So, I welcome Prasad Radhakrishnan to give his speech, as I said he will write occasionally on the board. So, those are the back if you have difficulty you can come forward to follow the lectures. Thank you for the invitation and thank you all for showing up. I hope what I have to say justifies your faith. So, I have I do not have very much to say I am going to tell you about one inequality. And we will try and prove that inequality and by the end of the talk hopefully you will see that you could have proved many such inequalities, but we will do this using a notion called entropy and I will tell you what it is. So, let me just get to the problem the Loomis Whitney inequality. So, I will draw some pictures, but what is going on there are n points in three dimensional space there is some n points. And I project them down and I see a certain number of shadows. I may not see n shadows why would not I see n shadows, because it could be that two points are one above the other and they cast the same shadow. So, that is there are n 1 shadows that appear on the x y plane. Now I shine the light this way and a certain number of shadows appear on this wall and that number is let us say n 2 and I do it that way I will not do any permanent damage. So, that way and then I see n 3 points on that wall and the Loomis Whitney inequality says that n 1 times n 2 times n 3 n 1 times n 2 times n 3 is always at least n square. Once again the picture is this there are n points here. I project them down I create n 1 points. I project them here n 2 points I project them back and n 3 different points appear. So, for example, if I had 10 points all lined up vertically 10 points all lined up vertically how many what is n 1 then sorry what is n 1 all of them are vertical I project them down how many points do I how many shadows do I see 1. If I project it that way or this way these 10 points give 10 I get 10 that side. So, I get 10 times 10 is 100 which is square of n. On the other hand if these 10 points were like this at an angle in a line, but at an angle then when I project I see 10 here 10 there and 10 here and then if I take the product of n 1 times n 2 times n 3 I get 10 cube which is 1000 which is more than 10 square. But the Lumis Whitney inequality says that you will never fall below n square and so maybe if my hand waving was not clear enough. So, here is I do not know everybody sees this differently, but there are 3 planes here and these beads are arranged in these 3 planes and there are 9 beads per plane. So, the if you project them sorry I have lost the picture, so if you project them somewhere you get 9 9 9 on each projection gives you 9 points and so the total number of points is 27 n 1 times n 2 times n 3 is 81 times 9 7 29 27 square is 7 29 the inequality survives. So, the question is so unlike the physics we are not asking about how why is this inequality always true and so how many of you are math Olympiad students. So, you probably proved this already and so, but I would like to introduce today a method by which one can sort of get a feeling for why such inequalities hold and that will be through information theory. So, that is the goal. So, here is so called proof of this inequality and so if I have n objects and if I want to describe these n objects to somebody how many bits do I need to describe n possibilities log n bits. If I have to describe something which is 1 among n things then I need log n bits. So, to describe a point you need log n bits to describe its projection on the x y plane there are n only n 1 possibilities. So, I need how many bits log n 1 to describe its projection on this plane its log n 2 and to describe the projection on that plane it needs log n 3, but n 1 log n 1 plus log n 2 plus log n 3 is giving me every piece of information twice. Why am I saying this if you look at the x coordinate of the point it is available from two projections. When I project down I project on the x y plane what information is lost when I project down which coordinate is lost of the point z is lost, but x and y both are available. When I project along the y axis y is lost, but x and z both are available in the other case x is lost and y and z, but nevertheless x the x value of the point is available from two sources. So, at least like heuristically this log n 1 plus log n 2 plus log n 3 is giving me every piece of information that log n contains twice. So, morally different people have different morals morally I should be able to write this inequality that is two log n must be less than log n 1 plus log n 2 plus log n 3 and by now. So, every logarithm is to the base two does not matter you exponentiate it you get this inequality.  Because there is this information what does information mean I mean is this mathematics and so we are trying to I will try to make sense of all this in the course of this problem. Question for now I am assuming Euclidean geometry, but at the moment when I say that I project x y z on to the x y axis I am just saying I am suppressing the z coordinate that is all.  So, the general idea I will like to address a philosophical issue about science and this is something which a famous computer scientist said about the p versus n p problem which you might have heard of, but this is not important. So, successful ideas in science are those that are pervasive and invasive are invitingly elegant and methodical are open to extensions and variants and answer an objective necessity and capture a widespread, but diffuse sense of dissatisfaction in a scientific community. Now, this notion of information was one such thing people use it we had information and quantum information even in the previous talk and you feel that there is something called information and, but you are not at least comfortable justifying what really information means if you get down to the mathematics and this was the situation when electronic transmission started may be in you know the early years of the last century and the one of the heroes of information theory Claude Shannon address this question and laid out what is called the mathematical theory of information and some parts of it I would like to introduce to you today. So, keep this in mind it turns out that this notion of entropy information etcetera it pervades many areas and there is always a way of thinking about various things in this information theoretic way and we will see, but for today I just want to prove the lumus vitni inequality using information theory I already gave you what the proof is going to look like the proof is going to be like this, but whenever somebody says obviously in the course of a mathematics proof that is the point to be suspicious yeah I mean if it was totally obvious you will usually people do not say obvious you know hence yeah, but then when they start using the word obviously it is a little shaky. So, this obviously here is what I am trying to formalize in the course of this talk. So, yeah and so somehow yeah it is customary to refer to two people in information theory one of them is always called Alice and the other is called Bob I mean once I gave a talk in Pune where Alice was I think Mastani and Bob was Bajirao, but it is usually Alice and Bob yeah. So, Alice observes an outcome of some experiment yeah x1, x2, x3, xn she observes an outcome of an experiment and she would like to communicate it to Bob. So, what does she do they both sit down in advance and they agree on a protocol. So, for example Bob says Alice if you see x1 send me 000 if you see x5 send me 0101 they come up with some arbitrary encoding codes for communicating the outcomes and their goal is that in the end Bob must find out what Alice observed. So, the encoding should be such that when Bob receives the message she should be able to he should be able to figure out what Alice really wanted to tell. Their goal is that they should try to encode these things with minimum number of bits because each time they transmit a bit over a phone or some other medium they are charged for the number of bits you transmit. Now this need not be communication this can even be storage yeah. So, we observe some experiment we put it in the computer's memory, but we might observe a color red and then we write down a set of bits into a computer. So, we would like to encode the colors using bit strings. So, that we can record our information with the smallest number of bits and. So, this notion of information transmission is a very important notion nowadays and Shannon studied what is the minimum number of bits that you need to encode n outcomes and here are the rules of the game Alice and Bob can agree on the code in advance yeah. What outcome will correspond to what code word the code words should be prefix free this is a slightly technical notion let me just tell you it is not a big deal. So, suppose I used a permanent marker or something. So, suppose I said red yeah is 0 0 and black is 0 0 1. So, suppose we both decide that whenever I see red I am going to say 0 0 and whenever I say black I am going to say 0 0 1. Now, this is not a good idea because if I tell you 0 0 now you wonder if a 1 is coming if a 1 comes then it becomes black otherwise it is right. So, this sort of coding is not allowed that is when the code word ends you should know that the transmission has ended. So, such codes are called prefix free. So, suppose this was 0 0 0 and 0 0 1 this is fine because when I see 0 0 0 I know that it is red when I see 0 0 1 I know it is black. So, they whatever coding they use it should be prefix free that is 1 code word should not look like a initial part of another code word and you cannot communicate by silence you cannot say that you know if I see red I will say 0 within the first second, but if I say if I see black I will wait 4 seconds and then say 1. So, you are not allowed to communicate using silence yeah I do not there used to be a old Hindi song may be from the 70s, but I do not know who remembers. So, you will be charged for top time even if you do not say anything yeah yeah. So, that is the rule that Shannon applied and then he asked suppose there are n possibilities x 1 x 2 x n then in the worst case how many bits must you communicate and many of you already said that it has to transmit at least log n bits because the number of strings. So, suppose Alice and Bob decide to use k bit strings they could encode one of the possibilities using all zeros one of another possibility all zeros and ones and one one one one one how many such strings are there 2 to the k, but he they have to accommodate n possibilities so 2 to the k better be bigger than n. So, k better be bigger than log n I mean nothing happened this is almost insulting to tell you this, but log n bits are needed. So, what did Shannon do Shannon asked well you know all my symbols are not equally likely yeah I mean. So, it is January and I want to tell my mother whether it is raining or not raining yeah the chances of it raining are rather low and not raining are rather high and there might be other n possibilities like if she asked me what did you eat yeah. So, you know it is unlikely that at this hour I would have eaten a samosa I mean at least I do not want her to know yeah. So, the possibilities there is a probability associated with each outcome it is not as if all possible all outcomes are equally likely and in that case should be still use code words for all the possibilities of the same length. One might assume that the outcome that is going to be transmitted more often should be given shorter code words and outcomes that are rare can be given longer code words and overall our goal should be to minimize the average communication it is as if this experiment is going to happen again and again and again and again and usually the high probability events will happen. So, we should try and minimize the encoding length for those high probability events for the low probability events it is ok if we assign them longer code words ok. And the question is can we save and how much can we save and may be an example yeah actually I was told that minister will be here and the organizers will appreciate the fact that I use numbers which sort of flatter the ruling party yeah. So, suppose yeah anyway these are numbers I made up. So, here are like four possibilities I mean I do not quite say whether it is for winning or losing, but you can yeah. So, the probability is 0.58 that it will be BJP it will be the Indian National Congress with probability 0.4 and these two parties yeah NCP and BCP. Now, I am observing this event somewhere may be and then I want to transmit this information who won. So, here is a solution we agree in advance that if it is BJP I will say 0 0 if it is Indian National Congress I will say 0 1 if it is NCP I will say 1 1 if it is BSP I will say 1 0 these are prefix free they