Good afternoon. We're here to share our absolute enthusiasm about the transformation that is happening in geoscience, teaching and learning, afforded by a virtual microscope. Behind this proposal are the four traditional Irish universities that have been teaching hands-on practical skills over centuries. Our task is to transform and translate this knowledge into the digital age. For this we have partnered up with the Open University, an internationally recognised leader in distance and e-learning. The faces behind this proposal are these. Today we've got here Theresa, myself from Trinity, we've got Simon from the Open University, Julian from UCD and Shane from Nuig Galway. Basically this slide encapsulates what we feel this G-Lab is really affording us to do. A virtual microscope is not only an enhancement, yes it's substitutes and augments a traditional microscope, but because we can direct students to a point on a thin section as we will show this affords a transformation in learning and teaching. Self-guided investigative study and for the first time peer group and learning on the virtual microscope. So we'll go through what, how, outcomes and impact and I'll hand over to Theresa. So what is G-Lab? G-Lab is a transformation. We are converting the traditional microscope from just being a magnifying glass into an investigation tool for students to learn by themselves. We can familiarise the students with the thin section of rock like this one I'm handing here or the one you have on the screen before the practical. When you stick a thin section under the microscope, the biggest area you're able to see is that black circle. So only up to four millimeters in diameter. So you don't have perspective. It's like if you feel, if you find yourself in a city like this one or a city like that one or like that one, you have no idea where you are. Only if you are able to zoom out from this image, you will realise you actually are in Dublin or in Cardiff or in two. So by being able to zoom in and out from the thin section, same as in Google Earth, our G-Lab is going to make the students be able to familiarise with the thin sections at different scales before they come into the lab. Therefore, when they come into the lab, we no longer will be a troubleshooting clinic. We will convert ourselves into an investigative session. Not only we can familiarise the students before they come into the lab, but also we can guide them better. So when we have a look at the thin section at the very different parts of it with a traditional microscope, we might be missing the most important bits of it. With G-Lab, we can actually share with our students a link that directs them directly where we want them to look at. For example, this image here which is a transformation process of one mineral into another, which they have a look at before in lectures as a quantitative process and they are able to see life in a rock, the frozen process throughout this vitro microscope because we are able to tell them where to look. So first of all, we familiarise them with the thin section, then we can guide them through the thin section and then after the lab is finished, we can ask them to do more at home. So for example, last year we asked 23 students to make 10 measurements of angles on a thin section and they can do that with G-Lab as well. They are able to measure these angles and then we asked them to put the results together. So they shared the results with each other and they built this diagram in which they saw that all the angles were the same and they had to discuss why this was happening and what kind of process on earth would provide them with this result. And then it was them who came to us and taught us what they had discovered. So we inverted the classroom and they were learning by themselves and pea discussing and pea learning. So we can familiarise them before they come into the lab, we can guide them better and we can ask them to discuss and learn and come back to us and teach what they learned. So what is the intention here? What we're going to do is to take 40 years plus of understanding a pedagogy. Each university has its own teaching collection and experts who spent many years teaching that. So that knowledge we will take, we will digitise and we will use teaching in the future. So it will become a much longer time scale. What we're going to do is convert or expand the existing collection that we have with Trinity to make it a complete Irish collection. What most universities, my experience is what most universities want is their own rocks digitised. So if you are in a particular locality you will tend to teach with rocks in that locality. We intend to employ an education assistant for the time scale of this and the point is the assistant will gather that information, will begin to create tutorials online and using the two parts of our platform to create this collaborative system that will allow the four universities to be able to work together and do something which has not been possible before. I'm from the Open University, I led the project Create the Virtual Microscope. Virtual Microscope is not unique, there are many virtual microscopes out there. This one is the only earth science one and we have several different collections. I'll explain a little bit about that in a second but it's very important that it makes these samples available to students that they wouldn't normally be able to get to and it makes it a very different experience. Virtual Microscope is a platform, it's a HTML5 app for those who are technical. You can look at rocks in plain polarised, cross polarised, you can rotate the samples which is a key point. The aim of the Virtual Microscope is to help students to learn to identify, classify, in other words to learn how to see like an earth scientist. It's a similar practical skill that we teach in other areas of science. The reason or one of the main reasons for doing this was that there's an old adage that the best geologist is the one seen the most rocks. It's that observational skills, it's not something you can pick up from a book. So you can look at these two pictures and they look like quite nice pictures but to a geologist they look quite different because we spent far too long staring down microscopes. So at the top there you have a basalt erupted from a volcano 55 million years ago. This happens to be from Giant's Causeway. I didn't knock the piece off Giant's Causeway by the way, that isn't a museum. And it's a particular style of rock, it has particular features, random blazer plagioclaves. The one at the bottom has random blazer plagioclaves, roughly the same grain size, the same mineralogy. But that one is from the moon. The point is the students can study moon rocks just as easily as Giant's Causeway. Because it is online and we built the system like this, it has built in analytics so that we can see what the students are doing. So on the left, yes, left, you can see the Trinity Collection. It's a series of about 18 rocks from the teaching collection at Trinity, which we digitized a couple of years ago. On the right is what they've been doing this year. So I can tell you which days they had their main petrology teaching classes, which days they were doing the exercises that Theresa was just describing to you. We can see what times of day even they access, how many students are access. I know that the average students are on an average of 9.24 minutes. It's just quite a long time, given that that's the average. It does help engagement, because you can expand beyond that Wednesday afternoon between 2 and 5. So the second part of the platform, so I should emphasize the first part, that's an open university, it's an open educational resource. We're using the same software in the site, which is open, as we use for open university students. In essence, part of the sustainability is the fact that we use the same system. The second part of the platform is Blackboard. We have what the intention is that we'll create a master module in Blackboard, which can be then pulled by anybody in the system using Blackboard and all the Irish universities are using Blackboard, so that they can use the teaching materials that we create, fit it into the particular module that they need it for. So there'll be the possibility of using samples from any of the collections, creating materials that can then be shared, reused, and obviously once they're digitized, they are lasting. Those glass slides, if you drop them, they break, and they honestly do need repairing and replacing, whereas a digitized system can last for a lot longer. The idea is we'll maintain a set of guides to the different samples. These can be updated, we could even add to them, and the value is longer lasting, because once it's digitized, you can use and reuse. Okay, so I'll go on to talk to you about key outcomes, and all this I think we'll achieve in the first 15 months. We'll have this permanent shared resource, we'll have staff trained in the use of the digital microscope. Simon's just pointed out there'll be lower costs, we won't be breaking slides or having to maintain the microscopes as much, but the main thing will be transforming the learning with what we hope will be improved learning outcomes, and I'll just take you through a few slides here to show what things are like now and what they might be like in the future. Here's some photos of a typical microscope-based geology class, and there are the students in blue and the microscopes in front of them, and the oranges, the staff member in charge. Now, under this circumstance, the staff member can tell the students what to