 Hi there and welcome back to Beyond Networks the evolution of living systems. Last time we left off with the conclusion that systems are real in the sense of being robustly observable pattern processes. They're not just in our minds but there's some there's something graspable out there a dynamic pattern but complex adaptive systems allow for a large number of valid independent perspectives we can look at them in many different ways and in each situation we have an indefinite number of different perspectives that may be making a valid point and I was also at the very end of the lecture saying when formalized in some way those perspectives become models of the system and this is very important because modeling is at the heart of course of systems biology and these models allow us to investigate what the system is capable of doing in this lecture we're going to have a look at what a model really is and how it relates to systems and perspectives and in the next lecture I'm gonna make the argument that these models are tools for understanding epistemic tools rather than representations of a system but we're gonna start out here by sort of looking at how actual systems these pattern processes interacting processes that generate some recognizable pattern or let's call it a behavior pattern is very sort of visual a recognizable behavior of any kind how they relate to more formal sort of systems and that can be in most cases it is some set of relations between mathematical objects for example variables that are described by equations or propositions two things to note here one objects don't need to be things if a mathematical object is a variable it can represent a process because the value of that variable can change over time that's very important the other thing to point out is that mathematical formulations are not the only possible way to make a model formal but you can you can draw a model you can build a model a scale model for example or you can formulate a model in terms of propositions you can logically describe it but the important thing is that a formal system is something that is expressed in our head and the actual system is something that's out there and somehow we want to connect those two things through the process the practice of modeling which tries to bring actual and formal systems into Congress somehow so this is difficult to do and this is a perennial problem in the philosophy of science is how can you judge whether the model that you've constructed the formal system is a good match for the actual system which is sort of out there in scare quotes because you cannot access as we have seen you cannot access that real world directly and so we need to think really hard about how this is supposed to work so let's take a very simple system so simple that it doesn't exist in biology so we'll take an example from physics the linear pendulum this is a very simple system it consists of a rod cord a wire or some such thing with a weight also called a bob at or near one end it is suspended from a fixed point so as to swing or oscillate freely under the influence of gravity of course you know that I'm just going to try to be formal so this is a sort of the sentences you see here already a formal description of the pendulum but we're thinking now about a physical system of pendulum that's swinging the rod can have a certain length the bob can have a certain weight and it can swing more or less widely right so these are variables and parameters of the system we're not going to go into sort of the details of how you make a mathematical model here today we're going to do that one or two modules ahead from now but what we're going to try and do is see how can you formalize this actual system in principle and so because this is physics we can start from general principles first principles and those are formulated in this case those that are relevant of course in Newton's mechanics and his theory of gravitation so this theory is formulated in terms of very abstract terms it uses masses and forces and stuff like that which are entities that you cannot directly detect so we need to somehow relate them to this particular these general sort of concepts to this particular situation to this particular system and also as a side note this is very important note that you don't have to have a general theory to build a model for a system mostly in biology we don't actually in history of course Galileo when he built the first model of the linear pendulum didn't have Newton's mechanics because Newton hadn't formulated that theory yet so there is no need to derive a model from first principles but in this case we can do it so how do we relate those general principles to this specific system how do we build a model that represents this physical system with a bob and a wire and so we need two steps here first we need to interpret the abstract entities of the theory in our particular concept so we need to think about what does force and mass mean for the pendulum in case of the mass it's quite easy so you have a bob and a wire of course and together they have a certain weight and that's gonna sort of influence the behavior of the pendulum actually is it where we have to abstract the weight of the rod out if the model is gonna work so how we actually apply these general sort of entities to a specific situation is not obvious at all take force so this pendulum the bob is attached the rod is rigid the wire is rigid and it is subject to the force of gravity on earth if we do this experiment with the pendulum on earth we have a swinging pendulum on earth okay so what are the forces that this pendulum is exposed to it's not immediately obvious so we'll come back to this when I show you