What's up, guys? It's Josh from We're Back again with another video. In today's video, I will be giving my completely, utterly honest review of how, I think, online college at Yale University went last semester for my senior fall. For those of you that don't know, my name is Josh Beasley. I'm currently a senior at Yale Studying Computer Science about to go into my last semester. This channel consists of college application tips, CS advice, magic, blogs, if any of that sounds interesting, hit the subscribe button down below and join the community. So last night I was sitting down with my brother who's a sophomore at UVA this year and was also doing online college for the entire semester. We sat down and kind of brainstormed a list of pros and cons of online college. So we have this list now, so I'm going to split the video into two parts. The first of which we'll be talking about the cons of online college, and then we'll move in and finish off on a lighter note and talk about what I actually enjoyed, the pros of online college. So without any further ado, let's get into it with my first con, which is something I think we can all relate to, which is Zoom fatigue. Zoom fatigue is when you're on Zoom call after Zoom call after Zoom call all day long and you have not moved from your office chair.  But when you're sitting in the same chair all day, staring at the same computer screen all day, it gets very, very tiring, especially when you've done a full day of classes and then you take a little break and then you have to go through like a whole afternoon and evening of online extracurriculars. It is just, it's not fun. My next con is when it comes to actually making friends or like personal connections, it's really hard to do that over Zoom. Luckily, like I'm a senior and I kind of already had my my friend group figured out, I feel really sorry for the first years because it's probably really hard to meet people that you aren't directly living with or aren't coming in contact with every day. Like I live off campus. So the only people I was coming in contact with were my eight other housemates. So it's really hard to kind of meet people and make new friends. Normally I would try to build like different study groups in each of my classes and we would kind of do the problem sets together and everything that wasn't really possible this past semester. Luckily, I had some friends in my house that were taking similar classes as me, but that wasn't the case for every single one of my classes. So I really, it was kind of missing out on that personal connection. And with that, it was also hard to connect with the professor. Like there was a significant decrease in the lack of professor and then like TA interaction. Even in seminars where the class size is super small, like 15, 18 people, I felt like I was constantly butting over, talking over each other. Like it was hard to kind of get that interaction with your professor face to face like where you would be normally sitting around a table when he's just a little square on your Zoom screen. And I didn't like that at all. Some professors didn't even turn their video on when they were giving lectures, like lectures, no interaction at all. Like I didn't even have to show up on time. I could watch the lecture afterwards if I needed it. And that was kind of disconcerting. Next is kind of a sad one, but like I think it's true. I think you're literally, like especially at Yale, like fortunately for me, like I'm very privileged to have an ROTC scholarship. So I'm not paying any tuition at Yale. The U.S. government's paying that so I can go serve my Air Force commitment after college. But for the people that are, I think you're paying, you're paying tuition for an arguably, like lower quality education. Like to say that the education quality of online college at Yale is even anything remotely close to the education quality of like in-person normal times at Yale, it just can't be compared. And that's a sad fact. The next con has to do with the number of distractions that you have.  Or like me, I have a different monitor, so I could be working on something completely else. Something, and I have a monitor, so I could be working on something completely different than actually going to class. And I felt like a lot of times I would just have to end up watching lectures over again just because I didn't catch everything. The next con is something I think we can all agree on. And that's when like your professor is trying to increase the amount of interaction in the class and he just puts you into a breakout room with like three random people you've never met and you just kind of sit there awkwardly. Like, breakout rooms are the most awkward thing ever. Like, especially when they're people you don't know.  And it's just like, it's nothing compared to if you are actually like in-person in a group. It's rough and awkward, but you know, that's what we have to deal with and make the most of. And with like breakout rooms and small groups like that, group projects are also super annoying. Because like compared to where you could just meet with your group after class, you know, go to a residential college like common room or go get a meal together and kind of talk about the project you're working on. That's not really the case. It's super hard to kind of coordinate times with everyone, especially when people aren't on campus or aren't in the same time zone as you if they're remote. Then your coordinated group projects with people that, you know, could be across the country or even in a different country. Like I had a group project with somebody who was in the UK and it was hard to coordinate times. And it just made group projects that much more exhausting to kind of get through and work on together. This may not necessarily have been the case that other colleges with Yale had very minimal, like almost zero in-person classes. So like labs or anything that required kind of physical, like I feel bad for the theater kids who have to take like theater classes virtually. Like all of that's just a bus. Like there's no way that's working out. Some of my friends that were taking like physics or chemistry lab literally had the lab recorded and then they like were given the data and they had to kind of make these inferences on their own.  And I kind of mentioned this earlier but like there's a very low motivation to actually attend in-person lectures. And especially in-person lectures where you kind of have the opportunity to participate and you can get that interaction. It's like, it's hard to like wake up for them and I'm not motivated to when I know I can just watch them afterwards. But then again, I'm missing out on that interaction. So it's kind of a trade-off. My next con is something I feel like we can all kind of say generally like throughout the semester, I felt like I learned less than I would have in an in-person semester. And that's like throughout the entire semester. Obviously during finals when I was cramming and trying to kind of teach myself all the content that I had missed out on when like within the lectures I had skipped I felt like I was learning a ton. But that's more just cramming, not actually getting this good knowledge base from all your different classes. And lastly, this kind of goes along with Zoom fatigue just the sedentary lifestyle. I forgot how much I valued being able to walk to class, get out in the fresh air, you know, like I'd hit like eight, 10,000 steps a day just from walking to different classes because I never had a bike or anything. So I actually enjoyed kind of walking through Yale's campus getting the fresh air, being able to kind of go somewhere between classes because now I feel like my lifestyle is just sitting in place. And if I don't make an effort to go work out or do something which is sometimes hard with the lack of motivation coming from everything else, then I'm just living a very sedentary lifestyle which is not only good, not only bad for my health but also just a terrible lifestyle in general. With those sad notes, I wanna move on to the pros and some things that I actually enjoyed about online school cause my list for pros was almost as big as my list of cons. Obviously the cons were a lot heavier than the items on the pros list. But you know, we gotta make the most out of everything. So moving into the pros, my first pro is because lectures are recorded. It allows me to have a lot more flexible schedule which means I can wake up later, I can have more time for other things because I always know I can watch the lecture afterwards. And although I'm missing out on that in-person interaction, sometimes the lectures don't even require in-person interaction, so there's literally no incentive at all to go watch