Come to the second day of if not I mentioned so I hope everybody's is doing well Before we start with the session just a quick update on today's schedule So we have the two talks now in the morning, and then we have a discussion session at 11 So, you know, we thought you know, there's so many amazing people here doing interesting stuff Yesterday you had a chance to see all the posters already quite a lot of talks, you know so, you know take over the terrace go around and and and enjoy the discussions and then We'll have a session in the afternoon You will have seen that on the schedule then at I think four or four thirty or something like this There's another talk that we wanted to advertise a little bit It's about how to do math in 2030 and how math, you know with transformers will you know how we will all get out of jobs basically and Since if you want to know about that feel free to join that talk and then we'll meet again for a little hike Which will be really just a walk through the castle down the seaside and then we'll have a little aperitif, okay? We'll tell you later exactly when we meet and where But yeah, this is kind of the the plan for today And okay We'll start with the first with the first session and our first speaker will be as I guess I Who's in the system of Western and he's gonna continue our sort of stream at this conference on on the dynamics of learning and the dynamics of SGD So yeah, thank you for coming and looking forward to your talk Thank you very much for the invitation to be here. It's beautiful setting very nice to be Here and thanks for coming to the talk.  So the general statistical framework we're thinking about is you know common one we have some IID data stream that's coming in That's these y sub i's and there's m data points capital M and they're all coming from some common distribution p sub y and We have some loss function that's l for me and There's a parameter space r to the p and input space r to the d so p and d will be the dimension of the parameter space and the input data space and There's some risk function Corresponding to this loss function. So we take the empirical average across the data set of the loss function and So there's a common framework it captures lots of problems that we've all seen before like parameter estimation tasks classification tasks neural networks things like that you can put into this language and the common goal is to minimize this empirical risk and Hopefully that gives you some good, you know the parameter that minimizes that gives you some good solution to the task at hand so Some typical features of this Framework are that you know as m goes to infinity as long as there's some reasonable Moments then you have a law of large numbers for the risk function So it'll converge to this phi that will be recurring throughout the talk So that's the population risk or the population loss for me it's just the expectation of the loss function at the value and parameter space that you're considering and So here's you know a simple picture of the risk on the left and the population loss on the right and you see okay So it's common for the population loss itself to be simpler in some sense than the noisy version The risk then the risk but on the other hand symmetries of the problem often lead to even non-convexity for the population loss So I'm really thinking about a non-convex problems throughout this talk and so SGD and non-convex Then the global minimizer or global minimizers of this phi will be good solutions to the classification estimation task that you're considering so otherwise, it's not a good loss function essentially and So okay, so this leads to maybe the empirical risk R is hard to optimize because it's you know Has lots of local minima saddle points things like that gradient descent doesn't do so well So people use things like stochastic gradient descent which isn't optimizing so much on that But it is some stochastic approximation to the phi and optimizes there Okay, so I'm I think most of us are familiar with this kind of thing so stochastic gradient descent is The following algorithm and I'm thinking throughout this talk only about the online one-pass setting so we have this M set of M data points and I move around in my a parameter space by iteratively making a gradient update according to the loss L Evaluated at my current parameter point on the next data point So the the point is that the next data point that I'm getting is independent of where I've moved to up to this point And little delta will be the step size for me okay, so The reason this works reasonably is that these are you know each of these incremental updates are stochastic Approximations to the gradient of the population loss in the sense that if I break up this grad L term I can split it into the grad phi which is the mean part plus a noise term The mean parts will be like what I'll call the population drift. It's a gradient update on the population loss which just really depends There's no randomness there It just depends on your point in parameter space and then the the random part the second term is a martingale increment So you expect it to average out as the step size gets small And you'd make many updates. Okay, and so in this way, you're really doing some kind of Optimization scheme on this smoothed out population loss landscape. Yeah. Yeah, so the grad five should not have the yk Sorry So the theory of You know stochastic approximations goes back to the work of Robbins and Monroe in the 1950s And they showed that kind of as you'd expect from the previous slide If you look at the trajectory of the stochastic gradient descent in the parameter space You take the step size to zero Then it converges to the solution of the ODE which is the gradient flow on the population loss Okay, so the martingale increments indeed average out and you can get this kind of a law of large numbers for the trajectory of the dynamics Since then I mean, this is a long time ago. Lots of other work has studied Stochastic gradient descent in what I'm calling fixed dimensions in the sense that the dimension of the parameter space is fixed The task is fixed the the data space is fixed everything's fixed And you're just taking the step size to zero and in that limit So you get this law of large numbers you can also get a central limit theorem for the trajectory or like an invariance principle large deviation principles All kinds of very precise information for how the SGD trajectory approximates the gradient flow But the one thing I really want to emphasize about this whole story is that this is all for a fixed problem fixed parameter space Fixed dimension etc. And only the step size is changing That's that's the limits that we're taking so the goal of this talk is to look at like the high-dimensional Setting for stochastic gradient descent and obtain some kind of limit theorems in appropriate ways Okay, so any questions about this just background so In modern data statistics where data science statistics, etc. We're often data constrained So we need to think about high-dimensional settings And by that we mean, you know, if I'm taking delta to zero the step size to zero that corresponds to taking my number of samples to infinity But taking my number of samples to infinity relative to the dimension of the parameter space is often impossible you know, that's not the regime that we're often in and so analytically the common approach to studying, you know, this kind of more data constrained setting is to take the the different things to scale together so the dimension of the problem to scale with the number of samples that you have access to and So in particular what I'm going to be thinking of is we have some family of statistical tasks now They're you know in some sense. There's some consistency that we're assuming on them but you have a family of tasks all indexed by n they each have their Input spaces their parameter spaces p sub n and d sub n being their dimensions and you have step sizes corresponding to these little delta sub n and So for instance just you know one thing you can think of is what I'll call the proportional asymptotic regime Where you know the dimension of the problems n the step size is 1 over n So the number of samples is proportional to the dimension of the parameter space So this is a kind of common assumption. I think in like high-dimensional So it's a couple simple examples to have in mind that will recur or you know, you can imagine you get rank k matrices and by n matrices that are corrupted by some Gaussian noise So here the parameter space says n for the n times k may be for the different vectors that are the planted ones and then the dimension of the input data is n squared for the matrices you're getting and Then you take you imagine that the number of samples you have access to is proportional to n another one is classification of some mixture of k Gaussians with some arbitrary labeling on them and similarly you have this kind of proportional access to a proportional number of data points to the dimension of the parameter space, okay, so When we have this kind of a Diverging family of tasks indexed by something like n Oh, we obviously can't look at the trajectory of the full stochastic gradient descent You know, it's on living on different spaces as I change n So we need to project down onto some finite dimensional observables or what I'll call summary statistics in order to get meaningful limits in any in any reasonable sense and so What I'm going to call summary statistics will be these this finite dimensional family of observables that we're going to track and so these will be what we want to prove limit theorems about and So let you know, we imagine that there's some k summary statistics that we want to track and the Important thing here is that k is going to be independent of n Okay, so k is going to be fixed and I take my end to infinity and get some limit theorems, okay, so in this level of generality, there's Many, you know, many people in this audience have worked on these kinds of questions. I'm not saying anything revolutionary and There's a few approaches, I guess to studying stochastic gradient descent in Non-convex settings specifically that have kind of made significant progress in recent years So I just want to outline a few of these to then talk about where our work fits into them so one of these approaches which I think a lot of people here have worked on is What I'll call I guess getting some kind of ordinary differential equation limits as long as you start away from critical points of this Of this population landscape so in the same way that we got convergence to gradient flow for the in the finite dimensional setting if you look at some Family of summary statistics that are the relevant ones You can take limits in the in this high-dimensional setting that I talked about