Using Formal Models to Study Strategy and Organizations
Thank. You very much for being here thank you, very much, when and more for organizing, there has been a great conference I've learned so much, so. Let. Me talk a bit about why. Using, formal models, and I say here in strategy, and organizations, because models. Are used differently in different fields. So, part of the I think it interesting, part of the discussion, will be to compare later how, different, fields think. And use models. About. This talk the, main audience when I was preparing this talk where. PhD. Students I was thinking, about getting. Students that were considering, to, do work on modeling. And, then I was thinking to try to explain what are the benefits of modeling, what's, the philosophy behind, modeling. I want. To share the. Sensibility. And the process, of creating a moral, and, I. Also closer. To, to to to the main topic of of of the seminar, our. Workshop, I want, to talk about how, moorlands, promote, robust. And reliable, research. Another. Thing is a lot has been said about formal. Models so I will quote extensively. Others, yeah who have said these, things in much better, ways than than, than I can. So. The. Agenda here is first, let's, talk about formal. Models then, when, they are appropriate, how, we build, models, and then, how to write a modeling, paper and this last part is mostly, based on my experience, as a reviewer, and as an editor, when. When writing this part I was saying what are the main problems, in. Weight, with modeling papers are, the most typical problems, that, the reviewers. Usually, find with, modeling papers. So. Quite formal models first. I would say there's there, are some practical, and fundamental, reasons let's talk about the practical reasons first so. The practice the first reason, is that. Organizational. Theories, involve. Many, actors, and levels, of analysis, and, it's very hard to predict, how these, many actors, and levels, of analysis, will interact, so. This is seeing a model as a. Tool, for your, your, mind yeah it's it's. A an. External. Representation that you can use to. Expand. The, kind of things and the complexity, of things that you can think. The. Other practical reason, is that. Organizations. Many times are hard, to observe and. Experiment. With, so. Models. Sometimes. They are not always at. A good way of a styling. Phenomena, for which you, don't have, IPL, data. But. I think that the really fundamental reason. Is. Something. About the, speed at what, fields. Developed. So. Why some, fields, advance, faster, than others there's, a very good art in 1964. In science, called, strong inference, and, the main idea of, that article, is that. Fields. That develop fast our field that have theories, that, are testable. So. Many people have thought about this the, main group of people that thought about this, how.
To How, to create theories to tear testable is, the. Vienna circle and, so this is one quote. Saying. What is required for that theory, to be tested, and the goal of the vienna circle was. To, eliminate what they called metaphysics, but these are statements. That you cannot accept. Or reject if, you if there's a statement that's like that, that's, about statement, will, get you your your reasoning, will, become slower if you have statement, like that so. The goal for. Them was to try to eliminate this. This, type, of statements. So. In practice, this, means that, for for, a field to develop rapidly. You, require measurable, things, that can be measured you. Require clear, definitions. And you. Require clear connections, between the different parts, the different constructs. In your, your theory and well. Formal, models, provide. Exactly. This. So. They are a vehicle, to achieve, exactly these. Things that make, for. Strong inference. Here. I have, a quote. From. Richard Fineman, so, when he died people took, pictures to his office and in. His blackboard, yet, several things written, so. This was in, one of the corners of that blackboard, he said but. I cannot, create I, do. Not understand, this. Was one of his motivations, young so. He what. He's saying is I'd really understand, something when. I can build a model if I cannot build a model it means I don't really understand, it. This. Is an echo of of of an older. Aphorism. One. Of the philosophers, of the, of, the Enlightenment. Giambattista, Vico. Said. Something like certain. Quad, factum, I am. Certain, about the, things that, I can do so, this is the spirit of of, more link. So, benefits, of modeling yeah but our, models, are always useful. And. Here. I'm using the same figure, that James, yesterday. Used yeah this is also one of my favorite. Papers. Its. Original in a book by the one I'm copying, here is is the, one the, chapter in the in in. This book and the. Chapter is called Isla Mattox yeah the, study of research choices, and dilemmas, and. The. Idea is that there's no perfect, research, method, some. Research, methods, give you one thing others. Give you some other thing but in order to advance science. You, need all of these things so, there's no research method that's that's the answer yeah, do we can. We always use morals. No. Morals. Are good for. Memorial, to be a generality, they're. Very bad, to. To. Talk about the effect of context, for example and there's are a number of of dilemmas, here. So. That's, why also this figure also give me give me hope in, that harking. And be, hacking that we have been talking during the workshop, but really not that important, problems. Because. You. Can be hack in one, method but you cannot, be hacking in all of the methods. So. Together as a science, yeah which, we should move the theories we will move the theories forward. So. Put the process yeah about building, a model. So. This is sort, of my workflow yeah, the first thing is, to be listening, yeah this, listening, can be listening, different. Sources. Yeah can, be your intuition, can.