them live when I know they're gonna be up afterwards. And then when I do watch them afterwards, I can watch them at two times speed so I can get through them way faster, get the information I need and get the notes. Honestly, this is something I hope they continue after online school is done and we're back to normal because I really did enjoy rather than trying to decipher the professor's scribbles after they fact to kind of like relearn the notes and something from a lecture, you can literally just go watch the full lecture and full afterwards. There were classes where I would watch the lecture multiple times, like I would watch the five or six lectures leading up to a quiz again, even though I'd already attended them just to kind of refresh myself on the knowledge, especially when you can do it at two or three times speed. So like I said in the cons, it was bad that I wasn't getting the fresh air and being able to walk between classes and everything, but that also meant that I had way more time in my day. It's funny how much time you save when you're not having to walk to classes and leave early and I can literally just roll out a bed, pull out my computer and get on the Zoom, like literally like the minute before class starts, which is super nice because it gives me more time in my schedule, but if you're not putting that time to good use then kind of what's the purpose of it? I also enjoy being able to make food. Like while there were a lot of days where I'd be kind of whipping up some breakfast or lunch during like my 1135 class and just be sitting there with my computer on my kitchen table as I was cooking something and then just being able to go back to my class and eat it, which was nice. Cause most of the time I don't normally eat in class and have to make time to go to the dining hall, but it's nice to just sit there and be able to get a good meal in while I was watching my lectures. And my next pro is something that's very personal to me, but with online ROTC this semester, we still had Zoom calls for classes and like leadership lab and everything, but whereas we would normally have two workouts a week that were in-person at the gym where they were cadet led and we would complete the whole workout. This semester we had one workout which was on Zoom, which was just like a video workout that was led by someone, but then the other workout, we didn't have to wake up early. We didn't have to do anything. Cause normally I'm waking up at like 530 to get on time to these workouts. I didn't have to do that anymore cause the second workout for the week was literally just on my own time. Like I could go run, I could go hit a lift and I could log it on Strava and it would be tracked just as if it was a normal workout.  I could be sitting there in sweatpants, a T-shirt. Like I found that the amount of my wardrobe that I actually wore on a consistent basis shrink drastically because all I was wearing was sweatpants and T-shirts every single day unless I was going out somewhere. You know it's good to be comfortable with some people like their style and stuff, but like when your video is off there's no point or even if your video is on, like they're only seeing this much of you so it doesn't really matter. I have two pros left. The next of which is I said distractions were con, but with distractions being con, if you're able to properly manage them then multitasking while class is going on is also a great process, especially with me where I have a computer, I have my monitor, so I have multiple screens. I can be working on different things. If a professor mentions something and I wanna Google it, do a little more research into it while he keeps talking, I can do that. If I have another assignment that I'm time crunched on, I can literally be working on that at the same time I'm in a different class. And that also means it's just easier to take notes because they're gonna have the lecture on one screen and then on my big monitor, I can have a Google Docs form or a Notion page set up where I'm taking notes. With online classes, a lot of professors have switched over to basically where they had a Canvas quiz or exam and that's the exam you have to take whether it be a midterm or a final, but they give you a open block of time to do it. Not all professors did this, but I found this very helpful. Rather than forcing me to come in and take this class within a fixed time period, the Canvas assignment would be open for a fixed time period, but I would have like any time during my day to take it. So like from normally some of them were 12 to eight, some of them were like 24 hours where I could just take it any time within that block. And that was super helpful, not only so I could kind of coordinate with my own schedule and I wasn't taking time to do that outside of my normal schedule, but also just because it was a lot more flexibility and I could take the exam when I felt like I was most ready, not when it was scheduled. So that pretty much sums up my pros and cons and kind of my honest review of what I thought of online school. Like I said, there were a lot of cons and there are a lot of heavy cons and I definitely can't wait to get back to normal school. Obviously I probably won't have an opportunity since this is my last semester, which is kind of sad, but I hope the up and coming Yale is finally, especially the first year to get to experience what Yale is really like in person and have that opportunity to do online college and all the extracurriculars and social life and everything that comes with it. But like I said, there are some pros and I love to look at the bright side, especially during these sad moments like this. So I was happy to find some positives within the online college curriculum. So with that, if you enjoyed the video, you can drop a like down below. It helps me in supports the channel a lot more than you think. If this is the first video you've seen, please hit that subscribe button and join the community. And if you wanna say hi or have any ideas or questions, drop them in the comment section down below. And with that, I'll see you guys in the next video.


Large modulus spring LWE is bigger or equal to module LWE and METEO is going to be the top. Can you hear me? Is this on? No? No. Okay. Can you hear me now? Yeah. Today I'm going to be presenting some joint work I did with my PhD supervisor, Martin Albrecht, that basically relates to how much module LWE and large modulus spring LWE. Since I'm the first talk of the session, I'll start by finding some LWE and the variants that we're interested in, so ring and module LWE along with a short motivation as to why we would even want these different variants. Okay, so secondly, I'll go into the main results of our paper that basically reduces from module LWE to ring LWE after some tangent parameters. And finally, I'll talk a bit about a consequence of the reduction. Okay, so to start off with, what does a generic LWE type problem look like? Well, the idea is that you're given some uniform random A from some finite set and a search version of LWE would ask you to decode a noisy product. So you'd be given some B where B is A times S plus E for some small error and you'd be asked to recover the secret S. And the decision version of LWE basically asks to distinguish between the cases where B is a noisy product or whether B is a uniform random element. Okay, so for the original LWE problem, AMS are actually n-dimensional vectors where the entries of these vectors are integers module OQ. So all sort of arithmetic here is done over integers module OQ. And E is itself an integer and it tends to come from some distribution. So usually we assume that the error is somewhere from a discrete Gaussian distribution of integers. So that's what this case of sigma stands for. So sigma is basically relating to the width of the discrete Gaussian. And we usually take the secrets from the same distribution. So this is what's referred to as a normal form secret. And we do this because sampling secrets from the error distribution leads to a problem that at least as hard as sampling secrets uniformly. Okay, so when we tried to represent M L W E samples using matrices and vectors, what we end up with is this first component being an N by M-dimensional matrix where the columns are uniform vectors. And the second component is this M-dimensional vector B because we have M L W E samples here where each entry is basically the result of a noisy inner product. Okay, so and now when we're considering practical ring L W E, all that changes is that B, A, S and E are now sort of ring elements. And a typical choice of a polynomial ring is given on this slide. So these rings are called parity cyclomic rings. So once again, the idea is that you're