Scientific models & semantic view of scientific theories (partial)

0:00 The following is possible, but their results have little generality. Models that sacrifice realism make unrealistic assumptions so that scientists can describe systems with general, mathematically unattractive equations that produce quantitative predictions. Qualitative modeling sacrifices precision for realism and generality by abandoning quantitative accuracy and focusing on qualitative relations between model variables. Now, Levin's distinctions were intended to capture general differences in modeling strategies, and I will treat them as such today without improving them. Now, Levin's thought that successful scientific research acquired all three modeling strategies, but each had strengths and weaknesses relative to particular goals and contexts. In a context of modeling and complexity, and especially to understand their dynamics, Levin's thought quantitative models based on important values. So, for those quantitative models that sacrifice generality, the first problem is just the pragmatic one of achieving the details needed for maximally realistic model representation. And we'll see an example of this in the discussion of the analysis. The second refers to the unmanageability of the model, which, with abuses and computations and institutions, is much more a problem with the limits of writing in the history of today. The third refers to the ability to explain or power of such models. Complex models that are difficult to manage are also difficult to comprehend, especially if they're extremely complex. models that sacrifice realism based different kinds of disadvantages these kinds of models focus on a small set of hopefully salient system components and avoid the three problems for models that sacrifice generality this involves making idealized assumptions and for example ignoring some variables interactions treating interactions instantaneous using continuous variables for discrete components and so on the underlying assumption is the differences between the predictions of these idealized models and observations will identify what assumptions

2:30 cannot be made for accurate description the cost of unrealistic idealization idealizations however is uncertainty about whether the modeling results demonstrate properties of the system being represented or are byproducts of these unrealistic assumptions so scientists are often unclear about which system components are primarily responsible for system dynamics so unrealistic idealizations therefore may significantly mischaracterize the most important aspects of the systems and as a consequence an increased sense of understanding conveyed by these models may fail to be about the phenomenon that the model was intended to represent. This is especially troubled lessons since biologists often uncritically emulated mathematically sophisticated models of physics to ensure that their modeling is mathematically rigorous. Consequently, quote, theoretical work often diverged too far from life and became exercises in mathematics inspired by biology rather than analysis of living systems. I'm leaving out a lot of details that we can come back to in the question and answer period. I now turn to the second part of my talk Levens thought that the best falling strategy for complex systems was all hit Molly and in the 1970s he systematically developed one method of qualitative problem loop analysis to describe ecological communities so the equations of one specified the behavior of an n-variable system x sub k are variables and the c are system parameters right side of course are equal to zero as equilibrium in the neighborhood of an equilibrium equations of one can be linearized as in is in two this gives a matrix of constant coefficients a sub ij that represents the effect of variable j on variable i now if a represents species interactions in a ij represents the effect of species j on species i now the reason for this linearization is that yapanov stability depends upon the behavior of a system in a neighborhood of an equal liberty and given this this linearization yapanov stability is defined as number three where x of t is a solution of two the initial conditions x of t sub zero and the brackets designates some distance in that area.

5:00 Now informally, 3 says that an equilibrium is Yapanoff stable if the system that begins in a neighborhood of an equilibrium remains in and after small perturbations. An equilibrium is asymptotically Yapanoff stable if and only if the system approaches the equilibrium as T goes to infinity. In 1892, Yapanoff proved that an equilibrium is asymptotically Yavanov's stable, just stable hereafter, if and only if all the real parts of the eigenvectules of A are negative. Now, unfortunately, Yavanov's theorem is not very useful for determining the stability of ecological communities, since the quantitative values of the coefficients of the matrix A are needed to know whether it holds, and measuring these values is virtually impossible in these situations. So for example, measuring all the coefficients of A would require quantitative estimation of n-squared species interactions, each of which would require numerous manipulative experiments. And there are some, and I have some quotes that are some references in the paper that show how difficult this is to determine. The coefficient signs, on the other hand, can be more easily determined. And since the coefficient signs often can be determined, hypotheses about ecological sometimes be evaluated in the absence of quantitative data one such hypothesis is whether the stability of the ecological communities depends primarily on the quantitative strengths of the species interactions or the qualitative structure of the interactions in the community whereas quantitative models require quantitative data the sacrifice of quantitative precision makes qualitative modeling well suited to address this question A loop analysis is based on an equivalence between matrices and directed graphs, and this was matrices with constant coefficients, and it was first anticipated by Sewell Wright in the late teens, early 20s, and it provides methods for assessing this question. so the system variables are vertices in the diagram and the value of the coefficients from the matrix a determine what vertices are connected by edges and the edges direction if a represents only qualitative information about

