other words, if you get the four Webcore Vitals worked out, you're going to have a pretty fast website. They don't want to use a stopwatch because everybody's Internet Connections Depth Rent. Everybody's, you know, phones slow, fast. Like, you can't baseline that, but you can baseline these four Webcore Vitals. So the best way to do this is the PageSpeed Insights tool, which will not only tell you how you perform as a score between zero and 100 on the PageSpeed 3 coming to be four Webcore Vitals, but gives you specific recommendations of what are the problems. Again, don't run this on your homepage and say, hey, I got 100 on fast website. No, that's a page by page tool. But, oh, okay, I didn't have the slide. However, thank you Google Search Console. We get an overview of our whole website and where it runs. You're looking for, it grades it into three categories. Red, which means almost your website's being paid, your web page is being held back in the Google Search Vault because it's slow. Yellow, which is, hey, got some work to do. And green, which is, we will give you an SEO advantage because your website is fast. So you're aiming for green. You don't have to get 100 that aim for green. Search Console gives you an overview of all your site. Good thing you installed SiteKit in Search Console, right? Okay, so measure. We know it works because we can tell it works. Google crawling it. That's what we need to worry about first cross crawl when it comes to WordPress. Now we're getting to the words. The words, wordy please. All right, the words. I know that you hate putting words on websites. I know. I've had the conversation with you so many times. I know, I know when I write content for your site, it looks like I've omitted a dictionary. But the Bible told me so, right? The definitive volume on web usability. Steve really brings out the idea that people need to see words on the page because it invokes credibility, right? He's not, this is not an SEO textbook. This is a web page credibility web book, right? If I put a picture of a lawnmower on a web page, that could be the most beautiful high res lawnmower photo you've ever seen, but you don't know what I do. Do I sell lawnmowers? Do I repair lawnmowers? Do I sue companies for lawnmower error accidents? Do I just really like lawnmowers? A picture is not worth a thousand words, right? You gotta give me some words to know why I'm on this page, or at least when it comes to search, if I land on that page to assure me I'm in the right place. I've landed on a page that can repair my lawnmower near me. Awesome. I see a lawnmower picture, cool, I'm in the right area, and there's words telling me I can repair your lawnmower. Whoo, I can work with this website, right? You gotta have words. I'm sorry. Don't pull out the pitchforks and the torches. You gotta have 800 words on your page. There's nothing magical of 800? In fact, if you do a thousand, even better, I'm sorry. I know you don't like to hear that, but you need it.  No, no, no, no, no, no.  With 800 words, you actually have to write something that's valuable and interesting. I find whenever I assign content to writers, if I do less than 800 words, it's just boring. They actually have to think about it to get to 800 words. So you gotta have words. Thank you. Those 800 words have to be unique. Don't use AI to generate content on your website. I know everybody's selling it. If in, sorry, when we move to AI, they do not want an echo chamber of AI providing answers based off AI-generated content. Right? I know it takes time to write website content. I'm just speaking to developers. I know your clients never get the content to you on time. Right? Hire a writer for them. Let them help your people write the content. Your efforts will pay off because everybody else is trying to trick Google. Everybody else is trying to cut corners. Initially, those websites will never be found. You taking time to write your own real content is going to be worth it. Invest now. Get the payments now. You don't have to wait. But we're talking WordPress development. There is a real problem in WordPress with the archive system. Whenever you have a category, gosh, if I meet whoever told someone that tagging blog posts is a good idea for SEO, I'm going to punch him in the face. Tags and categories create duplicate content, especially if the entire blog post is viewable on the blog post page, on the category page, on every page you've tagged, whatever word you thought some SEO thought, you're duplicating your content throughout your site. This has an SEO problem in that it makes Google try to figure out which page of these hundreds of pages with the same word should I serve in search results. We don't want Google to decide, tell them which one by using the excerpt function. This only shows on every archival page a small blurb, maybe the first paragraph, maybe the first hundred characters, and then make them go to the actual blog post. You can use the More button in every blog post to do this, but after doing that for a hundred blog posts, you're going to thank me to remind you about the excerpt function. Please just add that as you release posts. The RSS feed, another great source of duplicate content, only show the excerpt in your RSS feed, but images are important too. The fact is is that more people are turning to Google image search to find products in services, not just web search. So when you're building websites, make sure you use featured images within WordPress. This will help your social media marketing too, but it also on mobile search results. Again, more and more people are using mobile search results. You might find your featured image, make your website stand out in search results. Schema is super important. I'm going to get to questions in a sec. Schema is super important because it helps Google understand what you're talking about. I'll give you three digits, a dash, three digits, a dash, four digits, you know that's a phone number. Google does not pick up on the inference so well, so we use schema to encode things on websites, whether it's addresses, phone numbers, blog posts, whatever, to help Google understand what this stuff is. There's a whole thing we can do about schema. Yoast does schema really well. I know it's not cool.  