given some uniform random polynomial, now A from this ring. And the search version asked to recover S from B for these noisy products where small e basically means that each coefficient on its own is a small integer when considered module. Okay, so the decision version would be simply to distinguish whether B is a noisy product or whether B is uniform random. Okay, so once again our error distribution is usually taken to be a discrete Gaussian of narrow width sigma. So now we're basically sampling the coefficients from this error distribution. Okay, so how do we represent one ring L W E sample using the same matrix vector notation as we did before? Well, the first component is this n-dimensional coefficient vector A and the second component is also an n-dimensional coefficient vector where each coefficient is basically the result of a noisy inner product. And the interesting thing here is that this matrix, well, the rows of this matrix are basically heavily correlated. So we tend to say that one ring L W E sample is in some sense equivalent to n-structured L W E samples. Okay, so now for practical module L W E, well, all that changes now is that A and S are now module elements and by a module element what I mean is that a D2 for a ring element. So once again we have the same sort of analogous definitions for search and decision module L W E where module multiplication is basically given by this kind of analogous thing to inner products of the vectors. So once again we have the same error distribution so we usually take the coefficients to be some sort of discrete Gaussian with sigma and writing things out in matrix and vector notation we end up with the following. So we have first component being n times D-dimensional coefficient vector now because remember we have D-ring elements making up this A and the second component is simply an n-dimensional coefficient vector where each entry or each coefficient is given by some noisy inner product. So in some sense we have that one module L W E sample is equivalent to n-structured L W E samples. Okay, so what are the popular rings that people use in practice while we usually stick to a priority cyclotomic rings and one of the main reasons for this is that we can actually form extremely fast ring multiplication by using non-theoretic transform techniques. So when sort of restricting to this form of ring the effective dimensions we can achieve are essentially for ring L W E at least are essentially the powers of two. So typically a typical choice might be that we choose a ring dimension of 1024 but what happens if we want to increase security by increasing this ring dimension while we have to jump all the way to 2048 in order to do this. So there's a huge jump in order to potentially gain a small amount of security. Right, this might affect our scheme in terms of force it's quite a lot but this kind of drawback can be mitigated by using module L W E because you can basically fix a small underlying ring of say dimension 256 and then set your module rank D to be whatever you want so you can effectively go from 1,000 dimension 1024 to 1024 plus 256 if you want to sort of increase your security. So the only kind of drawback of playing this trick is that multiplying module elements kind of costs a little bit more than multiplying ring L W E elements or ring elements of the same effect as I mentioned. So here's a short summary of what we know about the efficiency and lattice hardness of these L W E variants. So the first row basically says how many integers module O Q are required to represent so N noise in the products or N potentially structured L W E samples. So as you can see as we read from left to right we go from the least efficient to the most efficient but on the other hand the second row basically says that L W E is at least as hard as finding short vectors of a general lattice is module L W E the same but for module lattice and ring L W E the same but for ideal lattice. So the idea here is that as we go from left to right we go from a general problem to a more structured problem and therefore potentially our hardness guarantee is less sort of less strong. Okay so just before we get into the main reduction about paper or the main result about paper it should be clear that you can reduce from ring L W E to module L W E. So you would do this by starting off with some ring L W E sample so everything in red is basically something and the way you produce the module L W E sample is simply to sample a uniform A1 and an S1 from the appropriate sequence distribution and then all of a sudden your bold A along with B plus A1 S1 is a valid module L W E sample for the bold A and bold S ring on the slide. Okay so it's clear that module L W E is at least as hard as ring L W E when we fix Q which was the modulus and the error rate alpha where alpha is sigma over Q. So remember that sigma is the effective size of your error. Okay so what happens when you allow yourself to change Q and alpha? Well you can actually go the other way. So in the paper we basically show that there's a reduction that goes from module L W E in rect D and modulus Q to ring L W E in modulus Q to D and the main proof technique or main analysis technique are basically inspired by the classical hardness of learning of various paper. So if you know that work you'll probably see a lot of parallels drawn to this presentation. Okay so just before we start with introducing the overview of the reduction what I've kind of already defined is what you would use or I've basically defined the practical definitions of ring L module L W E but now since we're kind of reducing between problems we should really use the form of definitions and basically what I have on the slide is basically one step closer to the form of definitions of ring module L W E. So what changes really is that B before each coefficient was an inch of module L Q but now we're going to consider it to be lying in the continuous interval between 0 and 1. So in order to do this what all we do is we divide by Q and then make the error continuous. So the division by Q explains where there's a 1 over Q in front of the 8 times S and then we also have to note that E is now continuous Gaussian of width alpha where alpha is sigma over Q so the division by Q comes into this width as well. Okay so as an overview of what we want to achieve in our reduction we want to send uniform module elements to uniform ring elements and we also want to map our map between secrets to be somewhat reversible if we want to form a search-to-search reduction. And the last thing we want is that B tilde where B tilde is sort of our final target ring L W E and since we want that B tilde is a valid noisy product of A tilde and S tilde so we want this E tilde on the bottom right-hand side to be a continuous Gaussian of narrow width. Okay so here's the sort of intuition for the case where D equals 3 so the idea is that we're going to set the lower bits of the coefficients of A tilde to be the bits of the first polynomial the middle bits of the coefficients of A tilde to be the bits of the middle polynomial and the upper bits to be the coefficients or the bits of the coefficients of the final polynomial. And the same sort of thing holds for X but we do the same thing quite in the reverse direction. Okay so concretely we have A tilde that is A naught plus Q A1 plus Q squared A2 and S tilde is S2 plus QS1 plus Q squared S naught and what we have when sort of doing this math thing is that the normalized product of A tilde and S tilde is roughly equal to the normalized product of our original module elements when taken to line the continuous interval between 0 and 1 which more or less suggests that we can take B tilde to equal B and this is basically the error distribution that arises when doing this sort of simplified version of the reduction. So the right hand side is basically our error distribution or gives rise to our error distribution and the good thing about the first term is that it's already continuous narrow Gaussian so in essence we're targeting continuous narrow Gaussian so the first term is basically exactly what we want and this first term comes from the error from our original module LW sample the second term is this sum and the good thing about the sum is that it's small so it's small because we're only considering entities where I is bigger than J but the bad thing about this sum is that it obviously doesn't constitute a continuous Gaussian because these A, J and N size are basically three things and the second thing is that the coefficients if you were to expand this entire polynomial out you would have that the coefficients aren't independent but you can somewhat overcome this second issue by using the canonical embedding because of