**John Blomster: **Welcome to DISCOVERY, a podcast where we explore today's biggest legal and legal-adjacent topics with distinguished guests and experts from around the globe. I'm John Blomster and today we're speaking with Ted Sichelman, professor of law at the University of San Diego, where he also directs the Center for Intellectual Property and Markets. He's also the founder and director of the school's Center for Computation, Mathematics and the Law as well as the Technology, Entrepreneurship and Intellectual Property Clinic. Ted also holds a master's in physics and in addition to his widely renowned work in spaces, including patent law, Ted's extensive scientific background informs much of his scholarly efforts, including his latest forthcoming paper, “The Mathematical Structure of the Law,” which is what we're discussing today.

These are some pretty unique concepts that have some profound implications for a number of important fields. And so we're thrilled to get into it, Ted, thank you for joining us.

**Ted Sichelman: **Thanks, john.

**Blomster: **So, the paper tackles the question of whether the social laws that govern people are foundationally the same as the scientific laws that govern the natural world. The answer that you posit is a resounding yes, which is backed up by a wealth of research in the paper, thought experiments and some pretty intense equations. So, I have to ask before we start to break it down, how did you become interested in studying the law from this particular angle?

**Sichelman: **So, when I was in law school, and this is now almost 25 years ago, not quite, so 1997, I took a class in real property from Professor William Fisher at Harvard. And we covered Wesley Hohfeld, who was a legal theorist in the early 20th century who came up with a system to classify what he termed legal relations. So, he had the concepts of right, duty, no right, privilege, power and so forth, that he said, could be used to categorize any legal problem, whether it was in real property, torts, contracts, even outside of private law, constitutional law and so forth. When I saw this system, and Hohfeld came up with some different relations, logical relations between these underlying relations, I thought this sort of reminds me of particle physics. Don't ask me why. But I just had this intuition.

**Blomster: **Naturally, right?

**Sichelman: **Something like that. I just finished doing a master's degree in physics a year before that, not even. So, I went back and looked up some of the work online about Hohfeld and saw people had done some logical formalizations of Hohfeld and I thought, could I sketch something out that's more mathematical like particle physics? Literally, like the next day I sketched out what's the basis of this paper. So, this is actually my oldest paper, right? And my most reason, and I wrote it up for a seminar I had the following year, and then sort of tucked it away and worked on it every now and then and got caught up with IP law and patent law and so forth. And now I'm coming back to it after all these years,

**Blomster: **Just to define the term, when we're talking about the structure of law in the sense of how we're discussing in regard to the paper, we're not talking about necessarily the interpretation or application. So, what are we talking about when you're talking about structure.

**Sichelman: **So, it's important to use this term structure because when I say social law and scientific law is similar structure, it doesn't mean the laws are the same that somehow scientific law determines what our criminal law will be or something like that.

Let’s start with criminal laws and example. So, what's the structure of criminal law? That some person has a duty or obligation to the state to the government, not to engage in certain types of behavior. Pretty simple. And now let's look at physics. So, in physics, we tend to think of the laws as merely descriptive. So, some categorization of what actually happens, but we can take another perspective where the law actually governs. So, it's more of a platonic perspective where the law has some meaning beyond being a mere description. So, Newton's laws in this platonic world, for example, those who are the end all be all laws, we know that they're not always exactly right. But let's suppose for a minute they are. They would govern, for example, the behavior of particles. So, particle has to obey Newton's law, just like some legal person has to obey criminal law. So, that's the metaphor. And then, and other people have recognized the same, and in fact, for many years philosophers thought there was a connection between the two. And it was only in the 20th century that this sort of fell by the wayside. But what I do in the paper is show from a mathematical perspective there are deep similarities between the two. So, if we take Hohfeld’s formalization essentially of these legal relations and extend it to the mathematical world from the logical world, we see that we can put it into a format of vectors and tensors and other mathematical objects that are very similar to what you find in in physics and in scientific law.

**Blomster: **And so there are two primary models that you discuss in the paper for analyzing legal systems. So, can you explain what a logical model is versus the mathematical model? And then what are some of the challenges that you have found with the logical model?

**Sichelman: **Sure. So, soon after Hohfeld, there were many theorists who proposed various formalizations of that model and, and similar models, what I call social law. So, this is where you come up with some fundamental concepts, whether it's duty or obligation, and so forth. And you put them into a logical hierarchy that you can then use to describe the law. So, for example, in deontic logic, if you're obliged to do something, then there's a basic assumption that you must be permitted to do that action as well. Because if you're not permitted to do something you're obligated to do you're right in a Kafka-esque situation and so forth. So, there are these various sets of logics that were developed, and that are used in artificial intelligence to model legal systems.

