 Okay, it is recording. So welcome everyone. This is our first research seminar from CryptoEconLab. So just to give a quick overview, the goal here is for our team to present interesting topics they have been working on or research papers they have been reading and they want to share. And we have Rota, so every month there's a specific researcher there is plan to present. And if you want to know more about the next sessions and see the notes and recordings from previous sessions, you can go to the dedicated page. And with this I'll kick off so we have Axel is our first ever researcher presenting and he'll be talking about how crypto economics is not statistical physics. You can go Axel. Thank you. Thanks. Thanks for you. Thanks for organizing is I think this is a really great initiative to do more. So let me just start with a little like preamble of what this is in relation to what you said so like, I think, as at CryptoEconLab, we're most of the time, doing like very urgent questions that are relevant to Filecoin and all of this. This is kind of a set of ideas that I've had just in the back burner for a while and this is more like theoretical wandering so I don't know that this will yet have like a productizable application to Filecoin and then your future or something but just a set of we are research scientists and are allowed to think of interesting things, I think. And disclaimer that in my previous life I was a statistical physicist and yeah this is why this is the kind of thing. So this has kind of been a personal game this way because what I know is statistical physics and the first intuition is like, where is this. Okay, I'm now doing crypto economics is crypto economics statistical physics. No. That's the end of my thought. So yeah so just like this exploration of like, okay so the things that that statistical physics with no one would like to do how is it different and what does it have to do or not so what kind of what, what, what, what, what the, the, the name that I can give that includes both of the subjects as I can call like these two areas like complex many bodies or many agent or many whatever systems. This is, to me, vaguely defined set of subjects that with a unified team that you have many, right, of whatever you have. And having many is different than having few. Right so this are. All sorts of things can be like that so this is like particle collisions in an acceleros of this like subatomic particles that you can have like molecules in in some material that are interact so interacting set of many that can do something that an interacting set of you, perhaps cannot. So you can have like bacterias forming colonies and some emerging patterns, or things like having a wave emerged at a football stadium or something. So all of these are kind of encapsulated in this name, but statistical physics and basically which helps describes these two pretty well stands in a different place in that is a very regular rigorous field with a lot of understanding and a lot of results, which is kind of a contrast with the idea which is like hacking away at these problems trying to figure out what we can but there's not like a, like a theory of what these things are are doing. And in particular there's a theory of like there's a very good understanding of the theory of phase transitions and connected critical phenomena so this is kind of what I mean by this let's take one example of like a magnet so this is. The magnet's work are that you have your magnet is made of little magnets. So the molecules in your magnetic material are like little magnets themselves which they have a little arrow, which is like the direction of their spin we call it so this magnetic variable that they have. And they are interacting with their closest neighbors the most right so this one has a strong interaction with this one, much smaller interaction with this one and with this one and so on. But out of this little interactions that they could have this, this, this little magnets could end up aligning and you have your magnetized face. So where all the, all the little magnets are now pointing in one direction in this magnetized phase now you have a whole piece of metal that is magnetized and it's a big magnetic field. Now if you start to hit this up, it can become the fluctuations are enough that it can become demagnetized. And this is critical temperature where it demagnetized. So, so at some point as I said so you start some of these stars fluctuating but still the alignment is strong. But at some point this fluctuation start becoming very large and in the end you have something that is no longer ordered in this way so there's a word that will come up also so this is an ordered phase and a disordered phase. I'll elaborate a bit more on that. And there's a couple of things that that that define that critical phenomena in statistical physics. One thing is that all this theory and very strong understanding that we have is only about equilibrium. So, I can't really tell you about how to turn this into this. We usually like appeal to is like adiabatic principle that if we do this close enough. If we do this change, slow enough, it should be roughly like that instant we're in some equilibrium kind of thing. But, but we understand these things only like in a static non equilibrium kind of thing so this moment this is order and this is disorder but we don't understand kind of movement from one to the other. I mean, in a very rigorous way. The defining aspect is like you have diverging correlation lengths close to critical point and at the critical point. You get a scale in variance right so what this means in this example is so when I introduce