And everybody welcome to moving with the keyboard using processing JavaScript with me Tokyo ed tech So before we begin let me give a quick shout out to my members Thank you so much for supporting the channel directly. I really appreciate it today What we're looking at is we're be moving something on the screen using the keyboard And so we need to learn a little bit about the coordinate system, which is like x and y It's a little different probably to what you're used to we're learn a little bit about movement physics Like how things move and we're going to take a look of course at how do we read input from the keyboard move things left Move things right. What do we do when a key is pressed and also of course? This is going to require some use of conditionals, which are if statements, so let's go ahead and get started So there'll be a link down below, but basically I'm on this website called editor dot p5js.org and And This is the default code that comes up now You can go ahead and sign up and create a free account if you don't already have one But you can just play around with it not have to do that. So if I go ahead and hit the run icon here And you'll see how this is what we get so we've created a canvas. That's 400 by 400 now I don't really like that size. I want to change just the 300 and That's important if you don't do that the numbers are going to match up later Let's go ahead and run that again now We have like a little bit wider than it is taller and then this background changes the background color now This is this can be done in like RGB style. So let's say we wanted No red say a little bit of green and let's say a lot of blue So we got RGB and we run that I got this nice little background okay, so what I want to do is I want to put a circle in the middle of the screen and When I press the W button, it's gonna go up when I press the S button It's gonna go down when I press a it's gonna go left and when I press D It's going to go right. So that's our job today. So let's get started So the first thing we need to look at and this is you know, what I was talking about under coding concepts Is the coordinate system of this particular program? So if I go back to this screen up here, this is 0 0 and you see here We said this is 400 wide. So over here is 400 0 Now this is where it differs a little bit from what you're probably used to Typically when we go down in what's called a Cartesian plane y becomes a negative But for some reason this doesn't work that way Why actually becomes positive? So if I go down from here my x is still 0, but my y is now 300 now 300 comes from Here so 400 0 and then down here would be 400 x 300 y so keep that in mind when you're programming. We're trying to move things around X is positive to the right negative Like you if you move the left net x gets lower If you go up y gets lower if you move down y gets higher So what I'm gonna do is I'll be creating a ball and the ball is gonna have an x and we're gonna start it in the middle Of the screen. So the screen is 400 wide. So 0 400. So the middle of course is gonna be 200 And I'm gonna say ball y equals same thing 0 down here is 300. So the middle is 150 now at this point, I'm gonna go ahead and run it and see what happens and Basically, you see nothing happens. This is to be expected Just because we said there's an x and a y We're keeping track of doesn't mean we actually created any type of object like that. So what we have to do is Inside this function now don't type down here Okay, a lot of my students do this this function starts here and ends here So what I gotta do is add a few lines. Let's say draw the ball and to draw the ball I'm gonna use the circle command and I'm gonna draw it at ball x ball y And I'm gonna make the diameter 20 pixels So if I go ahead and run that Now I've got a ball and it's 20 pixels wide the center is at 200 and In X and 150 in Y Yes, so far so good now The next part is here in the coding concepts is movement physics DX and DY now DX stands for change in X DY stands for change in Y so Right now It's not moving. Okay. It's stationary.  Okay, so Keep that in mind. Why should you tell me what let's go ahead and do it this way. Let's go ahead and do one DX enough I run this Nothing's happening. Okay. Again a lot of beginning programmers assume. Oh, well DX is one. Why isn't it moving? It's not automatic. You have to tell it what to do with that So down here. I'm gonna go ahead and add some more code to say move the ball So to do this, I'm gonna say ball X plus equals ball DX and Ball Y plus equals ball D Y And what this will do so in this particular case Ball X is 200 So this draw function is actually repeated constantly over and over and over and over again so Ball X is 200 We add D X to it, which is one so it becomes 201 Comes back around 202 203 204 205 206 207 etc etc So what'll happen is the ball should start moving to the right? Let's go ahead and run that Okay, you see it does move to the right and it moves right off the screen. Okay now if we go ahead and did dy equals 1 and reran it see now it's moving diagonally and down Okay, if we do negative one For DX it's gonna move to the left, but still down because dy is positive And if we want it to move up into the left Negative X negative Y and of course like I said it moves right off the screen so This is the kind of this is the basics of how things move At least in the real world to a certain extent of course Friction and gravity and things but we'll ignore that in this particular case So what we want to do next is The keyboard portion So if we go back we're looking at inputting keys So as I mentioned before it's gonna be w for up s for down a for left and D for right if we play games This is no surprise so As a programming approach What a lot of beginners do is they just copy all the code and then it doesn't work Okay, what you need to do is to do this step by step Okay, if you've gotten to this point and you've like say change DX you change dy And you run it and nothing happens. Don't keep going. It's not just gonna magically fix itself So that's just one of my my little coding pet peeves. I don't understand why you would think it would fix itself if it's not working at this stage so I'm gonna deal now with the keyboard inputs Now this is a feature or this is a feature of processing JS So they have these certain built-in variables that we can use So first I want to do is I'm gonna do if key is pressed Okay, so you see how that turned pink as soon as I finished it that tells you it's something that Processing recognized it's one of the processing variables that's built in So this tells us if a key is pressed or not So I'm gonna say so up Let's do let's tell the game we do love doesn't matter. So if the key equals W Now w is up So in this case if we want to go up dy is gonna have to become negative So what we'll do down here is we'll say ball dy equals negative one now this is where I'm gonna run it Okay, the ball is stationary you might have to click over here to make sure it has what's called focus now I'm gonna press w and see what happens Okay, so now the ball floats up and off the screen So I know now that this is working if it's not working. Don't keep typing code It's not gonna fix itself. You got to get this working first so Now that I've got one working what I'm gonna do is I'm gonna go ahead and copy this And I'm gonna paste it. So w a Snd so Do w? Let's do w s first so down and that's gonna be s and So in this case dy is positive So it's gonna give us one Then we'll do left which is a And in this case, it's not dy that's changing. We're not going up and down. We're going left and right So it's dx. So left is dx is negative one because x gets lower and lower each time And then let's go ahead and do right And that is D and again same thing This is dx and this is gonna be positive. So now when I go and test this so I can do a is a is left D is right Watch what happens when I push w Okay, and then I'm gonna push s so up and down is working left and right is working but you can see how It moves diagonally now and if you want that that's fine and that's not a big deal We can we could do that But if we wanted something it was a little bit more just vertical because what's happening is if x is positive And y is positive it moves right up right up right up right up or actually sorry dy is negative So right up right up right up right up Okay, so what we can do is when we go up we set ball dx to zero So ball dx equals zero, so we're only moving one direction at a time now in this case gonna be ball dy equals zero And then in this case it'll be ball dy equals zero Okay, so go ahead and test that and as there's a w up s down a left d right So now we have a bit more around if you know Pac-Man, but it's kind of moving up down left and right Okay, so that is pretty much how that goes That's about what I wanted to cover in this I want to cover one more thing since we're here What I want to happen is let me run that again what I want to happen is when it goes off the screen I want it to jump over here and just keep going Okay, so it's just kind of going around and around and around when it goes up here. It's going to jump back down to here Okay, so let's deal with that So We'll call it check the borders here So if we're moving right, so if the ball x Is greater than let's say 400 Okay, so if it's greater than 400 that means it's out here somewhere We want the x to come back to zero. Let me say ball x equals zero Let's go ahead and run that It's out boom and it pops over now notice 400 this is the center of the ball. So when it gets about halfway off the screen it jumps right back to there So by the same token we could do the same thing On the left side of the screen but watch this one carefully because this is where students often mess up So if I put zero here and 400 here And I run this it's not going to work right Okay, so let's go ahead and watch this it basically gets stuck at the border Okay, I can still move up and down, but if I try to move right it does this little flashy thing Okay, so it's the reason is that this is greater all of this is greater than zero So I need to reverse the sign here. So it's less than zero which is going off the screen Then I jump it over to 400 So I rerun that And x zero zero boom and then Boom so I can go back and forth often on the screen Now by the same token I could just do the same thing with Y Y in this case, it's 300 because it's only 300 tall Don't forget to change that to y And zero All y is 300 Okay, because remember we did 400 by 300 Let's go ahead and do that again So I'm going to test it make sure nothing broke So I just want to make sure this still works as as it did before Then now I want to add the extra test Does up and down work Okay, so you can see it works pretty well And there you have it So that is the basics of how you do kind of smooth motion with JavaScript and processing so just to recap We created x and y variables for our ball We created dx and dy which controls the x speed and the y speed respectively We've got a canvas. It's 400 pixels y by 300 pixels tall We chose a background color in this case was a kind of bluish color We moved the ball by adding dx to x And dy to y and we talked about you know positive is right positive is down Negative is left negative is up. We talked about why that's the case We checked to see if a key was pressed And if that key is pressed and if a key is pressed then we check if it's a w We're going to go up. So dy is negative one dx is zero if it's down dy is positive So that's the dx is zero. So we use s now note s and I think capital s would be different So if you have caps lock on it might not work So make sure you're using big and small there and then left is dx negative one And dy is zero and right is one and zero Uh, we just talked about the border. So I won't repeat that But I think you get the idea there and then at the end of all this we just go ahead and draw the ball That is it. Thanks for watching. Uh, keep on coding. Take care