Yoast does schema right on so many levels out of the box.  It's a great site, but the rich results for testing Google will show you what Google's showing with you as far as schema. Again, thank you for installing Search Console when you launch the website. You can see all the schema that Google's considering throughout your website. There it is. So now we've measured. We've set ourselves up for measure. Google can crawl our site. There's content that's not AI generated, thank you. And now we got to talk about what other websites say about you. Hey, your content in your website helps Google understand what you're talking about. But there's a lot of other websites that talk about lawnmower repair, whatever it is that you have to offer, right? Which is the best? The best website in Google's mind is the one that other people say, yeah, that's the great website. Awesome Paul's website is the best website. We know that because other websites link to Awesome Paul's website, right? So we need to make sure we consider how other websites link to us. Now, link building is another topic that probably outside the scope of building and serving up WordPress websites. But we do this by setting up proper URLs. We go into Search Console and Bing Webmaster Tools and it will show us potential errors on our URLs when it comes to link building we especially want to look for 404 errors. 404 errors don't pass link authority. So we need to set up a 301 redirect on every 404. By the way, if you see 404 errors in your WordPress website, you know those pages never existed. Another great way to find out if you've been hacked. So look for 404 errors, redirect those bad boys. This is the number one problem goes wrong. If you've ever launched a website and got a call a month later from your client and said, why has all my Google traffic disappeared? You might have missed the redirects. This is like after I checked the checkbox when I do a website audit. This is the second most common way new websites get launched. Make a plan, set up a bunch of 301 redirects for every page there. It will not preserve traffic, but it will help Google preserve the link authority. Make sure you set up canonical tags, especially if they're going to do web marketing. Canonical tags basically says, hey, I know this content, you can see through different various URLs, but we want you to consider this URL proper. Does it right? Just do it. All right, so we have gone through all the different aspects of SEO as it relates to WordPress currently. Please measure it whether you think your clients use it or not. Even if they won't use it, you will when they call you. Make sure it can be crawled by using these tips. Help your clients out by making sure they have a good amount of content that's unique on their site. And then make sure you set up things so that when the links come in, the website gets full credibility from them. And that's the beginning of an SEO campaign. Right? There's a lot more to do, but we've set our clients up for success with a better product. So one way to learn how to do SEO is Curious Ants.  You can visit this link so I know you can. But if you're thinking about maybe offering this as additional service for additional income, or you just think, hey, you know what? I keep getting all these SEO questions. I don't know what to do. Some of the things we talk about setting up is all documented in Curious Ants. So please partake of all that we have to offer. But I ended 10 minutes later than I wanted to because I thought you might have some questions. So let's take some time for some questions. Awesome, Paul. So when you talk about public account, especially with the excerpts and not, for whatever reason, if there is a website that has gone both in the archive pages by category, et cetera, most of the times, though, when you look in Search Console, it ignores category page one, page two, and all the tags. Is that like a... So if you've used the excerpt or the more tag, there's not enough on those pages for Google to serve it. But the problem is sometimes, for various reasons, usually because of internal linking, when Google will serve up a category page with an entire blog post, and that's what we don't want. Maybe that blog post is third on the page. So when a person lands on that page, they're like, I asked for about this. They see the first blog post, and they're like, I'm on the wrong place, right? And it creates frustration. If we use the more tag, the excerpt, we make sure when people do a Google search, they land on the proper blog post rather than have to find it on the page. Cool? Yeah. Awesome, Paul's friend. Whose name I've already forgotten? Charles. We used to use the featured image. I just wanted to clarify there. Are you saying use the featured image