the way polynomial multiplication looks like in that space so what are the technicalities in the full reduction so what do we do in our paper well the problem is that we end up with an unknown bad error distribution that depends on our secret this unknown secret so we actually end up with some sort of discrete distribution of a sum lattice that depends on this and then to solve this problem we basically form this in essence the same reduction but in some randomised way and then we end up having to drown out this structure in our error distribution in some way so in order to do this we basically apply some techniques from the DJI's white paper and also if you read our paper you can see that we do in fact consider the canonical embeddings and dual rings as well as basically considering brand new divergence arguments throughout because we kind of know that this allows us to target a final error distribution that is a spherical Gaussian so when all is said and done what we have is an error expansion of n squared times root d but if you had to be satisfied with a small error distribution rather than exactly targeting a Gaussian error distribution you would probably not bother drowning and you would see a square root n d error expansion in practice ok so here is the summary of the result and it turns out that you can also play the same game but within a ring so you can have a reduction that goes from ring on w e to ring on w e that halves the dimension but squares the modulus ok so briefly I'm going to sort of tell you what Fritz analysis says about the hardness of ring on w e when you increase q but fix alpha so a requirement for say the prime will have to work is that alpha must be less than or equal to q to the minus m plus 1 over m plus n plus 1 so here m is basically the number of samples available to you so if you have one ring on w sample you effectively have m noisy in a product available so m in this case would be less than or equal to n ok so what happens when you replace q by q to the d well you end up with this second inequality which is basically harder to satisfy than the first so for any kind of scenario where you have a maximum number of ring on w e samples available to you you can basically keep increasing this d until the second inequality is not satisfiable so in some sense it appears that ring on w e gets harder if we increase the modulus ok so what does the standard reduction from lattice problems say about ring on w e well it says as long as alpha q is going to something asymptotic in root log n then ring on w e is at least as hard as finding short vectors over ideal masses to approximation factor gamma so we're not looking for the shortest vector or the thing for things in length gamma times the shortest vector so the interesting thing is this gamma is independent of q so if we replace q by q to the d we get the same hardness guarantee so to summarize the different perspectives we have that for cryptanalysis it seems like increasing q makes things harder but increasing q doesn't really change things from the perspective of the theorem from a previous slide ok so if you try and build a hardness landscape around r reduction this is essentially what you get so you get the top row the top like double-ended arrow is basically in a equivalent between ring on w e and module l w in rank 1 the arrows going from right to left are a result of the trimmel or straight forward reduction that goes from ring on w the module l w in any rank and finally the arrows going from left to right are a result of the main reduction of bar paper so the one that goes from module l w to ring on w e so if you read down the right hand side you do get that the hardness of ring on w e appears to increase as we increase the modulus ok so just to conclude the talk corollary of our work is that we've shown that certain ring on w e instances are at least as hard to solving the module s i d p property and this kind of conclusion is basically utilizes the hardest guarantee given in the original module l w paper so also this result augments the result that says ring on w e so at least it's finding short vectors of ideal answers the only thing to keep note of is that when we perform our reduction from module l w to ring on w e we're actually reducing to a ring on w e problem that appears to be slightly harder than the ones used in the literature so in particular they require a larger module lattice rank in order to be able to solve nonetheless we basically showing that for any module l w problem you can define a ring on w e problem that's at least as hard to solve as your original module l w problem and we've shown especially what the relationship between the parameters should be ok so that's all I have to say and thanks for listening


Well, good afternoon ladies and gentlemen, thank you very much for joining us here today. Thank you and welcome to our audience who are viewing this issue briefing on our webcast platform at www.weforum.org. Very excited to be here. This is our first issue briefing in the history of the annual meeting in Davos. They're slightly different to the normal fare you have here. They're not press conferences, they're not announcements and such. It's simply a tool for taking some of the high-class intelligence that we are able to convene upstays in the Congress Center and bring some of the cleverest down here to answer questions on topics which we know of particular persons and particular interests. As I mentioned, it's the very first one. It's on the subject which is a perennial favorite on our own forum blog platform Artificial Intelligence. I'm going to keep this very free and hopefully informal. I'm going to ask our two speakers who I will introduce in a second to make some brief remarks on the session they've been participating in this morning and also give us the benefit of their experience in the field of artificial intelligence. And then we'll leave it open for Q&A. So without further ado, I'm very, very pleased to be joined by Alison Gopnik, Professor of Psychology at the University of California in Berkeley. And Ken, thanks very much indeed for joining us. Ken is a professor also from Berkeley and his specialist area is robotics. Alison, perhaps we could start by giving us a bit of a briefing on your particular entry point into this subject and perhaps share some thoughts from the session this morning. So I actually study how children can learn as much as they do. And about 10 or 15 years ago, we started collaborating with computer scientists who were trying to design machines that could learn in the way that children do, partly to figure out about machines, but also to use that as a model for children. And I think one of the things that, points that Ken made in his talk, is that the interest of AI has been to discover that many things that we thought were going to be very hard have turned out to be pretty easy. And things that we thought were going to be very easy have turned out to be very hard. So for example, it turns out to be much easier to simulate a grandmaster chess player than it is to simulate a two-year-old. And what we've realized is just, this has made us realize just how much, even say, what a two-year-old learns involves processes that we don't really understand very well and that are very powerful indeed. And I think that was one of the themes that came up in the meeting, is that things like chess or theorem proving the great ways that nerds prove their machismo have turned out to be not actually so hard, whereas things like picking up a cop or recognizing a face have turned out to be. Or getting to an appointment on time. Okay, robots are much better at doing that because they aren't distracted. So I think that was one message. And then another message that Ken emphasized and others emphasized is the question about value. So we know that if we have a goal, we can design a machine with a lot of, by using a lot of smarts ourselves that can get to that machine. But it can get to that goal. But then when the decision becomes, which goals are actually worth getting to, that's something that's a much harder thing to get a machine to do. Should I please follow up on that? Thank you, Allison. So we actually had, we came to a fair amount of actual agreement that in particular, you've heard so much of the press coverage recently about Stephen Hawking and Elon Musk talking about the singularity. And so one idea I want to propose is that it's time to actually move beyond the singularity. And instead, I propose the multiplicity, excuse me. The multiplicity is the idea of many people, groups of people working together with groups of machines to solve problems. So this is, I think this is actually a much more constructive idea because it actually is