are all of the same length no question of one being a prefix of the other. So, this satisfies the rules what is the communication that I will you know how many bits will I send on average well in each case no matter what happens I send two bits. So, per outcome it will be two bits yeah and suppose I have to do this reporting for all the constituencies. So, this experiment probably is going to be played out again and again let us assume independently. So, on average it will be two bits per communication, but you know I look at this data and say that assigning same length sequences to all of them does not make sense. It is okay if I could give this fellow a very short sequence meaning I will say that may be when BJP wins I will say 0. Congress wins I will say 1, but then I get stuck by some chance if NCP wins something what will I say if I say 0 0 that is not allowed because 0 is already taken for BJP and 0 1 cannot be used what did I say 0 0 cannot be used for NCP. So, how should I design the code so that nobody is a prefix of another yeah and still all events are covered and the total cost of transmission is minimum. So, here is may be a better solution and you can think about it this probably the optimal solution. So, what I will do is the party which has the highest probability I will assign a short code word for INC I assign 1 0 and for NCP 1 1 0 and for BSP 1 1 1 now notice that this is still prefix free this is very short, but there is no other word here which starts with a 0 yeah and 1 0 is shorter than these two, but these two start with a 1 1. So, this is a valid encoding of these four possibilities and if you compute the expected communication it is 1 with probability 0.58 2 with probability 0.4 3 with probability 0.1 3 with probability 0.1 you add this up if I did my computation correct it comes to 1.44 which is better than 2. So, the question is whenever you are faced with the set of possibilities and their probabilities you can always ask what is the amount of information that I get on learning the outcome and you can take a pragmatic view that let us declare that the information that you get is the amount number of bits on average that you need to transmit to communicate this information. So, here was this abstract outcome with possibilities and we are trying to quantify the amount of information in it and let us take this engineering approach saying that the amount of information in an abstract probabilistic system is the number of bits needed to transmit that outcome to another party. What is the best encoding that you can apply to that system of outcomes so that your transmission is as small as possible and that we will declare as the information you could do that, but mathematically it turns out that a certain formula associated with these outcomes is what Shannon called the entropy of this system. So, let me again I am using a slightly scary sounding word entropy and of course many of you done physics know it from a different point of view, but they are related actually. So, once again x is this set of possibilities x 1 x 2 x n and you have associated probabilities x 1 happens with probability p 1 x n happens with probability p 1 and what is the entropy of this system if somebody communicated the outcome here how much information did they give me and Shannon said measure the information by this formula. So, what is this formula? So, p 1 log to the base 2 for some reason because we are using binary log to the base 2 of p 1 and you add this up for each of these values once again. So, suppose all these values were uniform 1 over n 1 over n 1 over n if all of them were 1 over n equally likely. So, I would like you to tell me what this equation gives 1 over n log of 1 over n with a minus sign log n. So, our general our first idea that if you have to transmit some n things then you need log n bits that is strictly true only if all the outcomes are equally likely, but if the outcomes are not equally likely the number of bits you need to transmit might vary as we saw in the election example that we had. Then Shannon proposed that this quantity should be used for measuring the amount of information in a probabilistic system and by a probabilistic system I just mean this some number of outcomes with associated probabilities. So, it is a things alright so far. Now, why this formula what Shannon proved what is called the Shannon's first theorem is that no matter how you encode you will always need that many bits. How many bits you compute this formula this is a lower bound on transmission. No matter how you cleverly compute your prefix free code you will always have to send these many bits on average to communicate the outcome. Secondly you will never need more than this plus 1. So, this quantity it is mathematically preferable it does not capture the exact amount of communication, but it is within one of communication and then there are certain asymptotic properties that this formula enjoys which we will not be discussing today which makes actually this one also go away that is in the limit H of x is the true number of bits you need to send what limit what quantity I will not tell you today. So, is this clear? So, there is a probabilistic system n outcomes associated probabilities Shannon says compute this formula summation p i log p i with a negative sign in the front that formula captures the amount of information in this system and there are practical justifications why this formula is very important. So, this quantity H of x which Shannon defined measures the uncertainty in x or the amount of information you learn when somebody tells you about x and this H of x is a function of the distribution of x. You see if I change these numbers if I said that this p n was the probability or yeah so for example in the election example if I change this probability and then computed the entropy it will still be the same the entropy formula does not care what outcomes they are it just says what is the distribution of numbers of probabilities that arise. So, which make sense I mean we should not really care about what particular outcome the probabilities associated and it turns out that the entropy is never more than log n which you can sort of believe because you will never need more than log n bits to transmit an outcome which has n possibilities. So, these are facts about entropy I need to tell you one more thing before we can really do the proof of the lumus Whitney inequality. So, I am yes we are going to the next level now, but please ask there is lot of time. So, we talked about one outcome that is x 1, x 2, x n it was just x, but imagine that there are two kinds of outcomes. So, let me just give you an example this x 1, x 2, x n could be you know one of the participants in the Olympia. This y 1, y 2, y n could be the color of their shirt. So, I pick a person at random what is the probability that the person I pick is x 1 and what is the probability that they are wearing a color a shirt of color red or this person wearing a color of shirt of color blue and so on. So, these are the m people who are in this room these are the colors of their shirts and I am going to pick one person on a certain day and it might turn out that I pick person one with color red then this will be the probability. So, this is a joint probability of two things person color. So, all these numbers add up to one is this clear the total probability here I am going to pick a person with a shirt and it might be this, this, this, this or this and each of them has a certain probability and the total probability is one. So, we could compute the entropy of this joint random variable x y I have written x y please do not think of it as x multiplied by y x and y together x and y together how many possibilities does x and y together have m times n there are total m times n possibilities here one of them is going to happen. So, it is the same formula of Shannon this is the entropy of x y together. Now, if I ask this once I give me give this information there is also a distribution on x 1 to x m that is created what is the probability that I pick up this particular participant it is the sum of these possibilities. What is the probability that I pick x 2 it is the sum of these probabilities so I could compute the entropy of x alone ignore y compute the entropy of x alone or I could sum these probabilities this way and compute the entropy of y alone. So, this joint system has three kinds of entropies that I can compute the entropy of the combined system restrict my attention to only the person persons are being chosen at with various probabilities I could compute the entropy of the person alone or ignore the person and focus on the color of the shirt and that would give rise to a certain distribution that distribution would have entropy and these things will be called h of x y which I have written here h of x and h of y. So, what do we know so something called conditional entropy of y given x. So, there are various possible colors various possible persons and then I ask once I tell you the person how much uncertainty do you have about the color of the shirt for example if the person turns out to be me me then pink colored shirt is unlikely I do not have a pink colored shirt. So, whereas if it was all participants together I mean there are people who like pink shirts and it could be that pink is also a possibility. But once you tell me x the amount of uncertainty about y might change because it could be that you picked the person and that automatically eliminate some outcomes for y. So, Shannon proposes that the conditional entropy of y given x should be defined to be the amount of entropy that you originally had in the complete system subtract the entropy that you got by knowing the name of the person and the difference let us call the conditional entropy of y given x there are other formulas for this, but for today let us just call this the conditional entropy of y given x. So, what is the conditional entropy of y given x the amount of residual uncertainty about y about the color of the shirt that remains given that I know the person. For example, it was like the color of the Pagdi if you say Manmohan Singh color of the Pagdi always blue you notice. So, the entropy of the color of the Pagdi given the person can be become very small can be 0 actually there is no uncertainty if the person happens to be Manmohan Singh if it is some other person may be they have multiple color Pagdi's at home and they were one based on their choice for the good. So, anyway I hope you understand what conditional entropy of y given x. So, these are formulas that is if you condition your uncertainty only reduces originally when you are looking at the color of the shirt there was certain number of possibilities there was certain amount of uncertainty. If I tell you who is the person then the amount of uncertainty about y can only go down. So, this needs to be proved this needs to be proved because we have I mean intuitively it is all obvious if you give me more information y can how can uncertainty increase. But since we have committed to a formula to measure information we need to verify all these things, but this can be verified that is the entropy of y given x is less than entropy of y. Similarly, instead of 2 you might have 3 possibilities. So, color person color of the shirt material like cotton or I do not know what people were nowadays terry lane terry cot. So, the entropy in the material given the name of the person and the color. So, if you add give me more information your uncertainty can only reduce. This was the uncertainty in the material given only the person this is the uncertainty in the material given the person and the color. So, if you give me more information entropy only reduces these are formulas to be verified I would like you to accept them. Now, after having accepted all this we will go back to Lumis Whitney. So, let me erase the board yeah take me some effort. So, does it erase better with water or once again let me try let me try it is an experimental science mathematics. So, yeah. So, while the board gets erased. So, all right. So, we had these recall the Lumis Whitney inequality we had n points the projection was n 1 this way n 2 that way n 3 that way. There was no probability I mean we were supposed to prove this inequality there was no probability. I am going to impose a probability on this system just because I am comfortable with information theory and I know some inequalities in information theory and I insist that I use those inequalities to prove Lumis Whitney. So, I pick a point uniformly at random from these n points. Now, what does a point in three dimensions mean it consists of three quantities a point in three dimensions consists of three quantities x y and z. So, the entropy of the point p to say