fluctuations to this one. It starts looking like little bubbles of so like let's say if the correlation length is around three spins and maybe like a set of three spins here can can fluctuate together and so you have little bubbles of non order happening. The more I increase the temperature are getting closer to this critical point. This fluctuations can get arbitrarily large right so you get fluctuations of all length scales. The critical point what's happened is that there's fluctuations of completely any size and you get like scaling variance phenomenon like whether you look at a small circle here is kind of the same thing as if you look at a big circle here and this is an extremely powerful tool. Too powerful in that it's very tempting to try to apply it to other things where we don't know that it applies and that's one thing that I'll touch on connected to this and I'll show you how is that. If you have a scale invariant critical theory then you can characterize it by a set of critical exponents which is a very powerful tool to like classify different systems and understand them very well. Another point is that so these transitions as I described generally happened between some ordered and disordered phase so it's about about. So about destroying some about basically fluctuations destroying some order that was in some lower phase and so on. And another another important thing which I won't touch much on is that generally you can talk about and order phase transitions, which is like there's some discontinuity in something right so you remember this from like school that. You're increasing the temperature. So let's say you want to melt ice. So you're putting more heat in it and when you reach the melting point. It doesn't start raising the temperature right after that, but there's a discontinuity where you keep putting more energy but you're not raising the temperature because you're melting the ice. There's a discontinuity and with your input and this output so like it used to be that temperature is rising with the heat but at this point there's a discontinuity that it stops doing that but that can happen at and order and so on. I can see the chats I don't know if anyone I encourage people to ask me a question for writing because I'm not going to read it. So here is a bit more quantifying what what these things mean so ordered phase means that there is some observable some local observable that I can look at so I can put my little magnet reader here my little thermometer here or something at some point. Local means that that is I put it at some point here denoted by my eyes at this point and the expected value of that quantity will be non zero. Even though I'll get to be to this later like so this is kind of an emergent order like by looking at the starting equations that I'll show you you wouldn't expect this to be different than zero because things are symmetric but in this order phase, you get some non zero quantity. So in the disordered phase that has an expected value of zero so in this case, you can understand this as like what is the expected value of a given magnetization here of a given one arrow here. If I probe it here. I expect that it will be plus one in this direction that will be the my expected value. Here, it will be zero because it can be this direction can be in any direction is disorganized. So there's a. So this is called an order parameter is a local thing that you can measure that is zero in one phase and non zero in the other. So phase transitions are characterized by order parameter in this way. So critical point this is the thing I was saying about about critical exponent so basically since you have something that is scale invariant. You want to talk about correlation functions on the scale invariant thing so you can say, what is my correlation function between spin I and spin J. What I have here has to be something that doesn't that is scale invariant that doesn't have like scale parameters in it. And basically the only thing I can write down is some kind of polynomial like this. So it couldn't be like an exponential decay can be a sign or whatever it can only be power loss. So, and critical phenomenon everyone's always talking about power loss and so on. Once I simplify like this you see like understanding correlation functions, it's just a thing about knowing what am I said the set of critical exponents here is this delta, and kind of this structure constant whatever this are called. So it's like, if I understand a small set of numbers I understand my theory of what's happening in this critical point, which is extremely powerful. So this leads to, to like a lot of phenomenology in other areas that are not this will define and like a lot of publications like look I fall sound something that looks like a power law of something here this must be a critical phenomenon even though I'm talking about the wave in the radium or whatever. So there's a lot of like of power law hunting out there in the world of many body systems that are not necessarily equilibrium statistical physics, where it's not even clear what is, if this is a, is not clear this is a sign of criticality in general or even if this is well defined, which is kind of the question I'm going to do. So what is statistical physics a bit of a background and the, the joys of these in model. So this in model is a nice, nice thing that statistical physics is like to play with because it showcases all these ideas in a simple computable manner so it looks like this is a model for for something like the magnet I describe but one is that the spin variable this arrows can only be like either up or down so they cannot be in any direction so either