7:30 interaction between species the coefficients a sub ij take values 1 negative 1 and 0 corresponding to other species J is a positive negative or no effect on species i so for example for a matrix a for three species n h and p but the diagraph below it is the corresponding diagraph for that matrix for this system n is a predator of h h is a predator h is a predator of p and n and h are self-damped now a loop is a series of directed vertex to itself that does not cross any intermediate variable more than once and a number of edges in the loop determines its length and disjunct loops share no bursts so specifically this is a self damning loop of link one so is this there's a little of length two there's one that goes around all three for example this loop of length one is disjunct from this loop okay but the loop of length three is not to jump from any of the other loops now notice that if a is only representing say two species n and h look at this top corner the determinant of a would be a sub nn times a sub hh minus a sub n h times a sub hn and notice that is exactly the difference between the link 1, and the coefficients of the loop of link 2 between the two. So there were several papers in the 70s that let us generalize this relationship between determinants and loops with equation 6. And this allowed him to define, quote, feedback at level k in an n-variable system shown in 7. Now, the technical details of these equations are important here, but the crucial point to appreciate is that the correspondence between matrices and digraphs entails a correspondence between the terms of determines and products of loops. Now, 411s, feedback in a system

10:00 process is a system process by which changes in one variable are enhanced or mitigated or positive or negative feedback so for example if you increase one variable that sets up changes in other system variables which lead to further increase of that particular variable on the opposite for negative feedback and with this conception of feedback at a level 11 shows that two loop theoretic conditions were necessary and sufficient for stability the first criterion requires feedback at every level be negative. And the second criterion requires feedback at lower levels be stronger than feedback at higher levels. And that's all that this large determinant is saying. The problem, however, is that quantitative data are usually required to determine whether these conditions actually hold. And so, for example, in the previous digraph, that system is only stable if and only if this condition is met which required and furthermore the probability that quantitative data will be needed to determine whether they hold and the number of variables for which it is needed increases with the number of system variables now this limitation of the theoretical stability criteria prompted a search for completely qualitative criteria and two economists work and Rupert found the first set of completely qualitative stability conditions now these three definitions are pretty straightforward I'll just say informally that assign remain stable with any quantitative specification of the values of entries that preserves its sign pattern and with these definitions they prove that 8 through 10 were necessary and sufficient for science ability other more complicated conditions were found but like 8 through 10 they were all biologically impossible so for example condition eight requires every species to be self-damped and that seems to rule out things like elite effects nine requires the communities not contain simians or competitors that's extremely so to address a hypothesis I considered a few slides ago the

12:30 implausibility of the stability conditions make it probable that the stability of most ecological communities depends on the quantitative strength of the species' interactions, not merely on their qualitative structure. Now, the point of briefly outlining some of the formalism involved in the Apennop stability and glupinalysis is not technical collivalence. Pause. Rather, it's to provide an example of qualitative modeling that is very different from the kind of modeling that Orszak and Sober criticized. Specifically, this outline shows that qualitative modeling can be a formally rigorous affair. Before their critique of qualitative modeling, however, Orszak and Sober characterized a qualitative model as one that makes only a qualitative prediction, and in this sense, these models are not mathematical, unquote. Now, senses differ, of course, about the exact meaning of the term mathematical but their claim is indefensible if it's intended as support for the criticism that qualitative modeling unlike quantitative modeling is not rigorous because it's not mathematical quantification is not necessary for formal order in science any more it is in mathematics turn to the criticism third part or second silver criticized in 1993 that qualitative modeling was conceptually and methodologically problematic for two reasons i'll let you read these the first just concerns the basis for qualitative testing the second concerns what qualitative modeling can achieve And after criticizing qualitative optimality models of adaptation, Orzak and Sober conclude that the idea of qualitative modeling has hindered the development of an unbiased assessment of the truth of adaptationism. Now, these criticisms have several problems of one in three. The first is that the quantitative data quantitative testing requires often does not exist and cannot be collected feasibly in many scientific fields, or demanding quantitative data is inappropriate for the kind of phenomenon being studied.

