Models in Science – Opportunities, Mechanisms, Limitations
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Voelter, Markus
Models, as well as the explanations and predictions they produce, are on everyone's minds these days, due to the climate crisis and the Corona pandemic. But how do these models work? How do they relate to experiments and data? Why and how can we trust them and what are their limitations? As part of the omega tau podcast, I have asked these questions of dozens of scientists and engineers. Using examples from medicine, meteorology and climate science, experimental physics and engineering, this talk explains important properties of scientific models, as well as approaches to assess their relevance, correctness and limitations. For more than twelve years I have been interviewing scientists and engineers for my podcast omega tau. In many of the conversations, the pivotal importance of models for science and engineering becomes clear. Due to the pandemic and the climate crisis, the meaningfulness, correctness and reliability of models and their predictions is ever present in the media. And because most of us don't have a lot of experience with building and using models, all we can do is to "believe". This is unsatisfactory. I think that, in the same way as we must become media literate to cope with the flood of (fake) news, we must also acquire a certain degree of "model literacy": we should at least understand the basics how such models are developed, what they can do, and what their limitations are. With this talk my goal is to teach a degree of model literacy. I discuss validity ranges, analytical versus numerical models, degrees of precision, parametric abstraction, hierarchical integration of models, prediction versus explanation, validation and testing of models, parameter space exploration and sensitivity analysis, backcasting, black swans as well as agents and emergent behavior. The examples are taker from meteorology and climate science, from epidemiology, particle physics, fusion research and socio-technical systems, but also from engineering sciences, for example the control of airplanes or the or the construction of cranes.
 Alright, and a lovely welcome back to the Huck stage this evening. Here to present you a talk about models in science, opportunities and mechanisms, limitations by Markus Völter. He will be talking about scientific models, what they do, how they work, what are they, and they are quite in the news right now because of the coronavirus and climate change. And with models you can do a lot, you can model things, but for the public it's not always quite apparent how they work and what they do. So we have our own streaming site with an IRC and no JavaScript. If you don't like that go to live.hack.media. There you can also ask questions in the IRC or via Twitter with the hashtag R3Huck. And apart from that I think we're good to go. So I'm giving over to Markus. Alright, so talk. It's scheduled for 90 minutes. I might take a little bit longer, but it should be interesting. Alright, so I want to talk about models. I'll cover topics like the difference between analytical numerical parametric models, forecasting versus explanation, abstraction and simplification, statistics, forecasting the past sounds stupid, but it's useful. Sensitivity analysis, optimization, forecasting versus scenarios, fitting of data, fake numerical precision, chaos, emergence and unknown unknown. That's quite a lot of stuff. So I'll run rather fast as you'll notice. The examples will be taken from cranes, pendulums, weather and climate, flight simulators, sheep and ants, gravitational waves, fusion, the LHC, the event horizon telescope, cellular automata attribute, turquoise. And you might ask yourself why the hell is this guy talking about you have some background. I'm a physics engineer and a computer scientist, but more importantly over the last 12 actually years, I ran a science podcast called Omega tau, and just an engineer for about 600 hours. And that's basically where all of the material of this talk comes from. The podcast also gave me an hour in the backseat of an F 16, which of course was the highlight. Alright, so let's get started. Let's get started. You probably have all seen these large steel monsters. And if you look closely at these little traffic light kind of thing, the cabin, it signals to outside personnel the load of the crane, not the weight that is on the hook, but the actual stress on the crane, the load on the crane. And of course, obviously, that means what you'd expect. Okay, be careful and at the limit. And so what is the load of the crane? Well, one is the bending of the boom, right? The boom is a long stick that is of course bent from the weight that's at its tip on the hook. And of course, also the stability, the balance of the lifted mass and the counter mass, I should say counterweight. So how does the crane know all of these things? Well, there's a model that calculates this and drives the traffic lights. And let's investigate what goes into that model. Well, one, of course, there's the weight that is currently being lifted, the more weight, the higher the bending moment on the boom. The length of the boom is relevant. Of course, these booms are telescopic and if they're longer, you have for the same lifted weight you have or mass, you have more bending moment. The angle of the boom, obviously, you can lower it and also, you know, make the angle steeper and the lower the angle of the boom, again, the higher the bending moment because the radius is larger. There are additional wires and poles you can use to stiffen up the whole construction. And if you have those installed, then your bending moment is less for a given lifted weight. And finally, wind, because if the wind moves your lifted mass sideways, this leads to sideways bending of the boom, which lowers the overall stability. So that's for the bending. For the balance, obviously, the relationship between the lifted weight and the counterweight and their respective radii is relevant. So that is something that's taken into account and the distance slash radius of the stanchions. The further out you have moved them, the bigger is the, if you will, footprint of the crane and the more stable it stands. So these two aspects of overall load are calculated separately and whenever one of them reaches, you know, critical level, that is, that drives the traffic light. So how is this done? Well, for the stability for the balance, we simply use the lever principle, right? So you basically calculate the two moments, the actual lifted weight is measured from the pressure in the hydraulic cylinders, the counterweight is configured. And then you know the two radii, you can calculate those as well from the angle and the length of the boom. And then you can just simply figure out whether the crane is stable, the balance is in balance. For the bending, it's a little bit more interesting because here what you basically do is you run an FEM analysis, finite element analysis, where you basically simulate every little discrete piece of boom material and run a numerical simulation, a numerical model that figures out where the load is high and when it reaches a limited any of these discrete small finite volumes. And of course, you can't run this in real time in the crane, which is why the results of this analysis are abstracted into basically lookup tables, right? This is called a parametric model. We'll get back to these model categories later. But that's basically how it works. And so there is an interesting thing that happened this year, or maybe it was last year, this is a 750 ton crane, the LTM7050-9.1 manufactured by Leipzig. And again, it can lift 750 tons. Well, it was able to do 750 until earlier this year, because now it can do 800. Only because of a software update, nothing changed in the actual construction of the machine. In fact, existing cranes can be updated retrospectively. So how does this work? Well, there's something translated from the Leipzig website. It says, we completely recalculated the crane more and more precise FEM models, more and more precise FEM models, I should say, on faster computing hardware, permit a less conservative approach. The latest regulations regarding the load bearing capacity in compliance with polyplicable standards, blah, blah, blah. So basically, they have newer modeling tools, both in terms of algorithms and software and machinery, computers. And now they can be a little bit less pessimistic, conservative about what the crane can lift. And so the software update basically installed new lookup tables, and now the same machine can lift 50 tons more. Regarding the balance, I talked to a bunch of crane operators this year, obviously, and one told me, you know, today it's basically impossible to knock over a crane to bring it out of balance so that it actually falls over. Oops, this is from 2013, where one of these large Leipel tracked cranes fell over in Brazil during the construction of their Olympic Stadium. And the problem there was surface stability, right? So the ground gave in. These cranes produce a significant pressure on the ground. And if the ground isn't suitably prepared, then the whole thing falls over. And obviously, the model that, you know, takes that considers, as we have seen, the levers of the weight and the counterweight can't know about this. So this is a problem. Here's another example of something that went wrong. A large shipboard crane in Rostock, Germany, completely crashed. And so again, is this a modeling problem? Well, no, not really. It was very likely a material fall the production mistake in the hook itself, the hook broke, and then the whole boom basically snapped over backwards, completely destroying the crane, millions of millions of, you know, money lost and several people hurt. Big, big drama. So what can we learn about this? We have to be really careful about what goes in a model. The model sounds trivial, but the model doesn't make any statement about whatever hasn't been put into it. Like, for example, the status of the ground or the material quality of the hook. And these assumptions and constraints must be well defined that they must be communicated to the users. So is this a useful model? It's a Lego, actually, yeah, it's a Lego model of one of these LTM 1750 cranes. It's not useful for understanding the load capacity, because obviously the Lego has no, you know, relationship to the real thing in terms of stability. But you can explain in principle how the crane works, you know, with with extensions and telescopic booms and stuff. So it can serve as a model for illustrating that it might serve as a model for worksite planning. You know, if you have the worksite in the same scale, then why not, right? So this model also has its purposes, but it's not the same purpose as these mathematical models that we've talked about before. So again, the user of a model has got to know what's in the model, what the purpose is, and the modeler has to decide what is important, what impacts the results. So let's define the notion of model. It's an abstract representation of something that exists in real life in the real world, expressed in a suitable language like chemistry, physics, math, Lego should be an Oh, not ah, for the purpose of understanding, prediction, optimization, proof or production of that real world thing, the proof and production part will ignore in this talk, we're going to look at understanding prediction optimization. So when you build a model, you have to think about what part of the reality you want to represent in your model, what is relevant to represent that part faithfully in the model, how to represent and compute, right? I mean, you have to somehow make it quote, runnable, mathematically calculatable or in other ways executable. You have to think about how do you observe parts of the reality that serve as input to the model, and then what is the relevance and trust of the output. Again, if you don't input something about the ground, then you already gave you can only measure that unreliably, then the relevance of the output and the trust level of the output is low, we'll get back to that. So let's revisit analytical, numeric and parametric models. Here's a very simple analytic model. It's a differential equation of the movement of a pendulum, right? It basically says that the angular acceleration, which is what the left term says, basically depends on the angle itself on the sinus on the sign of the angle. And then you multiply it basically by the fraction of the earth acceleration and the length of the pendulum. And so an analytical model is basically where you use precise or approximate equations, as we'll see this one as approximate. And then for dynamical systems, these are often differential equations which relate a quantity to its first or second or whatever, a derivative. Again, here it relates the angle of the angle phi to the second derivative of that same angle. And so again, an analytical model is what we all know from school as formula equations. Now, a numerical model is more interesting because it in practice plays a more relevant role for what we hear about models today. What you do is you discretize your world. In the finite element analysis we saw in the context of Cranes before, you basically discretized the overall boom into finite small volumes of steel. In climate and weather models, you discretize the atmosphere into volumes of air. If you do epidemiology, you have subsets of the population. And then you reassemble the overall system by basically joining all these little volumes and computing a whole bunch of properties for each of these, I call these properties E for eigenshaft, sorry, change that, the properties. And you then again from the calculated properties of each of these small volumes, you reassemble the overall story. And then you also typically, if this is a system that evolves over time, you iterate over time. So again, for the weather, you have small volumes of air, you calculate various properties for each of them, and then you run this thing over time. There's a bunch of constraints. One is that you have to make sure that the changes are plausible both in time and space. What I mean by that is, if you have a weather forecast and it says, at time t equals one, the temperature at some location is 20 degrees, and 10 minutes later, it's 10 degrees, there's probably something wrong. Same is for spatial plausibility. If you have 10 degrees in Schuttgart and 20 degrees in Esslingen city nearby, it's probably strange. So you have to make sure that either by design, the model doesn't jump both in time and space or whatever other discretization dimension you've used. Or if this is an outcome, then your model is wrong if things jump. So basically, you still calculate with equations in numerical models, but these are discretized and often spatially and temporarily. These are the most obvious discretizations, but of course, others might be used as well. If you use smaller boxes, smaller discrete volumes, you get higher resolution. Same if you use smaller time steps. So this gives you increased precision. In some cases, it gives you correctness. For example, in control theory, if you have two large time steps, you might not get a control algorithm that is stable because of its large time steps. It can't see oscillations and control those. So the algorithm isn't just imprecise, it doesn't work if you don't use a fine grained high resolution time. Same thing in some cases for space. If you want to forecast thermals, the stuff that propels gliders up, warm air rising above mountain peaks and you have a coarse grained resolution of your terrain, then these peaks are averaged out and you will not be able to produce correct predictions of how and when thermals develop above those peaks. It's something glider pilots know very well when they fly in mountainous areas that the forecasts are often wrong. And then of course, the drawback of a high resolution is that you need more computational power. And even today, with faster and faster computers, it's still quite plausible. Scientists still have to make lots of compromises in various ways, for example, in resolution to make it feasible to run on existing machines. And then of course, you can compose these, for example, the ECMWF, the European Center for Medium Range Weather Forecasting, runs a worldwide weather model. They use 9 by 9 kilometers horizontal resolution and 500 meters vertical resolution, up to 80 kilometers by the way. And then the German Weather Service, the DVD, they have a higher resolution model, but only for Germany. And basically, they use the more coarse grained model from the ECMWF as a boundary condition for what the, and also means of initialization, initializing data for the finer grained model. And by the way, weather models calculate around 50 of these properties. So lots of stuff going on there. And so you can see easily why even large computers can be utilized completely with this approach. So let's look at parametric models again. We look at cloud formation. You can see a beautiful picture of clouds here. And the question is, you know, what kind of cloud forms, how much of the sky is covered by clouds? What is their lower and upper limit called base and ceiling? And there's a lot of parameters to go in, right? The position of the sun, basically time of day, how much high clouds you have that limit the energy imparted by the sun, then of course, humidity, pressure, temperature, properties of the ground, the elevation of the ground. And so you want to, if you want to compute this algorithmically, there's lots of chemical and physical processes going on. Some of them are theoretically not even known. Lots of small things happening, lots of complex interactions. So basically, what you do in principle, again, is you discretize and you associate all these interesting properties with each of these discretized air volumes. But you can't really run this as a numerical model, because again, some things aren't known, interactions are complex, it would take too long. So what do you do? You basically put all these things into a series of lookup tables, right? So for example, you know properties E1 and E2 from, let's say observations. And from those, you calculate some property X. And then this property X together with properties three and four, you put that into a simple equation, which gives you a property Y, which you then use in another lookup table together with property E5, and you get the result. So this is basically a very simple lookup table and or set of equations. And of course, those are as we've seen with the crane filled by numerical models, analytical models and experiments, right? Experiments, even if you don't know how something works, you can easily just take the experiment results and package them into a parametric model, which you then run to make a forecast. Another example of a very simple parametric model comes from medicine. This is actually the only software example, I think in my whole talk, I built an application in the healthcare domain not too long ago, where, for example, from the systolic and diastolic blood pressure, depending on the ranges there in, you calculate a risk factor, which you then use, for example, together with the age and the weight of the patient to make further decisions regarding treatment. At combining these different kinds of models, this is a picture of a aircraft, which many of you probably know from the movie Top Gun. Although this is not actually a picture of a real aircraft. This is a screenshot from the DCS. Here's another one looks beautifully realistic. So that would be another example of models is how do you model these surfaces and how do you reflect it. But we're going to talk about something else and that is the modeling of the aeromechanical properties of so let's say we are a Maverick and you know, you know, we're flying around in Top Gun with goose on the goose that he's going to turn right. So he'll smash the stick to the right. What happens next, right? How does the simulator simulate reacts when the pilot moves the stick to the right? So we have the stick movement, which basically is translated simply, you know, stick angle becomes a percentage of deflection. And that's the input to the hydromechanical flight control system. And now you have to think about to what degree the arrow surfaces in this case, it's elephants and spoilers on the wing to what degree they are deflected. And interestingly, they actually calculate that in the simulator. And they calculate that based on the current hydraulic pressure in the simulated hydraulic system, because if we 28 shot away half of it, you know, remember Top Gun, then you have less pressure and you had in your hydraulic system and the deflections are slower. Then you get the you find out what your flap settings are, you find out what the wings we angle is. As you remember from Top Gun, the wing, the F 14 has sweepable wings, right, to adapt the wing to different speed table. What is the coefficient of lift for that deflection for this flap setting and this wing sweep? And this is a parametric model, which happily NASA did in the 70s, they put one of these aircraft into the wind tunnel and measured all of these things. And those guys somehow got hold of this wind tunnel data. And now that we have the coefficient of lift, we can basically calculate the actual lift force. And we do that by multiplying the coefficient with a bunch of properties of the aircraft, but also specifically with the speed of the aircraft, which they get from the simulation environment. So there's another calculation. And then they look at again, the wings speak as wing sweep angle, which gives them an inertia. And they know how much fuel is in the wing in the simulator because they know how much fuel the engine has burned since they took off. And they take this information to actually calculate the inertial moment that acts against the movement from the differential