Test one two test one two three test one two Talking about baseball That's right, it's opening baseball season I'm here Even though it's not April 1st usually it's April 1st, but that's okay. It's March We're here baseballs are flying around the diamond all across the United States of America. Oh, this I love football I love hockey. I kind of like basketball, but baseball baseball is the bloodline of American sports It is America's pastime. Let's just call a spade a spade even though I'm a big runner I love me some baseball and believe it or not believe it or not Big big moment is about to happen on this daily vlog April 11th, April 11th mark your calendars. We will have been publishing a daily vlog For two years straight every single day for two years straight every single day April 11th So the first daily vlog the first one was called and I am actually gonna link to it I will remember is called losing pearls with Joe DiMaggio But this was the book every March slash April I order a book From Amazon or go to a bookstore and I purchase a book on the New York Yankees. I love the Yankees I love the New York Yankees for many reasons, which I won't get into now But this book is the book I purchased two years ago About Joe DiMaggio, which inspired me to title the first daily vlog Losing pearls with Joe DiMaggio now You just got to go watch it to understand the whole context as to why I called the blog the first daily blog that time Family So in 2016 it was Joe DiMaggio in 2017 It was the 1927 New York Yankees the murderer's row of baseball arguably the best baseball team ever assembled It was amazing But in 2018 we got a new book to read to kick off the baseball season because it's opening day folks. It's opening day. All right, let me just Dynasty the 1949 to 1964 New York Yankees. All right, the Yankees have won 27 world championships Don't tell you buddy. Don't want to make them feel bad. There's many reasons. I love the Yankees That's one of the reasons but the more important reason is that I was born and raised a Yankee fan meaning I'm not a bandwagon fan back You know the Yankees were actually not so good in the 70s and the 80s But in the 90s they had a resurgence and I know they have a lot of money You know a lot of people point that out a lot of other teams these days like the Dodgers and the Red Sox and the Cubs The Yankees They've been successful for Decades and now more than a century. Yes I've been a Yankee fan for a long time and I read the books. I do the research. I watch the documentaries I'm not a bandwagon fan. All right There's a lot of bandwagon Yankee fans out there if you're winning 27 world championships over the last 100 plus years Yeah, there's gonna be a lot of people that just kind of latch on and say hey I'm a Yankee fan, but they're not really Yankee fans. Let's just call a spade spade here folks So whenever I go to the Bronx whenever I go to New York I go to Yankee Stadium pay homage go outside take some shots like you're seeing on your screen right now bonus footage Almost forgot question the day. Do you like baseball? I a lot of people don't like baseball anymore because it's a little slower But it's like I feel like we need to slow life down a little bit slow down slower down All right, who's your team? Why do you love that team? Who's your baseball team who you're cheering for in 2018? Alright Blast for me blast for me at the D'Amore house


Welcome back to our lecture series math 4220 abstract out of 1 for students at Southern Utah University. As usual I'll be your professor today Dr. Angea Missildine. This is actually going to be a really exciting lecture. I'm really excited here.  You know this is going to be good stuff. In this lecture we're going to talk about the idea of public key cryptography. So suppose you are connecting to your bank's website. Well it's possible that someone could intercept any communication between you and your bank. So you want to encrypt the communication. Even though symmetric key cryptography can be modified to make it much more secure than the models we talked about in the previous lecture. The problem is that symmetric key cryptography, these methods require that both parties already have a shared secret encryption key. How can you and your bank agree upon a key if you have if you've not already talked to each other right? How do two people who've never met before set up a encryption with each other if it's a symmetric key? Well I'm going to give us a fairy tale here and the purpose of this fairy tale is to explain the basic goals of public key cryptography. To provide a way for two parties to agree on a key without a snooping third party being able to determine the key, the method relies on a one-way function. That is a function that's easy to do one way but very very very hard to do in reverse. So here is our fairy tale. So we have a king and queen, their brother and sister. So in one land we have Queen Alice who rules over the people and in another land her brother King Bob rules over his people. Now Alice wants to send Bob who lives in a far far far away kingdom a very valuable treasure. We can see the treasure chest right here. She wants to send this valuable treasure to her brother. Now since she is not able to meet Bob in person to deliver the treasure because again he lives far far far away, she hires servants to take the treasure chest to Bob. Alright these couriers will take the treasure to Bob here but not sure if she can actually trust the servants that she's hired here and not sure if they'll try to steal the treasure along the way. Alice places on the treasure chest a lock. A lock for which only she has the key to this lock. Okay so now we see our locked treasure chest right here. So because the servants don't have the key to the lock there's no way they can open it. So they faithfully take the treasure to Bob. So now Bob has the treasure chest right here but the thing is Bob can't open the treasure chest either because he doesn't have Alice's key to open the lock only Alice does. So what Bob is gonna do is Bob is going to place a second lock on the treasure chest. A lock that only he has the key for. Alright so what we saw here is that Alice sent this locked treasure chest to Bob and it has one lock on it. Okay and we'll say that let's say a little better this treasure chest had Alice's lock on it.  So this time it has two locks on it. It has an Alice and a Bob lock like so and so Bob sends his treasure chest back with his lock on it and Alice's lock on it. Alright so now when the box returns to Alice it now has these two locks on it. One that was given by Alice and one that was given by Bob. Alice is now going to remove her lock from the treasure chest and then her servants have to take the treasure chest back to Bob one final time but this time when the treasure chest returns to Bob the only lock on the treasure chest was the lock that Bob originally put on the treasure chest. Okay and so Bob who has the key to unlock the treasure chest is then able to unlock it and voila the treasure chest is open again yay. So Alice and Bob were able to securely share the treasure amongst each other and no one in transit neither the servants who deliver the treasure nor bandits who might have been along the way anyone who intercepted the treasure chest would never have been able to open it except at the very end when Bob removes his lock from the box. What I've now explained to you via this fairy tale is what's commonly referred to in the cryptography literature as the Deffie-Hellman Key Exchange. So this idea that's back and forth between Bob and Alice here is that we were able to have Alice share with Bob their treasure and no one was able to access the treasure except for Alice who knew what the original treasure was and Bob who was able to unlock it at the very end. We call this a key exchange because really the treasure that Alice is trying to share with Bob is going to be a secret key. It's going to be the secret key that is this is a key a secret key for a symmetric for some symmetric key crypto system that crypto crypto system that they're going to be able to communicate. So removing the fairy tale let's imagine you and your bank want to communicate with each other online or some other online purchase you're perhaps doing where you need a secure connection. Well if you've never communicated with this individual before how in the world can you set up a secure communication? Well one idea is that you could perform some type of Deffie-Hellman Key Exchange where let's say the bank creates a secret key and then you exchange digitally this key using this key exchange so that now you have the secret key that the bank came up with and then you can proceed to communicate with each other using symmetric key cryptography. The advantage of symmetric key cryptography is that it's very simple and the communications can be really fast rapid communication between each other but it depends on having a common secret key. And so this Deffie-Hellman Key Exchange although rather kind of slow it could be a secure way of creating the key and then all future communications then could be worked out with this symmetric key cryptography here. So we can see how this could actually be an effective thing and this Deffie-Hellman Key Exchange is essentially the first public key crypto system out there so that anyone could observe what they were doing. Anyone could see what Alice and Bob was doing but because it was public in that essence but no one was able to still break into the treasure chest. Now this Deffie-Hellman Key Exchange as you can see was rather quite slow but it can be implemented in any group it's really nice. Let's think about the following idea as a as a as being represented inside of a group. So imagine Alice wants to exchange the secret element g with Bob so maybe this element g in the group is valuable this we're going to be able to create us this will be the symmetric key for a new crypto system we'll do in just a moment so this is the secret so to speak this is the message that Alice wants to send to Bob but she can't just say g because then everyone will know what her secret message is and then their future encryptions will be compromised. So what Alice is going to do secretly is she's going to pick uh she's going to pick some number we're going to say m that should be somewhere between the order of g and the number one clearly one is a bad choice and perhaps even the order of g might be a bad choice but we're going to pick some number between those and then she is going to compute she is then going to compute the element g to the m and we're going to call this a this is then what she transmits to Bob so Bob receives the a he doesn't know what g is but he does see what a is and so this right here is the cipher Bob doesn't know what the original message is so what Bob's going to do is Bob himself is going to pick a secret uh he's going to pick some number n uh between the order of g and that's the thing is we don't actually know what g is little g so we really should be thinking of capital g here he's going to pick something between the order of g and one again picking the order of g and one or not the best choice he's going to pick something randomly and as this right here is supposed to be a big group uh you want this because you don't want eve to be able to do some type of brute force attack so we want the order of our group to be very very big and so the likelihood of Alice and Bob picking the same secret here is very unlikely so this is the secret that Alice has and this is the secret that Bob has these are kept secret these are not shared publicly but this message a was shared publicly with everyone so what then Bob does is he's going to take this element a and he is going to then compute a to the n power let's call that b b for Bob and then he sends it back to Alice so that Alice receives b now we know that b is just g to the m to the n like so and in which case because this is a group and we have associativity this is the same thing as g to the n to the m right and so what Alice then can do is because she knows what m is she can then apply the negative