Welcome to lecture 6 on measure and integration. If you recall, in the previous lecture, we had started looking at various properties of the length function. In today's lecture, we will continue looking at the properties of the length function and then we will try to characterize some other countably additive set functions on the class of all intervals in the real line. So, the first topic will continue is the length function and its properties and then countably additive set functions on algebras. Let us just recall what are the properties of the length function that we have already proved. So, length function was defined on the class of all intervals that is i and to every interval with n points left and point a and right and point b or need not be left and right. Normally, we will write the left end point a first and right end point b later. So, for interval with n points a and b, its length lambda of i we defined as the absolute value of b minus a. If a and b are real numbers and in case either of it is plus infinity or minus infinity, we will define the length to be equal to infinite. So, for all finite intervals, the length is a usual concept of the difference between the values of the end points. So, that is the absolute value of b minus a and plus infinity if the interval is infinite. So, we proved the properties that the length of the empty set and that is the interval is 0. Then, we proved the monotone property of the length function namely length of i is less than length of j if i is an interval which is inside the interval j and then we proved finite additive t property namely if a interval i can be written as a finite disjoint union of intervals j i i equal to 1 to n then the length of the interval i is same as summation of lengths of the individual intervals. So, if i is a finite disjoint union of intervals, the length of i is summation of length of j i's and then we looked at a slight extension of this property namely if i is a finite or an infinite interval actually we looked at that and it is contained in a union of intervals i i's that is i is covered by a finite union of intervals which need not be disjoint then length of i is less than or equal to summation length of the intervals i i's 1 to n the finite number of them. Then, so this was called for the finite i is covered by a finite union and now then we extended this property to the arbitrary countable union. So, if i is an interval which is covered by a countable union of intervals i i which need not be disjoint then we proved that length of i is less than or equal to summation length of length of the individual intervals and if you recall this property use what is called the Heimgorl property on real line. Let us continue our study. So, next thing we want to prove is the following that if i is a interval which is a any interval which is a finite interval say and it is a union of intervals i n's n equal to pair by disjoint intervals then the length of i is equal to sigma length of i n's and this property in fact we had proved it. So, let us prove it to once again. So, let us look at this property. So, if i is an interval which is written as a union of intervals i n's n equal to 1 to infinity i is finite. So, keep in mind we are keeping i as a finite interval and i n intersection i m is equal to empty then that implies length of i is equal to sigma length of i n's 1 to infinity. So, recall we have already shown that length of i is less than or equal to sigma length of i n's that is because of the property that just now proved i is covered by a union of intervals so length of i must be less than or equal to to prove the other way around. So, to show length of i is bigger than or equal to length of sigma i equal to 1 to infinity length of i i's this is what is to be shown. So, let us note that for any n i 1 up to i n these are the intervals which are contained in i and i is finite. So, let us say this is the interval with n points a and b that is i and i 1 is an interval which is inside a b. So, it has n points say a 1 b 1 i 2 has n points a 2 b 2 and i n has n points a n b n but these being finite numbers and they are disjoint. So, we can arrange the intervals like a 1 here b 1 here may be a 2 here b 2 here and so on and a n here and b n here. So, what we are saying is we can assume so without the loss of generality we can say that a is less than or equal to a 1 is less than b 1 less than or equal to a 2 less than less than a 2 less than strictly less than b 2 and less than or equal to and so on and less than or equal to b n less than or equal to b. And once that property is true we can so immediate that b minus a is bigger than or equal to b n minus a 1 which is bigger than or equal to now we can add and subtract consecutive terms.  So, add and subtract terms which are subtract a bigger term add a smaller term and so on. So, which is equal to sigma i equal to 1 to n length of i i's and this b minus a is length of i. So, what we have gotten is this is for true for every n so that implies length of i no sorry this is bigger than or equal to. So, this is bigger than or equal to sigma i equal to 1 to infinity length of i i's i equal to 1 to infinity. So, that proves the other way round inequality also. So, hence what we have shown is that the length function has the property whenever a finite interval is written as whenever a finite interval is written as a countable union of disjoint intervals then the length of the interval i is equal to summation of the lengths of the individual intervals. We would like to extend this property to not only to finite interval in fact to any interval. So, for that we need a result namely suppose i is a any interval then we want to claim that the length of i is equal to summation length of i intersection the interval n to n plus 1. So, this is the property we would like to prove and in fact one can have here the interval which is left upon n and right close n plus 1 because n point is not going to matter. So, we want to prove that the length of an interval i is same as length of its species which lie inside the intervals n to n plus 1. So, to prove this property let us observe the following. So, let us observe this is a real line. So, we can write it as the intervals. So, here it is say 0, 1, 2 and so on and here is on the other side. So, here is minus 1, minus 2 and so on. So, let us take an interval i. So, if possibly if i is finite, if it is a finite interval then obviously it will lie between two some bounds. So, in finite then there exists some n and m such that i is inside n to m. So, there will be some. So, here is some n and here is some m so that i is inside this. Now, let us look at the pieces.  So, this is n plus i and this is n plus i plus 1. So, intersection with this i. So, what we are saying is this i can be written as union of n to n plus i i equal to. So, 1 to up to up to n plus i equal to m so that i equal to n plus i equal to m minus n. Now, let us observe that these pieces these are disjoint union. This union is a disjoint union and a finite number of them. So, this will imply length of i is equal to summation i equal to 1 to m minus n length of n n plus i. Now, this interval i does not intersect with any other interval out which is bigger than m and which is less than n. So, all those intervals this is in the intersection with i is empty. So, what I can write is this is same as sigma of i equal to 1 to m minus n. This is the intersection of should have written the intersection with the interval i. So, the pieces because the interval may start somewhere here. So, let us write this is intersection with the interval i. Let me write this again. So, this is intersection with i. So, let us write this again. So, the i is written. So, i can be written as a union n to n plus from this is also not wrong. Let me just write n to i can be written as union n plus i to n plus i plus 1 intersection i i equal to it starts with n. So, 0 and goes up to when n plus i plus 1 is equal to so that is m minus. So, we want n plus this is equal to m. So, m minus n minus 1. So, that implies length of i because this is a finite disjoint union. So, this is equal to summation i equal to 0 to m minus n minus 1 length of n plus i to n plus i plus 1 intersection i. Now, for other parts they become 0. So, I can write as sigma over i belonging to integers length of n plus i n plus i plus 1 intersection i over all i integers all integers i because the intersection with the other intervals is going to be empty and that is going to be 0. So, this proves that whenever i is finite we are through. So, i finite case is. Now, let us prove the same thing when i is infinite. Let us take i infinite then I can write i is equal to union of same thing n to n plus 1 intersection i i belonging to integers. This is because keeping in mind that the real line is equal to union n to n plus 1 n belonging to integers. So, interval i is this intersection this and now because i is infinite let us say it looks like say something like a to plus infinity. So, in that case this intersection of. So, i infinite implies that n to n plus 1 intersection i is equal to n to n plus 1 for infinite ends. In fact, some stage onwards. So, in fact if n is say bigger than or equal to a then that is the interval. So, here is a and here is n then n to n plus 1 and so on. They are all going to be non-empty intersections with intersection being equal to that n plus 1. So, this implies that sigma length of n to n plus 1 intersection i is going to be equal to plus infinity over all n belonging to z and that is same as length of i because i is a infinite interval. So, that proves the property namely. So, this proves the property namely for any interval i for any interval i the length of the interval can be written as the length of its species, length of the species i intersection n to n plus 1. So, this is an important property. So, it says length of any interval is a summation of length of its species. This property and note that length of each one of this piece being a finite interval is a finite number. So, we have this says that any interval can be written as a countable disjoint union of intervals each having finite