lift of the two sides. So, you know, and this then gives you a role, role movement. So the point is that I'm trying to illustrate here how this overall model uses analytical, meaning calculations and parametric models jointly in one, if you will, big calculation, relying on previously calculated numerical data, in this case, stuff that NASA has figured out in the wind tunnel. Now, models aren't just relevant for controlling simulated airplane on a PC. There's also actually a model very prominently used in the flight control system of an Airbus A320 and of course, of all subsequent Airbus airplanes. So the way you actually fly an Airbus is that you move the stick. And what this does literally is that the stick flies an idealized airplane, a model of an idealized airplane in the computer. Then the various attitude sensors and, you know, air data computers, they measure what is the state of the physical aircraft, things like, you know, angle of attack, roll angle, stuff like that. And then there is obviously a difference between the model that the pilot flies, the idealized airplane and the real one. And then you have control algorithms that decide how best to get the state of the real aircraft in sync with what the pilot wants the aircraft to fly like based on its input into the idealized aircraft model. And it's interesting because if, for example, one of the flight computers has failed and you cannot control your ailerons, then you still use the same flight inputs. But of course, the system then figures out how to use, for example, the spoilers to produce the roll rate in order to bring the state of the real aircraft in line with the model. So to wrap up that part of the talk, we have analytical, numerical and parametric models. The models are basically functions, if you will, equations that take a bunch of inputs and you can calculate the output you're interested in directly for every point in time for every kind of combination of inputs. The quantities you calculate with are usually continuous and the equations are physics or whatever else chemistry, biology, but it's the real science in a numerical model, you discretize basically the analytical world, you iterate then. And typically the iteration, well, almost always your iteration will depend on the previous state of, you know, in the last time step, for example. And this means that you can't just say, hey, model, give me the state at t equals 5000 seconds, because in order to know that the model has to calculate, you know, for all 5000 previous time steps, and that makes these kinds of numerical models much less flexible. On the other hand, they're much simpler because solving complex, you know, systems of equations numerically is much easier than analytically. The equations are still basically the real science, but the quantities are discrete. In a parametric model, you can again have a direct look up, it's not expensive, but the quantities are usually much more coarse grained and the equations are not necessarily somehow resembling the real science. They might be completely opaque, right? They might be completely just numbers you figured out somehow, and you know they kind of work and you use them, but they don't tell you anything about how the real world works. They make a prediction, but they don't explain. So let's elaborate on that difference. Let's say you have the real world changing somehow as shown in this lower dark gray box, and the reality changes basically as a straight line. This wobbly change is sensed by your model as a step function, the model calculates and outputs some kind of reaction. Okay, that's fine. That is a prediction. So the model expresses or gives you information about how reality will change as a consequence of whatever impulse you are interested in. How does the weather change if temperature increases? How does the virus spread rate change if 60% of people will wear FFP2 masks, right? Stuff like that. But there's no explanation going on, which raises the question, what actually is an explanation? And I struggled with this quite a bit because what is the difference between the how and the why? Isn't the why also kind of how do you make the difference? And I interviewed somebody from CERN and he gave me a very, very interesting definition of what why means in this context. He says that if a model produces its prediction through applying a more general theory to this particular case, right? If you don't have, if you will, a theory specifically for this problem, but if you have a more general theory and the model, if you will configures that theory in order to produce a correct prediction, then if you look at the configuration of that model, you have the why you have the explanation. Examples for such for such general theories are of course Newton's laws or quantum chromodynamics or Darwin's evolution or some kind of reaction kinetics in chemistry, right? And so this really is a better model because it just doesn't just predict. It also explains why it makes that prediction. It explains the underlying mechanisms, which is again more useful. Now here is an example, a category of models that don't do that, right? You have probably all know what this resembles here. This is a neural network, which has a bunch of inputs and a whole bunch of weights and an output. So the neural network makes a prediction, right? It's the ultimate form of a parametric model because each of the weights here in that neural network and there are millions in real networks is a parameter. And it is not at all transparent what each of these millions of parameters means and what the model has learned. You can test and that's what people do. But if you forget to test certain things, you have no idea how the model will behave. And there is this funny example where people were trying to build a machine learning model neural network to recognize sheep, right? The idea was to, oh, it should be idea. The idea was to make the model learn the shape of sheep. But of course, what that particular model learned was the green of the grass on which shapes, sheep are usually photographed. And so when you showed the thing just green pastures, it also detected sheep. And so basically such an opaque pure parametric model will produce wrong results with some probability for new situations. And the problem is that you don't necessarily know what a new situation is because you have no clue, you know, what the thing has learned. Obviously you test. But testing as we all know from programming, but not sure if we all know, but as programmers know, testing can only prove the presence of the bug, never the absence of bugs. And you have that problem here. So this really doesn't matter for advertising. It's annoying if they try to sell me the same shoes that I just bought, right? Or tried to sell me, I don't know, you know, orange hats, which I will never buy. But it's not really a problem. It is more of a problem if people aren't given credit because some stupid machine learning algorithm has basically, you know, incorporated some discriminatory decision based on stupid training data. And it's really a problem. It's potentially fatal in autonomous driving. So there's a whole thing about, you know, trustworthy machine learning and, you know, understanding what a model learned, but that's in its in its early stages. So let's look at abstraction and simplification again, back to our simple pendulum. And we can ask how quickly will this thing pendule back and forth? And yes, I know, pendule is not an English word, but I thought it's funny. So what's the period of this pendulum? And if you look at the Wikipedia article for this, you get a very long formula and you can see the three dots. So it continues. I did actually a screenshot of Wikipedia because it was too lazy to type this up in a formula editor myself because it's so long. The point is that you can see that this period depends on the angle. So if you, you know, move the pendulum further out, it, you know, oscillates with a different rate than if you move it out only a little bit. And you can make a simple, you keep simplification for very small angles where the sign of the angle is basically the number, the angle itself, sign x equals x, then you can simplify for small angles that the period is two pi square root of L over G. And that is probably the formula you learned in school, which is completely fine. It gives you the right result. If you stay within that range for which the simplification is valid, right? And it gives you wrong results outside of that validity range. So this is another one of these things. If a model has been built for a certain limited parameter range, if you will, or range of inputs, and you use it outside, the forecast is wrong. The obvious example here also is Newton's mechanics because Newton's mechanics are wrong, right? Because Einstein showed that things are quite a bit more complicated with a special and general relativity. But we also know that for our everyday world, because we are at low speeds and relatively low gravitational forces, Newton is good enough. But you have to be aware of this. If you try to calculate the path and trajectories of spaceships with Newton, you will not get the results at the required position that you expect. So another question, will this thing oscillate forever? And if you look at this formula again, there is nothing that seems to slow this thing down. So this formula is actually given with no damping, right? So this thing will just continue forever and we know experientially that that's not the case. Stuff will stop oscillating at some point because of aerodynamic drag of the weight and also because of internal friction within the wire that holds the weight. So actually it looks like this, right? So it will become less and at some point it will stop. Now again, importantly, for your pendulum clock, right? I think it's called grandfather clock in English, right? I'm not sure. It doesn't really matter because you'll add additional energy to the clock every evening, you know, right around target show anyway. And so it doesn't really matter. But if you try to work with this kind of problem, then it is a concern. Not sure if you recognize this picture. It basically, sorry, represents the how a gravitational wave looks like in 2016. The LIGO gravitational wave detectors have heard gravitational waves for the first time. And again, here is here's this thing again. This shows time on the x axis and the frequency of the wave on the y axis and the darker the shape, the more intense the louder the stronger the wave. So they call this a chirp because it basically sounds like right because it gets a high frequency increases becomes louder like a bird's chirp. So how do those guys detect gravitational waves? Well, they have a interferometer, which basically sorry, which means that they send in a laser pulse along one arm, the laser is reflected, passes through a semi transparent mirror along another arm that is orthogonal to the first one, reflected again, and then back to a place where the two laser beams that went through either or both arms are interfered. And if the two beams arrive in phase, there will be constructive interference. Whereas if they arrive exactly out of phase, then the output will become dark. So any difference in length between the two arms will change the interference pattern at the output. That's the idea. And so if the gravitational wave passes by and makes one arm longer and the other one shorter, I hope you can see this on my great wonderful animation here, then you can see this thing basically vibrate the output vibrates visually. Well, I mean, lots of detectors going on, but principally, of course, this only works if these mirrors here on either end don't vibrate just so right. They told me the story when I visited the Geo 600 detector, whenever the package delivery guy drives too fast along the axis way to their side there, they can see the mirrors vibrate and they're telling the post guys to go slow. And whenever a new post guy shows up, destroys the measurement. So what they do is they attach these mirrors to two level pendulums because pendulums actually when they have a high mass have a very good damping about 1000. And so with this triple pendulum here, they can get a damping a passive damping of I think 1000 to the power of three, that would be 10 to the power of nine, right? And then they do some active damping as well. They precisely understand the behavior of the laser. They even optimize and understand and measure and change and, you know, try to limit shot noise. And so my point here is you don't have to understand the damping of a pendulum for your stupid clock, but you do have to understand it very precisely if you want to distinguish the natural pendulum behavior from, you know, environment, postal guys and little earthquakes, if you want to distinguish that from whatever a gravitational wave does. So all models are simplifications, even the one for the gravitational gravitational gravitational wave detector, but how and how far depends on a model's purpose. Let's look at another example. I visited the Wendelstein 7x stellarator fusion experiment in Greifswald and I asked them, so how do you guys model the plasma in the reactor? And they told me, well, it's not so easy. They have one model that models it as a fluid. It's called magneto hydrodynamics. The other one models it as a mix of two gases, right? The electron gas and the nuclear gas, basically. They can also model it as small particles that are disc-like and they can model it as point-like particles that move on this disc, on the circle around on this disc because of the magnetic field configuration. And they use all of them, right? Depending on what they want to do, they use all of them. Obviously, the MHD model on the left doesn't give you detailed information about a particular particle, but if you want to characterize the overall behavior of the fluid as, sorry, of the plasma as a body that is inside the reactor, then that's good enough. And obviously, each of these models have to make the same prediction when you get to a boundary case from which on you use the other representation, another kind of physical constraint. Let's look at this example. I'm not sure if people recognize. This is the configuration of the various accelerators at CERN. The big ring is the large Hadron Collider and the smaller rings are earlier colliders that are now used as accelerators as pre-accelerators before the Hadrons enter the large storage ring. And the LHC has these huge experiments. You see the person standing there at the bottom. These huge experiments which capture what happens when particles from these beams collide. And again, here's another picture here and again, consider the people for reference. The way these detectors work is basically that you have a whole bunch of different detecting elements arranged around the center collision point and when particles fly out, then they hit these sub detectors as they are called and produces some kind of electronic signal and that is then used. Quick comment to the technical people here. I get a lot of noise on my mumble channel. Not sure who should mute their microphone there. Here is an illustration of one of these collision events. You can see how the particles stream in from the center through which the two particles that collide travel. And then you can see how the various collision products stream out and how they light up the various detector surfaces. And what this shows here is the collision of two protons which forms a Higgs boson which then decays to two bottom quarks and to a W boson which then also decays. How do we know, right? How the heck do they know what's happening? What's going on here? So let's first understand a little bit how these detectors work. Fundamentally, what they do is they have a very strong magnetic field and if a particle that has some electromagnetic charge and most of them have, otherwise it's hard to detect them actually, then again a little bit of school physics, Lawrence force and stuff like that, the particle will be bent around a circular track by the magnetic field. And then they have different kinds of detectors. And for example, if you look at a electron here, that's the second example from the top, it leaves a trace in what's called the silicon tracker and then it decays in the electromagnetic calorimeter. And so if you look at the various different particles, each of them leaves traces in a different combination of detecting elements. So this gives you the type of particle. And then through the bending, you can measure its momentum and basically through type and momentum, you get a unique characterization of what's going on. You can even calculate the overall energy balance and stuff like that and the momentum balance and it's very sophisticated, really interesting stuff. So in this case, in the example I gave, we have a Higgs boson that decays in various ways. I've just called these particles A through F here, doesn't really matter what they are. And these decays, they are multi step. So what the detector actually sees is what they call the final state, which is these decay products. What the scientists are interested in is what actually happens in the collision. And so the challenges after observing the final state, the decay products with the detector, you want to calculate back what actually happened in the collision. Was there a Higgs or wasn't there a Higgs? And what is the mass of that Higgs boson? That was the big question back then. And I think 2013, when they discovered it, by the way, Einstein has nothing to do with this. I just used the picture. So in German, we say there are Haken, right? It's not so easy. There are problems. And so I used this picture of a hook. It doesn't really work in English. But so what are some of the challenges they have to overcome? Well, we have seen that the Higgs decays in multiple ways. And each of these decays happens with a certain probability. So they have to somehow untangle that. The decays are non unique. As you can see in this example, this hypothetical E particle can either arise from H to B to E or from H to A to D to E. So just because you see an E, you don't really know what happened in between. And these collisions are not unique, depending on how exactly, you know, how well the protons align in their collision. You either get hard collisions or soft collisions or any intermediate state. And so the created particles, the kind, their energy depends on whether it was a soft or a hard collision and all kinds of other parameters. So that is also a source of complexity. And then finally, this detector, I mean, these detectors are marvels of engineering. They're also terribly complex. Each of these components has their own failure modes and, you know, failure models. And these are complex systems in themselves. So again, how do they know what they're observing? And how do they know that with, you know, with five sigma? Five sigma is a measure of the, basically a measure of the trust in the result. Five sigma is the threshold in physics for a discovery. And five sigma means that, that there is a probability of 0.00057 something percent that the observation happened by chance and not and is not the effect that they assume in terms of physics. And this is also quite related to the P value that's used in statistics. It's inversely proportional to the amount of data, the more data you have, the higher the trust. And of course, also inversely proportional to the size of the effect, the bigger the effect, the higher the trust. By the way, it's interesting to compare these five sigmas to the P values they use in medical trials, right? They are happy if they get 5% not 0.00000057. It's quite a big difference. So how the hell do they do that? Well, statistics, right? They simulate billions of events to understand the distribution of what will happen. So how does this work? So they have what's called an event generator. It's a software model that simulates the physics of decay after a collision, right? So you basically specify collision parameters. Is it a hard or a soft collision? And then this thing gives you a distribution of particle vectors of basically what's streaming out of this collision site. Then they have what's called an experiment model. It's called GN4. It is a complete, well, obviously it's a simplification, but it's a representation of the actual detector and of the physics in the detectors themselves because I mean the detectors work by basically running certain physical processes when the particles interact with the detector material that is simulated in this model. This gives you then simulated detector hits. Then they have basically an electronic simulator that has a noise model for all of the electronics of these detectors. And this gives you simulated raw data and they run billions of these simulated collisions in order to get what they get. What they call the background, which is what would they see in this detector statistically if there wasn't any Higgs, right? So they run these simulations without Higgs, just the other nuclear processes. And then they take the measurements and they compare. And then this is the screenshot of what Atlas saw. And you can see that at 125 giga electron walls, there is some kind of peak and that is the Higgs boson. And they basically find this out through statistical calculations based on huge amounts of data. This is why they have some of the largest computing centers. They run millions and billions lines of code in these various simulators developed over decades. Of course, good old Fortran is still the backbone. They also use Python for a lot. And they have, I think it's terabytes of data. There's a whole worldwide distribution and scheduling infrastructure for calculating and running all these simulations. There's a huge infrastructure behind this in order to get enough data to find out with some degree of trust that in this case they discovered the Higgs. So how can we build trust in