the the inverse right there she can do the negative m power so then she's going to compute she's then going to compute b um she's then going to apply the inverse right here and we'll talk some more about this in the next video but she knows how to undo this process so there's going to be some element um some element here m uh excuse me there's there's going to be sort of a way of undoing m so that that is to say there's some element we'll say m d uh which is then congruent to one in this process here and so she then applies this element d here which then this would compute well it's but whatever it is she's going to send it back to Bob right so she sends back this b to the d right here and so what's happening here is that this is going to give this element b to the d uh this is going to be the same thing as just g to the n right so m and d cancel each other out in terms of these exponent rules so she sends this back to Bob and again this is public information everyone can see it and so when she sends this c back Bob on the other hand knows there's a number such that n times e is is congruent to one and so that's what then Bob's going to do Bob when he's going to take c to the e power since this is g to the n to the e power this will just give back a g and so Bob was able to get the secret message g that Alice wanted to send him now if eve is e-dropping which we should assume she always is what does eve see along the way she saw she saw the message a she saw the message b she saw the message c so she saw these back and forth and so is this enough information for eve to figure out what g is well again if the order of the group is chosen sufficiently large then it would be very difficult for her to able to solve this equation they solve solve the misinformation is it impossible for or is it possible to solve it of course it is but if we choose these things effectively enough it becomes a very hard process for eve to do but again there's a lot of back and forth going on here and so a way to simplify the diffie helman key exchange is the following again this makes a lot more sense as as in groups a lot less makes less sense as treasure chest but if you want the about paint it works out with nicely here so what Alice and Bob are going to do and so this is what really makes it a public key crypto system right here what bob and i can do is they're going to publicly they're going to publicly decide on some modulus here this is in the public here they're going to choose some number in okay and so this this is information that even eve knows about and so secretly secretly what they're going to do is so they're going to choose in and they're also going to choose some element inside the group so they're going to so this is like our modulus and we're going to choose some element g as well so we have a module so we have some specific element g so secretly alice is going to choose some number m and bob is also going to choose some number n right here and so then what alice does is she's going to compute g to the m this is going to equal some number a and she's going to transmit that to bob so bob receives an a on the other hand bob he's going to compute g to the n which we're going to call that number b and then he sends b to alice who then has the number b so alice will then compute b to the m which thinking about that for a little bit since since b is g to the n this will then give a composite g to the mn like so and on the other hand bob who receives a he's going to compute a to the n which as a is equal to g to the m you raise that to the n power that's going to give you g to the mn right and so you'll notice that they're able to compute the exact same number but eve who's e-dropping eve she'll have the she'll have the modulus she'll have the element g but she won't know n she won't know m she'll have a and she'll have b right but it turns out with these four bits of information in oh i used the word i used the letter n twice didn't i so we'll just call this the order of g so we're working where we're going modular arithmetic here so uh so yeah it doesn't even have to be modular arithmetic we really just need a group and we have an element of a group and then we just take powers of that element in the group so if the group is chosen sufficiently large then we're guaranteed that alice or eve excuse me would not be able to determine these common powers even though she knows this is a power of g and she knows this is a power of g the a and b she even know these she knows these are powers of g she can't figure out what the combined power is because the calculation is too difficult this is what we mean by a one-way function it's easy for alice and bob to compute the powers of g but it's difficult for alice to basically take the discrete logarithm in this situation uh we we can exponentiate easy but we it's it's hard to do the logarithm and so this is how one can communicate securely in a public domain and that's the power behind public key cryptography


The governor of Delta State, Sharif O'Barrevery, has said the special advisers should commit themselves to finding creative solutions to the recurring problems of youth unemployment and restiveness, cyber crime, poor environmental sanitation, insecurity and the distrust that breed inter-ethnic fields in communities. He made a statement while swearing in special advisers at the government house Asaba, the state capital. Our Asaba Correspondents at Bomegeri on Friday reports that the governor said that as public servants, they must be agents of unity, reiterating that Delta's strength as a state is in its diversity. Resistence and stretching the bonds that exist among our people. See the entire state as your existence and stand no effort when showing that there is mutual harmony among the various ethnic nationalities. We must guide against in natural activities to give professional treatment to people from your part of the states. As a public servant, you are obligated to serve the group of Delta States in respect of their ethnic nationality, party affiliation, socioeconomic status, or educational background.


What's up everybody? Jayz here for jayspeakscasebreak.com. Happy new release day guys 2021 Pinini one-and-one basketball just sold out. This is a 10 box case break pick your teams number one. 10 boxes per case one pack per box two cards per pack and the box break down of course is one autograph plus one base parallel or insert card so there you go and again guys we had to sell out a couple random number blocks to sell this out so of course here's the customers in straight up appreciate everybody that got spots straight up boom boom and then we had to write a number block for just the Timberwolves there's the customers there let's put that right over here and then here was for the 19s right there there you go so good luck guys let's get this rolling fresh case again guys if you guys want to run back another one before Joe gets here that about an hour and 20 minutes now that we have more viewers here it's closer to you know 4 30 in the afternoon on the East Coast 1 30 here on the West Coast maybe we get more eyes and more people wanting to buy into another one of these case breaks but I'm happy we got at least one of these done it's always good to get at least a new release day break done early in the morning or early hours of course before we normally start so let's pull out one card at a time first one is Kenyon Martin Jr 25 out of 30 for the Houston Rockets all right Kenyon Martin Jr that is for the Houston Rockets spot 5 which is going to Patrick there you go first card guys good luck is Devin Vassal for the San Antonio Spurs 82 out of 99 San Antonio Spurs were bought straight up by James there you go there's the first box next one we have Xavier Tillman 7 out of 15 rookie for the Memphis Grizzlies going to Brian S straight up the autograph it's first team signatures another one for the Spurs George Gurving wow back-to-back hits for the Spurs how about that San Antonio going to James Iceman next one we have Paul Reed for the 76ers 41 out of 99 76ers going to Nick there's a third one another first team signatures it is 17 out of 25 Jason Kidd and that is New Jersey Nets of course Brooklyn Nets going to spot 7 which is Paul Norton there you go little Jason Kidd Nets edition four of Fox 4 we have Calden Johnson another spur that's three hits already out of the potential eight there you go another one there for this first kill in this break already I don't think the Spurs were also that expensive either and for the Orlando Magic Cole Anthony 78 out of 99 Orlando Magic going to Tim straight up Cole's having a great second year at fifth box will be halfway through after this box here we have a Cal Laurie that's three out of 15 for the Raptors Toronto Raptors going to Steve Wright straight up and for the 76ers Tyrese Maxie 24 out of 99 very nice for the 76ers that is going to Nick straight up I call Anthony and Tyrese Maxie already in the first case alright guys halfway through five more boxes so at least ten hits and Carmelo Anthony 9 out of 99 for Portland Blazers R&B 9 that is Brian Wofford there you go little Carmelo for the box Jordan Nwara 47 out of 99 Milwaukee Bucks that is part of the R&B 47 spot 7 is going to Paul Norton all right four more boxes you got Tyrese all those guys man Wow LeBron James for the Lakers 64 out of 99 that's gonna sell well Lakers straight up is Mark there you go Mark LeBron James take that take that we have Nate Archibald out of 25 13 out of 25 for the Celtics Boston South is going to Wayne all right three more boxes guys come on big Ant-Man or Lamello come on come on I need a downtown as well guys we need a downtown I don't know if downtowns are one per case but Jay Chantate very nice rookie right there for the Houston rocket that's five out of 25 five is Patrick we've got a redemption yes this is a redemption all right this got to be Lamello right Jersey autographs card number seven no it's John Morant Wow John Moran didn't sign in this Jersey autographs card number seven John Moran for the Memphis Grizzlies going to Brian that is sweet wow that really tripped me tripped me out and it's still pretty nice though and that was going straight up all right two more to go guys and I don't know I think someone said downtowns almost fall one per case but sometimes I think it might be slightly off come on downtown we got to get at least one even one that's a gold Harrison Barnes one out of ten Sacramento Kings going to Wayne Tyrese Halliburton that is 89 out of 99 for the Sacramento Kings another one that's what Sacramento Kings box going to Wayne I think the magnetics a little scratched up on the top too so but the card is fine well so far we got maxi Cole and Tyrese Halliburton with a John Moran not a bad case but I was hoping well last box mojo still hoping for a downtown and then of course potentially either a atman or Lamello but come on guys come on come on good luck if not guys I don't think downtowns are per case I think they're like every two to three cases then nope Jaylen Smith 63 or 83 out of 99 for the Phoenix Suns at spot three going to Gretchen our last hit here guys good luck first team signatures it is Isaiah Thomas for the Detroit Pistons Wayne with the piston 65 out there you go all right unfortunately no atman no Lamello but we did get some solid players and rookies though Tyrese Cole Anthony and Maxi so do a quick recap right here so here was some of the base there's an autograph George Gurvey little base Tillman Devon Vaselle's a solid rookie I say Thomas of course like I said we got her Tyrese Halliburton RPA Harrison Barnes to 10 we got a John Moran that one I thought there's gonna be Lamello for sure that's a Jersey autograph John Moran for the Grizzlies Nate Archibald of course LeBron James I mean this is gonna sell extremely well Maxi Cal Aury Cole Anthony and Kellen Johnson but of course like I said every case is gonna sound like a dud per se because we didn't get a how we didn't get a Anthony Edwards or Lamello but the good thing of course is that a lot of these teams are we're selling them by the picker team so you don't have to buy the whole box potentially make back all that money so appreciate you guys again number two is on the website I'll random number block up the next one if needed if not somebody want to grab some spots it does help out if you sell spots straight up but it looks like Nick already posted up some random number block so let's get it going guys Jaspiescasebreaks.com