something we're already doing. In a sense, if you think about Google's search engine, is a multiplicity. The way it works is that every human, it's using all the human linking structures, human provided linking structures. It actually is testing humans all the time when you gives you a list of responses for a search term. It sees what you click on and it uses it to update so it's smarter the next time. So it's using humans and machines. And that symbiotic combination is something we don't understand enough about yet. So one of the areas of interest at Berkeley and their labs is how do we start really developing a science for this kind of both collective intelligence of humans but also collective intelligence where humans and machines are interacting with each other. So that, we think that that, and I don't think the term multiplicity has been put out there yet. We're hoping if you as a press can circulate it. This is our first announcement of that word. We'll see if it catches on. But I think that that idea is, it's time to start talking about that instead of singularity. And the other idea we talked about this morning was that there's been a big advance in the field of robotics, which is we've always assumed that robots have to carry all their computing on board. It's just an assumption we never questioned. But it's actually, we're now realizing that it's not the case. That robots will almost always be in a place where they can get access to the cloud. And now we can do processing in the cloud so that very complex statistical computations can be done in the cloud. But then the side benefit is that all that data is available in the cloud so that it can be shared across robots. So that the collective can grow and exchange ideas and information and models between each other. So collectively they get much better over time. So this idea of cloud robotics is another new development. So actually this is a press conference. We have an announcement. Multiplicity is a new word in the parlance of artificial intelligence. Both, can you perhaps say your personal highlights or key learnings from this morning's session? There were four people on the panel, I understand as well, and computer scientists, not just yourself. So it's a collaborative effort advancing artificial intelligence. Anything that our colleagues here should be considering writing about. Well, there's one thing I think we completely agree on, which is that there's certain categories, I would say, that have to do with aesthetics and art, emotion, and design. And one is humor. I don't think we'll ever see a robot telling a great joke in our lifetime. And so there's a lot of limitations or essentially areas where I conceded to the opposition on those points. I think that they're not going to make better jokes than humans. Maybe I'll be wrong. But and then the other thing that surprised me at least was, fascinating study of human nature. Everyone voted on which side they agreed on at the beginning and then at the end. And almost no one changed their mind, despite an hour of us trying to offer new ideas. Nobody changed their mind. So this confirmation bias is incredibly alive and well. I think that's true. But I think also part of the reason for that was, in a way, there was, for a debate, there was more agreement than in some ways there was disagreement. Because I think there's pretty general agreement that computers have gotten to be very good at certain kinds of things. So being able to learn from big data sets, for example. Those techniques for statistically pulling out statistical patterns from big sets of data, that's been a real advance. And everyone could agree that that's been a real advance. Using things like Bayesian probability theory to make inferences, that's been a real advance. And everyone could agree that that was a real advance. The places where, if it's going to be solved, as Stuart Russell said, it'll be three or four breakthroughs, at least down the line, are things like creativity, being able to actually think of a new idea, being able to change the idea you already have, integrating the kinds of things that we humans do with emotion into what AI does. That's something that we don't understand very well. And figuring out how exactly we manage our values. What it means to have a moral system, what it means to have a value system, how it is that we can decide, as people at Davos do, for example, that we need a new value system, that the value system that most people hold isn't working and we need to persuade people to shift their values. That's a very, those are all things that are way out on the horizon, that have been very, very far removed from what current systems. Although it just came from another session, we were talking about manners and digital, this sort of obnoxious behavior of holding your phone on where you're talking with someone. And we were saying that, well, we really can change, I mean, manners and behavior can change. And an example of this is smoking, right? It was just not too long ago when it was very common to just have cigarettes at the table, et cetera. And now, at least in the US and I think many other countries in Europe, you really can't do that anymore. And we've adapted in a relatively short time. So maybe we need a call for a kind of manners, change of behavior in terms of other, in terms of technologies, as there should be a school of etiquette that we should maybe learn and then start to adopt so before it's too late. I think another, I think another issue that came up in the meeting that I think is worth pointing out is that in some ways they were sort of two separate questions. One of them is, will we have the super intelligent computers any time soon? And at least things like being able to revise and change what we think, being able to be creative, to being able to have moral values. I don't think any of those are on the horizon. But I think another thing that came out is there can be lots of damage without having the super intelligent computers.  We have plenty of natural stupidity.  So we do have to think about how we regulate things like autonomous weapons, an example that Stuart gave, or things like a machine that can suddenly change the way the stock market works. And we need to think much more about how to do that. Now, that all is true even with machines that aren't anywhere nearly as intelligent as we are.  We should have two-year-olds at the World Economic Forum. Yeah. That would be a great session. Noted. Let's work with that. Before I hand over to questions, what was the voting? Give us an idea of what the voting was before the end of the session. Okay, so at the beginning... We won, by the way. Let me just point this out. They won by a slim margin. But it was about 50-50 about who we thought it was that machines would make better decisions than humans. And at the end, it was the same. There was a few points that they had changed. They had beaten us. It was interesting that it was 50-50. I wouldn't have predicted that. I wouldn't have either. Yeah. Very interesting. Okay, let's have some questions. Okay, we'll have a microphone down here for the benefit of our audience. Mike, could you also give your name, please, and your outlets? The gentlemen will take yours and Michael there in the front row. Hi, it's Jim Edwards from Business Insider.  Is he right?  No. No, absolutely not. First of all, thank you for being from Business Insider, which ranked UC Berkeley as the number one school to study robotics. So thank you. Sorry, Casey, isn't it? But I will say that, no, this is actually, this kind of fear is exactly what the wrong thing. What we need to be doing now is being constructive, not talking about this singularity, because I don't think that's even close. I think what we, the much better, more interesting thing is this multiplicity idea. Michael De Allen from Portugal and Denmark. Could you please broaden out the perspectives in these cloud robots you were talking about? Well, so there's really five, very quickly there's five advantages to having robots connected to the cloud. The first one is access to data, because you can suddenly, you can carry maps, you get access to maps and all kinds of models of objects around you. It's enormous. Second is computation. So when you want to be able to plan a series of motions, that is actually right now with uncertainty as the central problem for robotics, it requires vast amounts of computing, and you can't carry that much computing on board, so you can do that in the cloud. And the third one is the idea that the cloud is actually providing the ability for robots to communicate with each other and share information. So every time a robot is acting in the world, they're doing essentially an experiment. So they