up or down. So in statistical physics you have an energy function so like, I have a configuration of what all the spins were they're pointing at some moment and I can calculate what is the energy of that configuration. And this is the kind of the energy function that describes that what this describes here is that if a spin aligns with its nearest neighbor. That is good like that's lower the energy that is our lower energy state. Right so this is kind of the interaction between nearest neighbors here I wrote like nearest neighbor with this like set of one because I mean like nearest neighbors in all directions right so in x axis and y axis or whatever nearest neighbors you have. And here you could also up this is an external magnetic field, right so I could. I learned that encourages neighbors to align with each other and from that right that can lead to this kind of order, but I can also like push it externally by putting an external magnetic field that all the spins want to align in the direction of J. So that's the easy model here so. So after you define your energy function the next next thing you can do is like you define partition function right so. So you basically sum over all possible configurations of spins weighted with this Boltzmann weight here so it's just the energy function with your temperature, and this is the definition of temperature, this is what temperature is. So that tells you like how much to weight is configuration. And then you have expectation value so if I want to look at some observable, I calculate its average over all possible configurations with this weight. So that's statistical physics that's what I'm talking about equilibrium statistical physics, which you describe by some given temperature. So the comment, if you go back to the previous slide. If you think of it in terms of probability. Yeah, you think it in terms of probability of observing a given configuration. This said, is the normalization constant of these. Yeah, it's like probability distribution into the negative edge quality. Yeah, yeah, so see in this case, yes, it's just a, it has a bit fewer utility more utilities than this like it can also work like as a generating function for some things, but we can think of it now as a normalization constant. Okay. Yeah, so, that's, so, so that's kind of the definition of statistical mechanics but one one way to kind of go about it and like understand this a bit more is. So you can think of low temperature expansion right so in this case. So what you see here is that. So at low temperatures states so configurations that are very low energy are like the most important. And then configurations with higher and higher energy are more weighted down. So this is an example of an expansion that is about looking at the ground state of the model which is basically the lowest possible energy configuration, and then adding thermal fluctuations around that. But this kind of looks so if I look at let me first look at without including this external field so I'm just looking at this interaction. So with this to interact with this interaction has two ground states. So one is that all the, the energy is minimized by having all the spins, all the variables align up or all the variables align one, so either plus one or minus one here. So this is kind of an effective as I won't go into how this is generated but it's kind of like an effective potential of like, if I look at a given spin there so like what, what direction of that spin contributes the most energy. Basically it has two ground states here where the spins are expected to align here at plus one or they could align here at minus one and going away from this, from this points like you can do it by adding some more energy or so. So, so okay so let's say I have this field and this, this, this, these two ground states and I am in the, I remove all fluctuations basically I, I can start my expansion by, by going to one of these two ground states so it has two equivalent So, this is the concept of what we call spontaneous symmetry breaking, which is that this energy function here is completely symmetric in plus or minus one. But if I want to do a low temperature expansion, the starting state I have to choose is one that breaks the symmetry so I have to choose either start from plus one or minus one. Right. So, so, so you can also think of this as a spontaneous energy breaking and emergent order are kind of equivalent things so. Right. So, so this was first indifferent between plus and minus one but the ground state you have to choose okay now they're all aligned up. And then I think about alignment everyone up and fluctuations around them. So that's spontaneous symmetry breaking. You can also talk about explicit symmetry breaking which is for instance if I add the external magnetic field. Let's say I add a little magnetic field pointing downwards. Then that will bias this to be like a more real ground state than this one. The one where everyone is pointing down. So, so if I start at zero temperature I will be in one of these ground states I am here. And the question is if I start introducing thermal fluctuations will they be enough so that's a double main things will start getting higher and higher here at some point I will have enough enough energy to kind of overcome this. So I can move around between both ground states and that is the phase transition. So that is restoring the symmetry through high enough fluctuations. Right. So these are kind of the question I understand statistical physics. Can we look for this kind of things in economics right so can we look for things like spontaneous symmetry breaking emergent order. Can we think about