So, in our last lecture, we looked at optimization, multivariable optimization, unconstrained optimization. So, we derived conditions for optimality, necessary and sufficient condition followed by the next lecture, we looked at application to solving linear in parameter least square problem. What is nice about linear in parameter least square problem is that the solution, optimal solution or the optimal value of parameters least square estimates can be computed analytically. So, just to have a recap, so this is just solution of linear least squares. We have collected data and we have some model, this model could be in general I said the could be y is equal to theta 1 f 1 x theta m plus error. In general you have a model of this form where f 1, f 2, f 3, f m are some known functions. Simplest one we looked at was polynomials, but it did not be polynomials it could be any functions which are known functions and then you are doing a function approximation. If it is polynomials it is polynomial approximation, we have collected data we said this is u not y and one minute we did not use x we use z here. So, let me collect that. So, z is the independent variable it could be anything it depends upon in this case it did not be space it could be any independent variable. We looked at many examples from chemical engineering where we could use this method for and then we have this data collected which is u 1, u 2, u n at points z 1, z 2, z n and using this data we wrote number of linear equations and finally, we put it in a matrix form u is equal to a theta plus e where e is the modeling error and then you know we found out theta least square is equal to minimum or minimize with respect to theta e transpose. Now, I am going to make a little small modification here as compared to the previous development. I am going to say here e transpose W e where e is equal to u minus a theta I want to solve this problem where W is a positive definite matrix is a symmetric positive definite matrix in general you can solve the problem earlier we had looked a special case of this that is e transpose e where W was identity matrix identity matrix is a symmetric positive definite matrix. This is a special case which we have looked at earlier I am just generalizing this W can be see for example, in some situations when you collect data and fit a model you know that a particular observation is more reliable or particular observation is less reliable. So, you could attach weight positive weight small weight if it is less reliable a large weight if it is more reliable so that when you optimize the optimizer will give more importance to those which are accurate measurements will give less important to those which are less accurate we could actually twist this or sometimes you need to do this because of you know variables have different values and so on. So, this is in general formulation in which I have some weighting matrix here which is a symmetric positive definite matrix as you know that this will define a two norm and so on. If you take a positive definite matrix it will be defining a two norm. So, if I have this phi which is e transpose e e transpose W e then if I use necessary condition for optimality then it is dou phi by dou theta is equal to u minus a theta transpose u minus a theta and then we had these rules of differentiation of a scalar function. So, this is a scalar function from n to r this is a scalar function from sorry m to r r m to r theta is a m dimensional vector this is a function of theta theta is a m dimensional vector in general. So, this is a this is a scalar function and we had rules of differentiation of a scalar function with respect to a vector and using that we came up with a formula which is we will get this equation if you use it a transpose W a theta least square is equal to a transpose W u. And finally, we argued that if columns of a are linearly independent then this matrix is invertible. This is a symmetric matrix symmetric positive definite matrix very nice matrix and theta least square is equal to. So, my least square estimate my least square estimate can be written as a transpose W a inverse. We also said the special case when W is equal to i we look at a special case when W is equal to i a transpose a inverse a transpose is called as pseudo inverse of matrix a.  So, this is a non-square matrix say non-square matrix and then we will talk about its inverse or we talked about its pseudo inverse pseudo inverse is defined by a transpose a inverse a transpose. So far so good. So, we have this derivation one of your classmate was asking me in the last after the last lecture is that she knows about this formation formula using summations you know least square estimate using summation summation summation. Yeah you can actually this formula and that is not different they are one and the same and deriving that summation formula starting from this formula is part of one of the exercise problems. So, the exercise problem which I give you next for least square estimation will have that problem you will derive that summation formula for least square estimates. So, those two things are not different this is a more elegant compact way of expressing the same thing it is not different it is one and the same thing. So, the regression formula which you know with multiple summations can be very elegantly expressed through this a transpose a inverse a transpose the same thing exactly identical thing when you solve the problem you will realize that it is nothing different the same problem. What I want to do now is so far so good we have done lot of algebra we have found out the condition for optimality then we said the second derivative here what is the second derivative here the second derivative here that is dou 2 phi by dou theta square this is nothing, but a transpose w a 2 a transpose w a that will be second derivative the second derivative is always symmetric positive definite which means the stationary point which you have got through this is the stationary point this is the point at which the gradient is equal to 0 at this point at this point the second derivative is given by this matrix and this particular matrix is symmetric positive definite you have reached the global minimum. So, this is this is fine this is lot of algebra I want to give some geometric insights into what is really happening how do you relate this to your school geometry that is what I want to elaborate next. So, what was the thing here here you had a non square matrix right you had 100 data points may be only 3 parameters we saw the example of c p versus temperature. So, m was small n was large you are fitting some function some polynomial and the number of parameters where much much less than the number of variables to get in an insight into what is happening let us not work with 100 dimensional spaces we cannot visualize in 100 dimensional spaces right, but in 3 dimensions I can visualize. So, I am going to create a dummy problem from this which is very very simple 3 equations into unknowns 3 equations into unknowns it is a representative problem for this equation see what is the main thing number of equations is more than number of unknowns and then you are not able to satisfy all the equation simultaneously if you are able to satisfy all the equation simultaneously then you know error would be 0, but error is not 0 you are finding out least square solution. What is the error how do you compute the error here what is the error vector if you substitute this theta you will get the error vector into this equation. So, if I substitute here if I substitute E is equal to U minus A times A transpose W A inverse A transpose W U. So, I can write this is I minus A A transpose W A inverse A transpose W times U unless this matrix is 0 you will not get exact satisfaction. So, these equations are such that you cannot satisfy all of them simultaneously you are trying to find out a least square solution and then there is always going to be an error vector such that probably no equation is satisfied ok. So, the curve which you get here will not probably pass through any of the points quite likely it only captures the tendency in the data not going through every point in the data because ok. So, now let us let us try to get some insights by taking a simple dummy problem. So, I am going to take a simple problem in which I have this equation to be satisfied I want to solve this equation 1 2 3 1 2 3 is equal to I hope that this vector cannot be defined by just linear combination of these two let us I have not I have just created this problem right now I do not know whether. So, when can you solve this exactly just think about the geometric insight of it about it when can you solve this when can you actually exactly solve this how can you write this equation is there another way of writing the same equation ok I will move to here. So, I can write this as 1 2 3 is equal to theta 1 1 0 1 plus theta 2 1 1 1 0 plus e 1 e 2 right I have taken a very simple problem 3 equations 2 unknowns 2 unknowns in the terms of actually there are 5 unknowns actually there are 5 unknowns e 1 e 2 e 1 e 2 e 3 theta 1 theta 2 there are 5 unknowns, but well as far as the parameters are considered there will be 2 unknowns theta 1 and theta 2 parameter unknowns ok. If I write it like this do you get some more insight yeah. So, theta 1 times this vector let us call this as v 1 and let us call this vector as v 2 when can you solve this exactly when will the error be equal to 0 can you say something about the span do not forget the last quiz all possible linear combinations of v 1 and v 2 what will it give you ok let us say this is my v 1 and this is my v 2 let us say this is my v 1 and this is my v 2 ok what will it span what will it span v 1 and v 2 all possible linear combinations of v 1 and v 2 what will it span it will be a plane passing through the origin right when will the error be equal to 0 say it say it louder this is when this vector on the left hand side lies in the plane ok if this vector left hand side vector it exactly lies in this plane which is span of these 2 vectors ok all possible linear combinations any vector in this 2 dimensional plane can be generated by a linear combination if it does not what it means where is this vector outside ok let us picturize this as this vector. So, this is my u vector this is my u vector this is u ok. So, this is here this is my u vector. So, u does not lie in this plane it does not lie in this plane. So, I need to find out what do I need to find out a least square approximation see because ultimately I am finding out an approximation which is theta 1 times this vector plus theta 2 times this vector that approximation is going to lie where that approximation will lie somewhere here right a vector see this vector will be theta 1 times v 1 plus theta 2 times theta 2 times v 2 this vector theta 1 times v 1 plus theta 2 times v 2 cannot leave this plane right it is linear combination of these 2 vectors it cannot leave this plane ok. So, in your school geometry you have studied this problem point which is closest point which is closest to this vector in this plane how do you get it perpendicular ok. I just want to show that what we have done till now by so called least squares is nothing but drop a perpendicular ok. The point which you will hit the point which you will hit here if you drop a perpendicular what is the best approximation in the least square sense I will show that this point is nothing but the point which is the least square approximation of this vector in this plane ok I want to find out best approximation of this vector in this plane in the least square sense from the school geometry I know just drop a perpendicular ok this is the point which is closest to this to this plane point which is closest to this plane ok. So, this point and what I actually get by solving theta least square.  