Lecture dated 29 Iyar 5777
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Summary of the model: completing information and building a theory
- Data mining as an application of completing missing information
- The scientific analogy: “the common side” and identifying a shared property
- Every possible rule and the need to filter through a table
- Returning to the topic / passage of kiddushin: the full table and the preferred completion
- Moving from the abstract solution to identifying parameters through the actions
- Alpha as a hierarchy of strength and the “transparent action” of a document
- Scientific speculation and the systematics of the context of discovery
- A non-unique optimal solution and an alternative solution
- “Rotation in parameter space” and choosing a basis according to intuitive convenience
- Why the equivalence is not trivial: working with a partial table
- Returning to the halakhic results: the meaning of erusin, marriage, redemption, and yevamah
- Matching to physics: coefficients, mass, and matching
- Practical examples: cameras, tornadoes, companies, and a traffic judge
- The limitation of binarity and the need for a model for continuous values
- Notes/annotations
Summary
Overview
Rabbi Michael Abraham presents an algorithmic model that takes a partial data table, completes missing cells by constructing an “abstract theory” of microscopic parameters, and emphasizes that there is a two-way operation here: both mining information for the sake of predictions and building a theory for the sake of understanding. He connects the practical side to the field of data mining, and the theoretical side to the scientific process of identifying a shared property that explains phenomena. He shows how the model helps identify parameters in the topic / passage of kiddushin through a table of actions and outcomes, discusses the non-uniqueness of optimal solutions and understanding them as choosing a different “basis” for the same theory, and argues that this equivalence breaks down when working with partial tables. At the end he presents possible applications to camera data, tornado storms, predicting company collapse, and a traffic judge, and points to a central limitation: most problems are continuous rather than binary, so the model needs to be extended beyond 0/1 or to a graded binary approximation.
Summary of the model: completing information and building a theory
The Rabbi describes a situation in which there is a table with data and one missing datum, and an algorithm completes the missing datum by building an abstract theory of microscopic parameters that govern the data. He defines the completion as a scientific-style prediction, and the building of the theory as the opposite direction that tries to explain what lies behind the facts. He states that both directions have separate value: completing missing information is a practical tool, and identifying the parameters is a theoretical tool aimed at understanding and not only prediction.
Data mining as an application of completing missing information
The Rabbi identifies the work with the table as part of what computer science calls data mining, where one takes known data and extracts from it information that does not explicitly appear. He presents filling in the missing cell as a typical data-mining operation and notes that this has many applications. He describes the algorithm as a way of producing new information out of the structure of relationships among the existing data.
The scientific analogy: “the common side” and identifying a shared property
The Rabbi demonstrates the theoretical side through a physics example: a ball and a book that fall to the ground lead to the hypothesis that there is a shared property that explains this, even before one knows to identify it as mass. He describes building a broad table of responses to various phenomena in order to complete a missing datum such as “will a pencil fall,” even without directly identifying the parameter. He states that science does not make do with predictions but aims at understanding, and therefore it is important to identify what the “alpha” itself is and not only use it as a predictive tool, and he adds that the model does not identify parameters as such but can help greatly in identifying them.
Every possible rule and the need to filter through a table
The Rabbi accepts the possibility that a shared property could be defined arbitrarily, such as “belonging to a sequence,” and connects this to the Wittgensteinian claim that anything can be a rule. He states that the table is supposed to rule out rules that do not hold once additional objects are added. He suggests an intuitive hypothesis that if one takes all the information, one reaches the correct answer even without explicitly identifying the parameters.
Returning to the topic / passage of kiddushin: the full table and the preferred completion
The Rabbi returns to the topic / passage of kiddushin and presents a full table of outcomes such as marriage, erusin, redemption, yevamah, divorce, and against her will, as against actions such as property/money, huppah, intercourse, and document. He states that it has already been decided that the preferred completion for the missing cell is 1, and that from here the theoretical part of understanding the structure of the parameters begins. He also describes a constraint of “pleasure” in yevamah and redemption, and demonstrates how the completion dictates a graph and a parametric solution of the alpha, beta, gamma, and delta type at different strengths.
Moving from the abstract solution to identifying parameters through the actions
The Rabbi says that in order to identify delta, gamma, beta, and alpha, it is better to look at the actions (money, intercourse, document, huppah) and not at the halakhic outcomes that are not intuitively familiar. He identifies delta as “value / worth” because it appears only in money, and explains that the kiddushin document itself has no monetary value because its action is not carried out through transferring value. He connects this to the Talmudic statement “with a coin, his mind is on the imprint, and the imprint is made to be nullified,” and to the explanations of Nachmanides and Or HaChaim that a coin is all about its value and has no intrinsic content, and he formulates this by saying that money is the concretization of the concept of value. He identifies gamma as “pleasure” because it appears in money and intercourse and in accordance with the constraint, and beta he proposes to identify as an act of “joining” because in the first solution it is shared by huppah and intercourse.
Alpha as a hierarchy of strength and the “transparent action” of a document
The Rabbi emphasizes that alpha appears in all of them and at different strengths, and it is the only parameter that receives more than one value, and therefore creates a basic hierarchy that allows inferences of the kal va-homer type. He argues that this axis is a general strength that gets colored by parameters such as joining, pleasure, and value, so that strength attached to beta is strength of joining, to gamma strength of pleasure, and to delta strength of value. He points to a special difficulty with a document because it contains “transparent strength” without color, and proposes identifying alpha as the capacity “to contain legal effects” or create halakhic outcomes, while also suggesting that alpha might be interpreted as expression of will, and that a document is a clear expression of will because of deliberate writing and judgment.
Scientific speculation and the systematics of the context of discovery
The Rabbi states that identifying the parameters is always provisional and that scientific theory too is not certain, but he argues that the model turns the context of discovery into a systematic process that narrows down impossible options. He says that the same data set can give rise to different interpretations, but the model rules out identifications that do not fit the structure of the appearances of the parameters in the table. He presents the algorithmic nature of building the abstract theory as an alternative to a “mystical” intuition of discovery.