do, and a little bit, they can talk to each other, but of course each of them looks down their own microscope. They can't really look down their friend's microscope very easily. If you notice in the top picture, they don't even have all the same microscope. So, it's limited, and they certainly can't really easily ask the staff member what's going on. The staff member actually has to come along and go around one by one and say, what have you got down there? Let me have a look. Oh yes, all right. Have you thought about this? Have you thought about that? Move along to the next student, ask them, and so on. And so, it takes a little bit of time to actually interact individually with students. If we go to this situation here with a virtual microscope now, the gray boxes indicate rooms. So, the students and the staff are in the one room together. The virtual microscope is somewhere else. Now, of course, everyone can be guided to look at the same place at the same time, as previously explained. That's a huge advantage because now students can directly ask, well, we're looking at this, what is it? And then you can move on to another thing and the students can interact with each other. You know, what's that thing in there, for example? And of course, we don't actually all had to be in the same room. People could be in separate rooms. This could be an exercise where the staff member is somewhere else and questions are coming in because the students can do this from anywhere they like. And indeed, the staff member doesn't have to be there at all. It could be an exercise where the students simply interact with each other in a peer-to-peer discussion and maybe then come back, as explained, to the lecturer in the class and talk about what they found and then move on to the more interesting bit, which is what it all means, having made observations. And of course, it might be used in a group research project as well. Again, the students, in this case, don't have to be all the time in the same place at the same time. And then, of course, there's a situation with very large classes like this, and you can see there's not enough microscopes. And so the lecturer is now beginning to panic. There is the potential with the virtual microscope, not of replacing everything that you can do with a traditional microscope, but certainly of doing a lot, as really I've outlined already. And again, once more, the staff member doesn't necessarily have to be there. And yes, I thought you'd like that.  That's to indicate the students as the exams are coming around. One of the things they're really keen on is being able to access this sort of information for revision purposes. So, I hope that gives you a little idea of some of the changes it will bring about. So what are we going to do? We're going to widen the Irish and UK footprint of all this. There's going to be a significant step up in what we hope will be the learning outcomes. And this will be through various new sorts of interaction, peer to peer, inquiry-led, self-directed learning. And, we hope, expanding the use of microscopes into first-year classes, which is simply impossible at the moment because they're always too big. And of course, we've got to know each other more as a result of this, and we will do in the future. We'll be collaborating a great deal more, advising each other, sharing our students' feedback, and so on. In terms of breaking down discipline boundaries, a little bit to say here there are a few other topics that this can be applied to outside of geology, and I won't go through the details of that. And at the end of this, or near the end, we plan to give this as a presentation at the European Geosites Union in 2016. And I'll hand over. So I just want to talk to you very, very briefly about actually how we're going to evaluate the impact of this, of G-Lab. And actually, the way this is set up actually makes that pretty straightforward, because things drop naturally out from the process. And basically, we can divide this into assessing baselines. We already have baselines of how students have performed in microscopy-related labs, and we can compare those baselines with what we see after the G-Lab is implemented. So that's pretty straightforward. In terms of feedback, this gives us ample and different opportunities to collect feedback from the students, so we can collect conventional feedback from individual lab components and see how they're working over time. We can also collect online feedback from the students as well. We can also use group-moderated feedback, or we could get feedback from the lab demonstrators. The thing is that with four institutions using this facility, we can try different methods of getting that feedback back, so that we can sort of transform how we're actually developing these facilities. And the last element of that assessment of evaluating impact is actually all that data that's coming out of the website itself, the platform itself. All that analytical data is telling us how the students are accessing it, when they're accessing, who is accessing it, and how long they're spending on it. And that's something that we can calibrate back in with our feedback to actually show us a true picture of usage and how values attain from this. So I really want to leave it there, and thank you very much for listening, and this is just a summary of how this G-Lab proposal is addressing enhancements and transformations in teaching and learning in Geosciences. Thank you very much.


Microalgae and high-rate algal ponds, HRAP, can convert nutrients from wastewater into biomass and bioproducts, improving sustainability of wastewater treatment. Temperature and photoperiod significantly affect biomass productivity and water treatment efficiency in wraps, with temperatures between 15 and 25 degrees Celsius resulting in high removal rates of nitrogen and phosphorus from municipal wastewater. This article was authored by Liliana Delgadillo-Mercas, Filippa Lopez, Behnam Tidy and others.


It's a paradox. Inflation is dropping, but prices aren't coming down. How can this be? Because corporations have enough monopoly power to keep them high. Here's just one example that'll make you fizz. Pepsi. In 2021, PepsiCo, which makes all sorts of drinks and snacks, announced it was forced to raise prices due to higher costs. Forced? Really? The company reported $11 billion in profit that year. In 2023, PepsiCo's Chief Financial Officer said that even though inflation was dropping, its prices would not. Pepsi hiked its prices by double digits and announced plans to keep them high in 2024. Consumers generally look at our products and say, you know what they are worth paying a little bit more for? How can they get away with this? Well, if Pepsi were challenged by tougher competition, consumers would just buy something cheaper. But PepsiCo's only major soda competitor is Coca-Cola, which, surprise, surprise, announced similar price hikes at about the same time as Pepsi and also kept its prices high in 2023. The CEO of Coca-Cola claimed that the company had earned the right to push price hikes because its sodas are popular. Popular? The only thing that's popular these days seems to be price gouging. We're seeing this pattern across much of the economy, especially with groceries. Inflation is down. You see, the rate of inflation measures how quickly prices are rising. Prices are now rising far more slowly than in the past couple of years. And while supply chain disruptions really did make it more expensive to produce a lot of goods for a while, the cost to produce them now is rising more slowly than prices, allowing most corporations to keep their profit margins near a 10-year high. They can get away with overcharging you because they have monopoly power. Or so few competitors, they can easily coordinate price increases. If Pepsi and Coca-Cola had lots of competitors, they wouldn't be able to raise prices so high because someone would make cheaper substitutes and consumers would buy those instead. But Pepsi and Coke own most of the substitutes. This isn't just happening with Coke and Pepsi. Take meat products. At the end of 2023, Americans were paying at least 30 percent more for beef, pork and poultry products than they were in 2020. Why? Near monopoly power. Just four companies now control processing of 80 percent of beef, nearly 70 percent of pork and almost 60 percent of poultry. So of course it's easy for them to coordinate price increases. And this goes well beyond the grocery store. In 75 percent of US industries, fewer companies now control more of their markets than they did 20 years ago. So what can we do? Well, it's largely flown under the media radar but the Biden administration is taking on this monopolization with the aggressive use of antitrust laws. It's taken action against alleged price fixing in the meat industry, which has been a problem for decades. It's suing Amazon for using its dominance to artificially jack up prices, one of the biggest anti-monopoly lawsuits in a generation. It successfully sued to block the merger of JetBlue and Spirit Airlines, which would have made consolidation in the airline industry even worse. But given how concentrated American industry has become, there's still a long way to go. Inflation is down but many people don't feel it because prices are still high and in some cases are still rising because of continued price gouging. This is where you have more power than you might think. You might not be able to break up big corporations but you can keep up the pressure on our government to fight corporate monopoly power and help spread the truth by sharing this video.