models? Well, one way, we can run lots of experiments with lots of data and then do statistics. Now, experiments are nice because they give you controlled conditions. They allow you to isolate various influencing factors by controlling for them. And so you can, if you see stuff correlated, it's relatively easy to derive causality. So, instead of just saying, this happens and that happens. And whenever this happens, that happens. You can also say, because this happens, that happens. That is causality. But sometimes you can't do experiments in climate or epidemiology or economics or many societally relevant questions. You can't really run an experiment. I mean, in some sense, we run an experiment with our atmosphere, but you can't build another planet and run a climate experiment in that sense. So what you have to do then is you have to fall back on just observation where you do not have controlled conditions. You cannot isolate influencing factors, at least usually you can't. And so you really just get correlation. And then you have to make an attempt at deriving causality. But that's much harder. Sometimes you're lucky, right? You have natural experiments. The economics profession tries to use that when they say, in this country, when they did this and that, it gave them inflation. And in this other country, whether it was the following difference, there was no inflation. And so then because of that following difference, they claim this is what produces inflation. But of course, again, you never know what else has changed, right? It's harder. It's maybe a bit easier in epidemiology these days. The factors aren't that different. So maybe looking at other countries that do stronger lockdowns is a good idea. Different story. So what can we do, again, if we don't really have a way of running experiments in that sense? Let's say we want to run some kind of forecast. And we know that this forecast depends on some kind of parameter. P is a parameter that we have to tune in our model for the forecast to be correct. But again, we can't run, we can't validate easily. So we have no data for comparison because we want to forecast the future. Well, the forecast is a good example. Well, what we can do is we can forecast the past, right? So we can move back in time and run the forecast from a point in the past where we do know what actually happened in the real world. And then we can tune our parameter P, in this case, P2, some value P2, is the best setting for P in order to fit our forecast best with the actual data that we know because they happened in the past. And then we can continue using this parameter for the future. This actually happens in weather forecasting. There it's called re-forecasting. And these weather models that are continuously run the various weather services, they continuously basically go back and forth between re-forecasting for parameter tuning and also for filling in inputs that they don't know because there is not a way to find the temperature everywhere above the ocean, only where there are ships, right? And a bunch of weather buoys. So they can just go back and forth to do this kind of stuff. And so this is really the backbone of weather forecasting. So another way of building trust in models is re-forecasting the past. Now, all models are simplifications. We've talked about that, right? And so the question is, if we simplify which of potentially many parameters can we ignore, which are important, right? So here is another model M. It has three parameters P1, P2 and P3. I realize I used P2 as a value on the previous example. Here it's the name for a different parameter. Not a good decision. I'm sorry. So we have three parameters P1 through 3. And we don't know which of them is important. Well, what we can do is we can scan through the ranges of all of these parameters and see which scan has the largest output or the I should say the largest consequence on the output of the model. In this case, we can see delta M for P3 is the largest one, right? So we know P3 has the largest influence. By the way, there might be an even larger influence when we combine the scanning of P1 and P3. So we have a combinatorics problem. I don't know. I forget which scientist I talked with when I asked about that. And they said, well, we don't do these combinations. It's too complicated. So that's another simplification. They treat each of these parameters as uncorrelated with others, which might or might not be correct. Anyway, so we find out that this model here is sensitive to the value of P3. And so what does this mean? Well, it means we have to invest effort or computational power into determining P3 precisely. Or if we can do that again, because we might not have a way of finding the value because we don't have, you know, temperature sensors all over the ocean. Maybe satellites can help, but different topic. Then we have to always vary P3. And whenever we make a forecast, make it for the whole range of P3 and see what this gives us. And this is, well, more or less, this is what ensemble forecasting is called in meteorology, where they run different models, different parameterizations of the same models, and also different values of the input conditions, where they are not known, in order to basically get a probability distribution of outputs, right? So they might vary the temperature at a given point, run the forecast, and they get a probability distribution of the output. And then they either communicate the probability distribution to their users, or they just give you the result that is most probable. There is a weather forecasting service called Meteo Blue. And I like them because if you look at this screenshot from the left, you can see in German, of course, the Treff Sicherheit, the Wetterprognose is middle. The reliability of this prognosis is, sorry, is medium. And now you can click on a button and you now get what they call the multi model. This is essentially a, if you will, sensitivity analysis. It shows you what the different models forecast, and you can nicely see if you actually go to the page how they diverge more over time. They even give you the verification. They basically tell you how good this model was in the last three days. So they give you a lot of information in actually, if you want to invest the time in analyzing which, how reliable the model is. And this particular one is used by glider pilots. I used the example from GAP. It's a favorite gliding site in southern France and people spent half the morning over this and other forecast to figure out what the weather will be. Now, in epidemiology, things are really simple, right? It's exponential growth, meaning the infection rate will grow exponentially with some factor. This B here is kind of what we know as R. It's not exactly the same, but for now it's good enough, right? But we also know it's not really like that, right? If there are no more people left that can be infected or more generally, if there are no more resources, resources, which an exponential growth can, if you will grow into, then the growth has to stop. It's called the logistic growth model as opposed to an exponential growth model. And we know everybody knows now that if you will, the herd immunity is the step or is the amount of infection where there are no more people left to be infected or where at least the infection rate becomes quote inefficient from the perspective of the virus and the growth becomes slower and at some point increased infection stops. So what else could there be, right? Simple. Well, there is this website called COVIDSIM by a company called Xplosus and they have this COVID simulator. And actually, there's a whole bunch of differential equations they use, like the number of susceptible individuals, the individuals in various periods of infection, the number of recovered individuals, the number of people who have died. So it's quite a bit more complicated. Actually, it's way more complicated. There's lots of different dynamical equations. There are intervention effects you might want to model. And there's a whole long range of parameters that you can set and that you have to set, right? And so there's an interesting effect that I figured out when I talked to one of these guys. The ratio at which the population reaches herd immunity depends on how they break down the age groups. Now, I'm not talking about the actual age distribution in the population. Obviously, if you have more people, more people will die. We know that, right? That's our experience. What I'm talking about here is whether you split your population into three groups, zero to 30, 30 to 60, 60 to infinity, or whether you split that same age pyramid into 10 or 15 subgroups, the model makes different predictions. Who'd have thought, right? So this is an example of a sensitivity analysis where you have to somehow figure out what is a good way for this age structuring in your model. There's another nice example for sensitivity analysis in fusion. So one thing they might want to optimize in their reactor is how do you maximize the distance between the plasma and the reactor wall? Because as you perhaps know that the plasma is very hot. It's stabilized through a magnetic field. And if the reactor, sorry, if the plasma hits the wall, well, it might damage the wall, but more importantly, the plasma will be damaged and might collapse. So you want to keep the plasma away from the wall. And again, that's the point of the magnetic field. So one parameter you can tune is you can increase or decrease the field, you can increase or decrease the gas density, you can increase or decrease the number of neutral particles that are injected in as a way of injecting energy, basically, you can change the temperature of the plasma. Point is that it's 10 to the 100 combinations. And how do you do that? Right? So how do you make this optimization? Well, one way is you have to use the simplest of these various representations of the plasma I mentioned before. So this is something they do with the MHD, the fluid representation, because it's the simplest, it's the most efficient. But also, again, even then, you know, we only have 10 to the power of 10 to the 85th atoms in the universe. So 10 to the power of 100 combinations won't work. So this is where in these numerical models, computer science comes in, right? Where you have various different optimization algorithms, numerical solvers, you know, things like hill climbing, simulated annealing, not something I want to cover in this talk. But I thought it was important to point out that it's not just about finding the right model and the right abstractions and the right sense, you know, deciding on the right parameters. There's a lot of cleverness going on here in the programming and how you perhaps then also run this on a parallel computer. By the way, little anecdote, I talked to a meteorologist a few days ago, actually, for a podcast interview, and he said, it's going to be really painful when in the next or next next generation of supercomputers, everything will be computed on graphics cards, because we can basically throw away all our code and have to rewrite everything. So that's going to be painful. So how can we build trust in models? We can vary parameters, do a sensitivity analysis and analyze the impact. Now, I want to reemphasize something because somebody recently on Twitter told me that this modeling for COVID seems to be shit because the forecasts were wrong. And this is a forecast for wrong. And this person misunderstood something completely, and that is forecasting versus scenarios. So let's say you have a model and you want to make the model correct, you know, make the right predictions, but you can't take into account all of these millions of different parameters. You have to find out which ones are the most relevant. So that's when you, as we just learned, you run a sensitivity analysis, right? For example, you want to find out the cloud formation, depending on temperature and humidity, the radiated energy by the earth, depending on serious cloud coverage or the amount of precipitation, depending on layering of the atmosphere, right? Once you figured that out, you put that into your model, and then you can actually measure various data in the world and make forecasts, actual forecasts, that the output of the model claims that this is how the weather will behave. Okay? That's what we do in forecasting. Now let's look at another example. Let's say we want to figure out, or we're going to understand, how the one-to-one infection rate depends on how much virus people shed when they breathe, how the virus shedding depends on the kind of mask you wear, and how the one-to-many infection rate depends on the rate of interpersonal contacts. In this case, you can then also make a sensitivity analysis, run it on simulated data, and then what you get isn't the forecast, because you don't know how people will behave. But what you get is scenarios. You can say that if you guys behave in the following way, then the infection rate will increase. There's no point in saying the COVID forecast was wrong, because it didn't make a forecast. It gave us scenarios that give us hints about how we should behave. And of course, it's a bit frustrating. We have a healthcare model that says that early and hard lockdown works best, because it's easier to slow down exponential growth when the absolute numbers are low. An economical model told us that early and hard lockdowns work best, because shorter lockdowns, for the reasons above, means less total cost. There's also a psychological analysis that says, early and hard lockdown works best, because if you become harder over time, people are already fatigued. They have lockdown fatigue, so they won't comply. So Germany still started a lockdown light and did it too late. So it's quite a bit useless if you have all these models that make these useful and, I guess, rather reliable scenario forecasts, if you will, but then we don't care. But that's just a side note. It frustrates me a great deal, so I had to include that into the talk. All right. So again, going back to building trust in models, we were at this parameter variation story, but there is another way how we can build trust in models. And that is if we do have an explaining model, one that doesn't just tell us the how, but also the why, then we can inspect that model and see if this makes sense. Is this explanation plausible? Does it make sense? For example, if your plasma optimization thingy comes up with a great solution for maximizing the distance of the plasma from the reactor wall, but it predicts a pressure that is twice as high as what your reactor vessel can bear, it's not a good forecast. It's not a good result. But you can only do this because you can inspect the solution the model created for sensibleness, if you will. So you can check explanations if they are there. So let's look at how you get from data to the model. You probably all remember this picture. It's the first ever image of a black hole. Well, it's sort of an image. I should rather say this is an image, but what the EHT, the event horizon telescope, imaged wasn't really an image, right? Because of how the EHT works. Let's see how this works. So the EHT is a radio informator, an interferometer, which means you computationally combine several telescopes and there's lots of computing going on. So in this case, they combined a bunch of telescopes all over the world in something that's called very large baseline interferometry. The very large baseline comes from the distance between the telescopes and that is relevant because the resolution, the whole computational thing can resolve depends on the length of these baselines. So the further you can distance these telescopes, the higher resolution is the picture, well picture. This thing is going to take here is a picture of one of these telescopes. Okay, this particular one, Effelsberg, is not used in the EHT because it can't observe at the respective wavelength, but it's these kinds of telescopes, smaller some of them all over the world. Now, how does this work? So these different telescopes, they look at the same spot in the sky, right? But because they are some distance apart, the distance from the telescope to that point in the sky is different, right? So they see the same wave, the light wave that arrives, you know, with a certain phase difference because there is this difference D in distance offset, right? And of course, because light speed is constant, this is proportional to some time difference as well. Now, as the Earth rotates, and also as you look at different points in the sky, this difference also, sorry, this distance also changes because the angle of the object in the sky is different from each of the telescopes. So if you take these two observations or realizations and then apply a whole bunch of mathematics, which I'm not going to go into, I probably also couldn't in detail, you get the following equation, which again, not important in detail. But what this equation shows is a Fourier transform of the sky. So the EHT actually observes a Fourier transformation, a spatial, it observes the spatial frequency distribution of the radiation across the sky. And then the actual data point is basically there's a, in, we can basically observe this amount of radiation with this frequency, and by that I mean spatial frequency at the following orientation. And then they combine all of this data and the more different lengths of baselines they have, and the more different orientations of baselines they have, the better. But still in any case, they only have like, whatever, seven telescopes, so they have 10 different baselines. And the orientation of these baselines, well, there's only a limited number of these orientations. Sure, the Earth rotates, giving them a bit more, but still it will be incomplete data. So what they'll have to do is they have to do an inverse Fourier transformation of incomplete data. The question they're answering is which is which mathematical description of the object in the actual space domain represents or approximates best the data that has been seen by the telescope in the frequency domain. And so let's look at a simple example of this kind of problem. On the left side, you can see a bunch of measurements, some data. And on the right side, you see a mathematical model. In this case, a horizontal line, a simple equation, y equals y zero, no dependent z on x. And the total error of that model relative to the observation is, you can imagine that as the sum of all the red bars, right, the difference between what the model predicts, what was actually observed. So there could be different mathematical models, right, that approximate that same data. Question is, which one is the right one, right? So again, in the DHT case, what visual shape actually fits best to the observed incomplete data in the frequency domain. And this example here on the right is best, right, because it has a total error of zero. But actually, what this is, this is an overfit. If you put enough terms into your polynomial, you can fit every data with some kind of polynomial. But while it reproduces the data perfectly, it makes no use for prediction, because there's no way you can tell what the next, like if you extrapolate to the right would be. And it's no abstraction, it's not a useful model. It's just the encoding, encoding, if you will, of the measurements as a formula. So by the way, this is what's called overlearning in neural networks, just as a side note. So how do you decide between the three remaining ones? Well, you decide based on knowledge about the system at hand, right, you know something about how your observed system should look like, because you understand the physics, you have a simple analytical intuitive model about what's going on. So in this case, the model of the black hole tells us that between the center of the black hole and a distance of 2.6 times the so-called Schwarzschild radius, you will see black, because in the middle, you look at the black front side of the black hole, a little bit further out, the your light rays or the light rays coming from the black hole are actually bent by the strong gravitation so that you can see the backside of the black hole, which is also black. So we know that, you know, up to 2.6 RS, it'll be dark. And outside there, we will see a glow from radiation that is accelerated around the black hole from the gravitational force. So there must be something glowing and there must be a black thing in the middle. And we even know roughly how big this is, because we can calculate the Schwarzschild radius through other means, or at least a guesstimate it. And so we kind of know what it will look like. Well, it kind of looked like this donut. And so knowing that, we can use this knowledge and basically help interpreting the incomplete data. Now, of course, the problem is, how is that not self-fulfilling? How do we avoid observing exactly what we want to observe, you know, then we don't have to observe it because we know what it'll look like anyway. It will fake it. So what they did here is they used three different deconvolution algorithms to do this kind of inverse Fourier transformation with three different software packages for independent teams who weren't allowed to see everybody else's data. They also worked with synthetic data. They used the same magneto-hydrodynamic simulations of black holes and of other shapes, right? They produced such data of, I don't know, rectangles. And, you know, if the software still produced donut as a result, then something fishy is going on, right? And of course, they still minimized the error of the fitting. So there's a lot of work going into this reverse analysis of the data. It's fascinating to read. There's a nice book by Heino Feike, one of the leaders of the project. I think it's called Light in the Dark or something that talks about that and other things. So again, does the explanation make sense, right? We know how the physics work so we can say something