So, in the previous lecture we have started to look at objects such as inverses of linear transformations and we have seen that if you have an isomorphism from a vector space V to another vector space W then you can always define such an inverse not just that that inverse also turns out to be another linear transformation from the range to the domain right. The fact that it is linear is what is so beautiful because over finite dimensional vector spaces we have seen that if you have a linear transformation that is defined over just any one basis in the domain right that suffices not just that you can also look at it as uniqueness of this definition. For instance you take this phi 1 as a mapping from V to W and suppose you have phi 2 as another mapping from V to W and suppose there is a basis for V given by so of course these are finite dimensional vector spaces that means this is a basis for V and suppose these two fellows agree on the basis it turns out then they agree on every other vector which is to say that once you defined a linear transformation over any basis it is not only defined but it is uniquely defined. So this we can just check out a quick proof of this so you can take phi of phi 1 of V is equal to phi 1 of summation alpha i V i right where every V can be represented as a linear combination of fellows in the basis by the same token you can have phi 2 V is equal to phi 2 summation alpha i V i yeah. So then what can we conclude from this we have to show that these two must agree this V we have chosen as arbitrary but what do we know we already know that phi 1 V i is equal to phi 2 V i for all i belonging to the set 1 2 till n so then it is a trivial matter because what this results in is summation alpha i phi 1 V i and this results in summation alpha i phi 2 V i now since each of these terms equal the other therefore these are indeed equal right. So there is this uniqueness once you have defined a linear transformation over one basis that is the only linear transformation you get no other linear transformation can match unless it is exactly equal no other linear transformation can match just over a basis and yet mismatch over some arbitrary element once it matches over a basis you define it uniquely right so this means that the inverse that we have defined is also unique because once you have shown that the inverse is also a linear transformation and it is defined exactly over a basis of W remember if this is from V to W then the inverse was defined as something that existed as a linear map from W to V and it was defined over a basis in W so then not only have we shown that the inverse exists for an isomorphism but that also the inverse is unique and see now if you try to show this for matrices without understanding this notion of vector spaces and try to show that it is unique you might have to do some bit of work but we are not getting into any formulae that is the point we are dealing with a much more abstract notion of linear transformations of which the matrices just happen to be a special case right so once we have shown this is unique you also know that the inverse of a matrix a square matrix when it exists also has to be unique that is just another way of seeing that same fact right but now today we have promised a little more than just looking at inverses of square matrices or inverse mappings for isomorphisms we have also said that even if we do not have an isomorphism but if we just have a by a surjection or an injection there would also exist some form of a limited kind of an inverse for such maps right so now we shall investigate what kinds of inverses do we have in mind under such circumstances we have already laid out some hints for that in the preceding lecture when we talked about things such as left inverse and a right inverse right but today we shall look at them more closely we exactly prove the uniqueness of a linear map when it is defined over a basis if a linear map happens to be defined over a basis then any other linear map which also agrees with that linear map over that same basis must be nothing but the same map so if you take phi 1 and phi 2 as argue that these are two different maps but they somehow agree on this one particular basis any one basis then they also agree on every other point on the vector space every other vector on the vector space so because the inverse is also linear map like we showed the other day and therefore the inverse must also be unique so that was the point of this discussion right because that is how it fits in but that is of course the inverse as I said of an isomorphism when there is a bijective mapping between v and w that is the dimensions of v and w are equal if they are finite dimensional but now we are going to talk about mappings from v to w when v and w are not necessarily of the same dimension which is to say that they are not isomorphisms okay and investigate when we can cook up some different kinds of inverses so let us say we have v to w where v has a dimension is equal to n and w has a dimension equal to m right suppose suppose phi which is defined from v to w is an injection one-to-one map what do we know about these numbers n and m from our previous lecture what does this immediately tell us if phi is an injective map we have discussed this right in the view of the Rankinality theorem for finite dimensional vector spaces what do we know immediately about this of course if it is an injection that the kernels dimension is 0 because there is nothing in the kernel other than the 0 vector so the kernel dimension is 0 the image dimension must be equal to the dimension of the domain that's v right and the image is sitting inside w so the dimension of the image is less than or equal to the dimension of w but that is also equal to the dimension of v so the dimension of v must be less than or equal to w so we are essentially talking about a situation where n is less than or equal to m in the language of matrices like we said if you're looking at matrices as a special case of linear transformations then this is exactly the kind of what sort of matrices n is less than or equal to m yeah we're talking about tall matrices right because matrices that map from n dimensional to m dimensional spaces are m cross n so if n is less than or equal to m then it's a tall kind of matrix right what else are we asking for here so what is the other property that we need for this existence like this injection so suppose now again let us look back on the figure we had drawn the other day so this is v this is w right so there is this map phi that takes you from v to w and then if we want an inverse of this we must find some psi here which takes you back to v not just to any arbitrary v but then this mapping must be through the identity mapping right so any object v inside this must be mapped back to v itself which is the identity mapping over v right so this is what we are essentially asking for okay and we'll so show that the existence of such a phi is predicated on this property of injection in other words whenever you have an injective mapping you can always find such a phi and if the map is not injective then you will actually not be able to find such a psi did I say phi it's a psi so psi is the inverse of phi right so what we are saying is that this psi is then called the left inverse why because first we are hitting it with phi and then we are hitting it with psi so this is a composition all right so it's a psi of phi that should be the identity over v that is a definition of a left inverse remember this is the definition of the left left inverse now we are claiming that existence of left inverse for phi is equivalent to phi is injective right so we have to show both sides because this is an if and only if sort of a condition necessary and sufficient condition which is to say whenever you have a left inverse phi must have been injective to start with whenever you start with an injective phi you'll always be able to cook up a left inverse yeah so how do we go about establishing this fact okay this much is clear so far any questions on this yeah we may not be able to get a complete inverse like