sure of it but I am also not the cleanest so we are going to go and change that parking spot around here is just a quick shower I should be in and out of here in less than 45 minutes there's no truck racing around this bend here is a some drivers just think that it's a it's a race this way back in beside this red Volvo here probably or beside that the weasel at the same time while we're here probably might grab fuel before we leave later I might also wait until I'm a little further down south we'll see not a pressing issue the weather is nice outside and I've got half a tank right now park straight in here would you agree diesel here this is where we came around before 20 meters today is a good day necklace that my wife bought me from Christmas at home turn right on 215th Street Karen listen to me they have branded themselves the world's largest truck stop largest truck stop in the whole world the whole world everything whether or not that's true I've never seen a bigger one than this so I would back them up on that but it is awesome I'll tell you how much is the biggest one I know of and they have a 24-hour service center here which is perfect because I have an air leak 200 meters turn right on Sterling Drive I'll be quiet Karen I'm done with you for today welcome to Iowa 80 truck stop I'm pretty sure that this is the uncontested world's largest truck stop it is it's like a shopping mall for truckers they even have a trucking museum here just to my left which is awesome maybe we'll go check it out sometime but for today we got to go to the 24-hour shop it's not that bad of an air leak but it's bad enough that I need to get it fixed right now I just noticed it a little ways down the road and this was the closest shop so we came directly here called them up they said yeah we're open 24 hours perfect perfect we'll get this done taking care of tonight might even get a full service on this truck tonight while it's in the shop they said they weren't that busy it's a middle of the night so may as well take advantage of that and get everything done where is it though this place is so big I'll get lost that windshield so dirty yeah I think that there's parking here for 500 plus trucks somebody who actually knows let me know down in the comment section I think I heard it was 500 plus trucks can park here absolutely fantastic it's a beautiful thing beautiful the owners of this place obviously really love truckers what do you know we love them too we love them back how do I get to this shop I hope they're still not busy because when I called them they're like no it's pretty late no one's really in the shop we got nothing to do we should be able to get you in right away it's kind of hoping we can be you know in and out within an hour so I can go to bed thread the needle here nice and slow nice and slow is this the service oh there it is over here to the left more truck parking over here seriously you can get lost in this truck stop it's huge have I said that yet it's huge there it is TA truck service right in front right front and center hey boys I'm here but I want to fix my truck for me please it's an air leak in a spot where I can't really get to it that's why I need to ask for their help and I need a full service anyway right here for now go inside and talk to the good people 24-hour service center that's what I'm talking about world's largest truck stop one day we're gonna come here just make a vlog just of this truck stop it'll probably have to be in two parts because it's so big so I had to go drop my trailer and pull up to door three gonna do the whole kit and caboodle over here can you hear the air leak not good not good so as soon as they open this door here I'm gonna roll inside and I will check in with you guys after I guess hopefully this doesn't take too long hopefully it's not too expensive is what I mean well Volvo has found another way to frustrate me the part that I need is a Volvo specific part that only Volvo dealerships carry and they specifically don't allow other places like this to carry those parts because they want me to go to the Volvo dealership which is eight miles down the road and it's not 24 hours so I'm gonna go there right now park right at the dealership go to sleep and wake up when they open up in the morning good thing I got a little bit of time left I'm gonna go right there and sleep right then hopefully we can get this all fixed and resolved tomorrow morning and figure it out from there I really dislike Volvo they got to be special they got to be different to European truck which means that you can only use European parts on it and you can only get the European parts at a special specific Volvo dealer because they want your money they don't want me giving money to these people they want they want the smart business I get it frustrating it's late I'm tired I'm crumpy I'm just gonna go quickly park at Volvo and worry about this all in the morning I hope I don't have to replace the whole air compressor but it seems to be working just fine it's just it's got an air leak and I need to replace them part so let's bring it down to Volvo there it's all gonna same with that I need some sleep they're open so I got to go in there and see if they can get fixed up we'll have to check in with you guys in tomorrow's vlog to see how this goes don't forget to tune in hit the subscribe button so you don't miss it I don't know what's gonna happen I don't know how expensive it's gonna be kind of nervous about it helped me out a lot if you were there to watch my video tomorrow sirens I'm tired you hear that you heard it right for some reason whenever I hear siren like that in small town I always like air raid sirens I was two days more guys we're gonna go inside figure what's going on


And so it's already time for the third lecture. We're going to look at powers, and those powers are also going to include roots, and then finally add some logarithms. Now we use logarithms as well as powers all the time in data science. So this is a very important lecture. So let's start with powers, such an important aspect of algebra. And let's start with a little example. And if I might say something like three to the power two, what I mean by that is I have three and I multiply it by itself twice. So we have the number that we want to multiply by itself. And in the superscript we put the number that we want to. Now the number of times we want to multiply this with. So for pure definition we'll usually write something like x to the power a. And remember from last time x would usually be used when we refer to any real number. And a would be one of those symbols that we use when we think about whole numbers. And so in this x, since our x would be three, which is a real number, the more important the a is a two, and so that is a whole number. And this is just going to say multiply x by itself eight times. And now we have words that we apply to these different parts. This is called the base. Let's put the base. And this is called the power. Let's put that there. This is the power. It's also known as the exponent in some text books. And so that's what we mean by powers. So we have a little definition there. So let's put a nice little arrow there for us. And we're always going to remember that's the base, that's our power. And we just want to multiply this base by itself. And how many times do we want to do that? Well, we want to do it eight times. And so let's have another little example. Let's do something like, something like four to the power two. So this is going to be raised, multiply four by itself twice. And that's going to be something like 16. It's just a shorthand way of writing all of this. Now that might make sense.  But we want to do something a little bit more exciting when it comes to these powers. And so we have the properties of powers. Now the first properties that I want to talk to you about is the properties of the powers. Let's write powers of zero and one. These are very important and you'll come across them every now and again. So let's do a couple of these. The first one is if I take any base and I raise it to the power one. What I'm saying is I'm multiplying something by itself only once. Is this that number itself? And so nothing is going to change. We just still have the number, that number which was in the base, which is the base. The second one is if I take anything and I raise it to the power zero, anything raised to the power zero, we're going to define as being one. And I'm going to say here unless something, and I'm going to say unless x is equal to zero. And that's going to be something very specific and we'll talk about that when we talk about zero to the power zero. So let's assume for this moment that x is any real number, but it's not equal to zero. And if we do raise this to the power zero, we are going to define that to be the number one. And also if we take zero and we raise it to any power, that is always just going to be zero. And I'm going to say unless a is equal to zero. Again, I'm referring here to zero to the power zero. There was referring to zero to the power zero. So let's just have that. I'm going to have zero to the power zero. We're going to say that that's undefined. That is not something that we define in mathematics to be a real number. Now just be careful if you use certain computer languages, if you say zero to the power zero, it's going to give you this property up here. And it's going to tell you that it's one. But in mathematical terms, if we raise anything zero to the power zero, we're going to say that's undefined. But anything other than zero raised to the power zero, we're going to define that to be equal to one. And so those are the properties of powers. The first one we're looking at, and that's the powers involving zero and one. So let's talk about powers involving products. So let's say products. Products of powers. So let's have a look at that one. Now we're going to have two beautiful examples here. We're going to say x to the power a. That's our first power. And then we multiply that by x to the power b. And do notice that we have the same base. That is so important for you to remember. The base is the same. The powers are different, but the base is the same. And in between these two, we have a little multiplication symbol. I'll just denote that with a center dot. And what we're going to say is this is equal to x to the power a plus b. I'm going to add those two exponents to each other. And so let's have a look at a little example of this. So let's put our example down here. I suppose what we should do is just to show that we have a definition. So there's our definition. If we see the same base and we multiply these two powers, I can add those two powers. I can add those two exponents. And let's have a little example. I'm going to take two and I'm going to say two to the power three and I'm going to multiply that by two to the power four. And immediately I'm going to say, well, the bases are the same and I'm multiplying these two powers. And so I can add those exponents. I'm going to say that's three plus four and that equals two to the power seven to the power seven. And let's just check if this is indeed so. Let's just multiply, we're going to write all of these out. So two to the power three, that's going to be two times two times two. Multiplied by, and then four times two times two times two times two. And by our original definition there, we're going to say, well, there's one, two, three, four, five, six, seven. That is two multiplied by itself seven times. And lo and behold, we have the fact that if we have the same base, we can, and we're doing a multiplication there. Most importantly, we're not doing addition on these. We're doing multiplication of these two powers. Then we can add those two exponents. That saves us a lot of time. Now what I just want to say here, what you are not supposed to do, so it's very important to put this in, because we have to think about those. What if we have something like x to the power a, and let's have y, let's make that y to the power b for instance. Can I look and I do that? Can I say that's multiplication and now I can simply write x times y and I'm going to have a plus b? Well, we're going to put a big line through that to say that that is not equal to each other. We can only use this product of powers if we have the same base. And x and y, now it's a variable, that's a variable, it might be