the entropy of the point p means the entropy of x y and z and what is the entropy of x y and z well how much uncertainty is there in x how much uncertainty is there in y after knowing x and how much uncertainty is there in z coordinate after knowing x and y. So, if I is this clear. So, I picked a point p at random one of the n points and I picked a point p here and the amount of entropy in this there were n points. So, the amount of entropy was since I am picking uniformly when I pick out of n outcomes uniformly the amount of entropy is log n. Now, I project it down and this point is my point p 1 and what relation does it have to p we have just suppressed the z coordinate projecting down means suppressing the z coordinate. That means it is just the entropy of x and y itself and the entropy of x y is entropy of x plus entropy of y given x this was our definition of conditional entropy conditional entropy was this minus this. So, this is actually an equality although I have written inequality this is actually equality actually all these are equalities entropy of p 2 is entropy of x and z. So, I have suppressed the y axis y coordinate. So, entropy of x plus entropy of z given x and entropy of p 3 is entropy of y and entropy of z given y. So, is this clear I mean nothing is happening. Now, let us compare the sum of these three quantities and this quantity h of x. So, I am asking you to add these inequalities h of x appears once here in this mass h of x appears how many times twice h of y given x appears once here it appears once here and once it is h of y, but we know that h of y is h of y is greater than or equal to h of y given x. So, the total contribution here is at least two times this one contribution is directly available another contribution is h of y this is conditional entropy this is full entropy full entropy is bigger than conditional entropy. So, this quantity is bigger than this what about this is h of z given x y this is h of z given x this is h of z given x this is h of z given y this is the amount of uncertainty in z I am just repeating myself amount of uncertainty in z after knowing both x and y this is amount of uncertainty in z after knowing x alone. So, this quantity dominates this quantity is more than this quantity because of some formula that I had written in the previous page this quantity also this quantity also dominates this quantity. So, what is the net result the total amount of entropy in these three points the entropy of p 1 entropy of p 2 entropy of p 3 is twice at least twice the entropy of p. Now, we have set up our experiment with uniform distribution. So, entropy of p is exactly log n because it is uniform what about entropy of p 1 well p 1 log n 1 well it is equal to log n 1 well it is a distribution p p 1 is one of these n 1 points, but it may not be the same it may not be uniformly distributed. For example, suppose the original n points were like this heap of points here then the points in the center have much more chance of occurring because there are lots of points over them whereas points around have lower, but it is some others crazy distribution on these n 1 points, but it has only n 1 outcomes. And if an experiment has only n 1 outcomes its entropy is at most log n 1. So, you so and similarly log n 2 and log n 3 which is what I have written in the next slide. So, by direct inspection yeah no calculations we observe that 2 times h of p is less than this term by term matching. And then this is equal to 2 log n this 2 is the same 2 this is log n because we by decree said it is uniform distribution we decide design our experiment that way. So, this is equality this is an upper bound on f h h of p 1 because if an outcome has only n possibilities it can have a entropy at most log n. So, this p 1 can have entropy at most log n 1 this is at most log n 2 this is at most log n 3 and now you rearrange this inequality and you get this. So, we started with what appeared to be some hand wavy argument where at some point we said obviously etcetera, but if you use Shannon's formula that obviously can be made rigorous and you can extract the lumis Whitney inequality alright. So, once again I would like to yeah. So, this formula captures the intuitive understanding of information we define conditional information in this way and there are just other justifications for why conditional information should be defined like this. The entropy is maximum when the outcomes are uniform that is the most uncertain situation and we justified the lumis Whitney inequality using basically these considerations did not really have to dirty our hands with actual numbers and fancy inequalities, but all that is hidden inside the fact that conditional entropy is less than entropy improving that somebody has done the hard work, but now you internalize it and use it yeah and now there are many other combinatorial identities and there is an excellent survey article by David Galvin and I invite you to look at it. Now entropy shows up in many places and in other context there are many other situations in computation where this sort of entropy makes its appearance. So, I will just you know flash the thing that I wrote before. So, it is pervasive it is invasive it is elegant I hope you liked that everything turned out neatly and it is widespread it does capture a certain dissatisfaction in the scientific community. So, I think Shannon should be one of the heroes of our time. My own I have found entropy in unlikely places for example, I found it in Mumbai mirror. So, about two years ago I tried to solve this puzzle you know I do not know how many of you read Mumbai mirror and I usually try to find the longest word and I found poetry and I was really thrilled poetry you know how often do you find poetry and, but then I counted and it did not include all the letters and I cannot you would not believe me I spent like about 20 minutes trying to look for the word and then it turned out that it was actually entropy. So, I have been after that saying that I used to be satisfied with poetry until I found entropy. So, I will be happy to take questions and of course only scratch the surface that I hope it was useful. I have one question. When does equality occur in the inequality? What type of distribution will give us the equality of the point? So, I think we can, so the lazy answer is that wherever we used, so there are some, so certain variables should be conditionally independent given certain other variables then equality will appear, but I have not pinned it down here. There are continuous, loom is witness inequality is actually a inequality in the continuous setting I have presented the discrete version that is if you have a certain volume in space then you compute its area and then you multiply the product of the areas it will be at least this. By the way suppose this was, so here is a quiz now since I, you have any questions? Yeah, question. Sir, the definition of Shannon entropy that you gave, that is a good measure of the information or rather the lack of uncertainty, but how do we reconcile this definition with our concept of entropy because in classical thermodynamics we have a certain axioms for entropy like monotonicity positive derivative etcetera. So, does it also have some analogs like this? So, actually I do not know that much about Boltzmann definition of entropy, but I think that also talks about log of the number of possibilities and in that sense it is the same. Now Shannon entropy if you repeat an experiment many times and ask where most of the probability resides it turns out that the number of outcomes grows exponentially, but the constant in front of the exponent is the entropy. It is the rate of growth after taking log, but unfortunately I would not be able to give you a completely precise answer about how this ties to the physics notion of entropy. Yes. Question, yes. I think this is along the line what the person asked, but this may appear very strange. So I understand you say information theory system nothing to be physical system as such, but I am following the idea of Beckenstein. Beckenstein proposed entropy for black hole out of the blue completely. Something strange happening in dynamics of black hole he said it looks like entropy we are familiar with and he was ridiculed. He was thinking now you are talking entropy, next day you will ask me what is the temperature? He said maybe yes I will ask you. Can I just say same thing now since you have entropy of a information theory system, can one associate. Can you take a temperature? Temperature, yeah some kind of volume of information and change in energy cost or something like that. Yes, I mean so there are those are studied in the information theory. I mean the word temperature is not used, but the derivative of the entropy and things like that are of consideration even here. Some kind of energy cost is there. Thank you. Any more questions from the students? What is the difference between entropy and information? Are they the same? You are using it interchangeably? For me it is the same. So given a probabilistic system the information, uncertainty, entropy, they are the same for me. Other questions? Same, yeah most disordered, but this is a measure of disorder, measure of disorder. So yeah, so question. I am not able to figure this out to get my head rounded. The equation you wrote for conditional entropy, that is right. So I mean the example that you gave, obviously the uncertainty depended on x. That is right. So how can you write something general? How can I write like that, yeah? That is correct. That is a very good question. Where did it go? Yeah. So yeah, thank you. So x has various possibilities. This is the person that we pick. And then once we pick a person, that person might appear, show up, wearing this color shirt, this color shirt, this color shirt, or this color shirt. Whereas this person always likes to wear shirts of only one color. Whenever you have two variables x and y, this is the picture you should have. Each of these branches has an associated probability with it. Each of these branches has what is called the conditional probability associated. Now if it is this person, if you ask what is the residual entropy, it is the log, it is the formula applied to this conditional distribution. If it is this person, it is this. So when I say what is the conditional entropy of y given x? You have a valid question. Which x? If it was this x1, the answer is different. If it is x2, it is different. If it is x3, it is zero, yeah? Because there is no uncertainty about the color of the shirt. So what do we mean by h of y given x? Stated that way, h of y given x is compute this entropy, compute this entropy, compute this entropy, and take the average weighted by the probabilities that you wrote here. With what probability does this become your residual entropy? With what probability that this become the residual entropy and so on? And that average, it turns out that with that definition, also this formula holds. So that is an alternative definition of conditional entropy. Now it is no more clear why the average should be less than the whole, yeah? I mean the, yeah, so this is when I ignore x1 and look at the average of these distributions, why should that entropy be more than this entropy? This is what is called, so this is because of the convexity of some function. So what is called the Jensen's inequality or something like that will be used in the proof of this, not a big deal, but you prove all that 70 years ago, yeah? And then keep using it, yeah? But I have a quiz, yeah? So suppose the same question, I did it in d dimensions. There were points in d dimensions, yeah? Project it, remove one of the coordinates, suppress one of the coordinates, I get n1, suppress another one, I get n2, suppress another one, I get nd, yeah? There are d such projections, my point will have, yeah? And there are n1 different shadows on this plane, n2 different shadows, nd different shadows. Now, the total number of points was n and I write n1 times n2 times n3, n to the power d, what should I write as the exponent here? And why? Because every piece of information, yeah? The x coordinate is lost only in the projection along the x axis, in every other d minus 1 projections that information is available. So every information piece of information that is there here is available d minus 1 times here, so you get to write d, okay? Yeah? So many such inequalities can be proved directly from considerations of information. Thank you very much, yeah? I have gone over time. Any other questions? Okay, if there are no other questions, let's thank Jacob one last speech and both the speakers of this morning, thank you. And right now we have a break, a tea break outside and then we come back for the formal award function at 12 o'clock.