length. So, this is an important property which is going to be called as sigma finiteness property of the real numbers of the length function. So, let us we are going to use this property to prove what is called countable additive property of the length function and that says that the length function if a interval i is written as a countable disjoint union of intervals i n's then the length of the interval i is equal to summation length of i n's. So, to prove this property so let us start looking at the proof of this property. So, to prove this property let us write so i is a interval which is written as a union of i n's n equal to 1 to infinity, where the intervals i n intersection i m is equal to m t to show that length of i is equal to summation length of i n's n equal to 1 to infinity. So, let us look at a proof of this case 1. So, assume so let i be finite actually finite or infinite is not important. So, let us let us take general case itself. So, note i length of i is equal to summation length of i intersection n to n plus 1 and this is because of the property that we have just now proved. And now also note i intersection n to n plus 1 can be written as this is a finite interval and i is equal to so this is n to n plus 1 intersection this interval i is a countable discharge union. So, it is a union of i j j equal to 1 to infinity. So, we can write this as union j equal to 1 to infinity of i j intersection n to n plus 1. And now this is a equality for finite intervals only because i intersection n plus n to n plus 1 is a finite interval which is written as a because i j's are disjoint. So, these intervals are disjoint and they are finite. So, thus this implies by the additive property for finite intervals which are disjoint that lambda of i intersection n to n plus 1 is equal to summation j equal to 1 to infinity lambda of i j intersection n to n plus 1. So, here we are using the fact that whenever a interval i is a finite interval which is a countable discharge union of intervals 1 to infinity then the length of i is equal to summation of length of this. Now, look at this equation here and look at this equation here. So, length of i is equal to summation n over integers length of i intersection n to n plus 1 and that is computed to be equal to this. So, combining these two we get the property that length of i is equal to summation n belonging to z of length of i intersection n to n plus 1 and that property we are going to put it here. So, summation j equal to 1 to infinity lambda of i j intersection n to n plus 1. And now keep in mind that all these are double summation of the series and all of them are non-negative. So, I can interchange the order of integration. So, I can write this as summation over j equal to 1 to infinity summation over n belonging to integers of length i j intersection n to n plus 1. And now once again I use the fact that the interval i j length of i j can be written as length of i j intersected with n to n plus 1 summation over n belonging to z. Just now we have proved that fact the sigma finiteness of the length function any interval length i is summation length of its species inside n to n plus 1. So, this is here. So, that gives me the fact that. So, this gives me length of i is equal to summation j equal to 1 to infinity and this is length of i j. So, that proves the countable additive property of the length function namely if a interval i is written as a countable disjoint union of intervals. So, this proves the countable additive property that if a interval i is written as a countable disjoint union of intervals i n then length of i is equal to summation length of i n. Whether i interval i is finite or infinite that does not matter. So, the length function is countably additive. That is what we have proved as an important property of the length function. Let us extend this property to coverings which are not necessarily disjoint. So, that is called countable sub additivity. So, that is says that if a interval i is such that i is contained in union of intervals i n n equal to 1 to infinity which may not be disjoint then obviously we should expect that the length of i is less than or equal to summation length of i n and its proof is very much similar to the earlier case. So, let us just go through the proof again so that we understand how sigma fineness of the length function is used. So, i is a interval which is contained in union of i n n equal to 1 to infinity. These intervals i n may not be disjoint. Now, what we do is look at length of i. I can write this is equal to sigma n belonging to z length of i intersection n to n plus 1 that is sigma fineness of the length function. And now the interval i intersection n to n plus 1 is inside because this i I can write as union over i n. So, this is equal to, so let me write, this is less than or equal to sigma length over n. So, this thing is less than or equal to sigma length of i j intersection n n plus 1 j equal to 1 to infinity. So, here what we have used is the fact that interval i to this intersection, this interval is covered by the union of these intervals. So, and this is a finite interval. So, length of this must be less than or equal to length of this. Now, once again non-negative series of non-negative numbers I can interchange. So, this is equal to sigma j equal to 1 to infinity sigma n integers length of i j intersection n to n plus 1. And that once again, this once again is nothing but the length of the interval i j by the fact that just now sigma fineness of the length function. So, length of i is less than or equal to length of sigma length of i j's. So, this property is called countable sub-atiti property of the length function. Here is a very important property of the length function, which is called translation invariance. It says if I take a interval i and translate it by some number x, then the length of it does not change. So, it says length of i is equal to length of i plus x. When I take a interval i and translate, so this is a translated set, just shift it, push it by a distance x. So, i plus x is all y plus x, y belong to y. And this property is obvious, because if say for example, if i has got n points a and b, so this property of translation invariance is quite obvious, because of the fact that if i has got, let us say it is a interval with left end point a and right end point b, then i plus x is the interval with the left end point a plus x and right end point b plus x. So, length of i plus x is same as b plus x minus a plus x, which is equal to b minus a, which is equal to length of i. So, length of i is same as length of i plus x. That is for finite and the same proof very continues for infinite, because for example, if i is equal to say a to infinity, then what is i plus x? i plus x is a plus x to plus infinity and in either case, length of i is equal to plus infinity, which is same as length of i plus x. So, basically observing that if i is an infinite interval, its translation remains an infinite interval, so the values of both are equal to plus infinity. So, this is what is called the translation invariant property of the length function. Finally, let us prove what is called the finite additive property of the length function. We have used finite additive property of the length function for finite intervals and we proved countable additivity property for the length function. I just want to exhibit that the countable additivity implies finite additivity, when we have the fact that the length of the empty set is equal to 0. So, basically what we are going to say is, if i is an interval, which is union of ij, j equal to 1 to n, where ij intersection ik is equal to empty, then I can also write it as union of j equal to 1 to infinity ij, where I can define ij to be equal to empty set, if j is bigger than n plus 1, from n plus 1 to 1 put them everything equal to 0. So, then i is a countable disjoint union of intervals, so length of i must be equal to summation length of ij by countable additivity property and that is same as summation j equal to 1 to n length of ij, because from n plus onwards they are empty and so the length is equal to 0. So, countable additivity implies finite additivity whenever length of the empty set I can put it equal to 0. So, let us just recapitulate the various properties of the length function that we have proved, namely the length function is a set function defined on the class of all intervals in the real line with the properties that it is countable additivity, countable additivity, finitely sub additive, finitely sub additive and translation invariant. The important property is that it is countably additive. So, in view of this the next question that arises is the following, so is a measure length function is a measure which is translation invariant, because it is countable additive and length of the empty set is equal to 0. In view of this also observe the length of the singleton is equal to 0. This is also a property of the length function, because the singleton set can be written as an open interval with the or a closed interval with the same end points and so length will be equal to x minus x which is equal to 0. It is finitely additive and countable additivity, finitely sub additive, so that we observed. So here is the question that are there other countably additive set functions on the class of intervals? So, we will like to know length function which we just now proved is one such function which is countably additive set function on the class of all intervals. So are there other countable additive set functions on intervals? So, to answer this question let us make a notation. So, we will denote by i upper tilde, so there is a wave kind of a sign. So, this symbol is called calligraphy i, so the collection of all left open right closed intervals will be denoted by this symbol. This is calligraphy i with the upper tilde, so this is a collection of all left open right closed intervals. So, intervals whose left end point is not included, but right end point is included and keep in mind if it is infinite there is no right end point on the real line. So, this is the collection of all left open right closed