that they hold the same values, but what we usually mean by that is that these are not the same numbers. Then I cannot do this. This rule is only there for the bases being exactly the same. And so let's go on to some more exciting examples, because the more of these you do, the better and the easier it gets. So let's have something like 2 to the power 3, let's have something like multiply that by, I'm just going to put dots, multiply that by 4, let's multiply that by x to the power 6, let's multiply that by y to the power 5, let's multiply that by x to the power 4, let's multiply that by y. There's a long expression, and it's actually a single term if you think about it because I don't have addition or subtraction between different terms. It's just one big term, and a single term or more than one term gives me an expression. So let's rewrite this because we can rewrite four in a different way. Let's write 2 to the power 3, and indeed we can write 4 as 2 to the power 2 because 2 times 2 is 4, there's nothing wrong there. And then let's look at the x's, there's an x to the power 6 times an x to the power 4. Certainly the two bases are the same, so I can add those two exponents, 6 plus 4. Here I have y, I have y to the power 5, and y, the two bases are the same. Now if I just have y, I'm going to make use of this property right up here and say that's just the same as saying y to the power 1, because if I take anything to the power 1, it stays that thing. So here I have 5 plus 1 is 6, so 5 plus 1. And for this 2 to the power 3 times 2 to the power 2, the two's are the same, I can add these two, that's going to be 2 to the power 5. And I'm going to have x to the power 10, and I'm going to have y to the power 6. And I can also rewrite this as 32, x to the power 10, y to the power 6, because 2 to the power 5, 2 raised to the power 5, that's a 32. So look at some of these examples. If you do a couple of them, it helps cement your understanding of this idea of defining powers and this idea of the products of powers. So this means we can also talk about the quotient of powers, quotients, the quotient of powers. Now here we defined x to the power a multiplied by x to the power b, but what if we have x to the power a divided by x to the power b? In other words, that's just going to be x to the power a over x to the power b. And now look at these. I have the same basis, there's an x, there's an x, and what I'm now going to do is says that I can subtract a minus b. And that will only be, and usually in mathematics, I want to show you that because you'll see it so often in high mathematics, we say if and only if, and we in mathematics have invented this word IFF. If and only if. Again we're lazy so we have this nice abbreviation. If and only if. Now what I remember is I cannot divide by zero. So how can I get zero in the denominator? Well first of all if b was zero that would not help because any number other than zero raised to the power zero is one. It's definitely not zero. The only way that we can get this if the base itself is zero. So I'm going to say if and only if x is not equal to zero. Because if it's equal to zero and then b is anything but zero, this is going to be zero and I cannot divide by zero. So I just have to remember that when it comes to the quotient as opposed to the powers. So I'm just going to put it to the slightly to the side. They haven't left enough space for myself, but do remember I've got the same base divided by the same base. And that means I can do the subtraction of these exponents a minus b a minus b. I just have to remember that I cannot divide by zero. So now that we've looked at that let's look at another little example. So let's say there's our example. We're going to say something like let's do two to the power five and I'm going to divide that by say two to the power three. Now I see that the bases are the same, which means I can look at these exponents and I can consider subtraction five minus two. And that equals to oh that should be a three. That's two to the power three. So five minus three and five minus three is two. So two to the power two and that equals just four. And let's look at this another way. I've got two times two times two times two times two. And I'm dividing that by two to the power three. So let's do this two times two times two. Now you might remember from school is that if we have this multiplication numerator denominator we can start cancelling out. I'm going to cancel out that two with that two, that two with that two, that two with that two. And so in the denominator I just have left a one. So it's something to divide by one and the numerator I've got two times two. In other words I've got four divided by one and that equals to four as we had in our little example. So let's do another little example. We'll say try and do as many of these as you can. Let's do something like two to the power five. Let's have times three to the power six. Let's do five to the power five and I'm going to divide that all by say three to the power five and I'm going to do five to the power four. So first of all let's look at the numerator. I've got a base of two three and five. Nothing I can do there because these bases are all different. If I look at the denominator three and five for the bases I can do nothing about that. But I do see I have the same base in the numerator there and denominator there, numerator there and denominator there. So let's see what we can do about that. Two I can do nothing with. I'm still left with the two to the power five raised to the power five. But here I can make use of my quotient rule. I'm going to say that's three. The bases are the same. I can do subtraction of these powers. So that's six minus five and I have multiplied by five. The bases are the same. I can do subtraction five minus four. Five minus four. That's going to equal well two to the power five is going to be 31. You can write it whichever way you want. And I'm going to multiply 32. I should say where is my arithmetic? Two to the power five is 32. Three raised to the power one and five raised to the power one. So I've got 32 times three times five. And if you use your calculator please do. You should get four hundred and eighty. Four hundred and eighty. Let's do another example. Let's do something with. Let's do something with some symbols in them. Let's do four. Let's do times x to the power six. Let's do y to the power three. Let's do z to the power two. And we're going to divide this all by let's divide that by two. Let's divide that by x to the power four y to the power three and z. How should we go about that? Well first of all we have a base a base a base a base. They're not the same which is what we mean by these variables. The same goes for the denominator and they're not the same. Nothing we can do that about that. But we see in the numerator denominator we have similar bases. First of all four divided by two is this two. You can do that. But you can also note that four can be written as two to the power two. Two to the power one can be written. Anything to the power one just stays that number. And so I'll have two and two minus one is one and I just have two left. But in this instance it's so easy you can see four divided by two. This is going to be two. Let's look at the x's. Six and a four base and base is the same. So I can do six minus four. I have a y and a y. So I can do three minus three. Three minus three. I have a z and so I'll have two minus that'll also be a one. Two minus one. Whenever you see a variable on its own do remember it's always to the power one. And so four divided by two is this my two that I have there. X to the power two. Y to the power three minus three is zero. And z to the power two minus one is one. And just to simplify all of this I'm going to say two is going to be an x squared. And I do remember that anything to the power zero is just one. So it's multiplied by one and z raised to the power one. Well that's this z. And so I'm left with two x squared z. So please do see if you can get more of these examples. They are great to do. Let's talk about negative powers next. I'm still busy with my properties of these powers. Let's talk about something very important and that's going to be negative powers. So let's have a look at I suppose let's start with an example just to tell you what I'm talking about. Let's have x to the power two and I'm going to divide that by x to the power three. And you'll say well base in base I can do x to the power two minus three but that's negative one so I have x to the power negative one. And now I have to think what do I do if I have negative powers. How do I define that. So let's have a look. I'm going to take any number x and I'm going to raise it to the power negative a and I'm just going to put a little caveat here. Remember x now is just a is going to be a positive number. So when I say negative a I really truly mean a negative number. Now of course later on we can make a a negative number and the negative times the negatives are positive. So this all just turned out to be a positive. But for now let's just make it truly a negative number. And we're going to say that that is equal to the following. That's going to be one over x to the power a. That's how we define this x raised to the negative number. That's one over x to the power a. And once again I cannot divide by zero. And so I just have to have this little thing if and only if x is not equal to zero. If x is equal to zero zero to the power anything that's not zero is going to be zero. Zero to the power anything is zero. Except if it's zero to the power zero which is not defined remember. So I cannot divide by zero so I can't have zero to the power negative a. That's not going to work for me. But I do want you to remember from school just remember something called the reciprocal. So if I have a number four its reciprocal is going to be one over four. This was actually four over one and I just flip those around. Such as that when I multiply these I'm going to get equal I'm going to get this equal to one. That's something a bit more advanced that we can talk about at a later stage. But this reciprocal so that if I have a look at this once again that this is just going to be one over x. So I can take any number any number raise it to the power negative one. If it's one negative one that's going to be the reciprocal of that number. But now we can talk about what if it's negative two negative three etc. That is something else. I just want to remind you of that. Now let's put this as a definition because that's quite important. This is how we define negative powers. So I want you to remember that extra raise to the power negative a.  