about what we expect. So how far can we trust models? Here's a statement I've read. If we had started the lockdown one week earlier, 36,372 fewer people would have died. This is what I call pointless precision because the precision of whatever your model predicts must be proportional somehow to the precision of the input and the parameterization. And obviously, there's a lot of things we don't know precisely for this virus and how society reacts, right? So this leads us to this observation that there are models that are qualitative in nature. It only tells us tendencies, right? If input A increases, output X will also increase. There are relative models which give you comparative influences, like input A influences the output X twice as much as input B, useful. And then there are quantitative models, which actually give you numbers, right? If you increase by 10% the input A, then output B decreases by 33.3%. Now formula doesn't mean numerical, sorry, formula doesn't mean quantitative. There is this Drake equation, which tells you how many civilizations there are in our galaxy, right? And it's this equation, it has all kinds of factors like the average rate of star formation, the fraction of planets that could support life, fraction of civilizations that send detectable signals, blah, blah, blah, right? It's a formula has lots of factors, so it's numeric, right? It gives you quantitative outputs. No, it doesn't. This is really just a simple parametric model because none of these parameters has really known quantities. We have rough boundaries or, you know, boxings for each of those, but not really. So using an, just because you have an equation doesn't mean that it's a quantitative model, right? It might just be, it basically just says which things influence this thing and whether it's proportional or antiproportional. So let's look at fundamental limitations of this whole modeling business. So first is chaos, which means that a small change in the initial conditions leads to huge effects over time. So you've probably all seen this chaos pendulum, right? It's a pendulum with two hinges, is that the word? I don't know. And if you take the pendulum and put it into a certain, you know, position and let it go, it will oscillate in some way. And if you then take the pendulum and try to put it into the same position again, after a few seconds, it will move completely differently because the behavior is chaotic and you're not able to put the pendulum in exactly the same initial condition. Also, you don't know exactly what other factors influence it. You know, there might be some wind going on or whatever. So the other example that everybody talks about in the context of chaos is like, if the butterfly leaves, you know, starts flying in Brazil somewhere, this leads to thunderstorms in Europe. I did ask various meteorologists here whether they actually think that's true. And I mean, nobody disagrees that the weather is chaotic. But I think they said that this very small effect will very likely not lead to a thunderstorm, although in theory it could. So the point is that both of these systems are deterministic, right? There is no randomness, right? There's no randomness in the physics of the weather, of the atmosphere. The quantum effects really aren't relevant on that level. There's also no randomness in this pendulum, but we don't know the interactions, for example, the friction in these two hinges. And the initial conditions precisely enough, if we knew them precisely enough, then we could make a perfect prediction, right? So, or stated less absolutely, more input gives you a better prediction, more weather stations, more satellites, more ships, more airplanes with sensors gives you a better prediction. So this chaotic behavior of the weather really is the fundamental limit for weather forecasts, because, right, for any given data quality and computational power, right? So that's why I think what they told me was that roughly every 10 years, the useful range of weather forecasts becomes one day more, right? And so that is not just because the computers get faster. It is also just because they have more inputs and of course because they understand the mechanism better. So if we can't predict the weather, you know, for more than a few days, how then will the climate skeptics say, how then can we predict climate, right? This is all fake. They can't even predict the weather. And of course, this is bullshit because climate is a statistical prediction. It's not relevant if it will rain on 5th March, 2038 in Stuttgart, right? That's not what climate models do. They make statistical predictions. And just to draw home this difference, again, going back to the fusion example, we really cannot, because of chaotic behavior, we cannot predict the position of each molecule or element atom in this mix of two gases, kinetic model here. But what we can do is we can calculate the averages. In this case, the averages of these movements is called temperature and pressure, right? And so we can calculate that precisely. But despite not being able to forecast every molecule precisely. So there is an interesting thing in climate science. It's called attribution science. And so what these guys ask is, is this extreme weather event that happened there, is this caused by climate change, right? Really, what they're asking is, with which probability is this kind of weather event caused by climate change at this location on the earth at this time of year, right? How do they do that? Well, they take the current atmosphere, they modify the initial conditions like temperature, humidity, pressure, stuff like that, they scan through these, and then they run the, you know, climate models or weather models. Well, this is the same models anyway, it's a question of parameterization these days. And they figure out with how many of these modified or these initial conditions, will we get this kind of extreme weather event? Then they take the atmosphere without the human impact. They remove the CO2 that we've introduced over the last, whatever, 50 years and the methane. Because I mean, that is relatively well known how much this is. They do the same modification of initials, run the weather forecasts, and they get another ratio of extreme weather still happening versus not happening. So basically, they get different degrees of robustness of that extreme weather phenomenon, depending on whether they run the real atmosphere or the one without human impact. And then they basically take the difference between the two. And this gives you the probability of this weather event being caused by climate change. I thought that's a very ingenious use by climate models. Of course, it also really takes a lot of computational power because you have to run these models lots and lots and lots of times. Now, you could say, well, this whole chaos stuff, it's not really fundamental. It's just because we can't measure precisely enough. Really, there isn't any chaos. It's just because our engineering is too bad. Well, let's look at cellular automata. A cellular automaton is a mathematical abstraction that has a row of cells. A cell can be either alive or dead. And then we observe how the cells evolve over time or generations. So the generations or time is the y-axis. And then we have a whole bunch of cells on the x-axis. And of course, generation i depends on the previous generation. And each value of a cell depends on the value of the two neighbors in the previous generation. So we can see this here in this diagram. We have generation i minus one. And the value of the cell with the question mark in generation i depends on whether the three other gray boxes cells, whether they were alive or dead. And then we have an example rule. The one here, that says if all three predecessors were alive, then in the next generation we're dead. In this case, only if the three predecessors were all dead, then the next one in the next generation is going to be alive. So some kind of birth from nothing. Point is, if we plot this rule one, there is a way of classifying these rules and giving them names, if we run this rule one over 20 or 100 or 1000 or whatever, how many steps, you can see that a regular pattern occurs. So we can give a formula for this rule. In this case, it's very simple because only if, well, only in one case do we basically flip the values of the previous cells, except for these two cells in the middle, next and right to the center, they always stay zero. So point is, there is an iterative formula, and it takes into account the value of a previous generation. That's why it's iterative. But we can also give a closed formula, one that does not rely on the previous generation. We can distinguish between even and odd generations and just state which ones are alive and which ones are dead. So that's fine. That's deterministic behavior. We can predict it for any number of generations, and we don't have to iterate. Now here is another rule, rule 13. Here is how this one looks after 20 steps. And here is how it looks after 100 steps. And in these two other illustrations, top right, you can see how a simple change in the initial conditions, how it spreads through the whole, basically the whole row. So this is actually chaotic behavior. And it's chaotic behavior in pure math. There is nothing going on with measurement. It's a property of the math. So we cannot predict the value of a cell in the i-th generation. We have to run the iteration. This is also called computationally irreducible. In fact, it's a very good secure random generator because the behavior is random. It has been proven to be random. It's all work by Stephen Wolfram, who has written this book, A New Kind of Science. It's interesting. Not everybody takes it too seriously, but this work on cellular automata is not disputed. So it's cool stuff. So chaos is a fundamental property of our universe. And we have to somehow, you know, if it occurs in our systems, because our systems are complex, as we'll see, this limits the range to which we can say something useful with models. Another example is emergence. You've all heard about how ant colonies exhibit these very sophisticated group behaviors, even though presumably the brains of these ants are rather small and simple. So what's going on here? Well, we have what's called agents. Each ant is an agent. It has simple rules it behaves based on, for example, based on pheromones and smells and stuff like that. But then we have lots of interacting of these agents. They interact in different ways. And then they produce some kind of complex ultimate outcome. And the point is that we cannot predict the outcome just by observing and understanding the rules. We have to actually run also iteratively the system and see what can potentially come out. And then the thing is that in lots of systems we care about, they work exactly this way, right? Politics sets rules. And then we all as society behave in some way. We interact based on rules, maybe not based on rules. People know there's lots of game theoretical personal optimization going on, right? And so we really can't predict, right? So I did an interview with somebody from Theo Delft, Igor Nikolich, about socio-technical systems. He investigates how society interacts with technical systems and what resulting behaviors could come out. And again, he can't really predict because of these immersions. But what he can do is he can run these agent models and then look at the scenarios that could potentially happen and then discuss this with stakeholders, potentially go back to change the rules and run again and maybe iterate to a better set of rules. There's no proof there, right? There's no guaranteed understanding. But it can help. He has lots of interesting cases there. There's also a very nice counter example from politics in Germany recently in Berlin. They were setting an upper limit for rents, right? So the idea was to therefore have lower rents and so less affluent people will find apartments. What actually happened, at least initially, I haven't checked in the last few weeks, is that 37% more apartments were sold instead of being on the market for rent because this just became less interesting for people, for the renters. 28% fewer apartments were on the market, 200% more inquiries per apartment. And there was a shadow rent for the case when the law wasn't complied with the German basic law. So the point is this failed, right? And it failed because one tried to set simple rules in an obviously complex system with lots of emergent behaviors. Now, I do think that one maybe could have anticipated that even without running complex agent-based simulations, but still, it's an example of how rulemaking in politics really is challenging because you just don't know how the system will react once you put some kind of stimulus on it by changing regulations. There is also an interesting example from cellular automata. Game of life, you've probably all heard it, right? It's basically a 2D cellular automaton where the question whether the cell marked with X in the next generation depends on what happens around it. So this phenomena like dying from loneliness, dying from overpopulation, healthy environments, reproduction, the rules don't really matter. So here is something. So this runs a game of life simulation for, I don't know how many oscillations here or how many runs. And you can see there are things oscillating back and forth. There are so-called spaceships. There are glider guns. These are the technical terms for these seemingly coordinated behaviors, right? So who would have thought that from this relatively simple set of very local rules seemingly coordinated phenomena can happen? Almost looks like ants walking around a track, right? So again, pure math can produce complex or coordinated seeming behavior from simple rules that do not somehow presuppose that kind of coordinate behavior. So what can we do here, right? We just said we cannot predict behavior of the whole system by examining the rules. But what we can do is we can set a new, we can define a new set of rules that specify that are valid for the system as a whole, like whatever. If you have more than 100 ants and the temperature is over 30 degrees, they'll come out of their bunk or whatever it's called and will start rummaging around, you know, stuff like that. You can observe or create higher level theories. In fact, this happens all the time, right? Because the behavior of ants might be based on biology, but biology is just applied chemistry and chemistry as we all know, is just the physics of the of the of the electrons, right? It's a joke among physicists. So but the point is we couldn't predict the behavior even of a single ant if we try to do that with physics, even though it is physics that drives the ant, everything is driven by physics, right? We could try with chemistry, but that's probably also a bit too low level. We can maybe be more successful with biology or medicine by doing an MRI or an fMRI of the brain of an ant, right? I mean, I'm not a biologist, as you can probably tell. But the point is what we're doing all the time, we're stacking abstractions on top of another of one another, we're building models of aggregated subsystems in order to understand those. There is a very nice quote by Ezger Dykstra, a famous computer scientist who says, the purpose of abstraction is not to be vague, but to create and but to create a new semantic level on which one can be absolutely precise, right? This also relies to this averaging stuff in the fusion reactor. So very, very cool kind of framework that humanity has built for themselves there. Another example of stuff that can go wrong in modeling, path dependence, right? So there is a complex structure of decisions we've made over time, I don't know, it's just a cool screenshot, right? But we are somewhere out there on the outer edges of this path. How did we get here? And the answer is we got here because there were all these random and context and resource dependent and cultural and political decisions that we've made over time. For lots of phenomena, if you ask, so why the hell is something like the way it is in our society? There really isn't a good answer. It could just as well be different. But because of all these random things over the decades and centuries, we've just ended up there. There isn't a good reason. It just happened, right? And the only way to predict, if you will, is by going the path you cannot simplify. You can't run an analysis and say, well, obviously, you know, I don't know, the society has to do things this way. It's not like that. Even the obvious example is evolution, right? Evolution is not a deterministic process. It's just because of all kinds of constraints and randomness and a meteor impacted the earth, stuff happened. All of these things are examples of complexity. There are other things like hidden links, feedback cycles, tipping points, power loss. If you listen closely, you have heard all of those in the discussion about climate, right? Which just drives home the point that our climate is a complex system, which makes it hard to control it in a deterministic way. And by control, I don't necessarily mean just geoengineering, right? It's really hard to understand and decide what to do. I mean, obviously, we have to reduce CO2. I'm not discussing that, but in detail. I guess maybe the point is that geoengineering is risky. So last point before we wrap up this talk, unknown unknowns. Models almost always represent somehow knowledge and experience. There's no completely unknown stuff in models because nobody could have put it in there, right? So there might be also biases and prejudices. And we won't ever run a sensitivity analysis for unknown unknowns because we don't know them. We're not aware that they're unknowns. So we're not testing the model for what it would mean if that unknown parameter would have a different value. We don't know it, right? So the really nice example, I forget where I have it from. It's very well known. I actually know where I have it from, but I forget that it's clear. Whatever, it doesn't matter. So, you know, Turkey. Turkey gets fed by the farmer. Turkey likes the farmer because, you know, it's the guy who brings food. So based on Bayesian reasoning, updating its own perception, the Turkey builds a model of the farmer in their brain and, you know, becomes more and more, you know, on the good side. But then on day 100, thanksgiving, the farmer comes and kills the Turkey. Of course, the model could not have predicted that, right? Because there was nothing in the experiential world of the Turkey. There was no indication based on which the Turkey could have updated the model in their brain to maybe not be so optimistic because, you know, one day, thanksgiving comes around. So again, so this means that when we think about what we will all die from, we as a humankind, right? We can do some probabilistic modeling that estimates the likelihood of dying from volcanic, super volcanic eruptions or meteors hitting or natural pandemics because we have experience from the past. But we cannot use this approach to predict, well, how likely it is we're going to die from our own nuclear wars or AI eating us or a man-made pandemic. I did an interview with Toby Orto wrote a book called The Precipice where he discusses these likelihoods as well. Interesting story. So was this crane accident here consequence of an unknown unknown? I don't think so because they knew how important it is that the hook doesn't break, right? So they put a safety factor of three, they told me, into the hook design. But if the process in manufacturing fails, well, what do you do, right? You can't, your model won't predict. So, all right, models, they're not perfect, but what else? There is a nice example that maybe gives a bit of a counterpoint to detailed modeling. There is something called a fast and frugal tree, which is a very simple decision tree, basically, to decide whether a patient who shows up in the emergency room should be moved to the intensive care unit or to a regular care unit. And as you can see, there is only basically very few three yes, no answers. We don't have to discuss what these mean in detail. This thing performs better than a machine learning model that takes dozens of factors into account. So the doctors would say something like Hammersche Ermossog macht, which is German for, well, we've always known that we don't need this stupid machine learning stuff, right? But the point is more data, more detailed modeling doesn't always mean better outcome, right? Sometimes common sense and just experience of humans is something that is relevant, especially also when interpreting models. And of course, models change over time, right? That's science. As we get new insights, we update how our models work from Newton to Einstein to a grand unified theory, maybe at some point. So models are everywhere. The use of models allows us to forecast developments and quantity for quantified uncertainties. That's cool. Models make influencing variables and their effects explicit, right? The explanatory models can even help understand something. Models are the basis for constructive discussion. This is really important. When you have a model, you can constructively disagree whether some additional parameter should be taken into account or whatever. You cannot do that if you just run around and claim shit, right? As some people do in this pandemic. But of course, boundary conditions and limits of modeling must be considered. And in the end, in case of doubt, crap in, crap out is always true here as well. All right. This brings me to the end of the talk. Interestingly, I took two minutes longer than in my trial. Sorry for running a little bit over time. But I'm done now. There is a book that you might want to check out. And of course, there are the podcast episodes listed here that are most relevant to the stuff we talked about. Obviously, 330 more. But these are the ones that have direct influence on this talk. Second, whether path dependence isn't just a lack of proper accounting of state, or if the person asking missed something there. Sure. I mean, it's similar to this problem with chaos, right? If you could track everything to arbitrary detail and could keep track of everything, then maybe path dependence would not be a thing. But we know that's not possible in practice. Yes. I think that's it from my standpoint right now. There aren't any more questions. I am aware of. So chat has any more. There is something more in the IRC. It doesn't look like it. Yeah, I think we can end here.