So, the problem with these approaches are twofold. First, they tend to assume that there's always some right answer given the law and facts. So, people tend to think of it as a speed limit, right? You're either driving 55 or you're higher than 55. If you're 55 and lower, you're not liable. If you're higher than 55, you are. Well law doesn't always work that way. There are many gray areas in the law. So, the area I focus on outside of this one is patent law. So, interpreting a patent, like interpreting many contracts is notoriously difficult. Even with experts and all the facts in front of you, it's often very tough to determine with any certainty what a court's going to do. So, it's more probabilistic. So, many people say probabilistic patents right are a better term than like patents because a patent should give you some clear boundary of whether you're inside or outside of the patent, whether you're infringing or not just, like the boundaries to a piece of land. But it really doesn't. It's probabilistic entitlement in the sense that maybe have an 80% idea that I have this patent that someone's infringing, but I can't really know, because it's so difficult to interpret these darn patent claims. They're written in dense legalese with all this technical speak and so forth. Judges and juries have a real tough time.

So, we'd like to have a model that fits the probabilities of legal situations rather than absolute certainty. You can do that with logic, with fuzzy logics and other types of probabilistic logics. But even if we do that, we're missing out on a lot of rich metrics and quantitative measurements that we have already in mathematics of various systems. So, measures of complexity, measures of, for example, information content that relates to complexity, temperature, entropy, all these things that have been modeled using mathematics, meaning quantitative models that are—would be very difficult to do from logic. So, what I wanted to do with build a model where we could pull in all these other measures to get a more quantitative understanding of the law as a whole, particularly the core elements in the law, like, again, right, duty and so forth, and how those all fit together.

**Blomster: **It's just so interesting because, you know, law is a field where, you know, what you're studying here in the law is, you know, notorious for constantly evolving, right? But you’ve built out these quantitative measures for analyzing these types of legal systems, like how do you, how do those two things fit together when what you're applying it to just seems to always be changing?

**Sichelman: **So that's where the mathematical measures are very useful. So, we can determine how a law is changing by probabilities of outcome, we now have some quantitative understanding of what might happen. Now, doing that is very difficult. But once you can do that, and there are many people working on this, for example, predicting outcomes in patent cases, once you can do that you can fit it into a mathematical model where we can use these prepackaged measures, so to speak, to get a much deeper understanding of what the system as a whole is doing. So, if I want to understand where is patent law going in terms of various doctrines in the law—obviousness, clank, instruction, remedies, and so forth. If I can package that all up as a bunch of probabilities, and then measure how those are changing, I can bring in these concepts like temperature and entropy and so forth, that are used in modeling complex systems. And now I have much richer quantitative measures, and a whole bunch of mathematics, right in software and so forth that I can plug all this stuff into, to get a better sense of how to predict where the law is headed. Now, easier said than done, but we need the models to start with in order to get those richer descriptions.

**Blomster: **Have you tested this out on a specific case or examples?

**Sichelman: **So, I have not. So, I am still more in the theoretical phase. And a lot of this is to provide theoretical grounding to work others are doing. There are a number of academic researchers and law schools who are doing this. So, there's the Let’s Predict Project, where they predict Supreme Court case outcomes. And there are a number of other people who are working on prediction in industry. So, Ravel law—r-a-v-e-l—is another one. And there are a number of other companies, because you can imagine just like in sports, right? If you can predict outcomes, and you know which variables are driving the outcomes, you can now tell lawyers and clients, right? First, here's our prediction. And second, here's how you can change these outcomes, right, by citing different cases, by making different arguments. How do we know this because we have a data set of 10,000 cases and we can see what worked, what didn't and so forth. And I don't care, you know, how many cases you've read and how much local knowledge you have. We have 1,000 times the data of any single lawyer. So, there are many groups working on these sorts of approaches to law where you put in, rightr big data and you have smart models. And you get predictive capabilities beyond what any given lawyer can do.

**Blomster: **So, another issue you talk about is indeterminacy. This idea that where every legal rule and a legal doctrine is opposed by a corresponding counter rule, using legal reasoning. And so if a law is indeterminate, it's impossible to hold that law to a rational standard. However, you posit that even if a law is indeterminant, that it doesn't matter, it can still have a rational foundation. Can you explain that?

**Sichelman: **Sure. So, first off, I don't believe it's every law, every legal situation has indeterminacy. Some do.

**Blomster: **Right. Right. Right.

**Sichelman: **So, in those situations, many people would just throw up their hands and say, “There's no way to predict the outcome.” Right? It's whatever the judge ate for lunch, but analytical/right computational model say, “Wait a second, maybe if we have enough data, and we know what these extra legal factors are, we can start modeling.” So, what's indeterminant? It's the law, given the facts that are supposed to be relevant to the law. So, again, how do we interpret this patent claim? Well, let's take the patent and let's take all the relevant facts and so forth. And well, no, you need more than that. We need to know who is the judge, right? What's their legal training? Who’s the jury? And so forth. What's the court? All these other factors. And if we look at the history of all these other factors, we can start to get rational predictions.