We're going to write it as such. So let's look at some more examples just to make this clear. Let's solve two to the power negative three. How would I go about that because you know if we just look at our definition how do I multiply two by itself negative three times that doesn't make sense. So we're going to make use of this definition of ours for negative powers. Well we're going to say well I can just rewrite this as two to the power three. But I'm just going to put that in the denominator. Now it becomes positive three and I just put that in the denominator. That's going to be one over eight and that's going to be 0.125 0.125. And so that is such an important thing for us now how do we work with this example where we have a negative in our exponent a negative in our power. Well we do have a definition for that. We bring it down into the denominator such that we can still work out a value a solution to this problem. And that means we can also have something like this. What if I were to write something like this one over. Let's make it x to the power negative three. How am I going to solve that? I have x to the power negative three over there. And what I have to do is just to think about this at least in reverse order. That if I have x to the power summing I can rewrite this if this is my denominator rewrite it in this way. So I'm just going in this direction. So that is going to be well take whatever is in the denominator that is whatever is in the denominator. And I want to bring it into the numerator just you know bring it over to the side but I do have to take that a and a multiplied by negative one. So I'm going to multiply this by negative one. And so negative three times negative one well that's positive three and that's going to be x to the power three. So if I have that negative down here in the denominator that is nothing other than x raised to the power positive three. So this is actually I think a very powerful example that I want you to really think about and really concentrate on because that allows us to solve something like this what if I have this very weird fraction one divided by a quarter one divided by one over four. Well let's think about this let's think it through my numerator let's keep that one but I have this one over four there's a four can I not rewrite that as four to the power negative one. Let's have a look at this what is four to the power negative one well that is just going to be well bring that down into the denominator and one over that four to the power one that is just a quarter. So that's another way to write a quarter and there we have a quarter there's another way to rewrite it and now I'm going to make use of this example just putting all of my definition in reverse order so I'm going to have whatever was in my denominator and I'm going to take that power and I'm going to multiply it by negative one negative one times negative one's positive one and that equals this four a very long way just to write four. So take some time and look at these examples they are very very important when it comes to negative powers let's have a look at the next thing on our agenda and that's going to be the power of powers which sounds a little odd but I like to not use the term exponents here you'll see these written as exponents etc I like to say powers are powers powers of a power and let's define that I'm immediately going to write x to the power a and all of that is to the power b how do we define that now this is not x to the power a and then multiply by x to the power b that's what we had before this is x to the power a raised to the power b well that's just going to be x to the power a times b x to the power a times b let's put that as a definition very important and we do have to distinguish that from x to the power a times x to the power b that's not what we're saying we're saying take x to the power a and multiply it by itself b times multiply it by itself b times so the easiest way to consider this is to look at an example let's have two to the power three all of this raised to the power two and think about this I'm just taking this and I'm multiplying it by itself twice so that will be two to the power three times two to the power three and now we back to one of those original laws that we have this is the same base and I can just add these two so that's going to be two to the power six but notice that would just be three times two that is two to the power three times two let's put three times two and that's two to the power six so these can be very confusing it's not that I'm multiplying two to the power three and then I have two to the power four or something like that and I have to add the exponents no this is this whole value which if you think two to the power three is eight eight to the power two so two to the power three is actually my base and I'm multiplying that by itself twice and we can then multiply these two powers let's just do another simple little example let's have something like two to the power three I'm going to raise that to the power four well that's just going to be two to the power three times four and that's two to the power twelve that's a very simple concept but we can get a little bit confused by this this is rewrite this that's going to be two to the power three times two to the power three times two to the power three times two to the power three now these are all the bases are the same so I have to add those that's going to be two to the power three plus three plus three plus three and that's two to the power twelve let's bring those negatives in when it comes to an example let's have something like two raised to the power negative three and I'm going to raise that to the power two well that'll be just two to the power negative three times two to the power negative three or I can just remember that I can multiply these that's going to be two to the power negative six and that's going to be one over two to the power six there's so many ways that we can write this and 2 to the power of 6 is of course 64 so that's 1 over 64 and again you can rewrite this if you divide that with a calculator hopefully you get 0.015625 check that in your calculator make sure that that is correct so here we can still make use of this power of you know power of powers in my power yeah I'm doing multiplication I'm doing powers of my power one more example these are just so much fun and they're so important to work with let's bring in something like this let's take 3 I'm going to say x to the power 2 so x squared and y cubed y to the power 3 and let's take all of this to the power 2 well that's going to be 3 to the power 2 now remember this is 1 so it's 1 times 2 is 2 x to the power 2 times 2 is 4 and then y 3 times 2 is 6 and there we go so we can rewrite this 9 x to the power 4 y to the power 6 very simple to do if you think about it let's go on to power let's call it power roots there's so many names look in different textbooks you'll find different names and so one that I immediately want to show you is let's go for this let's say x to the power a divided by b now that is something very special in our power we have a fraction we have a fraction and that is actually called I'm going to call this whole thing a radical let's just call this we have here as a radical and we have to think about what do we do what do we do with us how do we define all of this and actual fact I think let's go there we've got different names for these this a in the numerator of the power we're going to call this the radicand and the denominator this b we're going to call this the index so do look out for different names and different textbooks but let's stick with these for now and I'm going to say that this is this is a a radical we have a number raised to the power of a fraction so let's have a look at an example and let's do something very familiar might have seen us before x to the power one half and you might have noticed that that is rewritten as a square root and we put a little two there but usually we'll just leave that two and then we have x to the power one so what happens to this index it goes right there when it comes to the root and we take the numerator there and that stays the power of whatever we have there and that's usually just written as the square root of x now do remember x must be non-negative for us to still have a real number when we define the square root of of um um a number let's have another little example I'm going to have x to the power two thirds and so what I'm going to do is I'm going to take my x my base I'm going to keep my numerator there and then the three the denominator is going to go into this root so that's what we're going to call a cube root of x squared so finally we can have let's write this this is still going to be my x I'm going to keep this raised to the power a and then I'm going to have the root right there I'm going to put the index right there so I'm keeping my reticant there's my base and my index goes there let's put that as a definition and by definition here I just mean this is the things that we really have to to remember now one thing we have to talk about I suppose as an example we can do that is if we have the same if we look at this power that's a fraction if those things are the same so let's do a very easy example I'm going to have the square root of x times the square root of y what am I writing here I'm saying x to the power a half times y to the power a half now I don't want to confuse you before remember when we could add these halves to each other but then we need these two to be exactly the same so don't make that mistake but what we can do here is we can rewrite this as the square root of x times y in other words I'm going to have x times y to the power a half so that means these two are the same and I'm multiplying then I can go ahead and do this so again a very very powerful example now one of those that we have to remember let's do it as an example with numbers in it so let's have two to the power half times three to the power a half I remember that's the square root of two times the square root of three and I can rewrite this as the square root of two times three which is going to be the square root of six just one of those things I think that is this useful for us to remember to get used to let's build on that let's do another little example this one might be a bit more difficult let's take x to the power two thirds and I'm going to take y to the power let's make it four thirds now what do we do these two are not the same those two are not the same can we make sense of this well yes we can rewrite this we can rewrite this in a number of ways actually now remember here we can take x and we can keep that ready can that too and this is going to be a cube root and we're going to multiply that by another cube root there's the three so I'm going to put a cube root there y to the power four we've got the same roots here cube root cube root that is going to just be the same as taking the cube root of x square times y to the power four now let's just think about that just a little bit here can I make this look like that so I do remember that these have to be the same for me and for me in order you know to use these examples and let's have that I can rewrite this as x to the power two to the power a third now look at these two they are exactly the same I do remember what I do have up here I can do a times b a times b two times a third is two thirds nothing wrong there and here I can take y to the power four to the power a third four times a third is four thirds no problem there and now I have a third and a third can you see there was a half and a half now I can make use of this so that a third which means it is a cube root and I'm left with anything to the power one is just that thing so I still have my x square there and I have my y to the power four there exactly as we had up there so I do remember if I can you know if I can rewrite this so that I have these same radicals there's to the power one over three to the power one over three which is nothing other than a cube root I can make use you know of these the the law that we're trying to develop here there's my x squared there's my y to the power four and even though these two don't look like each other they are actually the same and I can make use of this very idea and so what do we have here what is the law that we're trying to develop here we're trying to understand what we can do when these indices are the same remember the denominator is my index there was my index two and two they're the same there's my index three and three they are the same and I might have to do some extra work to remember the two thirds is two times a third four thirds is four times a third and I have the exact same and now we have three and three we have three and three we're thinking about this idea what do we do when this index when the indices are the same well then we can have all of these examples let's do one more example and this time we're just going to do division so what if we had two to the power a third and we're going to divide that by it's divided that by three to the power a third now first of all we can rewrite this of course that's two to the power a third divided by three to the power a third now remember this is to the power third which we have mathematical notation for we just write that that's the cube root of two divided by the cube root of three and we can make use of this rule where as same as with multiplication we can put this under the same cube root so that'd be two divided by three remember that's going to be the same as saying two over three all to the power a third it means I'm applying this to the power third to both the numerator and the denominator and