 Alright, and a lovely welcome back to the Huck stage this evening.  Here to present you a talk about models in science, opportunities and mechanisms, limitations  by Markus Völter. He will be talking about scientific models, what they do, how they  work, what are they, and they are quite in the news right now because of the coronavirus  and climate change. And with models you can do a lot, you can model things, but for the  public it's not always quite apparent how they work and what they do. So we have our  own streaming site with an IRC and no JavaScript. If you don't like that go to live.hack.media.  There you can also ask questions in the IRC or via Twitter with the hashtag R3Huck. And  apart from that I think we're good to go. So I'm giving over to Markus.  Alright, so talk. It's scheduled for 90 minutes. I might take a little bit longer, but it  should be interesting. Alright, so I want to talk about models. I'll cover topics like  the difference between analytical numerical parametric models, forecasting versus explanation,  abstraction and simplification, statistics, forecasting the past sounds stupid, but it's  useful. Sensitivity analysis, optimization, forecasting versus scenarios, fitting of data,  fake numerical precision, chaos, emergence and unknown unknown. That's quite a lot of  stuff. So I'll run rather fast as you'll notice. The examples will be taken from cranes, pendulums,  weather and climate, flight simulators, sheep and ants, gravitational waves, fusion, the  LHC, the event horizon telescope, cellular automata attribute, turquoise. And you might  ask yourself why the hell is this guy talking about you have some background. I'm a physics  engineer and a computer scientist, but more importantly over the last 12 actually years,  I ran a science podcast called Omega tau, and just an engineer for about 600 hours. And  that's basically where all of the material of this talk comes from. The podcast also  gave me an hour in the backseat of an F 16, which of course was the highlight. Alright,  so let's get started. Let's get started. You probably have all seen these large steel  monsters. And if you look closely at these little traffic light kind of thing, the cabin,  it signals to outside personnel the load of the crane, not the weight that is on the hook,  but the actual stress on the crane, the load on the crane. And of course, obviously, that  means what you'd expect. Okay, be careful and at the limit. And so what is the load  of the crane? Well, one is the bending of the boom, right? The boom is a long stick  that is of course bent from the weight that's at its tip on the hook. And of course, also  the stability, the balance of the lifted mass and the counter mass, I should say counterweight.  So how does the crane know all of these things? Well, there's a model that calculates this  and drives the traffic lights. And let's investigate what goes into that model. Well, one, of course,  there's the weight that is currently being lifted, the more weight, the higher the bending  moment on the boom. The length of the boom is relevant. Of course, these booms are telescopic  and if they're longer, you have for the same lifted weight you have or mass, you have more  bending moment. The angle of the boom, obviously, you can lower it and also, you know, make  the angle steeper and the lower the angle of the boom, again, the higher the bending  moment because the radius is larger. There are additional wires and poles you can use  to stiffen up the whole construction. And if you have those installed, then your bending  moment is less for a given lifted weight. And finally, wind, because if the wind moves  your lifted mass sideways, this leads to sideways bending of the boom, which lowers the overall  stability. So that's for the bending. For the balance, obviously, the relationship between  the lifted weight and the counterweight and their respective radii is relevant. So that  is something that's taken into account and the distance slash radius of the stanchions.  The further out you have moved them, the bigger is the, if you will, footprint of the crane  and the more stable it stands. So these two aspects of overall load are calculated separately  and whenever one of them reaches, you know, critical level, that is, that drives the traffic  light. So how is this done? Well, for the stability for the balance, we simply use the  lever principle, right? So you basically calculate the two moments, the actual lifted weight  is measured from the pressure in the hydraulic cylinders, the counterweight is configured.  And then you know the two radii, you can calculate those as well from the angle and the length  of the boom. And then you can just simply figure out whether the crane is stable, the  balance is in balance. For the bending, it's a little bit more interesting because here  what you basically do is you run an FEM analysis, finite element analysis, where you basically  simulate every little discrete piece of boom material and run a numerical simulation, a  numerical model that figures out where the load is high and when it reaches a limited  any of these discrete small finite volumes. And of course, you can't run this in real  time in the crane, which is why the results of this analysis are abstracted into basically  lookup tables, right? This is called a parametric model. We'll get back to these model categories  later. But that's basically how it works. And so there is an interesting thing that happened  this year, or maybe it was last year, this is a 750 ton crane, the LTM7050-9.1 manufactured  by Leipzig. And again, it can lift 750 tons. Well, it was able to do 750 until earlier  this year, because now it can do 800. Only because of a software update, nothing changed  in the actual construction of the machine. In fact, existing cranes can be updated retrospectively.  So how does this work? Well, there's something translated from the Leipzig website. It says,  we completely recalculated the crane more and more precise FEM models, more and more  precise FEM models, I should say, on faster computing hardware, permit a less conservative  approach. The latest regulations regarding the load bearing capacity in compliance with  polyplicable standards, blah, blah, blah. So basically, they have newer modeling tools,  both in terms of algorithms and software and machinery, computers. And now they can be  a little bit less pessimistic, conservative about what the crane can lift. And so the  software update basically installed new lookup tables, and now the same machine can lift  50 tons more. Regarding the balance, I talked to a bunch of crane operators this year, obviously,  and one told me, you know, today it's basically impossible to knock over a crane to bring  it out of balance so that it actually falls over. Oops, this is from 2013, where one of  these large Leipel tracked cranes fell over in Brazil during the construction of their  Olympic Stadium. And the problem there was surface stability, right? So the ground gave  in. These cranes produce a significant pressure on the ground. And if the ground isn't suitably  prepared, then the whole thing falls over. And obviously, the model that, you know, takes  that considers, as we have seen, the levers of the weight and the counterweight can't  know about this. So this is a problem. Here's another example of something that went wrong.  A large shipboard crane in Rostock, Germany, completely crashed. And so again, is this  a modeling problem? Well, no, not really. It was very likely a material fall the production  mistake in the hook itself, the hook broke, and then the whole boom basically snapped  over backwards, completely destroying the crane, millions of millions of, you know,  money lost and several people hurt. Big, big drama. So what can we learn about this? We  have to be really careful about what goes in a model. The model sounds trivial, but  the model doesn't make any statement about whatever hasn't been put into it. Like, for  example, the status of the ground or the material quality of the hook. And these assumptions  and constraints must be well defined that they must be communicated to the users. So  is this a useful model? It's a Lego, actually, yeah, it's a Lego model of one of these LTM  1750 cranes. It's not useful for understanding the load capacity, because obviously the Lego  has no, you know, relationship to the real thing in terms of stability. But you can explain  in principle how the crane works, you know, with with extensions and telescopic booms and  stuff. So it can serve as a model for illustrating that it might serve as a model for worksite  planning. You know, if you have the worksite in the same scale, then why not, right? So  this model also has its purposes, but it's not the same purpose as these mathematical  models that we've talked about before. So again, the user of a model has got to know  what's in the model, what the purpose is, and the modeler has to decide what is important,  what impacts the results. So let's define the notion of model. It's an abstract representation  of something that exists in real life in the real world, expressed in a suitable language  like chemistry, physics, math, Lego should be an Oh, not ah, for the purpose of understanding,  prediction, optimization, proof or production of that real world thing, the proof and production  part will ignore in this talk, we're going to look at understanding prediction optimization.  So when you build a model, you have to think about what part of the reality you want to  represent in your model, what is relevant to represent that part faithfully in the model,  how to represent and compute, right? I mean, you have to somehow make it quote, runnable,  mathematically calculatable or in other ways executable. You have to think about how do  you observe parts of the reality that serve as input to the model, and then what is the  relevance and trust of the output. Again, if you don't input something about the ground,  then you already gave you can only measure that unreliably, then the relevance of the  output and the trust level of the output is low, we'll get back to that. So let's revisit  analytical, numeric and parametric models. Here's a very simple analytic model. It's  a differential equation of the movement of a pendulum, right? It basically says that  the angular acceleration, which is what the left term says, basically depends on the angle  itself on the sinus on the sign of the angle. And then you multiply it basically by the  fraction of the earth acceleration and the length of the pendulum. And so an analytical  model is basically where you use precise or approximate equations, as we'll see this one  as approximate. And then for dynamical systems, these are often differential equations which  relate a quantity to its first or second or whatever, a derivative. Again, here it relates  the angle of the angle phi to the second derivative of that same angle. And so again, an analytical  model is what we all know from school as formula equations. Now, a numerical model is more  interesting because it in practice plays a more relevant role for what we hear about  models today. What you do is you discretize your world. In the finite element analysis  we saw in the context of Cranes before, you basically discretized the overall boom into  finite small volumes of steel. In climate and weather models, you discretize the atmosphere  into volumes of air. If you do epidemiology, you have subsets of the population. And then  you reassemble the overall system by basically joining all these little volumes and computing  a whole bunch of properties for each of these, I call these properties E for eigenshaft,  sorry, change that, the properties. And you then again from the calculated properties  of each of these small volumes, you reassemble the overall story. And then you also typically,  if this is a system that evolves over time, you iterate over time. So again, for the weather,  you have small volumes of air, you calculate various properties for each of them, and then  you run this thing over time. There's a bunch of constraints. One is that you have to make  sure that the changes are plausible both in time and space. What I mean by that is, if  you have a weather forecast and it says, at time t equals one, the temperature at some  location is 20 degrees, and 10 minutes later, it's 10 degrees, there's probably something  wrong. Same is for spatial plausibility. If you have 10 degrees in Schuttgart and 20 degrees  in Esslingen city nearby, it's probably strange. So you have to make sure that either by design,  the model doesn't jump both in time and space or whatever other discretization dimension  you've used. Or if this is an outcome, then your model is wrong if things jump. So basically,  you still calculate with equations in numerical models, but these are discretized and often  spatially and temporarily. These are the most obvious discretizations, but of course, others  might be used as well. If you use smaller boxes, smaller discrete volumes, you get higher  resolution. Same if you use smaller time steps. So this gives you increased precision. In  some cases, it gives you correctness. For example, in control theory, if you have two  large time steps, you might not get a control algorithm that is stable because of its large  time steps. It can't see oscillations and control those. So the algorithm isn't just  imprecise, it doesn't work if you don't use a fine grained high resolution time. Same  thing in some cases for space. If you want to forecast thermals, the stuff that propels  gliders up, warm air rising above mountain peaks and you have a coarse grained resolution  of your terrain, then these peaks are averaged out and you will not be able to produce correct  predictions of how and when thermals develop above those peaks. It's something glider pilots  know very well when they fly in mountainous areas that the forecasts are often wrong.  And then of course, the drawback of a high resolution is that you need more computational  power. And even today, with faster and faster computers, it's still quite plausible. Scientists  still have to make lots of compromises in various ways, for example, in resolution to  make it feasible to run on existing machines. And then of course, you can compose these,  for example, the ECMWF, the European Center for Medium Range Weather Forecasting, runs  a worldwide weather model. They use 9 by 9 kilometers horizontal resolution and 500 meters  vertical resolution, up to 80 kilometers by the way. And then the German Weather Service,  the DVD, they have a higher resolution model, but only for Germany. And basically, they  use the more coarse grained model from the ECMWF as a boundary condition for what the,  and also means of initialization, initializing data for the finer grained model. And by the  way, weather models calculate around 50 of these properties. So lots of stuff going on  there. And so you can see easily why even large computers can be utilized completely  with this approach. So let's look at parametric models again. We look at cloud formation.  You can see a beautiful picture of clouds here. And the question is, you know, what  kind of cloud forms, how much of the sky is covered by clouds? What is their lower and  upper limit called base and ceiling? And there's a lot of parameters to go in, right? The position  of the sun, basically time of day, how much high clouds you have that limit the energy  imparted by the sun, then of course, humidity, pressure, temperature, properties of the ground,  the elevation of the ground. And so you want to, if you want to compute this algorithmically,  there's lots of chemical and physical processes going on. Some of them are theoretically not  even known. Lots of small things happening, lots of complex interactions. So basically,  what you do in principle, again, is you discretize and you associate all these interesting properties  with each of these discretized air volumes. But you can't really run this as a numerical  model, because again, some things aren't known, interactions are complex, it would take too  long. So what do you do? You basically put all these things into a series of lookup tables,  right? So for example, you know properties E1 and E2 from, let's say observations. And  from those, you calculate some property X. And then this property X together with properties  three and four, you put that into a simple equation, which gives you a property Y, which  you then use in another lookup table together with property E5, and you get the result.  So this is basically a very simple lookup table and or set of equations. And of course, those  are as we've seen with the crane filled by numerical models, analytical models and experiments,  right? Experiments, even if you don't know how something works, you can easily just take  the experiment results and package them into a parametric model, which you then run to  make a forecast. Another example of a very simple parametric model comes from medicine.  This is actually the only software example, I think in my whole talk, I built an application  in the healthcare domain not too long ago, where, for example, from the systolic and  diastolic blood pressure, depending on the ranges there in, you calculate a risk factor,  which you then use, for example, together with the age and the weight of the patient  to make further decisions regarding treatment. At combining these different kinds of models,  this is a picture of a aircraft, which many of you probably know from the movie Top Gun.  Although this is not actually a picture of a real aircraft. This is a screenshot from  the DCS. Here's another one looks beautifully realistic. So that would be another example  of models is how do you model these surfaces and how do you reflect it. But we're going  to talk about something else and that is the modeling of the aeromechanical properties  of so let's say we are a Maverick and you know, you know, we're flying around in Top  Gun with goose on the goose that he's going to turn right. So he'll smash the stick to  the right. What happens next, right? How does the simulator simulate reacts when the pilot  moves the stick to the right? So we have the stick movement, which basically is translated  simply, you know, stick angle becomes a percentage of deflection. And that's the input to the  hydromechanical flight control system. And now you have to think about to what degree  the arrow surfaces in this case, it's elephants and spoilers on the wing to what degree they  are deflected. And interestingly, they actually calculate that in the simulator. And they  calculate that based on the current hydraulic pressure in the simulated hydraulic system,  because if we 28 shot away half of it, you know, remember Top Gun, then you have less  pressure and you had in your hydraulic system and the deflections are slower. Then you get  the you find out what your flap settings are, you find out what the wings we angle is. As  you remember from Top Gun, the wing, the F 14 has sweepable wings, right, to adapt the  wing to different speed table. What is the coefficient of lift for that deflection for  this flap setting and this wing sweep? And this is a parametric model, which happily  NASA did in the 70s, they put one of these aircraft into the wind tunnel and measured  all of these things. And those guys somehow got hold of this wind tunnel data. And now  that we have the coefficient of lift, we can basically calculate the actual lift force.  And we do that by multiplying the coefficient with a bunch of properties of the aircraft,  but also specifically with the speed of the aircraft, which they get from the simulation  environment. So there's another calculation. And then they look at again, the wings speak  as wing sweep angle, which gives them an inertia. And they know how much fuel is in the wing  in the simulator because they know how much fuel the engine has burned since they took  off. And they take this information to actually calculate the inertial moment that acts against  the movement from the differential lift of the two sides. So, you know, and this then  gives you a role, role movement. So the point is that I'm trying to illustrate here how  this overall model uses analytical, meaning calculations and parametric models jointly  in one, if you will, big calculation, relying on previously calculated numerical data,  in this case, stuff that NASA has figured out in the wind tunnel. Now, models aren't  just relevant for controlling simulated airplane on a PC. There's also actually a model very  prominently used in the flight control system of an Airbus A320 and of course, of all subsequent  Airbus airplanes. So the way you actually fly an Airbus is that you move the stick. And  what this does literally is that the stick flies an idealized airplane, a model of an  idealized airplane in the computer. Then the various attitude sensors and, you know, air  data computers, they measure what is the state of the physical aircraft, things like, you  know, angle of attack, roll angle, stuff like that. And then there is obviously a difference  between the model that the pilot flies, the idealized airplane and the real one. And then  you have control algorithms that decide how best to get the state of the real aircraft  in sync with what the pilot wants the aircraft to fly like based on its input into the idealized  aircraft model. And it's interesting because if, for example, one of the flight computers  has failed and you cannot control your ailerons, then you still use the same flight inputs.  