intervals. So, what we are going to prove is the following, suppose we have got a set function mu on the class of all left open right closed intervals such that let us say it is finitely additive, this mu is given to be finitely additive and also given the fact that mu for a finite interval is finite for every a and b. Then we want to prove that this can be characterized by the existence of a monotonically increasing function f from r to r such that mu of the interval left open right closed interval a, b is given by f of b minus f of a for every a belonging to r. So, what we want to show is that if mu is given to be a finitely additive set function on the class of all left open right closed intervals and mu with the property that it is mu of a finite interval is finite then we want to show that this must be given by a monotonically increasing function f with the relation that mu of a, b is nothing but f of b minus f of a and keep in mind this looks like if lambda is the length function if mu is the length function then the obvious choice for f is the identity function y equal to x. So, then it will be equal to b minus a. So, it is in some sense we are generalizing the length function that means if mu is any finitely additive set function then it must be given by this. So, to prove this let us observe that mu of a, b is given by f of b minus f of a. So, that itself tells us what should be the definition of the function f for example, if I fix here a point a if a is fixed that means f of a is fixed then I can calculate f of b as equal to mu of a, b minus plus f of a. So, this relation itself gives me a hint how should I define mu of the function f. So, let us fix n a and the most convenient point is to fix a to be the origin. So, and we will also show later on that if mu is countable additive then this function can be chosen to be also not only monotonically increasing, but the right continuous function. So, let us define our function f from the real line. So, f at any point x in the real line is defined as mu of the interval open interval 0 close at x. So, left open right close interval 0 x size or mu of that if x is bigger than 0 and it is defined as 0 if x is equal to 0 because that will mean mu of the empty set is equal to 0 it is countable additive and mu of f of x to be equal to minus of mu of x of 0 if x is less than 0 because f x is less than 0 then this point x is going to be on the left side of 0. So, left open right close interval this. So, with this definition of mu we want to claim that this function has the required properties namely first property that the first property namely. So, let us check these properties of this function. So, first this satisfies the required equation. So, we want to check that for a interval a b mu of a to b is equal to f b minus f of a. So, to check that let us take this is the point 0. So, if a and b are both finite numbers real numbers. So, let us say this is the interval a to b then mu of then f of b minus f of a is equal to mu of 0 b minus mu of 0 to a and this let us observe that mu is given to be finitely additive. So, this is same as mu of a to b because I can write 0 to b as union of 0 to a and union of 0 to b this joint interval. So, this joint p c. So, using that fact this is just mu of a b. So, that proves it and similarly if it is infinite. So, suppose the interval i is a to plus infinity then I can write it as then I can write this as equal to this is equal to mu of is finite. Now, let us observe one thing that we have not if the interval is i is infinite then what is mu of i equal to we have not defined what is the relation between. So, between this and the function. So, keep in mind we have defined f of x is equal to mu of 0 to f x is equal to finite and this is equal to if this is finite. So, we want to check that this satisfies the required property namely if i is equal to a to plus infinity then I want to check that mu of i is mu of i is equal to f of for a oh sorry this is only for finite intervals. I am sorry we want you to check that only for finite intervals this property is true. So, whenever a interval i is finite interval then we know this is finite and this property is true. So, now let us check the next property namely that f is monotonically increasing. So, let us check the property that this property is. So, let us take two points. So, let us take the case here is 0 here is x say here is y. So, we have got x less than y we want to check f of y. So, we want to calculate f of y. So, what is f of y by definition is mu of 0 to y and that I can write as mu of 0 to x using finite identity property I can write 0 to x union of x to y mu of that and that by finite identity property is mu of 0 to x plus mu of x to y and now this is equal to f of x by definition. So, this is equal to f of x plus mu of x to y and this is some non-negative quantity. So, I can write this is bigger than or equal to f of x. So, if x is less than y then f of x is less than f of y. So, that proves it is monotonically increasing in the case when both x and y on the right side of it and same proof will work if they are both are on the left side of 0. So, here is y and here is x. So, we have got y less than or equal to x. So, we want to look at what is f of y. So, that is equal to minus mu of y to 0 by definition. So, that is equal to minus y to 0. So, this I can write it as mu of y to 0 union 0 to y to x union x to 0 and that again by identity property is minus mu of y to x minus mu of x to 0 and this is equal to minus this is f of x. So, I have got this is plus f of x because f of x is defined as minus of this and this is a negative quantity. That means f of y is less than or equal to f of x. So, once again that property is true and the third case when the third case being let us take it is 0 here and y here and x here. So, in that case what is f of y? Let us look at y to x that is sorry what is mu of y to x from this I can write it as is equal to f of y minus f of x by definition and this is bigger than or equal to 0. So, implies f of this is f of sorry this is not f of this is f of x minus f of y. So, that means f of x y is less than or equal to f of x. So, once again in all possible cases we have checked that f as defined above is a monotonically increasing function. So, we want to check now that if mu is countably additive then this implies f is right continuous from the right. Finite additivity property gave us that f is monotonically increasing and we are claiming that if mu is countably additive then f must be right continuous. So, what is right continuity? So, let us take a point x let x belong to R and let us say take a sequence x n say that x n decreases to the point x to show that f of x n converges to f of x. So, that is what we have to show that f of x n converges to f of x. So, let us try to look at a picture. So, this is 0 and let us look at the case when x is bigger than 0. So, this is the case when x is bigger than or even equal to 0 we can take it. So, and here is the sequence x n x n decreasing to x that means here is x n here is x n plus 1 and so on and that is converging to decreasing to x. So, let us observe in this case. So, note look at the interval which is 0 to x n. So, this interval 0 to x n I can split it as interval 0 to x left open right close 0 to x and then x to union of x to x n union of this x to x n. Now, I want to split this portion also. So, the interval x to x n plus 1 x n this interval is same as let us start. So, this part so that is x n plus 1 comma x n the next part that will be x n plus 2 comma x n plus 1 and so on. So, can I claim? So, I want to claim that this is union of x n plus k to x n k equal to 1 to infinity. So, and that is because if I take any point between x to x n. So, take any point here this x n converges so it is going to cross over this point any point inside the interval x to x n. So, that means that it is going to fall inside one of these intervals and all these intervals are subsets of it. So, it is quite easy to check that x to x n this interval is a union of intervals x n plus k to x n k equal to 1 to infinity and here we are using the fact that x n decreases to x. So, this fact is being used here. So, now realize that x to x n is a countable disjoint union of these intervals and mu is given to be countably additive. So, what we have is the following property. So, that says mu of x to x n is equal to summation k equal to 1 to infinity of mu x n plus k comma x n. So, now let us write this in terms of f. So, that means f of x n minus f of x is equal to summation k equal to 1 to infinity of f of x n minus f of x n plus k. Now, this is a series of non-negative terms. So, I can write as limit of the partial sums. So, let us write limit of m going to infinity of summation k equal to 1 to m f of x n minus f of x n plus k and this is equal to limit m going to infinity. Now, this is a partial sum. So, what does that mean? So, this is k equal to 1 n to n plus k. So, n to n plus 1, n to 2. So, this is a sum where terms will cancel out. So, let me just write it.  The next term will be plus f of x n plus 2 minus f of x n plus 3 and so on. So, it will be going up to m. So, k equal to m. So, f of minus f of n plus m. So, that means what? So, note that n plus 1. So, we are starting with k equal to 1, n to n plus 1. So, n plus 2, k plus 1. So, what are the terms which are cancelling? So, this says that n plus 1, n plus 2, n to 2. So, n plus, sorry, it should be n plus 1 minus n plus 2. So, when the next term comes, n plus 1, n plus 2 and so on. So, these terms cancel. So, what will be left with equal to limit m going to infinity of f of x n minus f of x, sorry, x of n plus m. So, that means what we get is the following and this is independent of m.  So, that is same as saying that f is continuous from the right at x and that we approved when x is bigger than or equal to 0. So, when x is bigger than or equal to 0, this is right continuous. The other case when x is negative and still whenever x n converges to 0 or x n decreases to 0, we will show that f of x n converges to f of x showing that f is right continuous at x when x is negative also. We will do this in the next lecture. Thank you.