Bolivia, can I suggest that you might want to ask somebody to act as chair just to venue having to concentrate on chairing and giving your own presentation. Yeah, they want to be the chair. I mean, I won't because I just got it and I was all doubt that. One. I don't could be the chair. Sorry, yes, I was doing so. Sorry, you need a chair. Yes, I can do that. I'll also keep track of the time so 120 we're starting. Okay. Thank you very much. Okay, so yeah, so it's no in half an hour. Yeah, yeah. Okay. So, yeah, so, yeah, absorbal deforming of this or how to extend the day because they understand him as a whole argument. So, usually defined as environment sound transformation and this suggests like in the similar you have just environment plus the information is that to components. components. Actually there are three because do you see my mouse actually? Yeah, good. So there is the invariant part, there is the transformation, but then there is also what it transforms. So there is some variable which gets a new value and so on. So there are three components in a symmetry and more precisely. And if it is a theoretical symmetry and if you are interested in the ontology, then you would see something in the world corresponding to your symmetry. And if you have distinguished the components, then the advantage is that you can see these counterparts for each component separately. And symmetry reality influences an instance of this because it's interested in the component, which is the invariant part of your symmetry. And it says that this component should have a counterpart in the world. But this is just the basic claim. What about these other components? If the symmetry reality is interpreted in a strong sense and it not only says that the invariant has a worldly counterpart, but it also says that the other elements do not have worldly counterparts. But the transformation and differences exist only in the theory but not in the world.  But if you interpret symmetry reality in a weak sense, then it only says that the invariant part has a counterpart, but it also allows, there are other components of such consumptivity to have a counterpart in the world. And I will call it such consumptivity non-superfluous if it's interpreted as so that all its components have counterparts and non-chess invariant part. So you can think of this. So the superfluous, it would be Leibniz, I'm interpreting the boost on the universe and the non-superfluous is a Newton's interpretation of the boost on the universe. And we would like to know which symmetries are superfluous and which are non-superfluous. So consider usual distinctions in the formal kinds of theoretical symmetries. So here we are in this. This was about the ontology, so the correspondence between theoretical and worldly. But now for the moment we return again to just theoretical. And we classify different symmetries in theory in this usual way. So external or internal, this means special temporal, non-special temporal. And global local means in this, in the sense in which it's used in gauge series, so specified by parameters versus functions or roughly uniform versus non-uniform on the domain of application. And here are examples. So global boosts translation certifications are global and external. So there's special temporal and they apply uniformly on the whole domain in which you apply them. And then phase shifts and electrostatic potential shifts are global internal, while electromagnetic potential transformations are local external. And sometimes they are calculated with local phase transformations. And then the thermophys, as an example on which I will be concentrating on the talk, these are local and external. So they are special temporal and they apply non-uniformly on the domain in which you apply them. And we are asking which of the symmetries are superfluous and non-superfluous or which are of these kinds of symmetries. And actually we can we can argue that all of them are superfluous. So global external, because that is what's saying that boosts of the universe don't have a lot of the counter process to transformations and differences. And then we can make similar arguments for this. In particular for local external, so for the thermophys, you have the whole argument which says that the thermophysm should be interpreted as superfluous because this spurious you from the endothermism. And there are even ways to combine or generalize these arguments. In particular, that was the paper of 2003 implicitly generalizes the whole argument to other external symmetries beyond the thermophysms and the two other internal symmetries. And this means that the whole argument becomes no longer about space-time ontology because now it supplies also the symmetries which are non-superfluous or temporal, that is internal. Okay, so because you can help in determinism also about how internal values evolve through time. And then, but on the other hand, all the same kinds of statistical symmetry of formal kinds of statistical symmetries can actually be a side non-superfluous interpretations. And as I said, already, for example, you have diamonds and Clark, which disagree on the interpretation of the same symmetries. But you also have cases where symmetries are perhaps not the same, but at least they are all the same kind. But the important thing is that usually the superfluous interpretation was winning over the non-superfluous. But then there, like 20 years ago, we've got a new way to assign the non-superfluous interpretation, which is stronger than the previous unconclusively laws like the Gage argument. And this is direct empirical status. So you have direct empirical status when your statistical symmetry is matched with an empirical symmetry in the world. For example, for example, the Galileo ship. So in the world, you boost the ship and this transformation is observable. The transformation, the change in the velocity of the ship with respect to the shore is observable if you make it in the world. But the experiments within the ship stay invariant for the observer inside the ship. And so this is an empirical symmetry in the world. And it corresponds to a statistical symmetry of boosting a theoretical subsystem. And so we can say that the statistical symmetry is non-superfluous because each of its components, including the transformation and the differences, is matched with counterparts in the world in this Galileo ship and vehicle symmetries. And it happens that this new strong way of assigning a non-superfluous interpretation to statistical symmetries applies to all these kinds of symmetries. And in the Grievous and Wallace article in particular, it was shown to apply to many symmetries except for local external. So it looks like local external symmetries and the new different morphisms are sounds of what exceptional because there has not been an explicit demonstration of them being non-superfluous so directing vehicle status. While for all the other cases, we have such demonstration. Now, if you want to explain how does it happen that the same symmetries like boost can be at the same time superfluous and non-superfluous, then for all other things besides different morphisms, you have a great explanation namely symmetries are superfluous when they're they're applying on the whole universe or at least on the whole domain and they are non-superfluous when they apply on a subsystem or subdomain. This explanation worked well for all the things, but it does not work well for different morphisms because already the superfluous different morphisms are also applied on a subdomain. The whole can be accounted for subdomain or subsystem if you want and the differences on the whole are always supposed to be superfluous. So the usual explanation of how the same symmetries can be superfluous and non-superfluous because they apply to the universe versus its part does not work in the case of the formal system either. And should we leave it there? Well, no, because it follows actually from Goethe-Wolff's work and independently from my work, the different morphisms should have direct and legal status. If this can be proved explicitly, then we would restore this so to say a symmetry between different morphisms and all the other symmetries. But of course, we would then have a question how do we explain also about the philanthropism and about the rest that they can be both superfluous and non-superfluous. What is it that makes them superfluous and non-superfluous even if they have the same formal feature like being global external as a way for global or local external system? So how did it happen that the philanthropists do not have direct and legal status and all the others? These were all say, we were tempted to include this section about assigning the different morphisms, direct and legal status. While we are confident that some such relationship exists, the details are subtle and related to understanding disputes as to whether general relativity is against the theory and the status of general covariance in general relativity. So they say we are sure the philanthropists have direct and legal status, but it's just too difficult because it relates to so much things which are unsolved and so. But no, I disagree. We can have an easy way to derive the philanthropism with direct and legal status, and I will do this in this talk. And for this, I will reply to