15:00 And this predicament isn't unique to ecology, but it's often true of systems with complex dynamics, such as social systems. Orzeck and Sober's criticism therefore fails to appreciate that quantitative is a rare, or sometimes inappropriate commodity in some aspects of science, fields for which qualitative modeling is well-suited. The second problem is that the basis of Criticism 1 as a criticism of quantitative modeling is dubious. Now, Orszak and Silbert didn't discuss their first criticism in any detail, but they do decide to reference Orszak in 1990, which provides a clear understanding of the issue. In 1990, Orczak analyzed several studies of a model of mating competition due to Warren. Now, these studies tested the model by plotting observations of a sex ratio of appearance in wasps against the model's predicted values and then visually, quote, assessing the fit between them. Based on such a visual assessment, Warren characteristically judged, quote, the sex ratio data show the trend predictably, unquote, although he presented no statistical tests in support. Without going into the details, I just want to point out that the basis of Warren's judgment was the graph on the right, where the points are, the observations, and the lines, and the trend. Bells should be going off. Now, Orszak correctly identified two problems with this method of model evaluation. First, the appearance of fit depended significantly on presentation scale. And second, judgments about what could be concluded from such a, quote, fit vary dramatically. But these problems are misplaced as criticisms of qualitative modeling. The studies that Orszak analyzed specified the exact mathematical form of the model and estimated the quantitative value of the model parameters required to make quantitative point predictions. They were not qualitative for the model. Orszak's problems target only one obviously flawed kind of qualitative test, this visual assessment of them. The appropriate test of a significant fit between observations and quantitative predictions

17:30 is a regression analysis when you have quantitative data in a quantitative model. And in Warren's case, it would be a non-linear regression. Now, that regressions were not performed justifies suspicion that the results were not significant, and this was the reason those statistical tests were presented. So what Orzak and Patrick Biel was just bad scientific methodology, methodological problem with qualitative modeling. The last problem is that Orszak and Sober's second criticism seems to presuppose an overly narrow view of qualitative modeling in particular and scientific modeling in general. And I've repaced it. So for Orszak and Sober, the principal objective of modeling is to account for data. And the reason qualitative models of adaptation are fundamentally flawed is that, unlike quantitative models, they cannot do this. Testing quantitative predictions, however, against observations is, of course, a critical part of scientific modeling. But models also function to enhance scientists' understanding of systems, which is especially important in the development of scientific explanations. The understanding that qualitative modeling provides is especially useful contrasts the models that sacrifice generality or realism, it does not depend on unrealistic assumptions, and can be generalized. Now, most philosophical theories of scientific explanation agree that enhancing understanding is essential to the explanation, but of course differ about the kind of understanding required. But it should be noted that Sober takes a broad view of the kinds of understanding involved in scientific causal accounts that narrowly focus on understanding of the causal processes that underlie phenomenon. So in 1983, Soberr argued that equilibrium explanations 1-1 sex ratio in a population are counterexamples to such causal accounts. So he makes the argument put here. I'll agree with that. Now, what he means by a more encompassing structure is a set of disjunctions of possible