we got for isomorphisms but at least with injection there is one kind of inverse that you will get which is a left inverse yeah so what is this condition let's try and investigate by the way in terms of matrices what does this mean what does it mean to say that the dimension of phi sorry the dimension of v is equal to the dimension of the image when can you say that a matrix has a left left inverse because matrices we understand better their arrays of numbers so you have something that's in f m cross n right so we have a tall object such as this this is m this is n so when is it exactly that we say that the matrix yeah is going to have a left inverse think about it what is this n and m how is it appearing n is the dimension of v and what am I saying about the dimension of the image of phi what is the dimension of the image of phi also known as in case of matrices rank of a matrix right so we are asking for the rank of the matrix to be equal to n which means it is full column rank of course row rank and column rank are the same but what we are saying is that in case of matrices this is tantamount to full column rank in short FCR for matrices in other words if I manage to establish this equivalence I would have established in the parlance of matrices the fact that whenever you have a matrix that has full column rank then you will always be able to cook up a left inverse for such a matrix now of course if you have a tall matrix I mean if you have a wide matrix can you have a full column rank matrix because the row rank and column rank are the same if you don't even have as many rows how can you have that as a rank right the rank is less than or equal to the lower of the number of columns and rows right so if you are asking for full column rank you must have at least you know suitable number of rows it can at most be a square matrix or a tall matrix right so that is all implicit here so that means tall matrices if they are full column rank just being a tall matrix isn't enough but if a tall matrix has full column rank by dint of this assertion we have not proved it yet we will but by dint of this assertion tall matrix having full column rank will always have a left inverse yeah so you just try and understand the implication of this result first absorb it in in the language of matrices and then we'll do this proof any doubt so far on this the numbers add up right please be sure that you are grasping the essence of the numbers here how it looks it's important to have an image of the matrix picture at least okay so if that is clear we can move on to seeing a proof for this okay so suppose phi is injective phi is injective we have the fact that n is less than or equal to m so consider bv of course a basis for v basis for v given by v1 v2 till vn look at the set s defined by phi v1 till phi vn what can you say about this set s any special claim we can make about this set s is it a basis how can it be a basis see m a basis for w must have at least m but you are on the right track distinct or something more linearly independent set right so this s is a linearly independent set why so the claim is s is a linearly independent set of course it is distinct but it's something more than that more than just distinct it has it is a linearly independent set why suppose not suppose not yeah assume the contrapositive suppose not then what happens summation ci phi vi is equal to 0 let this be true this implies summation phi sorry the summation would go inside so phi acting on summation ci vi is equal to 0 but what do we know about phi the fact that it is 1 to 1 it's an injection we have assumed it is injective right so if it is injective then only the 0 vector can exist in its kernel so this is mapping it to the 0 of w so therefore this vector inside the argument of phi must also be 0 is equal to 0 this is a 0 of v but this is definitely a linear combination of vectors from a linearly independent set which is the basis it implies that ci is equal to 0 for all i but ci is are indeed the coefficients of these 5 vi's so any linear combination of 5 vi's that takes it to 0 must be the trivial linear combination where all ci's are 0 which means that this set is indeed linearly independent so this is linearly independent we have also checked that out if it's a linearly independent set and it's residing inside a vector space of dimension m which is greater than or equal to n what do we know about such a set we can always extend this linearly independent set until we get a basis for w right so let us go ahead and do that see at every step we are invoking nothing more than what we have proved earlier right ok so let me leave this it is the figure here right ok so extend s to a basis for w given by b w is equal to phi v 1 phi v 2 until phi v n and then you have w 1 w 2 until w m minus n right that adds up so there is exactly m vectors here we can always cook up a basis by extending that existing set that that was given to us we proved this earlier right any linearly independent set can be extended to a basis so this is a basis and now define psi as a mapping from w to v given by psi of phi vi is equal to vi and psi on wi what does this mean I don't care anything I don't care so never have I claim that this inverse map has to be a unique map you can come up with some map I can come up with some other map as long as this part is sacrosanct that's all I need see you initially you might feel this idea a bit uncomfortable because we are used to cooking up unique maps and so on right but I am saying this left inverse doesn't have to be unique yeah when you have inverses of isomorphism then we have shown the uniqueness right but here this is at my discretion the only thing that is sacrosanct is that if there is a fellow in w which came as a result of mapping by phi then that fellow gets mapped back to the identity element that is to vi itself but as for other fellows who did not even originate I mean look at this this wi see it's not a surjection so these wi's which are fellows here then need not necessarily have had a preimage with respect to phi so I don't care about the psi maps them back to it's really unimportant to me the only thing I am concerned with while mapping this if you now go back to that figure which I have erased here is that if something originated in V then after this mapping successive mappings by phi and then by psi it should lead back to that same fellow as for the other fellows who did not even originate in V just if I take up partial picture of that vertical line from W to V that psi doesn't really matter to me psi only matters when there are fellows from V that I have under consideration right so therefore this is indeed an inverse you can check right you take any arbitrary here so this means these are like don't care conditions yeah so I don't care about what happens to these I can map them to anything I like and this indeed also brings to if I like you can it's actually good for many design problems and things like that sometimes you might want some sort of a best inverse best left inverse from certain perspectives so you can play around with these assignments as long as you keep this fixed these you can play around with and you know get some best possible solution for your particular application right so that's a left inverse so we started with the assumption that this is injective and we've now shown you that we can always constructively arrive at a left inverse right now it's the other part that remains to be shown and unfortunately I have to erase this that's okay by the way I'll urge you to try and prove that this inverse whether it's linear or not just satisfy yourself yeah once you fix this up then it becomes uniquely defined but as it is left to itself since this is a degree of flexibility here it's not unique right so the other part is suppose psi composition phi as a mapping from where is this a mapping from by the way v2 itself right yeah exists so that psi composition phi is equal to the identity mapping in v now I have to show that this is also an injection because I had to show both sides you see I started with this being an injection and showed you