so these are actually quite easy to do and they are exactly the same thing as we did with multiplication what I do want you to remember though is the following what you cannot do if for instance we have let's do let's do the a th root of x plus or minus the a th root of y that is not equal to if I do the a th root of x plus or minus y that this rule only applies to multiplication and to division it does not apply to addition or subtraction only multiplication and division so let's do this example let's do a to the power four over three and we're going to divide that by b let's divide that by seven to the power seven over three and you might think well now I'm stuck it's not as if I have a third and a third and it's division or multiplication yet is division and so I think I want to make use of this rule but I do not have the same power there's four over three and three over three but what I do want you to recognize is the following that I can write this as a to the power four to the power a third and let's bring our ruler in and let's divide this by b to the power seven to the power a third and then we remember our law where we had exactly as we had appeared we had something to the power third something to the power third something to the power third something to the power third so we can make use of this law but I do want you to remember if I have a to the power m to the power n it's just going to be a to the power m times n and so four times a third is four third and seven times a third is seven thirds but now I have a power a third a third so I can rewrite this as a to the power four divided by b to the power seven all to the power third or if I want to rewrite that as a cube root that's going to be a to the power four divided by b to the power seven and no matter which way around I write it we try we mean the same thing so don't be fooled when these powers are not exactly the same look at this denominate here look at the index here the index it's the same and hence I can make use of this law that we learned about before so that I have these same powers please do remember that it is not applicable when I have addition or subtraction and then I want you to remember a couple of these they're just useful later on we're going to learn about factoring etc and these might make slightly more sense but it's just worthwhile to remember these if I have something like m and I have the ath root of say x plus let's say plus or minus n and the ath root say of x and you can see this is the same the ath root of x the ath root of x and what I can then just do is bring that m plus or minus n out on its own and what I'm actually doing is taking these out as a common factor but we will learn about that later and that is going to be the ath root of x so it's just one of common things that you might want to remember the next common one I want you to remember is if I have the square root of a constant times the square root of another constant now that's going to be the square root of c times c and I'm making use of this exact same law that we had up here that is going to equal the square root of c squared and remember I'm writing nothing other than here the c to the power 2 over 2 that's what I'm writing here and that's just going to be c because 2 divided by 2 is just 1 and c to the power 1 but what I do have to remember that it has to be the absolute value of c remember we can't take the square root of a negative number when we just want to deal with real numbers we don't consider the complex numbers so we are talking about the solution here if I take that the square root of c squared that I'm talking about the absolute value of c or the positive version of c one more that I want you to just to note if I have the ath power of x remember that I can just rewrite this as x1 over a that's what we've been dealing with all along so that one you'll definitely know and then if I have x to the power b a remember that's this x to the power b over a my radicand and my index it's just different ways of writing it and we've been doing it all we've been doing it there all along now the next big topic I want to talk to you about is exponential expressions now what do I mean by that up until now we've taken some unknown number x and we've raised it to a certain power but what if this becomes the power what if I have something like a to the power x now we're going to say that that is going to be our variable this is going to be a constant so it's a constant raised to the power variable here I had a variable raised to the power a constant so this is the other way around the most important one that we have actually is called the exponential function and you'll see some textbooks talk about the exponential function and that is where this constant is oil is number e and we raise that to the power x we're going to call that the exponential function later on we'll talk about the difference between expressions and functions but for now just remember when we use the term exponential function we're usually referring to this but in more general terms I don't want this constant to be just the number e oil is constant or identity I can think of this a being any constant but I'm raising it to the power of a variable and so how do I deal with these now there are some properties to these and these are so important properties there goes my pencil that is so important so let's have a couple of these I'm going to have a to the power x and I'm going to multiply that by a to the power of y so what I'm saying this is a constant this is a constant that's a variable that's a variable the important here my two constants are the same and I can simply keep them there and I'm can have x plus y and so that shouldn't be too surprising to you again if I have a to the power x and I divide that by a to the power of y my bases are the same so I can stick with my base which is a constant now and I just take x minus y I do have to remember though that I cannot divide by zero so I'm going to say if and only if a is not equal to zero I cannot divide by zero what about something a to the power x to the power y well this is going to be a to the power x times y and you think that well that's nothing that we haven't really seen before nothing that we haven't really seen before what about if I have a to the power x and I'm going to have b to the power x now these are not the same but these two powers that I have these two exponents that I have they are exactly the same well what I can do here is say a b and I raise those to the power x let's see an example just to make sure that this last property does indeed hold at least by one example three to the power four and I'm going to multiply that by two to the power four I have the fact that I have exactly the same values up there and I'm going to say well I can do this that's a three times a two which is a six to the power four and use your calculator I think that should be about one two nine six one thousand two hundred and ninety six but think about this three to the power four check this on your calculator as well that's 81 two to the power four that's 16 and 81 times 16 learn behold that should also be 1296 so check on that check on the fact that we have at least this one example where this would hold so we've had these properties of the exponents I really want you to look at them and you know do remember these they come in so handy when we work with when we work with all kinds of data analysis next important topic that we have spoken about before but I want to expand on that a little bit here I'm going to talk about logarithms and so by definition let's see if we can remember what that is we have the log and we have a base we're going to call that base b of x equals some value y what do I mean by that well that's going to hold if and only if do you like to use that term in mathematics we do so if and only if we have that b to the power y equals x what are we saying with us we're saying if we take if we think about a logarithm we're asking what must I raise the base by to get this value what must I raise b by to get x what must I raise b by well by y to get x and let's put a little green arrow there because I always want you to think along these terms that is such an important concept and so let's put a little green arrow there this is what we mean by taking the log of a number we're saying this base of the log to what must I raise this base by to give me this value that I'm taking the logarithm of well the solution to that is why I must take the base and multiply by this at least raise it to the power this number to give me this value and again as a little example to remember that if I take 10 to the power three that's 10 times 10 times 10 is going to be three zeros there that is going to be a thousand so I can think what is the log base 10 of 1000 well I'm asking what must I raise 10 by to get a thousand well I must raise 10 by three so the log base 10 of a thousand is going to equal three now a very important thing if we think about the base what values can the base take well for us here we just want to keep the base two three four and we're going to go up but we can also have other bases a nice base for us would be e when the base is e that is going to be the natural logarithm we're going to call that the natural log so we're going to write log base e of some value a so that's an e and we have different notation for that remember we just write ln of a that will be the same as log base e we have this ln for natural log many computer languages we just write log and by log we mean base e or the natural log now let's talk about properties properties of the logarithm very very important now the first property I want to talk about is if I have log base any base let's just keep that base b and I've got the multiplication of two values x and y now it is so important in data science I have a multiplication problem here it would be so much easier to turn this into a if I just looked at that multiplication turn that into an addition problem while the logarithm helps me turn in a multiplication problem into an addition problem because this is equal to the log base b of x plus the log base b of y so I do have to have the same base base and base and I have multiplication there I could also think of the log base b of something like x divided by y well that's going to be the log base b of x minus the log base b that's got to stay the same of y these are just two such important and aspects of algebra and we use them over and over and over again so my my base stays the same and I've got to have multiplication or division there that is the only way that it's going to work or if you see this the bases are the same and I'm doing addition you can rewrite it as such if I have the bases are the same and I have subtraction between two logs then I can rewrite it as such but I cannot have x plus y here and x minus y there that's usually where the confusion lies it's got to be multiplication here and I'm taking the logarithm of that multiplication I turn that into the addition of two separate logs I turn division into the subtraction of two separate logs the next one is let's have log I'm going to have base b and let's have a different number I'm going to have a to the power c so I'm taking the log base b of a to the power c now what I can do there in that instance is take this exponent and I can bring it to the front that is going to equal c times the log base b of a another very very important one and then the last one I want to show you the last one of these laws if I take a log and I have that to some base b of a I can change this by saying the log base now let's make a different base I'm going to make base c of a divided by the log base c of b and that's called the change of bases maybe I don't like the base b I want to change it to the base c so I take my number that I'm taking the log of there it is but I'm changing this to the log base c but now I have to divide it by taking the log with this new base but of the old base right there so those are names apologies for it being on two separate pages but those are the four very important properties that you have to remember when it comes to logs and again as with the exponents these are so so important for you to remember so let's do a couple of examples just to remind ourselves I'm going to have the log base let's make it base 10 and I have the number three times the number four well that's going to be log base I take keep that same base there and I have the log three plus the log base 10 of four so let's have an example of the log base let's keep it base 10 of three over four and that is going to be the log base 10 of three minus the log base 10 of four I'm taking this fraction I'm taking that product and I can rewrite this as subtraction and addition let's have another example I'm going to take log base let's take it log base 10 of let's make it a hundred to the power three now I do remember I can bring the three to the front so that's going to be three times the log base 10 of 100 and the last example let's do something like the log let's make it log base seven of five but I want to rewrite that say as log base 10 so that's going to be log base 10 I keep my five and I'm going to divide that by log base 10 so those have to be the same of my old base seven so I've changed from a base seven to a base 10 by doing this five divide by seven but it's a log base 10 of five divided by the log base 10 of seven that is this change of basis and there you go what you see now is the most important part of taking powers considering powers and considering exponents and lastly again considering logarithms you have to practice these if you are taking the course do remember to do all those homework problems for your credits