A non-unique optimal solution and an alternative solution
The Rabbi demonstrates that the optimal solution is not necessarily unique and presents an alternative solution in which certain components are exchanged, which changes the distribution of beta across several actions and outcomes. He notes that in reading the information there is no difference between the solutions because the missing cell remains 1, and the difference appears only in identifying the parameters on the theoretical side. He notes that in the alternative solution delta remains value and gamma remains pleasure, while beta shifts from a “huppah and intercourse” structure to “intercourse and document,” and he has difficulty finding an intuitive shared property for the latter two.
“Rotation in parameter space” and choosing a basis according to intuitive convenience
The Rabbi compares the solutions to the Greek descriptions of the four elements and to choosing a different basis that produces the same data by means of different combinations, and presents this as a choice of coordinates rather than competing theories. He argues that the two solutions are equivalent exactly like a description in physics in Cartesian versus polar coordinates, and that there is no principled preference, only a preference in terms of convenience of identification according to intuition. He emphasizes that genuinely competing theories are those that do not stand in a relation of full conceptual rotation/translation and may have different empirical content, whereas here it is the same theory at the same strength.
Why the equivalence is not trivial: working with a partial table
The Rabbi states that the equivalence between the solutions is relative to the table one is working on, because in practice one works on a partial data space and not on “all of Jewish law” or “all the data of the universe.” He argues that if all relevant and irrelevant data were included, the model would filter and return a group of solutions that are rotations of one another with no real difference. He adds that when working on a small table chosen intuitively, different solutions may yield different implications for data that were not included, and therefore the equivalence is not complete in a general sense.
Returning to the halakhic results: the meaning of erusin, marriage, redemption, and yevamah
The Rabbi interprets erusin as a state that requires only a minimal ability to impose halakhic effects, without any need for pleasure, joining, or value, and divorce as a similar requirement at a higher strength, which explains why a document works but money does not. He interprets marriage as requiring alpha and beta, that is, halakhic strength “colored” by joining, and connects this to the Talmudic distinction that erusin forbids “like consecrated property,” whereas marriage brings her into his domain and joins them. He interprets redemption as requiring value (delta) together with other components, and presents yevamah as a case that requires joining, pleasure, and greater strength, while discussing the intuitive difficulty of combining pleasure in a context of against her will, and the suggestion that דווקא “since he benefits” strengthens the involvement of pleasure.
Matching to physics: coefficients, mass, and matching
The Rabbi likens the abstract parameters to physical coefficients whose connection is discovered in experiments, and only afterward does one match them to intuitive concepts such as mass. He presents the process of identification as a matching between two kinds of parameters and not merely as adding external “meaning,” similar to the distinction between inertial mass and gravitational mass. He notes that pleasure, joining, and value are intuitive concepts that help perform the matching after the model has found a formal structure.
Practical examples: cameras, tornadoes, companies, and a traffic judge
The Rabbi describes a data table about cameras from the internet with features such as zoom, flash modes, price, and response speed, and suggests completing a missing datum by discovering correlations rooted in technical constraints or manufacturers’ design trends. He mentions data on tornado storms (Katrina, Ivan, Hugo) with many physical parameters, and argues that one can complete missing values even without understanding the internal physics. He describes an attempt to predict company collapse using a table of economic data, and notes a practical difficulty in testing the model on companies that have already collapsed. He presents the example of a traffic judge in which a lawyer wants to predict whether there will be imprisonment or license suspension according to the characteristics of the offense and the judge, and in principle suggests entering even factors like mood or weather as data.
The limitation of binarity and the need for a model for continuous values
The Rabbi formulates a central problem: in most fields the values in the table are not 0/1 but continuous, like the diameter of a storm’s eye or “to what extent” a company collapses. He proposes an approximation by turning continuous questions into binary questions with thresholds such as “more than half the assets,” and then gradually refining with additional thresholds in order to obtain higher resolution. He notes the possibility of building a continuous model through parameterization of the type “alpha times x plus beta” and additional techniques, and concludes with a comparison to methods that require many functions and multiple integrals.
Notes/annotations
That concludes the lecture of Rabbi Michael Abraham, Thursday, 29 Iyar, the eve of 1 Sivan 5770, May 13, 2010.
Full Transcript
[Rabbi Michael Abraham] The Rabbi
[Speaker C] Michael Abraham, 29 Iyar
[Speaker B] 5770,
[Speaker C] the thirteenth of May
[Rabbi Michael Abraham] 2010, lecture twenty-eight.
[Speaker C] So, in a few directions.