that there is an left inverse that exists now I'm assuming a priority upfront that there is a left inverse and I'm going to have to show that this is injective so what is the criteria for injection if it fails to be injective then I should have two different fellows in v mapping to the same fellow that would violate injection right so suppose v1 not equal to v2 and of course v1 and v2 belong to the vector space v such that phi v1 is equal to phi v2 which is when I'm assuming that there is not injective now I have to somehow prove that this is absurd this can never be true and I will do so exactly by using this condition look at what happens so psi composition phi acting on v1 is equal to what psi acting on phi v1 and psi composition phi v2 is nothing but psi acting on phi v2 but what do we know about phi v1 and phi v2 they're equal so I must have psi composition with phi v1 is equal to psi composition with phi v2 because of course the same fellow psi which is my left inverse when it takes up the same argument because phi v1 and phi v2 are the same they must map to the same point the same point cannot be mapped to multiple points otherwise it's not a valid mapping right so these must be equal but what do I know about this what is this whenever I'm saying it's a left inverse that's the definition of a left inverse that means that identity mapping on the vector space v on v1 is equal to the identity mapping on the vector space v that is v2 but identity map only returns the vector itself right so let me use a different color because I'm running out of space just to highlight this point which means that v1 is equal to v2 which is a contradiction of this claim that I made here so contradiction right in other words what I've shown you is that if you have a left inverse that exists then the map that you started with must be injective right so these equivalences have been established any questions alright then we'll move on to the next module


Right, you're very welcome. Eamon Rhinus, my name, I collect the parish priest here. I'm about to give announcements out at the start before we do anything. Next week, the IAA will hold an event. Choose the 24th of September. The director of the Global McKinsey Institute will give a talk on the technological social responsibility in the AI area. So I'll zoom over in here. You might be interested in that. I'm very glad to introduce Jonathan Rhin on the lecture or the talk. He's going to give on the economics of artificial intelligence the knowns, unknowns, and unknown unknowns. He's a lecturer in MIT and an adjunct lecturer at Trinity. I'm a member of the Global Economics and Management Group at the Sloan School of Management and MIT. And more than anything else, I'm proud to say he's a graduate of the University College. Jonathan, the floor is yours. Thank you very much. The opening session is on the records recorded, and then we go to anything afterwards. The content can be taken away, but not attributed to any one speaker. Jonathan. Thank you very much. So first of all, Deputy Ryan, Deirdre, and all the members of the IIEA, I'd like to thank you for inviting me here today. I visited here, I suppose. It's probably maybe about a year ago. And we talked about some of the ideas, and it's great to be back and actually talking to a wider group this time. So just before we get started, how are we doing for time? So I'll make sure I'm also starting on time. I think of that after about 25 minutes. Perfect. OK. So it's not often I get to quote Donald Rumsfeld. So I knew I was talking to some policy people today. And so I think Henry Kissinger called Donald Trumpsville, called, I think he said, Kissinger said he was the most evil person I've ever met. So I thought that was a good setting for talking about artificial intelligence and how it's all going to affect our lives. So there we go. Yeah, the reason I'm talking about knowns, unknowns, and unknown zones, it's really that so much to do with artificial intelligence today, there's a lot of hype around it. And one of the things I'm going to try and do is spit out a little bit between the hype and the reality. That's going to be the focus of it. So when Rumsfeld was given his knowns and unknowns and all that, he was asked a very direct question. And what he was using it is to be obtuse. I'm going to try and use it to actually as a framework to explain what we do know, what we don't know, and what we potentially have no idea about in simple terms. There we go. So before I get started, different people might have different interpretations of AI or whatever. But I think we'll just cut to the chase in terms of AI has a long history. But really, we're going to focus on a branch of it called machine learning. And that's where all the developments have been. We wouldn't be sitting around talking about this today unless it was for machine learning, a particular branch of artificial intelligence. There are other elements to it. But I wouldn't call it just the sexy one at the moment. This is the one that's had a lot of the development. But it's important before we talk about Anthem to do a policy or Anthem to do with implementation, but that we really understand the technology. And that's one of the real difficulties with the hype that's surrounding the topic at the moment. And this idea that it's sufficiently advanced technology is indistinguishable from magic. Of course, we'll all understand it in a couple of years' time. But today, it all looks like magic, and it's difficult to differentiate. So here's an example I'd like to talk about from anybody who's involved in computer science or development of products applications. We'll get this one. So you've got the guy on the left saying to the programmer, when a user takes a photo, the app, we're developing an app here, should check whether they're in a national park. And the developer said, sure, that's GIS lookup. I should take a couple of hours, and then the guy on the left said, that's great, I'm gonna have this app. Also, can you check whether the photo is of a bird or not? And then the researcher says, well, I need a research team, five years, and several million of a budget. So it seems like, if you don't know the differences to what you're asking for when you're developing something like this, that they don't seem like they're radically different requests, but except one is very simple and the other is very tough. The reason I showed this one is that this is a traditional computer science, a little joke, I suppose it's barely a joke, but let's call it a joke. And I think the interesting thing about this is with machine learning today, they've actually solved checking whether it's a photo of a bird or not. And today the programmer would say, yeah, that's no problem, give me five minutes for that as well. Okay, so artificial intelligence, I really think an awful lot of the hype has got to do with the name that's on it. When the original dozen or so men got together in Dartmouth College in 1956, and they had a little conference and they came up with the name Artificial Intelligence, we should remember where they came up with the name. And it's got to do with, frankly, they were looking to get a $13,000 grant for hold in the conference. There had been a conference on the same topic with the same rough bunch of men a couple of months before that. And it was on cybernetics, which is what the field was known as back then. But that was such a dud of a conference, they couldn't get funding for it. So they come up with a new name for the next conference. And when they went to the Rockefeller Foundation and asked for $13,000, they came back and said, we'll give you half of it, because honestly, we have no idea what you're talking about. So when they come up with the name AI, it's not to be taken literally. I think a lot of the confusion comes to do with, well, I know what my intelligence is as a human being and it's just a computer copying the same thing. It is definitely not that. And we have no, there's nobody, no serious scientists I know in the world actually working on that problem. But that does not mean that AI or machine learning can't do