and in fact Here a lot of the work that I've cited here includes, you know looking not just at online one past gradient descent But also considering like launch of and a type dynamics or gradient flow type dynamics where there's more memory And it's harder to understand and you can get some kind of ODE's coupled systems of ODE's as the limits of these observables and And then you can try and analyze those ODE's that you get either numerically or analytically So progress has been made on, you know several questions in this way One thing I want to emphasize though is you know the the population landscape that I drew it had something or if you imagine even like Rank one matrix corrupted by noise so like a spike matrix model oftentimes There's some inherent symmetries to the problem So maybe like in the one observable you have some landscape like this Due to some inherent symmetry and the important thing is like You have to start kind of macroscopically away from the saddle point or from the critical points in order for the ODE's that you get To actually do anything on the time scales that you get limits So you know if I if I get some limiting trajectory that's you know gradient flow on this landscape for my Correlation with some planted vector if I start any with any initializations that are converging to this saddle point They're not going to move in the limit That I'm ending up with so that's why I write that this is in some sense There's some warm starts and so the common approach here is you get some you take Limits you understand what the behavior of these trajectories do if you start like Macroscopically away from the saddle point and then you send that macroscopic amount to zero to try and like read off some behavior near the saddle point a different approach that's kind of been made successful in a few more problem specific examples, I guess in more restrictive settings is Specific problems where you can actually take Limits or at least get some kind of upper bounds or lower bounds on the behavior if you take even initializations that are converging to the saddle points so in in a lot of these problems like phase retrieval for instance, you do have some kind of basic symmetry like this and A random initialization in your high-dimensional space is going to lead to a sequence of initial points in the projected space That's court converging to this saddle point So for these for a few specific problems, there's been some progress in understanding like okay What's the actual time complexity of escaping this flatness near the saddle and then after that you can apply the kind of? You know warm start understanding from the from approach A third direction, which is a little separate from one and two is Problems where there's not so much these finite dimensional set of observables that are the relevant statistics There's been some progress in taking like empirical measures This is sometimes called like a mean field approach or infinite width limits kernel methods so you can look at like an empirical measure in the parameter space and Get partial differential equations instead of ordinary differential equations for the limit of those and then these become maybe I mean pretty Intractable, but maybe you can do something with them And understand this and pull back some information about the actual SGD from this approach. Okay, so this is a kind of different so my goal in the talk and the goal of this result was in some sense to Unify approaches one and two To allow for consideration of you know You have some finite dimensional set of statistics that are the relevant ones you maybe end up with some ODE's as the limits When you take some limits, but maybe you should allow your initializations to vary And you want to blow up around the saddle points at the same time and understand What's the behavior locally near the saddle points and so there instead of getting ordinary differential equations? Maybe there's some residual stochasticity because this is a very flat landscape So there's no strong drift so the the stochastic part of the stochastic gradient descent should persist in the limit also and so the general gist of the result is that you can take sequences of initializations that are you know converging to saddle points and get stochastic differential equation limits or Ones that are not converging to saddle points and get ordinary differential equation limits For a class of fam for a class of problems where there's some finite number of statistics that capture most of what you care about in the problem any questions so Let me say I think a little more precisely at what our setup is and what we're assuming about the problem So I apologize for this kind of ugly slide with assumptions I'll try and just give you a gist of what the assumptions are so first of all We have some we have some family of summary statistics That's the you know the observables that we're interested in tracking in this end to infinity limit and What I'm gonna assume on the problem in terms of regularity is You know threefold the first one is that the summary statistics aren't too spiky there You know their Hessian is has some reasonably bounded operator norm So I'll remind you that you can imagine delta n is approximately 1 over n or it's 1 over the number of samples Is the proportionality you should think about so we are allowing some of the norms of like the Hessian of the observables to blow Up with the dimension it doesn't have to be you know uniformly Lipschitz, but there's some regularity assumptions on them So that's item one item 2 is a matter of the regularity of the lost landscape So here again the thing I want to emphasize is we're assuming that the population loss is Uniformly Lipschitz, but not that the loss itself is uniformly Lipschitz Okay, so the unit the lost landscape itself can blow up It's Lipschitz norm can blow up with the dimension of the problem Which is the kind of this is the kind of scaling you'd encounter and I mean I'll give you examples But for instance the the spiked matrix or the mixture of Gaussians or a spike tensor all of these fall into this Class so those are kinds of so those are situations where the loss is more spiky than the population loss and That's why and the third one is basically that the noise So this is L minus phi is the noise in the loss once you recenter out the mean isn't Correlated with any of your summary statistics like too much so the idea is all of the information in the problem or most of the information in the problem should be captured by the Population part not by the noise part, which I mean the noise should be fairly uninformative Okay, so One thing is yeah these kinds of assumptions on the lost landscape is we're not assuming that it's uniformly Lipschitz But it's this is the kind of scaling that you'd get if it were like random vectors in D Dimensional space like random Gaussians for instance is that that kind of scaling and that's what leads right to this Okay, so here's some examples of yes so okay, so this is Infinity uniformly over compacts and not everywhere in space in theory You'd want you'd want to allow like maybe there's some atypical parts of the world where you know It has bad norm and but your SGD avoids them, but We weren't able to you know decouple the trajectory from the like bad parts of the Hessian Yeah, so it can blow up as you go off to infinity in perimeter spaces There's a five-fixel compact ball then you have these kinds of bounds on your there's some constant depending on the size so some some examples of reasonable things that we can track are You know correlation with some like spiked with some planted vector for instance or some ground truth Vector, so that's like a linear statistic Of the problem that'll always fit into this this set of observables Something like radial components so a lot of the times when we're thinking about a loss function We'll have some radial penalty to confine us to you know some compact set and so radial penalties should always fit into this so we can track them and Then other types of correlations and especially when I want to mention is like the population loss itself That's something that you know if you want to say you succeeded at a problem one way to say that is the correlation with some vector Gets good and other is that the population lot of Scott small so you want to include that in your family and one thing that's really important is that the Definition I gave on the last slide has enough room that not only do all of these examples fit into it But they fit into it even if I blow them up by like a root n factor So what I want to imagine I'm doing is I'm looking at this summary statistic Maybe it has some landscape like this There's some saddle point or some critical point here and in order to get diffusive behavior near the critical point I need to zoom in because at the macroscopic scale you're really not moving around here And so you imagine there's some central limit theorem going on you want to blow up by an order, you know Like this is a little low like an order 1 over square root n window so I want to blow up by a factor of square root n to get some limiting behavior near the critical point and The notion of like the regularity that we assume Has enough room to allow you to blow up by a factor of square root n and still be a well-behaved summary statistic Okay, so summary statistics are not only these kinds of things But also you can recenter them around a critical point and blow them up and they're still well behaved enough Okay, so then so this this you know up to here. We've only assumed regularity things You also need some consistency between your problems in order to get meaningful limits And so that comes in the following form. So we basically We assume that the gradient flow on the loss when it acts on these observables So that that first thing you see on the top left is the gradient of the population loss Grad of the observables that admits some meaningful Limit along with a second order kind of term that I'll describe in a second if these admit some limits as n goes to infinity So they're only they're approximately only functions of the summary statistics themselves Then you have the consistency criterion that you need So the first thing is like a drift for the summary statistics That's what this H will be and the second one is a diffusivity for the summary statistics, okay? One thing is if you you have freedom to take your step size arbitrarily small If you take your step size very small then both of the you know The orange and the green term both drop out and then it's just gradient flow for the population loss So you recover the only a like finite dimensional kind of behavior that'll become clear And then if your step size isn't too small then you can have these kinds of second-order operators that are relevant also So you might wonder like