So, my equation is error equal to U minus A times theta L s my equation is U minus if I just complete this parallel this you know law vector additions this is nothing but error vector in least square approximation the error vector is perpendicular to the plane this you know from your school geometry right I am just generalizing that result in any inner product space what is very very elegant is that same result can hold in any inner product space in any Hilbert space you can have the same result which you know from school geometry finding minimum distance of a point from a plane ok. So, this problem this problem see it is you cannot visualize when suppose suppose this suppose here let us go back here ok suppose you had 10 equations suppose you had 10 equations in two unknowns ok I cannot visualize in the 10 dimensional plane, but linear combination of two vectors in 10 dimensions what is it like it will it will look like it will look like a plane like this something like this if I wear a creature in 10 dimension I could be you know it would be possible for me to visualize a 9 dimensional plane, but we cannot. So, but it will look something like this and then what you are doing you are just finding out the point in the plane which is at a minimum distance from this point which is lying outside the plane ok geometrically what you are doing is what is called as projections ok I am projecting this vector onto this plane projections you probably have done when you are doing your engineering drawing right. So, projections is something which you know from your engineering or right from your school ok. So, even though you cannot visualize 10 dimensional thing conceptually or you know it is not going to be different I mean if you are able to visualize that it would look almost the same. So, I just want to show that if I just proceed through this geometric ideas I will get the same thing ok that is my next that is my next task ok. Let me do a general derivation with only two vectors in my notes there is a derivation with only one vector one vector means distance of a point from a line I start with that and then I generalize it to distance of a point from a subspace actually in general if there were three if there were three vectors ok see if this problem if I just modify this problem saying that if I just modify this problem and then here left hand side is let us say this is not coming from some physical problem I am just arbitrarily creating some set of equations. Let us say I have this problem ok now here what can you say the least square solution will be lying in the subspace spanned by this column vector this column vector and this column vector the least square solution will lie in the subspace spanned by this column vector this column vector this column vector ok the component which is outside the subspace is given by this error ok we are able to split actually geometrically speaking we are able to split a vector into two components one lying in the in the subspace and one orthogonal to the subspace ok we are able to split the vector through least square what is the subspace subspace is spanned by linear combination of columns ok linear combination of columns will give me subspace this even e 2 to e 5 will give me the component which is outside the subspace together they form this whole vector ok together they form this whole vector now I want to generalize this and then just show you that what we have derived but I am going to take a case where w is equal to i ok wetting matrix is equal to i I am not going to complicate life by so that will give me some handle to ok. So let us write so this is so this is let us let us call this ok in my notes I am calling this vector as a 1 this vector as a 2 this vector as a 3 ok. So in general in general I can write my model as u is equal to capital U this my original model is u is equal to a theta plus error and I am writing my a matrix as a 1, a 2, a m there are m columns these are column vectors there are m columns ok in this case there are 3 columns here there are m columns ok. So I can write this equation as u is equal to theta 1 a 1 plus theta 2 a 2 I can write this vector equation ok. Now to simplify life let us take a case where there are only 3 vectors ok. So generalization to m is not so difficult so I will just take theta 1 plus theta 3 a 3 plus e this is the case when we have taken m is equal to 3 there are 3 parameters theta 1 theta 2 theta 3 I want to find out least square estimates of these square estimates of this ok using ok I am going to call this vector see this vector this vector belongs to the subspace which vector this vector p I am going to call this as a projection vector projection vector theta 1 a 1 plus theta 2 a 2 plus theta 3 a 3 this is the projection vector this is the projection projection of u on ok this is projection of projection of see it is linear combination of a 1 a 2 a 3. So this p vector has to lie in the subspace by a 1 a 2 a 3 right it has to lie in the subspace by a 1 a 2 a 3. So this is a projection I am going to call this as a projection of u onto subspace spanned by what is it that I want to minimize how do I find out this I find this out by minimizing square of distance right I want to find out. So my problem is find theta such that error 2 norm is minimum right 2 norm of error is minimum right ok. So let us let us start doing this. So what does it mean?  But what is this is a 2 norm we are working in a inner product space. So 2 norm square is related to the inner product how.  Now my model is this u is equal to theta so I can write phi to be inner product of u minus theta 1 a 1 plus theta 2 a 2 plus theta 3 a 3 into u minus p p is again this vector I can write this vector again here right.  Now how do you find out the minimum what is the necessary condition can you do this see my necessary condition is we will have to expand this but before expanding let us apply the necessary condition ok. So my necessary condition for optimality is dou phi by dou theta 1 is equal to 0 dou phi by dou theta 2 is equal to 0 and dou phi by dou theta 3 is equal to 0 right.  If I differentiate this phi with respect to theta ok what will I get ok just look at just look at it you are differentiating only once ok. If I differentiate only to this first vector what will remain only a will remain ok. You can check this but I am just going to write the final result that dou phi dou phi by dou theta 1 this is nothing but you will get here a 1 comma ok. If I differentiate this I am skipping in between steps you can actually expand this you can expand this entire inner product ok. You will get many terms ok you have to patiently find out the inner product of each element by element you know the rules of expanding inner product right right. So what I will get is a 1 inner product with this is equal to 0. So actually what I am getting here is that a 1 inner product u minus p is equal to 0 because this is projection vector this is my projection vector ok. So what I am getting is a 1 inner product u minus p is equal to 0. What is what is this u minus p error vector so what it says is that error vector is perpendicular to a 1 direction same thing if you do with theta 2 ok. So setting dou phi by dou theta 2 is equal to 0 you will get a 2 u minus p is equal to 0 ok. You will get this equation and well the third equation that you will get is the third equation that you get is dou theta dou phi by dou theta 3 is equal to 0. So that is equal to a 3 u minus p this is equal to 0. So what is the meaning of this what is the geometric meaning of this that this error vector is perpendicular to a 1 a 2 and a 3 ok. If error vector is perpendicular to a 1 a 2 a 3 will be perpendicular to linear combination of a 1 a 2 a 3 yeah. What is linear combination of a 1 a 2 a 3 it will be in the span of a 1 a 2 a 3 it is in the subspace of a 1 a 2 a 3 ok. So this error vector is perpendicular to the span of a 1 a 2 a 3 ok which means which means best approximation of u in the span of a 1 a 2 a 3 is obtained just by dropping but you know this is just generalization of the result from your school geometry to have a perpendicular from a point to a plane ok that is the best approximation of that vector in that plane that is all ok. That is all we are generalizing into a general function space or into a general inner product space ok. Now when is this possible this is possible only when your inner product defined that is very very important ok. Why we why we are so much why we are so much you know why we like least square approximation as against you know one norm approximation or infinite norm approximation because because this least square approximation comes attached with you know inner product inner product can be related to the geometry. You can talk about perpendicularity you can talk about projections the same idea of projections which you use in three dimensions ok distance of a point from a plane it just drop a perpendicular ok same idea is actually being actually being said here. So all that we have proved is if I if I redraw this figure in two dimensions if I have this plane which is span by say v 1 and v 2. So this is my v a 1 let us say this is my a 1 and a 2 and this is a vector this is my vector u ok this is my u vector then this is the p vector projection vector this is the projection vector ok this is the projection vector and here here what we are getting is this projection vector and this error vector e here is u minus p ok. This is the special vector such that this error see if I take any other vector here this error will not be perpendicular. There are so many ways of approximating you know this in this plane I could approximate here I could approximate here somebody will say that this is the approximation this is one possible way of approximating what is the least square approximation perpendicular ok least square approximation is the perpendicular. Now I need to go back from here and show I should start with these three equations and show that well what you have got actually is nothing but the same formula of A transpose A inverse I need to derive that right. I have just showed geometrically that these three vectors. So if I take a 1 a 2 the plane span by this and the error is perpendicular to this plane plane span at this and and so on. So now I need to go back and connect to A transpose A inverse business I will do that ok. How do I get theta 1 theta 2 theta 3?   