But of course, the system then figures out how to use, for example, the spoilers to produce  the roll rate in order to bring the state of the real aircraft in line with the model.  So to wrap up that part of the talk, we have analytical, numerical and parametric models.  The models are basically functions, if you will, equations that take a bunch of inputs  and you can calculate the output you're interested in directly for every point in time for every  kind of combination of inputs. The quantities you calculate with are usually continuous  and the equations are physics or whatever else chemistry, biology, but it's the real  science in a numerical model, you discretize basically the analytical world, you iterate  then. And typically the iteration, well, almost always your iteration will depend on the previous  state of, you know, in the last time step, for example. And this means that you can't  just say, hey, model, give me the state at t equals 5000 seconds, because in order to  know that the model has to calculate, you know, for all 5000 previous time steps, and  that makes these kinds of numerical models much less flexible. On the other hand, they're  much simpler because solving complex, you know, systems of equations numerically is  much easier than analytically. The equations are still basically the real science, but  the quantities are discrete. In a parametric model, you can again have a direct look up,  it's not expensive, but the quantities are usually much more coarse grained and the  equations are not necessarily somehow resembling the real science. They might be completely  opaque, right? They might be completely just numbers you figured out somehow, and you know  they kind of work and you use them, but they don't tell you anything about how the real  world works. They make a prediction, but they don't explain. So let's elaborate on that  difference. Let's say you have the real world changing somehow as shown in this lower dark  gray box, and the reality changes basically as a straight line. This wobbly change is  sensed by your model as a step function, the model calculates and outputs some kind of  reaction. Okay, that's fine. That is a prediction. So the model expresses or gives you information  about how reality will change as a consequence of whatever impulse you are interested in.  How does the weather change if temperature increases? How does the virus spread rate  change if 60% of people will wear FFP2 masks, right? Stuff like that. But there's no explanation  going on, which raises the question, what actually is an explanation? And I struggled  with this quite a bit because what is the difference between the how and the why? Isn't  the why also kind of how do you make the difference? And I interviewed somebody from CERN and  he gave me a very, very interesting definition of what why means in this context. He says  that if a model produces its prediction through applying a more general theory to this particular  case, right? If you don't have, if you will, a theory specifically for this problem, but  if you have a more general theory and the model, if you will configures that theory  in order to produce a correct prediction, then if you look at the configuration of that  model, you have the why you have the explanation. Examples for such for such general theories  are of course Newton's laws or quantum chromodynamics or Darwin's evolution or some kind of reaction  kinetics in chemistry, right? And so this really is a better model because it just doesn't  just predict. It also explains why it makes that prediction. It explains the underlying  mechanisms, which is again more useful. Now here is an example, a category of models that  don't do that, right? You have probably all know what this resembles here. This is a neural  network, which has a bunch of inputs and a whole bunch of weights and an output. So the  neural network makes a prediction, right? It's the ultimate form of a parametric model  because each of the weights here in that neural network and there are millions in real networks  is a parameter. And it is not at all transparent what each of these millions of parameters  means and what the model has learned. You can test and that's what people do. But if  you forget to test certain things, you have no idea how the model will behave. And there  is this funny example where people were trying to build a machine learning model neural network  to recognize sheep, right? The idea was to, oh, it should be idea. The idea was to make  the model learn the shape of sheep. But of course, what that particular model learned  was the green of the grass on which shapes, sheep are usually photographed. And so when  you showed the thing just green pastures, it also detected sheep. And so basically such  an opaque pure parametric model will produce wrong results with some probability for new  situations. And the problem is that you don't necessarily know what a new situation is because  you have no clue, you know, what the thing has learned. Obviously you test. But testing  as we all know from programming, but not sure if we all know, but as programmers know,  testing can only prove the presence of the bug, never the absence of bugs. And you have  that problem here. So this really doesn't matter for advertising. It's annoying if they  try to sell me the same shoes that I just bought, right? Or tried to sell me, I don't  know, you know, orange hats, which I will never buy. But it's not really a problem.  It is more of a problem if people aren't given credit because some stupid machine learning  algorithm has basically, you know, incorporated some discriminatory decision based on stupid  training data. And it's really a problem. It's potentially fatal in autonomous driving.  So there's a whole thing about, you know, trustworthy machine learning and, you know,  understanding what a model learned, but that's in its in its early stages. So let's look at  abstraction and simplification again, back to our simple pendulum. And we can ask how  quickly will this thing pendule back and forth? And yes, I know, pendule is not an English  word, but I thought it's funny. So what's the period of this pendulum? And if you look  at the Wikipedia article for this, you get a very long formula and you can see the three  dots. So it continues. I did actually a screenshot of Wikipedia because it was too lazy to type  this up in a formula editor myself because it's so long. The point is that you can see  that this period depends on the angle. So if you, you know, move the pendulum further  out, it, you know, oscillates with a different rate than if you move it out only a little  bit. And you can make a simple, you keep simplification for very small angles where the sign of the  angle is basically the number, the angle itself, sign x equals x, then you can simplify for  small angles that the period is two pi square root of L over G. And that is probably the  formula you learned in school, which is completely fine. It gives you the right result. If you  stay within that range for which the simplification is valid, right? And it gives you wrong results  outside of that validity range. So this is another one of these things. If a model has  been built for a certain limited parameter range, if you will, or range of inputs, and  you use it outside, the forecast is wrong. The obvious example here also is Newton's  mechanics because Newton's mechanics are wrong, right? Because Einstein showed that things  are quite a bit more complicated with a special and general relativity. But we also know that  for our everyday world, because we are at low speeds and relatively low gravitational  forces, Newton is good enough. But you have to be aware of this. If you try to calculate  the path and trajectories of spaceships with Newton, you will not get the results at the  required position that you expect. So another question, will this thing oscillate forever?  And if you look at this formula again, there is nothing that seems to slow this thing down.  So this formula is actually given with no damping, right? So this thing will just continue  forever and we know experientially that that's not the case. Stuff will stop oscillating  at some point because of aerodynamic drag of the weight and also because of internal  friction within the wire that holds the weight. So actually it looks like this, right? So  it will become less and at some point it will stop. Now again, importantly, for your pendulum  clock, right? I think it's called grandfather clock in English, right? I'm not sure. It  doesn't really matter because you'll add additional energy to the clock every evening,  you know, right around target show anyway. And so it doesn't really matter. But if you  try to work with this kind of problem, then it is a concern. Not sure if you recognize  this picture. It basically, sorry, represents the how a gravitational wave looks like in  2016. The LIGO gravitational wave detectors have heard gravitational waves for the first  time. And again, here is here's this thing again. This shows time on the x axis and the  frequency of the wave on the y axis and the darker the shape, the more intense the louder  the stronger the wave. So they call this a chirp because it basically sounds like right  because it gets a high frequency increases becomes louder like a bird's chirp. So how  do those guys detect gravitational waves? Well, they have a interferometer, which basically  sorry, which means that they send in a laser pulse along one arm, the laser is reflected,  passes through a semi transparent mirror along another arm that is orthogonal to the first  one, reflected again, and then back to a place where the two laser beams that went through  either or both arms are interfered. And if the two beams arrive in phase, there will  be constructive interference. Whereas if they arrive exactly out of phase, then the output  will become dark. So any difference in length between the two arms will change the interference  pattern at the output. That's the idea. And so if the gravitational wave passes by and  makes one arm longer and the other one shorter, I hope you can see this on my great wonderful  animation here, then you can see this thing basically vibrate the output vibrates visually.  Well, I mean, lots of detectors going on, but principally, of course, this only works  if these mirrors here on either end don't vibrate just so right. They told me the story  when I visited the Geo 600 detector, whenever the package delivery guy drives too fast along  the axis way to their side there, they can see the mirrors vibrate and they're telling  the post guys to go slow. And whenever a new post guy shows up, destroys the measurement.  So what they do is they attach these mirrors to two level pendulums because pendulums  actually when they have a high mass have a very good damping about 1000. And so with  this triple pendulum here, they can get a damping a passive damping of I think 1000  to the power of three, that would be 10 to the power of nine, right? And then they do  some active damping as well. They precisely understand the behavior of the laser. They  even optimize and understand and measure and change and, you know, try to limit shot noise.  And so my point here is you don't have to understand the damping of a pendulum for your  stupid clock, but you do have to understand it very precisely if you want to distinguish  the natural pendulum behavior from, you know, environment, postal guys and little earthquakes,  if you want to distinguish that from whatever a gravitational wave does. So all models are  simplifications, even the one for the gravitational gravitational gravitational wave detector,  but how and how far depends on a model's purpose. Let's look at another example. I visited  the Wendelstein 7x stellarator fusion experiment in Greifswald and I asked them, so how do  you guys model the plasma in the reactor? And they told me, well, it's not so easy.  They have one model that models it as a fluid. It's called magneto hydrodynamics. The other  one models it as a mix of two gases, right? The electron gas and the nuclear gas, basically.  They can also model it as small particles that are disc-like and they can model it as  point-like particles that move on this disc, on the circle around on this disc because  of the magnetic field configuration. And they use all of them, right? Depending on what  they want to do, they use all of them. Obviously, the MHD model on the left doesn't give you  detailed information about a particular particle, but if you want to characterize the overall  behavior of the fluid as, sorry, of the plasma as a body that is inside the reactor, then  that's good enough. And obviously, each of these models have to make the same prediction  when you get to a boundary case from which on you use the other representation, another  kind of physical constraint. Let's look at this example. I'm not sure if people recognize.  This is the configuration of the various accelerators at CERN. The big ring is the large Hadron  Collider and the smaller rings are earlier colliders that are now used as accelerators  as pre-accelerators before the Hadrons enter the large storage ring. And the LHC has these  huge experiments. You see the person standing there at the bottom. These huge experiments  which capture what happens when particles from these beams collide. And again, here's  another picture here and again, consider the people for reference. The way these detectors  work is basically that you have a whole bunch of different detecting elements arranged around  the center collision point and when particles fly out, then they hit these sub detectors  as they are called and produces some kind of electronic signal and that is then used.  Quick comment to the technical people here. I get a lot of noise on my mumble channel.  Not sure who should mute their microphone there. Here is an illustration of one of these  collision events. You can see how the particles stream in from the center through which the  two particles that collide travel. And then you can see how the various collision products  stream out and how they light up the various detector surfaces. And what this shows here  is the collision of two protons which forms a Higgs boson which then decays to two bottom  quarks and to a W boson which then also decays. How do we know, right? How the heck do they  know what's happening? What's going on here? So let's first understand a little bit how  these detectors work. Fundamentally, what they do is they have a very strong magnetic field  and if a particle that has some electromagnetic charge and most of them have, otherwise it's  hard to detect them actually, then again a little bit of school physics, Lawrence force  and stuff like that, the particle will be bent around a circular track by the magnetic  field. And then they have different kinds of detectors. And for example, if you look  at a electron here, that's the second example from the top, it leaves a trace in what's  called the silicon tracker and then it decays in the electromagnetic calorimeter. And so  if you look at the various different particles, each of them leaves traces in a different  combination of detecting elements. So this gives you the type of particle. And then through  the bending, you can measure its momentum and basically through type and momentum, you  get a unique characterization of what's going on. You can even calculate the overall energy  balance and stuff like that and the momentum balance and it's very sophisticated, really  interesting stuff. So in this case, in the example I gave, we have a Higgs boson that  decays in various ways. I've just called these particles A through F here, doesn't really  matter what they are. And these decays, they are multi step. So what the detector actually  sees is what they call the final state, which is these decay products. What the scientists  are interested in is what actually happens in the collision. And so the challenges after  observing the final state, the decay products with the detector, you want to calculate back  what actually happened in the collision. Was there a Higgs or wasn't there a Higgs? And  what is the mass of that Higgs boson? That was the big question back then. And I think  2013, when they discovered it, by the way, Einstein has nothing to do with this. I just  used the picture. So in German, we say there are Haken, right? It's not so easy. There  are problems. And so I used this picture of a hook. It doesn't really work in English.  But so what are some of the challenges they have to overcome? Well, we have seen that  the Higgs decays in multiple ways. And each of these decays happens with a certain probability.  So they have to somehow untangle that. The decays are non unique. As you can see in this  example, this hypothetical E particle can either arise from H to B to E or from H to  A to D to E. So just because you see an E, you don't really know what happened in between.  And these collisions are not unique, depending on how exactly, you know, how well the protons  align in their collision. You either get hard collisions or soft collisions or any intermediate  state. And so the created particles, the kind, their energy depends on whether it was a soft  or a hard collision and all kinds of other parameters. So that is also a source of complexity.  And then finally, this detector, I mean, these detectors are marvels of engineering. They're  also terribly complex. Each of these components has their own failure modes and, you know,  failure models. And these are complex systems in themselves. So again, how do they know  what they're observing? And how do they know that with, you know, with five sigma? Five  sigma is a measure of the, basically a measure of the trust in the result. Five sigma is  the threshold in physics for a discovery. And five sigma means that, that there is a  probability of 0.00057 something percent that the observation happened by chance and not  and is not the effect that they assume in terms of physics. And this is also quite related  to the P value that's used in statistics. It's inversely proportional to the amount  of data, the more data you have, the higher the trust. And of course, also inversely  proportional to the size of the effect, the bigger the effect, the higher the trust. By  the way, it's interesting to compare these five sigmas to the P values they use in medical  trials, right? They are happy if they get 5% not 0.00000057. It's quite a big difference.  So how the hell do they do that? Well, statistics, right? They simulate billions of events to  understand the distribution of what will happen. So how does this work? So they have what's  called an event generator. It's a software model that simulates the physics of decay  after a collision, right? So you basically specify collision parameters. Is it a hard  or a soft collision? And then this thing gives you a distribution of particle vectors of  basically what's streaming out of this collision site. Then they have what's called an experiment  model. It's called GN4. It is a complete, well, obviously it's a simplification, but  it's a representation of the actual detector and of the physics in the detectors themselves  because I mean the detectors work by basically running certain physical processes when the  particles interact with the detector material that is simulated in this model. This gives  you then simulated detector hits. Then they have basically an electronic simulator that  has a noise model for all of the electronics of these detectors. And this gives you simulated  raw data and they run billions of these simulated collisions in order to get what they get.  What they call the background, which is what would they see in this detector statistically  if there wasn't any Higgs, right? So they run these simulations without Higgs, just the  other nuclear processes. And then they take the measurements and they compare. And then  this is the screenshot of what Atlas saw. And you can see that at 125 giga electron walls,  there is some kind of peak and that is the Higgs boson. And they basically find this  out through statistical calculations based on huge amounts of data. This is why they  have some of the largest computing centers. They run millions and billions lines of code  in these various simulators developed over decades. Of course, good old Fortran is still  the backbone. They also use Python for a lot. And they have, I think it's terabytes of data.  There's a whole worldwide distribution and scheduling infrastructure for calculating  and running all these simulations. There's a huge infrastructure behind this in order  to get enough data to find out with some degree of trust that in this case they discovered  the Higgs. So how can we build trust in models? Well, one way, we can run lots of experiments  with lots of data and then do statistics. Now, experiments are nice because they give you  controlled conditions. They allow you to isolate various influencing factors by controlling for  them. And so you can, if you see stuff correlated, it's relatively easy to derive causality. So,  instead of just saying, this happens and that happens. And whenever this happens, that happens.  You can also say, because this happens, that happens. That is causality. But sometimes you  can't do experiments in climate or epidemiology or economics or many societally relevant questions.  You can't really run an experiment. I mean, in some sense, we run an experiment with our  atmosphere, but you can't build another planet and run a climate experiment in that sense.  So what you have to do then is you have to fall back on just observation where you do not have  controlled conditions. You cannot isolate influencing factors, at least usually you can't.  