Be You're listening, to a manager, that's telling you something or, you're listening, for, gaps, in the literature you're you're open. Sometimes. And, at, some point you find something interesting, and. Then, what you try to lose to get to the structure, of that, problem what. Is the minimal, set of, mechanisms. That, are behind that, concept. But that problem. Here. In the listening, and the structuring parts two, things are important, here two, things about your black background, so, for the listening part is very important, your. Knowledge, your background, about different, theories. And. About practice, because, this will allow you to listen to more problems, and for. The getting to the structure, of the problem it's, very important, that you have tools to model this is your vocabulary the, more tools that you have the more things, that you will be able to model, so. This is from another corner, of. Fine, months blackboard. So, this other corner said, you. Have there know how to solve, every. Problem that. Has, been solved, what. He's saying there yes I want to know all, of the tricks so that I can model lost, the, most that I can. So. After these two steps there's. A process of simplification. So. Get try, to get really to the core of the problem. Here. Many times you will have to go back to you you will have to restructure. The problem you will change a little bit the problem. So. Here simplicity, simplicity is the most important, simplicity. Is the ultimate sophistication. You. Want to have the, simplest, possible model. Later. We I will talk more about simplicity. Why simple simplicity, is beneficial. But. One of the things there are some interesting demonstrations. Now about why Occam's, razor, tends. To lead, to better. Theories, the, simpler is a theory, the, more likely, it is to, be, true. After, you have your moral you analyze the, predictions, of your moil. And. Then. Sometimes. Just by looking at the results of your mole you won't understand, what's happening so. You need to go deeper. And try to understand, the, mechanisms. That are that are producing that behavior. So. The end product, of all this stage at the end of this you will have three things you. Will have a clear, question you. Will have a moil and you, will you will have results, this is the core of of. A modeling paper. So. The question is when is my model good enough when, do I have a good or a. Good. Model and I think it's. A combination of three things so the more that you have of these three things the better. How. Simple, is your moral how relevant is your model and how surprising, are the results, that you get from from your model so. Regarding. Why simple, is good well, we talked about well. It's more likely to, be true a very. Practical reason is, that a simple model, is, explainable. Within, the bounds of a paper so. If you have ten. Parameters, and, each one has, yeah. Ten levels, yeah the, the, space of possibility is so high that you cannot explain that in a paper so that that's a very practical. Reason for having simple moral and another practical reason, is it, will have fewer open, Flags from. The four, reviewers, to attack your. Your logic. So. Here's another quote here, with for from, for Norman with four parameters, I can, fit an elephant, yeah. With. Five and I can make make. Him wiggle his trunk. So. If. You put too many parameters you can explain, anything, so. Your theory is not very predictive. The. Other dimension that, makes for a good model is is it relevant. So. Which conversations. In my field I are affected. By this moment it, is something that many people talk about this, is something important, to, managers what, are the the, practical, and the theoretical implications. Of, this. So. Richard Hamming one of the fathers of of information, theory said.