specifically versus any other images or use an image versus no image? Okay. So a featured image in WordPress parlance is associated with the post. It's like sometimes it's encoded as the hero image on each page. You definitely want to make sure that's included. You can add additional pictures after that. You can choose whether or not to display that featured image on the post page. I don't care if you do or not. I just think that you need to have a featured image. And that featured image needs to be encoded so Google and Facebook and Twitter can all see that there is a featured image, a unique image associated with each post. Gotcha. So that's the key, is how many unique images you're exposed to? Encoded as a featured image. You go specifically? Yes. Because there are places where, especially for like a custom post type, you can turn off a featured image because clients never look on the bottom right there for that meta box. So I turn that off and I just put an image upload field in the main column there. Not every page needs to be SEO'd, but if this is a page that potentially could drive traffic from Google, you really, it's highly replicated. Okay, thank you. Yeah, back to the categories and tags. I don't need to ask you so many because it would pay you to get content. What's the suggested number of categories? We need to understand what the purpose of categories and tags are, right? Just get away from the idea that there's somehow more helpful to add tags or categories. I say every, if there are two or three posts that could be organized by a category or tag then create the category tag for them, but don't create them just for the sake of creating them, right? And then it has to do with how are you using them? Are you using them to help people navigate to learn more about different things or not? If you're not, then it's not helping anybody, right? But I like to think of categories as every post is part of a category and only one category. If I need a separate way to organize my content I might at that point consider tags and then I might allow posts to have several tags so those tags are going to be overlapping and the categories are going to be unique per post. I mean, the point for SEO is there's really no magic with tags. It's really all about helping your users find the content, but the SEO problem is created when people go a little tag crazy. Yeah. Yeah. Yeah. And back. I think it just comes up in search. In other words, I just did metadata for a client, a whole bunch of images. We want to switch for marketing a little bit. How do I know if that metadata was successful? So, that's a... So, the answer is why they want to? And so that might be a longer answer we can talk about. I would... I always measure in my contracts for SEO I say I will not measure rank for you. Full stop. Find some other fool on Fiverr if you want measuring rank. I measure traffic as it relates and results in conversions. So, if an SEO initiative is successful you will get more traffic from Google and if it's successful that traffic isn't just in the traffic it accomplishes the goal of the website, the conversion of tracking. So, just be careful about going into well, but it's not ranking. Well, things rank all the time but will never send a single customer. So, let's forget it but that's the downside of reporting rank. We start talking about stuff that maybe no one else ever thinks of that doesn't really bring us customers which is the whole point. So, we got to be really careful about vanity metrics like I rank number one, I have 10,000 impressions on Facebook aren't I? Who cares? Did you get any customers? Like isn't that the point? So, we just got to pivot the way we think to think about customer acquisition and not vanity metrics that make me pat myself on the back and rank is kind of one of those vanity metrics. Sorry. But I was talking about Nim into rank. I think this is for an interior designer. Sure. He wants lower business to another part of the country. Okay. I need to know people from that part of the country are starting to find their image. Great. Google Analytics will say, you can say there's traffic coming from Google in that part of the country and it is becoming customers. So, any effort that we're doing to improve that interior design website whether it's image optimization or content optimization with words should deliver more traffic from that area and that's the most consistent way to be able to measure the success on that. You can think about traffic as a way of averaging rank. We can theoretically rank for something no one searches for and we can rank really well for something that a ton of people or nobody is searching for and traffic is a way of averaging out rank. Thank you. Yeah. I have a general question about URLs and I'll be late with a couple of them. Let's say you have an article on a general site that's the deadline is, step on digs is completed. Okay. So, that slug would be step on a stack of digs is completed. So, with the URL to that site would you pick a, you know, my website.com slash NFL slash players step on digs is completed again or would you pick my site.com slash step on digs is completed again Okay. Okay. Right. Right. Right. Yes. Yes. So, you'll notice I didn't really talk about keywords in URLs because it's such a minor thing. Right. But the URLs are still important to consider. The, I was about to answer the question. I got, I got into distracting my, I distracted myself in my own brain. Oh, I just totally got, right now. And I'll, I'll