Now, let's look at what are the other interfaces that this router has. So, the other interface this router has is something called Gigabit Ethernet 0 slash 3 slash 0 which is this interface and IP address here is 1 dot 6 dot 1 dot 6. Now, this IP address as we saw in that slide does not belong to the private IP addresses. All the networks that we saw inside the campus were private IP addresses which anybody can use. So, any college which is trying to establish its own network could use any set of those IP addresses because they will be communicating only inside of the campus which is. So, inside of this router all those all these devices will have their own unique addresses. Now, as soon as the communication leaves this router which is which connects the campus to the internet it gets a globally routable address which is 1 dot 6 dot 1 dot 6. Let's look at the rest of the network. Now, what we see here is here is a router which is basically the internet service provider at Mumbai which connects to another router of the internet service provider in Delhi. So, here we have four routers which connect to the internet service providers of the relevant cities as we saw in our hypothetical hypothetical situation here. So, this basically becomes something like the backbone of the network in this topology and here what we have is another network. So, this is a network of a hotel a smart hotel I would say because this has something called the home gateway and internet of thing based devices like these lamps the door and this air conditioning and heating unit which could also be operated over the internet. And that is one of the beauties of packet tracer that it allows you to experiment with all these kind of devices. So, here we have another network of a company and another network over here. So, something interesting to look at here is if we look at this router and try to see what are the interfaces this has so, it has 0 slash 0 slash 0 0 slash 0 slash 1 and 0 ok this one is switched off let's look at this one this one is also switched off. So, here what we see is here it has a private address and here it has a globally routable address that means this is the edge router for the company and this company now has a remote site within that city which is maybe a different building in a different place in the same city, but it connects to that office through its edge router that means all the communication here first has to come to this building router and then only can leave to the internet. Now, why do this this could be because of a lot of reasons it makes it easier to implement company policies and it makes it easier to see what kind of communication is going over the internet. Now,


Hello everyone and welcome to this Moodle Academy webinar on facilitating Moodle forums, very pleased to welcome you today. So I am Mary Cooch, Education Manager at Moodle Academy. It may say Academy on the webinar, but I am in fact Mary Cooch, I'm not the whole Academy. I will be doing the presenting here and I have alongside me Anna Kraser who's going to be monitoring the chat. Would you like to say hello Anna? Hello everyone, nice to be here today. Hope you will enjoy our session. Okay, so let's get started. We do want this to be an interactive session. So it's not just going to be me talking and then Anna replying. We are going to ask for your experiences and your opinions. And I always like to begin by saying not only what we will be discussing, but what we are not going to be discussing. And it's important to realize that this webinar is at an intermediate level. It's for people who are experienced using Moodle. So we're not going to be showing you the technical side of how to set up a forum, enabling editing and so on. We have our Moodle teaching basics program for that. So we're going to look at it, not from a technical setting up point of view, but more from a pedagogical point of view. So we are going to be discussing how to, and I'm reading from the slide here, initiate, promote, encourage, optimize, monitor, moderate, facilitate, basically make the most of a forum. And you know the title is facilitating Moodle forums. In fact, facilitate, which is the word that I've put in bold on the slide there. Facilitating and moderating are two terms related to forums that are sometimes used interchangeably. I know I do it myself. If we want to be pedantic, there is actually a difference, although in our webinar, we're going to be discussing all of them. So just to be precise out of interest. So a forum moderator, when we're talking about Moodle forums, this is actually an actual role. Usually the editing teacher, but it doesn't have to be, but it's a role that has permissions. A forum moderator can edit other people's posts after the time. They can split them if they're going off topic. They can delete posts if they're inappropriate. And they can also send private replies to people who post that are not visible to others.  Whereas a forum facilitator, now they can be the same person and they often are, but they don't necessarily. So a forum facilitator is more of a nurturing or an encouraging role. So their role is to engage and encourage the participants in the forums and also to ensure that they stay on topic and that they don't say anything inappropriate. And all of these are things we will be covering in today's webinar. So let's get started. We have chosen to use a forum in our Moodle course. And the first thing we'd like to look at is why? What is the benefits of a forum over other activities? And we're going to briefly look at the different types of forum, not as I said in terms of setting them up, but what are their advantages and why you might be interested in them. And then we're going to also ask for your opinions too. My point of view that the best reason for using a forum is that it's asynchronous. In other words, it gives you time to think it's not like a live webinar or a live chat or a big blue button activity where you have to respond immediately. When people ask you a question, you can read it at your leisure, take time to reflect on your response and then reply. And forums also work very well in terms of inclusion. So universal design for learning suggests that we should give people different ways to respond. And in a forum, as we'll see, you can type your answer, you can record your voice. If you're brave enough, you can even use a video. Moodle, social constructionism and a lot of Moodle works around that is the basis of that. And certainly discussing things in a forum is part of that community building. You can add a search forums block and you can easily search through forums. And also one thing that I like that's not the usual use of forum, but it does help with basic sharing of activities. If you want your participants to share a file they've done, a document they've done, they can simply attach it in a forum. And you can also use it for easy peer review. The workshop activity is the best activity for peer assessment if you like, but you can also do it at a lesser, simpler level using a forum. And not only peer review, but peer support. So if you have a forum where people are asking questions, it doesn't have to be you, the teacher, answering. Obviously, their learners can answer each other and support each other. But alongside that, we have the announcements forum, which is a forum, but it's not quite, isn't it? Because it is for the teachers to post notices and it's not really for discussion or replying. But if you need that teacher led element, you also have the announcements forum. So we definitely want to use a forum. Which type will meet our need? If you don't do anything, you will get the standard forum for general use, which allows you simply to, which allows anyone to add a new discussion and reply to other discussions. But it's worth exploring the other types because they might meet different needs. When I was a high school teacher, which I was for 20 years and we started using Moodle in 2006. I used to often use a single simple discussion because basically it keeps the learners focused on one topic. They can't start another discussion on something else. They can only reply to what the teacher began. Now my favorite type is each person posts one discussion because this works very well for the sharing or the peer review and so on. You each have your own discussion topic, which you own, if you like, in the forum. Q&A forum is also very useful. I have an idea. Anna likes this one in particular ask her in a moment where a learner cannot see the responses of others until they've made their own contribution.  And then I've separated it because you don't really reply or discuss in it, but announcements is very useful. So these are the forum types and we've explored why we might want to use a forum. I'm actually going to now pass it over to you. Please would you like to type in the chat, which are your favorite types of forums or which ones do you not like? Why? And I'm also going to ask Anna if she'd like to comment on what she thinks about the different types of forums and the benefits of forums. Well, yes, as you said, my favorite one is I think the Q&A. I might use the standard forum, I think, like everybody mostly, but my most favorite is the Q&A. Because I have my experiences from corporate environment where the collaboration and the communication between people was very highly appreciated. Yet people wanted also the original ideas, the original solutions in some case studies. And so the Q&A was the perfect tool because participants had to serve their original thoughts and then had also the chance to collaborate and communicate with each other. Meanwhile, I can see we have some messages in the chat. So John says that I have explored the different types, but usually goes for the standard one. Brenda also mostly for the standard with some Q&A were appropriate. Yes. Actually, I like turning on also the grading, the rating in Q&A. So Salome says replying to, I have explored the, so I guess replying to, it's like a single, simple question. Single, simple discussion. Single, yes, discussion, yes. And Brenda says the ratings are very useful in forums. And I think that so the comments we have so far. Okay, now ratings is interesting because we will be talking about that later on actually, Anna. Oh, John says that she has never used the ratings. Now that's something very interesting to see. Yeah. And also grading as well, although we're not going to go into detail on that, but not only can you rate forums, you can also grade them. So let's move on then. So we've decided in our course, we're going to use a forum. We possibly decided the type of forum we want. But before we do anything, we really need to consider a code of conduct because even if we have mature adults, it may well happen. That something is said inappropriately, or there's some unsatisfactory behavior in our forums. So I'd like us to think presumably on your site, I'd like to believe that you have a general code of conduct for participants who are engaging online. Does this include forums? Do you have a forum code of conduct just for your course? If you do, if you do, do you actually