a lot of very interesting things in the short term. Just to give you a 30 second insight as to what actually happens. If anybody know Gary Kasparov, he was beaten in what was called a breakthrough moment for artificial intelligence as it was called back then, when he was the world champion, the greatest ever chess player at the time. And he was beaten by IBM. Big Blue, I think was Deep Blue, was the name of the computer application. In fact, they weren't using what we would call AI today. They were just using lots of processing power at the time. So there was nothing really that advanced in it. It was a development in computation power, not development in anything intelligent as we would describe it today. And so the problem with beating something like Gary Kasparov in chess, although it's very hard, it was a computation problem. How many, like if you know what a decision tree is, it's just basically a very advanced, very quick decision tree with a big computer that can go down about 10 steps. And Gary could only go down about nine. And so the problem with so many things that computers can't do is that they need rules for it. There's so much to do with our day to day life that we know so much more than we can tell. We can't describe how it is exactly that we know what a kitten is. My 18 month old niece knows that this is a kitten and she can't really speak at the moment. So, but yet she knows, so how do human beings do this? If we can't describe something in a set of rules, if this then that, then we can't traditionally tell a computer how to recognize something. And so this has been the hard-limiting factor in so much of computer science for 50 years. And what machine learning does, it really comes along and what in dramatically simplified butchered terms is by given some, by given these learning algorithms, lots of data. If you show 10,000 pictures of a cat and 10,000 pictures of a dog and in each picture you label where the cat is and where the dog is, at the end of the 10,000 you showed a new picture and it will tell you whether it's a cat or a dog.  And you say whatever's in that shelf, keep mixing it up with any random combination that you want, keep putting it in the oven, bake it for half an hour and see what comes out. Well, when I tell you that story, you could tell it's gonna take a long time for by random chance and by adjusting of parameters that the robot is gonna figure out how to make a perfect cake. It's gonna take a long time because it doesn't know it's putting tomato ketchup in with brown sauce and it's expecting a cake. Okay, so that's not gonna work very well. The problem with that is, as we can imagine, it takes the robot half an hour to do each iteration. The thing with a large-scale processing like this is that you can do a trillion of these, or, sorry, maybe not a trillion, you can do several hundred million of these iterations in an hour. And so with the advent of high-process computation, with these new algorithms, we're able to try out lots of recipes very quick and you find the one that works. And so it's not that it actually knows, in any sense, how to make a cake or how cakes are made or what ingredients are, but it just tried lots of combinations, kept adjusting the parameters of the recipe and it comes out knowing how to make a cake. That's really what a lot of machine learning is today. So what it does in economics terms, the economics of AI is the name of the thing and in an economist's parlance, really all we'd care about is cost because nothing is as interesting to us as cost. So Google dropped the cost of searching something to zero. I used to have to go into the library in Trinity and actually spend time or maybe even spend money in searching for something. Now it's instance of cost went to, of search went to zero. The cost of telecommunications when I use WhatsApp has gone to zero. I used to have to physically send a fax or post something, it took time and money and now it's zero. So what does AI change in terms of change in a fundamental in the economy? It changes the cost of prediction. And so this here is puppies or muffins and what we can do is you can check how good human beings are identifying. Is it a puppy or is it a muffin? And then we can train a machine learning algorithm and hey Presto, we can get machine learning algorithms that can do it better than humans today. So that's a prediction exercise. Now you can then take that and give it to lots of, train that on lots of applications. It's not like a human being. We can both identify puppy or muffin but we can also do, some people can do lip reading. And so we can train a different algorithm to start doing lip reading because it's a prediction exercise. And as long as we can train it sufficiently and we're getting quite good at it. So is this Bill Murray doing a Tom Hanks impression or is it Tom Hanks? Anybody got a thought on this? Don't feel too bad. Computer is better than you as a group. Tom Hanks. It is actually Bill Murray doing a Tom Hanks impression but we've trained a Google actually, trained an algorithm to identify stuff like that. I have spoken recently with a leading hedge fund manager who uses lots of advanced algorithms and computation. But the insight here around prediction and judgment is very important splitting those two things up. Human beings are constantly navigating the world using both prediction and judgment. I predict what it is that's gonna happen and then I'll use my judgment to decide how it is I'm gonna react. Computers and artificial intelligence still is only focused on prediction. We've got no real judgment in there. So for example, this hedge fund manager knew, statistically knew, you know what I mean? It's not enough certain but a high degree of confidence that Donald Trump was gonna win the election. Now you would think that's an incredible insight for somebody who manages $100 billion of money and you would think well, you know they're gonna make a ton of money off this. Well actually no because even though you have good prediction of what's going to happen you still have to judge what it is that you're gonna do with that money. So what? Trump is gonna win.  Where does that mean you're gonna invest in equities or gonna invest in bonds? You still need to lose, it's an outlier event. You still need to use human judgment. He didn't actually make any money off the trade. He pulled out of it because he was just too, too difficult to make the judgment cost but the prediction was there from the day that they were doing. And so then when we're talking about AI and a lot of the predictions about what's gonna happen it's really hard to make predictions especially about the future. And so that's one of the things that I'm cautious about doing and an example would be when Microsoft Excel came along and or let's say Microsoft Word. It's a bit like Mad Men, you know that TV show where it's a secretary pool. Typically it used to be all women back in the 60s or at least in the show. They sit outside and they type up the letters for the CEO and if you were to say bring a group of them together the typing pool and say well actually this new thing Bill Gates is inventing in his garage is gonna be a personal computer and he's gonna have Microsoft Word in it. And you would have thought to everybody there they're like great that's gonna make our jobs a lot easier because we don't have to, every time we mess up we don't have to go in and use a bit of tip-ex to clean up the letter. And you're actually saying no everybody here is gonna lose their job and the CEO is actually gonna do the letters himself. You're like well that sounds absolutely ludicrous.  