 Hello, and welcome back to Beyond Networks, the evolution of living systems. Last time we've looked at models and how they're sort of formalized systems. And I've ended the lectures saying that if we look at science as a process, we need to sort of shift our attention from treating models as abstract and sort of, you know, out there representations of real systems to their use in the context of the activity of modeling that is done by a model or a scientist. So we switch from representation to the activity of representing, from the product of science to the process that is based on scientific practice, modeling. And that gives us a sort of an agent-based perspective that involves the goals of the scientists, what they do with the model, their motivations, their intentions, the problems they want to solve and the questions they want to answer. So in this lecture, we're gonna take this idea a little bit further and I wanna show you that what is really important about models is not that they represent the real system that they model accurately, but that they fulfill their purpose. So models are not representations, but rather they are tools. They can still represent the system correctly, but that's not the main point. The main point, and that's very important here, the main point is that they are efficient as tools that help us gain new insights. So such tools are called epistemic tools, they help us gain new knowledge. So I want to present a view of models as epistemic tools in this lecture. And to do this, I'm gonna use an account by University of Vienna philosophy professor, Tarja Knodilla, who has done absolutely marvelous work on the nature and the use of models in all kinds of scientific disciplines. So she compares two different models of modeling. The simple one, sort of a two-step, two-place model, she calls it, relates a formal system, which she calls a model, to an actual system, which she calls a target system through the act of representing. A note just quickly that when she uses the term model here, it can be something else than a formal system. It can be a scale model, even a model organism. They are supposed to stand for something more general than they are. So this very simple view is based on what she calls a model target diet. So the meaning of the model comes out of its relation to the target system. Okay, and that's, as I said in the last lecture, a very problematic relation. Because as we've seen very early in the lecture series already, it is very difficult to assess whether a model is an accurate representation of the real world, which is sort of independent of our minds and out there. So there are all kinds of problems with this act of representing. One is to make this idea sort of precise. You could think, okay, there must be some sort of mapping from the model to the system. In fact, what people often argue is that there must be a specific mapping. Mathematicians call mapping from one thing entity to another entity amorphism. There must be an isomorphism, which means that every element of the model sort of links up to a specific element in the target system and vice versa. So that's nice, but we don't have direct access to this reality out there. So it's really hard to assess whether such a mapping exists. And there are other problems with this. For example, isomorphisms are reversible. So you map, it doesn't have a direction, but here you can see the model, the arrow from the model to the target system is very much one way. The model is representing the target system, not the other way around. There's a bunch of other sort of formal problems with this relationship, but it's really hard to establish. And there's been a lot of sort of discussion about how you can define a precise relationship with a model and its target by just using, that sort of resides in the model target relation itself. So there's nothing else involved. Because so the only criteria, criterion of success here is sort of the accuracy of the mapping. You have to get the mapping right in some way, but it's really hard. This is all I want you to know is really hard. And there's a lot of debate about how to do this. So this idea that model represents reality and there's a precise mapping so that the elements in your model tell you something about reality directly. This is called structuralism. It's a structural approach. And it interprets the sort of content, the rules in a model quite literally as rules that describe the real world. We'll come back to that when we discuss a tradition in biology, which is called process structuralism later on in the lecture. But there is another approach. And it's called a pragmatic approach or also deflationary approach because the deflation here means that other elements are added. And this other element that's added is the modeler who's constructing the model. So this step is still in parallel to the argument that I was describing the Rangiri makes about agent-based, an agent-based perspective of representing. So from the dyad, we've come to a modeler-model-target triad. And modeler, model and target system have a relatively complicated relationship. So the success of the model is no longer primarily based on how accurate it represents the target system. But it is judged by how successfully it answers the question it was supposed to answer in the first place, the problem it was supposed to solve. Remember, if you're looking at science mainly in terms of problem solving, then that is a pragmatist stance. That's why this is called the pragmatist approach. So the model works if it does what you want it to do. Whoa, of course, this is a very dangerous notion, right? Because you could build something that's very wrong. You could be delusional, but you could get things right by accident. So we have to think about this idea of what that means, the model being useful in this way. We have to think about this and make this notion a bit more precise, okay? So this is what Tarja does in this paper that I'm citing that I recommend you read from 2011. And so she says models to judge the success of a model, we have to consider a few characteristics that models have. One of them, the first one that she mentions is constraint design. This basically means that a model is designed based on the problem that you already have. So it is supposed to make your question accessible, manageable, your problem solvable. You want to test your assumptions. You build a model because you have an idea how things work already. You test the hypothesis and that constrains how you build the model. And often you don't try to be accurate at all. Instead, just like the subway map I showed you in last lecture, the subway map of Vienna, the metro map, you use idealization, simplification and approximation. They're different. Idealization leaves out, brings out the features that you actually want to treat. Simplification leaves out the detail you don't want to deal with and approximation makes compromises. For example, when you choose a sort of a larger scale of the map, you want to have an overview. You want to have less detail. It will be a less accurate description of reality. It will approximate reality less than a map with a more detailed scale. So modeling assumptions are very much influenced not only by the target system but by what you want to discover with the model. And it's very difficult to distinguish which assumptions, those that are based on your desire to get your question right or those that are based on actual features of the