take a cup of coffee and I'll help. But yeah. All right. One more question. Yeah. So, I have a client who wanted to, you know, right, but be on the first page of Google search. So, even if I follow all the steps of SEO, it'll still take some time. Absolutely. Absolutely. So, number one, rank doesn't exist. Right. Rank doesn't exist. So, you will do yourself a justice to make sure your client understands that your rank doesn't exist. Right. You will search for it from your computer with your search history and your Gmail account. And that will have totally different results than he, than me, than her. Everybody's search results personalized. So, there's no such thing as I rank number one. Right. Two, he can think of something for which he wants to rank, but that doesn't mean anybody else is searching for it. So, that doesn't necessarily bring him into customers. All right. So, we've got to be really careful about that. But, I always tell clients, SEO is slow. Three to six months before we see the return on the investment. That's reality. You want to go fast, you got to pay. That's what paid search is for. Right. This is slow. Now, this is a slow, this is an investment because three to six months, we're building and we keep building and that's going to last forever.  Right. So, that's the advantage and disadvantage of paid versus organic. You've got the time and the ability to invest, it's going to pay off. But you've got to have the long view. This is not, if you right now did all this stuff on your website, you're beginning. Right. It's still three to six months before SEO really takes a hold. And we just need to set that expectation for clients and get them away from thinking about ranking, missing out on real opportunities. Cool. I'm going to be around all day and I got nowhere to go to for dinner tonight. So, catch me up, take me to a wings place. I don't care. I look forward to talking with you. Thank you all for joining me today.


Hey y'all, welcome to What Chelsea Eats. Thank you so much for joining me today. I am almost done with my food series that I promised in the beginning of January. We have a few more weeks of strictly food videos and although I'll always make food videos We're gonna move on to some other topics to help you out on your five-brain shrinking journey. So in this video I'm gonna show you how to make this five-brain friendly fruit bowl if you'd like to see how I make it stay tuned Okay, y'all this recipe is very very easy. We're gonna start off by layering the fruit in the bowl I have a cup of blackberries and then I'm adding one cup of blueberries But I'm gonna layer it through the bowl as you watch the video. You'll see how I do it and Berries are so good for us because they're full of antioxidants And if you don't know what an antioxidant it is it's just in short means That it's a cancer fighter and next we're gonna add one to two sliced bananas It just depends on how much you can eat for this bowl. I'm using two bananas and Literally, you don't even have to use bananas for this recipe. You can use whatever fruit you like. It could be kiwi It could be oranges apples Strawberries whatever you want to add. So if you don't like bananas add mango add something else and This bowl held me a good six hours before I needed to eat anything else And I think it was largely due to the amount of food that was in the bowl. You'll see at the end Next you're gonna add one to two tablespoons of hemp seeds. You can use hemp seeds chia seeds raw Pumpkin seeds raw sunflower seeds you can add whatever you'd like I prefer hemp seeds just because of the way they taste and next is some unsweetened unsulfured coconut flakes That's about two tablespoons one to two tablespoons. You can add and next is Your nut milk you can use whatever you want mine is unsweetened coconut milk so you can add almond milk hemp milk Coconut milk whatever milk you prefer to eat Whatever you do do not add cow's milk because if you add animal milk, it will not be There you have it y'all The vibrate friendly fruit bowl that you can have for breakfast lunch or dinner But I'm always getting questions about what do you eat for breakfast? So this is one of the things that I eat for breakfast if I'm not having a juice or a smoothie If you like this video, please give it a thumbs up share it with a friend and don't forget to subscribe Until next time y'all talk to you soon. Love you


Okay, let me give you a definition of design thinking. This is a definition by Tim Brown. In 2008, he published an extremely influential article entitled Design Thinking in a magazine called Heartbreak Business Review, and this is what he said. Design thinking is a discipline that uses the designer's sensibility and methods to match people's needs with what is technologically feasible and what a viable business strategy can convert into customer value and market opportunity. It often entails a great deal of perspiration. I'd like to share with you a short video in which Tim Brown himself explains the concept. Right? You know, I'm sure you've all been thinking about one of the main aspects of design. That's probably one of the main aspects. What do you think about that? I think that's what we're talking about. So there are tools that are going to be personalized, particularly in the past one, that it might be countered only with the soul of the company. I'm glad that we're both starting on a couple. We have many people that go to school in many ways, but out of line. We're taking them on the path of so many