So if the goal of statistics is to go from information about the sample to information about the population, it's helpful if we're not overwhelmed with the amount of data in the sample itself. So what we'd like is some way of summarizing the information in the sample, and this leads to what's known as summary statistics, and the first portion of that is known as the measures of center. So one way of looking at the basic problem is the following. Suppose we have a set of data t. This set could include thousands or even millions of data values. We should treat each value as a unique individual. But in practice we can't, so we pick a representative. And this leads us to one useful definition. A statistic is a value that represents some feature of a set of data. So how can we do that? Well, let's work with some actual data. Suppose we have ten students take a quiz, and the quiz scores are four, five, eight, nine, nine, seven, ten, nine, two, and eight. So we want to pick a representative value, and so the important question is what shall we pick as a representative? So the least obvious answer is we'll apply some arcane mathematical formula to these numbers and obtain the number 7.1. But how is 7.1 representative? It's not even a data value. That would be like picking a multi-millionaire to represent you in the government. Who would do something like that? So there are much better answers. For example, we might pick nine. Since more students got nine than any other, nine is a representative value. Another possibility, maybe we could pick two as a representative value since every student got at least two. By a similar argument, we might take ten as a representative value since every student got ten or less. This analysis suggests three important statistics, which we might call the three M's. First, there's the mode. Given a set of values D, the mode is the most common data value. The mode is probably the most natural and obvious of the measures of center if the data value is held in election, the mode would be the winner of that election. We might also talk about the minimum given a set of data values D. The minimum is the least data value. And likewise, we could talk about the maximum given a set of data values D. The maximum is the, wait for it, greatest data value. The maximum and the minimum together suggest another measure of center which is known as the mid-range. The mid-range is the value midway between the minimum and maximum values. For example, let's try to find the mode, minimum, maximum, and mid-range for our set of data values. Definitions are the whole of mathematics, so let's pull in our definition for the mode, the minimum, the maximum, and the mid-range. So if we look at our set of data values, we see that 8 appears more than any other value. It's the mode. The least of the data values is 1. That's the minimum. The greatest among the data values is 10. That's the maximum. And the mid-range will be the midpoint of 1 and 10. That's 1 plus 10 over 2. Or 5.5. This is the mid-range. Now there are a few special cases we have to deal with. If we find the mode, we're looking for the most common of the data values. But every now and then we'll run into a data set like this one. If we look at this data set carefully, we see that both 2 and 3 are equally common, and they appear more commonly than any of the other data values. So which of these two is most common? In a case like this, we say this set is bimodal, and that the modes are 2 and 3. What about a set like this? Here we see that several values are equally common, and appear more commonly than the others. Typically we'll say a set like this has no mode. In some sense there's too many things that are competing for most common, and nobody wins. Now if we accept an answer like no mode exists, then the mode can be calculated for any data set, because all we have to do is find out which data value is the most common. But the minimum, maximum, and mid-range can't always be computed, at least not in any meaningful way. For example, suppose we take a survey over favorite colors, and we code our responses as 1 being the color blue, 2 being red, 3 being green, 4 being puse, no idea what color that is, and 5 being none. And so our responses might look like this. Now we can look at this data and say, well, our minimum is 1, the maximum is 5, and the mid-range is 3. But these values have no meaning, because the data is nominal. The numbers 1, 2, 3, 4, and 5 are just names that mean blue, red, green, puse, and none. There's no order of the color, so a minimum or maximum color doesn't make any sense. And since there's no order, the middle color doesn't make any sense either.


Coming up on DTS Google kicks free users off its workplace plans. Are they being unfair plus Amazon opens a clothing store and Controlling your earbuds This is the Daily Tech news for Thursday, January 20th 2022 in Los Angeles. I'm Tom Merritt and from studio Redwood I'm Sarah Lane from Austin, Texas. I'm Justin Robert Young draw the top tech stories from Cleveland. I'm Len Peralta And I'm the show's producer Roger Chang We were just talking about Netflix numbers and mail carrier problems on good day internet We may have invented a romantic comedy or a thriller you can find out at patreon.com slash DTNS big thanks to our top patrons today They include Dr. X 17 Dustin Campbell and Tim deputy. Let's start with a few tech things. You should know Google open sign-ups for a limited beta of Google Play games for PC to people in Hong Kong South Korea and Taiwan Beta testers have access to four games initially hardware requirements in the beta include a Windows 10 or 11 PC and 8-core CPU and Select gaming class GPUs although Google says spec needs will be lower in the future Twitter will now let you if you pay for the Twitter blue subscription show an NFT as your profile picture Subscribers to the $2.99 a month service can connect the Argent Coinbase ledger live metamask rainbow and trust wallets To Twitter the Financial Times sources say meta is also working on a feature for Facebook and Instagram users to let them Display NFTs on their profiles and the meta team is also working on a way to mint NFTs and has had talks of launching an NFT marketplace all of its own all these efforts are reportedly in the early stages Except for the Twitter one which is live Epic filed its opening brief and its appeal of the September district court decision that the iOS app store does not qualify as an abuse of a Monopoly position the filing in the 9th Circuit Court of Appeals makes the argument that the district court aired in its application of antitrust law regarding multiple behaviors Including tying its in app payment system to distribution in the app store Epic may look to have the appeals court to find the market differently in order to show a broader market dominance by Apple Round two begins Security researcher Brian Krebs points out that this summer the internal revenue service in the United States will transition to a new login service for your tax records Managed by the online identity verification service ID me this will require users to submit copies of identity documents and bills as Well as a live selfie and possibly a live video chat depending if you have problems confirming your identity Where an actual human will verify you 27 US states already use ID.me for state benefit sites a Couple of reports on new Google projects The verges sources say that Google is working on its own wire free AR headset internally code named Project iris that could ship as early as 2024 so not tomorrow, but Perhaps in the works Google's device reportedly uses outward-facing cameras to blend computer graphics with real-world video and according to emails sent Seen by Bloomberg Google engineering vice president Shiva Kamara then Karataman now runs a unit Focused on quote blockchain and other next-gen distributed computing and data storage Technologies within the newly reconstituted Google labs. All right. Let's talk about that clothing store Right right near Sarah where we once had a staff meeting. Oh man I mean I used to live not too far away from this so I would have been excited to play around I no longer am in the Los Angeles area But if you are Amazon announced it will open a clothing store later this year called Amazon style at Glendale's Americana mall if you're not familiar it's in a suburban area of Los Angeles. It's sort of an outdoor mall There's an Apple store there. It's you know, it's pretty cool And this is supposed to happen later this year You can use the Amazon shopping app to scan a QR code to see Sizes of things colors of things product details of clothing shoes and accessories Then if you want to try an item on you can send it to a fitting room Get an alert when the fitting room is ready saying you know room 24 is ready for you type thing Or have something sent right to the pickup counter if you're ready to buy and also leave the store Fitting rooms will be outfitted get it with big touch screens So you can keep shopping from there if you want you can get a different size sent over that type of thing But fitting rooms won't include cameras. There was some outrage I saw from folks this morning saying oh gosh who wants that in the fitting room That's not actually the point the point is no one and it's not there It is to be able to order things from the fitting room itself The store will use real-time machine learning for recommendations and Amazon one palm scanning for faster checkout Although will not use Amazon's just walkout technology at least not at launch not in this store No robots yet either actual humans will be employed in the store delivering items to fitting rooms Managing inventory answering questions like whether or not you look good in peace By the way, I do not the idea is to keep the store from getting cluttered So you got a you know warehouse in the back Minimal stuff in the front, but if you want something that you don't see Likely it's in the back So instead of having every size on the rack you can have one of everything and additional sizes and colors in the back You can also find items on Amazon itself have them sent to the style store to try on next time you're there So if you're at home thinking you know Really want to buy some sneakers on Amazon the prices are good But I really gotta try them on if you're in this particular area that would be a great way to do it Yeah, I assume that this would be good for returns too Like I was funny is my first reaction to this was like oh Smart experiment extending clothing buying Amazon really wants to increase clothing buying And and the one of the holdups is like yeah, but I want to try it on first This