Hey Ask yourself, three questions what. Are the most important, problems in your field and we. Have many in strategy, and organizations, are. You working on one of them and if not why. Not. So. That was his, heuristic. To choose research projects, and. Then. The, final one is is if this surprising. So. What's the sense of creating a model that ends up saying something that we already knew that's not advancing, how, much we know so, you need there for there to be a surprise. In the, in the results. This. Is very similar to how Bertrand, Russell thought about what philosophies. Is. That the point of philosophy, is, to start with something, so simple as, to, not seem worth starting, or. Stating. Them and to, end with something so paradoxical. That. One that. No one will believe it. This. Is their ideal model you, start with two things that we all agree we all know there's no, no. Discussion, about them you put them together and, you, see that there's this interaction, that unfolds, for example when you put time. One, typical question shoot my morale be a closed-form, or, should be a simulation is, there ant-man an answer, to this I think. Einstein gave, gave a good answer to this, if. God. Doesn't. Care about our mathematical. Difficulties, he. Integrates, empirically. So. If you are interested in understanding some. Phenomenon. That's. Completely unrelated, to, how you are going to understand, it if using a closed form or a simulation, so, the first thing that you should you try to do is to to. Model that to understand, it and then. At. Some point yes oh so you follow the steps first you listen then, you get the structure of the problem then you simplify the most that you can and at. That point is it's. Not your choice some. Problems, will have a form, that, that, will be you can write it as a closed form and some others will, not. So. This is not really a big, issue both. Are formal, models and they are formal, because. Their. Interpretation. Doesn't, depend, on a. Subjective, system. Their. Interpretation, depends, on a computer, or on the. Rules of math that's. What makes a model formal, but. Every. Time that you you. Execute, it you get the same. Then. Think. About how to write a. Modeling. Paper so, main problems, so. This motivated by main problems I seen in in the review process. So. The first thing to keep in mind is that. Formal. Model papers have two audiences, there. Will be a, technical audience and a general, audience. These, are very different you should, keep both in mind while, writing your paper. So. The technical audience will, care about. Reproducibility. They. Don't want to, see, any hand waving in the paper they, want to be able to read, the paper and then. Drip reviews, and the results. They. Want precision. So. They want clear definitions, clear processes, analysis. And that the math it's, all cleared. They. Also will. Care a lot about behavioural. Plausibility, are the assumptions, that you're entering. Into your model realistic. And. They. Will also care about modeling. Insights, that, they get for example if you introduce a new model okay, argue like providing, a. Toy. That then other modelers, can use yeah, are you providing tools that will be useful for others can. This moon will be extended, to study, other phenomena these are things that typically. Your technical, audience will care about. The. General, audience, will. Be thinking about other set of things they. Will think about is this, an interesting, phenomenon. Do.
Real, World, firms care. About this yeah in in strategy, and organizations, this is super important, yeah it is related to performance somehow. The. General audience will. Also. Think. About is this extending. Our, theories, so. If this paper building, on the state-of-the-art. Understanding, of this problem and is this moving. The state-of-the-art and. They. Will also care a lot about the, really will how. Riddle is this. Paper, can. I understand, maybe and this, is a typical problem people. Focus too much on the technical audience and then they they lose their. Bed, audience so. Traceability. Super. Important. So. How to serve the two audiences, I think. You have to serve the general audience first so. The phenomenon, and the. Theory, should, be front. In. Your paper. There. Must be a clear motivation and, that's what will motivate people to keep the attention reading, the paper. The. Paper must, be readable without, understanding all of the equations because. Most. Of your general audience will not understand, the. Equations. So. You, can, but. You, need to be reproducible, so, in order to do that I think the best is to move the more complicated technical. Things to, an appendix. So. Another. Quote from from harming the. Purpose, of computing is, insight. Yeah. That's what we want to do with a moral yet not not the numbers we want to extend our theories. Not. Because of the technical. Neatness. That we're doing this. Then. There's an issue about providing. A valuable contribution that's. Valuable. By by both audiences. So. Typical, things, that modeling, papers can contribute, so. They can shed light on, some. Important. Problems by helping solve a debate, there's, a theory predicting, these tears and now they're predicting that the. Formal. Model can say hey there's this other contingency. That explains when you want this theory or this other. Can. Also contribute. By, showing that there's a more general, way of, thinking. About some. Some, phenomena and we thought about the stood as two different processes now, we can say hey they are both special cases, of this. Other larger. Mechanism. Also. Another, way in which formal, moments contribute, is by presenting. Surprising. Predictions. That stem from Commons. Assumptions, plus logic in, a model you essentially you tie your hands you, just put assumptions, that we all agree and then you let the formal model derive the. Implications, of that when. That's surprising, that's that's really beautiful. And. The. Other contribution. That I feel, at least for me is the most important, is when, a formal, paper and this few. Papers are able to do this is, when. They allow. You to think more formally. About, something, that's important. But. It was very vaguely explained. Before, so, in strategy, two great examples. Relate. To value, and adaptation. So. Until. 1996. People. Hand, waved a lot when, talking about value, they'll. Say oh we. Create value we destroy value week this, value, value, you would hear the word value millions.