how Galileo actually constructed the model but for now let's just stay at the very abstract level and say okay so there's apart from that so we just we have to interpret what force and mass mean but we also have to identify specific elements of the model with real world entities and it turns out in the case of the pendulum that the force that's acting on the bob is of course dependent on its velocity and its position so interpretation and identification not only link the general theory to the specific model but also tell us what to measure for example so it is the position and the velocity of the bob in this case that we need to measure but without the theory without the model it wouldn't be clear what we would have to look at here so to summarize this Ron Geary in his book draws this whole scheme of how you construct a representational model so we've been we've started at the top we said we had first principles Newton's mechanics theory of gravitation and we had some specific conditions above a rod you know a certain angle of swinging and so forth and we apply that to the linear pendulum model specifically here which requires interpretation of general entities and identification how do they apply in this particular case we can then build this representational model which is the linear pendulum model and we can predict how the pendulum will behave even if we haven't done all the experiments and measured all the positions and the velocities that a pendulum can have so we can predict that is making a specific hypothesis through the model or we can generalize this model and say okay this not only applies to sort of rod and bob but all kinds of systems that behave in a similar way so we can if we can generalize the insight from the model very broadly then we talk about scientific laws or theories and I'm going to tell you in a minute why I put those in skip and scare quotes here another problem of course is how do we come how do we test the model how do we come to the model from the side of the data and there's some steps involved I'm not going to go into this but we're not just naively measuring everything we have to decide what are we going to measure right and and often that choice is already informed by our model and also we do not often fit model to raw data but we somehow model the data as well which is a different kind of meaning of model you can describe a data sets for example statistically variances averages means all these kind of tools that descriptive statistics gives us gives you a simplified model of your data so you're fitting a representational model to a statistical model mostly and not a theory directly to data so Geary is saying here scientific work whether you work in physics or in biology really always works through this intermediate step of building models that represent systems these models are formal systems that represent actual systems which are patterned processes so one really important thing here and Geary has another book apart from the scientific perspectivism book that I've already recommended it's called science without laws I like that title a law and in that book he argues that universal laws do not exist so basically this idea that we can describe the world with universal laws and that we should start our investigation not from a point of skepticism about everything but from those basic physical laws that is sort of upside down because the idea that the world is governed by universal laws and a specific set of universal laws remember this sort of naive realism that I was telling you about that goes back to the cart again him again he's done so much great stuff for science and philosophy that we can forgive him a few major lapses but his lapses were major and you know he invented the idea of a universal law because you could not imagine that God created a universe without law so the idea of a scientific universal scientific law comes from religion and there is no evidence that any such law exists even the broadest theories in physics are limited to certain domains and don't connect up smoothly and this search for a theory of everything in physics so far has been in vain as we have talked about very early on in this lecture so we have to move away from this idea there are laws and also the word theory is often used in this very broad sense so we always have to define where a theory applies and often we work through specific what Geary calls here representational models when we apply the theory to specific systems I can't repeat that often enough so what does that mean let's go back to whimsets beautiful diagram and look at these different scales of the universe remember here up here is that bio psychological causal thicket while down here at the atomic and the molecular macromolecular level up to the cellular level it's very orderly so there's different distinguishable levels we can describe events that happen at one level or another and often we can even combine them like what's the case with classical thermodynamics and statistical mechanics which you can derive used to derive classical thermodynamics okay this is much harder here in this area and the reason for this is that these levels up here are not so clearly separated anymore the world is much more messy so we should not expect to be able to describe this part of the world with very general theories this should not even be our aim I don't think it's useful to look for very broad theories and we'll come back to that when I will talk about the bullshit discussion about evolutionary synthesis later on so basically if you're a physicist and you're working at the level of the atoms a chemist working at the level of the molecules it's easy to have very generalized models