Okay, let's see, Mike seems to be working as well. Okay, that's good. So this is lecture 3, but as usual the L does not show up at the right time, but the other are the alphabets are there, so you can figure out its lecture. And let me remind you of what we did last time, we noticed that a k dimensional subspace of 0, 1, n was actually a code, right, it was a linear code. We'll have a notation for this, we'll call any k dimensional subspace of 0, 1, n as an n k code. Okay, this is denoted n k code. Okay, can there be more than one n k code? Yeah, I mean how do I specify one n k code? What should I do to specify one n k code? I have to specify one particular subspace, how do I do that? k linearly independent elements from that, I have to provide some basis, right? So there can be more than one n k code obviously and then if for each basis there will be a hopefully several n k codes. Okay, so this notation is quite standard n comma k, n is called the block length and k is there are several names for it, I'll refer to it as either dimension or message length. Okay, so that's how we'll denote a k dimensional subspace of the n dimensional binary vector space. By the way, people who are sitting rows 4 and after, I would strongly recommend that you come closer because I tend to speak low often and then you can't really hear it unless you don't want to hear me, you don't want to hear me, that's fine. Okay, all right, so that's the n k code and we've been talking about the dual subspace, right? So what's the dual? of this subspace is dual of, I'm sorry, dual of an n k code. Okay, so we saw before that this will actually be a n minus k dimensional subspace or in my terminology now in my notation, I'll be, I'll know it'll be a n minus k code, right? It's an n minus k dimensional subspace, so I know it will be an n minus k code, that's my terminology. Okay, all right, so you see, you see by specifying the code, you're also specifying what the dual is, right? So you can do it either way, right? How do you specify a subspace? You either specify the basis or you specify a basis for the dual. Okay, once I specify a subspace, you know how to find its dual. Once I specify a dual, you know how to find its dual and come back to the subspace, right? So both of these will be equivalent in some sense. Specifying one is the same as specifying the other, in terms of specification, you don't have to specify both. Okay, so in this class, we will see a whole bunch of examples to make this, to look closely at how these subspaces look like and I'll stick to this n equals 6 which was the favorite number somebody picked in last class. Okay, so we'll pick this n equals 6 and look at a whole bunch of examples to get a feel for how these things look like. Okay, how do these dimensions look like? What are the various codes of length n equals 6? And what can we say about it? Okay, without looking at any of its applications or using it in a channel or anything like that. We will do that later but for now, we'll just look at all the subspaces and figure out if there's anything interesting that we can say. Okay, so the main skills you have to pick up when you look at just subspaces are, how do I go from code to dual? How do I go from dual back to code? Okay, what's the point of the dual? Right, why is why does the dual seem interesting? Right, to go from the message to the code, from to go from the message to the code word, maybe the dual is not so interesting. It's also interesting, but maybe not as interesting as the generator matrix. But on the decoding side, you can see the dual is so nice because it gives you parity checks on the code word, right, you don't know anything about the message, but you have a receipt word to work with. So the dual is very interesting in that fashion. Okay, anyway, so let's see a whole bunch of examples. The first example presumably that one can see is say we'll set k equals zero. Okay, what will happen if I set k equals zero? Okay, so what can we do? I mean, this is like the 6 comma zero code. Okay, there's only one 6 comma zero code. What is that? It'll simply contain all zeros, we can take this as like a notation, you know, I mean, there's no real zero dimension, right, it makes no sense, okay, you have a basis with no element, right, maybe, maybe we'll take it as a convention that the 6 comma zero code refers to the all zero vector alone. Is that a subspace? Yeah, it's a subspace. We do do it, nothing will happen, right, you add and multiply nothing will happen. So it's a subspace, we'll call it the 6 comma zero code, it's a trivial code, right, there's really nothing in it, it's a trivial code. Okay, so whenever you have a code, what is the skill that you have to develop? You have to go to the dual, right, that's what we're going to do. So now think about it for a while, okay, this is my code, what is its dual? Okay, so the first thing you have to determine is what are the dimension, what is the dimension of the dual? What is the dual in this notation? If you have a 6 comma zero code, the dual will be a 6 comma 6 code. Okay, so that's also a trivial thing, what is it actually? Yeah, it is the set of all six bit vectors. Okay, so I have a notation for it, I'll simply call it 016. Okay, does it make sense are these two duals of each other? How do I check if these two are duals of each other? Any two vectors you choose from these two have to be orthogonal, right, dot product should be 0, yeah, it's very clear, right, you pick all the all zero, this is going to be orthogonal to every vector in the dual, right, and that will be the only vector that's orthogonal to every vector in the dual, right, you can also convince yourself that has to happen. Okay, yeah, yeah, in this case it contains. You see the dual and the code will even the subspace and its dual will anyway intersect at the origin in any vector space that will happen. So this is not that strange, okay, you'll see as we go along, there will be more non-trivial intersections. Okay, so something I mentioned in last class, we will see it. Okay, so k equals zero is not that interesting, it only gives you two trivial codes, the code which is, which actually corresponds to an uncoded system, right, 6 comma 6 is a uncoded system, you know, you're not adding any parities, okay, so one can think of this as an uncoded system, an uncoded situation. Okay, in the other case like k equals zero is just totally meaningless to talk about what it is also. All right, so the next interesting thing is to look at k equals 1, okay, 6 comma 1, will there be only 1 6 comma 1 code? No, there'll be, there'll be many, right, so there'll be many. So I'll have to say 6 comma 1 codes, okay, there'll be several 6 comma 1 codes. How do you characterize the 6 comma 1 codes? Yeah, I have to have one more, right, so like she's saying, she's saying you need one element in the basis, okay, and it has to be linearly independent. So if you have a singleton set, linearly independent is the same as being what? Non-zero, okay, the only linearly independent singleton set is what? Is the zero vector, right, so anything non-zero will be linearly independent, okay, so on the face of it, how many different 6 comma 1 codes will you have? Without worrying too much about going into detail, you should have 63, right, it looks like you'll have 63 different 6 comma 1 codes, okay, so let's take a few, 63 of them, I'll put a question mark, and then we'll come back and look at it very closely, okay, so let's see a few examples, what's the, so how do I, okay, so I thought, so to specify a code, I'll write down a generator matrix, so that it's consistent with the many of the notations, so a few examples, so I could take G to be say for instance 1, 0, 0, 0, 0, 0, okay, this will correspond to a code, what is the code, what is the code, how many code words will the code have, a 6 comma 1 code will have 2 power 1 which is just two code words, one of them is all 0, the other one should be this, right, you just take linear combinations of these two, there are only two linear combinations, one is 0, and the other is this vector itself, in fact you don't have to even worry about this G, you can directly come up with all the 6 comma 1 codes, what will they be, the all 0 vector and some non-zero vector, okay, for every non-zero vector you'll have that, is that a subspace, is this a subspace, just these two, yeah, when you add any two of them, what's the only non-trivial addition here, are you adding? 