symmetry or symmetry restoration through fluctuations, I don't have in an order and disordered phase. Can we, can we talk about this same kind of thing of divergence of correlation lengths and. And yeah, and even this would be the greatest if we can characterize things with critical exponents that would be very powerful too. But for for the specific kind of economic problem I'm looking at these two, maybe these two no. Which is interesting. So, I mean, in the way that I define. Okay, so what are we looking at here so what what what the economics are we looking at so so so we will let's start by having this consider something simple but something to start with which is like one shot game with approximately rational players that has some sense of locality right so so one shot I mean that they have like every player has one strategy to decide this will be my strategy for the game. I do this action and then see the outcome. So I think like, so to show to be like I play once, then see the outcome of this game and make my new strategy and play again, so that would be a, so it's like, make the strategy without knowing first and then doesn't the game is over. It's not based I assume like they're trying to optimize their utilities and so on, but perhaps, no, not perfectly and that's where the fluctuations will come in. It's like fluctuations around, not optimally optimizing right and some sense of locality kind of to have. So this is where we, I mean, so in this sense. So here the locality I'm talking about is kind of. So these spins are arranged in some space where there's a notion of distance and which of these things are closer to me and I interact more with the ones that are closer to me. So here doesn't need to be literal space as is in this case but some other notion of distance and some notion of I interact more with players who are closer to me. So that can be very geographic or can be about internet speeds or whatever. So some notion of distance and more interaction with my vicinity. So, so what I have here was I have a set of strategies of all the end players in the game and a set of utilities for each one of them. So, so the utility for the ith player depends on their own strategy and the strategies of the rest of the players but mostly of their neighbors. So that's where it goes. So this is like the set of others by bar I here I mean like the rest of the ones that are not I this is like the set of everyone else who is an eye. But here's a kind of a big legal bull I gave that the ones closest to them are the most important. So this is the kind of a problem I'm looking at. I have to understand what what are the parallels I'm looking at between what corresponds to what in the statistical physics and game theory so. So kind of I want to think about this expansion of we have a stable point like like at zero temperature and we have the ground state here. And then we add fluctuations around it. So the statistical physics is we have the ground state as our starting stable point, and then we can add thermal fluctuations around that. There's other like quantum type of fluctuation is another thing but not unrelated. It's a similar idea. So the analog version that I'm looking at here is that the kind of the stable points in this games are the nice equilibrium. I'll go a bit more on that. This is like what would be a stable point if everyone is completely rational. So these are stable points for rational players, but adding some fluctuations around that by what I what it's called give the reference someone called noisy interest introspection, which is basically adding some kind of noise around completely rational strategies. I'll go a bit more on right so what what nice equilibrium is how we're using that says so nice equilibrium is right so we have the strategy of the ith player. The strategy that they will they will choose is the actor should be max maximizing the utility but anyway. So it's the strategy that maximizes their utility, given that everyone else is also choosing the national equilibrium strategy. And what this means is so safe. So, so it's a configuration of everyone doing something that one player alone cannot improve the situation for themselves. So if everyone is in this nice equilibrium point, and this one person here is trying to improve their outcome. They won't be able to do it by themselves. This is the best they can do, unless some less other people also change their strategy. So it's a so this is why it's kind of stable because it would require kind of a larger scale changing strategy not that the individual skill. So the individual cannot do any better if everyone is doing the, the nice equilibrium. So it's kind of a distinction here that so this is kind of for like the optimal the stable optimal situation for non collaborative games because like this is the best I can do on my own. Kind of the best I can do is guess that probably everyone is thinking this and probably everyone you will just go for the nice strategy and then I can't do any better than the next strategy. But of course if they were collaborating, things could be a lot better like you could like optimize the overall utility for everyone or something like this if you can talk about the strategies and so on. So one key distinction here with statistical physics is that there's like n things to minimize or rather maximize here versus the one thing in statistical physics so so statistical physics you are minimizing the energy. So there's this one energy function. So it's very similar like you can talk about the statistical physics is rather a lot more similar to collaborative games. So you can define the total utility for everyone and maximize