Of Times but. What is value, if, you start asking questions very. Rapidly, you could realize there's no answer, at least at that point what what is this thing that everybody, talks about. Well. The nice thing about this paper is, that hey values. These things the difference between these two numbers once. You know that you, are this third number and then you can talk about value created, value captured. So. It creates, a very formal. Way to, talk about something that's important. I think. That this is the most important thing in strategy, where, we. Know that there are many, important. Concepts, out there but. We don't have to really clear words to, talk about them here's, where morals, can canal a lot of value. Another. Example live in Psalm 97, is. A model, about. What, is to adopt so. Before it was very entire how firms have helped what are they doing. After. That now we have a very clear language, to, talk about adaptation. The type of search that firms do while adopting so, this expands. The the. Realm of things that we can talk and think, clearly, about I, think. This is the most important, value that we can get from. From always. So. Practical. Things what's a good structure for a modeling paper this is my in my field I think that, the, five part, structure, is very useful, for the paper have. An introduction, theoretical. Motivation, then you present your model, then. You have results then you have a discussion. One. Thing to keep in mind is, that modeling, papers, they. Don't have hypotheses, you're, not testing, theory with a modeling, paper. If. They, have hypotheses. They. Are at the end of the paper they, are propositions, okay. If you believe this theory then, there. Are these other implications. That that that, stem from this theory, so. This is, something that that's very different from other, from. Empirical papers, hypothesis. If they are there, are RS propositions, at the end. Because. A mohel doesn't test theory but but proposes, theory. So. How to write a modeling. Paper. Clarity. Is extremely. Important, in modeling, papers why is that I think it's more important, than in empirical papers. Because. What. Happens is that understanding. A model is more complicated than understanding, and empirical and empirical paper the cognitive, load of. Understanding. Of up our modeling paper is higher because you need to understand, the English the. Theory. But. At the same time you need to understand, the, math so. The way that you can reduce, that cognitive, load to a manager manager, level is you. Have to write very. Very clearly, so.
Time Spent, writing and rewriting is, time, well spent. Here. Blonde. I said there, is no great writing, only, great. Rewriting. Yeah this, is super important, with modeling, papers, with all all papers. But with modeling papers, you. I think. Maybe. 50%, of the papers I've, seen, one. Of the main comments, of reviewers is. Essentially. I don't understand, what you're doing. Because. They. Are not clearly written. So. Ways to achieve clarity well. It's, about coherence. It's one part so how you achieve coherence, you, have you need to have clear connections, so how you move from one paragraph to the other how do you move inside, the paragraph from one sentence to the other for, that you need to keep your, subjects. Very clear and fixed, you. Need to try, to be succinct. You. Need to make things clear use. Intuitive, variable. Names that will decrease so, if you have incentives, call it I that, will be easier to remember I for incentives, rather than than, gamma or or, theta yeah. Use. Diagrams and tables, to summarize, the main elements, of your, of your model use, figures to, help communicate the results that that all, makes. This, easier, to explain. So. Spend time spend, time writing it is the very famous quote here I could, have written a shorter letter but I did not have time. So. You need to spend that time. Motivation. Also part, from clarity, is very, important, in a model. Because. Amal and paper doesn't have empirical contributions. So. Why, people will will, read the paper you need to create an unimportant, motivation. So that you. Readers. Will stay with you and. The. Other thing is that understanding, a model is difficult. For most trailers so the more need, of a motivation, in a modeling. So. There's something I call the macro motivation, of the paper so make sure that the theoretical, gap is very clear and that you are addressing a clear. And empirical. Puzzle so ideally you have both you, have a theoretical gap, and you have a practical. Gap. And. Then. There's the micro motivation, so the micro motivation, is typical in the in your, first page of the paper in the introduction, the. Micro motivations, how you motivate each, part of your paper how, you motivate each time you introduce a construct, each time you introduce. An analysis. You. Need to motivate that. So. Use for example X use, examples, here can be real-world or can be stylized, examples, but adduced, them that will motivate. People to continue and, also. Elaborate, your results, in ways that are useful for your readers to not just show, this, the relationship, about. That relationship, and. Describe practical, empirical, theoretical, implications. Another. Question, about. How. Complex, should, a model, be, and. This. The answer to this is that it depends, on the field and even, within. The field so this is this. Probably, different, in, strategy. And organizations, done in psychology, for example so. I think that the main. Contingency. How. You choose how. How simple or how complex is, how. Much you know about a phenomenon, so. The more that you know about, the phenomenon, the, more justified, you are to, build a complex model. So. For example we know a lot about physics and, then. We can build flight, simulators, flight. Simulators, have millions of parameters it's. The shape of the of the airplane, that, terrain where it's flying. If. You count all the parameters there easily millions, of parameters. Well, in organizations. We. Are not yet at that stage. So. We. Are probably here we know very few things so. We should build. Mostly. Simple, models. That's. Another reason for why moments. Should be simple so you, always should, try to resist the temptation, of filing bells, and whistles to your, morale which is very easy in, a model. But. It's super costly. If. The more. Parameters. That, you are the more mechanisms that you have the, less of the, problem space that you can describe in your paper then, the more doubts in the minds of your readers the. Less that your readers will understand, about, this phenomenon. So. In practice, I think, I agree with with, from Norman at the beginning about the five parameters moving.