1, 0 to itself, that will be the only non-trivial addition and that comes back to 0, right, so this is a vector space, it's no problem, all these things are codes, okay, but let's look at this other code, suppose I say, suppose I say instead of 1, 0, I pick G to be 0, 1, 0, 0, 0, it's just nothing really fancy here, what does the code look like, one code word is the same, 0, 1, 0, 0, 0, 0, okay, so well technically these two are different codes, right, when you can't say they are the same, because code word is different clearly, okay, but in practice suppose you say you're sending it over a symmetric channel, okay, independent channel, right, memoryless channel, each bit goes through an independent version of the channel and what's the difference between these two, there's really no difference, right, this is nothing but a simple reordering of the coordinates of the other code, okay, instead of sending the second bit, instead of sending the first bit, first time, you send it the second time around, since your channel is completely symmetric, not the big deal, since your channel is memoryless, it doesn't matter when you send the bits, these two codes really are not different, okay, they are the same, even though we would, they look, at least when you write them down, they look different, they are really not the same, not different when you use it on the, on the, on any channel, okay, as long as the channel is memoryless, okay, so typically people don't distinguish between these two codes, okay, so you don't think of these two codes as being same, different, okay, there's this notion of codes being permutation equivalent, okay, so I'll make it precise as we go along, basically if you permute the coordinates, if one code becomes another code, both of them are supposed to be the same, okay, there's really no difference, okay, so keep that in mind, so one can say 6 comma 1 codes, okay, many of them will be equivalent, right, how many codes will be equivalent to this first code that I wrote down, 6, right, so there might be more for the other things, but they'll all be equivalent, for instance if I think of g equals, let's say let's take some example like this, and the code would be this, okay, so this looks, this is of course not equivalent to the previous two codes, right, but there will be so many other codes that are equivalent to this, how many other codes will be equivalent to this, 6 e2, right, so that would be like some 15 codes which will be equivalent to this, if I pick a vector of, vector with three ones in the g, how many codes will be equivalent to it, 6 e3 likewise, so you'll add up, we'll ultimately get all the 63 codes, not all of them will be different, there'll be only six different classes, each of them will fall into that, okay, all right, so that's about just looking at the codes themselves, so what's the next skill, the skill that we really want is to find the dual of these codes, okay, so let's try to find the dual of the first code, okay, so maybe I should go to the next page if I can manage to, okay, so let's try to write down the duals, okay, suppose I started with c equals, okay, I write down usually c for the code, 0 0 0 0 0 0 and then 1 0 0 0 0 0, okay, so suppose this was my code, the dual we will denote as c perp, right, what will this be, okay, okay, yeah, everything with, it's like you're saying, so everything with 0 in the first place, okay, so that's, that seems like a good answer, you have to check a lot of things, right, you can't just happily accept that, first of all is that a subspace, it will be a subspace, okay, so all those things you can check, but there's also other simple mechanical methods, so you don't have to come up with all these fancy methods, what's the simple mechanical method, I want a simpler mechanical method, let me be more precise, you start with g, once g is in systematic form, you write it in ip form, i k p form, what is h, h is p transpose i n minus k, right, and the rows of h are my basis for the dual space, okay, so that's a very automatic way that in which you can find it without resorting to intelligently trying to find it, okay, if you can find it intelligently, that's great, but if you want to do a mechanical job, you can also do that, okay, so how do I do that, let me show that, I have g, what is g now at this point 1 0 0 0 0 0 0, okay, okay, I have to first write it in i k p form by doing elimination, whatever, okay, I have to do that, okay, but notice here what is k, k is 1, so i 1 is, it's already in that form, right, so what is, this is how you split it to see that it's in that form, okay, so now h becomes p transpose, okay, p is what, 5 zeros, so if you transpose it, you'll get 5 zeros in a column, okay, and then what do you have left, it should be i 5, so that's your h, okay, and what will c perp be, it will be that five dimensional subspace which is spanned by the rows of h, okay, so rows of h form a basis for c perp, okay, so this is the same as doing elimination, so how do you find null space for a matrix, this is what you do, right, you eliminate, get it into r r your form, and then you identify your free variables, put once there, and then it's the exact same procedure, it's nothing different, okay, just that we have a formula for it in the i p and then p transpose i form, okay, so this is the mechanical method, okay, you just reduce g to the systematic form and then use the formula to go from g to h and the rows of h you know will generate the dual which is the c, okay, very simple, so let's look at the other example, let's, this is for the first one, for the second one we had seemingly a more difficult problem, okay, because I had c being this and then this being this, okay, in which case g becomes 0 1 0 0 0 0, okay, so here it seems like elimination is not going to help you or will you get one to the left by elimination, okay, so you have to do a column swap, okay, and why is it that you can do column swaps without worrying about anything, only thing that column swap does is changes the order in which the bits are centered, nothing else happens, okay, so you can do a column swap, so the first thing to do is do a column swap to reduce g to systematic form, maybe you can call it g systematic if you don't want to say same g is equal to both vectors and now you can go to h systematic, okay, which will be what, which will be exactly the same as this matrix, right, right, you can do that, once you write write it in that form, this rows of hs will be a, will be the basis for the code, okay, but if you want the exact basis for this c what will you do, you undo the flip that you did column swaps that you did to go from g to gs, okay, so undo column swaps to get exact dual, okay, so that's the strict mathematical procedure, but in practice in coding nobody really will distinguish between these two codes, okay, a code with its column swapped is considered to be pretty much equal to the code which will add the columns in different order, okay, so nobody will obsess with this, okay, so you can just happily say this is the dual and be happy with it, just make sure you don't, you always use systematic form codes, so there's no problem, but if you want to be exact you might want to do these swaps and make sure everything works, okay, is that clear, so that's how you find the dual, all right, okay, so okay, so the next example we'll see will hopefully be a more interesting example for you, so you can keep going along like this for k equals 1, so k equals 2 will start to get more interesting, how many different possibilities will you have for k equals 2, okay, so if you want k equals 2, 6 comma 2 codes, looks like there'll be many more, okay, so we had 63 different, possibly different categories in the codes in the previous for k equals 1, for k equals 2 you have to pick two linearly independent code words, right, in the binary for binary vectors when will two vectors be linearly independent, when will two vectors be linearly dependent, believe me when one of them is zero, no, no, it's not, that's not the only credit, when both are the same, right, when one of them is zero, yeah, definitely it's linearly dependent, that's not the only case, both vectors can be exactly the same, if they are different can they be linearly dependent, no, for binary it's not possible, okay, but for instance in real vectors the vector 1, 1 is equal, is linearly dependent with the vector 2, 2, okay, why is that not possible in binary, everything is reduced, modulo 2, so you have only two scalars 0 and 1, so you can't multiply by the scalar 2, right, so there's no real 2 there, okay, so only way two vectors would be linearly dependent in binary vector spaces is they are identical, okay, so right now using that idea, how many different 6, 2 codes could you have possibly, 63 choose 2, right, it looks like all those things will show up, you'll have to actually consider all of them and then what maybe you can reduce based on permutation equivalence, you can just equate codes which are permutation equivalent and then reduce that number if you want and finally get to the really different 6, 2 codes, okay, that will be a lot of work, you have to do a lot of work for that, okay, we won't do that, we'll just consider some simple cases just to get started and think about how this is going to work, okay, so the case that we'll consider, we'll just see one example, I'll take g to be this way, 1, 1, 0, 0, 0, 0, 1, 1, okay, so the first thing I want you to do is tell me what c is, okay, all 0 of course, what will be the other vector and any other vectors in c, the rows of g will obviously be codewords, okay, so you can directly write down the rows of g, that will be linear combination, the first row multiplied by 1, second row multiplied by 0, that will give you this, the next linear combination is first row multiplied by 0, second row