agree this with your learners in advance of the course? I've had experience of courses like that online. Or is it something that either you, the teacher or your organization hierarchy impose on them, the kinds of information. So the content. Now I could give you a couple of examples before we ask your views. So for example, the two courses, the two sites where I am most active, Moodle.org. This is our global site where we have over 30 courses, which we call communities full of forums. And obviously in many different languages, many different types of people. So in our site policy, we have the forums code of conduct. And you can see this if you go to Moodle in English, it's right at the top in the hope that people will read it. And it's quite wordy. I'll just show you some of it. I'm not going to read it all to you. But this is a special case on Moodle.org because we have many questions and answers, people coming to help ask for help solving their problems. So for example, we ask you, I'm reading from the slide here, choose an informative subject line. So it's very difficult if someone with a problem comes and says, help or urgent because that doesn't tell us what they want. And maybe if we're in a hurry and there are lots of posts, we're going to ignore it. The same could also apply in your own course. It's not particularly useful if you just have a one word and non descriptive subject title. Something else also is to try and present facts and background in your post rather than just saying, I can't get this to work. This is terrible, which does sometimes happen. So that's specific to Moodle.org. We also on Moodle Academy, we have general discussion forums in each of the courses. They're not monitored, but we do encourage people who join the courses, perhaps to support each other, as mentioned earlier on. And we have a code of conduct here. And one of the things we ask is, for example, only post meaningful and relevant content. And every now and then we might get people who will come and post in a course. Our course is our self-paced and they will and they will post high as a subject title and high in the description, which is it's not unkind. It's just it's not particularly helpful. And if we get a lot of those, they can clutter up the course page. One thing that I will add before I move on to ask you for your thoughts on this is when I did a masters on Moodle. One of the things we were asked to do was to make sure that we typed our forum contributions in correct grammar rather than using text speak or WhatsApp messaging abbreviations. That was partly because our forum post formed part of the assessment. But that's something else you might have in your code of conduct. So first of all, I'd just like you to give me a quick yes or no. In your organization, do you agree on a code of conduct with your course participants type yes. Or if no, because maybe this is a code of conduct that you've decided or your organization has decided or maybe don't even have one, then say no. So I'd like to know how many yeses, how many noes and I'll ask Anna to monitor that. And then as people are typing whether yes, we agree with our course participants on a code of conduct or no, we don't. I'd also like to ask Anna and also you, if you'd like to make your comments. Do you suppose a conduct? Usually in corporate environments, there is a wider policy and corporate code of contact on how we communicate, how we do things and how the behavior is. But I have a very interesting experience to share, which is not from a corporate environment, but it's from my primary school. And that was amazing. It was a collaboration between two schools that were in a distance that they were collaborating on specific courses and they built together the code of conduct. And I found this absolutely amazing because it teaches help learners, students, young students to actually collaborate and be ethical. So they were nurturing this idea of code of conduct and of, you know, the right way of communicating. From the chat, let me just go quickly. We have like five yeses and one, two, three, and five noes. In the audience, these are half and half. I don't know if someone would like to share a specific case where you use a code of conduct or no. Or if there's anything in yours that you think might be of interest or helpful to other people, for example. Like, do you insist on correct grammar and no abbreviations and so on? Or that's my particular example. Well, in my experience, both in the primary school and the business environment, the answer is no, because the corporate academy was international. So language was not considered to be the main point of the work. It was just a medium. And also in primary school that could be considered, but because they didn't want to de-hearken young learners and their focus was based on something else, they didn't pay attention on that. Now, Karla is saying that in my case, I'm executive director at NGO, and we set up previous agreements of what we commit to and what we expect from participants. That's good. And John says, our participants speak a variety of languages, so we don't expect perfect spelling or grammar in English. Yes, that's common case. Brandon says that ours is informal. The four PSI agreed on before we start the course. We discuss preparedness, punctuality, presence and participation with a group of adults. That's really interesting. Okay, thank you. Another message from Muzman. As a drug post-pozology seed, better it's short, better it is. However, the shortness is a handicap, namely with big group in academic level. We try just to rely on self-responsibility. I can understand this. Yes, a long set of guidelines are not very appreciated by learners. Often they are just bypassed. Yeah, absolutely. And incidentally, on Moodle.org, we don't have any kind of rules about how you should write your messages, because again, we have many people whose first language isn't English and it's just communicating. That is the most important. And I want to say, I often see on Moodle.org people posting forum posts. And the first thing they say is, I'm sorry about my English and I will always go in and say, no, do not apologize. You are better than many other people that you speak more than one language. It's absolutely fine. So never apologize for speaking a foreign language. Okay, shall we move on? Yes, yes. Right. Now we've got our code of conduct. We've set up our forum. We're actually starting a new course, perhaps with some new learners or a new module. I'd like to briefly think about this concept of icebreakers. And I have to smile because for the first time in my life, about two weeks ago, I visited a real actual icebreaker in the literal sense. I was in St. Petersburg and it was a museum on a ship icebreaker. But what we normally mean as we do now an icebreaker and breaking the ice is when you have an activity to make people feel more comfortable who haven't yet met before. So you might have these activities in a face to face course meeting or online, just so that people can get to know each other. And I was wondering how you feel about using icebreakers like this in your forums, whether they should be obligatory or not, and the kinds of activities you might do. I can give you two examples. On that we've always liked when we used to have a learn Moodle MOOC twice a year, we ran a global MOOC to help people get to learn how to teach with Moodle. And when we did one online in the pandemic, we realized that no one could actually leave their house. And so as our icebreaker, we asked people to post pictures of what they could see from their window, which was a very good way of promoting discussions and getting to know people. And different people around the world posted different weather, we had snow, we had sunshine, we had a lot of pets and so on. If people weren't in a way didn't have a window because they were in a basement, they would post a picture of a picture that was on their wall or a notice board, for example. That's just one nice icebreaker. Another one that I've used, and in fact, I was a guest speaker in a teacher training session in Sri Lanka last week. And for their icebreaker, they were using the Two Truths and a Lie, which is a very simple activity in a forum where each person says three statements, two of which are true, one of which isn't, and then you wait a short while and people try to guess which one might be true, which one might be the lie. And then after a certain period of time, you can give your response. It's always useful if you, as the teacher, give an example as well. So just two examples. I'd like to ask you then, do you, I was going to say as well, that if you're going to do this, again, because of the way forums are set up, you don't have to type your answer. So here we've got student Mark, and this is an example, it's not a real one, who has decided he will video his Two Truths and a Lie. You can also, from the editor, you can press the microphone and you can record your voice, but not show your face. So you have different options to present what you want to say in the forum. But should an icebreaker be obligatory or not? Do you use icebreakers? What kind of activities do you use? I'm going to pass it over to Anna and then to you in the chat. Well, people is typing my experience. Well, it's not exactly obligatory, but I mean, an icebreaker won't be prerequisite for the course to be completed. That's for sure. But I usually put a requirement of one post to be added or two posts or discussions to be added. So there is some kind of notch to start from there. And I think that we don't have to force people to participate in the icebreaker. Icebreakers usually are the most easy going forums with the most participation. As long as you have a clever or a funny subject, I often found very attractive forum discussions to be revived, even not as an icebreaker, but as nudge during the participation. And just by posting a nice cake or a coffee that everybody loves. So it was a nice discussion of how you drink your coffee. And it's something from the everyday. And another great example that I've seen with with icebreakers was an idea that teacher was sharing three songs of different types, completely different types said which one would you choose. Now that was really clever because, you know, the music that you listen to and you enjoy actually reflects something from your own personality. So it was really, really clever to help people meet each other. Now, Alex says that they use icebreakers but it's not obligatory. John says I used icebreakers when I work with young people but not so much with adults, although it would be probably useful. Christina says I love an icebreaker at the beginning of a course. I asked students high school and university to take a picture of their shoes and set a favorite memory that occurred while wearing them. It helps me and their peers get a sense of who they are and help us start building community. That's amazing. That's very original. Yeah, now I'm trying to think of my shoes and something that happened to me when I was wearing them. Really clever. Thank you, Christina, for saying it. Brenda says