What I'm doing is introducing a theoretical model that shows there's at least some rationality at a probabilistic level. It's not a situation where we're nihilists and throw up our hands and say, “Hey, the law is finished. It has no role to play.” The traditional law might not get you to the final point, but it can get you pretty far. And then there are a whole bunch of other factors that tend to be the same in case to case that we can now collect data on and use. Now, is that the best type of law we can have to model a governed society? Maybe not. But that's what we have. And we need to work with it and understand it, rather than throw up our hands and just say, “It's all based on things outside the law. That's not what lawyers should know.” No, lawyers should know what these factors are and good lawyers do. But not only should we know what they are, we should collect data about them and model them so we can get better understandings of how it all works.

**Blomster: **As we've been discussing, you know, we, you can see how this can apply to the legal field. But beyond that, where are other opportunities to apply, you know, the model that you're developing and these concepts, what are other fields that this could really make a difference?

**Sichelman: **So, the end of the paper, which I presented today, but have yet to write, hopefully soon, that's the last piece, takes these understandings and applies it back to scientific law. What's interesting in social law is this extra layer of law that we don't seem to have in scientific law. And that's laws for making laws or law about law.

So, when you think about a contract, what does the contract do? A contract changes the legal rights and obligations of the parties. So, it's kind of a little private law. So, we don't have a contract between the two of us right now for anything, but suppose all of a sudden, I tell you, “Hey, I'll pay you $5,000, if, you know, you paint my house.” All of a sudden you have an obligation to paint and I have an obligation to pay. What do we do? W e change the underlying rights and obligations of parties. How do we do that? We do that with a legal power. The legislators have legal powers to change the laws, right, for everyone, more than just a contract between two people. And then the constitution tells us also about higher order powers and immunities. What restrictions there are on changing the law and how laws get changed, and so forth. We don't have that in scientific law. We don't have any language, mathematical language, that tells us how laws get made. That's why we think they're mere descriptions. But if we think somehow laws play a more fundamental role, meaning they're governing material objects, and they exist out there somehow beyond the mere matter that we're looking at now, we need some language to tell us how those laws came about, how they change, if at all, and so forth.

We also need a language of measurement. So, in the classical system of measurement in science, the measurement device, the observer was neutral. So, you measure something going 55 miles an hour, and it's 55 miles an hour. I measured 55 miles an hour, I'm done. But in quantum mechanics, it's very different. So, things exist in these indeterminate superpositions. It's kind of like what I was saying with the case law of some percentage that it's right outcome A. Some percentage it's B and let's see, we don't really know what it's going to be. And then somehow after measurement, it happens to be in one of those three states. But we don't know how that works. Well, if you look back at what we're doing in social law, there's a judge, and the judge says, “You know what, I'm going to pick option A, or I'm going to pick option B.” And they do that using a legal power. They need some power to make a judgment.

Well, maybe there's something similar going on in scientific measurement. Maybe there are these physical powers or scientific powers, not the power that we have in physics today to move something but a, what I call a second order power that exists above the level of the laws we have right now—laws about laws. And people would call this metaphysics, but I actually think it's just another level of physics or of science that we can describe mathematically and my long term goal is to take what I'm doing and try to write more in the area of philosophy of science and science to come up with mathematical descriptions of these laws about laws—laws about scientific laws,

**Blomster: **This is deep stuff. And you know, we were talking on the way down to the studio, that the overlap in the Venn diagram between experts in physics and law that you occupy, it's very small, but for law students who are really interested in this approach and exploring these kinds of concepts, what advice do you give them?

**Sichelman: **So, today, those sorts of students are very fortunate because many law firms and many companies and clients want people who have scientific training for a variety of reasons. One, the rise of intellectual property law, particularly patent law, but two, now the rise of AI in the law. There are so many artificial intelligence-based applications coming into law firms and companies that are legal in nature. So, the simplest one of course is a TurboTax type of application. But there are many more sophisticated applications now, all the way from e-discovery to again brief writing and arguing in court that require people not only to produce the applications, but also to know how to use them. And the more scientific training you have, and the more understanding you have of these types of issues, you'll be much better situated to use the tools or if you'd like to, right, go participate in the creation and production of these tools and the many, many hundreds of startups and other companies that are working on AI-based applications.

So, there's a huge opportunity for students and certain law schools are taking the lead in this area by providing courses on AI and the law. But I think every law school very soon will start to have a number of courses and then eventually permanent professors to teach in this area because law firms are demanding.

**Blomster: **Ted Sichelman is professor of law at the University of San Diego, where he also directs the Center for Intellectual Property and Markets. He's also the founder and director of both the school's Center for Computation, Mathematics and the Law as well as the Technology, Entrepreneurship and Intellectual Property Clinic. You can learn more about Ted, his scholarly work and more information on everything we've discussed today over on our DISCOVERY podcast page on law.uw.edu.

Ted, thanks so much. This was a lot of fun.

**Sichelman: **Thank you, John. Same here.