[Rabbi Michael Abraham] I hoped we’d finish this today, but I’m not so sure anymore. It may spill over into next time too; we’ll see how much we manage to cover. Okay, basically, if I summarize for a moment, we drifted a bit in the last two meetings, or really mainly in the last one. I’ll summarize anyway where we were in terms of the model itself, because I want to get back to the model itself. There are a few more things I wanted to show about it. We saw there that when we have some table with data and one item is missing, we can go through some algorithm in order to fill in the missing datum, and that algorithm, in order to fill in the missing datum, basically constructs some—call it an abstract theory—that governs the data in the table. Meaning, the parameters, what we called the microscopic parameters, are basically a kind of theory, and that theory governs the data that we see in the table, and the datum that we fill in through the theory is a prediction, exactly as in the scientific context, where the prediction is what is supposed to be in the empty cell. So in fact there is a two-directional operation here. I already mentioned this. One direction is basically completing the missing information, and the second direction is building the theory that stands behind the data that I use—so this happens together. I use that theory in order to complete the missing information. Now each of these two things has its own value, separately, and in a different context, and that’s what I’ll try to show today. Basically, the first context—completing missing information—is somewhat connected to a field that has been developing a lot in recent years in computer science, and it’s called data mining. Information mining is basically taking some set of known data and trying to derive or extract from it information that is not known, or at least does not appear explicitly. What we did with this model was basically just data mining. Meaning, what we did there was take known information in a table; we had some missing information, one cell or even two cells—we did that in a few cases—and we filled in the missing cell in light of the data in the existing cells. That is exactly data mining, which is basically an information-mining algorithm, what we did here, and it has many possible applications. At least I’ll try to talk about that a bit today. The second direction is of course the theoretical direction, less practical and more theoretical, where, as I already mentioned, as I mentioned in connection with the common side—if we take two data points, right, a ball, we let go of it and it falls to the earth; a book, we let go of it and it also falls to the earth—we infer from this that there is some shared property of the ball and the book that is responsible for their falling to the earth. We don’t know how to identify that property, but we know that some such property exists, and if that same property exists in another object, then it too will fall to the earth. How do I know that this property also exists in another object if I don’t know what the property is? It’s mass, right? Physics has already identified it as mass, but right now I’m reconstructing the process the physicist is supposed to go through. So he looks at the fact that a book falls to the earth and that a ball falls to the earth, and he asks himself what that means. It means there is some shared property of these two objects that causes them to fall to the earth. I don’t know how to identify what it is. There is some shared property. But what can I do? I can see which additional objects also fall to the earth, and maybe other things those objects do, and build some wider table than just two cells or four cells, and then from that larger table I can infer some conclusion. Suppose I ask myself whether a pencil also falls to the earth. I still haven’t identified that the important parameter is mass. I only know that there is some parameter shared by the book and the ball, and I don’t know whether it also exists in the pencil because I haven’t identified it. So how will I know? I’ll check more things. I’ll see how they react to additional things. I’ll burn them all—will they all burn? I’ll kick them all—will they all accelerate or not accelerate? Meaning, I can try to check all kinds of physical phenomena, build—without identifying at all that the relevant parameter is mass—complete the missing datum, and say: the pencil too will fall to the earth. So in order to complete that missing datum, I’ll define all kinds of parameters alpha, beta, gamma that appear in the book, in the pencil; some will appear in all of them, some only in some of them, and that will complete the picture for me, where one of those parameters will presumably be mass, but I don’t know how to identify it. Meaning, this model does not know how to identify it—but that’s not important. Meaning, I’ll be able to complete the information even without identifying the parameter. So what is the value of identifying the parameter? First of all, theoretical value—just knowing that it’s mass and not merely knowing that the pencil falls. The goal of science is not only to make predictions; predictions are just an indication. The goal of science is to understand. First of all, technology’s goal is application; science’s goal is understanding. So if we want to understand, then I want to know what is really responsible for these phenomena; it’s not enough for me to say that there is some alpha responsible for these phenomena—I want to know who that alpha is. Therefore it matters to me to identify that alpha, something the model cannot give. In a moment we’ll see, though, that the model can help a lot in identifying that alpha, and the value is first of all scientific value. But later we’ll see that it’s not only scientific value; it’s also practical value, because we do not work with all the data that exist—and we’ve already discussed this more than once—we are actually dealing only with a partial table. We are not dealing with a table containing all the relevant data, and therefore it becomes more critical to identify these parameters, and I’ll get to that in a moment.
[Speaker D] Basically, yes. Tell me if this is something similar—suppose they have a shared property if I say that “book” is a Hebrew word of three letters? Yes, yes. No, but that one doesn’t have three letters, that one has four and that one has five.
[Rabbi Michael Abraham] You’re absolutely right. So then it’s not shared, but check it in the table.
[Speaker D] No, wait, no—so there could also be a cause and there is no such cause?
[Rabbi Michael Abraham] No, but the table will throw it out.
[Speaker D] Maybe the cause is, for a pencil, I’d say three four five?
[Rabbi Michael Abraham] Not exactly, so that’s why you’ll see that three letters is not a relevant parameter.
[Speaker D] Not three letters—I’m saying it’s not three letters but a sequence.
[Rabbi Michael Abraham] Ah, a sequence, fine.
[Speaker D] That’s still—
[Rabbi Michael Abraham] Nonsense, because you’ll see there are other objects that won’t fit into that sequence and will still fall.
[Speaker D] So I’m asking you whether that also counts as a shared property, that it’s in a sequence.
[Rabbi Michael Abraham] Why not? We talked about this with Wittgenstein, right? Here there’s no law at all; that’s exactly his claim, that basically anything can be a rule. If you set up any sequence, I can always attach a rule to it and determine that this thing is—
[Speaker D] And that counts as a shared property? Yes. That’s this alpha?
[Rabbi Michael Abraham] Yes, it could be that alpha. Absolutely. And you have to rule it out through the table. If that sequence works also for additional objects, fine, and if not, then not. And the hypothesis I suggested, without knowing whether it’s true—but I have some intuition that this is how it should be, I don’t know if it’s true—is that if we really take all the information we have, then we will discover the correct parameters without identifying them, but we will arrive at the correct answer. Okay, so basically the first benefit of the model, we said, is reading information—that is, adding missing information. The second benefit is scientific benefit, that is, theoretical: trying to understand what theory governs this collection of facts, which is basically scientific generalization. Now here, as I said before, the model does only partial work, because it only defines that there are some parameters, maybe divides them—some of them are found in this action, in that action, others are not found; in the outcomes they are found—but it builds some abstract schema in which nothing is identified. We do not know who each such parameter is that explains the collection of phenomena. Let’s see how to do this practically and what this gives us, how it works. So for that let’s return to the topic / passage of kiddushin. And in the topic / passage of kiddushin, after we finished the whole process—I’m obviously not going to review the whole thing—but after we finished the whole process, in the end we had a table, a full table. I’ll write it again because I want to show you how to continue from the point where we stopped, just to see what this thing actually gives us. Let’s add some interesting things here. I’m already writing the correct table, meaning the assumption enters as a constraint; the assumption is not a column but enters as a constraint. All right? I’ll fill in the table for you for a moment. That’s it. This is the table that basically presents everything there is in the topic / passage of kiddushin. After we gathered everything, this is what we get. Now, we already analyzed this table, and we saw that the preferred completion is one. We already saw that. What? This is marriage, erusin, redemption, yevamah, divorce, and against her will. All right? And this is property, huppah, intercourse, and document. It’s a mix of Hebrew and English, doesn’t matter, that’s just how we marked it, I don’t know how that came out. In any case, we reached the conclusion that the correct completion is one, so I’m not going to decide this table all over again now—we already know the completion is one. But let’s see what that means; we’re only at the starting point. We reached the conclusion that the completion is one, meaning that we carried out the process of information mining. We filled in the table of missing information, right? We discovered the missing item of information. But together with that—after all, how did we do it? We found that if the completion is one, then that means that basically the graph looks like this. Let’s draw again the graph of completion one. It turned out to be the correct graph, okay? After we already reached the conclusion, that means this is the correct graph. There. So this is the correct graph that comes out in the end. And I remind you that we have a constraint: in yevamah and in redemption there is pleasure. I explained there that basically the constraint is that money and intercourse involve pleasure; huppah and document do not. In order to get that, one must constrain those two to include a parameter of pleasure. Never mind. In the end we arrived at this solution. I’m not going to go back over the solution because we already did that.