multiplied by 1, that will give you 1, 1, 1, 0, 0, the last one is both multiplied by 1, so that will give you 0, 0, 1, 1, 0, 0, is that fine, okay, so that's the code, okay, so I want you to do some work and get the few codewords of the exact dual, okay, so I think how many codewords will the dual have, what will be the dual? Dual of this 6, 2 code will actually be a 6, 4 code, so how many codewords will it have, 16 codewords, why is that such a difficult thing to do, it's just 2 power 4, right, 16 different codewords, okay, so just write down a few of them, don't have to write down all of them, at least write down four linearly independent ones and then a few combinations just to see how it works, what's the first step, first step is to go from g to gs, right, in systematic form and you'll have to do some swaps, right, it won't come without swaps, remember what swaps you do, go to hs and then undo the swaps and you'll get h, okay, shall I write down gs, okay, enough of you have done gs, okay, it's not too difficult, I think gs would be 1, 0, 1, 0, 0, am I right, you can have 0, 1, 0, 1, 0, 0, did you get it in this form, okay, what's the only swap you have to do, you have to swap the second and the third bit, right, you don't have to do anything else, okay, right, so what's hs, let me write down hs here just to save some space, it will be a, what will be the dimensions of hs first, this is a 2 by 6 matrix, so hs will be a 4 by 6 matrix, right, and the first thing to do is to write down the split, this is your i2 part and this is your p part, okay, hs the first part will be p transpose, what's p transpose now, 1, 0, 0, 0, 0, 1, 0, 0, okay, and then you'll have the identity part, which would be 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0 and 0, 0, 0, 1, okay, so now we have to undo these two swaps to get the exact h corresponding to this g, so the h will be what, okay, let me write down that also, actual h will be, the first column is going to be the same, second column will also be 1, 0, 0, 0, third column will become 0, 1, 0, 0 and after that you can happily repeat what you have in hs, is that fine, okay, so now we readily have four linearly independent vectors in the dual of c, okay, what are the four linearly independent vectors in the dual of c, the four rows of h, okay, so you could write for instance c perp is generated by 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, okay, this is a very mechanical way of getting this, okay, so what is a generator matrix for c perp h, which is the parity check matrix for c, okay, so both these roles are played by these two things, so what would be a parity check matrix for c perp g, okay, so all those things are there, okay, so let us let us try a few smart things now, okay, could you have guessed that these four would belong to c perp just by looking at the codewords of c, try some intelligent guesses, for instance look at the last two vectors, those two should be in the dual, right, you see why it is in the dual, okay, for any vector in c just by looking at g you can figure out those things, okay, so likewise even these two vectors it makes sense that they form parity checks for c, now I mean looking at the codewords, right, that is those are interesting things to look at, okay, okay, so now for instance people might want to think about intersections between c and c perp, what is the intersection between c and c perp, okay, so remember these are just the basis elements, c actually has c perp actually has how many codewords, 16, okay, go ahead let me see, what is the intersection between c and c perp, yeah, so you will see c will actually be present in c perp, okay, so you notice, notice what is happening, so all these interesting things will happen, so this is a surprise, okay, c is contained in c perp, okay, codes like this are called self orthogonal, okay, it is a very nice natural terminology, this is called self orthogonal, so such crazy things can happen in binary vector spaces, these things won't happen in real spaces, right, so you cannot have a non-trivial real subspace contained in its dual, right, it will never happen, the inner product is nice inner product there, here it is a little bit different, okay, alright, so any questions, basic questions on how I went about getting c perp from c, okay, so it is very important to be very comfortable with this, it is one of those very basic skills that is taught in the beginning of every coding class, okay, so you should know this very, very well, okay, it can get non-trivial, just do it by hand, for instance one nice computer assignment I would suggest is code this in c or matlab, okay, so it is a very nice assignment to try, okay, so you will have to take care of a lot of things in practice, for instance the rows of g might be linearly dependent, so when you eliminate you will end up getting rid of some of them, so the k that you initially thought you had may not be there, might reduce, the rank of g may not be exactly equal to the number of rows, right, can be less than that, so you have to take care of all those things, you will see all these utilities are not readily available in c or matlab, okay, using dating binary rank, matlab has some binary rank programs which are very, very slow, they don't run very fast, you might want to write these things, it is good training, okay, all right, so let us look at just one 6-3 code, okay, one 6-3 code which I think is very interesting, okay, we will just see one example, okay, so let us do a simple computation before we proceed, in the previous case we expected 63 choose two different codes on the face of it, could be permutation in equivalent or something, in this case what can you say, is it easy, is the computation easy, okay, how will you choose three different vectors which are linearly independent, right, that is what you need to do, okay, the first vector can be chosen to be any non-zero vector, the second vector should be chosen to be something which is not equal to the first one, what about the third one, not its sum also, right, so it is very easy to do that computation and you also have to take care of the fact that you could have chosen them in any order, so you have to divide by some three factorial or something, so you can easily compute the total number of different 6-3 codes that one can expect, maybe some of them will be permutation equivalent, that is different, okay, so that computation can be done, it is an interesting thing to do, okay, so the one 6-3 code that we will, I will try to give you as an example, it is following code, okay, it is a very, very simple code, so you notice that the way I have written it down, rank of g equals 3, right, you can very easily see that it is 3, 3 rows are linearly independent, so it is in fact, this g in fact defines a 6-3 code, you can easily write down the 8 code words which are what, which are members of this code, it is not, it is very easy to write that down also, okay, what I want you to do is find h, okay, so I think it is, so you have to do how many, I mean there is no elimination required here, but you need how many to reduce it to systematic form, what do you need to do? Column swaps, right, so you will do 3, 3 or 2, yeah, maybe 2 column swaps depending on how you do it, it is enough to do 2, 2 column swaps and get to the permutation and then you will see, you will notice to your surprise that when you undo the permutation, what do you get? You get the exact same thing as h, okay, so what does this mean? It means, in fact the c equals c perp, okay, this is, the situation is called self-dual, okay, so in this case it is very easy to analyze, right, the code and its dual are the same, okay, so finding self-dual codes is a very non-trivial problem, as I said it is very active, such problem as well, people work on it constantly, okay, so that is the only case I wanted to consider, so this thing can get a little bit non-trivial, if you are not used to it, particularly in exam pressure, if I give you a generator matrix and ask you to find the parity check matrix, I have seen a lot of people make mistakes, okay, so it is good to practice this just for you from an exam point, all right, so that is about code and the dual, I want to point out one further fact which is, which usually is not emphasized in the beginning of coding class, but it is becoming more and more significant today, now that you have so many, so many advances in coding theories, what is important, so I will go back to some k, the k equals 2k's just to highlight this fact, so we will look at a 6-2 code with g equals, let us say let me pick something, something in systematic form, 1, 1, 1, 0, 0, 1, 0, 1, 1, okay, I will pick it in systematic form itself, okay, what is the code, okay, what is the code, all zeros, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, okay, so that is my code, okay, well I think I should, that is my code, okay, all right, so if you try to find the parity check matrix, what will the parity check matrix be, did I make any mistakes or what, people are staring at me, I am not telling you what mistake I made, oh there is a, okay, there you go, it should be 0, 1, right, is