20:00 causal scenarios. So, causal explanations specify what scenario is the actual cause. Equilibrium explanations do not. They situate it in these structures. And notice the original emphasis on understanding. So this argument supports rather than is contrary to the position that loop theoretical explanations of the stability of ecological communities provide sound explanations. For example, satisfaction of the qualitative stability criteria 8 through 10 in the previous slide entails that a system is stable, but this is consistent with an infinite number of quantitative specifications of coefficient values so to use the language loop analysis does not specify a particular causal scenario in this case stable system behavior but does situate it within particular qualitative constraints on how system components interact so this raises a puzzle about why a decade later silver is critical of qualitative modeling so for example, although they mention that qualitative modelings have provided a better understanding of adaptation, this doesn't mitigate their judgments that qualitative models have hindered the scientific search for the truth about the adaptationism debate. And I believe the answer lies in a tension between Levens' emphasis that qualitative modeling, quote, stresses qualitative understanding of the primary goal rather than numerical prediction, and a more a restricted view of scientific modeling that Wurzak and Silver's analysis seems to presuppose. Qualitative modeling prioritizes enhancing understanding of model systems over generating quantitative predictions. But their second criticism, however, seems to presuppose that scientific models that focus primarily on enhancing understanding are of secondary importance, or worse, that they're a hindrance to scientific progress. so to conclude as section 2 of this talk I hope indicates I think this is a mistake qualitative modeling assists in scientific research not by generating quantitative predictions but by broadly and rigorously contributing to better representation and understanding modeled systems that it has different but complementary objectives when compared

22:30 with quantitative modeling does not indicate conceptual or methodological deficiency thanks I like the paper a lot I guess I'm just not familiar with how biologists decide whether the modeling technique is qualitative or quantitative because you said that even the qualitative modeling is mathematical Maybe it involves graph theory or something besides analysis or something like that or calculus, but could you just say a little bit more about how that's supposed to go? Because I guess the worry is that what Sober was criticizing in qualitative modeling is not, maybe there's just a difference in terms of how you're thinking of qualitative modeling. Okay, so the Wurzak and Sober piece had three main criticisms. The first criticism was of the distinctions that Levin was making. The second was of his conception of robustness. And the third was of qualitative model. Now, so your question really depends on the first piece of projects. And I'll just say, although I don't want to get into details of it, is that in many ways, Orszag and Soberg just misinterpreted what Levin's different decisions were. So for example, with respect to the virtue of precision, they conceptualized it as a dichotomous, or rather, whereas for Levin's, it's clearly a matter of degree. To give you an example of the kinds of different degrees of precision you could have in a model, on the one hand, you could have just a sort of verbal description of a process. Then you could have some sort of graphical representation of a process. Then you could have an almost formal description of whatever process is going on with clear restrictions on the kinds of relations between variables. And so, for example, you could just restrict them to being monotonic. Or then you could put further specification on them, like it's concave up or concave down. And then you can specify the exact mathematical form between the two equations, and then at

25:00 sort of the extreme, the continuum, you could actually specify the quantitative value of how they're related. So you can instantiate the mathematical form. So that's it. Does that answer your question? Well, I guess you're saying that there's no rigid line in biological parameters between quantitative quality the example that you pick is it's not a borderline case so it's it's a fair case right I wonder about your second criticism because clearly what the degree I'm not sure that silverware was assuming that the only function of the models were to get a good fit with the data I think that's they pose the problem as well this is a major question about it so it's not clear to me that to respond to it, say look models play other roles given that Sober himself acknowledges that they do play a role that doesn't seem to well, on the other hand if they did play a sound and justifiable role, you wouldn't expect the conclusion that they have hindered the search for the truth about adaptationism I think those are separate issues, right, because the way they seem to be framing the question is, well, if you don't have a good fit with the data, that's one way in which it looks as though that the model is hindering the truth. It may be playing other roles, but at the end of the day, unless you get this good fit, what else can you do in order to decide that the model actually is adequate? Right. Well, I mean, if these kinds of models, right, did contribute to your understanding of the phenomenon and possibly even suggested different explanations of it, right, would you then say that they were hindering the truth, the search for the truth in that faith? And I think the answer is no. So that suggests that although they may recognize some import to this kind of mallet, it's clearly at a vastly inferior status when compared to quantitative mallet. And if that's the way you want to describe the criticism, then I still disagree with it. Right, but then I think in that case, your response is different.