[Speaker C] I’m only reminding you of it schematically. Here it’s two alpha, beta, and gamma. Here it’s alpha and beta. Here it’s alpha, gamma, and delta.
[Rabbi Michael Abraham] Okay? That’s basically the solution. And now if I write it for the actions—for the actions—then how do I carry out the solution for the actions? I remind you. I look, say, at money. Okay, money contains P and I, right? I go by P and by I. So that means that money has alpha, manages to contain I, and money has alpha, gamma, and delta. All right? So basically, in money there is alpha, there is beta, there is gamma, and there is delta. Right? Alpha, beta, gamma, and delta. Okay, now huppah. So huppah contains—the completion here is one, I already know that it’s one, so I can already mark one here, this is the correct table. I’ve already discovered that it’s one; the information has already been mined. That’s the information; I’ve already added it. So now let’s see what it means in theoretical terms, in the opposite direction of utility, the theoretical direction. So I’m saying H contains N and I, and N and I are alpha and beta. So that’s one, one, zero, zero. Right? B, intercourse, contains N, I, Y, and K. N, I, Y, and K, all four of those, so that’s two alpha, beta, and gamma.
[Speaker B] Two alpha, beta, gamma, and no delta.
[Rabbi Michael Abraham] And a document contains I, G, and K, which is alpha, something like three alpha, three alpha.
[Speaker C] Three, zero, zero, zero.
[Rabbi Michael Abraham] Now look, this solution actually isn’t unique. One could have found another solution. My claim is that it’s minimal, it’s optimal; it’s not unique. Meaning, I could have defined another solution, only it wouldn’t have been preferable to this one. There is no theorem that the optimal solution is always unique. Right now this is going to be very important. Why? Because we’re going to try to identify the parameters. Until now, what have I done? I built a model. I know that in the picture, behind this picture, four parameters are at play. That I know: alpha, beta, gamma, and delta. What else do I know about the parameters? I know, for example, that in A there is only the parameter alpha, in K there are two alpha, in G there are three alpha, and so on. I know the distribution of the parameters, which of them is present in which outcome. I also know which of them is present in which action.
[Speaker C] Present in the product. The product, right.
[Rabbi Michael Abraham] You need to. And which of them is present in which action. Right? That I know; the model gave me that. Now I want to take the theoretical step that the model itself does not give. But let’s see why the model helps us here too. Because I basically want now to make the scientific generalization. This is the context of discovery, right? I take the data and build a theory out of them. That is usually perceived as something done by a shot in the dark, right? Divine inspiration. So here—you see?—first of all, we have already arrived at the abstract theory in a completely algorithmic way. No context of discovery and no mysticism. This is the context of discovery. This is a rigid theory. Now let’s see the identification. When I look at delta, all right—how am I supposed to identify it? I want to know who this delta is; now I want to understand, right? Now this is the theoretical step, the second side of the coin. Who is this delta? As a rule, at least in this case, one should look at the actions and not at the outcomes. Why? Because the outcomes are halakhic concepts. I don’t know what the characteristics of erusin, marriage, redemption, yevamah are—these are concepts I don’t know. Jewish law defines them, and there are probably things behind them, but they are not given to me. I don’t know. What do I know? I know the actions. I know what money is, what intercourse is, what a document is, what huppah is—I know exactly what those are. And I know their characteristics. So let’s look at the actions. Delta appears only in money and in none of the others. What does that fit? Let’s try to identify it. A hypothesis. Of course this is never certain. Value? Value, right, worth. Meaning delta is simply worth or value. Right? Only money has it; all the other actions don’t. So probably delta is value.
[Speaker D] A document has no value?
[Rabbi Michael Abraham] No, a document has no value. This isn’t a monetary document. A document where one writes that the woman is divorced or betrothed—that’s only the idea. You write it in that form.
[Speaker C] No, it’s for validity, but the document itself has no value. It has no value; it isn’t fit for—
[Rabbi Michael Abraham] It may be that the paper is worth two pennies, but the value is not required; the value is not what does the work. Money also has mass, but it’s not plausible that this delta is mass just because money has mass, because it’s not the mass that does the work. Here again, the model is not what works; intuition is.
[Speaker D] But which value do you mean? Monetary value. But that’s strange—what is monetary value? Purchasing power, what is that—
[Speaker C] Monetary value.
[Speaker D] Purchasing power.
[Rabbi Michael Abraham] Purchasing power? Yes, and worth, that you can exchange it for things.
[Speaker C] How many kilos of corn it’s worth.