report back the outcome of that experiment and that gets shared and integrated together. The fourth one is the idea that the cloud is facilitating the exchange of humans sharing software, and this is accelerating research in robotics. So there's an open source platform called ROS, and something else called Robot, Robotics has a service that is a new idea, which is basically where you'll be able to very quickly, it's a software architecture that lets you very quickly get access to robot algorithms. And the very last one is that no matter what system you have to program your robot, there'll always be cases where things fail, or it gets stuck. And then, because you're access to the cloud, the robot should identify those situations and then can tap into a human call center. So it sort of reverses what we have now where we get a robot on the phone, the robot will call and get a human on the phone, it will help diagnose the problem and resolve it. The robot will say, oh no, not one of those humans again. Yeah, so I think those things are all, that's opening up all those five channels are brand new and they're really accelerating the field. Fascinating. Gentleman at the back there, please. And then after that, the gentleman there in the middle. Hi. I'm Zontek. I just would like to add to that question before, do you have an idea or a vision what kind of jobs are going to be replaced by robotics or artificial intelligence the next five to ten or even beyond? Yes. So I do have one answer to that and I'm going to yield it to Allison in a minute because in the Swiss expertise, they have scheduled me to be at a panel in seven minutes. So I have to dash over to there and I apologize. But I will say this, that I do have an idea about that. I think that there's huge opportunities right now for teaching. That there's a vast need for teachers, not just in classrooms but for teaching all kinds of things. And that is under tapped right now. So could we find a way economically to allow people to be rewarded for teaching? We feel, and I think most of us have experienced, teaching is extraordinarily rewarding. So someone out of work, if they have even part-time jobs teaching in some fashion, I think there's enormous potential for that. And so if we can transform the people who are put out of work, which will be inevitable in the short term, start to use technology to allow them to teach in new ways. I think that could be a really constructive outcome. So is it okay if I depart? Please do. All right, I apologize. Thank you very much. You're in excellent hands because Allison's terrific. All right, thank you. So get your hard questions ready now. We just have Allison here. Do you have any comments, Allison, on that one point? The jobs and I guess the most obvious economic impact? Yeah, I mean, I think it's fairly clear that jobs that were just as jobs that were once mechanically done by people in factories are now being done by robots. Some jobs that were done using our minds and brains are going to be increasingly done by artificial intelligence. But I think part of what comes out of the session is that there's enough scope for the things that people are much, much better at than computers. That the optimistic thought, and those are the things that are the most human ones anyway, being able to do things like have creative new ideas or consider changes in values. If more of us were engaged in doing that, if we could find a business model for creative thought about progress in the future, then that might not be a bad thing to happen at all. Okay, if I may, we'll take one more question before we close this gentleman here by the middle. Tetsuya Gorashi from NHK Japan, nice to meet you. I have like three questions, but I'll just take one. I've been researching about the advancements in technology, and well, in the past five years there's big advancements. What do you think the societal drivers of... Those advancements. There's a very interesting point, Ken mentioned talking about his multiplicity idea, which is that a lot of the big advances have come because the computers have really been using these millions and millions of examples of these incredibly high-powered computers that have been chained together in a way that they never were before to solve problems, namely all the human beings who are using the internet. We have these fantastically powerful computers, and they're all working together to put cute cats out on the internet. And then Google can actually use the output of all of those people finding the best cat picture to get an algorithm that actually lets you recognize cat pictures, which is something that every one-year-old can do with much less data. So some of the advances have come because there's been big improvements in our ability to do things like pick out statistical patterns. But a lot of the advances have come because there's now data available, not only big data in large quantities because of the internet, but also data that's been pre-digested by human beings. So to take another example, machine translation depends on the fact that we have access to millions of human beings who are translating data all the time. And a lot of the advances, you know, the terrible dystopian picture in the matrix of, you know, we're all lying there thinking that we're having fun, but really we're just feeding the machines. That's actually just true. So as we're sitting there putting up Instagrams of our cute cats, what we're also doing is giving data and information to machines in a way that they didn't have it before. So it's an interesting question. Is a computer aided by a million human beings who are doing the work without knowing it, a super intelligent computer, or not? It's not super intelligent in the way that a baby is super intelligent, but it can do things that we really couldn't do before. So I think there's quite a lot of reason to believe that having the internet, having computers be able to have access to all of those brains and the output of all of those human brains and use that in their computing has been the thing, or at least one thing that's made the big difference. Alison, a final word if I may. What would be the focus of your work in 2015? Well, what we're interested in, so let me back up for a minute and say what Alan Turing proved all those years ago was that if we can take any process and describe it in a systematic step-by-step way, then we can program it onto a computer. So when we say computers can't do things, what it means is we don't really understand how they're done yet. So the thing that we're trying to understand is what is it possible for people to be creative? That's something we just kind of take for granted. But if you think about creativity from a computational perspective, what it really means is there's this infinite enormous scope of possibilities, possible ideas that we could have, possible skills we could have, possible ways we could organize ourselves into a society. Somehow you have to decide which one of those is going to have the best outcome without knowing it in advance, and somehow human beings, in fact, not just even, but especially three and four-year-olds, can get a sense of, here's a crazy weird idea, but it's sort of in the ballpark of something that would work. And we don't really know how that's possible for adults, creative adults who are innovative like scientists, or for two and three-year-olds who are pretending, or for computers. So what I'm working on right now is to try and see, can we give some kind of story about how things like play and imagination could actually be implemented in a computational way. Well, thank you very much indeed. We're running out of time, and like all Swiss organizations, we must.