Bill W became a member of DT&S today and now has access to secret things you don't. Unless you're a member at patreon.com slash DT&S. This is the Daily Tech News for Friday, July 12th, 2019. My wife's birthday, happy birthday, Aline. In Los Angeles, I'm Tom Merritt. And from Sir Dewey Fielin's grandma's house, I'm Sarah Aline. Back from a well-deserved vacation, I'm Len Peralta. Without any disturbing vacations, I am the sweltering producer, Roger Chang. I'm already in slip there. I'm glad it's good to have you back. It's good to be back. It really is. I'm excited. And it's a suspicious day because not only is Len back from his vacation, but Nicole Lee, senior editor from Engadget is back on the show as well. Hello, happy to be here. Happy birthday to you, wife as well. Oh, thank you. I will pass that along to Aline. We're gonna talk a little bit about the accuracy of menstrual tracking apps and fertility apps. We're gonna talk a little bit about the upcoming strike in Minneapolis against Amazon, but let's start with a few other tech things you should know. Sources tell the Wall Street Journal that the U.S. Federal Trade Commission voted this week to approve a roughly $5 billion settlement with Facebook over an investigation into the tech giant's privacy violations. And now for something completely different, Google is really not a redesign of its news tab on desktop that is more prominently highlighting headlines and publishers and a new carousel that notes what people are also searching for. The redesign does mean fewer links per page, so it will be a new look and fewer related in-depth or opinion articles appearing underneath the story. Starting next week, Twitter is rolling out a new hide replies feature for users in Canada. The posts are not removed from Twitter, just hidden from your default view. The company says it knows that distracting irrelevant and offensive replies can derail discussions that people want to have and we believe people should have some control over the conversations they start. Gartner and IDC both report that after more than six years of quarterly PC shipment declines, both 2018 and 2019 showed positive growth in the Q2 after Q1 slumps. Both point to a Windows 10 refresh contributing to at least the game this year, but IDC predicts that the game won't last and Gartner points to a U.S.-China trade war or a potential trade war eventually affecting the PC market as more laptops and tablets, as most laptops and tablets rather are still manufactured in China. Volkswagen will invest $2.6 billion in Pittsburgh based startup Argo AI, which coincidentally, well, not coincidentally, it's actually a team up, also has a $1 billion investment from Ford. Ford and Volkswagen have been teaming up a lot lately. As part of this deal, Ford will get access to Volkswagen's electric drive matrix system, which Ford says it will use to build a fully electric vehicle for Europe in 2023. Ford and Volkswagen will both use Argo software in their separate autonomous cars. They're both making their own versions. If you're keeping track, there's a lot of autonomous car team-ups going on. Apple bought Drive AI, Honda's partnered with GM's Cruise, Volvo and Uber build an SUV together, Waymo is teaming up with Renault Nissan and Fiat Chrysler, Hyundai and Amazon are all partners with Aurora. Spring is a wonderful time for autonomous car people to fall in love with each other. Also a wonderful time to be a Hulu user if you care about 4K because 4K streaming is now back for Hulu users on fifth generation or later Apple TVs and also Chromecast Ultra devices. Only Hulu originals are available in 4K though the company says it intends to expand availability in the future. All right, let's talk a little bit more about what Amazon's doing in the research lab. Bloomberg sources say Amazon's lab 126, the company's R&D arm is working on a higher quality version of the Echo speaker and continues to work on its home robot that we've heard some things about before. Prototypes of the new Echo are reportedly wider than the current Echo so you can have four tweeters in there that would put it closer to being on par with the sound of a Sonos one or a HomePod in audio quality. As for the robot, internally it's known as a Vesta. It's said to navigate by computer vision and now the sources are saying it rolls around on wheels so now we know how it gets around and can be controlled as you might guess by voice command. It was hoped they would launch Vesta this year but it's not quite ready. Amazon is putting more engineering and development resources into the team working on its release according to Bloomberg sources so it doesn't seem like they're giving up on it. They're just trying to push forward and get this ready. Who wants an Amazon Echo that rolls around your house? I do and also I love the fact that they're like, and now sources are saying it has wheels. Like how else would it get around? Well, I mean, I guess it could walk. I don't know. I guess that would seem like there would be a lot more R&D. We didn't know and now the sources are like, no, we saw it rolling around. It definitely rolls around. I want this. I want this very much. Nicole, I don't know how you feel but the home assistant, I've got a whole smart home thing going on with mixed results but yes, the robot would be welcome in my home. As long as it knows when to go into rooms when it's supposed to and when it's not supposed to, like it doesn't like barge in on me when I'm sleeping. If it works, I want it.  I don't think it has any ability to open doors. Well, that's good. That's good to know. So unless it's strong enough to barge through one.  Oh, like, could the echo on wheels? Could the Vesta play you a recording of you saying to itself open? Yeah, no, that's it. I don't know. Ooh. Yeah. Well, another Amazon news workers at an Amazon warehouse in the Minneapolis area are planning a strike next Monday, which happens to be Amazon Prime Day. It's a big day for Amazon. The workers want higher wages and they also want better working conditions. The strike, which will be accompanied by a rally and Shakopee, which is in Minnesota, is being organized by the A Wood Center, which advocates for Somali and other East African workers and is a partnership between the Service Employees International Union Local 26 and the Minnesota chapter of the Council on American Islamic Relations. Nicole, you've been covering this story for Engadja, right? Yeah.  Obviously, Amazon has faced these accusations before. But however, this kind of large, this kind of the scale of this protest is more part of the largest in as far as the US goes. And it's very interesting because Minnesota and Minneapolis is like the hotbed of this issue, partly because they have such a strong community there of these East African immigrants who've immigrated there. And they have actually already set in with Amazon, they've sort of negotiated a few things here and there. But this upcoming protest will be, I think, it might be the tipping point, I think, because some workers in Staten Island are trying to unionize as well. So yeah. Is there any chance Amazon could avoid this strike? But could they agree to demands and? They could. Here's the thing, they've given them notice. They've given them a week's notice, even in the December round. They've given them a month's notice. And they could very well say, hey, if you just make it so that we don't have to work so hard, they have to, every one of them, they have quotas to me, they have to pack 350 items per hour or something like that. It's a very, very pressurized environment. So they just want not so pressurized kind of thing, better job security in general. So if they had just said, okay, instead of like 300, you can pack 200 or something. Even that would be like something, but they haven't made anything like that. So.  