[Rabbi Michael Abraham] Fine, that’s what characterizes money. Meaning, the Talmud says about money—the Talmud says that with a coin, his mind is on the imprint, and the imprint is made to be nullified. Nachmanides and Or HaChaim explain there that the whole idea of a coin is only its value; it has no essence at all, no content of its own at all. All there is in it is that we agreed this thing has value. All right? Especially today—once money was actually worth a lot, but… With a document? No, you can purchase with a document, but it won’t be at the value of the document. There is a deed of purchase.
[Speaker D] But what I’m saying is that it has monetary value, and monetary value is exactly the mass.
[Rabbi Michael Abraham] No, no. When you purchase with a document, you still have to pay in addition to the purchase. Meaning, they do not give you the land in exchange for the document. The document is simply the act that acquires the land. Transferring the document is the act of acquisition. But nobody will give you land without your paying. Meaning, you need value. Okay. And today’s money? Today’s money is a document. The whole idea of money is the embodiment of the abstract concept of value. That’s the whole idea of money. The idea of money is to take a concept that once was very abstract, give it concreteness, turn it into an object. Once there were sheep, there were watermelons, there were houses. Each of those had value, but you couldn’t point to what value itself was. Value is a property of the thing. Money is turning the property into an object.
[Speaker C] That’s the meaning of money. The point here is that something is missing. The concept of a document—we think of a contract. Marriage is a contract, and there are financial commitments, and there is financial content there, and so on. The comparison of the document here is to a kiddushin document, which creates no financial obligation. Basic point. The kiddushin document says: this is it, this is the act that constitutes the legal effect. It’s an act that constitutes a legal effect, but it has no monetary value. Monetary value is found elsewhere. By the way, two small comments. First of all, the handshake of the Yemenites.
[Speaker D] They finished the agreement, now they do a handshake—
[Speaker C] —and say “mazal u-verakhah,” and that’s what—
[Rabbi Michael Abraham] Didn’t I say that before? No, no—not of significant value. Even if the document were made of gold, it wouldn’t matter, because the action of the document is not done through transferring its value. By chance it also has value, just as I said before, money also by chance has mass. That doesn’t mean I should identify this delta with mass. It’s not the relevant parameter.
[Speaker C] If it’s really money, that’s not an exact term—maybe because of money, or money’s worth. Value. Not something that has—it doesn’t need to be worth money, it has to be worth value. Right. And really, it’s not that we found the big idea, in quotation marks, that money has value, but that basically one has to give the woman something that has value.
[Rabbi Michael Abraham] Right. But why is it called acquisition by money? Because money is the noun form of value. It turns value into a thing. That’s the meaning of money. Money has no meaning other than that it represents value. Any other object—a leaf, you can eat it, so it’s worth something, right? A house, you can live in it, so it’s worth something. Money is worth something just like that, not because you can do something with it, but because it was determined that value itself would now undergo objectification, right? It would become an object. It would stop being an abstract property. All right? Okay. So money is this delta; it is plausible to identify it as value. Right? Okay. What is gamma?
[Speaker C] Gamma appears in money and in intercourse.
[Rabbi Michael Abraham] We know what gamma is.
[Speaker C] Pleasure? Pleasure?
[Rabbi Michael Abraham] Right. You would have added it even though in fact you wouldn’t have—
[Speaker D] —needed to.
[Rabbi Michael Abraham] It was a constraint of the graph, yes, you had to because of the constraint. Beta? What is beta? It’s in huppah and intercourse. Sexual relations—
[Speaker C] —between him and her?
[Rabbi Michael Abraham] Maritality? I would actually say some sort of joining. Meaning, huppah is bringing the woman into his domain. Right? Basically, being in one territory. Right? And intercourse is joining in the most physical sense possible. Meaning, there is here—I would say, and this is all hypotheses—but it seems to me this is a pretty good hypothesis: a joining action, right, an act of joining. Okay? And alpha appears in all of them. That’s the hardest one. What is alpha? And it also appears at different strengths. You remember, there is only one parameter that can receive more than one strength, right? So that’s alpha. Now here it really isn’t completely clear how one can identify alpha. Who is alpha? But we already saw, when I discussed this requirement, that there cannot be any parameter—only one parameter can have a value higher than two, such that it’s not only zero or one but also two, three, and so on; there can be only one such parameter. And I explained there, if you remember, we drew some picture there with many consecutive arrows, and I tried to show that in every such map, in order for the model to be applicable to it at all, there has to be some basic hierarchy. Meaning, some one parameter that determines the basic hierarchy among the players here—the actions, the outcomes, and so on. On top of that basic hierarchy, additional parameters are layered. For example, if something has the property beta and two alpha, it is stronger than beta and one alpha. Why? Both have the character of beta, but that one has beta at a higher strength than this one, so it is stronger. So there is an abstract parameter that represents only quantities, meaning only strengths. It gets colored in various colors. Beta, gamma, and delta color it in various ways. So if it is connected to beta, it is strength of joining. If it is connected to gamma, it is strength of pleasure. If it is connected to delta, it is strength of value or amount of value. But there is some parameter that is responsible for the hierarchy itself. Meaning, it has to determine here—because otherwise, understand: if there is no hierarchy among these parameters, that means they are not relevant. Meaning, there must be a hierarchy here in the background, because how is an inference of kal va-homer built? This has alpha equal to one, that has alpha equal to two, and therefore it is more stringent than this. If there is no connection between those two, this is alpha and this is beta, then they do not speak to each other. Meaning, whenever we make some inference, there has to be something, some axis, on which I determine the hierarchy of the actions or the outcomes. So alpha here really does that. It’s one one two three. Meaning, it establishes some hierarchy here among the actions. But there is some problem here.
[Speaker D] What’s the problem? With the document. In the document what is it?
[Rabbi Michael Abraham] Exactly. The problem is that in the document it has no color. Meaning, it’s transparent strength.
[Speaker C] It has the ability to have an effect.