27:30 So, because now you say something that it's not only that they have a limited notion of the model, they're presupposing a very limited function of the model. What you're actually saying now is, look, even granting them a broader notion of the model, then we realize that the model in question may actually play a positive function. So, that's a different criticism. And I think it's actually much more plausible. Right. taking board whatsoever himself has said I guess maybe I should I should make sure that I clearly present my case that's right okay yeah that that's the interesting one I think good so you say the value of qualitative analysis is in enhancing explanatory power, and that assumes that there's value in explanatory power. So then the question comes, We all agree. Not everyone does. So then the question comes, what's the value of explanatory power? I believe that the only value in explanatory power is in helping to develop quantitative models so that you could then argue that the only value of qualitative modeling is if it enhances your ability to create quantitative models. Yeah, I guess I'm not sure if I have to disagree for that criticism because it could be framed like, well, yes, I could accept that and then say, well, yes, So you would hope that these qualitative models would eventually play a very important role in the subsequent development of those quantitative models, but it could be that the time frame between the two is very large. so you wouldn't have to see immediate development into some sort of quantitative model to in some way indirectly justify the qualitative models that I'm talking about

30:00 but actually I'm not sure I want to accept her so let's just go to the next one James one of the response I mentioned first I was taking with Green even as a part of the line quantitative modeling. In some sense, it is. Because it's a matter of degree? Maybe it's a matter of degree. I think you can still criticize Sober and Orzak because Levin's qualitative modeling has been existing in the literature for quite a while. And he doesn't sort of just ignore what he's been doing. Yeah, I agree. Why do you want to say the qualitative models just to give explanation and not prediction. It seems like the qualitative models, I guess it depends on what you mean by qualitative, but if you can say, for example, behavior of a certain variable is periodic over time or monotonically increasing, that's a qualitative prediction, but it's a prediction. And rather than just, it doesn't just give me a feeling of understanding or allow me to understand why certain data is. It actually makes a prediction about what the behavior would be. Yeah, I don't want to say that. Which? You don't want to say that? I think you've just understood. Okay. Bill. I think this came down to the same thing. That is, the idea that somehow the apocalyptic end of science would be to have as full and as quantitative a theory as we want in different areas, I think it's wrong. That is very often you not only are okay with qualitative theory in a given area, but you actually want it. I mean, going back to the original idea of robust theorem, you may want to quantify over a bunch of heterogeneous systems in which a lot of the details don't matter, and you want to be able to show that the details don't matter, and both the loop analysis and the earlier robustness of ways of keying into that. I mean, you may still need to know quantitative values very close to crossover points and so on. So that would be the justification for not accepting your consent. Thanks. Well, when I went outside and had to take a little break, I was firmly dressed down by Dick Grandy, my very senior and esteemed colleague, for not taking that 10 o'clock coffee break.

32:30 And I said, I was under very strict instructions, and I have the email from Miriam Solomon, who is like possibly for the conference, and he said, but it's tradition. And so I am now diverting from my instructions, because Dick Randy is... A man. What's the... No, because Dick Randy helped me out when I was just a kid, and because I realized that we only had four papers, and that we do have time to take a coffee break, and belatedly, I thought it was appropriate, before we hear Dmitri Cortizia's paper, that we go ahead the main reason is that I love biology and I believe in it and so that's the main reason so let's take a 20 minute break and meet back here in 20 minutes Thank you. Hi, welcome back. Thank you for giving me tonight, and thank you for your correction.