And so it's very difficult that's even a first order effect on the implementation of a radically new technology into something that we already know. So that's first order. The complexity of trying to predict what's gonna happen with the full economy just and with jobs and everything to do with that it's far too complex and it's not that we just didn't get enough smart people in the room or throw enough compute and power with it. It's an actual unknown, okay? To talk about in Rumsfeld's parlance. So the other thing is that just because something is technically possible doesn't mean that we're absolutely gonna do it. So technological feasibility is not enough. I would love to go over and back to in Boston on Concord but it no longer exists even though the technology is there to do that. So now looking at some actual real unknown unknowns. This is what Rumsfeld was talking about. Things that we don't know that we don't even know. How would we know them because I don't know what I don't know. One good example going back quite a bit in history is when in around the 1600s when they discovered optical lenses somebody could have sat around and they had a version of this back then.  We're gonna have a real problem with unemployment and that could have been the policy discussion. Who would have known at that point that actual discovery of optical lenses has pretty much led to all of science since because there was no microscope, there was no telescope. That two of those things effectively would not have anything like we know as science today. So that discovery of the glasses led to all science. That's an unknown unknown. Who would have guessed where we were today coming out of it? Does artificial intelligence and machine learning have that capability? Very difficult for us to say because it's an unknown unknown. Those who are making those predictions are just guessing. But I will say that there are tiny little examples of it. One I really like is a group at Stanford did a piece of research on diabetic retinopathy which is for diabetic people. And traditionally you had to go to an ophthalmologist and they would have taken image of the eye and they would then have a look at it under a microscope I guess and be able to tell whether this person, their disease was getting worse and eventually would lead them to blindness. And so the guys at Stanford and a couple of them at Google as well, they got together, they took these images, they trained them up and now the machine learning was better than humans. The best Stanford ophthalmologists at predicting whether this was going to get bad or worse.  So not that interesting so far. The really interesting part is that the computer scientists came back in one of the meetings and they said, you know, and also our statistical reliability and identification of the gender of the patient has also increased. And the ophthalmologist said, sorry, I don't know what you're talking about. Actually the machine learning algorithm had been able to identify from the image whether it was a male or a female. We did not know whether that was possible. No human being had ever been able to look at the image and tell the sex of the patient. The response from the ophthalmologist was that we also have a way of doing that. We look at the patient. So it's not a particularly useful thing. It hasn't in any way brought it forward but it's an unknown and known in terms of coming into the research. And maybe there's a whole bunch of stuff out there. Maybe there's lots of unpicked apples on the tree. So one thing that I think everybody likes to talk about is how is this going to impact labor? And so Rumsfeld was asked a very definitive question about is there weapons of mass destruction? And he gave this convoluted obtuse answer. I'm gonna use that same framework to try and answer is there a threat that a substantial part of the workforce has become in the economic equivalent of horses because of artificial intelligence?  Well, I think that's particularly prevalent in Ireland. We've always be, every country is, but I think particularly in Ireland this kind of stuff really resonates. There I should say that the economic lens is not the only one we should be using to look at this. Valterra said, work saves a man from three great evils, boredom, vice and need. And so really the economic side of it is barely touching the need part. Let's say it's maybe only partially covering it. So I think when it comes to universal basic income and lots of other discussions that I'm not gonna be able to cover today, I think the boredom and vice parts are very important parts of the equation, but I'm not gonna talk about them just now. So what it is that I'm gonna talk to you about is that we do know from history about previous automation technologies and that machine learning is a type of automation technology. And we've modeled these and Dan and plenty of other people who work in the economics field will understand there's a long litany of research that goes back into study and automation. But when we come along today, lots of people are talking about us and there's lots of pushback. Every time a new automation technology comes along from the Luddite since everybody thinks, wow, we really need to worry about this one. And then there's a lot of talk, well, would this time be different? And so you get different people on different sides of the aisle talking about, usually it comes to the point of view that I'm a techno optimist. And to be honest, I'm gonna find reasons to explain to everybody here why it is that my point of view is right. And then you've got the technopessimists and they've got very valid reasons as to why they think the future, which none of us know, is going to be right. And really, this is a false dichotomy is that it's really not about these two camps. What we do know, and there is some knowns is what I'm gonna talk about. So how will an economist, this is the economics of AI, what will a serious economist do to try to model some of these things? And the devil is in the detail because loads of people like, say, and 40% of all jobs are gonna be gone. I don't know where they got, well, I do know where they got those figures from, but I don't pay any heed to them. This little modeling, I'm gonna show you, obviously if it is written on economics model, it would be horrific to look at, nobody wants to talk about it. But through your four steps, we can actually show you where we're looking for the impact of AI and the economy. So the first one is what we call the displacement effect. And this is the easiest one for us to understand. But the key point here is that automation, artificial intelligence does not replace jobs. It replaced tasks. Nearly everybody in the economy has lots of different tasks that they do in their job. So if you're a lawyer, you do an awful lot more than review in the documents. There's a hell of a lot more to it to being a lawyer, and depends on where you are in your career, you might do more or less of it. And so nearly everybody is the same.  So somebody, not easy to do of course, but somebody who works in the Amazon fulfillment center, they used to have to do two tasks. They'd have to go retrieve the, go to where in the big warehouse, the item that they're getting for Jonathan is, they'd have to retrieve it, and then they'd have to physically go in and pick it. And now what Amazon have done is they've automated one of those tasks, using plenty of machine learning, and that is the retrieval. So the little robot here on the bottom, if you can see it there, that goes off into a little orange one. They key the robots they were originally called. It was a company just outside Boston that Amazon bought. And they'll go out into a three story warehouse the size of a football field. And they'll, American football field, not a real football field, like a park. So half the size. So they'll go out and they'll retrieve the quarter palette that contains the item Jonathan won. And all the human does is stand in that little bay. He's not actually allowed outside into the rest of the warehouse. The warehouse shuts down if he starts moving around at his sensors for humans, against humans. And he stands in that one place and then he picks and he puts it into the box. Okay, so machine learning has half the labor here for simplistic terms, because it's taken away one of the tasks. On aggregate, we'd expect that you need half as much labor. So that's the displacement effect. We all know that and we can all really understand it. What's really difficult to start to understand is some of the other effects that start to happen. So let's say now Amazon, as an entity, you'll have to go through this with me, but Amazon costs decline because they now, let's say the cost of those robots is free. Over time it probably gets to almost free for Amazon, whereas previously they had to pay somebody $15 an hour. So now Amazon costs decline.  