okay, this seems fairly restrictive Or how do I come up with what the family of observables such that this closes? So yeah, some problems might not have you know If I took a rank n to the epsilon matrix and corrupted it by Gaussian noise that does not fit in our framework That's why we need like a finite dimensional set of Observables that you can track but to get that finite dimensional set of observables You can start with like the population loss and then just try and close this so take the gradient See what other observables you need to add in in order to close this and that'll give you your set of summary statistics that you want to track for the problem and so under these two assumptions then the main result is that if I take the Trajectories of the stochastic gradient descent projected by these observables and I take the n goes to infinity limits Then they converge to the solutions of the stochastic differential equation Whose drift is the limit of the drift term the first term and whose volatility matrix is the limit of the second term So that's the volatility All right, so it could be that sigma is zero and this will be an ODE in Particular when delta is going to zero fast enough So you have access to enough samples then you shouldn't expect any like volatility and then you should just expect the finite dimensional ODE limits and that's what's gonna happen So you know you take delta going to zero fast enough the the orange and the green term dropout This is just gradient flow on the population loss But it could also be that there's some residual stochasticity Which will happen for instance near saddles, and then you'll have this space dependent volatility matrix sigma Okay All right, so Let me give a kind of general remark of how this relates to this kind of picture that I was giving here When we see ODE limits when we see SDE limits and then I'll give a few examples Of how you this can be applied to study certain problems Any questions about the statement of the result? So a few Yeah, maybe one comment or a couple comments. I want to make are one of them is H here does not have to be a gradient flow So it doesn't have to be that there's some like lost landscape for the finite dimensional Observables on which you're doing a gradient flow this second order correction term can really make it a non gradient ODE and This the volatility matrix I mean sometimes it's common to assume lower bounds on the diffusivity of your lower bounds on the variance of your stochastic Increments things like this We don't make any such assumptions. And so in particular the volatility can be highly degenerate certain places so you can lead to degenerate diffusions and Things that would actually like keep you stuck at saddle points because there's not enough volatility to let you escape Things like that. So the Sigma can be ranked efficient. It can be degenerate in that sense So when you look at this when you take the kinds of summary statistics I was saying before for a generic problem that fits into the framework oftentimes. What's gonna happen is that? Because of the scaling relations the first limit you get for the summary statistics is just an ordinary differential equation So the volatility part goes to zero in the limit and you're left with just the solution to the ODE DUT is H DT and Now if you stare at this one H was the limit of these two operators if your step size is going to zero fast enough It's just gradient flow for the population loss and you recover the finite dimensional picture But there's exactly a critical scaling of Delta. So there's for any family of summary statistics There's gonna be one scaling of Delta at which that middle term doesn't vanish and at that scaling There's a second-order correction, which is coming from the high dimensionality of the problem so this was observed by Sod and Sola and a while ago actually in a In like teacher-student setups that there's this kind of second-order ETO correction that persists in the high-dimensional limit And so we're finding this in this general class of problems I guess and so you have this potential second-order operator that's changing the landscape in this high-dimensional setting now This gives you some some dynamical system for your set of summary statistics. It'll have you know It's gonna be potentially non-convex or oftentimes it'll have many fixed points some of which are unstable some are stable and Now suppose we want to probe the behavior near maybe an unstable fixed point because a random initialization might converge to an unstable fixed point or like If you start somewhere, maybe you'll get to some saddle point and then you want to understand How long does it take to escape that saddle point before getting to the ground truth and actually solving the problem? So the next the next thing we can do is kind of do this zooming in around a saddle point of the landscape instead of just looking at ODE's So suppose that your initial initializations converge to some fixed point you star of this dynamical system What we can do is we can zoom in about the fixed point by you know Recentering my statistics getting some new statistics you tilde which are just the ones where I've blown up in a window around the fixed point So you're imagining this is my fixed point where my initializations converge to or midway through training my SGD is converging to some saddle point I want to understand the behavior locally near that saddle point now to understand how long it takes to leave for instance Let me blow up in a window around that saddle point to get some new summary statistics that are also in this well-behaved family Now they'll admit their own you know drift and Volatility matrix and what typically will happen is that these rescaled ones now don't have their volatility going to zero They have some persistence stochasticity Okay, and so this will now satisfy a stochastic differential equation limit Which is this one you know it's some it has some new drift function, and it has some new volatility matrix so This is a kind of heuristic picture of what we're doing so let me give a few examples of How this works for the you know the matrix spiked matrix type of Problem that I mentioned as an example in a mixture of gaussians type of problem Okay, so here's example one is denoising a rank one matrix Let's say the very simple problem. I have some planted vector V and We're given IID Samples of lambda V V transpose plus some Gaussian noise, so it's just corrupted by Gaussian noise and We just take you know the log likelihood so this L2 loss function, which is just y minus xx transpose Norm squared and the summary statistics for this problem It's pretty easy to see that the things you need to track in order to understand how this behaves Under the SGD are the correlation with the vector V. That's this planted vector and The some kind of like penalty term. There's some kind of radial Term and so here. I'm just tracking the orthogonal radial part. Okay, so together the two give you the full norm of the Right, so obviously you have succeeded at the task if m gets close to plus or minus one There's some inherent symmetry to the problem. Okay, so With this if you just take the the first kind of limit, which is the ODE limit No zooming in no blowing up. You just take these summary statistics. You apply our theorem You end up with the following system of coupled ODE's for the Correlation and the orthogonal radian the the orthogonal radius It's not too bad But you know it you can pretty easily stare at it and find the fixed points and in particular What you find is that it has a couple fixed points when lambda is bigger than one and just one when lambda is well It's less than one. So you're recovering a transition at lambda equals to one, which If you know if you look at like the spectrum of the matrix That's also where you have a you know something jumping out of the semicircle spectrum And if lambda is bigger than one so the problem can actually be solved There's an informative fixed point, which is correlation square root lambda minus one So that means there's some it has some positive correlation with the ground truth and some Uninformative one, which is the unstable one. That's basically in the m-coordinate. You have this kind of picture. Okay, and so that's the that's the first order limit and if your delta is actually Scaling like proportional to one over the dimension then there's a there is a second order correction The second order kind of term operating on the radius. That's it's somewhere in there Okay, so you can take this limit then you want to ask well, you know If I do a random initialization my initial correlations are one over square root of the dimension So in this limit, they're going to zero. I'm just saying put at correlation zero I'm not leaving the the fixed point zero one. I'm just stuck there for all time So let's try and understand how long does it actually take for me to leave this or what's the mechanism for actually leaving this? Flatness at the origin so you zoom in around the unstable fixed point zero one so what that means is I define, you know, this rescaled correlation, which is I blew it up by square root of n and blown up orthogonal radius which is blown up around its fixed value and for that you get a system of stochastic differential equations now. These are just two Ornstein-Ulenbeck processes and just some interesting things are This itself has a transition at lambda equals to one Which is where the problem goes from you know solvable to unsolvable where it goes from an Ornstein-Ulenbeck that pushes you mean reverting So you're never going to leave this saddle point when lambda is less than one to a Ornstein-Ulenbeck That's mean repelling and so that one is going to drift exponentially fast away from the saddle point when lambda is bigger than one and You also something fun is that the two systems actually decouple so whereas the the two Observables were coupled in the first limit I took when I blow up around the fixed point You get a decoupled system of stochastic differential equations and from this you can read off that like okay in an exact Constant times log n time. I will leave this Flatness around the origin and I'll get to this ODE regime and quickly zoom in this direction or that direction to the solution. Yes Yeah, yeah, so at lambda equals to one. I mean this limit will give you just basically just a Brownian motion at the so this Yeah, so I think that exactly at lambda equals to one instead of being either mean repelling or mean reverting you'll just You'll have no drift and it'll just be stochastic And then you can do some other time rescaling So it should be like a it'll take longer to escape because it doesn't have this drift away from the origin But the randomness will take you away from it eventually because it doesn't have this push towards the origin