[Rabbi Michael Abraham] Ah, exactly. And therefore I think that here one has to expand more. It seems to me—again, I’m only suggesting—that here one should give the interpretation of alpha as the ability to contain legal effects, or the ability to perform halakhic acts, to create halakhic outcomes. That is the meaning of the strength. Now, it turns out that a document has a very high ability to perform legal actions; it manages to do this whole row. Right? It has a very high ability. Now, anything that requires some color—that is, ability, meaning strength of pleasure, or strength of value, or strength of joining—alpha will not be enough, because you also have to color that strength. But the document performs the transparent action.
[Speaker C] Intercourse performs more actions. What? Intercourse does more.
[Rabbi Michael Abraham] No, obviously, because there are many—in this case, there are outcomes that require colored actions. Meaning, you need strength of pleasure; mere strength of action is not enough. Energy alone is not enough—you need thermal energy, or kinetic energy, or potential energy. It’s not enough that there be a lot of energy here; the question is what kind of energy there is. Not every action is carried out with every kind of strength. All right? So it seems to me maybe that this is a possible interpretation.
[Speaker B] The ability to contain legal effect is the result of the process. The question is whether there is zero or one in the table there. Alpha is more about expressing the will to create here a bond of marriage.
[Rabbi Michael Abraham] It’s enough; it’s not will.
[Speaker B] No, expressing the will—meaning, a document is the thing that most clearly expresses the will. Because you have to sit with a scribe and write it, and there is deliberation. That is the ultimate proof that you had the will to create here this thing. An act of intercourse, because it is the most obvious thing that characterizes a spousal relationship between a man and a woman. Giving money, being together under a huppah—that could also be many other things. It’s not so unequivocal. Maybe. Therefore it expresses the will.
[Speaker C] It depends on—
[Speaker B] If one changes there where there is a connection. Okay.
[Speaker C] The Jewish people.
[Rabbi Michael Abraham] Now tell me how you’re going to make a living from alphas instead of money.
[Speaker C] Well.
[Speaker B] In any case,
[Speaker C] Okay, that’s the idea. I’ll say it again: at this stage, here, we can manage with it. What? Why did it have to be a major canopy? No, with the canopy actually…
[Rabbi Michael Abraham] No, but the canopy in the formal sense—the canopy in the formal sense—was not the performance of the act itself. It was doing some symbolic act that says: you are entering my domain. It’s not life itself. Life itself is only a result. Okay, I’ll say it again: here it really is hard to decide, but I’m only showing a direction for how one can proceed—not just to build the abstract model, but actually to discover that what a book and a ball have in common, if we go back to the previous example, is mass. Meaning, basically, after I collect a great many examples, I’ll be able to see that same abstract parameter that exists in the book, exists in the ball, doesn’t exist in the photon, exists only very slightly perhaps in the air.
[Speaker C] Because it’s “discover” in the sense of a theory. Yes, not in the sense of certainty.
[Rabbi Michael Abraham] No, of course not. So therefore this identification is always provisional. Certainly. And in fact every scientific theory is provisional—that’s exactly the point. Meaning, on the contrary, even the abstract model here isn’t certain, because it could be that we’re mistaken. I said, it only imitates our form of thinking; it doesn’t mean that in reality it will also work. So all the more so the identification is some degree of speculation. But I’m saying: all science, the generalization there is done through speculation. What I’m showing here is that the model succeeds in helping us make the generalization systematically. Of course we can be wrong; it doesn’t become a deduction. But you see that the context of discovery suddenly becomes something that is really not mystical at all. Meaning, we work in a very systematic, orderly way, trying to think in light of our intuitions and see…
[Speaker C] Someone else with exactly the same data set could put forward a different theory. It could also be wrong. Right.
[Rabbi Michael Abraham] I’m saying again, I’ll get to that in just a moment.
[Speaker C] To assign delta, gamma, beta, and alpha in a different interpretation.
[Rabbi Michael Abraham] I said, there’s a degree of speculation here, that’s obvious. But it rules out a great many possibilities, saying they’re impossible. Meaning, properties that don’t exist in money you’ll never be able to identify with delta, or properties that also exist in others. So there’s a sufficiently strong constraint here for this to be a model. Exactly—that’s the point: to make the generalization in certain directions and not in all possible directions. And all in all, in science you can’t expect more than that. So it seems to me that if we manage to locate this, that’s the maximum we can hope for in the near term. More than that won’t happen. Okay, but I—I’ll soon get to another important point in this context. Before that I’ll try to do something on that same board. I said earlier that this solution is not unique, okay? The same model itself, the same model itself. Now look: this solution is not unique. Okay? The same model itself—let’s try again for a moment. Okay. It’s exactly the same diagram, just to show you that there is also another solution, and what it will do to the identification. Okay? So look, the other solution—what I’m doing, of course, is that I always begin from here. You remember how I built the solution. I start from here, this is alpha, and when I go back two x’s, then it’s always alpha and beta, and this is two alphas. It always splits in this way, and then you continue onward. What I’m doing is simply reversing it. Meaning, this will be alpha and beta, and this will be two alphas. Let’s see what that does to our identifications. Okay? So look, this is alpha and beta, this is two alphas, and this is alpha. Here I already—listen, this involves all kinds of bookkeeping, so I’m already giving you
[Speaker C] the result, to make sure things don’t generate one another and so on,
[Rabbi Michael Abraham] so I’m already giving you the result.
[Speaker C] Alpha, alpha, gamma, delta.
[Rabbi Michael Abraham] This is the alternative solution. How is it different? Look: P is the same, A is the same, these two switched places, and this—now instead of three alphas it’s three alphas plus beta, and here there’s beta—oh no, here it’s the same thing, Y is the same thing. Okay? So basically what changed is that these two switched, and as a result this changed too, the G as well. Okay? What does that do to the solutions? What it does to the solutions is: for money it leaves exactly the same thing; the canopy changes. Is the stage you’re doing now also one-to-one?
[Speaker C] Yes, yes, one-to-one through it, fine. What? To its left. There’s room. It just goes to…
[Rabbi Michael Abraham] Ah, it just
[Speaker B] goes to two sides in this diagram.