that and that's very similar to the question here of minimizing the total energy. But here there are n things to minimize versus one thing. So this noisy introspection and here's a nice reference to this kind of a way to model kind of noise around the natural equilibrium so let's say I'm trying to do the natural equilibrium but but but have some noise around it right so. So the idea is this this is a process that is done iteratively and like so there's a lot of introspection so the first layer is like. If I assume everyone else is doing Nash. So what let me explore my the neighborhood of my possible strategies around this Nash equilibrium. And I do give some my expected strategy here will be like a strategy that is weighted by the difference so this is weighted by my utility. So this might actually be a plus here because I have to mean a maximum stop here but doesn't matter. Anyway, it's similar to this kind of Boltzmann waiting for for statistical mechanics where I will. The maximum weight will come from my maximum utility and then I'll get decreasing weights away from that and so on. But I'll allow myself a more range of strategies weighted by probabilities and so on. Now, then I think on a second layer like, okay, I'm thinking this, but the rest of the players may also be thinking this on their own so so I'm allowing myself some randomness around Nash equilibrium. But I actually shouldn't have the word Nash here so. But there's a second layer here where the strategies of everyone else are also determined probabilistically where they are themselves thinking about moving around Nash equilibrium and so the target the strategies of the other players are chosen probabilistically with. So we're defining the set of temperatures here where this is kind of the level of fluctuations I'll allow myself. This is the level of fluctuations I believe others will have. And then here this ones also could be set this way by other so this, the other players may also be thinking that the other players will be probabilistic so they will model things this way and then those will think that and, and so on so everyone. Probably probabilistic but I know others will be probabilistic and I know they know that others will be probabilistic and so on so you can do this like to the end level of introspection. And then kind of the strategies, taking this to infinity and that's that's that's how that's where this is going. And that is kind of a model for fluctuations around Nash equilibrium. So this could be characterized by a set of temperatures for for each level. And so this could be, I mean, so, yeah, there's there's more thought to be had about these temperatures, they be all the same should they be as in this particular paper they actually argue for like, these are like, just like exponentially increasing the sense that each level of introspection is more mysterious than the last so it would have a higher temperature and so on so that's something they argue there but not again here. But so I was saying so this is different from a cooperative game which would be very much like statistical physics in a sense that so so we just have to maximize the total utility for everyone so here I have kind of the sum of all utilities here or the product of all this Boltzmann weights. And we all maximize that together. Everyone wins by maximizing that one thing right. Right so but then something like essential difference between this and this is that this cooperative model is actually interacting right so so because you're cooperating your strategy is actually interacting with the actual strategy that other players will have. So, if I look at like correlation functions between strategies. I expect to see correlation links right so this is the correlation of this one here is correlated to this one here. And because of this locality that I talked about I expect higher correlation between neighbors than between a further. But this is something that comes about. Only if the strategies are actually interacting with the real strategies of the others. But this is not what is happening here and this is like the very interesting very different point here that you still have interactions between strategies of neighbors. But they're not really interactions with what the neighbors are doing there are interactions with what I think the neighbor will do. So, kind of something you can so the way you can kind of mathematically see this year is that if you want to like, you're only interested in calculating things about this ice strategy. So this probability distribution here you can kind of integrate out every other strategy. Right so you can sum over all this possible JP has a hand. Yeah, sorry, I probably missed it but what is the, what is the concept of being of neighborhood in this, in this context. So, that comes in the, so in the utility so that's a description of what the utilities look like that. So I assume there is some notion of distance which doesn't have to be physical distance but some notion of distance. So your utility depends not only on what you do, but on what others do. But it will depend more on what your closest neighbors in this distance do. So this is that notion of locality. Okay, so it's not that everyone is neighbors. Well, you know, everyone but there's some sort of. Yeah, that would be the opposite. So that would be like, no notion because like I can interact at any distance that's non local. Global, but local means that I can really only interact with the closest people to me. Thanks. Right, so you can kind of mathematically understand this about the interactions in that. So I can kind of derive from this and effective probability distribution. So