35:00 We all know that the semantic view claims that a theory is or can be presented as a family of models. I want to bring out three of the three of what I consider the most important elements of this matter. And they are that defining a theoretical structure really implies that you have a family of model types, or to talk in more simple terms, a family of models each theoretical model belongs to the theoretical structure and the second point is that all the auxiliary hypothesis the theories of experimental design and the raw data entering the construction of some other structure that people call a data model md And the third element of the semantic view is the relation between the theoretical structure and the data structure, which I just symbolize like this. And I don't wish it to stand for anything specific, just a structural mapping. Different versions of the semantic view, which interpret the theoretical structure in a different way, are led to different interpretations of this relation. We know that Van Prassen, for instance, interprets it to be an isomorphic relation. Geary interprets it to be a relation of similarity that Constance, French, and their collaborators take it to be a partial isomorphism, an isomorphism between partial structures. and Fred's soup he takes it to be the relation of being an idealized in the abstract replica of the data model my quarrel with this man you will whichever

37:30 version of a semantic view is that these two things the theoretical model and the data model cannot always be individual I'm going to present the case where it is contrary to what Chris was saying I claim that this money gives us an excellent picture of the result but then I move on to another case nuclear physics in particular where I will show you that the semantics you doesn't help to enlighten anything about nuclear models very quickly the structure of my argument is this if the semantic view asserts the three points are here as another way to capture scientific reason practices modeling in particular then And the features of every scientific model that represents its target physical system must be reducible to either those of an MT or those of an MD. I claim that in nuclear physics such a distinction cannot be, is not tenable, hence the semantic is not adequate in describing at least applications of quantum mechanics in nuclear in the nuclear domain but let's let me clarify a few things what is an empty and what is an empty an empty is something that a lot of the proponents of the semantic you have spent time explaining hence it's quite clear it is a structure which is defined so let's look at one simple example that I have put up there if we define if we we take we define a theoretical structure by means of the momentum and position variables standard classical mechanics If we specify a function which we commonly refer to as the linear restoring force, it gives rise to a model, a particular equation of motion, which describes a model that we refer to as the linear harmonic oscillator.

40:00 If we define a different force function, which is no longer just a linear restoring force, but another dumping factor, let's call it, this gives rise to a different model, which physicists refer to as the dumped harmonic oscillator. and we could go on and on defining some such models and whichever is most convenient for a particular representation we choose it and we use it of course whatever the model whatever the theoretical model that will be used uh is there has to be i claim a respective data structure a respective data model to which it can be contrasted otherwise it's no use talking about theoretical models it's no use the semantic you does not enlighten us in what goes on in science if however there is a data model then the semantic view works fine what are data models i claim that well i don't really claim it i interpret fred sappy the fred suki as claiming that uh because i i think he's the only one who has devoted some work on this issue but the only one among the proponents of the you to be more or less the following data models are constructed by lumping together all the theories of experimental design and auxiliary theories raw data and transliterating everything so that we can convert the data into what they would have been had the idealizing assumptions of the theory been true I'm going to demonstrate this again by means of an example because I want to I'm in the process of understanding what a data model is I want to understand if I and I also think that if I don't understand what the data model is I don't really is about so I'm going to try to explain to you what I think the data structure

42:30 is by means of this example now we have seen earlier on the simple pendulum model it is described by this equation of motion the second derivative of the position variable and the sine function of course we assume infinitesimal oscillations and we convert the for reasons of mathematical tractability we would convert the equation to the linear harmonic oscillator equation which is this equation if we solve this we get a relation between the acceleration due the the chord length and the period of oscillation now physicists know that if they were well the experimental problem of determining the acceleration due to gravity becomes the simple matter of measuring the cord length L and the period of oscillation physicists however know that because we started from the which is it holds under several idealizing assumptions and it does not hold for a real system in the world they know that the period of oscillation is T naught is going to be nowhere close to the actual period of oscillation so they start working on ways of how to relate the experimental value to the theoretical and they commonly they talk in the following language they say we introduce correction factors into the equation you introduce a correction factor due to the buoyancy because of the air medium we introduced a correction factor because of the stretching of the wire a correction factor because of their resistance and on and on now all the all that the influences from these correction factors are to the period are very small because they are very small