You could take a different limit maybe to get to probe that we didn't do that Everything here is yeah correct for lambda equals to one It's just you you won't read off this exponential drift away from the origin because it's not there you'd have to rescale some So this is in the parameter M the correlation parameter Something like you know the drift is down is this way or that way if you're Macroscopically away from the origin and then locally so this is for lambda bigger than one I guess this is what the landscape looks like when lambda is less than when it looks something like this And so what we're doing here is zooming in around this fixed point, okay? Yes, possibly, but we did not do this so Yeah, it's a good question. I just didn't look at it Okay in the couple minutes that remain let me Give a more complicated example. This was a really simple example in some sense So the more comp and so here you just see the mean reverting and the mean repelling or encinol and back processes for that All right, so in the couple example minutes that remain let's take a quite a bit more complicated model So this is a mixture of four gaussians, but they're labeled in an XOR structure so in the sense that these are your four means for your gaussians and we label the Antipodal ones blue and the other direction Orange so you have two labels for four gaussians a mixture of four gaussians Why this task because this is kind of a very simple task that requires a two-layer network to To classify well, so there's no it's kind of easy to see there's no linear classifier for this problem So you can study this on a two-layer neural network So that's what we did we looked at it on a two-layer neural network where the middle layer is a fixed size and You have some like let's say re lu activation on the first one and sigmoid activation on the second you end up with some binary cross entropy loss function Okay, so then You figure out what are the relevant summary statistics and this indeed falls into the kind of class of problems that fit our theorem with some 22 summary statistics, which are like the last layers weights the correlations of the first layers with the four means that you're interested in and then some radial terms are like Orthogonal parts is in our products things like that and so with these you can approximately close the problem and therefore you can take their limits and What you get is okay an awful equation but The point is you you get some equation you can do some stability analysis on the fixed points of this and if you do that you can find for instance like Fix the middle with layer to be four, which is the smallest one so that you can express a classifier Then you know you there's 39 critical regions. They have varying topological dimension in this problem You can figure out which ones of them are stable and then you can look at things like over parameterizing this problem so taking that middle layer with to be larger and larger and seeing how the number of Critical regions changes and for instance ask what's the probability under a random initialization that I'm in the ballistic Basin of a ground of a good classifier So in the sense that I converge in it with an ODE like very fast to a good solution Versus what's the problem probability that I'm in the basin of a saddle point instead of one of the good classifiers? And so in this problem We studied you know some notion of a power of over parameterization as I take that middle layer going larger and larger the Probability that I'm in the true basin that I initialize in the basin of a good classifier is going to one as the middle layer with goes to grows You can then also look at you know, there were these critical regions that were saddle regions, so they're not stable They're unstable you can blow up around these regions and if you do that you get Diffusion you get diffusions instead of ordinary differential equations and something interesting You can see is these diffusions are indeed rank deficient in the sense that I mentioned earlier So they they're really degenerate diffusions They move only in certain coordinates rather than all of them and so they can get stuck for arbitrarily long times in these critical regions All right. Thank you very much Yeah, sure instead of M and R per yeah, so I guess it's what makes the equations nicest But like in order to just get a if you have a problem to get like this X or Gaussian problem For instance what we started with is okay We need to know the correlation vectors and then you try and close these if you try and get what's the minimal family That's going to close the drift. Maybe there's different minimal families But that's at least like how you'll get a valid set of finitely many summary statistics for which you can then start to do some analysis of like the dynamical systems you get So that's the point if I don't do any rescaling then I'll just be stuck here So of course I can't probe this log d time. So what I do instead is I blow up space And if I blow up space by root n then I'm actually moving So I'm moving an order 1 over root n in order one time and then what's happening is you're doubling in order one time So it's like the first scale is order root 1 over root n the next one is like 2 over root n then on the next time scale It's 4 over root n and that's what leads to this log d and so you can probe the log d by doing a Set of these rescalings and then stitching them together and you can actually get the log d escape from the saddle by doing this kind of stitching


I'm a third day of Christmas, my true love came to me. Snowflake Dortie Core. You really want to sing that whole song. That's nice.  Sorry, sorry, sorry. Hey there. Today we're doing a Christmas craft. We're going to cut out snowflakes and make a resin snowflake dortie core. I have my little helpers here. I've got Kai. I've got McKenna. And we've got Ethan. So what we're going to do is we're going to cut out snowflakes. I'm sure you guys have done this before. And then we're going to resin them. These are some that I cut out earlier. I spray painted some of them with gold and silver spray paint. So I thought the kids today could use marker. And then we're going to cut it out. And it's going to look really awesome when it's resin. OK, so if you guys want to go ahead and pick your colors, you can use red and green Christmas colors. You can do whatever you want. You can go on the internet and find snowflake templates. And I'm just going to show you how you start folding. I'm just going to cut off this excess here. Fold this in half to make a triangle. Fold this in half again. OK, now we've got this triangle. And what we're going to do is we're going to fold this in equal thirds. And we're going to end up with something that kind of reminds me of the Star Trek symbol here. You can cut it off right at the edge here. OK, guys, now we've got our patterns drawn onto our triangles. It's time to cut out our snowflakes. OK, it's time to reveal our snowflakes. This is my favorite part. Amazing, that's so good, you guys. These are going to look so good when we resin them. All the color is just going to pop. You can see what's happening here. Because these were folded, they want to keep curling up. So what I'm going to do, actually, is I'm going to iron them down. No water, steam, or anything, just a dry iron. Now we put them on acetate. What we're going to do is resin them right onto the acetate. And when they've dried, tomorrow I'm just going to cut them out, and I'm going to cut right on the acetate. Thanks, guys. Thanks for helping. Merry Christmas. When this dries tomorrow, it's going to peel right off the silicone. That's why these mats are so handy. I'm just going to torch out these bubbles. OK, so now these are covered. We're going to leave them overnight, and we'll check on them tomorrow. Hey, guys, so we've got our finished craft. Here, I'm so happy with how this turned out. We've got our resin snowflakes. And I chose to hang them from a piece of birch for that natural look. And because they are resin, they're waterproof or weatherproof, so why not hang them outside? I think it looks amazing against the brick wall. But you could easily hang these inside in your window, or you can hang them from an inside door. So I hope you enjoyed this and happy holidays.


Welcome back to tennis talk my name's Cam Williams and over the last few weeks There's been a big conversation whether or not the new coaching rules for the ATP and the WTA are actually fair We've had some players like Taylor Fritz coming out saying that he hates the new rule Of course There's other players that have obviously liked the new rule because they were getting pinged for coaching violations Let's break down the rules. What are the rules that we've had since Wimbledon and going into the US Open? What are the coaches allowed to say and do during matches? So these are the rules that have been changed as per the ATP website They have said that off-court coaching will be trialled for the second half of the season and it will permit coaching from Designated coach seats during qualifying and main draw matches basically where the players have their coaching staff But to what extent can they talk that has been the question So off-court coaching will be permitted under the following conditions Coaches must sit in the tournament's designated coach seats meaning that they have to be in the coaches box Coaching verbal and nonverbal is allowed only if it does not interrupt play or create any hindrance to the opponent Verbal coaching is permitted only when the player is at the same end of the court So at most tournaments the coaches boxes are spread out one on one side one on the other So you can't have coaches yelling from one end of the court to their player down the other end nonverbal signals are permitted at any Time so that means if there's a secret hand sign language They have between them and their player that is permitted verbal coaching may consist of a few words or short phrases So no big conversations coaches may not speak to their player when the player leaves the court for any reason So let's say there's a bathroom break for a medical time out and the players are walking past their coaches They are not allowed to go to the back and talk to their coaches while they are having that treatment or having the bathroom break Penalties and fines will still apply for the abuse or misuse of the above coaching conditions So they have it they are the coaching rules for the next I guess six months until the end of the season and the US Open is gonna have it and on the ATP the WTA Have never really had a coaching problem. They used to actually permit coaches coming on court once every couple of sets or once every set I think it was but let me know down in the comments below Do you like that they're allowing coaching to some extent now?