Welcome. I welcome you all to this lecture in the course, Samasa in Paninian Gram. Two, as is our practice, we begin our lecture with the recitation of the Mangalacharan. Vishvesham Satchitanandam, Vandeham Yokilan Jagat, Charikarthi Bari Bharati, Sanjariharthi Leelaya. Vishvesham Satchitanandam, Vandeham Yokilan Jagat, Charikarthi Bari Bharati, Sanjariharti Leelaya. In this course, we are focusing on the three types of samasas stated in the Paninian grammar and also the Paninian grammatical tradition, namely the Avyaibhava Samasa, the Bhuvrihi Samasa and the Dhvandva Samasa. Currently, we are focused on the Avyaibhava Samasa. This is an extremely important type of samasas in Sanskrit. The features of Avyaibhava Samasa can be represented in the form of an equation mentioned on this particular slide where we have X and Y as two independent and separate entities in terms of the word form as well as the meaning as well as the accent. These X and Y, they are semantically, however, are related. Now, the speaker of Sanskrit decides to merge them together and bring out an output as one unit which is XY. So, XY is one unit which becomes a part of the sentence as such. Now, XY is one unit in terms of the form as well as the meaning as well as the accent. So, XY has got three important features. Now, this XY which has got these two constituents X and Y, amongst them X operates as the head of the unit XY. Both formally as well as semantically. Now, in the Avyaibhava Samasa, X which is occupying the initial position always is an Avyaibhava. Now, this influences the overall formal state of XY as well because XY is also termed as an Avyaibhava. XY is an Avyaibhava Samasa and Avyaibhava Samasa is also stated to be an Avyaibhava by the sutra Avyaibhava stha 1141 of the astradhyayi of Manini. So, XY is an Avyaibhava. Now, the term Avyaibhava turns to be significant over here because Y is not an Avyaibhava. So, XY cannot be called an Avyaibhava, but now it is termed as Avyaibhava. And so, an Avyaibhava, Avyaibhavati Avyaibhava, this is how X formally acts as the head of the Avyaibhava Samasa. Also, the meaning of X namely Avyaibhava will act as the head when XY is semantically related with any other word in the sentence. And therefore, X is marked with the bold characters on this particular slide. These are the features of the Avyaibhava Samasa that we have studied so far and we have been studying for some time now. Some of these features are mentioned repeatedly primarily because they should be highlighted regularly. And because of this highlighting, the student should get them into his or her system without too much effort. That is the aim of this particular repetition. In the astradhyayi, the Avyaibhava Samasa is treated at different places in different ways. For example, the Samasa Vidhayaka Sutra or the compound prescribing sutras stating specific particular conditions under which the Avyaibhava Samasa takes place from 215, which is Avyaibhavah, up to 2121, which is Anyapadhar Thecha, Saudhnyayam. This is a section of rules in which we find sutras stating the prescription of the Avyaibhava Samasa. Incidentally, 2122 is Tattpurusha. From 2122 onwards, the sutras prescribing the Tattpurusha Samasa begin and we have studied these sutras in the first course on Samasa in this particular series. Then we have one more small section from 54107 up to 54112 in which the Samasanta Pratyayya is stated, is prescribed. These are the Samasanta Pratyayya Vidhayaka Sutras, sutras which prescribe the suffix to be added at the end of the Samasa. And then, Svaravidhayaka Sutras are there, for example, 62121. This is how Avyaibhava Samasa is treated in the Ashtadhyayi. Right now we are focused on the Samasa Vidhayaka Sutras, so we have been studying them one by one. We have already studied Avyaibhava and then the big sutra, Avyaayam Vibhakti Samipa Samraddhivridhyartha Bhavatyaya Sampratishabdha Pradur Bhava Pashchad Yathanupur Vyagapadyasadrishya Sampatti Sakalyanta Vachaneshu. And then we also studied Yathasadrishya and Yavadavadharane. Let us proceed further and study the next sutras. 219 is Sup Pratina Matraarthay. There are three padas in this particular sutra, Sup, Pratina and Matraarthay. Sup is one slash one. So, this becomes Upasarjana by the sutra Prathamangirgistam Samasa Upasarjanam. And so it occupies the initial position of the Samasa by Upasarjanam Purvam. Then Pratina is three slash one of the word Prati, which means together with the word Prati. It is to be noted here that the pattern is slightly changed in this particular sutra. So far avyayam which was in Prathama was continued in every sutra. And so because avyaya is in Prathama, it used to occupy the initial position of the Samasa. Prati also is an avyaya. However, in this sutra it is not mentioned in Prathama. Prati is mentioned in Truthiya and therefore the difference in this particular sutra and the output generated by this particular sutra is that the avyaya namely Prati does not occupy the initial position of the Samasa. Whereas the other interrelated Subanta does occupy the initial position of the Samasa, avyayibhava Samasa. This is the difference. Now matra arthe is seven slash one of matra artha. Matra artha is matra artha. Artha or meaning of the word matra in the sense of less amount. Matra means bindu, stokam, alpam. These are all the synonyms. Matra bindu, stokam, alpam. Small amount, less amount, a drop that is what the word matra stands for. The words continued are avyayam, sahasupa, samasaha, avyayibhava and samartha padavihi from 211. Avyayam from 216. This gets transformed into Truthiya however avyayena. Sahasupa continues from 214. Samasaha continues from 213. Avyayibhava continues from 215. So the meaning of the sutra available to us is the following. Any Subanta is compounded with another semantically related avyayasubanta namely prati. When less amount is the sense conveyed by the compound and the resultant samasaha is called avyayibhava. I repeat any Subanta, sup is compounded with samasya te another semantically related avyayasubanta prati. When less amount is the sense conveyed by the compound and the resultant samasaha is called avyayibhava. This is an exception to the general rule that an avyaya or indictlinable occupies the initial position of the samasa. Here the avyaya is occupying the final position of the compound. This is why it is an exception. Let us look at the example. So the meaning to be conveyed is there is less amount of vegetable. There is very little amount of vegetable in this. This is the laukika vigraha. So now this gets transformed into shaka plus su plus prati plus su. Prati here denotes asti atrakinshet the less amount. Because prati is stated in tritya it does not occupy the initial position rather the word sup occupies the initial position. Prati occupies the final position of the compound. So we have shaka plus su plus prati plus su as the laukika vigraha. Then samasa saudhnya takes place. Then the pratipadika saudhnya also takes place. Then we apply supodhatup pratipadika yoho 2471 and delete both the sup pratyayas namely both the su's. So we have shaka plus zero plus prati plus zero. And when we join them together we get shaka prati as the finally derived compound output. When we use it in the sentence we add the sup suffix su shaka prati plus su. And then because shaka prati is an avyayya we apply the sutra avyayadab supaha 2482 which deletes su and so we get the word shaka prati as the subanta form from shaka prati which is a compound. Which means asti atrakinshet shaka. Now in the absence of the semantic condition matra less amount when that is not intended the compound does not take place. For example when you have vaksam prati vidyutate vidyut. Here the word prati is used. It is also semantically related with vaksam because it indicates that the word vaksha and its meaning is the mark or the sign where the lightning shines. So it is the laksana and therefore vaksam has got the vidyavibhakti. Prati has become karma pravachaniya because of the sutra laksanittham hutathhyanabhagavipsasupratiparyanabhaha. And then because of the sutra karma pravachaniya yukte vidya vaksha has got the vidyavibhakti. And that is how vaksha and prati are semantically interrelated. In spite of this because the sense is not that of matra vaksha and prati are not compounded in this particular sutra. The lightning shines where the tree is that is the meaning of the sentence vaksam prati vidyutate vidyut. Here vaksha and prati are not compounded because there is absence of the semantic condition stated in this particular sutra namely matra aratha. This we must note. In the previous sutra 219 the word prati na occurred in the tratiya vibhakti. As a result prati which is an avyayya did not occupy the initial position of the avyayi bhava samasa which is the general practice. Something similar happens into 110. The sutra is aksha salaka sankhyaha parenah aksha salaka sankhyaha parenah. So there are 2 padhas in the sutra aksha salaka sankhyaha which is prathama bhavachana 1 slash 3 and therefore the padhas stated in this big compound aksha salaka sankhyaha. They become upasarjana by the sutra prathama nirvistam samasa upasarjanam and they will occupy the initial position in the samasa on account of the sutra upasarjanam purvam. There are 3 constituents of the samasa aksha salaka and sankhyaha. Now the second padha in the sutra is parenah which is 3 slash 1 of pari and the word means with the word pari. Words continued are avyayam 216 sahasupa from 214 samasa from 213 avyayi bhava from 215 and of course samartha padavidhi from 211. Avyayam is transformed into avyayena. Now the meaning of the sutra is the following. The subanta aksha salaka and sankhyaha are compounded with another semantically related avyaya subanta