yes, I have used the what do you see outside your window in an introductory asynchronous forum. For live session we use waterfall a lot. For example, ask a question then everyone types the response and presses enter at the same time. A waterfall of responses. Okay. That's nice, never heard that before. Hayat says reacted to I love a nice breaker with. Okay, there is a reaction with clap. I see reactions. Okay. Aaron says I love the photo of Susan the memory was wearing them. This is a wonderful idea indeed. And okay, I was a little bit confused before with the reactions. I see people is reacting in the forum messages, the chat messages. But we are ready to move on I think. Okay, so let's assume that we've broken the ice we have our participants engaging in the forums and some of them have asked some questions. The next thing to think about is something very close to my heart actually. And that is the response time in other words, you as a teacher you're monitoring your forum and you see that some people have asked questions but have to have a problem. How long before you feel you should reply how long before you feel you should acknowledge a post in a forum. And the reason I'm asking this is because this is a major fault of my own in many ways in that on moodle.org people do post problems. And I'm there all the time and I'll sometimes answer within a few minutes. And although they might be grateful that we have helped them with their problem. In terms of community building a forum community. I've actually prevented other people from from replying who might have known the answer but perhaps they needed to spend a bit more time phrasing it because English wasn't their first language. Or perhaps they just didn't see it because I'm virtually looking at the forums all the time. So is it a good idea to give a prompt response. When do you think might be the optimum time in order for other participants to reply. And then for you to reply should it be you the teacher. When I did my masters again and as part of the forums code of conduct or whatever we were informed that our tutor would aim to reply to any forum posts within 24 hours. Which is slightly longer than my within five minutes. But is there a good balance in between. So I'd like to ask you how how do you react to that. Maybe your forums are only for participants to reply to. If it's a forum where there are questions. When do you as the teacher or the course manager. When do you reply. You do a lot of this. So what's your experience is best. Well as you said usually in corporate environments the 24 hours is the expected norm I would say. But it's also depends on the course depends on the users. Typically mood will have these 30 minutes delay for the forums. The form was to be posted so you cannot really have a very quick response. You cannot stay there and be around waiting for a response to your message or to your question. But it's always good to to give some time to other learners. Contribute especially if your course is based on collaboration. If the course is based on peer interaction. And if that's your goal then you have to step back as an educator I think and wait. Let's see. Well hi it says that it depends on the importance of questions and the type of forum. Makes sense. Brenda says that I usually set an activity completion condition that after posting a participant should also reply to at least X other responses. I come in where appropriate and necessary. This really increased interaction I guess Brenda Elizabeth says no Elizabeth reacted. Usman said that in the case of my hybrid course I have to give all the responses prior prior to the next face to face session. Yes yes so yes I guess everybody is adapting based on the needs of the course and the learners which is the right thing to do I guess. Indeed okay. Shall we move on. Now we were talking about adapting to meet the needs of the learners and how sometimes it's better if you step back as Anna says to allow the participants to contribute themselves. And this is something that I want to move on to now in terms of what I would like to call. Nurturing and so if you remember the definitions of a forum moderator and a facilitator facilitators role is that of nurturing encouraging time to engage the participants to participate in the forums so I'd like to look at how you can best do that. Perhaps the way that you use language in whichever language you're using and then also in terms of motivating them what we can do with things like ratings and rewards and so on. So I'm going to talk first of all about something which I used a lot as a high school teacher, which is the sandwich method I know this looks like a burger. It's supposed to be a sandwich but I'm sure if you've heard of it before you understand what I'm saying which is that if you need to give feedback. Then and if there is something that's that's perhaps not right, or that is perhaps you're not comfortable with, then it's always a good idea to sandwich your less comfortable thing in between something that's more positive. So you will start with thank you for that forum contribution and I'm glad you took the time to reply. And then in the middle you would say, perhaps you might think again about your comments about such and such an issue. And then at the end you will say, I'm looking forward to seeing your, your, your modified contribution or looking forward to seeing more from you. So you're couching your sandwiching the thing that needs improving the slightly negative thing in between. Now I believe this is a cultural thing because my understanding is not all cultures think that this is a way to do it and that you should just be direct and say, this isn't any good. You should improve on this rather than this polite sandwich making, but it's one way that some people try to nurture and to engage people in forums. If your forum is one where there are discussions taking place, that there are debates, it's always useful, I think, to ask open ended questions rather than close questions where it's a yes or a no or a don't know to kind of phrase them by saying, well, what do you think about? Why do you think that? Or even in a conditional, what would happen if such and such or what is your experience of? All of these are forcing the forum participant to actually write or type or speak more than a simple one or two word answer. And you can also use these, of course, if you have issues where the forum discussion gets quite heated and goes off topic, you can politely say, yes, now we've discussed that. So let's go back to our original theme or so returning to our original theme and gently bringing it back. Now, we will look shortly at other ways of dealing with when people go off topics. But if you can couch your language in a subtle way, that can also help in this nurturing. Now, many people also are encouraged if they get a kind of a reward perhaps. So what are your thoughts on ratings? So here we have, for example, average of ratings, and it's very easy to set up ratings in forums. But how useful is it? Do you think on moodle.org? We have a one word rating, which is useful, which someone can post if they think a forum post is useful. And in actual fact, if you get a certain number of useful posts, you can become what we call a particularly helpful moodler on moodle.org and have a badge, which many people are proud to own over the years.  I know we on moodle academy, we give badges for completing whole courses, moodle role management, one of our recent new intermediate level admin courses, for instance. And although we don't discuss this here, because we do have a course on assessment, looking at forums, you can in actual fact, you can grade forum posts. You can show the number of words that people have posted, and you can use grading even with rubrics on forums. I wonder if anyone actually does that. How motivating is this? I have never done it because I've always wanted my forums to be an area where people feel comfortable. But it'd be interesting to know now, how you go about nurturing, engaging, motivating in your forums. Well, I think I will start until everybody else puts their thoughts in the chat. On the contrary, I have to say that in my case, I almost always rate forum posts as a completely different approach. And that's because in corporate environments, forums are excellent tools for assessment. And if you see the forums from that point of view, they are so powerful because you can rate a post and grade forums normally as any kind of assignment. And at the same time, allow participants to interact and learn together. So it's not just a communication. It's much more than that. Through this prism, I found amazing the fact that we can easily set up assessment and use specific scales or create our own scales to assess things. And sometimes, assessment and rating can be just a reward. For example, in a primary school environment, when you want kids to start writing thoughts and practice, you can just create a positive scale. It doesn't matter what it is. You can use emojis instead of words and create a scales with fun little icons that will be like the stickers often teachers award to the learners. So I'm very, very fond of the ratings and the possibilities that can have. Let's see in the chat. Usman says that, you know, that was the previous hour says that we haven't used ratings. However, we have tried highlighted interesting forum responses in a weekly roundups. That's nice. Yes. So Brandon says that as participants to each take a turn to facilitate that forum, huge improvement in focus. Also, symbol rating of zero one or two, where two would be for a meaningful contribution, one for somewhat useful and zero for a greeting or affirmation without contributing to the discussion. This could would count towards a participation mark. Definitely plus one for this Brenda. I can, I can confirm I have tried and it worked really, really nice. And just to point that you mentioned already just to clarify that we have another course in the Academy about assessment with forums. Well, you can see a lot of ideas. A lot of ideas that could be interesting about this specific subject. And I think we are ready to move on. Okay, thank you. Actually, it might be useful posting the assessment with forums link in the forums course in which this webinar is found so that people can easily get to it because I think it complements nicely. This this course. So we are in the middle of our course where we've got people contributing to our forums. We've been trying to nurture them as best we can and encourage them as best we can. But unfortunately, despite our best efforts, we are still having we are still encountering some problems. And these problems is irrespective of age or maturity or whether it's an educational establishment or a commercial corporate establishment. Sometimes they occur. People might, for example, go off topic. You might start with a nice discussion, but then people go off and talk about different things on tangent. Occasionally, and we've unfortunately had this on Moodle.org, flaming where people are posting things in the knowledge that they are going to cause controversy. Maybe they