We'll see what happens on Monday, which will be a big day for Amazon shipping. They'll wanna ship more things, not better on that day. Well, just about every government official in the United States and then multiple countries around the world have criticized the Libra Association Project. Facebook gave an interview to TechCrunch's Josh Constine about some of the measures it will take to address concerns with the Libra Associations. There are multiple people that are working on this. We're talking to Constine. The company says they expect Libra to incur sales tax and capital gains tax. Really the upshot of this interview is they're trying to say Libra Association is just going to be the currency management. And all of the things that people are concerned about will happen because other entities will take care of them. It'll be a store or a wallet or something that will have to be governed by regulations to do this. So if you're paying for something with Libra and sales tax applies in the region where you're paying for it, then that sales tax should be collected. Capital gains taxes will be collected based on whatever wallet you're using. And they point to things like Coinbase as an example of how this already works. They're in talks with convenience stores and money exchanges to apply anti-laundering checks when you buy or cash out Libra. Anti-laundering checks already happen if you're in say WhatsApp and you wanna link your bank account. That already is part of that. So they're like, that will already happen if you use Calibra in any of these other situations. But if someone wants to use a cash checking place for cashing out Libra, then we're working with those kind of checking, cash checking places to have the anti-laundering checks in place for people who wanna use Libra. The spokesperson emphasized that Libra will not operate as a bank or interact directly with consumers. Facebook's head of Calibra, David Marcus, of course, testifies in front of the US Congress, Senate and the House on July 16th and July 17th. So it does seem to me that the Libra Association is actively engaging with regulators and all political spectrums who are standing up and condemning it haven't really talked to the Libra Association yet. Not that there aren't concerns to be worked out, but it sounds like Libra wants to work them out. Yeah, Nicole, I don't know how you feel about this, but I'm sort of in, I'm in the crypto world of like, if I can use a Calibra wallet to interact on Facebook in any way where I get a better rate than I would somewhere else, I'll do it. The more regulation, the more that certain people will feel, they can rest easier that this is currency that's going by the rules that govern other currencies, but also continue to kind of take back the fun part of this, that this whole sort of like, oh, the new currency, this whole thing, it's a sovereign nation, blah, blah, blah. Well, it sounds like it's gonna be a lot harder than that. Well, that's the thing. I think most of these regulators and government entities, they're very critical and skeptical of this because Facebook's name is attached to it, obviously, because there's a lot of concerns about privacy and all of those issues, which Facebook has understandably, that's why they're so skeptical of Facebook, but the way this is being done and whether or not you trust it or not, the way at least what it's presented as seems to be kind of on the up and up, just because there are 28 members of this organization, Facebook is only one of the 28, so they have, there is no majority voting sticks for Facebook in this liberal association. Each of the 28 members have an equal vote, I guess you could say. And the 28 members are Visa, MasterCard, PayPal. So these are not like run by night, like random companies, these are as well-established financial entities. So, you know, and here's the thing, people still don't really understand cryptocurrency to be fair, like there is still a lot of confusion about what is Libra, what's cryptocurrency, what's Bitcoin, so what's a blockchain? And I think because there's so much confusion and people don't really know what it is, whenever there's like this confusion, people don't know things, whenever there's ignorance around something, people are going to just point your finger at somebody about something. And Facebook, unfortunately, is the favorite punching bag of everyone right now, and it doesn't surprise me that there's all this confusion, but honestly, if you look at the documents, if you look at the white paper, it seems to be on the up and up for now. The biggest problem with Libra is gonna be whether anybody wants to use it. Yeah. Telling enough for someone like Sarah to use it, who already has access to banking and whether it will be accessible enough for people who are unbanked to be able to use it. Libra has answers to that. We'll see. At VidCon going on this week, YouTube rolled out a new monetization tool, a few of them actually for creators, such as Super Stickers, which will roll out in the next few months that lets viewers purchase animated stickers to display in chat during live streams. YouTube also updated channel memberships to include up to five different monthly membership levels, each with its own set of perks. YouTube's Merch program is also expanding partners with CrowdMade, DFTBA, FanJoy, Represent, and RoosterTeeth joining its debut partner, Teespring. YouTube is also launching learning playlists, which offers dedicated landing pages for educational videos on topics like math and science and music and language. Playlists will feature chapters around key concepts and be ordered from beginner lessons to more advanced videos. And learning playlists will not show recommended videos and videos won't autoplay after the playlist is over. Learning playlists is a great idea. It's right now limited to a few partners, which is fine. Part of me says, well, you know what? You roll these things out slowly. You pick the people who can make the best advantage of them. Ted Tox is gonna make great advantage. That's a wonderful thing. I love that it doesn't do the autoplay. It doesn't fall for a lot of the things that are a problem with YouTube. But if you can roll this out to limited partners, which is picking winners, saying these are the people most important, I don't understand why YouTube also can't moderate its homepage and its recommendations better and pick winners there. They keep saying, well, we don't wanna touch the algorithm. We wanna stay unbiased on one side, but whenever they roll out new features, they limit it to people. Yeah, it's almost as if they can control it. Oh, I think they could. Yeah, I suspect they could. And actually, YouTube will say, yeah, we could, but it's a bad idea in this case, but it's a fine idea in this case. And I guess eventually they will roll this feature out to everybody. And I think it's a great feature. I don't mean to... Yeah, it's good, I love that. I think the educational playlist is something we could take advantage of on the Daily Tech News Show channel. Yeah, absolutely. Researchers from the Bangurian University of the Nejiv have developed an attack called Control-Alt-LED that can exfiltrate data, that means get data off of a computer by reading the LED lights on caps lock, and them lock, and scroll lock keys. Now you may say, why would they wanna do that? Well, that means it would work on a secure air-gapped system. So this is a hack for intelligence agencies, for governments, for secrets, for classified information, but you have an air-gapped system that you have your super classified information on. It's unconnected to anything else. There's no network connection at all, not even close to an internet connection. First, how do you get stuff off there? Well, you got to infect it with malware. That's not impossible. These air-gapped systems can be infected with malware by tricking someone into putting a USB drive into it, or some such thing. That's probably the most difficult part of this exploit. Once you got the malware on there, even if the malware is running, it can't use the internet. This is an air-gapped system. There's no network connection. So how do you get the data off? Well, you make the LEDs on the keyboard, blink at rapid speeds to transmit the data. The attacker has to have some kind of line-of-sight view of the keyboard to record the flashes and decode them. You could just record the flashes and decode them later. A smartphone would work. That would mean you'd have to be in the room with the device, but if you could get a CCTV camera pointed at it and you could get that footage, that could also work. The possibility of this method was explained in a 2002 paper. So this isn't a new concept, but this is a good demonstration of it. And the same team that's demonstrating it here did a similar method using hard drive and router LEDs in the past. So it's kind of their thing. Wow. Yeah. Before the show, Tom was like, what's your follow-up question here, Sarah? And I was like, I'm not sure I have one. Don't have a lot of air-gapped computers in your house, I guess, yeah. Right, but no, and this is sort of, there's one of those stories where you're like, okay, somebody would really have to be going for it to make use of this at all, but it's very genius, isn't it? It's like using the caps lock almost in Morse code form to transmit data is really genius. I'm not saying you should do it, but I'm just saying I'm somewhat impressed just by the idea of how this would be effective. This is the kind of thing you're gonna see in Mr. Robot, right? Yeah. Or the next hacker heist thriller film that wants to try to get something right is they'll figure out how to get the USB malware on there and then they'll hack into the CCTV cameras and be able to read the LEDs flashing on the keyboard screen and that's your most likely to encounter it in the movies or TV much more than in real life, but it's a real life thing, it could happen. Hey folks, if you wanna get all the tech headlines each day in about five minutes, be sure to subscribe to dailytechheadlines.com. So apps that track your menstrual cycle and often your fertility are quite popular these days. Garmin added cycle tracking last April, Fitbit added what they call a female health tracking feature last summer, Apple announced at WWDC, it's going