people. But the money we do is different than that. Often, money is essentially around the means of what we do in terms of thought and how we do it ourselves. The customer, when you think of your professional environment, money is a coin. It's essentially about that. So to start thinking hard, thinking hard, thinking hard, and understanding what's going on in this business, you have to think about what's going on in the company. How do you think about it? How do you think about it? How do you think about it? Okay, did you get what he said? No, you're too tired. Was it difficult to follow? Difficult to understand? Okay, basically what he says is that design thinking is extremely versatile and you can use this in lots of different situations, in your own personal life. And he refers to the five different phases or stages in design thinking. Well, this design process, he says, is best described metaphorically as a system of spaces rather than a predefined series of orderly steps. The spaces demarcate different sorts of related activities that together form the continuum of innovation. Its architecture differs from the linear, milestone-based processes, typical of other kinds of business activities. To put it more simply, he refers to five different phases. The first one is called empathize, which is to say, put yourself in people's shoes, to try to understand their needs, their worries, their interests, so that you can find the best solution to the problems. Define means to frame the problem, that is to say, to shortly describe, what the problem you want to solve is. Just to give you an example, think about your clear classroom. I've got a serious problem, for example, dealing with written texts or oral text in English because lots of the materials I find on the internet are too difficult for my students and I have to simplify them and adapt them to my students' age. That could be a problem that you want to solve in a clear setting. That's defined. Ideate means to look at the problem from multiple perspectives, lots of different angles and that's something that you have to do in a group, collaboratively, because you can come up with lots of different solutions but if you work together with other people, you will find lots of different wonderful solutions to the same problem. At this stage, at the ideation stage, the important thing is to come up with lots of different ideas regardless of whether they are crazy or impossible ideas. Then you've got the prototyping phase. At this stage, the important thing is to make a real solution using your own hands. So you can, for example, use a mind map. You can build a model, different kinds of recycle materials. So the point is to make the solution visible and tangible. We'll look at different strategies to do that. And then you've got the testing phase. So once you have come up with a solution to a problem, you need to put it into practice and see whether it works or not. Are you with me? Very simple, as you can see. You have to tackle a problem. First, you empathize with the audience, the people, the users that you want to find the solution for. Then you define the problem very clearly, briefly. Then you start thinking of different crazy solutions to that problem. Then you start prototyping.  And then you test it. You put into practice and get feedback that is going to take you back to the beginning. This is not a linear process. It goes forth, it goes back. It depends, right? Because creativity is unpredictable. So those are the five stages, the five phases of the design process. Any questions so far? No. Okay. So let's start thinking about the pedagogical potential of design thinking. This is a very personal meditation. This is nothing I've found anywhere, any chapter, any article concerning this. This is my own thinking, so to speak. Well, I would say that there are four basic lessons which have got a tremendous pedagogical potential that we can use in our own clear classrooms. Well, in education, in general. One of them is empathy. The other one is integrity thinking, optimism and experimentalism, and collaboration and active listening. So those are, to me, the four greatest advantages implicit in the whole process of design thinking. Well, design thinking is not a methodology. I would say it's a set of tools, a resource that you can use to solve problems in your classroom practice, but it's not really a methodology, right? So empathy. Empathy is fundamental in education, in clear and non-clear settings. Well, empathy is a virtue. Would you agree with me? It's a virtue, the ability to be able to look at the world from someone else's perspective. And your students need to cultivate empathy in classroom and in their everyday life. They will need empathy when they are doing peer work, or group work, when you're working as a whole class, when they are interacting with their peers, when they are interacting with the teacher. Okay, so empathy is developing a sort of sensibility towards perspectives and worldviews and points of view other than your own. For me, it's the basic ingredient, the basic prerequisite for learning to happen. This is the second advantage, developing what I call non-linear forms of thinking. You've got analytical and integrity thinking. Analytical thinking is looking at one object, at one problem, at one phenomenon in the world, and divided into constituent parts. So you sort of draw an anatomy of the object or the phenomenon or the problem. Whereas integrative thinking means approaching an object, a phenomenon