gives you a place to try it on but sorry you you you hit on the way to like crash the system immediately, right? Well, so here and again, I know this is one store and it's not in an area that I'm in But it wasn't that long ago that I would have been within reasonable driving distance You know, maybe 15 20 minute drive away from the store and I would have um I I think I would have um Taking advantage of the idea of like yeah, I don't want to buy certain things without trying them on this This works really well But let's just say that I'm in the market for new running shoes happens a couple times a year What if I send a bunch of running shoes in my particular size to the store and then I just sort of never go I wonder how much the warehouse in the back is going to have to deal with Kind of weird inventory that may not apply to the next customer And to that I would say it's literally what Amazon does it is Reason why Amazon is a successful company They did not get big because they sold books and books were something that randomly became the the Basis the foundation of this massive company They figured out how they could have enough warehouses that were next to enough publishers And then eventually figure out through algorithmic solutions Where to put different things at different times because they can predict the kind of people that would want certain things That will be ahead of the game so No, that you're you're very right That said a book does not come in lots of sizes and colors. You get it if you want, right? You know, you know, you have a little inventory of books that needs to be moved You know, somebody's gonna get it eventually It's a little different when it gets into like body stuff Sure, and if they only sold books in the intervening 20 years, I would agree with you They've said sold literally everything that comes in literally every size shape or fashion So I I think that that's that's something that that Amazon really When you think about them their real skill is logistics That that's what they have always been able to figure out and that's what that is what separated them It's not even e-commerce. They're good at e-commerce But they're not nearly as good as that as they are at logistics And and I could imagine a system where and I don't know that this is what they're doing But I could imagine a system where there's a truck going every day And when you put those 12 pairs of running shoes to to try on on the store It tells you you have 24 hours to get to the store and try them on Take some to the store. If you don't pick them up take some away Right, right. Yeah, it's not just gonna be there forever. Yeah. I mean, it's fair. It's department store ask just in Amazon's Eyes a more efficient way to do it. I do I do think of a world where An amazon style store or anything that really amazon sells but style is a good A really good Example of something that it's it's very personalized, right? You know, I always use shoes an example because I need them to fit really well Even if it's my size still gotta try them on Before i'm comfortable buying something. This is great for that sort of thing Robots being able to get stuff from the back in your size Take it to the fitting room. This is not what they're doing right now But in the future, I can see where amazon is like this is kind of our stopgap thing Let's see how this works and how we can make this a real warehouse situation in the future Now that was another part of this that I felt was a really good example of what amazon does well Is they said they're using the same system they use in warehouses to fulfill orders fast To deliver things to fitting rooms So as soon as the warehouse robots are good enough to do what they're doing in these stores Those warehouse robots are going to show up in the store, right? Yeah One last thing on this I think that it gives them a lot of politically way that they can hire people that aren't just Factory workers or aren't just warehouse workers Right the idea that you can get a job with amazon that is forward facing It's something that people understand I don't know if it's a forever solution But in the near term it does give them political leverage that there are more than just the peeing and bottles, you know Jobs that that are available to you at amazon You don't have to be an engineer or a grunt that here is a forward-facing retail gig Also, why not both? Why not robots delivering fast to the fitting room at some point when that gets better But still humans around to help you out tell you if you look nice answer questions Yeah Yeah, uh, you've probably heard of algorithms that are trained to recognize photos You know algorithms that can tell a cat or a dog or something more useful You've also probably heard of algorithms trained to speak in natural language or to create texts But you've probably not heard of algorithms that do all of those things because Before this none of them could this is the one good reason not to fear that we're too close to general purpose AI that can think on its own However Meta AI scientists have developed an algorithm called data to veck That can train a neural network to recognize images text and speech all in one not three different algorithms one algorithm That can do it all data to veck was trained with self supervised algorithms, which is that that's not new. That's like gpt 3 Uh, that's where it learns to spot patterns and data sets without needing guidance or labels The way it is trained. However, I thought was pretty clever Two neural networks are used a teacher and a student bit like a gan If you think of it that way the teacher network is trained on images or text or speech So you're gonna have multiple teachers pretty normal stuff these days for neural networks to do that That part's not hard The student network is not trained on the images the text or the speech But it's trained to predict what the teacher Will say So you're just doing one input for the student algorithm The teacher network sees an image of a dog And then the student network says I bet he's gonna say dog And then the teacher says dog And there you go That's how the student network is trained that may sound like a distinction without a difference But it means that the student neural network doesn't need to be tailored to a particular kind of input But only to predicting what the teacher will say and eventually gets good enough You just take the teacher out of the equation The way this work means the student can only be trained on one type at a time Because the teacher can only know one type before it's switched out But eventually you get there data to vex performed a little better than similarly sized existing techniques Round 100 megabytes of data at images and speech And it was about the same on text So a little better on images and speech same on text Specialized models may still outperform as they continue to learn Because they can have bigger databases But this is this is a big stepping stone towards generalized intelligence certainly doesn't get us there But but it's a very clever way and and I think what's significant is that it was a clever moment to say like Yeah, we can only teach it on one input But what if the input was this then the effect would be like we had three inputs I think I think the idea of uh Trying to expand the base of how you're programming and ai is is a really really interesting idea And uh, I'm curious to see where it goes. Yeah. Yeah, it's good good good advance Hey any uh music fans you guys like music I like music. Yeah, good. I can only think of one person I know who doesn't like music Who's that I bet I know who that is it's allison Well everybody but allison likes music teams uh media research estimates music streaming subscribers rose 26.4 percent year over year as q2 Of 21 data would tell us making it easy to listen and control your music experience in a big market Tech crunch reports on a paris based company called wise ear that just got a round of funding And is now looking for companies to license its hands-free earbuds technology wise ear uses electrodes in an earpiece to detect muscle activity It's based predominantly on jaw movements The goal this year For ios is to perfect two controls Bite down on your own teeth twice to pause or three times to skip in the next three years They hope to be able to have 12 different control gestures The benefit if they can make a work is that it isn't affected by noise and requires very little movement And no speaking from the user your general movements won't cause accidental activation It can be useful for hands-free control of music as well as vr and ar headsets co-founder yacin acchic told tech crunch that wise ear had an 80 success rate from people who tried it at their booth at consumer electronics show or cef Cef's heard of it. Yeah It happened You may have heard of it on the show Yeah, I I was fascinated by this as a sort of like oh, yeah, definitely hate using voice controls sometimes And and to be honest there there are moments when I'm walking a dog and I got a bag of poop in one hand and the dog leashed in the other where I can't reach up and tap As easily as I like or at least not comfortably And and so being able to just use like a facial expression or a jaw movement To control like play pause alone would be fascinating So I I know that this company is saying like look we're not quite there, but we think we're close But I would love it if if this does work and it gets licensed out I I'd be in line to buy one of those earbuds my first reaction When I read the story this morning was like Okay, so I have a teeth grinding problem.   I'm like, that's just bad behavior. Yeah, you were like no way No way. Yeah, like I'm not I'm not supposed to do that. That's all I think about is Not doing that. This is not gnashing of teeth in order to like skip a song You know, it's like it's a little tap tap tap and I love the idea that for a lot of folks It's like wow, it's it's almost like my brain telling you to You know to to go front or back or pause or that sort of thing It's not quite that But it it it is it is getting there where like you said, tom Not using your hands not using your voice. Um if if it works as Um as hoped It is a pretty cool way to Almost think something into existence for me. I still I'm like no jaw stuff, please Uh that you've hit it, uh sarah if it works because the ideal way that this works is that you don't even think of it as tapping Your your teeth together you it is just an involuntary thing that you do with your jaw That is the closest thing that triggers it and and it is not in the same way that you would clack clack clack Your your teeth together in the way that we are thinking that being said I don't know if an 80 success rate is going to get you over the finish line and that's not yet their best Version of it right now. I think we got some time in the oven on this idea Yeah, and and to be and to be fair in the tech crunch article, uh the the co-founder Says like we're not there yet. We're hoping to get the two perfected this year and then have 12 in the next three years Uh, I thought they were very honest about where they are with it, uh, but but I am I'm hopeful for it because They what what was genius about the tapping of the teeth? outside of the jaw concerns Is it's not something you would do a lot normally In just talking the neighbors are walking along. You're not likely to do a double tap, right? You might do a single tap of your teeth, but you're less likely to do a double So finding those gestures that you can do with facial movements, you know, squinting or whatever where it knows Yeah, you you actually are talking to me.  