which we call laws and theories they apply to very broad domains of reality while in this bio psychological thicket on the right-hand side here you need to work with much more specific representational models and it doesn't make sense at all to try and unify those a priori just before you even have looked at specific cases you can maybe generalize to some extent but it's always a question how far you can generalize the model it's not obvious so let's illustrate this by comparing these representational models this is what Geary does in his book scientific perspectivism he compares a model to a physical map so this is a very complex system it's the center of Vienna and you can see the canal and at the upper right corner probably covered by the little window where I'm talking is the Danube the map shows you a lot of information names streets parking lots restaurants all kinds of things it's a bit overloaded but it's very informative and as you zoom in you can find all kinds of information in this map but of course it also abstracts a lot of information and the point is here that you can imagine to have a lot of different maps for Vienna for example if you're a tourist and you only use public transport you may not know need this whole map that includes also that the sort of suburbs around here outside of the Vienna ring around the center of town so you'd rather use this kind of map which is a tourist map of the first district of Vienna which shows you where all the major sites are that you want to see much more overlookable you can see much more detail where to walk to what to see but of course if you want to go to Castle Schoenbrunn which is on the outskirts of Vienna you need to take public transport so there is this great map off the metro system in Vienna that abstracts away a lot it doesn't even preserve distances or angles it just shows you an abstract grid of the metro lines the suburban train lines where you can connect very simple these bars here they show you where you can connect from one train to the other and the little round circles are just stops very practical and all the unnecessary information is left out so these maps are very simple or very similar to to representational models remember Vienna is a complex system I don't know if it's adaptive we'll see about that but history will tell but you can have all these different maps that make a valid point about Vienna and which map to use depends on your purpose on your problem on your intention so a slightly different aspects of maps and why they're a good sort of metaphors for such models think about depicting the whole world on a flat map this is a problem because the world is a globe and the map is flat and classically people used of course mercators I think it's from the 15th century classical projection that preserves and this was the most important thing for navigators especially it preserves direction so if you follow a straight line on this map you are following a straight line in reality on real earth the downside of this map of course is that it hugely inflates the pole regions if you look at Greenland is massive huge and Antarctica is gigantic on this map which is obviously not the case so lots of people have suggested different alternative projection here is one that was particularly popular when I was in school it tries called Peter's projection it tries to correct for these distortions of the area poles so this map is trying to preserve direction preserve area so it gets a little better than the Mercator one in this sense but it distorts the shape even at the equator none of the continents actually look like that look at Greenland it's totally squished now and all the Canadian islands but also equatorial Africa is pulled like a spaghetti and it doesn't look very good another projection is Winkle triple it's called a triple projection because it preserves direction area and what was I saying direction area and distance okay so it can't be square anymore so it has to be sort of simulating the round shape of the earth but it still suffers from problems for example look at Antarctica just it doesn't look that way this is my favorite world map projection it's very recent Winkle triple was early 20th century the orthograph is from 1999 it depicts all continents on the planet while trying to preserve distance shape and depicting Antarctica as it is so this is a very sophisticated projection that works with tetrahedra and it's really cool but the main point about this is that need none of these maps captures the actual shape you cannot capture a globular shape on a flat surface it's not possible so there's always a compromise you get some ideas some some properties right you get the distance right you get the area right or you get the direction right you can you can sometimes you know shape and you have to compromise between those so you have to sort of choose the projection that suits you for your purpose and the same thing happens with models so with the map you actually design the map Mercator knew that it wasn't a real accurate representation off the globe but for the purpose of preserving direction going straight on the map going straight in the real world it was good enough that's why he chose that projection so basically maps and models are very similar both are objects not statements remember when we were talking about truth I told you that a lot of philosophers are sort of stuck in this world of propositions statements utterances language while we live in the real world and models are not just theoretical constructs they are objects that we use so maps are physical objects and models are abstract objects they can be physical models too I mean scale models again are also a type of a model