I am only interested in asking questions about this one strategy here. I can basically integrate out all other strategies. So this is a sum of overall strategies. I go ahead and perform the sum over all the other strategies now there are no longer variables and maybe that's not what I wanted to say but let's say I want to let's say I want to calculate the correlation function here but I have si and SJ. I can then integrate out everyone else than I and J. Then get a distribution here that describes the relationship between I and J. But the point is that will produce something non trivial something a distribution that is not just a product of something from for si and a product for something for as for SJ. It will produce something that is not the composable like that and therefore there will be some correlation. And that comes from like all the interactions in between I and J. In this level, I'm kind of doing all the integrating out here. So, so this introduce this has some information of what your neighbors would do but not from what they're actually will do. Yeah, so, so I can integrate out. Let's do the same thing here I have si and SJ I integrate out everyone else. And if you look at this goes enough she was but you will have is a distribution for si times a distribution for SJ, which means this to will be not correlated because this attribution is factorizable like this. Yes, I find this very interesting so it's very interesting because I mean it doesn't really have a parallel in normal statistical physics in a sense that so you can still talk about order, because yours, your, your strategies are still aligned with neighbors, but in the sense of what you think is good for them to do, but you cannot talk you will not have correlations. So it is possible to talk about a critical phenomena in this in this kind of non cooperative games, where there is a change from order to disorder, let's say, but you should not be expecting to see scale in variance and talk about critical exponents and all that good stuff. So things that make. So I mean, I'm lacking. I would like to have simple prototypes of games to put where I can see all this phenomena happening but what I have is what is possible to look for and what will not happen right. And all that something like this happens. I don't have an example yet that I'll show you here it happens, but this is a reasonable question to ask, which is kind of what we're talking about here. So you could have a game where you have an ordered phase where as I described so you have some observable that results on let's say some function of local strategy here that for some small set of temperatures for some small level of fluctuations will be around zero. Right. So, so some order parameter here that you have some expected value. But if I introduce high enough fluctuations, you will kind of lose that order. So things like so what what what can this kind of things be so so let's say like some clients and storage providers or something like this. So, so there's an order. There's, there's, there's, there's a possible equilibrium state where the optimal strategies are people to make these deals where, where there's, where so you can look at the expected price like the payment at this point in space where for this client and this storage provider interact. And there's an expected non zero payment because it has become an accepted and reasonable thing that people pay each other for, for, for data storage or whatever but given enough noise of like people, not just behaving rationally but doing whatever people do on the internet. It would not be expected so the expected deal amount you would see within a random data holder and a data store will be zero. So these are the kind of things. But so you could have an ordered and disordered phase and transition between these two, even while not having this phenomena of like strategies being correlated. And this is what I find very interesting that this is an order that can emerge from what players think other players will do, but not from what they actually do and this is something that I don't know, a parallel in statistical physics. So you can't have order without correlation, but in this game, order can emerge from thinking. So that's cool. Yeah, a little note here as I've been talking about this kind of one shot games and where the, what, what players want to do is like, there will be this short game, we will play, then the game will end. I evaluate all my winnings throughout the game and what I want is to have won the most by the end of the game. And, and this is kind of how this snatch strategies are chosen like what will optimize what I will have won by the end of the game. But you could also have that's not the only thing you might want to do so you might have like long games where you know there is an end to the game at some point and you will want to have won at the end of that. But you also want to survive for now. You know, something comes to mind like retirement right so you're working now and you hope by the end of when you're 65 you will have a one with the most utility and can one that life, but you also want to survive now while you're working at 37. So there's infinite games basically where this end is not inside and your best strategy is like look for utilities for now so what will work for me right now. And so I bring all this because in relation to like how would all this eventually relate to, let's say Falcon or whatever. And we kind of want to think of, of it as infinite games in the sense that we don't want Falcon to end. Right so we want. So, so we expect people to be getting good things for themselves, live, but not necessarily