the question which seems to be superfluous and non-superfluous. So here's what David Wallace was explaining in his talk, but now I will be formulating this in my terms. Okay, so he was criticizing Das Gupta. So Das Gupta proposed this symmetry to reality inference, and he is studying how to make it valid. And for this, he is using different definitions of symmetry, and he prefers those which are more ontologically allowed than because it makes easier to satisfy his symmetry to reality inference. While Wallace says it is boring and so on, it's trivial. You should try to derive ontological things like symmetry to reality inference from formal things. Okay, we have just seen this, and now I will just reformulate this in my terms. So you remember that I was speaking about symmetry to reality inference, and I introduced my distinction superfluous, non-superfluous. So either just invariant part has boundary parts, or also the differences in the transformation. Okay, so since I formalize the symmetry to reality inference as a distinction between superfluous and non-superfluous, I will also formalize this other side about definitions of symmetry as also as a distinction. So I will speak about the correspondence between superfluous, non-superfluous on the one hand, and the ontological distinction or formal distinction on the other. So the trivial question will be how to match an ontological distinction with superfluous, non-superfluous, and the non-trivial question will be how to match a formal distinction with superfluous, non-superfluous. Superfluous, non-superfluous itself is an ontological distinction. So since I'm formalizing this debate as a debate about distinctions, sorry, I just forgot I should stop at 15 minutes, yeah, because I started You have only taken 13 minutes, so you have 7 to 20 minutes. Okay, so since I am formalizing this debate as a debate about matching distinctions, it is useful to introduce some relationships which can in principle hold between distinctions. So here you have two distinctions, so each of them has two sides, here is superfluous, non-superfluous distinction, I'm taking binary distinction. Okay, so suppose this is superfluous, this is non-superfluous, and then you have some other distinction like global, local, external, internal, subsystem universal, domain subdomain, or something else. And so you can see the two side distinctions, and here are some possible relationships. So one is a certainality within each block, so to say within each term of one of the distinctions, you have representatives of both terms from the other distinction. So this is a certainality. The opposite is co-extensionality. The distinctions, they can be matched side by side. Okay, so you have suppose, you have superfluous, non-superfluous, global, local, so the usual idea was non-superfluous corresponds to global, and superfluous corresponds to local, and there is no intersection between them. So this would be a co-extensionality. Okay, one of the terms from one distinction corresponds to just one of the terms of the other distinction, and they don't mix. And skew is in between any option, but I'm going to start here a particular option. And after we have introduced these relationships between distinctions, we return to my formalization of this debate, and I'm saying that the right relationship, which is in question here is co-extensionality. What does it take to determine which ontological distinction and which are formal distinction are co-extensionally superfluous and non-superfluous? So I'm saying that when we want to know which symmetries are superfluous and which are not, we should find a distinction which is co-extensional. And then we just look at whether our symmetry satisfies one of the purposes of this other distinction, and it helps us to infer whether this symmetry is superfluous or non-superfluous, because there is no mixing between having some property of one distinction and being either superfluous or non-superfluous. Okay, the co-extensionality works such that as soon as you know that, for instance, all global symmetries are superfluous, okay, you just check whether it's global because it's easier than to check whether it's superfluous, and you infer that it's superfluous, you get your answer. So this is in principle a useful tool, but now the question is besides, what does this distinction co-extensional which is superfluous and non-superfluous? And here are my replies. So if we seek an ontological, so firstly concentrate on the question, which ontological distinction is co-extensional with superfluous, non-superfluous? If we really answer these questions, then I agree with that it was that it would be trivial because you would be matching two ontological distinctions together. There would be two as difference between them. If you don't know already how to tell whether a symmetry is superfluous or not superfluous, it does not help very much to, if you put it in correspondence with another distinction, which means quite the same, it will not be helpful, okay? But you can replace example is the interior, non-interior from the Grybson Wallace article. So they define or they presuppose that interior symmetries are all subsystem symmetries, when you combine them with the environment, they yield universal symmetries. And universal symmetries are defined in Leibnizel or Newtonian terms. So they are defined like, or characterized like symmetries which relate representations of the same, which link representations of the same state of affairs and so on. So it's like, it's a synonym of superfluous, okay? So matching interior and non-interior with superfluous, non-superfluous is trivial. But if we can abit your distinction, you'll require the matching of superfluous, non-superfluous, not with ontological distinction, but with just some substantial distinction, then I'm claiming that it's becoming non-trivial already.  So what's the difference? Ontological is about the world, but observationally, completeness or incompleteness, it's about the predictions. How many predictions are changed by your symmetry transformation in your theory, okay? Whatever your theory, whatever change or absence of change that your theory predicts, it does, you're not guaranteed that there will be a corresponding change or absence of change in the world. So this is not an ontological notion because it still stays within the theory, but it's notion about predictions and if your symmetry is particularly adequate, then it entails that it is superfluous or non-superfluous if you, as long as this superfluous or non-superfluous character is determined by observability, okay? And even this slightly non-trivial co-extensionality is always a very explanatory, successful, because it explains, for instance, why Lednitzel arguments and the whole argument, why do they privilege the interpretation of symmetries concerned by them as superfluous, because these symmetries are observationally complete, they do not predict any change, okay? If there was a prediction of change, you could go into the world and see whether this change obtains and you would infer whether the symmetry is superfluous or not, but if they do not predict anything, then you by default interpret them as superfluous. So even this has a lot of explanatory value, but the more interesting question was which formal distinction is superfluous, is co-extensionally superfluous and non-superfluous. And here I propose this boundary trivial versus boundary trivial subsystem symmetries, okay? So this is, I take these invoices distinction, which is SQ, okay? So they have a distinction within symmetries, which have direct and vehicle status. And it is between asymptotically trivial and especially, no, asymptotically constant, especially constant, okay? And so I say that I transform it into a first national distinction and the result is boundary trivial versus boundary material subsystem symmetries. And importantly, in David Wallace's presentation, it looked like there is this trivial question and there is a non-trivial question and we should deal with non-trivial question instead of the trivial, but I will show that we should not deal with one instead of the other. We should deal with one with the help of the other and this is more fruitful. So I will combine that, okay?  