This isn't going to work in the cold. You always forget the cold weather people Oh, okay, you know All right, folks, uh, if you are uh in the cold weather and you got something to say about this Or if you're anybody in any kind of weather join our discord, you can you can talk to folks in there Uh, Larry and Atlanta and zoe brings bacon are talking in there right now You can join them by becoming a patron at patreon.com slash d t n s Back in 2006 This is the the bush administration. All right 16 years ago Google let users create a domain name based version of its services for free called google apps for your domain I did this with sub brilliant.com back in the day That service has had many name changes over the years You probably think of it as g suite, which it still goes by sometimes most recently just in last year They changed it to google workspace So you'll hear it referred to like that as well But the the idea was the service would let you use your own domain name with g mail and calendar So daily tech news show dot com for google services like email google drive, etc in 2012 10 years ago This is now the obama administration google stopped offering the service for free 10 years ago and encouraged free users to either pay for a business account Or transitioned to the free versions of its services, which did not allow you to use a custom domain, but they were free however Google did not immediately kick the free users off At the time that they made the change the paid version was $50 a year Google now 10 years later has finally started to email users of the free service to let them know They will not be able to continue to use it for free Users have until may 1st to pick a paid version after which they will be automatically upgraded If they don't provide payment info Then their account will be suspended after 60 days, but suspension doesn't mean it doesn't work On july 1st you'll get 60 more days And on september 1st if you still haven't paid You'll lose access to core services email calendar and meet But google says you may still retain access to additional google services like youtube and google photos through that account so to sum up You had almost 10 years to move off You now have four months to pick a plan after which google will pick one for you Then they'll give you two months to start paying or the limit your account and two more months before they cut it off mostly The plans are not cheap anymore. They're not $50 a year. There's six to 18 dollars per user Per month depending on the features. They max out at 300 users These are these are meant for small businesses if you're bigger than 300 users You need an enterprise plan. Anyway, google is offering a year-long discount for anybody making the switch And if you're done with this which a lot of people are I want to ditch all together You can use google's data export tool that however will not Let you export things associated to that account Like purchases for books movies music and apps You may also lose google voice. That's unclear and google is not providing a seamless way to transition the data to free consumer accounts It's not Immediately apparent how many people are still using the free version of google workspace 10 years later I know there's at least One on our team and A couple in our discord probably a higher percentage here in the audience That then in the general populace Do we think this is unfair of google to do? Uh as a person who is using a free version of google workspace For a domain that I've had for quite some time, but I poured it through you know the the google Uh I was very confused by this. I still am a little bit confused. I understand the timeline of like here's what you got to do Uh, it's not a free red anymore. Sarah. You have to figure out like yeah, what is do you have a you know enterprise need? Which I don't really it's just me. Um, do you have some sort of you know, is is the google workspace option? Uh, does it make sense for you? You have all these add-ons Most of them I don't need either but some people do so I get that A lot of folks have very different reasons for being in this kind of limbo Um mode that I I find myself in as well I'm also Not scrambling because it's like I kind of have till september right to like figure things out But it is pretty convoluted. I'm not totally sure what my option is and my option if I were to say You know what I'm just going to move from google. What would that be? Well, yeah, uh, if you if you you'd you'd have to go to proton mail or or microsoft Yeah, there are options, but it's other things, but yeah, it's just when you're so used to this it's like Is it just you?  Yeah, I'm not so that's six dollars per month That's that's your other is to say just pay six dollars per month. Which is not the end of the world It's just something where I was like, I just never thought I would be here Okay, what's funny about this is that so much of google's initial offering into consumer services We're really to undercut microsoft if you think about email docs and enterprise level stuff like what we're seeing With this they have since then realized that there is a profit center here Especially on the on the enterprise level where microsoft continues to make so much of their money What's interesting to me is that they don't just let these early adopters ride I can't imagine how many of them they are I can't imagine that the conversion rate they're going to get out of this would even be a Rounding error of a rounding error of a rounding error on the balance sheet for for alphabet But then again This is a company that has never been afraid to piss off early adopter nerds Elsewise they would not still have the dripping blood of google reader on their hands I think what happens sometimes is when a Population of users gets small enough. It just becomes annoying to the engineers They're like, why are we maintaining this for this number of people? Uh, and that's what pushes them to be like, let's just get rid of it There's not that many people using it anyway, but you got to remember those people are loud Uh, I look at this and I I'm split part of me thinks like look you had plenty of time You got to realize you got to pay On the other hand google should have done better communications in the intervening 10 years Continually, they should have been emailing you saying like hey, you're on a free tier.  Yeah, keep it in mind. You got to keep that top of mind I mean they did tell people but the kim and pa and our twitch chat was like, I don't recite So, you know, you got to you got to realize like if you don't want people to be angry You have to make sure they know and then give them a give them an easier way to transition beyond a business level Account because a lot of people doing this. We're doing it for family They're doing it for personal reasons like sara where they had just been trying it out and it never went away So so make it easier for those people to either switch to the free service and keep all their data and services Or provide like a mid-level plan like we're going to start charging in three bucks for this one Okay, you know I don't know there there's got to be a Couple of other things they could do to keep people from getting upset if this part of their business gave a rat's Ptoot about The goodwill of of an average customer. It's not going to pay at least six dollars a month Then maybe they would but they don't I mean, I will say I never saw one email about this Maybe I'll get one. Um, I've been looking But you know, you get enough span Spam through the gmail interface alone that I could see a lot of this Reaching out of google being like we're giving you ample time to figure out your next You know, if you want to pay us great if you want to move away great and people saying I never saw this Because I didn't Yeah, I don't think this is a big enough audience for it to be a cash grab either. I see I I think it was Uh skelly saying I haven't received or no, it was uh Someone saying my guess is their revenue from other sources is dropping. That's not motivated. This is This isn't a revenue. This is them buttoning up Exactly. Yeah. Yeah, this is checking a thing off of this. All right. Let's check out our mailbag Let's do it. James from Columbus, Ohio wrote in and said Netflix making new gaming announcements right after a Netflix price hike makes me feel that the two are related I would gladly pay less for a service that did not include gaming I wish they broke out the gaming part in Into an added fee instead of increasing the cost for everybody Even though even if we have no interest in their gaming service I'm currently on netflix hiatus and this makes me drag my feet even slower about coming back Uh, this is is it the recency bias where when when two things happen in succession You see causality whether it's there or not. Yeah, you wonder if that's why I think and that's that's It's perfectly normal human behavior. I have to fight against that all the time to be like this happened after that I wonder if the first one caused the second one. I don't think that's the case here. James The the if if they deducted the amount of money that the games are Costing them per user from your account. You wouldn't notice The true reason for the price increase is the cost of their video programming total global spending on tv and movie content Is supposed to hit 230 billion this year and netflix is the third largest investor in video content And they're trying to keep ahead of disney They're trying to keep ahead of comcast mbc They also hit a subscriber plateau netflix just announced before the show They added 8.3 million subscribers and they were expected to add 8.5 million They they missed their target and their stock price dropped So that's where that price increase is going they have to make more money per user Right now because they're not gaining them as fast and they need to keep spending money on content to stay competitive Yeah, don't don't don't blame the games james Blame all of the players amas and comedies that you're not watching Ask for a deduction of those And you might see something different in your bill if they ever offered such a thing which they will not nope Well, if you have feedback on anything that we talk about on the show anything We might talk about on a future show you have ideas you have concerns questions All of those things should be sent to feedback at daily tech news show dot com We love your feedback keep it coming We also would like to thank a brand new boss that brand new boss's name is john wiggy wilkenowski Just started backing us on patreon if I can call you wiggy. I'd like to thank you wiggy wiggy on john Excellent Also, thanks to len peralta who has been illustrating today's show. What have you drawn today len? Well, you know, I am kind of with sarah in that whole idea where I don't I don't really see why is it me using a wiser and clenching my My jaw I'm I'm at that age now where I feel like that could be very detrimental to my health I do find it very interesting, but it seems more of kind of a way to break up frustration, right? So that's what this image Shows it's are you frustrated? Well, you know working out with tom's top five It's a playlist that lets you clench your jaw skip and pause and you can kind of take a look I don't know. I just Imagine dragons that we can but love slayer like I see where I see where you're going with this And tolerates bootle-deedle do is which is a which is on the playlist as well Which is very interesting and hates walnuts is you know, it's kind of strange, but yeah, I I um Is walnuts a band or just the nuts? It's just walnuts in general. It doesn't like it. It's like crunching on them He wouldn't be the only one. Yeah, right. Well, this if you're interested in this piece.  Oh good stuff. As always lend everybody Take care of your jaws. Uh, no matter what kind of music you like or don't like, uh, but yeah, good good stuff poor frustrated crunch guy Justin rubber young also thanks to you for being with us today Uh thursday usual, uh, what's been going on since you saw you last Well, uh the bite administration turned one and so we take a look back at the year that was in the new president's term And uh where he might go forward. It's all in a brand new episode of politics politics politics available Everywhere you get a podcast tomorrow morning Well, we sure thank both of you for being on the show with us today Reminder for everybody. We're live doing this monday through friday at 4 30 p.m Eastern 21 30 utc. You can find out more at daily tech news show dot com slash live And we will be back doing it all again tomorrow with Lamar wilson talk to you soon This show is part of the frog pants network get more at frog pants dot com Club hopes you have enjoyed this brover