What they do is pass on the lower cost to Jonathan and everybody else. So with this additional income, I now have more money in my pocket, me being the universal person out there in the economy.  I used to only get it cut once a month and getting it cut every fortnight. That actually increases demand for labor somewhere else in the economy. Now if you're able to model the exact impact of the substitution effect over to this increase in barbers, well then I'm pretty sure you'll win lots of economic prizes. We don't know how to do this. It's far too complex in the economy, but we know in total this kind of stuff definitely happens. But that's not the only thing. There's actually an interesting effect that happens with automation that also boosts labor that maybe might not be insured about the start. Lots of the economy is already automated. So this is a Google data center. These are the mechanism they use to cool the servers that power Google searches. And this was already automated. It just wasn't done very well. So when machine learning came along, the very smart people at Google trained their algorithms to improve the efficiency of this system. And they had remarkable improvements. Something that they used to eke out one or point two percent year on year improvements. This came along and brought a 40% improvement in efficiency because they use machine learning. So when machine learning was applied to that Google problem, no human being lost their jobs. However, let's follow my model. This reduces Google's costs. It drops the cost to all its customers. Google doesn't, it works a bit funny like that. But let's assume Google drops the cost or at least Amazon in the equivalent would drop its cost to everybody. And now we all go out and get more haircuts. That happened on the replacement effect but with no substitution effect, okay? So that's the second thing we might want to think about it again. If you can model that, there's probably a Nobel Prize in it for you. Okay, so the third one then I want to talk about is the creation of new tasks that are complementary to the technology. So every new technology that comes along, what you'll see is that the self-driving, an MIT professor back there who runs the Toyota Self-Driven Car Institute and he now, he left MIT and actually took a bunch of his researchers with them. They got replaced at MIT but they all have new jobs now working for the Toyota doing self-driving cars. They're new jobs that didn't exist, okay? So all these different factors that interplay are very complex, impossible to model in advance. This in terms of like have the absolute numbers but this is a much more solid framework for thinking about some of these problems. Then maybe lots of the headline factors that like 40% of people are gonna lose their jobs. They simply are I would say a bad way of looking at it. This would be a lot better. And so as the technology develops these are the kind of things that we're gonna be looking at. So do we know how all these things are gonna balance out? No, we don't. So what I will talk about, one thing that we do know that's happened to previous technologies, again think about the total economy. It's not the only driver of this but it's a reasonable one is that as you put more machinery into the economy, more technology, more robots let's call them, then more of the share of the spoils of the economy are going to the people who paid for those robots, the capital, and less is going to the workers, the labor. And so that is one thing we don't really know the ins and outs of it completely but certainly over the last several decades the share that's going to labor is getting lower and lower and lower. And one concern I would have about automation driven by machine learning is that's likely to continue. So if you think about that guy working in the Amazon Center less money is going to the employee and more is going to Jeff Bezos because he owns the robot, if that makes sense. The other big thing I would actually be worried about is again from the outside it's maybe not so obvious but what we call source or technologies. So when you, it turns out actually when we model all of this stuff when you look at the really big technologies that have come out. So something like the internal combustion engine or the personal computer, the smartphone, the internet those really big things what we call general purpose technologies. Some people are most afraid of those. Actually when we model them all they're the ones that tend to have positive when you add up all those different effects they have positive impact on total labor. So they're not the ones we should worry about. The ones we should worry about are what we call Soso technology. So an example of this is you know when you ring the reception of a lot of small and medium sized companies they no longer put you straight on the receptionist. They say you know it's an automated machine saying press one, two, three or four whatever. Okay, that clearly had some substitution effects and some people lost their jobs in the total economy because of that but it was not a big enough technology that you had all the other things. We had no new people working on this technology. You developed it and then you know we don't have the equivalence of the self-driving car engineers and all the other stuff that goes with it. It wasn't big enough to feed through into the general economy so no people went getting their hair cut because of the extra savings they have. So these Soso technologies they're what I kind of would worry about a bit more in terms of the total economy. I don't think machine learning is one of them. Inevitably though there's gonna be winners and losers. So even Isaac Newton used to talk about this. We enjoy today higher standards of living because we're standing on the broken backs of those who paved the way for technological progress but did not live long enough to benefit from it. The interesting thing that's probably different the only thing that's different today from Isaac Newton is that a lot of the people whose backs are broken to use his analogy will still be around and will live long enough because the technology has happened so quick and we're all living a bit longer. So the adjustment costs for an economy when you add all those things up somebody who only cares about the total economy could be happy enough because machine learning is gonna come on it's gonna improve productivity. The long-term that actually makes us all wealthier but if you're that individual person who's just lost their job it doesn't feel very good. And that is something that we really should be worried about. We have plenty of research to suggest that these are real problems. I don't need, you know there are lots of examples from Limerick and Delpoldout or Fruit of the Lume and Donegal or you know there's so many of these examples that we're used to that are embedded into you know the Irish psyche but you know it usually takes economists about 10 years after everybody else knows something so they can model it. So this is an example of a couple of my colleague or Darren, a colleague of mine at MIT and their research they did, Haypresto showed that when they introduced lots of robots basically to a city like Detroit where they used to make cars that was bad for labor. So that's the big insight there. So if your job is taken by a robot and everybody in your town does that same job it's going to be bad for house prices in that city. We've managed to prove it. That's the big insight. Okay, everybody knew this already. And so that's what we're really working at. Since World War II, you know there's lots of these technologies that came along before World War II but for the Western world, Ireland about 20 years later we put in lots of these safety nets. So the old age pension came along, early 1900s then unemployment insurance then we do retraining programs.  