It's raining again here in Cooksville, Wisconsin, which is just as well, because today we'll be looking at part two of the Low Tech Innovations panel discussion from Earth Day last week. We'll be hearing from people working on water, cooking, and energy, which are all key components of a sustainable future. This is the Low Tech Podcast. Hello and welcome. I'm Scott Johnson from the Low Technology Institute, your host for podcast number 47 on April 29th, 2022. Welcome to you at the Low Tech Institute's gardens in Cooksville, Wisconsin. Thanks for joining us. Today we're going to be listening again to a panel discussion on Low Tech Innovation that was hosted by the French Embassy's Office of Science and Technology. This is the second part of a podcast on this topic. If you haven't listened to part one, just head back in your podcast feed. And don't forget to follow us on Twitter. Our handle is at low underscore techno. Like us on Facebook, find us on Instagram, subscribe to us on YouTube, and check out our website, lowtechinstitute.org. There you can find both of our podcasts, as well as information about joining and supporting the Institute and its research. Also, some podcast distributors put ads on podcasts. And unless you hear me doing an ad, somebody else is making money on that advertising. This is where it usually makes a short pitch for you to visit our Patreon page and support the Institute directly. But instead, just like last week, I'd like to call attention to the organizations represented in these presentations. You can find links to all of their respective organizations in the show notes and also at the bottom of the screen if you're watching this on YouTube. Please check them out and consider supporting them directly. To kick us off, I was very honored to be asked to speak a little bit about my own work as part of the panel. So I'll just give you a quick presentation on my work. So sharing my screen here. I work at MIT D-Lab, a program at the Massachusetts Institute of Technology in Cambridge. My background is in civil engineering and I came to D-Lab because I was really interested in sort of the social impacts of engineering and how we could be more participatory about the types of projects that we engage in as engineers. So D-Lab is about designing for a more equitable world. And we do that by working with people around the world to develop and advance more collaborative approaches as we seek practical solutions to global poverty. And because we are at a university, our program is very focused on engaging students effectively in socially impactful work, which is by nature low tech. We were founded 20 years ago. We're celebrating our 20th anniversary this October. And we have offered 24 different classes at MIT that look at various aspects of low tech. You can see in this photo a prosthetics class that is working with users in Indonesia. And over 2,500 MIT students have enrolled in our classes, many of whom have gone on trips around the world to engage in effective user design and participatory development. We have a number of different research programs and field practice programs. And our staff is made up of practitioners with deep experience in various parts of the world. So we work in over 25 different countries. And COVID permitting, we hope to be able to start taking our students on field experiences again soon. So we have a few design principles at D-Lab, which you'll see have some overlap with the principles of low tech that we've been discussing today. We think about how to be more inclusive when we are designing for users living in poverty, whether they be in the U.S. or abroad. And we engage in co-creation or co-design processes with people living in poverty to engage them, to teach them the design process and to make that process as participatory and open as possible, as we're thinking about projects in the food and water and energy spaces around the world. And the methodology we've developed at D-Lab is really focused on what we call creative capacity building. So building the confidence and the capacity that is needed for users to engage in the design process to address whatever it may serve them for in their lives, regardless of whether they're working together with trained designers or not. So we think about the design process and how it can be applied to these low tech projects more effectively. So I've worked with students for the past 10 years at D-Lab, engaging them in low tech projects that are really thinking about how to make that design and engineering process more inclusive. I'll just tell you about one of those today focused in the water and sanitation space. This is a picture of me with two of my students who are wearing yellow shirts and a family in El Salvador who engaged in material experiments with us to be able to construct compost toilets with local materials as cheaply and effectively as possible while maintaining cleanliness and the effectiveness of the compost toilet system. So just for those of you who are not familiar with compost toilets, this is a method of very low water toilet building. The compost toilet basically separates liquid waste and solid waste because then that solid waste in the absence of excess moisture can be composted in a chamber underneath the latrine and can be used as fertilizer, as soil, once it is composted over the course of six months. And so it's a technology that's been deployed all over the world. It has a very low environmental footprint. It is flood resistant. It addresses some of the issues with more traditional pit latrines in parts of the world that are prone to seasonal flooding. And it is an odor-free method of building a latrine that has been well received by people who need latrines in many different parts of the world. So these latrines obviously could be built out of many different building materials, but we were really looking at how to radically reduce the cost of building these latrines in Central America. And so you can see in this photo, if I go back to this photo, oops, you can see materials like bamboo, adobe bricks underneath the plaster that have been used to bring the cost of this toilet down from an original proposal that was more focused on exported materials like concrete blocks. So we have three goals with this project, which are goals that I could say extend to a number of different D-Lab projects. One of them was to really radically reduce the cost by focusing on local materials and on verifying our comfort with using those materials from a structural standpoint. So bamboo is a fast-growing renewable resource in many parts of the world, including Central America. And so we were really looking at what we could do with bamboo and engaging the family members, the community members in learning how they already constructed bamboo and how that could be used in the context of the toilet. So rigorous engineering analysis of these materials was an important component. The second goal was to really guide the students to be thoughtful participants in this design process, not the authorities. So in terms of thinking about using indigenous materials and really ensuring that the users of the toilets felt confident in how to compost the material and maintain the cleanliness of the toilet, the students really had to sort of pull back from maybe roles that they had played before as more leaders of the design process and think about how to be effective participants in the design process. And so here you see students interviewing, sort of spending time with potential users as they go about their daily tasks to learn more about what their needs are. The third goal was really to follow up and reflect on the impact of the design project. So although we spent a month working with families building these initial prototypes, we came back six months later and a year later to continue analyzing how the materials were holding up, performing more tests and making improvements to the process of the composting to ensure that families were comfortable with it and were using it effectively. So that follow up with future groups of students who come back and sort of help maintain experiments and gather feedback from the users is a very important component of our work. So thank you very much for letting me give you a short introduction to my work. I'm happy to take questions and very excited to engage new partners around the world in D-Lab projects. Thank you. Without further ado, I will resume wearing my moderator hat and move on to our next speaker, Sophie Lyman, Executive Director of Solar Household Energy in Washington, DC. Sophie, I'm looking forward to hearing about some solar technologies from you. All right. Thank you so much, Libby. Yes, it's an honor to be here. Thank you for inviting me to be a part of this panel. My name is Sophie Lyman. I'm the Director of Solar Household Energy, and I'll be talking about solar thermal energy for fuel-free cooking. We are a small-known profit based in Washington, DC with international projects, and our mission is to unleash the potential of solar cooking to improve social and environmental conditions in sun-rich areas around the world. We primarily carry out field projects, but we also do education and research and development for solar cooking technology. So before I talk about solar cookers, I've got to talk about the problem of dirty cook stoves. So the three-stone fire is used by, or rudimentary cook stoves, is used by three billion people around the world. That's more than a third of the world population. You can see these three-stone fires here, and it, collecting fuel for these fires can be dangerous. Women go out, walk for miles to collect fuel wood.  As you can see, it's also backbreaking labor and time-consuming. It can be very costly, especially for families living in cities who have to buy fuel. So for example, the family of Ait and Haiti, for them it costs $2 a day, and that's, you know, many of the world's poorest families live on $2 a day. Here's a stark example of deforestation it can cause. In Haiti, they primarily use fuel wood and DR. They use gas to cook. It is also a big factor in mortality 4 million. It causes 4 million premature deaths per year, according to the World Health Organization, primarily from respiratory and cardiovascular disease. And it is, of course, a contributor to climate change and black carbon, the soot emits heat. So now I'll talk about solar cooking solutions. I'm just going to fly over these slides because there are so many different types of solar cookers, and I just want to make you aware of them, and you can, you know, research them later on on the solar cooking wiki or look at these slides. So this is a low-tech technology. I'm not talking about solar photovoltaic, which uses electricity. We're just talking about black pots and reflectors. So you need a black pot to convert sunlight to heat energy. You can retain that heat with the greenhouse enclosure, transparent plastic bag or glass top, and you can capture more sunlight with reflectors. And this is a feasible viable technology for most of the developing world, as you can see in the red-orange-yellow areas. So your basic, very low-tech solar panel cooker is a cooket. It's basically cardboard covered with aluminum foil.  