just want to be difficult. Sometimes people disagree and that's fine. But if it degenerates into something more heated, you as the forum moderator and facilitator, you need to deal with that. And then spam. Now spam, that is probably an issue if your site is open to the world and people create accounts. But again, these are all issues which need to be thought about on Moodle.org. So we do have some moderator guidelines for the people in each of our communities who look after the forums. We can't facilitate or moderate all of them. So we have particular guidelines in terms of unsolicited advertising. I'm reading from the screenshot here or spam. On Moodle.org, we have a reporter spam link that people can alert us to. But it's more difficult when you get issues relating to people having a disagreement, for example, that becomes more heated. If it's someone who's brand new, who's very new to the site, it might be that they joined deliberately and we might need to politely remove them. Remember that as a moderator, you have the possibility to send a private reply to someone so you could privately reply saying perhaps you should tone this down a little bit. Also, you're also able to go in and edit someone's post. So we have done that. Aurélie Soulier, who is community engagement lead. Helen Foster, who has done this role for many years and myself, we can go in and we can remove unsatisfactory or inappropriate words. Aurélie has also actually met online with some people to try and discuss why there is a problem and gently encourage them to calm down a bit. You could also temporarily suspend someone. But these are all different methods of dealing with it. More difficult than if people go off topic. So if you're gentle, let's go back to the original theme doesn't work. You can, of course, as a moderator, you can split discussions. But I would like to ask you for your thoughts on what approach do you take in your organization? So on Moodle.org, because we want to encourage our community, we take a subtle approach. We try to just get people to understand the errors of their ways rather than just simply banning them for one wrong thing. Or are you in a place where you have to be very tough? So a quick question. Yes, if you prefer a subtle approach, the way that we do know if it's no, no, you are out, right? You are punished or some kind of reprimand. So a yes or no, please. And while you're doing that, I'm going to ask Anna, perhaps what Anna's thoughts are on in terms of approaching problems with forums. Well, in my experience, I never had cases where we had to ban someone from the forum because they were environments where nobody had a reason to react like that. They weren't open forums for where someone could come in and just start flaming or create noises. They were meaningful and concentrated to some learning. So in, we never had such cases. I mean, I've never had this problem. But one thing that I'm always suggesting to facilitators or moderators of forums is to do not be afraid of getting involved. A split discussion if the topic goes away. Don't hesitate to reply privately to help learners get back on track. Because one family post could be a very interesting post on a serious discussion or a debate could derail the whole discussion and ruin your course. So in such cases, of course, you need to remain a government polite. But you shouldn't be tolerant with these little things. You can put them in another place and get back the class into the focus. And I see that. Okay. We have an anonymous. Yes. That's great. Yes, definitely. I agree. I suppose my experience is mainly from Moodle.org, which is open to the world and anyone can make an account. And so there are more possibilities of problems. My other experiences within a high school where we did occasionally get problems. But it was interesting because in one of the forums when I was a teacher in a high school, some students were making inappropriate comments. And one of the students said, you shouldn't do that because you know the teachers are watching these forums and they will come and find you. So I thought, yes, self moderation also. They are aware of it. Okay. Now, I think this is all that I wanted to discuss. We've hopefully gone through from deciding to use a forum, choosing it, having our policy and so on and trying to encourage and then solve problems. Is there anything else in general that any of you would like to comment on before we wrap up or finish this webinar in a few minutes on the hour? Anything else anyone would like to say in particular? And if you do miss something, please do comment in our general discussion forum in this forum course. Well, it seems, okay, Elizabeth said that tips on policy subscription is optional. Usman asks, just take the advantage of teacher fear to deal with the big group. Yes, that's, yes, that's clever. Elizabeth, yes, subscription is optional. Subscription is forced. This is, I think it can be a discussion on so on, especially when you contextualize it on specific courses and learners. It always depends what you want to do. But my comment would be just to explain learners why this forum has forced subscription and why this forum is optional subscription and explain them how they can unsubscribe. Really, this is something that is often bypassed by teachers. I can see that a lot of learners get upset with a huge number of emails coming in there and they feel like being spammed from the course. Well, before we finish, I'm actually would really like just to point out to you a few things about helping us to to grow Moodle Academy and get involved in Moodle Academy. One of those is please come into this, the course facilitating Moodle forums and look at the activities if you haven't already. And also by all means go and have a look at and do the assessment with Moodle forums course, which I think Anna has posted the link in there. And if you have any ideas for future webinars, please suggest them in our Get Involved course. We have been running webinars based on people's suggestions and also perhaps you have a good idea for something that you have experience in and you'd like to volunteer to contribute to a webinar. We would love you to do that. I'm going to get a presenters badge and you will help give Anna and me a little bit of a rest while you do the work, please volunteer. And also perhaps you enjoy writing courses on a particular aspect of Moodle and teaching and you're welcome to contribute and sharing in creating a course and get a course builder badge. And in terms of the wider community and promotion, please tell your friends about Moodle Academy, get badges and share them on social media to help us grow. And if you are an experienced Moodle educator, then why not take our quiz to check if you're ready to do the Moodle Educator Certification Program, which is a very, very strong program for experienced educators.  So that's all from us. And I'm just going to say thank you from me, Mary Cooch. Thank you for me, Monica, Sam. See you around. Bye bye.


the Father and the Son of the Holy Spirit. So Team Grace, we continue our homely series on mercy, and during this portion of ordinary time, as we end this series, it's important for us to go back to the figure of St. Joseph. As we end ordinary time, this Wednesday as we enter into Lent, it's helpful for us to go back to St. Joseph. We spoke about Joseph last week, and again it's important we go back and see what else can we learn from this Holy One, from this Patriarch, this great Father in our faith. It's particularly good for us to look at the consecration to St. Joseph, a very popular devotion. And I'm going to encourage you to make that consecration to St. Joseph. As soon as I say that, perhaps multiple questions might come up. For example, what is the consecration? Can anyone make it? Why is it important? What does it involve? What's my commitment? And how can this really help me or my family? All great questions which I'll address in the homely. So first, what is this consecration, and can anybody do it? Let me answer the second part first. Not everyone can do the consecration to St. Joseph. What? I thought everyone could do it. No. Only to baptize. You must be a baptized Christian before you can make the consecration to St. Joseph. But why? Because dear friends, baptism is the definitive, foundational consecration that we have received by God the Holy Spirit, in Christ by the power of God the Father. In baptism, the Lord Jesus has wiped away all our sin. God the Father adopted us as his own son and daughter and we've literally became a member of the body of Christ the Church. No devotion can compare with that. And all devotions in the life of the Church are in service to that consecration. So why is the consecration so important? Because it helps us to live out our baptism. It brings a new dynamism into our baptism. It allows us to fan into flame what we have received by the power of God. But we have to be baptized in order to be able to make the consecration to Joseph. Because we don't have our baptism. The consecration to St. Joseph can do nothing. It relies on the strength our identity that we have received by baptism. Look at our Gospel today. That leper was so dirty. Was not allowed to be in the community. Had to be kept outside and had to yell to his great shame, unclean, unclean. And the Lord purifies him, consecrates him and calls him to obedience. Tell no one. And what does the man do? He takes the consecration and he goes and he willfully disobey the Lord. Announcing to everyone what was done. And the Gospel tells him he hurt the public ministry of our Lord. Jesus was not able to enter into some villages or towns because of the disobedience of this man. We have been purified and consecrated by baptism. Are we living a life of obedience? Are we seeking to listen to the ways of God and to follow his path of love? We need baptism to help us do that. We need the grace that comes from baptism in order to strengthen us. And dear friends, this is where the consecrations and the devotions of the church come in because they help us. It's good to consecrate ourselves to our Lady and to St. Joseph. It's good to have these various novenas and acts of piety that the church gives us from her treasury in order to strengthen, to enhance at baptism what we have received. But we have to be baptized. That's why as you walk through the preparation for consecration to St. Joseph, your task your principal task will allow this consecration to make your baptism take deeper root in your souls, in your hearts, and in your actions. Let me just take a quick aside. Would it surprise many of you to learn that the number one goal of the Second Vatican Council was to strengthen the baptized to be good disciples and strong witnesses in the world? So many people have taken Vatican to misinterpreted it and they are so worried about coming up here and doing my job. You are not many priests. You are the baptized of Jesus Christ. You have received the dignity that is beyond this world. And that will take you into eternity if it's lived well. And the whole task of Vatican II was to help you understand and appreciate what we have received. We claimed that inheritance. Good Pope John St. John the 23rd looked out at Mother Church and said, it's getting stuffy in here. We need to open up the windows and let some fresh air in. We need to tell our people to go out into the world and proclaim Jesus Christ. That's why he called Vatican II. That's why what we have received at baptism. So the second question can then be asked, well why is this consecration important? You know Pope John the 23rd who called Vatican II was the exact same Pope who once again elevated Joseph and told us all we have to look to Joseph. He understood that if there was going to be true reform in the church, we had to bring Joseph back. Devotion to Joseph had become eclipsed. He was there in glimpses and in parks. But good Pope John said we need to bring Joseph back because if we're going to reform the church, he is the patron of the universal church. We need to bring him back. We need his help. That's interesting because there are some people who tell us, no, no, no, no, no, no. Vatican II did away with all the devotions. Years ago when we started on the Venus, the miraculous medal of our lady a now former personer said to me, we're not doing that. We don't do that anymore. That's from the past. We've gone beyond that. Oh, we haven't. You can't get beyond Mary. I said, no, no, no, Vatican II said we need to do away with that. No, it didn't stop.  