that fine, okay, good, so if you write down h plus by doing the IPP transpose I switch, you will get 1, 1, 1, 0, 0, 1, 1, 1 and then you would get 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, okay, okay, right, okay, so I have been emphasizing that the dual and the parity check matrix are likely to play a very good role in decoding because without any reference to the message they tell you whether or not a six-bit vector in this case is going to be a codeword or not, why is it, why is it true, so you see is a codeword, a vector is a codeword if and only if, h times that vector transpose is 0, okay, so that is, you can see that itself gives you some information about decoding, maybe you want more information, suppose for instance what does, what does, what does it mean to say this is in the dual, okay, so for instance since that is the second row you know this belongs to C perp, okay, what does it mean, one way is, one way of interpreting that is that if you take a dot product of this vector with any codeword you should get 0, okay, so suppose I have a codeword that I will not specify, I will simply say it is C0, C1, C2, C3, C4, C5, an arbitrary codeword C, C, I know these two dot products have to be 0, okay, so suppose evaluate the dot product, what do I get, okay, C0 plus C1 plus C3 equals 0, okay, in every codeword of C, I should have C0 plus C1 plus C3 being 0, okay, so that is the power of that statement by saying 11010 belongs to the dual, okay, so likewise there are other parity checks, right, okay, so this is, this is called a parity check, okay, it says check the parity of the first bit, second bit and the fourth bit in your codeword, if it has even parity what does it mean, that vector could be a codeword, why am I saying could be a codeword, because I do not know about the other bits, right, when is it a codeword, when it satisfies all these four independent parity checks specified by the parity check matrix, then it is a codeword, if I know it satisfies one parity check it could be a codeword, if it does not satisfy what do I know definitely, there is no way it will be a codeword even if you give me all the other bits, okay, so that is a powerful check to have, okay, so likewise you can write down other parity checks, for instance the first row will give you what, C1, C0 plus C2 equals 0, third row will give you, I am sorry I think I am going a little bit here, it will give you C0 plus C1 plus C4 equals 0, okay, and the last row gives me C1 plus C5 equals 0, okay, I think I am writing all over the place but you can see that those are the parity checks, okay, those are four independent parity checks which together when satisfied also mean that the vector is definitely a codeword, okay, but are there other parity checks, can you come up with any other parity check? Yeah, any linear combination of these four will again be another parity check which has to be satisfied, so what will be the total number of non-trivial parity checks, of course if you use the all zero codeword then 0 equals 0, what is the total number of non-trivial parity checks in any nk code? 2 power n minus k minus 1 which is equal to the number of non-zero vectors in the dual code, okay, so every non-zero vector in the dual code gives you a parity check for the code, okay, so that is the important in today's context that is a very very important fact to note and I am bringing it up very early in this class because we will soon move into this and that time it should not surprise you, okay, so that is a very important fact. Every non-zero vector in C perp is a parity check for C, okay, it may not be, so if you take enough of them you will get a set of independent parity checks which together will mean and if and only if, if all these things are satisfied it is definitely a codeword, but you may not, you may also have partial information, you know, I may say, okay, these bits satisfy this information, okay, so that is the power of parity checks, so somebody says what is the total number of non-trivial parity checks it is 2 power n minus k minus 1, okay, so those are some facts about the parity check matrix, okay, all right, so I think there are about five minutes left, I do not want to start something new, I think I am happy with the way we have done the basic vector spaces idea, I think it should be reasonably clear but you will see easily that when this number becomes large, when n becomes 1000 and k becomes 500 you are not going to be able to do this by hand, okay, given a G you are not going to be able to do elimination and go from G to H by hand, it is very difficult, right, and it is also not possible to list out all the codewords, it is very clear, so you need computing tools that can do some fancy things for you to come up with parity checks, but you can come up with parity checks, right, you can come up with a lot of parity checks, maybe not all of them but lot of them and that kind of thing is useful for decode, okay, all right, so I think to sign off we will just see one example of a situation where I will ask you to go from G to H, which could be slightly interesting, okay, okay, this is my G, okay, so what are the, what can you say about the parameters of the code that G generates, okay, what is n? n is 8, that is very easy, can you decide k immediately? No, okay, so even to decide k, what should you do? You have to go through elimination and reduce it to systematic form, once it comes to systematic form, you can decide on k, okay, so I want you to do that, I want you to do the elimination, you might need to do swaps also, right, come bring it to systematic form, go to HS, go to GS and then go to HS and then come back to H and complete this picture, okay, so maybe some of you are very good at doing this, but I am sure some of you recognize that this can be slightly non-trivial, even in the very small, simple case, you have to do a lot of swaps, you have to do a lot of elimination, so if you are not used to doing this thing very fast, you can make a mistake very easily. See, you can also do row interchange, right, that does not change anything, right, from your linear algebra background, hopefully you realize row interchanges, do not change the row space, row space is my code space, so it is not a problem, three, which is your linear combination, which is in this four, so to get the exact dual, remember you have to remember your swaps, then undo them after you get, if you do not do that, you will not get the exact dual, you will end up with a dual which is not orthogonal, you say, okay, where did I go wrong, okay, you have to undo the swaps, okay, how many of you have concluded K equals 4, okay, so K equals 4 is the right answer, in fact, if you do a lot of work and find H, what do you think you will get, somebody make an intelligent guess, yeah, at the end of the day, you will get an H which is the same as G, okay, so this is also a self-dual code, it is a very famous code, okay, it is a very, very, very famous code in coding and you might want to get acquainted with it, in fact, if you find all its code words, what do you think it will be, it will be a very interesting set of code words you will get, okay, so it has got lots of, take a look at it, yeah, even parity, yes, but there will be a lot of structure to a lot of its code words, it is a very wonderful code, okay, so it is good if you like such things to list out the code words of this code, just stare at it for a while, see if you notice some patterns, it has got some beauty to this, okay, so I do not know, if you see beauty in ones and zeros forming patterns, you will like this, okay, all right, so that is, in this case G equals H, okay, all right, so I will just sign off with a couple of facts which you might want to prove when you have time, so first thing you can show is if G and H are generator and parity check matrices for a code, what will G times H transpose B, it will be a big zero matrix, right, what will be the dimension of the zero matrix, yeah, whatever, K by N minus K, whatever, some big zero matrix it will be, okay, so G times H transpose will be zero, what are the facts which you would like, for instance, G times G transpose is zero implies C is contained in C perp for instance, okay, and C is contained in C perp and K equals N by 2 implies C equals C perp, okay, okay, so all these things are nice things to try and show if you want to play around with these things a little bit more to try and understand, it is very trivial but still it is good practice to have, for instance in this eight, in this four by eight matrix G that I have here as an example, you will see G times G transpose is zero, what is G times G transpose being zero means any two row should be orthogonal to each other, the row should be orthogonal to itself, you will see all those thing properties will be satisfied, so you see immediately C will be contained in C perp but you notice what K is N by 2 which means the dimensions of C and C perp are the same, so the number of code words are the same, so obviously C should be equal to C perp as well, so you can easily conclude those things based on these kind of stones, okay, all right, thanks.