[Rabbi Michael Abraham] Okay. So here it’s two zero zero zero. It’s the same thing. It’s the same thing. And here one more is added. These two changed. Fine? Now let’s try to think what this actually does to our identifications. This is also a solution. The same kind of solution as the previous one. I don’t know which of them is right and which isn’t. Okay. What does it do to the identifications? So let’s begin again. What about delta? Again, delta doesn’t change, right? Delta is found only in money, so that’s value. It’s very likely that this stays. The second, gamma—gamma is in money and intercourse, that’s of course pleasure; that also won’t change, right? And of course that’s very good; it fits us. But beta does change, because beta was previously in intercourse and canopy, right? And now it’s found in intercourse and document. Before, we identified it with an act of connection, because canopy and intercourse are connection. Now what do canopy and document have in common? Intercourse and document, sorry. Acquisition. They’re all also acquisition. That’s more or less our alpha. Alpha. Yes. I didn’t find it. And I think—in a moment I’ll explain what I think the interpretation should be. And alpha is the same thing; notice it even preserves the hierarchy. Only what—only here before there was one here, and now it’s one, two, two, three. Before it was one, one, two, three, meaning the line passes here instead of here. But overall the hierarchy is preserved, so that actually very much strengthens the interpretation we gave earlier to alpha. Alpha basically speaks about the axis of intensity. Okay?
[Speaker C] And the one in W is a bit disturbing. What? What is the second dimension, beta? What does the one in W mean?
[Rabbi Michael Abraham] That’s what I’m saying. Beta we still haven’t identified; I’m talking about that now. Meaning beta—what?
[Speaker D] Where is beta located?
[Rabbi Michael Abraham] Beta is the second number. You see, here it’s in the document, and here it’s the same thing, so it’s found here as well, in intercourse. So basically before it was in these two. Now it’s in these two. Okay? So before it was easy to identify: canopy and intercourse really do seem like similar acts; they’re both acts of connection. But intercourse and document—I couldn’t think of something shared, and that’s actually good for me, because I want to clarify what the relation is between the different solutions.
[Speaker C] What do intercourse and document do together? Let’s say if we go back for a moment to that table of yours over there—intercourse and document—what’s special about them in terms of acquisitions? Do they have a shared property? Intercourse and document.
[Rabbi Michael Abraham] They don’t have anything that’s special only… no, they do. Against their will. Against their will. That they operate against the man’s will. Intercourse and document. Document is in divorce, and intercourse is in the yevamah. That’s all. Well, it’s hard for me
[Speaker C] to see,
[Rabbi Michael Abraham] hard for me to understand from that.
[Speaker C] No, on the contrary, I—
[Rabbi Michael Abraham] I’ll get to the results; we haven’t gotten there yet. In a moment I’ll get to the results.
[Speaker C] But before the results, wait, in a second—
[Rabbi Michael Abraham] We’ll see what “preferable” means. What needs to be understood is this: here this stage is not a one-to-one stage. There’s something here—the number of optimal solutions may be large, more than one. Every optimal solution will lead me to a different identification. Meaning, we already see that in reading the information there will be no difference whatsoever. Meaning, the result—that I have to fill the empty slot with one—that is true both according to this solution and according to that solution; that’s obvious. The difference will only be on the other side of the equation, in the theoretical part, in the identification of the parameters. And now what does that actually mean? In my opinion, what it means is the following. Look, if, say, we talk about the four Greek elements—earth, wind, fire, and dust—no, fire, earth, wind, fire, and water. It’s easier for me than talking about our periodic table, which is more complicated, but it’s exactly the same thing. Meaning, we take these four elements and say this: let’s say that—I don’t know—a bench or a chair is a combination in a certain dosage of fire, dust, and water, something like that. Okay? That’s how the Greeks looked at it. How material it is, how light it is, how hard or not hard it is—so it’s a combination of dust, water, and fire or wind, no matter, in such-and-such quantities. Fine? Now let’s assume someone else comes along whose mind works differently, and he wants to describe reality not by means of those four concepts but by means of four other concepts. And it will probably also always be four—that’s a mathematical theorem; he is simply choosing a different basis, that’s the point. And what he will say is: I want to describe reality with these four parameters. Dust, a little water, half-water if you want to be more mathematical, and three-quarters of wind. And the second element will be fire, minus half wind or plus, I don’t care, yes, I don’t care whether it’s minus or plus, it doesn’t matter—four such parameters, and with these four new parameters I can also build every object we have, right? But why isn’t that simpler? What? No, not simpler, but still both are possible. Right? A non-orthogonal basis.
[Speaker D] Right. As opposed to what he’s presenting, as though something unnatural—but here it’s not like that. What? On the board it’s not like that.
[Rabbi Michael Abraham] No, no, wait, in one second I’ll get to the board and then we’ll see whether we agree or not. I just want to finish the explanation. So what am I actually saying here? The second description is completely equivalent to the first description. Every result produced by the first description will also be produced by the second description. Except what? Our intuition knows what wind is, what dust is, what fire is, so we chose that basis. We chose those four concepts as concepts each of which separately is understandable to us and distinctive for us; each is separated from the others. But if someone else comes along for whom fire doesn’t look distinctive at all—it’s half dust and half water, or half wind—a different conception of reality, and it’s only a function of his mind. His mind is built differently, so for him the most natural thing will be the second set of four concepts, right? And he will be able to describe all reality with that other basis. It’s just a rotated basis of those four concepts. Meaning, every new concept is a combination of the four previous concepts; build four such combinations, and you can build whatever you want with them. That is exactly what is happening here. What is happening here—notice—gamma and delta remain the same; what changes? Alpha changes only in the intensities, the intensity hierarchies. Right? It now becomes two, two, three instead of one, two, three. And beta. What does that mean? That they got mixed together. It means that the new beta, the red beta, is actually the black beta plus half an alpha. Never mind. Some kind of combination of them. And basically what we’re doing is choosing four new concepts, and with them we build the totality of the halakhic / of Jewish law phenomena. And the question is which basis to choose. Why is this basis preferable here—why is the first basis preferable for us? Because it simply fits our intuition better. It has no principled superiority whatsoever. If someone comes along who doesn’t understand at all what a document is—he has no documents in his world, no—sorry, not document, but he has no concept of connections and the concepts we use. He only has such compound concepts as half-pleasure and three-quarters-connection. Doesn’t matter. These are the fundamental concepts he uses. Then no problem—from his point of view this solution will be the natural one, he’ll choose it, and then for him those four parameters will be his theory. Fine? So basically the relation between these theories is: there is no problem at all; they are completely identical theories. The difference lies in the question of which one is convenient for us to use. For us it’s convenient to identify the parameters from the first solution. We choose it because it’s more convenient. But that isn’t important. We could also have chosen a basis more complicated from our perspective, and it would have given exactly the same solutions. Meaning that these two solutions are overall just a rotation in the parameter space, for those who know a bit of mathematics. That’s all.