But really the problem is not that there was not enough effort or care in my opinion or consideration for the people. The problem is it's just really not worked very well. And so if there was another Dell moment to happen, you know when Dell pulled out a limerick. If Intel were to pull out of League Slip, something like that, certainly if it had happened during the crisis, it's not that we wouldn't be willing as a nation to support those people, it's just that we don't really have the tools to do very much for them. And why is that? Actually something called, an economist talked about this about I think it was the 1950s, there's the human being putty and clay. It's the putty and clay problem. When you're young and you're at school, your mind is like putty. You're open to all these different opportunities. You might work here, you might work there. You haven't locked down on your skill set and your jobs. So you're like putty. By the time you're 40, let's call it, you're now like solid clay. You don't want to change. You wanna keep doing what it is that you keep doing. And so this is, once again, we all pretty much know this. You can't teach an old dog new tricks or so, but now we have an economics term for it. So the problem is that even if something like this new automation technology comes along, truck drivers cannot easily become orthopedic surgeons or radiologists because the market needs more of orthopedic surgeons. And we now have all this excess labor in the truck drivers. That's a really big problem. And again, this is something that's known. We know about the problem, but it's unknown in terms of how we solve it. And I don't think it's a bad actor problem. Certainly, I mean, even in America, they care about now trying to look after these people. So, I mean, if the Americans are after it. And yeah, the one good thing I would say about Ireland, though, is that if you look at the US, for example, for decades from after post-World War II, all the way up to the 70s, late 70s, US productivity went up. In other words, things were getting better. We're all becoming more productive and thankfully wages stayed in line with that, which is great. That's what you want. The workers who bring about the productivity when they work with technology. But since then, those two things have diverged. And productivity continues to go up. The returns go to capital and the returns are not going to the average worker. That's a major problem in an economy like the US, which is not very focused on redistribution. Ireland is highly focused on redistribution. Relatively, everything's relative, of course, but relatively high transfers from people who are doing better to people who aren't doing so well. In fact, we're one of the most redistributive economies in the world. So I think that the same automation type effects are going to come into America and they're going to come into Ireland with AI. But I think Ireland, because of our social contract, because of the way we all get on with each other, we don't want to see our neighbor particularly lose out. We do, everybody knows somebody from Limerick or from Donegal whose jobs get affected. So we're all in this together. That solidarity is very important. That stops these kinds of things happening at the net effect. It's almost impossible to start to really affect it before tax. But after tax, we should keep going with what we're doing in Ireland because if you are in an economy which you don't have it, such as America, it's a lot bigger problem. So I'll talk maybe about one more quick thing which is when it comes to artificial intelligence, it's not just about the technology. Really, a lot of the development that's happened in the recent past, it sits pretty much in a very small number of companies and a very small amount of researchers' heads. But we're getting this out very fast. And the companies that are first to adopt it, that really makes a big difference. So to give you an example, going back to previous technologies, when electricity came out first, you know the United States story better, the people, let's say, I mean, this is a simplified story, of course it didn't happen, but the guy who was going around selling electricity, he would go to a factory owner and he says, hey, do you want electricity? You're doing it by a steam engine today. Now we would think that's pretty much an easy decision to make for the factory owner. And for about 30 years, the factory owner says, no, you're good, we don't need electricity, we're fine without it. So it's bonkers to us today. Why would you not use electricity? Well, the interesting thing is you have to understand that the factory was already in place, the factory owner has already built it, and maybe they've paid and depreciated the entire building and all the machinery. So like, I have this one for free, well, I'm gonna pay you a million dollars for these new motors and getting connected to electricity. The next thing that happened in its interest on the electricity one is previously, and you can kind of see it here with these belts that are going on the wheels. We had one big steam powered engine in the middle of the factory. And then we had lots of these belts feeding these machines that come out of this one big engine. And so factories were laid out according to this. And all the science in terms of operational effectiveness, it wasn't called that then, was how do you get the belts to be more efficient, et cetera. And that's how factories were laid out. And it took a full generation of managers and probably owners to figure out, with the electricity, the original motors they were selling were just one big motor to replace the middle steam powered engine. And then they figured out actually we can have lots of little motors all around the factory and we can lay the factory out completely differently. And it was with that insight from a managerial point of view, coupled with the technological advancement that enables us to change how factories were laid out and we had a dramatic increase in productivity. Henry Ford figured this out famously with many of his factories. So it can often take a long time for new technology to diffuse into the economy, even though sitting around here today we think, well, why won't every factory manager just take it over? So yeah, so why that really matters is that these interdependencies matter a lot. When Netflix wants to use machine learning to improve its recommendation engine, it doesn't have to call anybody else. It just builds it into how it does its software. When Google wants to introduce a self-driving car, there's a lot of interdependencies. It doesn't just have to create the car, it also has to figure out about insurance, it also has to figure out about other road users, vehicle manufacturers and a whole pile of other things. So when we think about AI and how it deploys into different use cases and different industries, these interdependencies make a big difference. And the final one I maybe talk about then is that like another thing holding it back or accelerating is the tolerance for error because when a machine learning something, algorithm knows something, it has a statistical insight into whether it's likely to happen or not. It's different than how a human knows it. So when I'm using Gmail, as I've had this experience, you're typing along and it's trying to predict the rest of the sentence for you. Well, so what if it gets it wrong? No big deal, okay? It'll keep iterating. It'll be allowed the chance to keep iterating and get better and better and, you know, I find it brilliant now. The same company brings out a self-driving car. It doesn't have the, human beings don't have the same tolerance for error with car driving as we do for email text prediction, okay? So when Google, the self-driving car crashes, it has to take it off the road. So if you can't go out there and experiment a lot and try and iterate an awful lot and the tolerance for error is very high, it will slow down the introduction of the technology. And let me see, I think, yeah, let's finish on that one. Yeah, okay.