And so you really just get correlation. And then you have to make an attempt at deriving  causality. But that's much harder. Sometimes you're lucky, right? You have natural experiments. The  economics profession tries to use that when they say, in this country, when they did this and that,  it gave them inflation. And in this other country, whether it was the following difference, there  was no inflation. And so then because of that following difference, they claim this is what  produces inflation. But of course, again, you never know what else has changed, right? It's  harder. It's maybe a bit easier in epidemiology these days. The factors aren't that different.  So maybe looking at other countries that do stronger lockdowns is a good idea. Different story.  So what can we do, again, if we don't really have a way of running experiments in that sense?  Let's say we want to run some kind of forecast. And we know that this forecast depends on some  kind of parameter. P is a parameter that we have to tune in our model for the forecast to be correct.  But again, we can't run, we can't validate easily. So we have no data for comparison because we want  to forecast the future. Well, the forecast is a good example. Well, what we can do is we can  forecast the past, right? So we can move back in time and run the forecast from a point in the past  where we do know what actually happened in the real world. And then we can tune our parameter P,  in this case, P2, some value P2, is the best setting for P in order to fit our forecast best  with the actual data that we know because they happened in the past. And then we can continue  using this parameter for the future. This actually happens in weather forecasting. There it's called  re-forecasting. And these weather models that are continuously run the various weather services,  they continuously basically go back and forth between re-forecasting for parameter tuning and  also for filling in inputs that they don't know because there is not a way to find the temperature  everywhere above the ocean, only where there are ships, right? And a bunch of weather buoys. So  they can just go back and forth to do this kind of stuff. And so this is really the backbone of  weather forecasting. So another way of building trust in models is re-forecasting the past. Now,  all models are simplifications. We've talked about that, right? And so the question is,  if we simplify which of potentially many parameters can we ignore, which are important,  right? So here is another model M. It has three parameters P1, P2 and P3. I realize I used P2  as a value on the previous example. Here it's the name for a different parameter. Not a good  decision. I'm sorry. So we have three parameters P1 through 3. And we don't know which of them is  important. Well, what we can do is we can scan through the ranges of all of these parameters  and see which scan has the largest output or the I should say the largest consequence on the  output of the model. In this case, we can see delta M for P3 is the largest one, right? So we  know P3 has the largest influence. By the way, there might be an even larger influence when we  combine the scanning of P1 and P3. So we have a combinatorics problem. I don't know. I forget  which scientist I talked with when I asked about that. And they said, well, we don't do these  combinations. It's too complicated. So that's another simplification. They treat each of these  parameters as uncorrelated with others, which might or might not be correct. Anyway, so we find  out that this model here is sensitive to the value of P3. And so what does this mean? Well,  it means we have to invest effort or computational power into determining P3 precisely. Or if we  can do that again, because we might not have a way of finding the value because we don't have,  you know, temperature sensors all over the ocean. Maybe satellites can help, but different topic.  Then we have to always vary P3. And whenever we make a forecast, make it for the whole range of  P3 and see what this gives us. And this is, well, more or less, this is what ensemble forecasting  is called in meteorology, where they run different models, different parameterizations of the same  models, and also different values of the input conditions, where they are not known, in order  to basically get a probability distribution of outputs, right? So they might vary the temperature  at a given point, run the forecast, and they get a probability distribution of the output. And then  they either communicate the probability distribution to their users, or they just give you the result  that is most probable. There is a weather forecasting service called Meteo Blue. And I like them  because if you look at this screenshot from the left, you can see in German, of course, the  Treff Sicherheit, the Wetterprognose is middle. The reliability of this prognosis is, sorry,  is medium. And now you can click on a button and you now get what they call the multi model.  This is essentially a, if you will, sensitivity analysis. It shows you what the different  models forecast, and you can nicely see if you actually go to the page how they diverge more  over time. They even give you the verification. They basically tell you how good this model was  in the last three days. So they give you a lot of information in actually, if you want to invest  the time in analyzing which, how reliable the model is. And this particular one is used by  glider pilots. I used the example from GAP. It's a favorite gliding site in southern France and  people spent half the morning over this and other forecast to figure out what the weather will be.  Now, in epidemiology, things are really simple, right? It's exponential growth, meaning the  infection rate will grow exponentially with some factor. This B here is kind of what we know as  R. It's not exactly the same, but for now it's good enough, right? But we also know it's not  really like that, right? If there are no more people left that can be infected or more generally,  if there are no more resources, resources, which an exponential growth can, if you will grow into,  then the growth has to stop. It's called the logistic growth model as opposed to an exponential  growth model. And we know everybody knows now that if you will, the herd immunity is the step or is  the amount of infection where there are no more people left to be infected or where at least the  infection rate becomes quote inefficient from the perspective of the virus and the growth becomes  slower and at some point increased infection stops. So what else could there be, right? Simple.  Well, there is this website called COVIDSIM by a company called Xplosus and they have this COVID  simulator. And actually, there's a whole bunch of differential equations they use, like the number  of susceptible individuals, the individuals in various periods of infection, the number of  recovered individuals, the number of people who have died. So it's quite a bit more complicated.  Actually, it's way more complicated. There's lots of different dynamical equations. There are  intervention effects you might want to model. And there's a whole long range of parameters  that you can set and that you have to set, right? And so there's an interesting effect that I figured  out when I talked to one of these guys. The ratio at which the population reaches herd immunity  depends on how they break down the age groups. Now, I'm not talking about the actual age  distribution in the population. Obviously, if you have more people, more people will die. We know  that, right? That's our experience. What I'm talking about here is whether you split your  population into three groups, zero to 30, 30 to 60, 60 to infinity, or whether you split that same  age pyramid into 10 or 15 subgroups, the model makes different predictions.  Who'd have thought, right? So this is an example of a sensitivity analysis where you have to somehow  figure out what is a good way for this age structuring in your model. There's another  nice example for sensitivity analysis in fusion. So one thing they might want to optimize in their  reactor is how do you maximize the distance between the plasma and the reactor wall? Because as you  perhaps know that the plasma is very hot. It's stabilized through a magnetic field. And if the  reactor, sorry, if the plasma hits the wall, well, it might damage the wall, but more importantly,  the plasma will be damaged and might collapse. So you want to keep the plasma away from the wall.  And again, that's the point of the magnetic field. So one parameter you can tune is you can increase  or decrease the field, you can increase or decrease the gas density, you can increase or decrease the  number of neutral particles that are injected in as a way of injecting energy, basically, you can  change the temperature of the plasma. Point is that it's 10 to the 100 combinations. And how do  you do that? Right? So how do you make this optimization? Well, one way is you have to use the  simplest of these various representations of the plasma I mentioned before. So this is something  they do with the MHD, the fluid representation, because it's the simplest, it's the most efficient.  But also, again, even then, you know, we only have 10 to the power of 10 to the 85th atoms in the  universe. So 10 to the power of 100 combinations won't work. So this is where in these numerical  models, computer science comes in, right? Where you have various different optimization algorithms,  numerical solvers, you know, things like hill climbing, simulated annealing, not something  I want to cover in this talk. But I thought it was important to point out that it's not just  about finding the right model and the right abstractions and the right sense, you know,  deciding on the right parameters. There's a lot of cleverness going on here in the  programming and how you perhaps then also run this on a parallel computer. By the way,  little anecdote, I talked to a meteorologist a few days ago, actually, for a podcast interview,  and he said, it's going to be really painful when in the next or next next generation of  supercomputers, everything will be computed on graphics cards, because we can basically throw  away all our code and have to rewrite everything. So that's going to be painful. So how can we  build trust in models? We can vary parameters, do a sensitivity analysis and analyze the impact.  Now, I want to reemphasize something because somebody recently on Twitter told me that  this modeling for COVID seems to be shit because the forecasts were wrong. And this is a  forecast for wrong. And this person misunderstood something completely, and that is forecasting  versus scenarios. So let's say you have a model and you want to make the model correct,  you know, make the right predictions, but you can't take into account all of these millions  of different parameters. You have to find out which ones are the most relevant. So that's  when you, as we just learned, you run a sensitivity analysis, right? For example, you want to find  out the cloud formation, depending on temperature and humidity, the radiated energy by the earth,  depending on serious cloud coverage or the amount of precipitation, depending on layering of the  atmosphere, right? Once you figured that out, you put that into your model, and then you can  actually measure various data in the world and make forecasts, actual forecasts, that the output  of the model claims that this is how the weather will behave. Okay? That's what we do in forecasting.  Now let's look at another example. Let's say we want to figure out, or we're going to understand,  how the one-to-one infection rate depends on how much virus people shed when they breathe,  how the virus shedding depends on the kind of mask you wear, and how the one-to-many infection rate  depends on the rate of interpersonal contacts. In this case, you can then also make a sensitivity  analysis, run it on simulated data, and then what you get isn't the forecast, because you don't know  how people will behave. But what you get is scenarios. You can say that if you guys behave in the  following way, then the infection rate will increase. There's no point in saying the COVID forecast  was wrong, because it didn't make a forecast. It gave us scenarios that give us hints about how we  should behave. And of course, it's a bit frustrating. We have a healthcare model that says that early and  hard lockdown works best, because it's easier to slow down exponential growth when the absolute  numbers are low. An economical model told us that early and hard lockdowns work best, because  shorter lockdowns, for the reasons above, means less total cost. There's also a psychological  analysis that says, early and hard lockdown works best, because if you become harder over time,  people are already fatigued. They have lockdown fatigue, so they won't comply. So Germany still  started a lockdown light and did it too late. So it's quite a bit useless if you have all these  models that make these useful and, I guess, rather reliable scenario forecasts, if you will, but then  we don't care. But that's just a side note. It frustrates me a great deal, so I had to include that into the talk.  All right. So again, going back to building trust in models, we were at this parameter variation story,  but there is another way how we can build trust in models. And that is if we do have an  explaining model, one that doesn't just tell us the how, but also the why, then we can inspect that  model and see if this makes sense. Is this explanation plausible? Does it make sense? For example,  if your plasma optimization thingy comes up with a great solution for maximizing the distance of  the plasma from the reactor wall, but it predicts a pressure that is twice as high as what your  reactor vessel can bear, it's not a good forecast. It's not a good result. But you can only do this  because you can inspect the solution the model created for sensibleness, if you will. So you can  check explanations if they are there. So let's look at how you get from data to the model. You  probably all remember this picture. It's the first ever image of a black hole. Well, it's sort of an  image. I should rather say this is an image, but what the EHT, the event horizon telescope,  imaged wasn't really an image, right? Because of how the EHT works. Let's see how this works.  So the EHT is a radio informator, an interferometer, which means you computationally combine  several telescopes and there's lots of computing going on. So in this case, they combined a bunch  of telescopes all over the world in something that's called very large baseline interferometry.  The very large baseline comes from the distance between the telescopes and that is relevant  because the resolution, the whole computational thing can resolve depends on the length of these  baselines. So the further you can distance these telescopes, the higher resolution is the picture,  well picture. This thing is going to take here is a picture of one of these telescopes. Okay,  this particular one, Effelsberg, is not used in the EHT because it can't observe at the  respective wavelength, but it's these kinds of telescopes, smaller some of them all over the  world. Now, how does this work? So these different telescopes, they look at the same spot in the  sky, right? But because they are some distance apart, the distance from the telescope to that  point in the sky is different, right? So they see the same wave, the light wave that arrives,  you know, with a certain phase difference because there is this difference D in distance offset,  right? And of course, because light speed is constant, this is proportional to some  time difference as well. Now, as the Earth rotates, and also as you look at different points in the  sky, this difference also, sorry, this distance also changes because the angle of the object in  the sky is different from each of the telescopes. So if you take these two observations or realizations  and then apply a whole bunch of mathematics, which I'm not going to go into, I probably also  couldn't in detail, you get the following equation, which again, not important in detail. But what  this equation shows is a Fourier transform of the sky. So the EHT actually observes a Fourier  transformation, a spatial, it observes the spatial frequency distribution of the radiation  across the sky. And then the actual data point is basically there's a,  in, we can basically observe this amount of radiation with this frequency, and by that I mean  spatial frequency at the following orientation. And then they combine all of this data and the more  different lengths of baselines they have, and the more different orientations of baselines they have,  the better. But still in any case, they only have like, whatever, seven telescopes, so they have  10 different baselines. And the orientation of these baselines, well, there's only a limited  number of these orientations. Sure, the Earth rotates, giving them a bit more, but still it will  be incomplete data. So what they'll have to do is they have to do an inverse Fourier transformation  of incomplete data. The question they're answering is which is which mathematical description of the  object in the actual space domain represents or approximates best the data that has been seen  by the telescope in the frequency domain. And so let's look at a simple example of this kind of  problem. On the left side, you can see a bunch of measurements, some data. And on the right side,  you see a mathematical model. In this case, a horizontal line, a simple equation, y equals  y zero, no dependent z on x. And the total error of that model relative to the observation is,  you can imagine that as the sum of all the red bars, right, the difference between what the  model predicts, what was actually observed. So there could be different mathematical models,  right, that approximate that same data. Question is, which one is the right one, right? So again,  in the DHT case, what visual shape actually fits best to the observed incomplete data in the frequency  domain. And this example here on the right is best, right, because it has a total error of zero.  But actually, what this is, this is an overfit. If you put enough terms into your polynomial,  you can fit every data with some kind of polynomial. But while it reproduces the data perfectly, it  makes no use for prediction, because there's no way you can tell what the next, like if you extrapolate  to the right would be. And it's no abstraction, it's not a useful model. It's just the encoding,  encoding, if you will, of the measurements as a formula. So by the way, this is what's called  overlearning in neural networks, just as a side note. So how do you decide between the  three remaining ones? Well, you decide based on knowledge about the system at hand, right,  you know something about how your observed system should look like, because you understand the  physics, you have a simple analytical intuitive model about what's going on. So in this case, the  model of the black hole tells us that between the center of the black hole and a distance of 2.6  times the so-called Schwarzschild radius, you will see black, because in the middle, you look at the  black front side of the black hole, a little bit further out, the your light rays or the light rays  coming from the black hole are actually bent by the strong gravitation so that you can see the  backside of the black hole, which is also black. So we know that, you know, up to 2.6 RS, it'll be  dark. And outside there, we will see a glow from radiation that is accelerated around the black hole  from the gravitational force. So there must be something glowing and there must be a black  thing in the middle. And we even know roughly how big this is, because we can calculate the  Schwarzschild radius through other means, or at least a guesstimate it. And so we kind of know  what it will look like. Well, it kind of looked like this donut. And so knowing that, we can use  this knowledge and basically help interpreting the incomplete data. Now, of course, the problem is,  how is that not self-fulfilling? How do we avoid observing exactly what we want to observe, you  know, then we don't have to observe it because we know what it'll look like anyway. It will fake it.  So what they did here is they used three different deconvolution algorithms to do this kind of  inverse Fourier transformation with three different software packages for independent teams  who weren't allowed to see everybody else's data. They also worked with synthetic data. They used  the same magneto-hydrodynamic simulations of black holes and of other shapes, right? They  produced such data of, I don't know, rectangles. And, you know, if the software still produced  donut as a result, then something fishy is going on, right? And of course, they still  minimized the error of the fitting. So there's a lot of work going into this reverse  analysis of the data. It's fascinating to read. There's a nice book by Heino Feike,  one of the leaders of the project. I think it's called Light in the Dark or something  that talks about that and other things. So again, does the explanation make sense, right? We know  how the physics work so we can say something about what we expect. So how far can we trust models?  Here's a statement I've read. If we had started the lockdown one week earlier, 36,372 fewer people  would have died. This is what I call pointless precision because the precision of whatever your  model predicts must be proportional somehow to the precision of the input and the parameterization.  And obviously, there's a lot of things we don't know precisely for this virus and how society  reacts, right? So this leads us to this observation that there are models that are qualitative in  nature. It only tells us tendencies, right? If input A increases, output X will also increase.  There are relative models which give you comparative influences, like input A influences  the output X twice as much as input B, useful. And then there are quantitative models, which  actually give you numbers, right? If you increase by 10% the input A, then output B decreases by  33.3%. Now formula doesn't mean numerical, sorry, formula doesn't mean quantitative.  