to bring cycle tracking to the health app or at least improve it and add it to the health app on the Apple watch. But Nicole, I know you've been digging into a feature on this very gadget, do these things work? Are they useful? Are they helpful? What's the story with them? I think first of all, there are, it depends on what you're gonna use these trackers for. I think that's the number one question that I would have. If you're using them just to track your period, right? I think that's important for a lot of people, just for a lot of women, especially they wanna know what their cycle length is and when to expect their next period just because it's easier to like plan your vacations if you know what your cycle is like. Or are you using it to like get pregnant? Completely different use case. Like now you wanna know like what your fertile window is, what your ovulation time is, like all of those things. And having an app does make it easier because you just enter it into your phone and it taps into it. Of course nowadays, they're incorporating it into all kinds of things, the Garmin, the Fitbit, the Apple watch. So it's more like convenient on the go. Part of me wondered if this was like a weird like, oh, this is for you women now. And I wondered if there was like a weird like gender, like a gender marketing thing for these devices. And maybe it is, right? Maybe there is some aspect of that. But I also think it is actually somewhat useful. But then so I kind of looked at a few studies. I talked to a few researchers. And a lot of them kind of come to the conclusion of what I just said. It really depends on what you wanna use it for. And even then all of these apps have different algorithms of how they calculate it, depending on what you enter in each month. And truth be told, the difference between one app and another, there's almost like no difference between a glow or a dot or a clue or whatever else app name I can think of. It's almost always based on body temperature, right? And there's some sort of, there may be a thermometer involved it may be only app-based it might be something you're wearing on your wrist but it's something that it can be quite accurate but you have to feed it some accurate information as well. Yeah, it's still up to the user to provide that information, essentially. Even if you do wear it on your wrist if you forget to wear it like that's not gonna be entered into the database. So it's still up to the user to have that information. And not last thing that it isn't useful, it is useful. It's just that it's not any more useful than so-called traditional methods. You know, as somebody who I have not used any fertility apps in order to have a baby but I have used them and being able to have some data on your own cycle, super interesting and helpful as you mentioned vacation, great example of that. It's also just, I think at least for women it plays into this whole kind of these data points of what we're doing with fitness trackers in general are just interesting to us. Do I really care if I climb 10,000 stairs rather than 9,000 stairs? Like, no, but I kind of wanna know, I like that.  Yeah, I think another point to sort of keep in mind and to be mindful of with any of these tracker apps. You know, this is data that you're feeding into this app and the company is getting your data. They are finding out when people ovulate and what their cycle is, what their cervical mucus is like each month. No, maybe you don't care that these companies know about it but just know that it is being fed into these companies and they're probably gonna use it for some kind of marketing, some kind of data, database of information. So whereas like if you just kept it to yourself and just give it to your doctor, that's private information that only you and your medical professional will keep because that's under the oath, a medical oath thing. Whereas this one is kind of like, you know, if you want this information, head at it, which it's up to you on how you feel about your data privacy. Which I mean, that's a good reason to maybe not use an app. Roger, I know your wife was using a device for fertility tracking, right? Yes, and we did it for our first child and, you know, it was just a simple ovulation tracker.  I'm just wondering, do these apps provide any advantage other than convenience in terms of like, oh, these are more accurate.  I think those sticks, you mentioned the ovulation stick tech. I think those are still probably more scientifically accurate than an app just because the app does rely again on user input and all of those things can be variable entities. Whereas the electricity just literally adjusted the amount of luteinizing hormone in your urine, which is, so that's a very specific, you know, quantitative thing.  Like 30 bucks. But, you know, it's very interesting that, you know, all these fitness trackers, I mean, they're using data that they already collect or based on user input. And I've always been curious to know if there are ways to track parts of, you know, the human physiology without necessarily having something invasive. You know, using a strip isn't terribly invasive, but it's still kind of, you know, awkward to use. Yeah, it's not passive collection environment. I also wonder, and you know, this is me just being dramatic, but I wonder, okay, if data like this is leaked to a third party that may not have your best interest in mind, marketing, fine. But, you know, when is going to be, and maybe this has already happened, when is going to be the first situation where someone's like, well, hold on, look at that fertility data. This doesn't sound right. Now we have a paternity lawsuit involved. Wow. That's the kind of situation where it might not be leaked, but if someone is conducting a lawsuit and knows that data exists, they might subpoena it.  This is complying with the court order. And our terms for all of our data say that if the courts, you know, tell us to turn over data, we're going to turn over data. That is a really interesting aspect of that, too. That's a very good question. Just remember, all of our parents got pregnant and none of them used apps. So, you know, you have to decide. That's true. I mean, I'm not, it's not like you have the audience to turn over data. Yeah. You know who else has options? Everybody participates in our subreddit. You can submit stories about fertility or other stories that you think might be great for the show, vote on them at dailytechnewshow.reddit.com or also on Facebook. We've got a group there. Facebook.com, slash groups, slash dailytechnewshow. All right, let's check out the mailbag. Got some good stuff. Yeah, we did. Mohan wrote in about our conversation about Amazon training its existing workers in new skills. Could do in some retraining going on in Amazon, saying that they're going to put quite a bit of money into it, 700 million if I'm not mistaken. Mohan says one aspect that wasn't discussed was sometimes that's all the option that people have. For example, if a warehouse worker is giving the opportunity to become a data scientist, then they might. Without this, they might not have any other way. People get into most of these types of jobs out of necessity and oftentimes can't get themselves out for various reasons, financial reasons being a major part of that. I know this personally because I have family members in that situation who are much older now and set in their ways. Yeah, good point. And we certainly, you know, we're trying to make it sound like the retraining would solve all the ills of everyone but it's better to have those opportunities than not as Mohan is saying. Chris in Fresno, California says, I continually get frustrated when hearing stories about paid subscriber numbers for major music streaming services. I can't open a webpage without seeing an offer for 99 cents a month Amazon music or Spotify free for three to six months. I know Apple has discounts for students for a limited time. Basically he's like, I'm not going to believe any of these numbers until I see average revenue per user, which is perfectly sensible. Like that's really the apples to apples comparison. Pardon my pun. Spotify reported $5.29 average revenue per user in Q1 of this year. Apple doesn't report its average revenue per user but it did announce 50 million paid users in January, a number that does not include free trials. So they announced a number that didn't include their free trials at 50 million. They had previously announced 50 million that did include the free trials. So if you scrounge around there's a little bit of that number, but I'm with Chris. I would like to see just give me some ARPUs so that we can really compare these to each other. All right, let's check in with Len Peralta who has been illustrating today's show. What have you come up with today, Len? You know, I found this topic pretty interesting. My wife and I are beyond this right now. We don't need it at all, but I can kind of see how it would come in handy for someone who's trying to be pregnant or not become pregnant. And what kind of made me interested about