Welcome to the Insta Mat Reaction, Everton 1 Arsenal Nill, Gwerson Park today in the Premier League. Before we begin this video is sponsored by One Football, One Football's app makes it possible to keep up to date with all the news, scores and transfers all in the one place at downhill. One Football's app simply click the link in the description. Everton 1 Arsenal Nill at Gwerson, another victory for the Blues, fifth clean sheet in six games. How good does that sound? Really good performance from Everton. It's the only disappointing thing is, you'll have been more. One Nill doesn't do it justice. As you can see there in the stats, 23 attempts a goal for the Blues to Arsenal's seven, six rather. But we won the game and that's all that matters. Another excellent performance from Marco Silversman. Really, really put the shift in today, Everton. It was fantastic. Had to make a change before the game had even started. Michael Keane was named in the start on 11 but was ill. So Phil Jagielke stepped into the breach and put in an absolutely marvellous performance. What a display from Everton's club captain. Absolutely brilliant. 36 years of age. There might have been a slight fear with the likes of Lacazette and his pace and then a Bamiang's second half but Jagielke's experience and ability to defend and want to defend really pulled him through and it was a massive win to the Blues with that clean sheet. I thought Everton started very well. Jags gets the goal on, throw him a look at the end. Jagielke actually wins the first header. Dominic Calvert-Lewin goes for it. It breaks back and Jags is in the right place at the right time to knock home to give us a perfect start. After that, some will always pass it down. They're a good side. Lovely to watch. Nice little touches. But I thought Everton defended everything brilliantly.  He pressed high up the pitch again. We had opportunities to increase the lead. We had two breakaways with the talisman which he should have picked out a blue sheet. That would have given us that cushion that we needed. There were some lovely moments in the first half but now it's spinning back here to put Gomez through and some lovely football play from Everton. Nice and controlled. We really did press Arsenal back and we got in a half time. Five attempts to day one. You sat there a bit disappointed.  You're thinking we needed that second goal. They made two substitutions at the break and brought on the fantastic Aaron Ramsey and a Bami Angus brilliant. He got back into the game a little bit more ramsey. They had probably their best opportunity in the game when Jordan Pickford punched the ball through him and he tried to loft it back in but he put it over the bar. Other than that, they had a micaterian shot which went close but they offered very little really. They knocked it round brilliantly but they showed to me today where Unai Emery needs to strengthen and that is in the defence. I don't think the defence was great today and I think that's where he'll be looking to improve them for next season. As far as editing it can say, we just built on what we've been doing each weekend. Bernard has an opportunity, a poor back pass from Miles Knightland and it's such a good but the finish is way too long really. Lenno makes a good block. I'm going to call it living, made the wrong decision a couple of times we broke. He could have slipped Bernard in for one on one and I don't know what he was trying to do. He ended up falling over. Gilffy should have scored, a Charles had two opportunities, Dave has had a shot block. The list went on. The list went on when you're thinking don't be one of them days where we end up regretting it. But luckily the lad dug in and Arsenal didn't really offer that much for us to be that worried about they can cut through your times with some fantastic displays but today I'm a good value for the win. Like I say, the only disappointing thing is it wasn't by more goals. We keep playing like that someone is going to get a hide and hopefully it'll be full next week and we keep this run going but that's five clean sheets in six games is brilliant since we had that breaking. 25 minutes at Newcastle which makes you want to pull your hair out. It's been very, very good for Marco Silva's men. The last three home games Liverpool, Chelsea, Arsenal we took seven out of nine and the away games we've had three in a way, a two in a way and we've two in a lot but Newcastle should have seen that game. So the boys really stepping up to the plate. Made up for Marco Silva today, absolutely made up. Made up for the fans who have thought we're magnificent today. Even in a couple of sticky spells in the second half where Arsenal are getting on the ball with Ramsey. The crowd just pulled them through and it was a proper edit and display today. Pace and power attacking, some good tackles going in and the crowd helping the team out in the little dips. So fantastic win. I'm absolutely delighted tonight. 46 points and I'll point off seventh and that's what we need to keep aiming for to finish as high as we can.  Arsenal nil, enjoy the rest of your night. Check out Paed's maths reaction of you having sucked. Please do so but it only takes a sec. See you later.


After capturing London's literary wonders in her captivating blog series, Arpita Karva sets out on a new adventure, the college tour. She's been delivering insightful lectures in India's top colleges, sharing wisdom about UGC-NET, exploring career opportunities in the field of English Literature, and generously answering students' questions. In each college, she's been igniting the flame of literature, weaving tales from her UGC-NET preparation journey, exploring career opportunities in the field of English Literature. Arpita's college tour is not just a series of lectures, it's a transformative experience that has left an indelible mark on minds and hearts. Thank you, Arpita, for your unwavering dedication to the world of English Literature. May your journey continue to kindle the flame of passion in countless hearts.