The The trunk, that. Is sort of the upper bound in, organizations. Models. So. Someone let's say this so. Good models, are like. Haiku. I I, subscribe, to that vision. The, extreme, case of the super complex model even has a name it's, called Bernini's, paradox. So. What's a panini's paradox, is when you have a model, that is as complex, as reality, and. If you have a model that's like that so the map is the same as the terrain then. You don't learn anything from, from. The model. So. Another, reason for keeping morale. Simple this is another reason for why you should, probably. Never analyze, a model, by running regressions, yeah. We, will analyze a model, by running a regression because the model is so complex that they cannot understand, what's going on in the model so. You use them you want. To have a simple model where, you can understand, the, mechanisms, that are driving the. Results of the model. Reproducibility. So. You, have to provide enough, details. In the paper so. That a technical reader, can. Reproduce your, results. That. Means. So. You. Have you need to provide everything so, that you give this to someone and that someone can, can, create the same results, as you have you, should test that before, submitting a paper give, your paper to a technical trader see if that person has enough to, get to the same results as you do. And. The other thing is keep your files clean, and organized, important. If you write a computational. Model so. Try to write clear and succinct code, comment. Your code. Imagine. That you're writing code for someone else and that someone else needs to understand, your code usually, it will be you you, will need to understand, your own code but, it's your future you it's, your you in five years from now at, that point you won't remember anything about the details of the model so so make, a favor to eat to your future you and write simple, and clear. Documentation. Of, your, model and keep, backups. So. Summary of the main challenges faced. By modeling, papers, I think these are there are several challenges, and they are tough challenges, so. You need to have a clear contribution. You need to have a clear motivation, you. Need to, be to have a very clear exposition, of, the mechanisms. You, need this to be very simple and you need this to be reproducible, many, many, challenges, the. Common theme here if, if, clarity, and um, this, is right this the way it should be because. What's, the promise of a model is that it will create clarity. In, one part of our field so. That's. What we strive to do with morals, creating. Clarity. So. If you address all of these challenges you. Will have expanded the realm of things that, we can reason and that, we can talk about and I, think that's a great contribution. So. Finally. Building. Models is hard. Work that. Requires, you to know to, explore many theories many mechanisms. It's. An iterative. Process, you. Need to be willing to change how you think many, times until you get to.