You can make this for a few dollars at home, and you can cook a chicken in two hours with just this very low-tech technology. The hot pot on the right is basically a more durable version of that. It'll last over 10 years. That works like a crockpot. Now we have our ovens for baking, roasting veggies, etc. We have parabolic solar stoves that work like your oven top range, like solar flames under the pot and make it so that temperatures reach frying and sauteing temperatures. We also have tube cookers with vacuum insulation for good heat retention. We have Fresnel lenses if you want to cook from above. We have solar or electric hybrid cookers, which have backup electricity if there's no sunshine or backup gas when the sun isn't shining. We also have fixed focus solar cookers for indoor community cooking and slightly more advanced cookers with thermic fluid that allow cooking when the sun isn't shining, even at night. I'll end with one of the world's largest solar cooking system, I think the largest, which cooks for 100,000 people per day at the Shirdi Sai Baba Temple in India. This is a map from Solar Cookers International, which shows that there are over four million solar cookers used worldwide, impacting over 14.3 million people. I'll talk a little bit about some of Solar Household Energy's projects. We carry out humanitarian aid. We work with local partners, so we usually plant the seed and let the local partners continue without us. We started with a 50 hot pot project in Gaga refugee camp in Chad, and they added another 200. We are one of many partners in an education project, creating a university level course, and these are our many partners. We carry out research and development, so we helped design the hot pot over 20 years ago, which is a very simple solar cooker, and then our partner in Mexico, FMCN, has distributed or sold over 20,000 hot pots in Mexico, and there's over 30,000 in use worldwide. One of our latest projects focused on trying to kickstart a social enterprise. I'll go into a little bit more detail about this one. We use the Hain solar cooker, that one there is basically a more powerful yet far more affordable version of the hot pot, still very durable. We started out by doing market research. What are the existing cooking technologies? We see a very simple open fire, some charcoal grills, a few people of gas, and our entrepreneur, our field project manager, who wanted to start this enterprise, can be seen here recruiting and training solar cooking ambassadors. These are women who live in very rural remote communities who want to promote and sell solar cookers to their neighbors and friends. Here's Bibiana on our left, she's our star promoter, and here's some very happy customers who you're seeing, solar cooked rice and beans. One of the beauty of these solar cookers that they're very safe and easy to use, you know, instead of hovering over a smoky fire with her baby, this woman can just set in the sun and leave a beef for a couple hours and come back and her food is cooked. Even the husband got into it, which is great. One of the nice things about these panel cookers is that they act as ovens. So most people have a stove, they've got something with big flames, you can't really bake cakes or big bread and things like that. So this is a very affordable alternative to make cakes, and they love it. And so we use these solar cooking ambassadors because they're in their community, they know everybody, these are small towns, and they're there in the long run to ensure long-term adoption and satisfaction, and they're there to make any repairs, make any replacements if needed, and they're always in touch with our main entrepreneur, and they help carry out surveys too. So she's role is to, of course, kickstart these things, find a field project manager, help with the training, and then also do some monitoring evaluation. So we have usually people on the ground carry out surveys and focus groups. We measure adoption, how much are they using, are they keeping it in good condition, as well as impact, what are they noticing in terms of like any health improvements, are they coughing less from reduced smoke exposure, and are they, are they seeing it in their pocket books. We try to use international standards for M&E, such as those developed by the UN Foundation's Clean Cooking Lines, as well as Solar Cookies International and the International Standards Organization. One of our board members is part of a committee of the ISO to develop clean cooking standards. So this all sounds wonderful, but of course there are many challenges on the ground. Most people cannot afford to buy a Solar Cooker, even though in the long run it saves you a lot of money because it's cooking for free for five to ten years, and they don't know how it works. So most people are not willing to risk that kind of investment. And also even though the woman who does the cooking, the husband usually makes the financial decisions. There's many social and cultural challenges. Solar Cookers are really unlike any other cook stove you see. So if you don't understand how light reflects upon reflectors and it can look like witchcraft, and it can lead to incorrect usage. And often women don't have the luxury of trial and error. Women's got to be ready on time and they can't throw food away if it just doesn't work for whatever reason.  And of course there's the obvious challenges of the fact that you cannot cook in cloudy weather. And for some Solar Cookers you can't cook in very cold weather. You can cook in the snow with box cookers and parabolic, but not with panel cookers. So I'll just talk a little bit about partnering with us. If you're an on profit who's working with women to help reduce their fuel usage, we are developing an online training course right now which should reduce our project costs substantially. And you can look at this later if you're interested or shoot me an email. And I'll end with why everybody needs a solar cooker just even in the US. It's great as an outdoor grill alternative. There's some powerful parabolics which will grill your food.  It's also great for living off grid. If you live in a tiny house for camping for sailing, reduce the fuel you bring on a boat. And that's it. That concludes my presentation. Thank you so much for listening and I look forward to your questions. Thank you so much Sophie. I love seeing the diversity of designs and all the different ways that you can harness solar energy to cook something. It's fascinating and we already have some questions coming in that we will get to later. Our next speaker who's going to be switching over to the topic of energy systems is Alexis Stigler who is the Director of Living Energy Farm in Virginia in the United States. Alexis. So Living Energy Farm, we are a community and technology development center in central Virginia. The big difference with us is that we live the technologies we are trying to encourage other people to use. So for over 10 years now we've been developing renewable energy systems. Our intention is to keep them as small and durable as possible. Most of my slideshow is going to be about what we call a DC microgrid. It's a way we've discovered to use DC energy that solar energy that has proven very effective for us. So the way DC microgrid works and also I should say from this first slide we published a book Empowering Communities. You can go to livingenergyfarm.org and you can download that or you can get it directly from us. So the way DC microgrid works is we have a multi-leveled energy system. The biggest thing that we do that's different than traditional upgrade systems is that we do a lot of what we call daylight drive. So we have all kinds of equipment, including solar cookers incidentally, that run directly from the solar panels. So we can run, we can grind green, we can cut firewood, we can pump water, and now we're doing about 70% of our cooking now with insulated solar electric cookers. This is a project in conjunction with a working group at Cal Poly to develop these cookers and disseminate them around the world. It works great. The cookers now, we were using thermal cookers before and doing maybe 10% of our cooking. Now we're doing about 70% of our cooking with these cookers. So that's the big thing we do that we do a lot of daylight drive, running things straight off the solar panels. Surprisingly you can run, you can really overload these systems with an AC based system, alternative current based system, alternating current based system. You have to have more supply than you have demand. With the DC system you can actually run about 3,000 watts worth of motors off of 1,000 watts worth of supply. It's simply industrial brush motors and these thermal systems tolerate tremendous power input swings very gracefully. It doesn't do any harm. The second aspect of how these microgrids work is because we have a dramatic reduction in how much money we're spending on batteries and inverters and that sort of equipment, we increase the amount of, we can increase, improve the equality of what we're using. So this picture on the left is my daughter with a nickel iron battery from 1946. This still works. The nickel iron batteries, they're big, they're bulky, but they last for many decades. They're somewhat more expensive. This isn't a critical aspect of the design, but we do like them. They do work well. So a graphic display of how this works is with a traditional off grid system, you've got battery costs are quite large. You've got significant inverter costs, then you've got your PV costs and that gives you how much total work you can do in a day. With our system, the battery cost was reduced about 90%. There's no AC power, there's no electronics, small amount of inverters, perhaps some of the larger investment in PV power and the total daily work accomplished grows significantly. And you notice we use, we don't use the phrase total power output because the power output doesn't matter. It's how much work you can do. So we're not worried about stored kilowatts. We're worried about what we can do in a day and we can do a lot more with our systems than we can do with battery-based systems. So another aspect of how these systems are much more effective is that the components we're using are extremely durable. Solar panels, they are made by big corporations, but they last for many decades. DC industrial motors in the thermal systems as well. But the DC industrial motors, they're copper wire and magnets, they last for many decades. This particular machine is in our shop. We run a fully-tooled machine shop. It's actually a drill press from the late 1800s running on a motor that will last for decades with a solar panel that will last for decades. This equipment will last multiple lifetimes. My computer is misbehaving on here. All right, there we go. The other advantage of this system is that the annual cost, we have no cost for replacing batteries. A normal off-grid house spends hundreds or even a thousand or two thousand dollars a year replacing batteries to run a bunch of AC equipment. We find ways to store energy that don't involve batteries