Okay. Vatican II said that the devotions of the church are to be explained to the faithful. That you might know what we're praying. That you might fit the saint aren't equal to Christ and that you might understand the relationship between these devotions and baptism. So quite the opposite Vatican II said instruct the faithful, but keep the devotions. And good Pope John gives us Joseph as he calls Vatican II and entrusts the work of the church to St. Joseph. Father Callaway in his preparation book tells us two reasons why we should make the consecration to St. Joseph. First, he reminds us that we need the spiritual fatherhood of St. Joseph. We have the spiritual motherhood of our lady. We need the spiritual fatherhood of St. Joseph. Incidentally, this is why in most Catholic churches, Mary and Joseph flank the altar. If you go to a Catholic parish and they don't have Mary and Joseph by the altar, it's a different parish because we need these two spiritual motherhood and fatherhoods if we are to grow in the spiritual life. But what does a good father do? Well, the scriptures tell us. A good father protects, provides, and teaches. And that's exactly what St. Joseph wants to do for us. He wants to protect us, protect our discipleship from the allure of the evil one, from the secularism that is running across our society. He wants to guard our faith which can be so precious and so vulnerable at times. Joseph wants to protect our vocation. He protects my priesthood. He protects our widows and widowers. He protects those who are single. He especially protects those who are married and he protects the Christian family so dear to his own heart. He was the head of the holy family and the most perfect of the three. But God called him to be the shepherd of that family. We call on Joseph to protect us. We live in interesting times dear friends. Men do not know what it means to be a man and women do not know what it means to be a woman. It is further displayed in the transgender movement. Such a sign of confusion.  Of what it means to be a human being of a particular gender. But far before that men had forgotten to be men. When I told my father I was going to the seminary, he said, you have my support. But make sure you work hard. Because too many men and too many priests are pampered. They have forgotten that men are to work hard and to provide for their wives and their families above all else. Men need to be reminded what it means to be a man and women need to be reminded what it means to be a woman. We have to remind ourselves that God has so ordained a Christian family in such a way that the spiritual life can flourish, virtue can flourish, stability is given to children as they are raised in the faith. Our Christian families are attacked from the outside and on siege from the inside. Oftentimes the very ones who are called to the vocation are the very ones who are willing to throw under the bus to sacrilegiate or to abandon it. We need Saint Joseph. We need Joseph's help. We need him to protect us. We need Joseph to provide. He desires to intercede for us and ask God's grace for each one of us. And we need Joseph to teach us. Joseph throughout the scriptures always placed God's will above his own. God could ask Joseph to do anything and he knew that Joseph would do it. A beautiful legacy. I pray the same can be said for each of us on the day that we die. God asked and that Christian always said yes. We ask Joseph to teach us the ways of God and the ways of obedience and docility. That's the first reason we would make the consecration. We need Joseph's spiritual fatherhood. Father Calaway gives the second reason. He says that we need Joseph's help and evangelization. This is why Good Pope John would turn to Joseph and ask for Joseph's help. As he sought reform and renewal in the life of the church. Because Good Pope John looked out at the world and he saw the church and he saw so many people who were doing the right things but their hearts were far from Christ. Some of you shared that with me. Our older Catholics. We were taught to go to Mass. We were taught to make sure we paid the tithe. We were taught to make sure our kids went to Catholic school. But we were never taught how to pray. Or to read the Bible. Or to have a personal relationship with Jesus Christ. Unacceptable! Unacceptable! That should never have been the state of Mother Church. When Pope John saw it. We said we need to change this. We need to make sure that the baptized understand what it means to live as a son or daughter of God. And what it means to be a disciple of the Lord Jesus. Pope Saint John Paul II who followed Pope John. John Paul II. 27 years as Pope. One of the longest serving popes in our 2000 year history as a church. God blessed him with 27 years in order to implement the Second Vatican Council. And what does he tell us? He kept telling us to hope for a new springtime. Because he looked at the church and it was bleak. As he looked out and looked and said we have so many baptized pagans. So many who have received the sacraments, the mysteries of the Christian faith. But who do not know Jesus Christ. Baptized pagans. The catechism of the Catholic Church would phrase it in this way. But the church needs a post baptismal catechumenate. A catechumenate is the way in which an unbeliever becomes a Christian. And if you have a post baptismal catechumenate, that means we have baptized pagans. It means there are people who have been baptized who don't know Jesus Christ, do not think as Christians, speak as Christians, or act as Christians. But supposedly Christians, they don't know Jesus. And the church calls for reform. And we are told that Joseph could help us. Because look at Joseph. He has been described as the first missionary of the Christian faith. Long before the Lord began to preach the gospel, Joseph was so fashioning and teaching Jesus that he was able to fulfill his ministry. We can say he was one of the pre disciples of our faith. And we need to turn to Joseph in particular to help us in our discipleship. We need to ask Joseph for the reform of our parish and the reform of Mother Church. So Father Calloway gives those two reasons. Spiritual fatherhood and evangelization. Now maybe at this point you're saying, okay, okay Father, fine, I'll get the book, fine. Okay, you convinced me it's important. But what does this involve? What's my commitment? Well, you get the preparation book. And there are 33 days and each day has about a page or a page and a half. It's a reflection on some part of St. Joseph's life. There are some pious practices that are recommended. It will take you about 10 to 30 minutes a day. And as you walk through the preparation, the task is to look at Joseph and seek to bring again that new dynamism to your own baptism. How can I imitate Joseph? How can I be a better Christian? And after 33 days on the Feast of St. Joseph, March 19th, you make the consecration. The prayers are in the book. You can make the consecration at home by yourself.  You have that power. Or you can make an appointment with myself or Deacon Doc and make the consecration privately. Or you can join us on Friday, March 19th at 7 p.m. for a big mass in honor of St. Joseph. And you can make your consecration then. That mass will be in person and by live stream. So that's the commitment. 10 to 30 minutes a day for 33 days. Perhaps at this point you're asking the more pressing question. But really how can this help me? I get everything. I hear everything you're saying but how can this help me? Why would I take on something else when I'm just trying to keep up with what I've got right now? Perhaps some are even saying, Father, I'm hardly even praying at all. And you're asking me to take on something else. And here's why I'm going to ask you to make the consecration to St. Joseph. First, because this is the second lent of this pandemic. And there are a lot of hearts that are heavy, anxious, confused. I read an article the other day that says it will take us seven years to return to normal before the pandemic. I hope that's wrong. But there are a lot of people whose hearts are in many places. And this consecration, this preparation can bring our hearts back through Joseph to encountering the Lord Jesus. So we need it during this pandemic. But also this consecration, this preparation can help us once again to be renewed in our own baptismal consecration. It can help us to become better Christians. People of prayer and virtue. It can help us to live our own vocation well. To become better husbands, wives, fathers and mothers. And this consecration can help us understand how much God truly loves us. And the workings of His providence. And how we can come to that total surrender to God's will in the invitation of St. Joseph. In the Old Testament, the patriarch Joseph was the favored son of Jacob Israel. The other brothers were jealous of him. But when a plague hit, only Joseph was prepared for it. And when the other brothers ran the risk of starving to death, God told them, go to Joseph. And they went to Joseph and Joseph had food and mercy for them. Go to Joseph. Here in the New Covenant, Joseph, the husband of Mary and the father of Jesus, once again the Holy Spirit is telling us, go to Joseph. Not a famine now, but a pandemic. Go to Joseph if you want reform in your heart and in your homes. If you desire the hope that is ours in Jesus Christ. Go to Joseph. Make sure you get the preparation done. Do those 33 days of preparation. And on March 19, please join me. And together, let's make this consecration and ask Joseph to bless us and help bring true reform to the church and help to make us all better Christians. Dear friends as you approach this altar, hear those words of the Holy Spirit. Go to Joseph.