So I will get another equation theta 2 into A 2 transpose A 2 plus theta 3 A 2 transpose A 3 just write the third equation just follow with this same thing I will get A 3 transpose u is equal to theta 1 A 3 transpose A 1 plus theta 2 A 3 transpose A 2 plus theta 3 A 3 transpose A 3 is everyone with me on this I have just written those equations I started with the geometric I started by saying that well what we have done is nothing but projections ok this error vector is perpendicular to A 1 error vector is perpendicular to A 2 ok these are the equations which I have written error vector perpendicular to A 1 error vector perpendicular to A 2 and in this case error vector perpendicular to A 3 how many equations and how many unknowns three equations three equations and three unknowns what are the three unknowns theta 1 theta 2 theta 3. So what do I get here what do I get here right hand side I can write this as A 1 transpose A 1 A 1 transpose A 3 and you can just collect it in the vector matrix form this is A 3 transpose A 1 A 3 transpose A 3 this into theta 1 theta 2 theta 3 right the right hand side I can write as a 3 cross 3 matrix just check this matrix is nothing but if I start with A is equal to A 1 A 2 A 3 these are the three columns of A matrix ok very very easy to check that this matrix is nothing but A transpose A is multiplication of A transpose A is this matrix ok the algebra ties in with the geometry very very nicely ok algebraically we we arrive at this condition A transpose A theta is equal to A transpose U. Now just look at this left hand side what is left hand side the left hand side I can write here the LHS I can write as A 1 transpose A 2 transpose A 3 transpose U what is this A transpose U right A transpose U ok that is the result which we got purely by doing you know algebra of necessary condition of optimality. So A transpose U is equal to A transpose A times theta this square solution right. So this is my theta ok I started with the geometric argument of projection onto a subspace I was able to recover the least square formula which is A transpose A transpose A times theta is equal to A transpose U what is the least square estimate this theta will be least square estimate of course we call it estimate so we give a hat above it. So this is estimate of theta this is not there is no way of unique way of finding out theta there are multiple ways but least square estimate is unique how it is computed A transpose A times theta is equal to A transpose U A transpose A if columns of A are linearly independent ok A transpose A is always invertible this is always a square invertible matrix symmetric positive definite square invertible very very nice matrix ok this matrix which we study in linear algebra does appear in a very very practical application we are trying to fit a curve in some data or fit try to fit a function in some data positive definite symmetric invertible matrix ok. So this this particular result A transpose A times theta least square is equal to A transpose U we could we could recover this result purely through geometric arguments of projection we said that basically what is happening here is we are trying to find out that vector in the plane span by A 1 A 2 which is at the closest distance from a vector which is outside this plane why we need least squares because this vector is not lying in this plane what will happen if this vector was lying in this plane error would be 0 ok what is the extreme situation this this U is perpendicular ok. So what is the best approximation 0 ok if U is perpendicular probably you are done wrong modeling you know error should be small lot that error the vector is perpendicular to. So this is this is a very very nice result this ties in with actually there is one more angle to whole whole of this thing. So we derive this result through algebra we derive this result through geometry we can derive the same result to statistics and you will get those summations which you are familiar with I am not going to go into statistical interpretation of the same thing I will upload my notes on statistical interpretation but if I go into statistical interpretation of this result it will take at least 2 weeks of you know I have to introduce so many concepts but finally you will derive the same results you will get a different insight from the statistics view point see I got a different insight into the same result to geometric view point ok algebra didn't tell me much you know it just said that derivative equal to 0 here I can relate to my school geometry that is very very important ok. So that is the beauty of this result you can actually show that the least square estimate obtained algebraically is nothing but projection of a point on to a subspace ok finding out this a vector in a subspace which is at the minimum distance from a point outside the subspace ok that is the that is the that is where you know that is why we work with inner product spaces Hilbert spaces because angle comes you know attached with the inner product you can talk of orthogonality ok all these things are not possible in other you know one axis spaces so that is why Hilbert spaces are so special ok. So next lecture we will continue on some more algebraic properties of v square I will show something more and then we will move to variety of fields engineering applications that is function approximations and also solving partial differential equation or boundary value problems we will revisit our problems again through this least squares approximation.


Okay, we have a very rough agenda that I've posted in the community call channel. Feel free to follow along, and with that we'll start with the recording here. Hi everyone, welcome to the JanuaryAphidium.org community call. We can start with a quick round of introductions. Then we'll highlight some of our community contributions. We'll discuss what's on our Q1 roadmap. After that there might be a pull-up, so stick around for that. Look, I'll spend a bit of time talking about our translation program, and we'll answer questions from the community. So as far as intros go, I can start. I'm Joshua from Glasgow in Scotland. I'm the community lead for aphidium.org. Feel free to ping me with any ideas or feedback you have for the community, or if you're interested in finding ways to contribute to aphidium.org. And I'll pass it to Paul. Hey everyone, it's just Paul. Wackero, I am a front-end dev here on the ethering.org team located up on the west coast in Oregon. I will pass along to Corwin. Hi everyone, I'm Corwin or Corwin Teens. I'm a web developer on this year about our team as well. And I live in Calgary, Canada. And yeah, if you have any questions about contributing to the code base, feel free to reach out. I'll pass it to Luca. Hey everyone, my name is Luca. I am working on the translation program for athium.org, and link the translation stuff. Yeah, based in Slovenia, Central Europe. I guess with that, I'll pass it on to Sam. Hey guys, good morning, good afternoon, good evening. Yeah, my name is Sam, or Samajamin on Discord or GitHub. Thank you all for joining. Excited to be here for another community call. So yeah, I'm a developer as well as the team lead here at athium.org. And I'm based in Lake Tahoe, California. I'll pass it over to Pablo. Hello guys, hello everyone. My name is Pablo Pettinari. I'm from Buenos Aires, Argentina. And yeah, as well, I'm working for the athium.org team, and I'm a front-end developer. I'll pass it back to Shosh. Awesome, yeah, I think that's everyone. Yeah, and once again, please, if you aren't speaking, make sure you're on your mics muted. One thing before we start this call, what we always like to clarify is this is the community call for athium.org, the website. And obviously not a community call that represents the athium network or the protocol directly. We have set up a slido for this call, which allows anyone to ask any questions they may have for the team. If someone from the team could help me out and just post that again in the community call chat if you've got any questions. You can be completely anonymous, please do drop them in. And as much as possible, we've tried to keep the conversation around athium.org itself, how to contribute. There's different ways in helping to push the ecosystem forward. If you've got any other questions, feel free to ask them and we'll do our best to answer. Okay, moving on to community contribution highlights. Yeah, so as I'm sure you're all aware, athium.org is an open source project. If there's anything on our roadmap or even if it's not on our roadmap that you'd like to contribute, you can get in touch a lot of the really high-value work on athium.org involves community members, taking the initiative on something that we feel really passionate about. So I am sharing my screen. The first thing we'd like to highlight was the work done by Joseph. I think I've seen him here on this call on our energy consumption page. So yeah, the page itself is just a marked-in file, so it's all text. We're looking to create a new template for that with our impending design hire on the roadmap. I digress a little. But the content itself is just awesome. It explains the overall goals of athium in terms of energy consumption, the sort of why athium's energy consumption is currently so high as to why burning energy for athium was necessary. It also prevents the current solutions to this problem, backs it up with hard numbers and highlights like the timeline of the marriage and things like that for solving this. And ends on a nice, I guess, optimistic note about our hopefully solar-punk future. The thing I really like about this and if you haven't seen it already, you should check it out because it assumes very little knowledge about athium itself as a protocol. So if someone who doesn't know what they're talking about says you shouldn't use athium because it's really harmful to the planet, then you can just drop them this link and I guess set the groundwork for a meaningful conversation on the problem itself. One thing we did want to highlight is that we did drop the ball on this a little bit. With the timeline it just took us to close in August. It took us until December to actually get it live. One thing we did was reflect on this as a result, outside of the work that we're doing for our roadmap and our goals that we've set, we've also committed to allowing no PRs that are made by the community to be open for more than one month so hopefully we can do a bit better in the future. That's all I've got to say on that. I think Luca went through the chat a little bit about the work done on our translation certificate. So I'll pass it over to him. Real quick, one fun fact I wanted to add on the energy consumption page just to give some data behind it that we launched the page just over a month ago. It's already received 10,000 page views and gets a couple hundred page views every day. Really good to see the impact that a community member can make just by contributing content. I think it shows the reach that the ERM.org has in terms of trying to provide a credible source of information for the community. I'm so excited to see it continue to be referenced elsewhere as well as something to point to. Moving on. Another major contribution that we wanted to highlight is the translator certificate that we introduced at the start of this year. I've just posted a link in the community called chat. This was designed by Scott an amazing developer who has been very active on Ethereum.org. He previously designed a lot of our PoApps suggested the designs for our community hub revamp. You can find him on our Discord as Scott won up. If you're looking to get some design work done he might be exactly who you're looking for. Thanks for the great work on this, Scott. We really do appreciate it. A couple of words on the translator certificate itself. This is our latest effort to acknowledge our translators and support them in any way possible. The requirements for the certificate are a bit more strict than other acknowledgments we have since this is somewhat more professional and we want to ensure we're issuing active translators providing high quality translations. The translators can use this as a reference if they are professional translators or want to start translating professionally. It can also serve as a basis to add another field of expertise to their translator portfolio something like that. Or contributors who aren't professional translators they can use as to show their active involvement in this space and showcase their dedication to Ethereum. Anyone else can just print this out and put it on their wall or whatever they want to do with it but yeah, we are happy we are able to acknowledge our translators in more positive ways that can help impact their curses their development of this space. This is the coin, the community. This is one of their people. Hi, so could everyone please make sure you are muted once again? Yeah, and just to add to what Luca was saying I'm sharing my screen just now if you want to check it out definitely caused a lot of jealousy and the teaming for the people who aren't bilingual and can't actually get this. So yeah, if you're interested in that please do check it out. So once again thanks to once again thanks to Joseph thanks to Scott for their contributions and just helping to make Ethereum.org just a little bit better. So moving on to our Q1 roadmap so it's the start of the year which means we've decided what we want to be working on for the next three months and we'd like to just spend a few minutes chatting about specific roadmap items so first up we've got Paul who's going to speak a little about our about our run-of-node Epic. Sure, go ahead one second I'll see if I can share my screen. Is that okay? So I