that involve near zero daily monthly yearly costs. So for water, for instance, we have a DC pump that pumps into a storage tank. That equipment is not free, but that is a, it's called a fiber wound tank. It'll last for many decades. So you're looking at a zero cost to run that on a daily basis. Instead of having an AC refrigerator with inverters or with centralized industrial power systems, we have thickly insulated DC refrigerators that store a stake hole overnight so you don't have to worry about running AC power. This is a graphic layout of our whole system at Living Energy Farm. The blue squares are power supplies. The red squares are loads. The green squares are battery-supported loads. So because this is a multi-linear system, there's never a general power failure. Basically, the lights never go out. In 12 years, a dozen people living off-grid were economically self-sufficient, largely food self-sufficient, living on a poverty level budget, and we've never had a, never had the lights go out. So we have very small systems, such as a PV panel running a pump to pump hot water for a thermal system. The biggest system we have is a high voltage DC system with over 22 loads on it. That runs a machine shop. It cooks 70% of our food. It runs the heating blowers for our buildings. So it's a very resilient system. There's never a general power failure. Another advantage of these systems is that it's very scalable. You can do very small-scale systems. You can do larger commercial systems. So we have three projects now. We have run that we started in Arizona and the Hopi and Navajo Nations. We have one ongoing in Jamaica, and now we're starting a project in Puerto Rico. We can do small battery kits that are very durable, that can charge laptops, cell phones. This is a kit workshop in Jamaica, assembling those battery kits. We have commercial scale equipment at Living Energy Farm, a machine shop, agricultural equipment. We set up a commercial scale food processing facility in Jamaica. And again, the difference here is that, so this is Charlie, who might help me put those solar panels on the roof. That is in the poorest part of Jamaica. Once this system is set up, it's not free, but it will run commercial scale equipment for many, many years to come with no ongoing power bill. So they're processing breadfruit and other agricultural products into value-added products that the farmers can then sell. Another advantage of our DC microgrid, several people have mentioned the war in Ukraine. The supplies of fossil fuel are, of course, a big issue for all of us. The one of the things that has crippled solar thermal in general, particularly solar space heating, is that it has been over-designed, over-built. It is basically because it tries to imitate grid power. It's the same problem, it's the legacy problem, the same problem we have with big battery systems, where we have a battery and an inverter to make AC power to power the appliances that we're accustomed to. It's the same problem with solar thermal in that we want a thermostatic system. So some thermal systems have been built with big solar storage tanks, computerized controllers. This system is simply a very cheap glass over black metal collector on the roof, daylight drive, pumps, air blowers. So again, the blowers are connected directly to the solar panels, just like all our other equipment. It pulls the heat off the roof directly, goes directly under the floor. So we're using thermal storage instead of electrical storage. This is very cheap and it runs, it'll run forever, many, many years. So all of this works so well, well, haven't you heard of it? There's several issues. The first is the lack of DC equipment. All our markets have been standardized to AC equipment. So if you want a solar fan or a solar refrigerator or a good solar cooker, you can't get it. It's not on the market. So what we're doing in Jamaica in Puerto Rico is we're setting up supply chains to bring this equipment in. Some of it, like this little solar fan, pretty cheap, $20 out of China, but you've got to have $20,000 to bring in a container of them. So we're bringing those in. Some equipment, a lot of household appliances. Any appliance that you can pick up and walk around with will actually run DC. They have universal motors in them.  You do have to swap out the switches. You can't run AC switches. Computers and electronics, you simply have to get the right charge cords. This solar cooker here on the right is our latest version. And solar cooking is a great idea. This cooker actually is much better in terms of usability. Like I said, we're doing 70% of our cooking now with this style of cooker. So these can be manufactured locally, which is, of course, an economic benefit to the people there. So we'll be setting up production facilities. We have a production facility now in Virginia making those. The other big issue that is the reason we don't already have DC micro grids is that because of the solar energy has become very politicized to the extent that the big power companies and our economy in general supports the centralized development, centralized power companies. So we now have these big solar fields. And it's a bit of a no-brainer that if you put where the locus of capital investment, where you put the money is where you tend to have good things. So we have very expensive, very well-built power plants, whether they're fossil fuel powered or nominally renewable. And then we have badly built houses. This house that's shining red, that's an infrared camera on a house nearby living energy farm. In the middle of winter, the sun doesn't shine in winter. So that house, no matter how much solar energy you build, is still fossil fuel powered. Whereas our house at Living Energy Farm, we went through this past winter in Virginia. This is the same night. Those pictures were taken minutes apart. Our house is leaking almost no heat. We went through this past winter with basically no firewood. Just pulling the heat off the roof, put it in the floor and it works. But it's not, it doesn't fit our current consumer economy. It doesn't fit our current tendency to want big centralized solutions. The two goal, the two prizes, the two things we can achieve if we can spread DC micro grids all over the world is that it can provide energy to it's, they're much cheaper systems. They're scalable. There are 2.2 billion people worldwide who do not have reliable grid power. This can supply power for them. And the bigger prize, we all know that the climate change crisis is a huge issue. DC micro grids have a radically lower environmental footprint. We can make a dramatic impact on climate change gases if we can spread this energy system around the world. So I'll leave you with Greta Thunberg and her, I don't want you to panic. I don't want you to hope I want you to panic. I've used the phrase constructive panic that we don't need. We need to respond to this with the appropriate, the appropriate emotional response, which is to do what we need to do quickly. What a great note to end on. Thank you, Alexis. And can I just say how much I love how people come out of the woodwork during these conversations with their own low tech stories about using a solar cooker or using a compost toilet or being exposed to a micro grid. I think this is, I'm so glad you're all sharing so many examples. So we do have one more speaker.  If you're able to stay with us or share your resources and stories before you leave. Our last speaker is Olivia Borey, a PhD student from France who is going to tell us about her research on energy for autonomous households. Olivia. So good morning, everyone. I'm Olivia Borey-Debis. I am currently working at Integral Engineering as a PhD student. This is a company specialized in building conception. This is a research project in collaboration with Energy Lab at the University of Rhinon Island and at this laboratory from Grenoom Institute of Technology. So I'm happy to share with you my research thematic, which is called DC architecture, micro grid architecture development with energy production and hybrid storage for standalone building. So to start, I will begin with some words about the context. As we know, it's essential that we reduce our greenhouse gas emissions, which are currently strongly linked to our energy production, dependent on oil and gas. This is an even greater priority for isolated territories, which due to their geographical position require finding autonomous and sustainable energy production solutions. Currently living in Rhinon, a French overseas department located next to Mauritius, I would like to introduce you to the energy issues that we encounter here. First of all, the part of renewable energy represents only 32% of Rhinon's energy mix. So as part of the energy transition for the green growth and the French decree, one of the goals is to reach energy autonomy for overseas departments in 2030. Moreover, in 2025, according to the BICS decree, buildings will have to justify their energetic constructions by instrumentation. So if we take a look on the Rhinon energy, tertiary and residential buildings are the main energy consumers and due to a really nice climate, sometimes too hot, air conditioning is the main energy load. So this concerns city, but other problems exist here for isolated sites, such as, for example, Mafat, which is a wild, natural place where the houses are only accessible by foot. So the autonomous electrical architecture required most of the time generators are generally oversized to meet the energy requirements. So this is not a solution for resilience because growth in the number of solar panels and batteries is not the best choice. And finally, with renewable energy insertion in the grid this last year, a non-debate is growing up between alternative and direct current. Indeed, to use solar energy, we need many converters between solar panel and our equipment. First, we convert direct current in alternative for our grid and then we converted a second time for DC equipment like LEDs, screens, computers, data centers, and some motors. This is not optimal and creates a lot of energy losses, but currently we don't know exactly how to quantify energy savings which are possible with DC current. That's why my research was all divided in three points. First, develop new DC architectures to reduce energy losses linked to converters and electrical light transport. According to the state of art, experts have an estimation of almost 50% for the motor. So I'm currently standing up an experimental DC measurement bench in a laboratory. I'm also introducing many environmental and current sensors to control the efficiency of the architecture and to control this data, I will use statistical indicators in an application. And suddenly, my main objective is to set up an energy management system to deliver energy at the right time, taking into account external conditions, user comfort, and the state of health of the storage equipment. This is in order to reduce the overall energy consumption of the system. And the main constraint is to have no fuel support. On this slide, you can see a simplified diagram of the architecture of the DC test bench that