45:00 they the physicists treatment is relies on the theorem of linear independence of differential equations so they treated as if we have separate differential equations completely independent of each other and they solve for each different correction factor and they they take that the corrections and add them to T naught and then they match it to the experimental body the semantic you I think can be best defended if it reverses the story if it if story in the following way. All these computations that the physicist does are not corrections to the theoretical value of T naught, but they are corrections to the experimental data, the experimental period, such that the data is converted to what the period would have been if the idealizing assumptions of the linear harmonic oscillator were true. now of course this is I claim, despite what Therese was saying earlier, I claim this is a very good picture, it works fine for classical mechanics whether I view the correction factors as being extensions of the linear harmonic oscillator or as being parts of the corrections in the data model it makes no difference because it's a very good way to reconstruct And it works. Of course, the reason I think it works is because each and every correction factor that is used for correcting the period of oscillation is based on a particular auxiliary that is antecedently available, and it is considered to be closely connected to Newtonian mechanics. This is not the same case in quantum mechanics.

47:30 Auxiliary hypotheses are not antecedently available so that we can assume that they are related to quantum mechanics, But we have to try, and we have to try very hard to relate them to quantum mechanics. And despite the fact that classical mechanics can be reconstructed according to the rules of the semantic view, in nuclear physics, which is the area that I primarily study, this cannot be done because we are searching for auxiliaries. We want to, and once we find them, we want to construct models by which to explain, by which to provide a description of the physical mechanism which explains the auxiliaries. I chose the liquid rock model to cash out this story, because it's the simplest model. But just because it is simple, it doesn't mean it is on its own. There are plenty such examples in nuclear physics, and the liquid rock model is very important because it is the basis of many of them. more sophisticated models it is based on an analogy between the mean free path of nucleons which must be significantly small compared to the nuclear radius just like the liquid tropics and the molecules of a liquid drop and it is based on the assumption that energy is quickly shared among the nucleons. The nucleons are strongly coupled together, so there are no individual motions. This is an idealization, of course, every nuclear physicist knows that, of course, there are nuclear motions, there are nuclear motions, independent nuclear motions. The series of idealizing the classical assumptions that are used in setting up the energy equation of the liquid drop are the following the nucleus in its stable state is considered to be spherical for small deviations from sphericity where

50:00 the surface undergoes deformation oscillations at constant density the surface tension of the nucleus acts as a restoring force and finally and very importantly as we'll see later on the energy of the nucleus is the sum of the volume energy surface energy and cool image these assumptions lead I'm not going burden you with the physics I'll just put them up here they lead to a classical Hamilton function which eventually is quantized its deformation parameters of of the liquid drop of the vibrating oscillating leave the liquid drop are quantized and it takes the final Hamiltonian takes this form the The process of constructing this Hamiltonian is particularly important, but for other reasons, not reasons concerning my argument here. I think it is important because this quantization step, I find it to be arbitrary. There are no general rules why we choose to do the quantization at this stage and not at some other stage. But it's a different story. If people have such a question, I don't think it relates to what I have to say today. No doubt, I said it earlier, no doubt the liquid drop is a semi-classical model. We can dispose of it. We don't have to talk about it. It's not really a quantum mechanical model. So the semantic view can simply just say, these are not the models I'm talking about. But in order to fill in the details of answering the semantic view, we have to talk about lots of other models, many of them based on the liquid drop. So there is going to be something missing from my argument because of time and space. It's missing from my paper also because of space. Now, it is quite obvious that the liquid drop, despite being a semi-classical model, serves some explanatory purpose.