target system. It's very difficult to judge which one of those assumptions make the model successful. Hard to analyze that. So we always have to be careful with models in this way. The second characteristic of models is, Tariya actually calls this non-transparency. I would call it opacity, which means it's not transparent. A bit like Austrian politics, maybe. So opacity means that a lot of the means that you use to model are not obvious. They're not explicit. So for example, we use mathematical formalisms. We'll introduce sort of dynamical systems theory a little bit later on. And just the general ideas that underlie this approach. But you have to know that these sort of means they often come from other disciplines. They were built to model the solar system and not biological systems. So can you just trust all those sort of established traditional formalisms means by which we represent if we transfer them from one area, one domain of inquiry, physics to biology? We have to be very careful with that. So we've already alluded a bit to this, but the third characteristic of a model is it's built to get something done. It has result orientedness. So we build models that we suspect will produce the effects we expect. There's no other way to do it. You wouldn't build a model that you think is not gonna do what you think it's gonna do. I modeled for 20 years. You're not gonna do that. And that's a problem, of course, because it biases your approach. And as I said already, before the formalisms that we use, they're often transferred without further scrutiny from one area to another. Actually, for a lot of discourse, I'm gonna argue that the sort of modeling formalisms that we imported that are assumptions are opaque to us now. Those modeling assumptions that really deeply underlie those physical models, they are no longer adequate to model biological systems. And we need to develop new tools, new mathematics to deal with biological systems. But we'll come to that. So we have to be careful here. Sometimes it's good to be pragmatic, to build toward a result, but sometimes it's really gonna bias our approach in ways that are not productive. Okay, the fourth characteristic is manipulability. What does that mean? We want to model what the system can do. We want to not only know what it does, but we want to play around with it and predict stuff. What it could do, what it maybe testably does in other circumstances. You need that to verify a model, for example, as far as you can do that. So a model can be used as a tool to explore possible worlds instead of the actual world. And that's very interesting. So if you have, so if it's used in this sense that you have a model, it can be handed around, it becomes sort of embodied in an abstract way. It's still an abstract object. Remember, that's the idea that a model is an object, but it is an object that we can manipulate. So it's somehow embodied in the actual world, but we can use it, play around, and think about possible worlds. I don't know if that idea is entirely clear, but if the model is sort of out there to be manipulated, it can also be used by very different people, okay? So in this sense, models are real. They're real tools that can be handed around. We can all use them together to get a better insight because we all use these models in slightly different ways because we have different results in mind. Okay, and the last characteristic that Tarja points out is what she calls distributed justification. So often we think we have a reality and we sort of build a model and the model has to fit that objective reality. But what we're really doing is we're fitting both the model and the data and tailor them to each other. Remember the model of the pendulum. So we already know what we can measure in the pendulum, the velocity and the position of the bob. So we're gonna build a model that incorporates those measurable quantities. We'll come back to that when I actually go through building the linear pendulum model in a few lectures. So it's not that this is a one-way sort of activity, but the justification of our model has to be distributed along both sides. So models are constructed with a specific purpose in a specific context again. And this context is often not random but it's tailored to the use of the model. Well, this was a lot of really sort of abstract sort of discussion, but I don't want you to remember the details of this, but look at these characteristics of models here. Constraint design, opacity, result-orientedness, manipulability, distributed justification. So the design, you work with what is given, what you have, opacity, you don't always question the tools that you have. Result-orientedness, tools are for something. Manipulability, tools are to manipulate. Distributed justification, tools fit their context. When you have a hammer, everything is in a nail. All these characteristics, they point at one thing and that is that models are tools, okay? A model's value does not lie in how accurately it represents its target system, I'll say it again, but instead a good model gives us a robust answer to a question or a robust solution to a problem. And we have to think really hard about all these caveats that come from these sort of characteristics. So they are not only a good thing, they are a good thing because models are great tools, but if we think about them as tools and not as abstract representations, then it's much easier to think about these sort of problems that are also inherent in the opacity, the bias of result-orientedness and sort of matching both data to the model and the model to the data. So we'll spend a lot of time in this course thinking about models in this way. So keep this picture in mind, models are tools and a model provides a trustworthy perspective on the target system under study. So each model can be idealized, simplified, approximated, but can still make a particular valid point. And different models can focus on different characteristics of a real system. And in this way, you get different, what Wim said called cuts through the phenomena and that is how models relate and represent perspectives rather than aspects direct representation of the real world, actual system, the target system. They give you different perspectives and you, if you treat them as models, have the right to use what you could call misrepresentation, idealization, simplification, approximation. These are features and not a bug of modeling. You want to bring out, if you draw a map, you want to bring out those features that are important for your current complex. So think of models as tools for the rest of this course. Tools for better thinking, tools for epistemology for the generation of knowledge. And that of course brings us right back to this picture. I define the formal system, a model in its most abstract sense as a set of relationships between mathematical objects. And this network is precisely what that is. A network is a formal model. A network is a tool. A network is not, and that's the central point of this lecture. A network is not an accurate representation of a cell or an organism. So in the next lecture, in the next module, we'll dive into this idea of how we use networks as tools to study organisms. And also how those networks relate to what we call mechanistic explanation. And we'll examine whether there are other types of explanation that may be complementary and useful to study life and living systems. Thank you very much for listening. And I hope to see you next time.