or a problem in a much more holistic way from different angles, from different perspectives. And while it seems to me that design thinking helps develop both kinds of thinking, both analytical thinking, which is necessary, particularly when you want your students to assimilate, to absorb curriculum knowledge or disciplinary knowledge, and integrative thinking as well. Cultivating optimism and experimentalism in class. Design thinking or designers in general believe in the power of the human creativity and intelligence to come up with wonderful solutions, no matter whether it's a serious problem or not. So no matter what the problem you have to tackle is there will be a solution. And sooner or later you come up with a solution to that problem. And then collaboration. I don't know whether you use comparative learning in class, but comparative learning is a good example of what I mean by collaboration, right? I'd like to share one more video with you. You're going to watch the video. It's called Austin's Butterfly. And after watching the video, I'm going to give you a couple of minutes to talk to the people sitting next to you on your right and on your left. And you're going to put into practice one strategy that designers use very often, which is brainstorming. Do you know what brainstorming is? So just watch the video. Let yourselves be impressed by what happens in this video. And then spend about three, four minutes talking to the people next to you. And one person in the group of three, for example, is going to be the secretary, and he's going to write down the brainstorm ideas. Right? So here's Austin's job. He was supposed to do a scientific drawing of that butterfly. But remember, Austin was only a portrayal. And you know what he did? Austin had to do this photograph as a model, and he had to draw after a scientific drawing of this butterfly. This is called the tiger swallow tail. Wait, wait, wait. Wait, wait, wait. Wait, wait, wait, wait. Wait, wait, wait, wait. Wait, wait, wait, wait. Okay. And you only just evenly look like a scientist. Carefully. He judge me, and please tell me if you all used to do the butterfly. It didn't have a effect. And he wasn't looking like a scientist. And so this was real. It's not bad, and it is a butterfly. But does it look exactly like this? No, it doesn't yet. It doesn't look exactly like this yet. Luckily, this wasn't originally school were also meant. It was a exclamationary learning school, because I was in that school. And so they did look at this and say, good, often they're not. They said, often really start. And now we can start creating a screen that we want to have a black, white, black and yellow player, and we know that it's much, much closer to this than we really are. All of the first graders were in the 2000s or a lot of you guys were. And they decided to split their children. First, just to shake off their names. And then on the chain with the black, they hid from the black side. Inside the black.  Good. These ones would be much much better. Who else would have something?  A little. A little. A little. A little. A little. A little. Just, you're not exact. So, okay, so don't need a lot of their time. Don't need to really ask them to do what you need to do. Well, we're aware. Okay, so pull this out more. That's very specific. You know, I love that. So you're saying more like a kind person. And I agree. Well, you know that those first graders came up with most of those same ideas. You know what I often said? That, okay, how long have you been in school? And you went back to the school when you were young. Does this look more like a triangle? Yeah.  Do you have a positive impression? Do you add some gadgets here? Did you get rid of that body thing? So if you're going to listen to your friends and they, that is not perfect. How do you show when you show them that you're going to listen to them? Okay. You listen to your friends and they say this is usually a lot better often. That's how the graph really is better. And so with this graph, as you spin that graph that graph just right, oh, I don't even notice that. Well, one point is more about what you're doing right now. And that sign is going to work. Which here it doesn't have the inside of it. Okay. You need a little bit more of that now. So, do you think you should do a work graph? Yeah. Well, that's just what he said. Okay, about that one. I'm going to go back and do a work graph. Do you listen? Does it look more even like a life of a subject? No. And does it look like it's a life of a subject? And what the graph is saying is a little bit of an angle of the work graph. So now Austin was doing a really good work. He said, am I really going to add some pattern? Some of the pattern? And then he said, Austin, you're going to do a work graph. Let's look at his last graph. And what do you think? Is it going to look really good? Yeah. Let me show you where to start. I'm just going to give you a quick reminder. And then, what do you think about how much progress we've made? How long would you say that? We've put a lot of progress. It was really good. Oh, these friends were honest with us. What wasn't that kind of advice that they gave you, that allowed me to get better with my work? What? What? What was going on? And were more specific about where to start? The士 graph. And so does that something that other patients learned from? Or was it even from that? So if it's not right, then you can do a more graph than they'd like. We had a lot of work. We used the eyes in the sun.