The Core of of a problem. So. Good quote here, from. David walpert he said to purchase inside, you. Must pay beforehand. In confusion. While. You're creating a moment you are confused, yeah but but the real word is that when you are done you have created, clarity. In this part, of little part of the universe and. Building. Models is rewarding. It's. A creative act and. You create something, that lives outside. Of, you. You. Gain new insights you learn. You. Contribute. To our field, by, building, a better, foundation and. This, is important. The words, of Leonard Savage he said no science, can. Be more secure, than its foundations. And that's how molds, can that's, it thank, you. Well. Thank, you I, agreed. With most, of what you said. I'm. Going, to just take. Issue with one, thing that's which is the surprising, finding. Part, I. Get. That from. Reviewers when I submit, my papers and my, response, is that's. Why I keep a bunch of petri dishes in my office I, might find the next penicillin, when. I create, a model, I'm usually, not trying, to find surprises. Listen, all, right I'm also not trying to find surprises, and what. I'm trying to do is that motivational, part right usually I'm trying to explain, usually, some empirical, puzzle, or I'm. Trying to represent the. Herbal theory and so, it's not necessarily. Going to be surprising, but if, the, end result of this modeling, exercise, is not surprising then. This is not having any any valuable. Information to, the field so. It won't, be. Publishable. Yeah. I if. You if there's an empirical, problem. Here's. A I don't understand why this is going on oh here might be an explanation yeah, turns. Out if I represent this explanation as a formal model it, accounts, for that I can that I'm not I would say it is surprising, because I didn't know so. What's a surprise something that I didn't know that I know now. I know how to explain, that that phenomenon okay that's what I was hoping you'd say we want surprise, doesn't, mean some. Prediction. That, we wouldn't have expected it means it. Explains. Something we didn't think was is that easily, to explain there it is there's a question, so that's what, we mean by surprise, what you mean by surprising we, fully agree okay. Yes. So. I think it's. Important. That you talk so. Remember, that this is all about listening that's the first step so that. Conversation is, very important, where you will understand, how they think how, you think from. That conversation. You. Will come up with, the core of the model and you will be in charge of that core of the model you, cannot expect, them to create. The model or to, build. The, results, section, yeah but. But, the collaboration, is important, in that first, stage so. That your Gurian what's the problem, what are the main elements and, then. You will be in charge of of. The core of the paper and, then. Hopefully, your. Co-authors will. Collaborate with the. Rest of the paper I. Find. That collaborating. With others is very valuable, because. You, learn, how others, think and, you, will get new ideas we will and trying. To to be empathetic, with, others you, have to understand, how they think I, feel it's it's the first step in creating a, good model understanding. What are the problems of others. Yeah. I'm, gonna expand. On that answer, I mean first I say, take, notes while this is happening because, in the end what. We're probably gonna want is a field, where you've, got a modeler. And a, theoretician, and an empiricist, and, maybe an engineer, but. In biology and my biology department, they've got those three things cirrus modelers.
And Empiricists. And the, modelers, translate, the theorists into. Models and then use the fiercest. To, test them and you. Can't not, that they're not all three of the same expert in the same head so, we want to be able to understand how do we create a science, where. We can have these people all talk to each other so that we can make progress and so not, only would you have this model paper but a paper about how you create that model paper would probably be a really good, paper. And. I would say it has something to do with how. Familiar the, field or the journal you know the community in the journal is with. Modeling, as a tool for, theory. Building but, I would say just. Relatively. More new to this than Jeff for example, but we're also trying to do things that are multi-level. And, focus. On, phenomena. Over time and our. Initial. Experience, James may want to, elaborate. On this comment. But we spent, a lot of time convincing. The reviewers, that we're writing a theory paper because. We included some empirical data to, show the plausibility, of the theory. That the model was describing. And that. Was, a big heavy lift just, to get the mindset changed, around for, them to understand what. The. Role of a model was know if you want to yesterday. So. You can contribute also, by, explaining. To your co-authors making, your courses familiar with the philosophy, of. Modeling. And. It. May be an educational, experience, for particular. Journals, that are new to it. Something. That I see both, when. When handling, papers as an editor or even some of my own work is that. There's. Sort of attention among reviewers to. Novelty. With the model itself not, just looking for novelty, in terms of the contribution, of the outcomes that come from the model and the, reviewers saying oh that's just a standard. XYZ. Model, that they use in economics, therefore. This, is not a worthy paper. And. And. That tension there is very it's very difficult to resolve as you, talked about to different audiences a technical, audience and, the. General audience yes, but there's also the. Methods. Audience, versus, the substance, audience, yeah and and. That can mean, challenging, their the role of the editor, is very important, so, the editor, needs to. Wait. Yeah. And these two audiences. Yan to some point say okay yeah this is as a. Case. Of this other model but, no one ever thought about using this model, to, think about this problem that's. A huge. Contribution. Because. Now you're giving people tools, to think about the problem before they didn't have the tools in our. Degree what why try, to develop a new model when. There, is a. Perfectly. Acceptable well. Tested. One. That's been applied in other contexts. You, you have a tool to work with yes, and and and to me it's why, do you want to reinvent something that. That's there when. What you come up with isn't, markedly. More efficient, or more elegant, or it. Doesn't function better I guess is really what it could yes the, contribution, of this is giving, tools, for. Thought not. Not, the, numbers or the mathematical tricks, yes.