we want to put in place. And this is where Lotte comes in because to carry out our environmental measurements with test virus components, including wired and wireless sensors, they communicate according to different communication protocols, such as local world technologies, the openness and accessibility of equipment in terms of development depends on the supplier and the degree of stability that someone wish to deploy. For data storage monitoring, we use a free database management system. And with the help of fellow IT developer, we connect the database to a mobile app to automate data analysis. Concerning the electrical loads, they are managed by the power of an internet protocol, which operates at 48 vote DC and allows us to power and control the equipment via a single RG45 network cable. In resume, the innovation of architecture is mainly in the fact that we have the consumption of each element and we will have the possibility to adjust the power of each point separately. It also means that the energy management system will have a lot of new and numerous parameters. And this is a challenge to associate energy constructions and user comfort. Thanks to the development of this system, the goal is to promote self-construction as much as possible and drastically reduce the use of storage. So for the moment, we are starting for the lighting and the fun. So the main goal of this test bench is to test first a classical architecture with a lot of converters between alternative currents and DC currents and do the same thing with same equipment but with DC architectures and evaluate which is more efficient. So we will take all the data in the database and generate automated evaluation of the electrical architectures in the form of a multi-parameter radar chart which will compare for each architecture, total of raincoats, electrical line transport losses, resilience, carbon impacts and energy savings with taking into account user comfort. So thank you all for listening. Thank you so much, Olivia. This is fascinating and I look forward to reading more about it. So it is 12 o'clock Boston time. I totally understand if anyone needs to jump off. Thank you so much for coming. But we do have a few questions that I'd like to ask the panelists before we conclude. We have a couple of questions for Sophie. Someone asked what do you think of cooking bags in the chat? Is he talking about heat retention baskets? That would be my guess. Yes, definitely. Yeah, heat retention baskets are great and they should definitely be used in conjunction with solar cookers. They can finish the cooking process just with the retained heat. So that's great for using not just solar cookers but any type of cook stove. Yeah, I didn't have time to go over every single type of technology, unfortunately, and there's plenty of other types of solar cookers I didn't even have time to address, but yes. And I have sort of a behavioral question. Someone said the cooking with a solar cooker is sometimes longer than a classical fossil fuel cooker. Should people that change to a solar cooker modify the organization of their day by cooking at different times of day maybe? And is that a problem for families? How have you found that behavior change to go? I mean, yes, if you cook longer, then you'll need to start earlier generally. But for some people that can be a bonus. The nice thing about cooking with a panel cooker, which is like a crock pot, is that you don't need to stick around and keep on stirring the pot and you don't need to stick around. So you can just put it out in the morning, leave for a few hours, come back and it'll be done. So in many, maybe it will require you to reorganize your day or maybe it'll actually be easier. Right, right. So behavior change doesn't have to be a bad thing. Yeah. Well, I would like to ask a similar question to Alexis in terms of, you know, are there any sort of behavior change expectations or sort of issues that you run into in thinking about your work that have required a learning curve or a different approach? Yeah, definitely. And the interesting thing about the DC microgrid, and I did not predict this, is it actually encourages people to conserve energy. We tend to think of energy consumption as this negative side of human nature. What we have at Living Energy Farm, the electrical systems, the water system, every system that we have weakens slowly. So for most people, it's about a 48 hour learning curve. Within two days, you get it. You have to pay attention to the weather. You're not going to water the garden at five o'clock in the afternoon because we'll drain the water storage tanks. You won't water it at nine o'clock in the morning. As Sophie mentioned, cooking, you know, you think about it ahead of time. The advantage with these I6, the insulated solar electric cookers, is you're actually indoors using them. But in any case, there are behavioral changes that have to occur. But it's usually only two or three days. Most people get it. Some people take a little longer. And the net result is a dramatic reduction in total environmental impact and a natural kind of people learn to have an inbuilt tendency to conserve energy rather than an inbuilt tendency to waste energy because that's how the system is set up. Interesting. Well, I hung on to a question that was asked in the first hour, but I'd love for Olivia or Alexis to answer to share their thoughts. The question was, does the low tech school of thought believe that electrical based infrastructure is sustainable? Any thoughts about sort of electrical grids versus other solutions? I mean, in the long term, no, it's not. But what so a lot of people have a lot of ideas and that's great.  And it would be brutally inconvenient to not have some external energy sources. And the solar panels, most of the big economic research institutions have estimated somewhere around 500 watts per person to sustain people were about 200 watts per person. Food self sufficient economically self sufficient. So no, 500 years from now, we might not have photovoltaic panels. I'm not sure. But for now, it's not a question of moral purity. It's just the question of what works. This is what works. And if we can use them in a moderate and intelligent way, that's what makes sense. Moderate and intelligent. I like that. Olivia, any other thoughts to add in terms of your research? Electricity versus versus other solutions or any potential unintended challenges that have come up? Yes, those are challenges. One of the changes, many changes is different standard for equipment, because we didn't have any rule. So each constructor made his own voltage, for example. And so the research is how to make a transition with all the different equipments and switch with DC distribution, electrical distribution. And we have one question from Greg in the chat saying, where can we find a database with impact data for different low tech projects? I know Linda and Sophie have answered in the chat. But do any other panelists have anything to add? Any other resources where we might sort of be able to dig into some of the data on this work? I'll throw one in. Engineering for Change is a website. It doesn't talk about impact, but it does sort of crowdsource a lot of different plans, products, designs, ideas in one place. So I would recommend googling that. And Cedric, I saw you unmuting yourself. Yeah, of course, there is the solar, the low tech magazine. These people, they are based in Netherlands. They make a great work for years now. And of course, Palio Energetik, you can also like share it. You can push some ideas inside. You can make a group to look for a great innovation and patent into the US patent office. I think there is with the MITD lab, you have a huge resource into your country. And I can say we have the plan to make the website translated in Russian because the Russian, they have this tradition of making sort of sustainable product because of the communism. So they have an approach of the technology that is totally different from our approach in Europe or in the United States. So in energy, they have a lot of patents that are really powerful, interesting. But the patents, they are not translated in English. It's only in Cedric. But we are interested to bridge with the people. Okay, there is the war, but we have to take care of the people of the Russian. We have to make a sort of bridge for peace with the Russian. And I think they realize because the war is destroying the economy also. So I mean, the people, they would suffer in Russia also. And we have to bridge with the people. So that is one of our goal and to translate in Chinese, in Indian also too. Because all the territories, their resources, their roots, their people facing crisis and innovating when the crisis is there, the people are innovating a lot. So yeah, thank you for those thoughts. I feel like we need to put a pin in that discussion and have another webinar just about that to take it in a different direction. But thank you all so much to honor your time. I'm going to wrap it up here. I encourage you all to make use of the resources that everyone has shared in the chat. And we will be sharing the recording and the chat transcript with you afterwards so you can pursue those connections. Thank you to all seven of my colleagues who agreed to speak on the panel today. And thank you to the French Embassy for inviting me to moderate. I wish you all a wonderful Earth Day and stay safe and healthy. Bye-bye. That's it for another extra long episode. We'll be back to our regular programming in a week or two. The low tech podcast is put out by the Low Technology Institute and at the moment the show is hosted, edited and distributed by me, Scott Johnson. But stay tuned for changes in that team. This episode was recorded in the Low Technology Institute Gardens. Subscribe to the podcast on iTunes, Spotify, Google Play, YouTube and elsewhere. We hope you've enjoyed this free podcast. If you'd like to join the community and help support the work we do, please consider going to patreon.com slash Low Tech Institute and signing up. The Low Technology Institute is a 501c3 research organization supported by members, grants and underwriting. You can find out more information about the Low Technology Institute membership and underwriting at lowtechinstitute.org. You can find us on social media and you can reach me directly. I'm Scott at lowtechinstitute.org. Our intro music today was Early Sun off the album Bitter Sweet Endings by Crowander. That song is under the Creative Commons Attribution non-commercial license and this podcast is under the Creative Commons Attribution and ShareLag license, meaning you're free to use and share it as long as you give us credit. Thanks and take care and I'm going to come in out of the rain now.


The word that arose in the 1700s was sharp. Someone is a card sharp. Card sharp with a K came later. They used to call them card sharps because if someone was playing a card game, but they were getting a little sweaty about it. They're playing a little too hard. They're trying too hard to win. They would be considered sharp play.  Like, oh, put the rover in the desert. There's some nonsense like that.