So I will have three co-extensional distinctions, superfluous non-superfluous, obsolescent and complete, obsolescent and complete, and the boundary trivial boundary and not trivial. The whole co-extensionality, as much as I need. So now we get to my task, which was I was promising to derive for different methods which have direct and critical status, okay? So now we have these three distinctions which I have just introduced. And direct and critical status is just a particular case of being a non-superfluous. So, and we apply this to the form of this. And we can do this side by side. So we first do this side which concerns the superfluous symmetries, okay? So they are supposed to be, all this notion should supposed to coincide in the extension, okay? So the same symmetries are supposed to be superfluous without direct and critical status observationally complete and boundary trivial, okay? And we check this because the whole diffromortions of the whole argument are superfluous. So they should be obsolescent and complete. They should be boundary trivial and subsystem symmetries. We just check this, okay? And yeah, we always know that they're obsolescentally complete because otherwise there would be no danger to about indeterminism. Indeterminism rises precisely because you have the same, what looks like the same and you don't know which of the options of this, okay? This is indeterminate. And that's why what makes them superfluous. But and they are subsystem symmetries because they apply on the whole. So the main thing to check is actually whether they are boundary trivial. And this is indeed actually said explicitly by Roman and Norton. They say so the whole diffromorphism is something which differs from the identity within the whole, but becomes the identity on the boundary of the whole. So this is boundary trivial and it says that it becomes identity as a boundary, okay? So we can say that one side of my distinction is consistent because when applied to the diffromorphism, it characterizes as well as the whole diffromorphism which are superfluous and so on. But the question is of course about the other side, okay? So now we check the other side. And it says so boundary material subsystem diffromorphism should be obsolescentally incomplete and they should be non-superfluous nor precisely they should have direct and empirical status. And we just check all these things. And we get diffromorphism with direct and empirical status which are different from diffromorphism which are boundary or subject to the whole identity, okay? So first stage we should start by boundary and entry or subsystem diffromorphism. And we do have boundary and entry well diffromorphism in Bellot's article about the response, but they are not subsystem. Here I've used that they should be interpreted as symmetries of the universe and not of the subsystem. But we can interpret them back as symmetries of subsystem by using losses that now the cosmological assumption which is presented. So by we can say that physics is essentially about subsystem and not about the universe. And so we should say let's interpret Bellot's transformations as being about subsystem and not the universe because for instance supposedly we live in the cosmological assumption at least in this case. Okay, so now we have Bellot's symmetries interpreted as final subsystems. And we now should prove that they are observationally incomplete. If they are observationally incomplete, by definition this means they entail some predictions of something observably incomplete in the world. So something which some symmetry which preserves something, but which also induces some change. And so we need an example of what Bellot's symmetries entail. Okay, which empirical change they predict. And here we have this article by Luz. And she takes Bellot's example, interprets it as applying to subsystem symmetries. And she says that it entails the predictions that if you apply your differential offices to a star, then the star can be observed at one or two a.m. instead of three a.m. at some time instead of another time. Okay, so the fact of applying differential offices to a star, this boundary material subsystem deformation of Bellot, is it entails the predictions that you observe in the star at a different time. Okay, so and now we have the third stage to prove that this prediction leads to a direct empirical status of this deformation. And here we get to the boundary between the theory in the world, because observational completeness is still about predictions. But to prove direct empirical status, you should prove that the corresponding empirical symmetry indeed exists in the world, not just predicted by your theory. And here we have a problem because if we use Luz's example, we would have to apply worldly differential offices to a star. And we do not know how to act on stars yet. So we cannot practically implement the initial conditions for the star example to see whether it indeed yields an empirical symmetry predicted by the differential offices. This means that it's not enough to have derived just this one prediction about the star. We need a general range of phenomena implied by this differential. And not just one star. We need in particular such implications, which would be practically realizable, and which we would check and so as to ensure that they indeed obtain in the world. And to do this, we can use my proof. So in the series and beforehand, I proceeded in this way. I started with an empirical symmetry. You can imagine a little shape of the sketch. I took a global symmetry which has direct empirical status by workshop representing this empirical symmetry. And I built a local symmetry out of this global symmetry. So for this applied to the global symmetry, which has direct empirical status, some local symmetries which do not have direct empirical status, they don't have the status precisely because they preserve all predictions of the original symmetry. This means that the symmetry they yield has the same prediction and it also has the same empirical status. So the status is preserved, but the symmetry is changed. It becomes from global to local. This is how you generate local symmetries with direct empirical status. And now I will do this in reverse. I will start by the formalisms with direct empirical status and then I will derive which predictions they entail besides the star example.  So you still need to keep the boundary non-triviality because this in my approach is what entails direct empirical status. So since you cannot change the behavior of the boundary, you can only act on the bulk. So what you do is, so instead of having some local symmetry which is non-uniform in the bulk of your subsystem, you make it uniform. And now it behaves in the bulk, like in the boundary, and so it becomes the low bulk. But what is this behavior of the boundary which is now spread onto your whole subsystem? Well, the flow of the boundary until the flow of the subsystem, the behavior of the boundary resembles usual translations. So this means that the global analog of this differential with direct empirical status are simple translations. And we know which phenomena yield the direct empirical status for translations. These are just displacement of usual objects in the world, which now need not be the star. In the star, you perform a temporal translation by one hour, but you can also translate a usual single, which is much smaller, and you can also translate, especially instead of temporarily and so on. So it follows that the empirical symmetry is corresponding to observable deformities are what usually looks like translations. So here we have. And where is the place of whole deformities? Well, these are precisely the symmetries which allow you to pass between global and local symptoms with direct empirical status. So they preserve predictions, but they themselves do not entail these predictions. So they don't have empirical status. So, and here I'm finishing. So even the matching of a subsocial distinction with superfluous non-superfluous is already informative, but you can also use it as a stage in your proof of the co-extrationality between a formal distinction and superfluous non-superfluous, which is less, even less trivial questions. Okay, once you have demonstrated that the thermos have very typical status, you now see that local external symmetries are just like local internal and global external and so on. They are all alike. You have completed the last missing piece in this assignment of direct empirical status to different kind of formal symmetries. And the final is the fact that I put in correspondence all differences that translations with disproves, Friedrich's association of them with a localized boost instead of translation. But the only thing which is missing in this whole account is that my formal distinction was actually about just subsystems. But my subsocial distinction was about the whole universe. What is missing on the formal side is the account of the environment. And I do it in another, I'll call it in another talk, and it should be, you can find an announcement and afterwards the recording of this website of my financial board. And I thought that we will put recordings of this workshops there, but we'll see about this with you later on. So that's all, thank you. Thanks. Okay, there's comments. Sorry, I'm checking the problems. Sorry. All right, take it away. Thank you. Great. So first thanks to Larry for organizing the workshop and the talk and asking me to comment on it. I enjoyed reading the paper and I just have a couple of sort of disjointed things to say about what I take to be the general and specific contributions of the talk and paper. So the title of the paper she shared with me is non-superfluous symmetries and post-sensional distinctions. And among the distinctive features of her discussion, as we just saw in the talk, is a way of framing exactly what the question is that we're after in terms of distinctions and how they line up. So I take it to the sort of general starting point for the big picture question is something like the intuitive thought that doing some conceptual analysis on the ideas of symmetry and observation will let us say something general about what physical theory says about the world, just based on knowledge about its symmetries. So the symmetries of a theory are related to invariances of measurement results. And as far as the physical theory privileges measurement results, we have some sort of protanto reason to disregard features of a theory that make no difference to measurement results. Of course, whether some future makes a difference is at least partly something that theory is supposed to tell us. And so it's the theory's job to explain what causes what. But the general idea that I take it is that by appealing to general features of mathematical representation and observation, we might be able to say something about visible theories in general. So just so the structure of this general thought in terms of how various distinctions line up, and I think that when you use a feature of this approach is that it helps you identify which parts of symmetry arguments involve merely premises about representation in general, which I take to be the words that she's calling formal, and then which parts involve some claims about how the world is or how it's likely to be. And she calls these substantial. So substantial distinctions concern features of the world and how they're represented, while formal distinctions concern representation as such.  