this was that the Fitbit was not really working properly. And I can just see this would be something that would happen to somebody. I tracked my monthly cycle on my device and all I got was pregnant. Not that it's a bad thing, but if you don't know. But there was someone in our chat room a minute ago who was saying, you know, what about people who are using cycle tracking to not get pregnant? You know, they're not in a situation to get pregnant. And yeah, it's like addresses that head on. Thank you. Yep. And it can get it at Patreon, patreon.com forward slash Len or at my online store, lenproffstore.com. Excellent. And so good to have you back, Len. And also so great to have Nicole lead back on the show today. Nicole, where can people keep up with your fabulous work? You can just go to twitter.com slash Nicole for any updates that I have about links to my stories. Excellent folks. Don't miss out, get the cool stuff, the early stuff, the ability to chat with other people, listen to the show live and all so much more by becoming a member at patreon.com slash DTNS. And if you have feedback or email addresses, feedback at dailytechnewshow.com. We're also live Monday through Friday. Join us if you can for 30 p.m. Eastern 2030 UTC and find out more at dailytechnewshow.com slash live. Be all Monday. This show is part of the frog pants network. Get more at frogpants.com. Hope you have enjoyed this program.


Hello everyone, this is Dan from Smokartel. Happy Croptober! Today we're going to talk about the best way to store your dry herb, whatever it may be.  Here in the south we love our humidity. It's when the air is wet. Humidity is important when it comes to dry herb, because if it gets too humid it can get moldy and mildewy, and if it gets too dry it can get stale. So you've got your normal container of herb, that's great. It's just chilling, whatever. What's just as important is all the space outside the container. This is called ambient humidity. Wherever the container is, the space around it is just as important because it affects the humidity of the space inside. Little science for ya. 62%. That's the ideal percentage for storing your dryer. Your house, if you have heat or air conditioning, is probably around 20 to 30%. So what do you do? Well, you could cry, or you could get one of these little humidity regulators. This one in particular is by Integra, which I think I'm pronouncing correctly.  There's a four gram size recommended for up to half an ounce, an eight gram size recommended for an O, and a 67 gram size, which you can use for up to a pound. Store one of these little packets in your container of herb. Make sure it's air tight, and the packet either releases or absorbs moisture to make sure that it stays 62% humidity inside this little box. This little dot is the replacement indicator, which turns blue when it's time to replace it. Now, I've got this little bowl here. This is made by Sea Vault, and it's an airtight container. It has these little locks on the side, and it's pretty big. So this is ideal. It's $18. That's nothing. So you can put your herb in here and seal it up with one of these little humidity regulators, like this one by Boveda, which is included with the container. All these great options to keep your herb dry or wet and happy. So check them out on our website. This stuff is going to make you a big dog. If you have a stash that's just in a ziplock bag, to me that says you're dropping out of college.  You're functional. You're successful. So think about it.


Hello, I welcome you all once again to my channel, Explore Education. I am Dr. Rashmi Singh, Assistant Professor, Department of Education, S.S. Khanna Girls 2D College, University of Allahabad. And in the series of discussing educational implications of various philosophies, yesterday I have discussed educational implications of idealism and naturalism. And this time I am going to cover the educational implications of realism and pragmatism. These are very important philosophies, very relevant to educational world. The lecture will be in bilingual mode, and it must be useful for you all. So let's start. We have talked about all types of views, your idealism, idealism, nature, nature, nature, nature, and pre-ojan. So let's talk about a quick review of philosophy and its scientific views. Let's talk about scientific philosophy. What have these views given in education? So, realism or pragmatism is started by an Aristotle, Aristotle believes in the birth of realism and the birth of science. So you can understand that realism and pragmatism are parallel to each other. Then reality, what is the reality for realism? Objects. That is, they can be used only by you, who you can see through your knowledge. What is the basic notion of realism? Reality exists. Independent of human mind is the most important thing. They are saying that reality, that is, the reality, that is, the truth that exists, is independent of the human mind. Meaning, there is no need to take reality from the human mind. We have that thought in our mind. We have that thought in our mind. It's not like we don't know anything about anything, we don't have that thought in our mind. So it can't be true. Aadarshwar says the same thing. Aadarshwar says that every thing is true, whose thought is in your mind. So they are contrasting. Your idealism and realism. Then according to them, the truth is material and can be viewed. This thesis holds the reality, knowledge and value exist independently of the human mind. And according to this promise, the truth, the knowledge, the mouth, our thoughts are independent of our mind. There is no need to take that thought. It exists. In other words, realism rejects the idealist notion that only ideas are real. We have already said this. According to this, Aadarshwar's basic notion of realism denies that the same thing can be found in our mind, in our thoughts. The realist asserts as a fact. That actual sticks, stones and trees of the universe exist, whether or not there is a human mind to perceive them. So what does Aadarshwar say? Actual sticks means a stone, a tree, anything in the universe. It exists. There is no need for a human mind to perceive it or not. This is your basic notion of realism. What did Aadarshwar say in his teaching? Aristotle says that education is the creation of sound mind in a sound body. He says that education is the demand of a beautiful, healthy body. So this means rational development, cognitive development, intellectual development. We talk about this plus physical development. Physical development will improve your body and intellectual development will strengthen your mind. Then what is education? Education should be fun and interesting for the student and education should prepare students for life in the real world. He says that education should be a demand of a beautiful, healthy body and a real world for the student. I mean, we don't have to prepare for the world for spirituality, spirituality or divinity. We have to prepare for the world where we are living our lives. Realism considers the sense organs as the gateways of knowledge. You also read in naturalism that senses are the gateways of knowledge. Similarly, the ones who believe in realism also say that the intellectuals are the doors of knowledge. They are the windows of knowledge. That is why they have given a lot of attention to the teaching of the intellectuals. Since the object is the truth, since we have to prepare for our intellectuals, we have to prepare for the world where we are living our lives. That is why Milton is saying that there is power on the excursion, there is power on the field, there is power on the trip. Let the child learn how to roam, let him take the first-hand experience, let him sit in the classroom, sit on the wall, don't study from the book. So, the progressivism, the liberalism that has come has come because of realism. Apart from this, Locke says how to study, how to teach the child how to roam, so for them, what methods have they given them? Learning by doing, that is, how to teach the child, learning by self-experience. The child should learn from his own experience. And that is why all the workshops, laboratories, all that has come in the teaching, laboratory work, lab work, library work, all that is given by realism. Yathatwar did not tell. On the practical aspect of the teaching, Yathatwar gave. Realism considers the objects as the basis of experience that they started to use these objects as means of teaching. Because he said that the basis of our experiences are the objects. That is why he taught by the objects. That is why you can say that all the teacher training is going on. In which TLM is spoken. What is TLM? The teaching learning material, the model, chart, and through which the child is taught, you can say that Yathatwar has met the teacher.  