know that one of the previous community call we had had a chat about one of the upcoming endeavors was to form a more user-friendly page to discuss running a node trying to bring it down to the level where you're potentially getting people who have never considered it, have no idea what is involved in it or may have previously thought that the only way to do this was to recommend line or required expensive machinery. So this is still in preview mode right now and there's still going to be some changes to it but I can just quickly walk you through the idea here. This page is, like I said, it's more geared towards a little bit of this before what it actually means to run a node and then kind of scrolls through and gives some emphasis to who, which is really anyone and that's kind of the point of this page is to emphasize that anybody who's part of this network should consider running a node and it is actually relatively easy nowadays. For why run a node, we got some different cards here and some different things that people can go through and read a little bit more on. This will change a little bit in the order when it finally goes live but the idea here is that we're going to have two different paths for people to pick from. You can either go down the build your own path or you can buy this thing fully loaded. There's a couple of different services that exist right now, DAP node and Avado that are both supply hardware that comes pre-loaded with software that will essentially make it an app-like experience, kind of a point click and literally control it from your mobile phone and you can manage some staking and using smaller, you know, lighter weight computers in here as well in some context as far as how far we've come. We used to be pretty much all command line based if you wanted to run a client and now we have some better options. Hopefully some people will be able to check this out and maybe reconsider the idea of running a node in the future. Obviously there's still a lot of nodes out there but the more the better. I would encourage everyone to check it out once it's live. Awesome. Thank you, Paul. And I'll remain everyone so we're going through this that we do have the slide though so if you have any specific questions about anything we cover, please do pop them in there and we'll try and get to them at the end. Sorry about that. Yeah, so next up I think Corwin wants to speak a little bit about the work he's been doing on the EVE 2.0 rebounds. So I should unmute myself. Sorry about that. Yeah, like you talk about the EVE 2.0 rebrand that we're doing on ethereum.org. This has been a pretty high priority work item for the start of this quarter. It's used or rather it's touched every aspect of our website from the translation program to what our developers are working on, just content to trying to rebrand away from the EVE 2.0, EVE 1.0 references for ethereum. Part of the reason we want to do this and the main reason is because EVE 2.0 has been kind of deprecated as a term for ethereum. Originally this was referring to the proof of stake chain in an old roadmap for that transition and has since changed with the merge to be referred to as the consensus client and then eth1 formally eth1 is now referred to as execution client and with this change we've gone through the website ethereum.org to reflect these changes in the naming. So if you go today and you look at the website you'll still see ethereum 2.0 We have a release coming out that was put up for version 3.7 of the website so today we'll be putting this release out and this changes from ethereum 2.0 to ethereum upgrades and within this change you won't see any references to eth1 or eth2 without them being like what happened to eth2 type of thing and we'll go in and explain eth1 is now the execution client on the handles, the transactions the data or as eth2 is now the consensus client so we're trying to move away as a community from referring to these two clients as eth1 and eth2 mostly to have an accurate representation of what's going on with the actual roadmap but also to try and move away from kind of an attack vector for scams so if you ever see someone come in to a discord channel or someplace you might find scammers being prominent if you ever see someone being like oh you need to switch your eth for eth2 to work on the proof of state chain or on the eth2 chain there is no eth2 if you want to make it clear there's no eth2 and if you see any malicious activity like that try and call it out and make sure that people aren't getting hurts in this attack vector of confusion with the term of eth2 but with that all being said we have a change with this roadmap to the upgrades so every page now you'll find whether it's the beacon chain, the merge, shard chains the vision all the pages that used to be under eth2 will now be just housed under upgrades this also will allow us to as the roadmap develops we can just throw it under the upgrades bucket of the website instead of trying to have to find a new section for this so it helps us avoid scope creep in our drop downs as well which is going to be great yeah, pass it back to Josh here thanks, thank you Corwin and I'll just reiterate that yes although the naming of Ethereum 2.0 or eth2 or whatever you want to call it is being phased out this doesn't change the actual Ethereum roadmap at all so don't freak out in that sense everything's still staying the same apart from we're just using a different name to hopefully be a little bit more accurate right, I'll reiterate that as well I'll just make sure it's very clear that this doesn't change the roadmap overall it is more just the naming change and it goes more for clarity I think there's a lot of confusion over the eth1 and eth2 names being sequential like one is after the other and replaces the other which isn't quite accurate over time eth1 has been used to refer to more the mainnet we're used to and eth2 has been used to refer to this other currently proof of stake beacon chain and in the end these are going to be merged together to replace the current consensus model for our current mainnet so it's not one leads to the next and when eth2 there is no one upgrade that leads to quote unquote eth2 it's a whole series of upgrades that are being rolled out over time obviously to handle the scaling problems and other issues that we have with the network so hopefully this helps clear things up where we have two different layers execution, consensus and they will soon be merged into one network thanks paul yeah so I'm going to share my screen again if you'd like to follow along the last item that I'd like to chat about is creating a web free explainer page on ethereum.org so this is a little bit earlier than the other two items we've just shown so we don't have anything nice and pretty to show you just yet one interesting thing to look at on our roadmap is this chart pretty steady for the last two years then in October of last year the search volume for web free just absolutely skyrocket so people are clearly motivated to learn about this and the problem that we've noticed is that when you search for what is web free you largely get you largely get a bunch of articles some of them are well written most of them aren't well written a few of them are just completely wrong so maybe a controversial opinion but I don't really think so I don't really believe that we want journalists who aren't really involved in web free and probably don't know what it is explaining web free to people who are interested in maybe taking a bit further we've just had the holiday season I'm sure many of you were sat around tables with family members who might have known about your interest in crypto I'm sure you got hammered with different questions about what is web free, what is this decentralization and magic internet money the whole idea of this page is to answer that question for people a sort of gentle introduction for non-technical individuals without all the buzzwords that you'd normally find in this sort of thing and as always because all of the items on our roadmap are on this site they're all open source so if you have comments, feedbacks or are interested in helping out in any way please do ping us in discord or leave a comment on the issue itself anything else anyone wants to add on the roadmap before we move on next up po-apps yeah so I'm sharing my screen on it and on the agenda itself there are some instructions for how to actually claim your quote so I've just put the passcode onto the screen share if you're interested in grabbing it it's all lowercase all one word January community to claim it you need to go to our discord server and in the top right you'll find the po-app bot just send a message to the po-app bot with the passcode once again that's January community all lowercase all one word and if you click on the link that the po-app bot sends you then you should be able to claim it to your wall address and we'll just wait a minute or so just to let everyone do that before we jump on to something else just what we've got this moment I'd just like to ask to make sure that you are muted if you aren't speaking otherwise when we get to the questions you'll be muted at the server level and you won't be able to speak up okay so let's give it another minute or so just after this our translation leap look at is just going to speak a little bit about the different translation efforts across the project just now so I'll stop sharing my screen and pass over to you so I guess we might as well just get into it as people are claiming their po-apps so the translation program as many of you probably know is an effort to get the website translated into as many languages as possible and make this content accessible to people who might who might not speak English at all or not speak English well enough to be able to learn in English especially about complicated topics such as Ethereum one thing that I wanted to highlight today is the recent update to source content in crowd-in and the new pages that we've uploaded to crowd-in so I've just pasted the link to the content versions page on the website where you can find more information about how we divide our content into different content buckets and what that what each content bucket contains let me just share my screen and show you in practice what that looks like so we've recently updated a lot of source content in crowd-in we do this occasionally in order to make sure we're actually translating the latest version of the website moving forward we plan on updating source content every month we have also uploaded new pages to crowd-in these are the pages that have been recently added to the website and aren't being translated yet examples of this contain the community hub the energy consumption page the Ethereum support page security and scam prevention page basically just the recent pages that have been added to the website similarly we have added all the recently added developer tutorials to crowd-in that weren't being translated yet these are some of the most popular developer tutorials on the website like the energy tutorial series similarly to the updates we will also be uploading new pages to crowd-in every month to make sure we're translating all the new content on the website and finally we have created some new content buckets which will allow us to get translated content reviewed and added to the website even faster this includes a specific content bucket for Ethereum upgrades that you can see here a specific content bucket for the community pages and also have divided the developer tutorials into different buckets based on their popularity based on the number of page views that these tutorials get so this will also allow us to add translated developer tutorials that are high impact that have a high volume of traffic to the website faster now as Corwin presented earlier we are also currently working on the ethere brand and moving away from using etheterminology once this is done we will need to get the updated content translated as well in order to remove mentions of etheterminology from the translation this means that the ethereum upgrades