It is defined some formal criteria and that one form is about the furniture of the world according to the theory. So the particular version of the attempt at this dream, which I was interested in, started maybe with Peter Casso. So Casso argued there's a distinction on the one hand between global symmetries like Lorentz-Boost and local symmetries like electromagnetic gauge transformations. And then on the other hand, there's a distinction between symmetries that can be directly observed and those for which we can only have indirect evidence. And he argued that these distinctions coincide, that the world exhibits a particular symmetry can be directly observed just in case the symmetry is a global one using galleyship as sort of the paradigm example. So this brings me to my first question about this way of carving things up. So the virtue of dividing things up this way is that it clearly separates mathematical issues and physical issues. And to the extent that mathematics can be less controversial, this is helpful. The danger is that you don't want to separate these things too much because the game is defined the two distinctions that coincide and there's going to be people like, say, the trivial semantic conventionalism types that Jill talked about earlier today. There's going to be people who are going to be skeptical that you can do this, that you can talk about the two distinctions coincide without making it coincide without making some pretty substantial assumptions or story about how they're supposed to relate it. So the worry is it's hard to see how many facts about mathematics could have any bearing at all on physics unless you've already answered the questions that we're trying to get at here. And so it's hard to see how we're going to get something out of these arguments that we don't directly put in. So maybe this is too broad to be a fair question given this sort of questioning the literature. But the first question is just whether you had anything to say, Larry, about this to this kind of skeptic who thinks that, well, these sorts of appeals to formal criteria just can't be separated from the substantial ones. So moving on to the second question, right, there's cases and cases, Casso's paper, I mean, we've sort of renegotiated this distinction many times, and at the risk of simplifying maybe the biggest development of the debate since Casso has been shift towards formal criteria that concern subsystems, especially in light of or in reaction to the Greaves and Walls paper that's been mentioned a few times. And I think, you know, the reason for this shift is clear enough. If you want to observe that some system has undergone symmetry transformation, we have to be able to observe a difference and the way to reconcile the invariance of the symmetry transformation with an observable difference is to perform the symmetry transformation on the subsystem, and then observe that the world as a whole has changed. And I think I take it that Casso's account of direct empirical significance is a version of this, but she argues that we should be concerned with pairs of a state of a system and a state of its environment. There can be discontinuities across the system environment boundary. And Casso argues that a joint transformation of the system environment will have a directly observable effect if it changes the existence or degree of this discontinuity. So in the gallows ship scenario in the paper, she is an example, there's a discontinuity if the ship is moving with respect to the shore. And by changing the velocity of the ship, we can create or remove this discontinuity. So one thing we could do is to discuss the essential adequacy of this proposal, whether transformation is directly empirically significant just in case it changes this discontinuity. I don't know exactly what I think about this, because I don't know exactly what I think about this pre-theoretic notion of direct empirical significance. So I have two other sort of sudden questions about this. Number one, I'm a little worried about the notion of discontinuity being underspecified. So I think it's clear enough that the velocities of the ship and shore are changed in the interesting cases of boosting the ship. But there's also going to be discontinuities if you leave the ship alone and boost the shore. And so it seems like we've lost our original focus on subsystems exactly if we want to have subsystem environment be asymmetric. And that was sort of just talking about the relationship between two systems. And maybe this is okay in general. Maybe, you know, one of the environments, the subsystem of the sort of system, which is its environment, or maybe these things are symmetric is all I need to say. But in a lot of the controversial cases, like fairy loose cage, it turns out that in order to apply a symmetry transformation to the subsystem, you also have to adjust the environment. And so it's not clear that it's a symmetry of the subsystem that's accounting for what we're observing, rather than just this change we made to the world. Right. So this is Simone Friedrich has, I think, made this has this complaint or worry or whatever. So, so, you know, question two, part one, is there a principle reason to say that what we're getting in this case is a direct observation of a symmetry? Part two question two is maybe fuzzy. And so you don't, you know, maybe there's nothing to say about it. But it's not obvious to me how we should determine the symmetries of the subsystem and of the environment. So the sort of recipe from the group's wall's paper is to start with the symmetries of the total system sort of assume that these are known. And then consider how these can be restricted to the original system and to its environment. And so and as David was just saying, this is maybe something you might be satisfied and about or it's an incompleteness in the analysis. Right. And so I guess the general question is something like why should the symmetries of a particular system be determined by the symmetries of the entire universe? Or why should the symmetries of the system coincide with the symmetries of that system qua subsystem of some environment? This seems especially pressing to me if we're going to move away from the idea, the cosmological assumption that Larry mentioned, right? If we move away from the idea that what we're doing in interpretation is treating a system of interest as a cosmology, and instead take physics to be about subsystems, then there's not going to be sort of the determinant answer about the symmetries of the system are because we should always think of it as embedded in some larger and determined environment or embedded bowl and some further environment. And so we can't determine the symmetries of the system this way without making the environment determiner. So these are two questions about the sort of formal side of it. Third question moving on to the main example of defumorphism freedom. I wanted to ask you Larry to say something a bit more about the whole argument. I guess just sort of what you take it to be precisely and how exactly it's being avoided here. So I assume you have in mind the version according to which the defumorphism variance of the Einstein equation leads to a kind of indeterminism. So the question here is where exactly does the indeterminism come about on your view and how exactly does your interpretation of defumorphism symmetry avoid it? So if I understood correctly the example, the argument is that the defumorphism symmetry can have direct empirical consequences when we transform a subsystem and the environment in a way that changes measurable relations between them. This seems like at least a considerable difference but it's not clear to me that this is a case of observing a symmetry because this isn't the defumorphism of the whole thing because we change the observables. And so I don't see myself immediately how it's related to the whole argument. And I mean maybe to spell out why I don't see it as well. I mean I take it that the reason people feel like there is a tension between the whole argument on the one hand and endowing defumorphisms with direct empirical significance on the other is sort of in light of some background assumptions, one of which is that we should