There is this Drake equation, which tells you how many civilizations there are in our galaxy,  right? And it's this equation, it has all kinds of factors like the average rate of star formation,  the fraction of planets that could support life, fraction of civilizations that send  detectable signals, blah, blah, blah, right? It's a formula has lots of factors, so it's  numeric, right? It gives you quantitative outputs. No, it doesn't. This is really just a simple  parametric model because none of these parameters has really known quantities. We have rough  boundaries or, you know, boxings for each of those, but not really. So using an, just because you  have an equation doesn't mean that it's a quantitative model, right? It might just be,  it basically just says which things influence this thing and whether it's proportional or  antiproportional. So let's look at fundamental limitations of this whole modeling business.  So first is chaos, which means that a small change in the initial conditions leads to huge  effects over time. So you've probably all seen this chaos pendulum, right? It's a pendulum with two  hinges, is that the word? I don't know. And if you take the pendulum and put it into a certain,  you know, position and let it go, it will oscillate in some way. And if you then take the pendulum  and try to put it into the same position again, after a few seconds, it will move completely  differently because the behavior is chaotic and you're not able to put the pendulum in exactly  the same initial condition. Also, you don't know exactly what other factors influence it. You know,  there might be some wind going on or whatever. So the other example that everybody talks about  in the context of chaos is like, if the butterfly leaves, you know, starts flying in Brazil somewhere,  this leads to thunderstorms in Europe. I did ask various meteorologists here whether they actually  think that's true. And I mean, nobody disagrees that the weather is chaotic. But I think they said  that this very small effect will very likely not lead to a thunderstorm, although in theory it could.  So the point is that both of these systems are deterministic, right? There is no randomness,  right? There's no randomness in the physics of the weather, of the atmosphere. The quantum effects  really aren't relevant on that level. There's also no randomness in this pendulum, but we don't  know the interactions, for example, the friction in these two hinges. And the initial conditions  precisely enough, if we knew them precisely enough, then we could make a perfect prediction, right?  So, or stated less absolutely, more input gives you a better prediction, more weather stations,  more satellites, more ships, more airplanes with sensors gives you a better prediction. So  this chaotic behavior of the weather really is the fundamental limit for weather forecasts,  because, right, for any given data quality and computational power, right? So that's why  I think what they told me was that roughly every 10 years, the useful range of weather forecasts  becomes one day more, right? And so that is not just because the computers get faster. It is also  just because they have more inputs and of course because they understand the mechanism better.  So if we can't predict the weather, you know, for more than a few days, how then will the climate  skeptics say, how then can we predict climate, right? This is all fake. They can't even predict the  weather. And of course, this is bullshit because climate is a statistical prediction. It's not  relevant if it will rain on 5th March, 2038 in Stuttgart, right? That's not what climate models  do. They make statistical predictions. And just to draw home this difference, again, going back to  the fusion example, we really cannot, because of chaotic behavior, we cannot predict the position  of each molecule or element atom in this mix of two gases, kinetic model here. But what we can do  is we can calculate the averages. In this case, the averages of these movements is called temperature  and pressure, right? And so we can calculate that precisely. But despite not being able to forecast  every molecule precisely. So there is an interesting thing in climate science. It's called attribution  science. And so what these guys ask is, is this extreme weather event that happened there, is this  caused by climate change, right? Really, what they're asking is, with which probability is this kind  of weather event caused by climate change at this location on the earth at this time of year, right?  How do they do that? Well, they take the current atmosphere, they modify the initial conditions  like temperature, humidity, pressure, stuff like that, they scan through these, and then they run the,  you know, climate models or weather models. Well, this is the same models anyway, it's a question  of parameterization these days. And they figure out with how many of these modified or these  initial conditions, will we get this kind of extreme weather event? Then they take the atmosphere  without the human impact. They remove the CO2 that we've introduced over the last, whatever, 50 years  and the methane. Because I mean, that is relatively well known how much this is. They do the same  modification of initials, run the weather forecasts, and they get another ratio of extreme  weather still happening versus not happening. So basically, they get different degrees of  robustness of that extreme weather phenomenon, depending on whether they run the real atmosphere  or the one without human impact. And then they basically take the difference between the two.  And this gives you the probability of this weather event being caused by climate change.  I thought that's a very ingenious use by climate models. Of course, it also really takes a lot  of computational power because you have to run these models lots and lots and lots of times.  Now, you could say, well, this whole chaos stuff, it's not really fundamental. It's just because  we can't measure precisely enough. Really, there isn't any chaos. It's just because our engineering  is too bad. Well, let's look at cellular automata. A cellular automaton is a mathematical abstraction  that has a row of cells. A cell can be either alive or dead. And then we observe how the cells  evolve over time or generations. So the generations or time is the y-axis. And then we have a whole  bunch of cells on the x-axis. And of course, generation i depends on the previous generation.  And each value of a cell depends on the value of the two neighbors in the previous generation.  So we can see this here in this diagram. We have generation i minus one. And the value of the cell  with the question mark in generation i depends on whether the three other gray boxes cells,  whether they were alive or dead. And then we have an example rule. The one here,  that says if all three predecessors were alive, then in the next generation we're dead.  In this case, only if the three predecessors were all dead, then the next one in the next  generation is going to be alive. So some kind of birth from nothing. Point is, if we plot  this rule one, there is a way of classifying these rules and giving them names, if we run this rule one  over 20 or 100 or 1000 or whatever, how many steps, you can see that a regular pattern occurs.  So we can give a formula for this rule. In this case, it's very simple because only if,  well, only in one case do we basically flip the values of the previous cells, except for these  two cells in the middle, next and right to the center, they always stay zero. So point is,  there is an iterative formula, and it takes into account the value of a previous generation. That's  why it's iterative. But we can also give a closed formula, one that does not rely on the previous  generation. We can distinguish between even and odd generations and just state which ones are  alive and which ones are dead. So that's fine. That's deterministic behavior. We can predict it  for any number of generations, and we don't have to iterate. Now here is another rule, rule 13.  Here is how this one looks after 20 steps. And here is how it looks after 100 steps.  And in these two other illustrations, top right, you can see how a simple change in the initial  conditions, how it spreads through the whole, basically the whole row. So this is actually  chaotic behavior. And it's chaotic behavior in pure math. There is nothing going on with  measurement. It's a property of the math. So we cannot predict the value of a cell in the  i-th generation. We have to run the iteration. This is also called computationally irreducible.  In fact, it's a very good secure random generator because the behavior is random. It has been proven  to be random. It's all work by Stephen Wolfram, who has written this book, A New Kind of Science.  It's interesting. Not everybody takes it too seriously, but this work on cellular automata  is not disputed. So it's cool stuff. So chaos is a fundamental property of our universe.  And we have to somehow, you know, if it occurs in our systems, because our systems are complex,  as we'll see, this limits the range to which we can say something useful with models.  Another example is emergence. You've all heard about how ant colonies exhibit these very  sophisticated group behaviors, even though presumably the brains of these ants are rather  small and simple. So what's going on here? Well, we have what's called agents. Each ant is an agent.  It has simple rules it behaves based on, for example, based on pheromones and smells and  stuff like that. But then we have lots of interacting of these agents. They interact in  different ways. And then they produce some kind of complex ultimate outcome. And the point is that  we cannot predict the outcome just by observing and understanding the rules. We have to actually run  also iteratively the system and see what can potentially come out. And then the thing is that  in lots of systems we care about, they work exactly this way, right? Politics sets rules. And then we  all as society behave in some way. We interact based on rules, maybe not based on rules. People  know there's lots of game theoretical personal optimization going on, right? And so we really  can't predict, right? So I did an interview with somebody from Theo Delft, Igor Nikolich,  about socio-technical systems. He investigates how society interacts with technical systems  and what resulting behaviors could come out. And again, he can't really predict because of  these immersions. But what he can do is he can run these agent models and then look at the scenarios  that could potentially happen and then discuss this with stakeholders, potentially go back to  change the rules and run again and maybe iterate to a better set of rules. There's no proof there,  right? There's no guaranteed understanding. But it can help. He has lots of interesting cases there.  There's also a very nice counter example from politics in Germany recently in Berlin.  They were setting an upper limit for rents, right? So the idea was to therefore have lower rents and  so less affluent people will find apartments. What actually happened, at least initially,  I haven't checked in the last few weeks, is that 37% more apartments were sold instead of  being on the market for rent because this just became less interesting for people,  for the renters. 28% fewer apartments were on the market, 200% more inquiries per apartment.  And there was a shadow rent for the case when the law wasn't complied with the German basic law.  So the point is this failed, right? And it failed because one tried to set simple rules in an obviously  complex system with lots of emergent behaviors. Now, I do think that one maybe could have anticipated  that even without running complex agent-based simulations, but still, it's an example of how  rulemaking in politics really is challenging because you just don't know how the system  will react once you put some kind of stimulus on it by changing regulations. There is also an  interesting example from cellular automata. Game of life, you've probably all heard it, right?  It's basically a 2D cellular automaton where the question whether the cell marked with X  in the next generation depends on what happens around it. So this phenomena like dying from  loneliness, dying from overpopulation, healthy environments, reproduction, the rules don't  really matter. So here is something. So this runs a game of life simulation for, I don't know how  many oscillations here or how many runs. And you can see there are things oscillating back and forth.  There are so-called spaceships. There are glider guns. These are the technical terms for these  seemingly coordinated behaviors, right? So who would have thought that from this relatively  simple set of very local rules seemingly coordinated phenomena can happen? Almost looks like ants  walking around a track, right? So again, pure math can produce complex or coordinated seeming  behavior from simple rules that do not somehow presuppose that kind of coordinate behavior.  So what can we do here, right? We just said we cannot predict behavior of the whole system  by examining the rules. But what we can do is we can set a new, we can define a new set of rules  that specify that are valid for the system as a whole, like whatever. If you have more than 100  ants and the temperature is over 30 degrees, they'll come out of their bunk or whatever it's called  and will start rummaging around, you know, stuff like that. You can observe or create higher level  theories. In fact, this happens all the time, right? Because the behavior of ants might be based on  biology, but biology is just applied chemistry and chemistry as we all know, is just the physics  of the of the of the electrons, right? It's a joke among physicists. So but the point is we couldn't  predict the behavior even of a single ant if we try to do that with physics, even though it is  physics that drives the ant, everything is driven by physics, right? We could try with chemistry,  but that's probably also a bit too low level. We can maybe be more successful with biology or medicine  by doing an MRI or an fMRI of the brain of an ant, right? I mean, I'm not a biologist, as you can  probably tell. But the point is what we're doing all the time, we're stacking abstractions on top  of another of one another, we're building models of aggregated subsystems in order to understand  those. There is a very nice quote by Ezger Dykstra, a famous computer scientist who says,  the purpose of abstraction is not to be vague, but to create and but to create a new semantic  level on which one can be absolutely precise, right? This also relies to this averaging stuff  in the fusion reactor. So very, very cool kind of framework that humanity has built for themselves  there. Another example of stuff that can go wrong in modeling, path dependence, right? So there is a  complex structure of decisions we've made over time, I don't know, it's just a cool screenshot,  right? But we are somewhere out there on the outer edges of this path. How did we get here? And the  answer is we got here because there were all these random and context and resource dependent and  cultural and political decisions that we've made over time. For lots of phenomena, if you ask,  so why the hell is something like the way it is in our society? There really isn't a good answer.  It could just as well be different. But because of all these random things over the decades  and centuries, we've just ended up there. There isn't a good reason. It just happened, right?  And the only way to predict, if you will, is by going the path you cannot simplify. You can't  run an analysis and say, well, obviously, you know, I don't know, the society has to do things  this way. It's not like that. Even the obvious example is evolution, right? Evolution is not  a deterministic process. It's just because of all kinds of constraints and randomness and  a meteor impacted the earth, stuff happened. All of these things are examples of complexity.  There are other things like hidden links, feedback cycles, tipping points, power loss. If you listen  closely, you have heard all of those in the discussion about climate, right? Which just drives  home the point that our climate is a complex system, which makes it hard to control it in a  deterministic way. And by control, I don't necessarily mean just geoengineering, right?  It's really hard to understand and decide what to do. I mean, obviously, we have to reduce  CO2. I'm not discussing that, but in detail. I guess maybe the point is that geoengineering is  risky. So last point before we wrap up this talk, unknown unknowns. Models almost always represent  somehow knowledge and experience. There's no completely unknown stuff in models because  nobody could have put it in there, right? So there might be also biases and prejudices.  And we won't ever run a sensitivity analysis for unknown unknowns because we don't know them.  We're not aware that they're unknowns. So we're not testing the model for what it would mean if  that unknown parameter would have a different value. We don't know it, right? So the really nice example,  I forget where I have it from. It's very well known. I actually know where I have it from,  but I forget that it's clear. Whatever, it doesn't matter. So, you know, Turkey. Turkey gets fed  by the farmer. Turkey likes the farmer because, you know, it's the guy who brings food. So based  on Bayesian reasoning, updating its own perception, the Turkey builds a model of the farmer in their  brain and, you know, becomes more and more, you know, on the good side. But then on day 100,  thanksgiving, the farmer comes and kills the Turkey. Of course, the model could not have  predicted that, right? Because there was nothing in the experiential world of the Turkey. There was  no indication based on which the Turkey could have updated the model in their brain to maybe not be  so optimistic because, you know, one day, thanksgiving comes around. So again, so this means that  when we think about what we will all die from, we as a humankind, right? We can do some  probabilistic modeling that estimates the likelihood of dying from volcanic, super volcanic eruptions  or meteors hitting or natural pandemics because we have experience from the past. But we cannot use  this approach to predict, well, how likely it is we're going to die from our own nuclear wars or  AI eating us or a man-made pandemic. I did an interview with Toby Orto wrote a book called  The Precipice where he discusses these likelihoods as well. Interesting story. So was this crane  accident here consequence of an unknown unknown? I don't think so because they knew how important  it is that the hook doesn't break, right? So they put a safety factor of three, they told me, into the  hook design. But if the process in manufacturing fails, well, what do you do, right? You can't,  your model won't predict. So, all right, models, they're not perfect, but what else? There is a  nice example that maybe gives a bit of a counterpoint to detailed modeling. There is something  called a fast and frugal tree, which is a very simple decision tree, basically, to decide whether  a patient who shows up in the emergency room should be moved to the intensive care unit or  to a regular care unit. And as you can see, there is only basically very few three yes, no answers.  We don't have to discuss what these mean in detail. This thing performs better than a machine  learning model that takes dozens of factors into account. So the doctors would say something like  Hammersche Ermossog macht, which is German for, well, we've always known that we don't need this stupid machine learning stuff, right?  But the point is more data, more detailed modeling doesn't always mean better outcome, right? Sometimes  common sense and just experience of humans is something that is relevant, especially also  when interpreting models. And of course, models change over time, right? That's science. As we get  new insights, we update how our models work from Newton to Einstein to a grand unified theory,  maybe at some point. So models are everywhere. The use of models allows us to forecast developments  and quantity for quantified uncertainties. That's cool. Models make influencing variables and their  effects explicit, right? The explanatory models can even help understand something.  Models are the basis for constructive discussion. This is really important. When you have a model,  you can constructively disagree whether some additional parameter should be taken into account  or whatever. You cannot do that if you just run around and claim shit, right? As some people do in  this pandemic. But of course, boundary conditions and limits of modeling must be considered. And in  the end, in case of doubt, crap in, crap out is always true here as well. All right. This brings  me to the end of the talk. Interestingly, I took two minutes longer than in my trial. Sorry for  running a little bit over time. But I'm done now. There is a book that you might want to check out.  And of course, there are the podcast episodes listed here that are most relevant to the stuff  we talked about. Obviously, 330 more. But these are the ones that have direct influence on this talk.  Second, whether path dependence isn't just a lack of proper accounting of state,  or if the person asking missed something there.  Sure. I mean, it's similar to this problem with chaos, right? If you could track everything  to arbitrary detail and could keep track of everything, then maybe path dependence would  not be a thing. But we know that's not possible in practice.  Yes. I think that's it from my standpoint right now. There aren't any more questions. I am aware of.  So chat has any more. There is something more in the IRC. It doesn't look like it.  Yeah, I think we can end here.
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