buckets so this is content bucket number 4 for anyone watching my stream or active in crowd-in this upgrades bucket will be updated again in crowd-in next week with the new content of etheterminology and we would definitely appreciate some assistance in getting this bucket translated as soon as possible so there will also be other notifications and we will highlight this and point it out to the community and for the time being this content bucket will probably be highest priority to get translated so that we can also move away from the etheterminology in the translations as well so yeah that's pretty much what I wanted to highlight about the translation program great thanks Luka thanks to all the translators involved in that work as well I'm going to share my screen again so for the remainder of the call we'll spend that on Q&A we have a list here ready to go courtesy of our Slido but feel free to add more as we go or if you want to you can unmute and speak up I guess we can just start with the most upvoted so yeah if you go through the list and you see something that you really want answered the likelihood is we won't get to absolutely everything so make sure you upvote the questions that you want to see answered the most top voted comment is from anonymous asking that saying hi I want to contribute but I'm not a coder anything else I can do and contribute to yes if you're bilingual please get in touch with us on discord and join the translation program if you understand the freedom well then find areas that we don't have content for on our site and make suggestions or write the content yourself or if you're just learning about a freedom I guess you can highlight any simple mistakes you might find on that site that's really helpful or perhaps you see something that's too complex call it out or maybe try rephrasing yourself to make it simpler for the the next person you can do that too anything I missed anyone yeah I would broadly just say I mean from a content perspective like it's hard to understate how valuable that is even if you don't code to help keep the website up to date as you folks are all probably aware like Ethereum as an ecosystem just moves incredibly fast right so like as ethereum.org continues to add new content for instance you know we highlighted this energy consumption page we now have hundreds of pages of content in English on the website which then gets translated into tens of languages to create thousands of pages on the website right like just making sure that resources are up to date that we're linking to accurate information that we're removing stale information it may not sound sexy but can be a very helpful way for you to kind of I mean keep tabs on the ecosystem and keep yourself up to date but also be able to help out the millions of people who are reading this content and helping ensure stuff stays up to date is like just a huge way to do that so in the community chat I link to our main contributing page from there there's a lot of detailed information whether it's adding products or community articles or you know new exchanges that might provide additional features adding glossary terms I feel like glossary terms are a nice easy one in the sense that with the translation program Luca talked about one thing we're really trying to do with Ethereum.org is like become a canonical resource for web 3 related translations all the content Ethereum.org is licensed under Creative Commons we want other projects to be able to use the translations that our community has put together to just make the entire ecosystem more accessible to more people from more languages overall right so like even if you only speak English there's open issues on GitHub to add additional glossary terms and add additional content that I think can have a huge impact across the ecosystem and it's a great way to you know build your resume and get noticed in the space as someone who's contributing to open source Yeah, thanks I would disagree on one thing I think fixing typos is definitely sexy and if you find any please do open an issue or a PR for it Next up we've got Jay I think Joseph I've seen you on the call Hey Joseph I said I was sorry about that Yeah, so Joseph says road maps great Re L2s to encourage adoption it's critical to explain why L2 over alternative layer ones and nuance over which L2 and why ideas to do this most effectively and this is on our roadmap I guess and we're building a layer to page I am very conscious that I'm talking a lot here if anyone wants to jump in and speak to this I'm happy to have this one Yeah, no thanks Jay Cook for posting this I definitely agree there is a big difference obviously between layer twos and alternative layer ones we do look forward to highlighting that soon we've talked about the ETH2 rebrand a couple of times now part of that change is going to be the slash ETH2 page on our website is now going to be slash upgrades which is going to broaden what it actually makes sense to go in that section for example potential EIPs and potentially layer 2 scaling solutions because there's more to the upgrades than just the protocol upgrades that were focused on scaling which is kind of the original bucket of ETH2 so as that broadens out I think that would be a nice home for that we've discussed this a little bit internally I'd like to bring some content about twos to that page but also discuss potentially having a dedicated layer 2 page and have this be something that's more beginner friendly and user friendly something that's not buried in the development many people are lay users are likely to miss I want to use that as an opportunity to help educate and explain what you're talking about here for differences we'll necessarily go into all those differences now but briefly they rely on Ethereum security essentially you can do a lot of things with L2s that keep the trust model of Ethereum at its core and you don't need to rely on a whole different distributed network or hopefully distributed network for the security of your funds and activities so definitely on the list I do agree that bringing more education around this stuff is pretty important and we're going to try to do that through the expansion of the upgrades page yeah and I think some things to note that we would be adding is like we'll obviously be talking about L2s what they are kind of like you were asking here but we'll also be talking about bridging so when you want to bridge your assets over internet or exchange we'll highlight some bridges that you would use we'll go into kind of like what bridges are so that we can clarify that because that's definitely an important piece to L2s at least to like understand how to get on to them at the very least so we'll highlight some information around that we'll also add some information around like resources for finding like token lists for let's say you're using a decentralized exchange looking at a little bit of a list on that page to make make it easier for users to use L2 as well and we'll probably link out to some pages like arbitrems portal which highlights applications that are on their L2s already so try and make it as accessible for someone new to see what's going on in L2 and quickly understand what it is versus kind of what's in our developer docs which is more of like a technical description of what L2s are Thanks Corwin, thanks Paul Joseph if you're still with us I know you're very into this stuff and you've probably put some thought into it before the question so if you've got any thoughts or ideas feel free to share them now or yeah okay thank you hello yeah well I mean that's great to hear everything you just said really the question just came to my mind when I was looking at the roadmap because it looked like what was there on the L2 was mostly practical instructions for how to onboard and I just think even now even fairly technical minded people that are already well into Ethereum it's easy to get confused about the firstly why you would use layer 2 if it's just cheap transactions why you would use L2 over just going on to another chain where the transactions are as cheap or possibly cheaper and also which L2 to use and you know you might spend a bunch of gas moving some funds over from layer 1 onto layer 2 and then not really know what to do once you've got there so it just seems like Ethereum.org is kind of a lot of people's gateway onto the whole Ethereum ecosystem and if we can optimize for explaining some of those things and why it's important to inherit security down from Ethereum layer 1 and you know even going into the multi-chain versus cross-chain arguments from Talix Post about why you might want to keep your funds on an Ethereum inside the Ethereum ecosystem rather than go into another chain might just be really useful for encouraging more adoption but I mean I guess that's just a bit of background to the question if you've kind of already answered it in your answers and I appreciate that, thank you. Yeah that's great, yeah I appreciate that and definitely you know Vitalik's discussion on this recently is definitely worth noting and we'll definitely go into how we frame the page in the future I appreciate it. I completely agree I think similar to what Paul just demonstrated with the run a node page that we'll be releasing soon it's critical to explain the why in addition to the what and the how and I think that's exactly what you're getting at of what are the specific benefits outside of just transaction fees that layer 2 provides and yeah if you folks do you have ideas to collaborate and we'll definitely continue to seek feedback as we iterate on that page but clearly that's a key component of it right like if there is an outage on this network can you recover your funds or are you completely reliant on whoever's operating that network important considerations when bridging your funds to anywhere else then layer 1 Ethereum. Thanks very much Joseph I guess we'll move on to the next question Sean what are you all most excited about in 2022 I like this question Sean are you with us on the call maybe? No? Maybe we could do a quick round robin with the team it's not very clear if you're talking about Ethereum or just generally so I guess I'll answer both I'm really excited for the marriage this year the adoption of L2s real world really excited to go on vacation overseas for the first time in a while with my son pass it to Paul Let's see yeah I'll try to keep it brief too I'll second the events IRL in real life events all year long and I'm just putting that out there in general I'll drop our events page in the community call chat check them out because there's a lot of them this year that are already planned there's more beyond just this which we are continuously trying to update this page to keep it accurate but a lot of events all over the world this year I plan to go to a handful of them obviously not all but I'd encourage everyone to check these because this is one of the especially if you're interested in getting involved in the community this question has already been floated these events can be excellent ways to go get your face out there go see other people in person who are working in space they're going to just people exude enthusiasm at these events so if you haven't been to one yet I would definitely consider checking one of them out if there's one nearby and you can't get tickets I would go anyways honestly go you'll see people there you can find people really really fun events definitely encourage everyone to check it out that being said also the merge definitely said about that who adoption watching the ever continuing expansion of dows in this space that's what I'm excited about pass along let's go Corwin what you got I think for myself both specifically what I'm excited about this year is L2 and bridging I think we are just starting to see player twos come online and more specifically like generalized L2 is kind of like arbitrum where you can deploy your smart contracts on there but I'm also curious to see what happens with more application specific L2 as well I think we'll see some cool stuff like the reddit like reddit partnered with arbitrum I