with an object of winning the game at the end of Falcon. Right so I promised to talk about crypto economics so what is what is crypto economics and what what what should crypto economics do. So, so I understand this so. So what crypto economics should do is so we have incentives that could, or sometimes are set to be temporary like block reward, but we said it to disappear. So, so, so we want to introduce this, this temporary incentive, but thinking it will somehow achieve a stable long term behavior that we want. People at random on the internet. So let's say we first introduce like all the IPFS technology right and with this people can make store data if they want right and so have strangers on the internet store data if I pay them. But they're not necessarily doing this even if this would be a win for everyone and a good thing they could do. So we are like, let me push people to do this a bit. Let me introduce. So kind of the system of people with data on the internet has presumably two stable points, one where they're not making deals, and one where they are making deals. So basically these are, we know the non making deal one is stable because like this is what people are doing, just not doing it. But we would hope that the other one is stable too and so so what crypto economics is good is to, is a tool to introduce explicit symmetry breaking right to bridge gaps that could have been spontaneous symmetry breaking where we were not where we wanted to be. So let's say these are two things that could happen like people could be making data deals, or people could be not making them but right now we are here. We want this to be stable because in the end we want to leave the system alone and then not to decay so it's good idea to have a target in mind that is a stable target. But what we want to do is kind of not that way so here into the economic incentives that introduced this explicit symmetry breaking that make this a preferred stable point than this one. And then we expect that okay so we introduced this this this incentive for a while. So this is exactly how it works with magnets also that okay so you can, you can be up oriented or down oriented. I can introduce a magnet to get it to be in the orientation of I want an external I can introduce an external field. And one is that when I remove the field, the magnet will stay there and that is a, it will stay there because it was in an ordered phase that is small enough situations around a stable point. Yeah, so this is kind of what what what I think this means for for crypto economics that we need. Yes, some what we should be aiming for our things that are stable points with small enough situations around them, but that we are just currently not in them and crypto economics can help us. Just towards that point that we want but it's less hopeful that it will help us get to an artificial point that is not stable I mean that would be an example okay so I push everyone here. And then I let it go and then it all comes almost done. So the desired behavior we should incentivize should be a stable point. It's not necessarily one that people would have chosen on their own. So here it's like, presumably things that are stable is that is presumably stable that we could have a market where users pay for transactions fees to have the transactions written on a ledger because that's valuable. So that block reward as this external magnetic field that pushes into this region. And you would think if this is stable you remove that magnetic field and people will remain doing that. And that's the, that's the goal here. Maybe that's reasonable sounds like could be reasonable. Another question of a little reasonable are these questions about so, so some stable coins are kind of relying on a network or questionable if they're relying on this network effects or not so. So you have coins that start by saying we have our coins are one to one backed by Fiat reserves. And this will push people to this desired behavior that they treat this fake internet token as if it was worth $1. Now everyone is in this point where we all agree this fake token is worth $1 and we trade it we don't accept anymore or less than $1. It could in principle reduce the reserve because now we're in this point where people are trading it as such. And it is at least unclear if some stable points are doing that and to one to one extent right so like, yeah they claim they have it all backed up but it's no longer backed up now. This is a stable point simply by interactions of people who now refuse to trade it at any other than than a dollar. Right so this is so you kind of align everyone into this ordered phase where we pretend this is a dollar, then you remove the magnetic field of the of the of the reserve. And you hope people keep trading it for a dollar but it is questionable, or how stable this is and to this end we're just to touch on the last subject of like false vacuum decay which is a thing in physics. Right, so this would be what this looks like like. So this is what the situation looks like when I distort it with my reward or with my reserve for something so it can be like, also this is the stable points to treat this thing as $1. I can remove my reserve. I got people to be at this point but but but my system without that external field actually looks like this, where people are here, but in a very precarious situation where a little bit of fluctuation can make them all cascade down here. So this might be the status of some on back the on back the stable coins that's my speculation here. Yeah. That's it. Yes, so that's all. Thank you, Axel. Are there any questions. And you still have six minutes. Nice. I wasn't