so in this sense a map or a model cannot be true or false it can only be similar or applicable to certain sections sections of reality or to certain problems you may want to solve okay even this concept of being similar is problematic we'll get to that in the next lecture maps and models are always partial you have to select the features you're interested in imagine drawing a map that has all the details that's not a map anymore that's a reproduction a copy a simulacrum of reality and that doesn't work it's not useful at all so they have to be of limited accuracy and also but at the same time they have to be similar they have to accurately so some things they get wrong they're not accurate but other things the features that they're trying to represent they are trying to be accurate in this sense so they're trying to give you an accurate idea of those particular features that you've chosen to represent and this is why maps and models are always interest relative question relative problem relative it depends on the map maker the model or what these maps are doing and what they're supposed to do so map makers and scientists conventions are also very important this will come back to in the next lecture you there are certain ways symbols tools that we use to make maps and actually if we make a map that's using a very sort of unusual idiom or language to convey its meaning we will have problems using that so maps are only useful if they're built with these standard sort of elements and the same applies to models as well we'll come back to that so to sum up basically we have to switch from seeing models as abstract sets of propositions that represent reality to modelers building models to represent some aspect question dependent aspect so we have to switch from examining the idea of representation to the activity of representing which fits nicely into that picture that I presented to you a few lectures ago about science itself being an adaptive process so it doesn't make sense to take the models out of the context in which they are used so we shift from the products of science to prompt to the process based on actual scientific practice this is an agent-based perspective it focuses on the scientists on the map maker the modeler and involves their intentions their actions their problems their questions how I mean we're gonna take this idea a step further in the next next lecture just before I end this one I want to sort of connect to two insights that we had in the past in this lecture already the first is I want to connect Ron Geary's idea of a representational model and perspectives to Thomas Kuhn's idea of a paradigm they are very similar you may have noticed that already in that in the sense the claims about scientific truths are always made within a certain paradigm or a certain perspective so in this sense the two concepts are almost interchangeable but the idea the notion of a representational model the way that Geary presents it is much more price-related precisely defined you can it's much more graspable and also you can test the idea much more rigorously and argue about it than what Kuhn means by a paradigm in fact there is a paper out there by a guy called Winkleman which analyzes Kuhn's 1962 book very carefully and finds that he uses the term paradigm in 21 different ways and Kuhn himself comes back and says yes paradigms in the second edition of his book he says at least there are at least two ways in which you can interpret the idea of a paradigm one is a very broad you could call it a disciplinary matrix sort of the overall set of theories of tools of methods that a scientist has available at a specific time and place in history so notice that this is broader than a perspective this is everything that exists in science at one time while several perspectives we saw that can coexist at the same time but paradigm in in his book can also mean an exemplar which is exactly the same as one of these representational models for example the model the linear pendulum model is a paradigm way of looking at simple oscillators in all kinds of different contexts okay so the the word paradigm is a little problematic and maybe perspective actually makes this word and and representational models these sort of terms are much more useful because they're more specific one last point here is that also the problem of incommensurability is no longer a problem in a perspectivist framework while coon said that people who adhere to one perspective or another they cannot even talk to each other and they don't use the same language they don't live in the same world in some way. Perspectivism is much more mellow in this sense and says of course it is exactly by comparing different perspectives that we learn about the limitations of our own perspective how we transcend those limitations and learn more about the robust features of the real world. This brings us right back to Miquela Massimi and her distinction between the context of use of a scientific claim and the context of assessment when we talk about perspectival truth. She says knowledge claims are always sensitive to their context of use always made within a perspective just like Geary says but she also says when we assess those claims that are you know claims that are actually accessible across different perspectives those are the ones that are getting things right those convey some perspectival truth and so this is a sort of a way forward from coon's very sort of constructivist way towards staying inside our head but still trying to learn something robustly trustworthy knowledge about the real world. So next time we look at models as tools and the problems with the idea of representation. I hope to see you again. Bye now.