believe but kind of seeing what some larger applications are going to be doing with layer 2 technology on Ethereum I'm curious to see where some mainstream adoption of Ethereum goes this year we just saw that twitter this week put out twitter blue or their NFT support in twitter blue at the very least and so I'm kind of curious to see where this goes with mainstream companies this year especially as we've seen Ethereum settle more more value than like the visa network for example in 2021 what type of things our other companies can experiment with on Ethereum so that's kind of what I'm excited just to see what type of adoption gets used this year with layer twos coming online and making it a little more accessible for people pass it on to Pablo I guess okay yeah for this year I would say of course the merge and yeah I agree with Corwin I would like to see more adoption on layer twos I want to see how the applications evolve in arbitrum or optimism I'm looking forward to that yeah talking more about the site the ethereum.org site I would say I would like to see if we could make more web 3 features on the site and yeah make that transition I don't know if that is going to be possible this year but yeah I would like to do that okay I pass it to Luca so excited about a couple of things first of all the merge it's been in the works for a while looks like this is going to be the year that is going to be super exciting and I'm also like the guys have already mentioned very excited about layer twos specifically the improvements that they are making and will continue to make the year has started off incredible optimism just on board curve AVE governance has voted to deploy AVE on optimism they've had two 30% few reductions in the last two weeks alone the arbitrary ecosystem is already large and keeps on expanding TarkNet just came out with a massive upgrade this week that and they basically contain all the functionality you would expect from a production ready blockchain ZK Sync is making improvements and is ready to onboard more people so yeah the ZK rollups in particular are looking like they're making progress and I feel like this year so many more people are going to get onboarded to layer twos and experience what it is to use Ethereum with instant confirmations and super low fees and I feel like most people will be surprised by how amazing layer twos can be and will stay there forever basically that's what I'm excited about and with that I guess that's it all on to Sam yeah thanks guys I mean all I guess just echo what everyone mentioned I think a lot of great points I'd second Paul's point in particular I think if folks on the call have never been able to attend like a real life Ethereum event I know it is like a fortunate privilege to be able to do so but I would highly recommend it just like the friendly community the contagious energy the atmosphere it's a lot of what pulled me into the space and keeps me around so I know I'll be at ETH Denver in less than a month if anyone's going to be there feel free to reach out would love to connect and I'll post a link specifically DevCon which we haven't had an event since DevCon Osaka in Japan in 2019 that's essentially the annual primary conference that the Ethereum foundation puts on every year and I would say is seen as somewhat of the main event in the Ethereum world each year and that'll be in Bogota, Colombia later this year so pretty stoked for that hope folks can make it I know a lot of moving pieces with with events this year otherwise you know plenty of virtual virtual based metaverse conferences to potentially try out but yeah highly encourage people to get involved with those and can be a great way to you know connect with people find new jobs find interesting opportunities so I think worthwhile if you can make it happen yeah I'll plus one that I just want to make maybe a second just to make some space in case anyone on the call wants to unmute and ask a question and feel free to do so if not we can just move on to the other questions but again you don't have to feel shy cool we'll move on we've got another question from anonymous asking how do we stop the scammers from ruining crypto as education that won't be answer I think so education in time I guess we already have the page on a security page on aphelion.org is there more we can do to help with this problem? probably I also think that overtime as more people start to understand the pitfalls of crypto things will get better as well this happens with every evolution of money if you're interested in diving into that rabbit hole a little bit I'd really recommend everything that Robert Breedliffe has written on his blog I'll post a link in the chat to that anyone else have any thoughts on this? yeah I agree I think education is going to be a big part of it however I don't think it'll ever just go away I mean there's scams that are littered throughout our world in different forms where there's the opportunity to take advantage of people for economic gain people are going to try I think it's going to be a combination of education as things that scored captures and blockers things that you know fortunately have to put people through to try to clean up these these social spaces online to try to limit you know who gets in unfortunately you have to go through on a regular basis and ban people from the server because they're they're obviously trying to take advantage of people in different ways that's not always clear for us you know who is who is not it's a challenge for sure I'm going to do to open suggestions I do think it's going to get better with time we'll learn a bit more but sadly I don't go away fully to be honest yeah I agree next question from Ammar what are you doing to make Ethereum more accessible I guess that depends on what you mean by accessible so we do have our Q1 ethic around accessibility I'd be curious if Pavel maybe wants to weigh in on that and that's about the yeah go ahead yeah sure so yeah as Josh mentioned this is a goal for us for this quarter it was a goal too in our previous quarter but for different reasons we couldn't make it so to give a little bit of context we are trying here to make our website more accessible for everyone basically we have users that navigate our site only using the keyboard for example or using a screen reader so we want to make the site accessible and that is have a good experience navigating with those devices so answering the questions I would say that at first we are planning to basically make an audit in our code and trying to follow well-known guidelines or standards from the web3 for example and then we want to improve the navigation experience using screen readers or navigating the site with only the keyboard so we are going to audit first and then of course we are open to hear suggestions from you guys we don't have any accessibility expert in the team so we are open to suggestions and finally I just want to mention that this goal is difficult to establish an scope it's a never-ending goal to increase the accessibility so for sure we will have in the future more goals on improving the accessibility of the site so happy if you have any suggestions or if you want to discuss this on the chat or you can message me I also have a couple of very quick points I'd like to add so if you are talking about making ethereum.org more accessible we have the translation program the goal of which is to make the content related to ethereum more accessible to everyone who might not speak english or maybe they don't feel comfortable reading in english learning about highly technical topics in english if you are talking about making ethereum more accessible in regards to fees use layer 2s you inherit the security of ethereum and the fees are minimal that's it just go back to very broad topic and also in terms of content I think most of the content on our roadmap is also aimed at making ethereum more accessible certainly the webreaksplaner, layer 2 page, a wallets revamp, run and owed all of that we are trying to tackle that problem from quite a few different angles very conscious of the time we can quickly fire through a couple more what sort of plans are there to highlight more of the public good space from rory that's a really good question not one I immediately have an answer for, maybe someone else on the team wants to speak a little bit about the other work I've been doing with the CLR yeah I can touch some on that I think that's Roy a great question we encourage input on that I mean it's a pretty broad area but obviously the ethereum community and the crypto community more broadly are realising like hey this technology gives us some incredible coordination power whether it's focused on climate change or open source software or public goods generally like this global movement does have the capability to influence a lot of change and a lot of capital formation that even nation states can't necessarily tackle on their own so the whole design space and the opportunity space is pretty boundless so we definitely want to do what we can to highlight that we do call out certain public goods on our grants page which basically just shows different grant opportunities that people can find who are trying to for instance build open source software or public education goods so there are paths to receive funding through that you know on our DAPS page for instance we mention get coin grants as a well known crowdfunding platform for public goods and our team over the past almost year part time has been contributing to a project clear fund clr.fund and I guess I just touch on that you know the ethereum foundation is thinking about this more holistically and more broadly in the sense that you know the ethereum foundation is a non-profit and our primary activity is giving money to public goods in the space to just like benefit the ethereum ecosystem more broadly and you can find allocation updates on blog.ethereum.org around how the ethereum foundation thinks and about how they distribute those funds encourage you to check out a recent post on the client incentive program for instance and it's not something our team focuses on specifically but I can tell you the ethereum foundation is looking to experiment with more ways of funding public goods and distributing and decentralizing the power of deciding which projects receive those goods so if you have ideas maybe it's you know creating an additional use case on ethereum.org to specifically talk about crowdfunding potential and like ability to coordinate and fund public goods just to help grow awareness of like what public goods actually are how much our world relies on them in general I think it's a much broader movement that's bigger than just ethereum.org but I think there's definitely stuff we can do and again would encourage input on it because yeah I think it's a huge opportunity and a very important space for us to potentially help solve yeah great answer thanks Sam so we've seems we've not managed our time very well I'm aware we've got quite a lot of questions left but I think we're going to have to call it at that what I would do after the call is we'll go through and just spend some time answering all of these questions in the community call chat so even now if you've got another question like answered feel free to pop it in there and I'll spend a little bit of time later on today just going through those and answering them for you and with that yeah sorry go ahead I was going to say real quick the Slido in the future do use this method again just encourage people take a look at the questions that are there and upvote ones that may be similar to a question you if possible the way we don't kind of fragment the same question over multiple things and then they end up lower down on the list that's one little hack to try to get your question answered yeah great point thanks Paul so yeah I think we'll call it at that thank you so much everyone for attending sorry if we never got to your question but we'll answer that later hopefully and we'll see you all again next month hopefully thanks everyone take care thank you thanks everyone thanks everyone