52:30 It explains in particular two phenomena which in 1936, around that time when it was proposed, it was essential to explain nuclear fission and the electric quattrovolts moments. the question I asked is how could proponents of the semantic view accommodate such a model into their conception of theories I can think of I can think of three options the first option could be to classify into the class of theoretical models, but in doing so, we have to provide a set of theoretically justified rules by which we can convert the deformation coefficients, the alphas, into the canonical conjugate momenta. And I don't think, in fact, I know there are no such rules available. so it's not an option a second option could be to regard the liquid drop as a data model but of course since the semantic view requires a sharp distinction as I claim between the theoretical and the data model we must have a theoretical model to construct it to contrast it to and we don't have such particular stage of the development of nuclear models so finally a third option could be to undervalue the models importance and dismiss which is the one I read Steven saying in history recently that's how I read it but I don't think that we can dismiss models, and particularly their representation power and explanatory power, just because they don't fit the underlying conception of representation that either the semantic view or some other view may have. I think we have to answer the important question

55:00 whether the model represents a target physical system and if it does, why it does. And I claim that the liquid drug model represents the nucleus because it explains certain properties of the nucleus, even though it explains them partially. But we found that out five years later, not at the time when we proposed the model. To understand why it explains some of the properties, 25 minutes, we have to look at the principles used in constructing the model. So I'm going to run through them very quickly. First, what happened before the development of this model was that mass spectroscopy was developed, and via that, we were able to discover several experimental results. One such result was that the binding energy of the nucleus is related to the mass of the nucleus. And among other experimental results, They led to the Weizsager semi-empirical mass formula, which is, I claim, the auxiliary which the liquid drop model was designed to explain. The Weizsäcker formula, which was proposed by von Weizsäcker in 1935 and by Beite in 1936 independently, is the auxiliary that the nuclear physicists of the time were searching in order to explain that to take apart the nucleons, which is what the binding energy is, We need to take into account volume energy, a coulomb, a surface energy, a coulomb energy, a pairing term, and a symmetry. The two last are parameters which the liquid draw cannot explain. However, the first three are, if you recall, the essential parts of the assumption which was used to build the liquid draw.

57:30 And the liquid drop had that assumption because it had to explain the Weizsäcke formula, which is really nothing else but the auxiliary we used in order to relate the target physical system to quantum mechanics. in order to argue for what I say I must burden you with the physics but they are all in the paper so you can read that just in a qualitative description I just want to say that what we have is in constructing a model such as liquid rock we have a constant interplay between theory, model, and auxiliary Weizsäcker formula and the function of the model is in fact to relate to explain the Weizsäcker formula to provide a description of a physical mechanism which explains the formula But at the same time, to relate the formula to the principles of quantum mechanics. And the liquid drop provides such an explanation for three, the first three terms in the formula. The volume, the coulomb, the surface area, energy. And I find it extremely hard, supposing my understanding of the picture is correct. I find it extremely hard to view the model in terms of the distinction between the theoretical model and the data model that is the prescription given by the semantic view. In fact, if I try to view the model by means, but through the lens of this distinction, then I think it would obscure the fact that the model served the very particular purpose of explaining the

1:00:00 Theoretically explaining the Weizsager Auxiliary. I'm just out here, and hopefully we'll have a few questions, specifically for Demetrius, and then we'll open it up and have the rest of the discussion for all the speakers well this is actually a beautiful paper but actually i think it supports the semantic view here's why i don't think that the proponent of the semantic view need to be committed to the sharp distinction that you have between the theoretical model and the data model actually a lot of the defenders of the view have highlighted there is actually a hierarchy of models, from the data to the theoretical models. And I think... Yeah, there are people like Xelpes and others. And what is interesting is what your work indicates is exactly that the liquid-drop model is an intermediary. And you highlight exactly the function that it plays in these hierarchies. In particular, I think, if you understand that there are several partial relations linking these various models, what part of the liquid drop model is relevant in doing the explanation in the way that you indicate so i think it's actually a beautiful uh example of how the semantic approach works good job well yes and no well first of all i agree with you with that conclusion in fact my conclusion is that the The only thing that is required by the semantic view, this is not leading to a rejection of the semantic view, it leads to just one thing, that it has to be something by non-structural relations between data, as Stephen calls it, model of phenomena, and theoretical model, if I'm right. But it's going to be, this is my suggestion, the semantic view has to be supplemented with something stronger, a relation which is non-structural. Because there is no way to individuate what we are mapping into what in such cases.

1:02:30 But why is that? Because look at what the physicists at the time were doing, right? They had the WISAC formula. Thank you.