That would be funny! That would be funny. We're talking about stuff that you can't hear. That's not even gonna be on behind the scenes because it's offensive, rude and just the kind of thing we talk about. About Weeners. Yep! Oi.  Yeah I was supposed to watch a movie Wow You can do it, you can do it real quick Okay Hold on Today we are reviewing On Your Itashi Oups Done Technically, second film What? But first released film Oh right Right I think they were made around the same time His first film still has yet to be To my knowledge Has yet to be released because of the sensor board Screw you, sensor board Yep But and I believe when we talked to him The original one was supposed to be Five and a half hours I think that from what my memory serves If that's correct I think you're right But anyways We're doing Black Friday I found out how they requested it It was actually a Patreon request We do a poll on Patreon every month And they pick a film This was one of them One of the benefits you get For going on to Patreon So this was it And this has been on the list Forever So we've At least We're coming in October I was gonna say Probably a year and a half When we started On Your Itashi Oups Basically Yep When we first got notice Of him The first directors we were Immediately exposed to Were On Your Itashi Oups Michel Sanjay Lila Bansali And Michel Martin Those were the three Right off the bat And this was like Right insta So for all of you Been waiting for us to watch this Thank you for patiently Enduring It's no joke The memes about having to wait To the R-127 For us to get to your request Yep And you're still going to have to Yep But anyways This is I believe Done on a shoestring budget Like less Probably less than a shoestring Budget Yeah But you probably funded it The way Quentin Tarantino Funded his first film It was like Rentals And on credit cards And the only shot on the weekends Yep And it's a film about The investigation that falls In 1993 Serial Bombay Bomb blast Right That's a lot of bees That is The Bombay bomb blast Told to the different stories Of the people involved Police Conspirators Victims And middlemen Directed Written by Onyoy Kashiop And starring A thousand people Yeah But the main people Are KK Mennon Mm-hmm Say his name Pavan Malhotra And And then obviously There is an appearance there By the very young Very vibrant Very vivacious Noisy density And of course The legendary Ustaji Zakir Hussein Yes We actually thought that When we did the trailer reaction to this We saw his name Right And we thought it was ours Zakir Hussein Right It's just some actor Names like you Hussein Yeah But We're dumb Anyways So this is going to be How much it's worth of you One You all know about this event Yes I think everybody in India Knows about this event It's a film So A hundred spins for review If you haven't seen it Go watch it Come back And you're about to be spoiled There you go So, Rick Your initial thoughts I don't have a paragraph Because This is one of those where My Personal take on it Is my personal take Mm-hmm But I have an appreciation For the film Based on where it falls In the landscape Of Indian cinema What he had to work with And how he had to work with it Mm-hmm How much it changed Indian cinema It's place in that Yeah Pantheon Mm-hmm For me personally It never really grabbed me And held me In its clutches Even at the beginning and the end Yeah The end it did The last 30 minutes for me Was by far the most engaging And captivating I thought the first 30 minutes And the last 30 minutes Were definitely very engaging And the first The first part of it Was the last 30 minutes More I actually The last 30 minutes I started to think to myself Okay, this is What I was expecting Yeah Right? So yeah I Especially in the middle It's I don't know what it is I think It was probably a bunch of things One, we're not familiar with this event Which is actually one of the things I did love about it Because I learned, I think, a bunch Yes About what was going on At the bomb blast About the riots Right And all that kind of stuff I'm looking at my notes From when I was watching And so I really enjoyed that I There was a bunch of stuff That I did really enjoy Especially, let's talk acting-wise I thought KK Mennon Did a phenomenal job As the Inspector I thought a lot of the And there was some good parts In the middle of the interrogation Parts With Nawaz And then a bunch of other people Any time it was red Anirakashi Oops, we need to talk about Which was interesting Used red For any interrogation I thought A lot of those scenes Were really good I thought he did really well As well Say his name again Pavan Malhotra We've seen quite a bit We've seen quite a bit of In the Punjabi film It was the last one Bag Muka Bag So we've seen Quite a few times now He's a good actor So I thought he did really well Obviously Nawaz And his tiny little part Did well Obviously we're not going to Talk about that one He was in it He was in it, did a good job For one scene But yeah So I really, really enjoyed that And I thought I can't imagine What the budget was And then Being his first film And obviously He worked with That other director Whatever his name was Yeah, from Satya Probably a bunch of times Before this But he was like I believe writer Or assistant director Or assistant writer Or something So being in his first film Basically because his first one Had yet to be released I guarantee his budget was tiny And like he probably Wasn't given very much time Like so For doing what he did With that amount It was very, very impressive And when you consider The place that Indian cinema was at the time He is an absolute maverick Someone who has his own Sense of what he wants to do Why he wants to do it He's not trying to be anyone He's not catering to anything He just simply said I have a vision This is what I'm doing And if people watch it That's going to be great Which we kind of We know that based on What he has said in his interviews And we've heard about him But when you look at What was being released And this was 2004 I think Right? We look at what was being Released in Indian cinema But I think he made it before that Right, that's when it was released Yeah You know, comparatively To what was going on In American cinema There were films like Hotel Rwanda came out that year Which so Granted they had a lot more money Higher level technology This looks like he got Like a phone camera at the time Yeah, he really did Had a lot of time But for me And I think maybe it was Because so many things Were introduced at once I don't know if it was script I don't know if it was Just because I got lost in it I didn't feel connected To any characters Enough to care about them Or even track With who was who I got lost with a lot of the story The two that I coded was K.K. Men and Poppin Poppin Yeah, those two I knew who those guys were That was pretty clear They basically functioned As our protagonists And our antagonists But the other players The main thing for me There were a lot of them And other than Just your stereotypical Like jihadist mindset I didn't understand Motivation for them Yeah, and so it might have been Different obviously Cause let's say they made a film About D-Day Or 9-11 Or whatever We would know everything Oh, we'd know everything Yeah, like when we saw Saving Private Ryan We knew what had happened You knew the players Four years up to that And so I'm assuming Like we know who was behind it Right And so we already have An emotional investment In the story Or like a story about Watergate Right An emotional investment I'm assuming And from what I've heard from Superbabies If I was Indian And I was familiar with the event Yes Obviously it wouldn't be as confusing And I would care more Cause you were like Okay, that's who that is And I would care more And I'm not saying I didn't care About the fact that Innocent people were being blown apart I mean, that's a foregone conclusion That's awful I thought When you consider Probably my highest praise Besides it being groundbreaking For the day And on your eye being a maverick And having his own vision Is considering how Clearly he was low budget He took on a Herculean task To replicate that level Of special effect And actually You could see what he was doing Closer shots Not wider shots But still managed to make me believe That a lot of what I was seeing And I do believe he interspersed it Documentary He actually interspersed In actual news footage And news coverage So I tried to accept it more For like a documentary Yeah It was definitely very documentary So it would be interesting To talk to him again Yeah Obviously just because He's an interesting person But about this film And everything that went into it Because, man, there was To talk to him about one His ideas for using Those different filters Yeah If it's red, it's an interrogation scene If it's blue, it's a flashback And when it's