even looking at the time. That is a pro at presenting. Okay, if there are. Oh, any questions. Yeah, one of the things I don't know it's just kind of a comment one of the things I was thinking about while you're talking to Axel is like in in physics right like your feedback to the whatever is happening is immediate because it's an electromagnetic field or, you know, a gradient of in a chemical solution like you get feedback like oh I should move this way or swim this way because concentration is forcing me that way. So like you get that that immediate feedback. And now we're dealing, trying to make this analogy into the economic space where people are are there. And there's so many like blockers to that you kind of alluded to this like it's not the same thing like people. A lot of time like if you don't have their attention. They're not going to do it like maybe the ROI changed dramatically due to some new stimulus but this person is there investing in cosmos and Ethereum and and Filecoin and they've got different bots going and different contracts going and like you can't get their attention until like whatever ramifications of that change have come and gone. And so like that you don't get that immediate feedback in an economic situation necessarily just due to due to like attention attention span and like the attention economy. And so then like I was thinking like the intersection of AI will some of those things become more and more automated. There's so many things to think about as this economic agent. Can we outsource that to AI and become a little bit more like a physics article so that we like reacted more immediately. And so this so there's several points here so this concept of locality that I talk about is also like very related in physics to like speed of information. So, so yeah I get information right away, but from my closest neighbors, faster, and there's a limit to how fast this information travels. And that's related to right to the way I said this is actually something that is provable when you have a strong enough sense of locality in your model. Then you can prove that there are some bounds on the speed that that information travels, but here. Yes, so the thing I was mostly discussing like there's no traveling information right because it's just like me thinking alone here about my best strategy. And the next, like in this version that I also discussed is also very simplistic in that this would still be like a one shot game with coordinated premeditation. So let's all talk about the strategy we will all do at once as I'm the coordinate. And okay now we all put our cards and we'll do it in a way that we coordinated previously that will maximize our thing. But yeah the questions you asked more will be more relevant in things like this so this is like, like, so these are not one shot things and these are things where we're saying an infinite game. So there will be an active situation going on and you will be getting information, presumably with locality as well you'll get information from your nearest neighbor, sooner, and then depends what happens then. So there should also be an ocean of speed of of traveling information. So that in that sense shouldn't be that different to the situation in in physics. Do you have any like, I like that these frameworks I think are really useful when we're thinking about economic problems. Are there any like, maybe you would have mentioned it in the talk. Are you thinking about applying these to any specific problems already or just kind of like hey this is a framework that I want to like share with me. I mean, so the, I mean, the theories in me would like to like look at put so I can put some resources so that I think there's a worthy exploration and like in the same level as using model is working physics and like, we find an example model that we put a simple function to show this, this different phenomena actually exists. So, so we can try it like a simple model like this. We're going to I was also even thinking like we can use this, these in model as a utility function so that that's one thing we can do where we have strategies that are up and down. We can, if this is my utility I can use that to read and put it in this formalism instead of partition function. If these things if there's some simple ways to see phenomena like this right to kind of proof of concept of this possible effect here. That's something like toy project to look at. So one thing I take away from my, from my little questions right here is to. So this was inspired by actual lot of papers in different fields and a lot of so there's a lot of phenomenology when it's not justified there should be so like I say like, you will see a paper of like we spotted this power loss in crypto economics this may hint that critical phenomena and this and this and this gives us a way to understand this like is this something important or nonsense and depends on the context but Yeah, I mean like there's already a lot of work on like the critical theory, critical phenomena like theories of anything that is a complex system. And a lot of it is unclear if it's meaningful or not. So this is kind of what I'm going to say. So if I read something about economics in the future, I can be like, does this make sense. This kind of where where I'm going coming from. Perfect. Thank you, Axel. I think we are on time. So thank you so much for the presentation, I will upload the recording to the notion page so everyone can can see it later. And the next seminar we have is on January 11, and it will be our own Tom melon presenting. So if you are curious just come back and see this presentation. Thank you so much everyone. Exactly.