Then realism gave special attention on objective methods of teaching. We are not angry with verbalism and subjectivity in education. In order to make the process of teaching more effective and useful, it suggested these scientific methods. That is to say, do not teach in a bold way. Do not teach in a classroom. They are saying that you should teach the child with a scientific method. Like practical experience. They learn by themselves. Inductive, deductive. They make rules by themselves. They learn the generalization of the rules. They learn by using it. They learn from the practice. They learn from the visualization, they learn by themselves. That is why the training of sense organs has been given a lot of strength. Apart from this, they said that we are not reading the whole word to the child. Do not teach the child in a bold way. Do not memorize it. They ignored the fact that the child should remember in a bold way. They are saying that you should give the child so much freedom that he can discover the knowledge. And give him so much freedom that he can remove things from the situations. And authority as a source of knowledge is not there. The teacher has said that this is why the child should not be like this. They learn from themselves, learn from them, do the logic, do the scientific method, do the practical, do the experimentation, and then reach the truth. This means that learning will be permanent if the child learns. And they have done this. That is why your scientific methods are there. You can make the hypothesis, choose the problem, then you can make a prediction, then you can use it. Then you can test the hypothesis with the results of the practical method. These are the steps of the scientific method. Realism has also done the same steps. Then what is the principle of this? It is a practice on practical education. It is based on practical education. It is based on liberal and vocational education. It is based on scientific subjects. It is based on healthy education. It is based on new and new teaching methods. Realism has given us the concept of teacher training. Realism has given us the concept of teacher training. It is based on experiments. The child is talking about child-centered education. The book learning is being denied. The book is being denied. It is being said that reality changes in our lives. The reality changes. It is also called Pregnantism. It has been given on the discovery method. It has been given on the social nature of the school. It was a student and the society has given importance to both. You can understand that the contribution of realism is in the area of education. Similarly, your second philosophy is Pregnantism. The principle of pragmatism is the use of the practical. It is about what your prayojan will do the work, education and work which is fruitful for you. It can be done for you. So, pragmatism is generally viewed as an American philosophy. It is also considered as a preojan. It is called experimentalism or consequentialism too. Why is it experimentalism? Because it is the universal practice. Why is it consequentialism? Because the consequence is that you do your work and the result is that the work was good or bad. done first and then on the basis of the result, principles and ideas are derived. They are saying that you do the activity, you do the experiment first and then the result will come and it will decide whether the experiment was good or not. When will it be good? When our purpose will be solved, then it will be good. If a thing works in practice, then it is valuable, desirable and should be up there. They are saying that what we are doing, what we are doing in practice is of our work. So what is the implication that nothing is absolutely good, like the idealists tell us about truth, beauty, goodness, they are not talking about pragmatism, they are saying that absolute good means that it will always be good, it will always be good, it will always be good for everyone. But what are they saying? The things that are good according to our needs, so things will change according to the situation and the concept of good will also change for us. Then you can say that pragmatism is very close to modern education or you can say that modern education is based on a lot of pragmatism. It believes in change in education and opposes traditional education. So they have opposed our traditional education, they have said that humans will make their own ideas and principles, according to them, we have to teach the human being, we have to teach the human being and only those educational institutions can survive in this world, according to them, who are flexible, who change according to the needs of the time, according to the needs of the time, so this is absolutely right. Then what is good according to them in teaching, learning by doing, project method. See, D.V. Sahab's disciple Kilpatrick and Kilpatrick Sahab has brought the project method to school. So what is the project method? Many children will collaborate on some work, so they can learn a lot from it, learn leadership, learn collaboration, learn creativity, learn sharing of work, so the project method is the teaching of pragmatism. Then utilizing the educative process is the first criteria. What is most important to teach is the work, the utility, the meaning that you are getting out of it. What should the school do? Give the child more, give the child more experience, which is beneficial for him. Don't study at all in a traditional way, accept the challenging role. And so, a way that pragmatism philosophy has been developed is based on the weaknesses that you had in your practice, which were overcome. So what will happen to the educational pragmatism, that what is the teaching? The teaching is a continuous, that is, the re-organization, reconstruction and integration of its experience. This is D.V. Sahab's definition that education is a continuous re-organization and reconstruction of experiences. So what is the use of giving education, that you give it such an experience, which will get a good experience for it, then it will be a good education and it will get its work in the use of it. Then according to it, education is growth, growth, according to it, education is a social practice. So growth means the growth of the individual and the society. Social process means that we will not leave the society and move forward, individual and social, we will talk about them. And the reconstruction of experience has been talked about. A very important concept has been given to us by pragmatism, that education is the responsibility of the state and education is the birthright of each individual. This was not said by any philosopher before pragmatism and today's progressive education, modern education has also come to our right to education, that education is the right of every child and the state will give us education. This point is given to us by pragmatism. So what is the overall effect of educational and indication of pragmatism? This is an experimental method, that is, learn from primary studies, activity centered, that is, learn by doing children, student centered, that is, study according to the subject, study from project method, do field trips, work in the lab, work in the library, problem solving, learn by doing it, learn from the study of the problem and co-operate with it. So we have given so many new concepts to us by pragmatism. So you can say that the whole modern education is based on pragmatism and more or less. So, this philosophy is of a lot of work, a lot of work. And today's society, whatever your work is good, whatever your work is bad, it doesn't have any value, so we do more or less follow pragmatism today. So this educational indication happened, your realism and pragmatism. So now you are idealism, naturalism, realism and pragmatism. You have the educational indication of all four, look at the characteristics of all four, you will understand yourself, what is the nature of it. So in this way, I have completed these two philosophies and their educational implications too. So thank you and don't forget to like and subscribe to my channel Explore Education. I have done from my side.


Jewish point of view, or we don't believe in the divinity of Christ. I think that there you can make an argument that the Gospels which were written he was just a prophet and significant. No, no, no, we don't believe he's a prophet What do you think he was? What do you guys think? I mean, I what I what I think he was historically I think he was a Jew who tried to lead a revolt against the Romans and got killed for his trouble Just like a lot of other Jews at that time who were crucified for trying to lead revolts against the Roman and got killed For their trouble Jesus was unlike every other man who ever existed his arrival and ministry was prophesied about hundreds of years before it Happened, but he was pierced for our transgressions He was crushed for our iniquities upon him was the chastisement that brought us peace and by his wounds We are healed Jesus was not merely a social Revolutionary or good teacher John the Baptist said behold the Lamb of God who takes away the sins of the world This wasn't an ordinary man. Jesus is Lord repent for your sin and put your faith in him today He will bring you from spiritual death into spiritual life. That's good news