regular It's current time Yeah That's not done a lot No, and it definitely wasn't done back then No And so I'd love to talk to him about Like what was your Was it budgetary? Right Was it accidental? Yeah I just did that because that's what I could do Yeah, right I didn't have There was no tricks I could have done We do know that's the way He does his scenes In city streets Like if you see people Running through the street Chasing a criminal Those are background actors That they put in there Yeah They just let the actors Run through the streets Yeah And captured it And hopefully there's no cops around And say, where's your permit? Yeah So, yeah, that's where For me, it's a movie where For my own personal aesthetic It didn't grip me and make me Be something that I would want to watch But I can't deny the fact I would call this an important film It's telling about an important Woman in Indian history Especially if you're Indian Yeah Especially if you're Indian Because like, like I said If I would love One, I love that I learned stuff Me too As well because I didn't know anything Outside of I knew there was a bomb blast Right And that's all I knew I didn't know the connection With the Bombay riots Right And all that kind of stuff I didn't know that That whole connection Right With it So that was all very, very Interesting And the final shots were Just one phenomenal After the bomb blast And they really They zoomed in on the people That got hit Very, very good Very powerful Very good And so I loved that So I thought that A lot of the performances were It's on your kasha He just gets natural performances There was nobody that was bad No mistakes There wasn't While there wasn't anything For me that was like That connected you But they weren't bad Not at all Yeah, it wasn't bad It was actually It wasn't bad about the film It was actually Like a documentary Very much It just felt like You were watching these Normal people I wish I could go Through their day life In an American film Where other people have said I freaking love that movie And I'm like I have one What? All fiction Oh For me Yeah, for you Because a movie that everyone Loves and you're like It's actually very comparable Because obviously We've seen quite a few Of his work already Yeah And then we're going back To his first Right So he now has The budget All the budget he wants Right And he's a more Experienced director Right Same thing with Quentin Tarantino All Quentin Tarantino films And then Me too I watched Pulp Fiction Right, and I saw I saw it early Around two years ago I think I watched Pulp Fiction For the first time And I was like Okay, that's good But I like his other stuff Better And you would Yeah When you look at it From the vantage point You got But if you saw Like at the beginning Right, like for us Who saw it when it came out It means a whole lot more That's a very good comparison Yeah And there's films Where you Either you saw it At a specific time Where it doesn't resonate There's movies where someone Will say to me Man, that's my favorite film I don't feel it's my favorite film Yeah But I have no problem With that It's your favorite film I can see why that would be So stupid babies who say Man, Black Friday My favorite Anurakasha film I would not say I have a problem with that I would just say I don't agree It's definitely not On my list of favorite Anurakasha films Yeah Although I did appreciate As well With the limited budget Yeah, I would I would love to know What the actual budget was Yeah To know Because that would make it Probably even more impressive Because I bet it was pathetic I'd also like to know I'd love to know What's on the editing floor From what I remember In the interview He said it was five and a half hours Yeah That's a whole Another film It just pains me The two things that pain me They censored this one too Yeah Big time There was bleeps Like what? The two things that bother me And I know you're Preaching the choir saying About the artists being Short-circuited is Obviously censorship That's first and foremost But also not just from Like the censorship board Or the rating system Which the censorship board Is very different than The rating system We've talked about that before But studios Studios who tell the director We don't want that And the director's like But And then Over in the corners The writer going Can I say something here? Yeah You know, if anyone's Really getting the shaft It's the writers And if you didn't know that Writers get the shaft Unless you're the writer-director And they're probably the most important And they're the most Freaking important parts Of you don't have the film But that's also why He's so good Because he's the writer That's why Yeah, that's why A lot of writers Become directors Because they know If they really want to Have the control And even then The studios And if you're nobody like He was at the time Yeah, the studios and the producers Are going to go Nope They won't release it Like they did And it was actually Probably more Controversial Censorship Yeah With his first film And I'm betting this one I think most of his films Struggle with censorship Pretty much everyone I'm pretty sure most of his films do Another thing I did Appreciate about the film Was the score For how Minimal the film Like For how Minimal the budget was Because, one I thought it complimented it Yeah, it complimented it But it was a very subtle score And I did appreciate that For what it was I thought the sound Like the sound mixing For the bomb blasts Yeah, that was good It was really good When you take into consideration That cost money, don't you? Yeah, when you take into consideration The shoestring he was working with There was nothing in the film That you're going to Jump up and down about And say, man That's my job to design The art direction The special effects No, but when you consider the fact That this is so early in his career And he had so little to work with There's far more to say Man, this is an important film It deserves to be In the list of the films That consider the important films In cinematic history for India But, for me, like I think also for you It's just like not One of my favorite on your films Well, I would watch this Before I would watch Debby again Interesting I'd probably watch Debby You think so? Yeah, I would probably watch Debby I'd watch Devdas Before I'd watch Debby I'd watch Devdas Before I'd watch any of them I would But I would Of those two Yeah, I would watch I would say I think I liked Debby A little bit more I think that engaged me A little bit more than this Yeah Yeah But he's It's one of my favorite things About Anurag I mean, there's a lot of things, obviously But The fact that he just He gets great performances Out of all these actors There's Outside of The only time I can remember It was in Debdy Where I didn't like Some of the performances In a film of his Yeah That's the only time I can think of it So usually And again, nothing glaring Usually it's like this Yeah Where everybody is It's like a natural person On the street Yeah And from what I remember This was The film that Nawaz He wanted Nawaz for a bigger role Which was what he was saying Yes And Nawaz was like I need a job Please give me a job Please give me a job And so he was like There's this small part And he was like Of course I'll take it And so that That's great But I love that he loves Great actors Yeah, he's an artist That's He's an artist And he always gets a good performance Just like for show of art Always gets a good performance Out of his actors Yes In a natural performance And he's a cinephile He's very similar to Quinton In that respect And that he adores the art form Has an encyclopedic Mind And Library of film The number of films he knows And he's seen that has inspired him He's very much like Scorsese These guys And DeCaprio These are people in the industry That come to mind immediately Who adore film Yeah And that's my favorite thing About On Your Own Yeah But let us know What's next of his films We should watch Yes Gulal I believe is high on the list I believe with K.K. Menon as well I think Is it? I think But we do need to explore K.K. Menon more That is one of the actors I feel That is at the level of Anoaz Even though we've seen him We saw him in Header We saw him in the And we've seen a scene And we've heard Yeah But we haven't gotten to know him The way we've gotten to know The first thing we saw him in Was Header Yeah With Frissel Bardowich Right But I feel like he's Like the level of the Manoj And Noaz That we have just yet to Fully explore And I also want to know Because we've really not We have You know, we paid attention Early on to Alia and Deepika And Priyanka A little bit of a Shwari Rai A little bit But like the heavyweight Female actor in India First comes to mind for me Is Tabu And I want to know Who else is out there right now That falls into that category Of the heavyweight Legendary Female actor That we have not yet to explore Oh, not yet Yeah, that I really I was going to say the other one Was her name from Sacred Games And that Noaz Yeah But she doesn't As far as I can tell I love her She's never done bad work Yeah Riddhika Abdul But hasn't Like She's not at the level Like Tabu As far as I know Tabu is a legend Yeah, she's a legend Yeah But she's also much younger Right Yeah, I want to know Who we're Because we talk Consistently about You know Noaz it in And KK Menon And the list goes on We have seen I really would love to know Who are some of the Other women That are the heavyweights That are Not the star stars No, no, no But they like Thespians Like Irfan Yes Style of Actress She was a good Riddhika was a good example Yeah Because she's a great great actor As is She's much younger But in the same category Is Kalki Yeah And I think We've yet to see The best work Right I mean she's young But I think The work ahead of her That's going to Be really great Yeah Let us know Let us know In the next On Rock film Because you know We're going to explore All of them Yep Let us know Down below