pari and the resultant samasa is called avyayi bhava. I repeat the subanta sup aksha salaka and sankhyaha are compounded with another semantically related avyaya subanta pari. parenah avyayena samarthena subantena sahah and the resultant samasa samasaha is called avyayi bhava avyayi bhava. Now it must be noted here that the output samasa is used in a very very specific environment that of the game of dice. As the traditional commentators say kitababh vyavahare or jyutabh vyavahare samasoyamishyate. We don't use this output in any other context but the jyutabh vyavahare the game of dice or kitabh vyavahare the game of dice. And that too there is further specification and that too only in the context of defeat or loss. So kitabh vyavahare or jyutabh vyavahare is supposed to generate two results loss or defeat or win. And this particular samasa indicates or denotes the state of loss. vipate or parajaya eva this is the specification specified context in which this output generated by this particular sutra is to be used. Let us study the specific context in some more detail. A game of dice called panchika is played with five dices. So panchika nama divtam panchabhir aksayi shalaka bhirva bhavati. Now when all five dice fall in the same manner either facing up or down the thrower wins. Otherwise the thrower loses. That means if one amongst the five dice falls in a different manner the thrower loses. That's what is stated in the Sanskrit commentaries quoted on the slide. If aksayi shalaka bhavati krtsnaha all uttanaha facing up avanchova or facing down patanti tadapati tajayati only then the thrower wins. Anyatha means when all krtsnaha are not uttanaha or krtsnaha are not avanchaha then the thrower pataita parajayate. Then the thrower loses. It is thiti. This is the rule. This is how the game is played. Now in order to denote this loss or this defeat the compound is used and various compounds generated by this sutra are used. Let us see the example. The dice behave differently or in opposite manner. Akshena viparitam vrittam which means that all five did not fall in the same manner either facing up or facing down. Perhaps four faced down and one faced up or something like that. Akshena idam natatha vrittam yatha purvam jaye. So in the game of dice initially you win when all five fall in the same manner. But now the times have changed and now the dice is falling in different or opposite manner. That means not all are falling in the same direction. Akshena idam natatha vrittam yatha purvam jaye. So now this laukika vigraha akshena viparitam vrittam gets transformed in the form of an a laukika vigraha aksha plus ta plus pari plus su. Since parena is mentioned in tritiya even though pari is an avyaya it does not occupy the initial position of this avyaya bhava samasa. Aksha however occupies the initial position so aksha plus ta plus pari plus su is the laukika vigraha that we have here. This gets the samasa saudhnya and then it gets the pratipadika saudhnya and then we apply the sutra supodhatup pratipadika yoho to delete both the soaps. So we have aksha plus zero plus pari plus zero. So we have aksha pari after joining them together as the finally derived compound output. Now when we use this samasa in the sentence we add the suffix su in order to make it a padha. So we have aksha pari plus su and then we apply the sutra avyaya dhap supaha which deletes the su after an avyaya. An avyaya bhava samasa is an avyaya because of the sutra avyaya bhavascha. So we have aksha pari plus su and then su gets deleted and so we have aksha pari plus zero and finally we have aksha pari as the padha to be used in the sentence. What it means is that jaya yatha parivartita vyam tatha na parivratam. The dice which should fall in a particular manner which would result in the win, the dice did not fall in the same manner. That is what is the meaning of aksha pari. Similarly shalakaya viparitam vrittam in the same sense.  So we have shalaka plus zero plus pari plus zero. So we have shalaka pari as the finally derived compound output and then when we use it in the sentence we add the suffix su.  Which means shalakaya piparitam vrittam. The dice behaved in an opposite manner resulting in the loss. Now the word sankhya stated in the sutra refers to the words meaning sankhya ek dvi, tri, chatur etc. Now when the meaning to be conveyed is differently or opposite behaved by only one. So four out of five behaved similarly only one of them behaved differently. When this is to be stated and when the defeat is to be the meaning come to be conveyed we say ekena viparitam vrittam. This is the laukika vigraha and then we have ekha plus ta plus pari plus su as the laukika vigraha. Then samasa saudhna takes place and pratipadika saudhna takes place and then we apply supahadhatu pratipadika yoho to delete both the subs. So we have ekha plus zero plus pari plus zero. And when we bring them together we get the finally derived compound output namely ekha pari. When we decide to use it in the sentence we add the suffix su to it. So we have ekha pari plus su and then we apply the sutra of yahadap supaha and delete the suffix su and so we get the form ekha pari. Which means only one amongst the five ties behaved differently thereby resulting in the loss. Similarly when we have the meaning differently or opposite behaved by only two the vaphyam viparitam vrittam we follow the same process. The meaning here is that two of them, two of the five behaved differently.  Then we get the samasa saudhna and then the pratipadika saudhna because of which then we apply the sutra supahadhatu pratipadika yoho and delete both the subs. So we have v plus zero plus pari plus zero and when we join them together we get the form dvipari. Then we add the suffix su after dvipari when we decide to use it in the sentence. So this su gets deleted because of the sutra avyayadap supaha and so we get the form dvipari. Which means only two amongst the five ties behaved differently thereby resulting in the loss. Now the next example is differently or opposite behaved by three. So trivihi viparitam vrittam and here we have three plus vhyas plus pari plus su as the laukika vigraha. So we get the samasa saudhna and we get the pratipadika saudhna.  And then we add the suffix su tripari plus su and we delete it by the sutra avyayadap supaha. So we have tripari plus zero that is tripari which means three amongst the five ties behaved differently. Perhaps they fell with faces up or face down and remaining to behaved differently thereby resulting in the loss. And finally we have the example where the meaning to be conveyed is differently behaved or opposite behaved by four. Chaturvihi viparitam vrittam. So this is the laukika vigraha and the laukika vigraha is chatur plus vhyas plus pari plus su and then samasa saudhna takes place. The pratipadika saudhna then takes place. So we apply the sutra supahadhatu pratipadika yoho and delete both the sups. So we have chatur plus zero plus pari plus zero and so we have chatur and pari and then this ra becomes the visarga. So we have chatur and pari and then finally this visarga becomes sure. And so we have chaturpari as the finally derived compound output. Idudupadhasya cha pratyayasya is the sutra which substitutes sure. So now we have chaturpari plus su and then this su gets deleted because of the sutra avyayadap sobhaha. And so we get the form chaturpari to be used in the sentence. What it means is that the four amongst the five tithes behaved differently thereby resulting in the loss.  But it resulted in the loss. This is a very specific semantic condition the game of tithes and that too the loss that has become the subject of this particular sutra. So this entire process of semantics is summarized in a verse available in the tradition. Which is quoted on this particular slide. It says, When the five shalakas or dice they are a group. This will result in the victory or win. Aksha dayah atratiyan taha urbhoktasya yathana tathu. However when aksha etc when they do not behave in the similar uniform fashion urbhokt then they get compounded with the word pari. And then we have the samasa kitavabhya vaharecha ekatve aksha shalaka yoho. So kitavabhya vahara is what is the specific semantic condition that we have here. This is the explanation of sutra 2110. Very specific semantic condition. Next we continue how the processing of the ave bhava samasa happens with remaining semantic conditions stated in the subsequent sutras. And we study that and how this process progresses to derive the final output in the form of a nominal root or prathipadika and how that output behaves in the sentence. This is what we study in the subsequent sutras which come in the next lectures. These are the texts referred to. Thank you very much.