want to identify defumorphism related possibilities on a fixed manifold to avoid indeterminism in the whole argument. And then the second is that like possible subsystems are possible systems that can possibly be related to the environment or something like this. So as I understand the kinds of complaints often voiced by Gordon a lot, what he wants or what he's complaining about some of the more sophisticated substantivalous pictures is that he wants to, we need a principled story about how the way we count possibilities at the level of universes or space times is related to the way we count possibilities for subsystems. And so in particular if we want to avoid the whole argument by identifying defumorphism related to manifolds, then it seems sort of ad hoc to just unidentify them when we're treating them subsystems. And so this is the third question I wanted to ask. What exactly is it that you want to say about the whole argument such that you've now offered a distinctive sort of way to reconcile it with direct empirical significance of defumorphisms? And then yeah, how that scares with the treatment of the defumorphisms on subsystems. So that's all for me. Thanks again for the paper and to the talk. Yeah, thank you very much. I should explain that the version which I sent to John, there was an extra section after the section about defumorphisms. So this is what I did not tell in the talk because this now became a second article, he's becoming a second article, and it's, I will be talking about this next day. So, but the idea there is that, as I said, my formal distinction was about subsystems, but my substantial distinction was about the universe. So what is missing on the formal side is the count of the environment. When I'm saying that boundary trivial versus boundary non-trivial correspond to superfluous versus non-superfluous, I mean that the environment is supposed to be un-transformed, as in the US and Los article, or just transformed by an induced transformation by mobile cell. Okay, in the second article or this last section, which I have not talked about, I am generalizing this to arbitrary states of subsystem and environment. And what is important in that case is the discrepancy at the boundary, the discontinuity at the boundary between the subsystem and the environment, whatever the subsystem and environment assumptions are, which yield this discontinuity. So as long as you have this discontinuity, you have direct and bigger status or at least non-superfluous interpretation. And if you don't have a discontinuity, you have superfluous and definition and direct and big, and the absence of the identical status. So what I'm saying about the forward argument, so we are here in the context where the environment is unchanged. So that's why we can say that whether the subsystem transformation is boundary trivial or boundary non-trivial determines whether we have the forward argument option or the directed recall option. So what I'm saying is that indeterminism in the forward argument arises within the whole, but the observability or inobservability arises at the boundary. Since by the time we get to the boundary, the diffuseness within the whole, it vanishes away because at this boundary, we don't see any effect. If you are able to go inside the whole and keep the track between, well, and you have a discrepancy there because of the diffuseness, then you get transformation which is non-superfluous. So ultimately, the superfluous and non-superfluous character is relative to a boundary and you can in principle put it everywhere within the whole, outside the whole, but as long as around your boundary you get identity from both sides or both things change in the same way so that there is no discontinuity arising. You still have a superfluous character and the boundary of the whole is a particular case of that. Substantial, what you said in the beginning, no substantial distinction, it's not nontological. It was maybe even clearer in the Torah than in the article, but substantial is about predictions. Predictions are not about ontology because predictions can fail. They only became about ontology when they are empirically adequate, so then observationally incomplete becomes non-superfluous. So substantial is still, so to say, formal, but it's less formal than a global, local, boundary preserving, boundary trivial, whatever. And the block of questions, how subsystems, how substantial and formula related? Well, you can believe that whereas the observational completeness, so substantial distinction is observationally complete, observational incomplete. Formal distinction was a boundary trivial versus boundary material. My response was, as I said, you can feel that these two distinctions do not coincide because the second is about subsystems, the first is about the universe. But as long as you generalize it in the way which I have just explained, it's plausible that our series are built in such a way that discrepancies signal observational changes and smoothness signals no observational changes. It's claimable how our series work. What about my work in the universe? No, I'm undecided whether the cosmological assumption is right. But if it's right, then my account is not indentured by this because just replace the universe by the universe in the square clause. So the universe just means the greater subsystem. That's all it. I think you can still get the whole account, it still works. It's a force of my account that allows to transform the environment independently of the subsystem. You can boost the universe, sure, you can keep identity on the ship by the usual account. As I said, identity on the ship means it is a subsystem vocal transformation, so it would have to have no direct and big assist. But as long as you boost the environment, you will still have an observable difference and direct and big assist. My account allows to account for this because it does not make any difference between what is the subsystem and environment. You can switch them independently. This is just the generalization of the ideas that every subsystem can become a system. You switch the levels, but as long as there is a discrepancy between the subsystem and environment transformation, whichever of them is transformed, my account works. It's a force of my account, it's not a weakness. Okay, yeah, in these transformations, this distinction is wrong. So in Gryffindor's article, it's argued that fair discussion vehicle symmetry is represented by transformation of the subsystem, which induces a transformation of the environment. While in the Galileo ship case, the subsystem does not induce a transformation of the environment. I'm arguing in the second article that this distinction is contextual. If instead of boosting the ship with respect to the shore, you boost the ship with respect to the water, you also get a change on the water just as much as you get a change on the environment as your father's case. So the difference which Gryffindor thought was fundamental within the symmetry of the activity, because there was a difference between both the boson and the unbounded boson symmetry. This is actually a contextual difference, which is just about which kind of the environment you transform your subsystem with respect to. Okay, I think we just took a lot of time, but I answered one last thing. Can I have one follow up real quick? So this is just to clarify about the relationship between direct empirical significance and superfluousness, superfluity, whatever. So it seems like one way that something could be superfluous, sorry. The way that superfluous was being used, I understood was something like it's purely a feature of mathematics. It doesn't reflect anything about the world at all. And I took it that the reason that Casso introduces direct empirical significance is because he wants to say something like, well, look, maybe you can come up with some sort of argument that some unobservable feature has physical effects somehow because like down the chase, so I think notice theorems is the kind of thing he feels to do that. Well, we can explain certain things by positing these unobservable features. And then the question of DES is, well, here's one way that it could be, one way to get evidence that something isn't superfluous is that you can just see it. But as I understood, Casso's distinction, non-superfluous is a broader category than DES because something could be not directly observable, yet still be non-superfluous. Is that also the way you're using the superfluous non-superfluous distinction? Well, firstly, I have a precise definition of superfluous. Well, non-superfluous is where each component of a symmetry, so including transformations and differences, has a counterpart in the world. This corresponds to direct empirical status, but that does not necessarily correspond to indirect empirical status. So Casso's notion of empirical status in general is perhaps the same as superfluous except that he was not going into details. But notice theorems, so this is indirect empirical status here. So this is indirect because you broadly associate your statistical symmetry with something in the world, but you cannot perform the analysis component-wise. While in direct empirical status, you can't because your boost of subsystem in theory correspond to the boost of the ship. Your differences