Item number SCP-867 Object Class Euclid Special Containment Procedures Specimens of SCP-867 are kept in Section E of Biocontainment Site 1. Regular maintenance on SCP-867 is only to be performed using remote rovers and automated irrigation systems and personnel entering the containment area for any reason must wear full-body NBC protection with a Kevlar underlayer. Any personnel exiting SCP-867's containment area must undergo a full herbicidal treatment and inspection and any personnel found with possible puncture marks must be placed under quarantine for a minimum of 15 days. Experimentation with SCP-867 requires the written consent of at least 2 level 3 personnel. Description SCP-867 is a species of coniferous tree visually similar to Pisces pungent or blue spruce except for its distinctive red coloration and a complete lack of seed cones at any stage in its life. SCP-867's leaves are hollow structures similar to hypodermic needles containing a single long thin seed and a tiny gas pocket at the base of the leaf. When a living animal brushes against the leaves, the gas pocket expels and injects the seed into the skin of the animal using a mechanism similar to that of an auto-injector. The tiny size of the seed, which is coated with a liquid with anesthetic and coagulant properties, renders the injection essentially undetectable. These seeds can lay dormant in the skin of an animal for up to two weeks, after which the seeds begin to grow, extending tendrils throughout the host animal's circulatory system. This growth causes excruciating pain within the host animal, can last for up to 24 hours and invariably ends with the host's death. Following host death, the new SCP-867 specimens will burst from the host's body and grow to full maturity within 30 days, consuming the host's body in the process. SCP-867 was first discovered in Data Expunged, Colorado, following a bizarre series of disappearances of hikers and park rangers in the area in 1991. A Foundation team was dispatched and able to retrieve several young specimens of SCP-867 with acceptable losses. All wild specimens of SCP-867, approximately one in number, were destroyed. Lesson complete. If you missed the previous orientation, go watch SCP-866, Supercomputer, right now. Or for the complete course, watch this playlist.


Once we understood that light was electromagnetic waves with a wide range of frequencies created by accelerating electric charge, a great deal of research went into studying the nature of this radiation as it related to matter and temperature. Because all matter above absolute zero contains vibrating or oscillating molecules colliding with each other, all matter radiates. Take a look at this iron rod. On the right, where it's cool, it's radiating any infrared, so we can't see it. Its gray color is based on reflected light. As it heats up, it turns red, then orange, yellow, and at the hottest it is white. If we could get it hot enough, you'd see it turning blue. These colors are emitted, not reflected. The problem with studying the emitted radiation is that you can't separate out the reflected radiation. What you need is a body that emits without reflecting. Such a body is called a black body, and its radiation is called black body radiation. Here's an example of an early construction of such a device. It's a closed container with platinum interior walls and a small hole at one end. The ceramic exterior keeps the temperature constant throughout the device. Inside, it is literally filled with a wide array of three-dimensional standing waves emitted by the hot platinum walls. Any radiation entering the device through the small hole will have little chance of finding its way back out through the hole. So for all practical purposes, all the radiation that leaks out through the hole will be radiation emitted by the platinum walls of the device.  We knew that the amount of radiation, its intensity, goes up with temperature. The question was, do all frequencies or wavelengths increase in intensity at the same rate? Here's how this is measured. A black body is heated to a known temperature. It radiates a beam out of the opening. We then pass this beam through a prism to separate the various wavelengths. As we move a detector across the output, we measure the intensity at each selected wavelength. Then repeat the process with ever-increasing temperatures. We see that three things happen. One, the object emits more radiation at all wavelengths. Two, the peak emission frequency shifts towards shorter, blue wavelengths. And three, the intensity drops precipitously as the wavelengths enter the ultraviolet range. Using Maxwell's equations and the laws of thermodynamics, physicists developed the equation that should describe black body radiation behavior. It's based on the assumption that each wave contributes equally to the total radiation energy and the electromagnetic spectrum is continuous. But the equation predicts an increase in intensity in the ultraviolet range, not the drop-off we see. This dramatic inconsistency between the theory and observation became known as the ultraviolet catastrophe. Something was dramatically wrong with our understanding. In 1900, Max Planck came up with a solution for black body radiation behavior that fit the observations. But he had to break with two universally accepted fundamentals. He proposed that electromagnetic wave energy was not averaged over a range of the frequencies. Instead, energy is a function of each wave's frequency. And he proposed that electromagnetic waves emitted by oscillating atoms are not continuous. Instead, they come in discrete multiples of a minimum quantity. In particular, he proposed that wave energy was described by the simple formula energy equals a constant times the frequency. The new constant, h, is now known as Planck's constant, the fundamental constant in quantum mechanics. Unlike the speed of light, that's a really big number, Planck's constant is a really small number. Remember that a joule was the energy needed to lift an apple one meter? Planck's constant is 66 billion trillion trillion times smaller than that. That's why we don't see the effects in everyday life.


Team masculinity versus team feminism. Team masculinity, we have individual rights versus women's rights, right? Group rights. We have the quality of opportunity versus the quality of outcome. We have patriotism versus globalism. We have the rule of law versus the rule of women. We have believed evidence versus believed women. Personal responsibility for all evade all responsibility. We have men and women are different versus female supremacism.  It's not a but, it's an end.  It is disgusting, nasty, and it destroys women. It destroys families and it hurts men. It drives men to suicide, left and right. America will not survive this century and the West without feminism ending. One way or another, all these different mechanisms, birth rates, demographics, family formation, the institution of marriage itself, these things are going to die. They're not going to last if feminism lives. The future of America and Western civilization hinges on destroying feminism.


It feels fantastic to be a part of this great list, I think primarily because there's a lot of accomplished women out there and it feels good to be part of this list now and I hope to see a lot more people coming in every year. I was told that 25% of this list is new and I hope to see more of that as we go forward. There is a different leadership style. I think they bring a kind of focus, a collaborative attitude, they bring people together and I also think they use intuition and fact and intuition to take better decisions. So I think that's really what I would say in terms of leadership style, a little bit of a difference between women.


this. Today is December 7th. Today we are actually going to watch my friend's show. We're going to watch it and I also bought some blueberry muffins. I want to make those so we can have blueberry muffins for the week to eat whenever we drink a protein smoothie and I just worked out trying to work out more so that I can feel good. So let me get ready for the day and then we can watch the show. I am realizing what a day I have today. I have rehearsal at four for my acting class and then at five I have a two-hour meeting with alum club so I did this six-week program for actors to get your priority straight and career-wise and personal life etc and now I'm part of the basically the alums of that which we help each other stay productive as if I need it right now because I have been doing so much but I'm still so happy to be able to socialize with somebody and work together on something to get feedback. So I have that meeting from five to seven and then from seven to ten I have my acting class so I need to watch that my friend's show right now because it is almost 1 p.m. I just uploaded the video for today and I'm realizing how much stuff I have to do today but also remember how I said I was done with matcha? I remembered that I had this matcha left over from Trader Joe's from when I tried it once so so turns out that I actually like this one the best out of all the ones that I have tried and I don't know I think it's because it's not as strong whoa because it's probably not as strong I have this from Trader Joe's and they come in individual packets I bought this so long ago to try matcha and I remember hating it because I didn't put any sweetener in it but this time I put a little bit of agave so I definitely have a lot of energy and I like the flavor of this one a lot more because it tastes more like green tea than matcha it still tastes a little bit like matcha but enough so that I'm like okay this is fine so let's put the show on the TV and let's finally finally finally watch that oh my god I was oh I was bringing some lights into the living one because it's so dark because I'm gonna watch the show and one of them fell look at this mess and I'm just standing here in the middle well that was so much fun to clean up I went to the show and then apparently you can't cast it onto the TV I don't know what kind of what they're using so I have to watch it either on my phone or my desktop and I definitely don't want to watch it on my phone so I'm gonna have to watch it in my room so breaking that lightbulb to get a light in the living room didn't even need to happen my name is Jasmine Mulan Williams and I'm an actor in the Bay Area and I wrote this piece or I was inspired to write this piece by my friend Phaedra Tilery Button she commissioned this piece for me and she was just like I want you to come on and be yourself she's like I have you have this positive energy you do this beautiful stuff and I also want to expose your talent and I was like oh okay great and so I wrote this piece this Christmas piece and I just wanted to bring joy and cheer and to remind us that life is still going to continue to go on this year's been kind of crazy kind of crazy but if we just kind of take time to slow down and love upon each other and smile and remember the traditions and the holiday spirit that we've always had then we can survive I hope you enjoy it's out till December 20th Oh my gosh okay so I I'm I think yeah I'm about halfway through the show and it's so cute I originally thought that everybody in the show had created their own original piece original songs but I was wrong a lot of people are singing songs that are definitely classics and it's a really cute show it's so Christmasy and of course my favorite has been my friend scene so adorable I almost cried at the end even though I already have read it a couple of times but it's so cute I'm gonna eat some lunch and get ready for all of these calls that I need to do today usually for lunch I make a sandwiches but I also want to make this these blueberry wild blueberry muffins that I got and I've never had this took a very long lunch break because I know I'm going to be on my computer on different calls from 4 p.m. all the way to 10 p.m. and I will have little breaks in between I'm sure a couple of the calls will have at least a couple of bathroom breaks but I'm setting up my room right now for my calls and since I broke one of my lights usually I use my bulb lights just the normal ones to light myself here but today I have to set it up with my ring light because I broke that and I'm pretty sure all camera stores are closed right now so I can't even try and go get a new one I'm gonna see if I can make these lights work so I don't have to buy a new one in general so I don't have to order anything get anything delivered but let's get on let's get all this set up because I'm going to be rehearsing in 19 minutes and if I set up early I'm gonna go clean the kitchen organize the kitchen go do something else because I don't want to be in front of my computer this whole time I'll make some more tea oh my goodness those muffins those blueberry muffins so good the apartment was smelling delicious and I'm pretty sure it's because the blueberries were canned versus dry dehydrated blueberries and then they were maybe two or three dollars at Target Christie's my zoom calls I usually sit in this chair and I try to use that wall over there to bounce off some light back into my face and I honestly will know until I get on a call but good thing the first call is a I think it should work the first call is a rehearsal so I can play around and be like it's my face lit okay do I look crazy oh that light this light actually looks really good what I did was I put let me turn them off so you can see them better but I put this light here so that it would bounce off the white and then my ring light as well I got good light but right now it's too much I guess I'm done that was so fast and I still have so much time until my rehearsal so let's go into the kitchen I want to reorganize everything because when we moved in here I when we moved in here a few months ago I am pretty sure we just wanted to get everything out of the boxes so I started throwing things everywhere in the kitchen and now that we're actually living in it it doesn't seem very well organized let me show you so at the bottom we have trash because I like to hide my trash and we of course clean around it all the time then we have some of the electronics and we have alcohol and then a bunch of food and alcohol glasses and stuff like that so I'm thinking of putting all the alcohol stuff down here and putting all of those electronics up above the fridge so we don't really go up there so if we put these electronics up there then you know we won't go don't have to reach all the way up there that much and then I can put all of the emergency food all the way at the top and reorganize these as well I mean this is okay but I want to reorganize it in a better way over here up here it's really empty too we like never ever ever use disposable stuff I'm pretty sure we accidentally kept that from like some gathering years ago I remember having that since we lived in Hayward in 2018 1718 so make this better use of this and then here's a bad one spices you know how sometimes when you start organizing has to get really messy before you actually clean up yeah I I just did that I mean this looks okay alcohol looks more organized and then there's you know there's more work to do but it is 359 and my rehearsal is and my rehearsal is in one minute so I need to log on I just got done with my rehearsal so now I am looking for the zoom link for this meeting but I really should try and use the restroom and get some tea before I do this because I think this is two hours an hour and a half it's an hour and a half let's go make some tea really quick yes Griffin very nice okay I'm gonna go have dinner because I have class at seven thank you guys okay this meeting is over this alum club meeting accountability meeting is over so I need to go have dinner and then come back for the acting class okay right now we are about to start class okay thank you the class just ended finally I'm done with all of my calls and during one of the breaks from class I got an email from my agent for a voiceover audition for a an audition that I did already earlier this year a few months ago so I'm hoping that they liked my voice but they weren't able to use me for that other commercial and maybe they want to hear me again for this one oh my god I would be so happy if I got one gig this year one paying gig this year so I'm really excited about that so we are going to film a voice over tomorrow morning thank you so much for watching I'm gonna close down this vlog here and I'll see you guys tomorrow at the end of every video I feature another channel this is today's feature if you would like to be featured on my next video make sure you're subscribed like this video and make me a comment


I'm Sassie. I'm 19. I'm from Stockport. I have a little baby called Zanea, and she's one year and three months old. After series two finished, I concentrated on getting Zanea in a routine. I just worked, cleaned my house, fed Darren, same old. Zanea has changed into like a whole different little person now. She can now walk, run, feed herself. She's just all, she knows it's not hard. She's so cute. At the end of series two, I feel like me and Darren hit a really, really rocky stage in our relationship. We was arguing over who was doing more with the baby, who was doing more in the house, money-wise. And I'd say now, both me and Darren are just trying to be good parents for Zanea, really. I am absolutely rubbish with money. I could have the last five p in my account and I'd find something I need to buy with that five p. Like it's just a joke. I need to learn how to better handle my money, really. I feel like the biggest challenge I'm facing right now is trying to realise that I've got a baby now. My life isn't my own anymore. And sometimes I can get really worked up and upset with myself because it's like, well, I told Darren I don't want to be with him, but he can go out and do this and I'm left here with the baby. I feel like motherhood is really, really difficult. I'm just loving being alive, breathing, being a mum to Zanea. That's all I'm really loving right now. My life's not going too great at the minute, but you know, you've got to be grateful for the things that you have got. I hope people will understand that I am hard on the outside, but I generally have got hard on the inside and I do sit back sometimes when I'm on my own and nobody else is about and think like, oh, what I just did was really out of order or no, sometimes I just speak before I think or act before I think, but that's just me.