between initial and final velocity correspond to the differences of your real ship in the world. Your invariant part with predictions about what happens within the ship corresponds to what really happens within the ship and really stays invariant. So you perform the analysis component-wise and each component of your statistical symmetry has a counterpart in the world. This is direct empirical status. And more precisely, this counterpart whole should amount to, should be Galileo-ship-like, if you want to call it direct empirical status. Yeah, but in general, direct empirical status is a sub or like a sub. And there is an option within how to be non-superfluous if, for you understand non-superfluous, merely in the sense of having a counterpart in the world without the component-wise analysis. Larry, do you want to wrap things up and stick to the original schedule or should I give people a few minutes to ask questions? Yeah, let's finish in one of the minutes. So if there is one, I'll do the short questions. Okay. If you have questions. Yeah, David. So I'm just trying to get a bit clearer on the route by which we're supposed to be getting direct and empirical significance from boundary and non-trivial diffeomorphisms. So there are two relatively clear cases. If there's diffeomorphism advantage of the boundary, that's fine. It's just a gauge transformation. It's just re-descriptive. It's just a whole argument case. Fine. If I'm in some sector of the theory with some relatively friendly boundary conditions, so let's say the sector I'm in has asymptotic Leningkowski and boundary conditions. And now I have a diffeomorphism that asymptotically doesn't vanish but preserves those boundary conditions. Now again, we have a relatively clear understanding of how we can think of that as a physical transformation with direct and empirical significance. Indeed, that's exactly how we're going to want to think about the asymptotic, the Poincaré transformations of subsystems in, of isolated subsystems in young relativity and analogously how we're going to want to think about asymptotic phase transformations in gauge theory. I'm struggling to know how I should think about what's even going on in trying to say there could be empirical significance of some gauge transfer, some diffeomorphism, that is some hideous mess of the boundary. He doesn't faintly preserve the boundary. He doesn't preserve the sector. Certainly can't be understood as a rearrangement of the system against other things. Now, of course, you could change the boundary, but, and this is the problem with Hilary now, bound stuff against the bit and didn't really have a completely satisfactory thing to say to it. Of course, you can change the environment, but if you're not careful, you just end up reversing the transformation. So I'm trying to get a handle on what's, I mean, what, what concretely we're saying when we say an arbitrary boundary non-trivial transformation has directing variables and difference. Yeah, I guess you mean by changes about the, I guess you mean changes the environment, like in the Greaves and Wallace article. So I don't know what it implies in general, but in the case of diffeomorphists, boundary non-trivial diffeomorphists are supposed to behave at the boundary just like translations. So if you don't have problem with having translations for the acting because that is an issue we have for diffeomorphists because they are indistinguishable. As I said, in Bellot's example, Bellot's transformations and the goods example, the diffeomorphists behave at the boundary like translations, like time translations. Okay, so they don't change the environment, they change just where you see the subsystem. Okay, so maybe this is my misunderstanding, but I feel boundary trivial versus boundary non-trivial was supposed to be exhaustive. There are plenty of transformations which are neither interpretable as asymptotic translations nor asymptotic vanishing. I mean, there are some actually innocuous ones like rotations or boosts, but there are also some hideous ones that don't deserve the boundary conditions. Yes, I think I forgot to mention maybe the problem is boundary trivial and boundary non-trivial, in my case, refer to the subsystem side of the boundary. It does not say that the environment changes. In your Greaves and Wallace article, boundary preserving versus boundary changing, this says versus the environment changes. Okay, I'm saying versus the subsystem changes. I'm thinking about that as a side of the boundary. It's still the case that not all boundary non-trivial things will be translations. Bellot's diffeomorphists to which I'm interested in assign direct and bigger status behave at the boundary like translations. Oh, so it isn't true that boundary trivial, boundary non-trivial is meant to be exhaustive. There are plenty of transformations which are not regenerative. It's meant to be exhaustive, but there are lots of transformations which clearly are not interpretable straightforwardly as translations. Again, just let the diffeomorphism be non-zero everywhere at the boundary, but do different things in different places so it doesn't preserve the boundary conditions. The boundary condition preserving transformations are absolutely interpretable as, well, not just translations, but Poincaré transformations generally. But that isn't an option if my boundary, if my asymptotically non-vanishing gauge transformation shatters the boundary conditions. You seem to suppose that if the change at the boundary is different in different places, then it will also change the environment. No, it just won't change the boundary. It just won't preserve the boundary conditions. Yeah, but by boundary condition, you mean the environment. This is a formal mathematical statement. Yeah, I understand it as a Gryffindor-Sertzikov. So there is subsystems, there is environment. Okay, diffeomorphism is non-trivial in the bulk, but it can be trivial or non-trivial in the boundary. If it is non-trivial, it can be more of a constant or non-constant. Okay, if it behaves like translations, this means it's constant on the boundary. It's non-trivial, but it's constant. It adds the same value everywhere. Okay, translation in your account, it is boundary preserving on the environment. So if it adds, if you add one hour everywhere around your star, because time translates in it, then the environment can still be identical. Okay, so for my purpose of diffeomorphism, constantity at the boundary, non-trivial constantity at the boundary is enough. Why do I generalize non-triviality? Because of Tase 2016 article where he is dealing not with diffeomorphism, but with internal symmetries and here he is saying that they should be they can be also non-constant at the boundary. And yeah, and yield there can be the status as long as they are non-trivial. Yeah, we just hit the one hour mark for your session, Valeria. So perhaps we should end so we don't get too late on the next one. Does that make sense? You mean that we finish? Yes, it's been one hour since you started. Yeah. Okay, thank you. Thanks everybody.


to one of the bigger match ups of the entire day and certainly the marquee matchup of our afternoon games. The Kansas City Chiefs going to New England to look for some revenge from last year's elimination in the AFC championship game where of course the Patriots won the coin toss and ultimately marched down the field and scored the game winning touchdown. So it came down to a flip of the coin last year. Patrick Mahomes and company wants to not let that happen again here and just get the win on the road and really establish their chances of maybe getting a higher seed in the playoffs. Right now the Patriots are fighting for that number two spot where they can get a buy, maybe even the one seed if Baltimore has a hiccup here over the last four games. But can the Chiefs go in and beat the Patriots in Foxboro, something that hasn't been done in a few years now? We're talking about 18 consecutive home wins for the Patriots. That's an amazing streak, the third longest in NFL history. Yeah, it really is. And what more could you say about the dynasty up in Foxboro? They seem to do everything right over there. Now I think this is a situation where the Patriots are to find themselves in where I think you have the nail on the head. I think the Patriots understand that to make the Super Bowl, you have to have that first round buy. Over these last few years, you've needed a first round buy to make the Super Bowl. You need to play fewer games. Otherwise, you subject yourself to more punishment, injury, things like that. And so I think now the Patriots are going to put a few more things on film, get a little bit more creative, actually play these games the right way because they think they have those losses out of the way.  And so I think they're going to play Kansas City seriously, maybe not as much as they did against Houston. So that's number one. Number two, in terms of passing EPA, the New England Patriots passing attack brings 13th in football. They are an average offense under Tom Brady. So I'm not expecting them to score too many points, maybe in the low 20s, but I do think they can cover the minus three, which means I think the real play in this game is beyond there. I think the total is way too high here. I think Pat Mahomes will be largely contained.