[Speaker C] That’s all—is that it? What?
[Rabbi Michael Abraham] That’s all, is that it? No, it’s not. In a second I’ll explain why it’s not. It really isn’t. Maybe I’ll get to that already now. What are you actually claiming? You’re claiming that if so, then I’m saying all theories are equivalent, and the theory is basically a statement about us and not about the world. Right? That’s basically the claim. And we’ve gone back to actualism, which I’m constantly trying to prove is not correct. That basically theory is not a claim about the world but only a way for us to organize the facts. But that’s not true, because the relation between these two theories really is actualistic. Because they have the same theoretical content too, not only empirical content. They have exactly the same content. A rotation is not a different theory. If I describe physical theory in Cartesian coordinates and describe it in polar coordinates, no one will say that one of us is right and the other is wrong. Those are two ways of describing the same theory itself. They are not two competing theories. What I was talking about there was a different theory with a different conceptual system, where none of the concepts is a combination of the concepts of the competing theory. And it may also have different empirical content. Right? After all, in the end we want to choose between them by experiment. Fine? Those really are theories where I claim one is correct and the other is not. They are theories about reality. But where it is merely a transition in a coordinate system, then it’s describing the same thing in two languages, and there of course it is actualistic.
[Speaker C] But theories that claim to have the same empirical content?
[Rabbi Michael Abraham] Theories that have the same empirical content—granted. But what does that help you?
[Speaker C] Theories that have the same empirical content are the same theory.
[Rabbi Michael Abraham] Wait, but that’s actually not resolved. Why? Is it the same theory? That’s the actualist claim, that they’re the same theory—that’s what… no. The actualist claim says that… just one more second. I’ll get to that in a moment because I need one more sentence for it. Now look. Why nevertheless is there a difference? Why nevertheless is the choice of solution an important choice and not trivial? The reason for that is very simple. Because the table we started from is not a full table. Meaning, if I were to take all the data of the universe—or of Jewish law in this case, fine?—and build a solution from them. All the data already inside it, the relevant and the irrelevant. We said the model will sift out even the irrelevant; that’s not a problem. You would put everything in, all of Jewish law into the table, fine? And I would operate in this way. I would get a set, a collection, a group of solutions. Fine? That group of solutions—there really would be no difference between them. Meaning, they have the same empirical content; each one is a rotation of the other. That’s all. Nothing besides that. But in fact we are working on a partial space. We are in fact working only on part of the data. Why? Because we don’t know how to work on enormous tables. We also don’t know all the data. And the technique is also insufficient—I don’t know how to solve such a problem with an infinite table and huge amounts of data. So I try to make an intuitive clarification of which data are relevant, and I take only a very specific table, in this case a rather small one. Fine? And I build on that basis. Now on that basis, what happens is this: true, these two solutions are completely equivalent with respect to this table. But they can have many implications for data I did not take into account. And I very much hope that those data are not relevant and that my result is correct. But I can’t know that. Therefore the equivalence between the solutions is an equivalence only relative to the table on which I worked. But it is not a real equivalence. It is not true that the equivalence here is a real one with respect to other problems that were not included in the table. It could be that they will give different results.
[Speaker C] Is not one of them
[Rabbi Michael Abraham] simpler?
[Speaker C] What? Is not one of them simpler? No, no, no. I’m taking the minimal set, with less complication, say half-water is…
[Rabbi Michael Abraham] No, so I’m saying no, it isn’t simpler. Because it is still four independent parameters. It’s just that one of them is alpha plus half beta. That doesn’t matter. Call alpha plus half beta “alpha-hat.” It makes no difference. As long as it always appears together. Meaning, alpha will never separate from beta. It’s always alpha plus half beta. You can call it alpha-hat; it’s the same thing. It doesn’t matter. That’s also true in mathematics. Meaning, the basis is always in dimension four. If you started in dimension four, every rotation will leave you with a basis in dimension four. You won’t leave that dimension. Therefore basically it’s obvious that this is the same theory at the same strength. And that’s under the assumption that all these solutions are equally optimal. Therefore it’s clear that one is a rotation of the other. Fine? As if without changing the radius, if we speak of the radius as simplicity. Right? Meaning it’s only a rotation. So yes. That’s it, I don’t understand.
[Speaker D] This matter of one and a half and so on—if he were saying, if we were saying four different things like, say, black and white.
[Rabbi Michael Abraham] No, if you could build black as a combination of dust, wind, water, and fire, and white and cold and so on, doesn’t matter, it’s the same thing.
[Speaker D] Then why here do you prefer the simple solution? Yes, that’s all.
[Rabbi Michael Abraham] Just our preference when we try to identify the parameters in the sense—notice, I am always working in two directions. No problem, then choose this solution. It doesn’t matter—that’s exactly the point. It isn’t important. Meaning, when we work here, after all, in two directions simultaneously, on the one hand we fill the empty slot, we read information, fine? That is on one side. There all the solutions will give the same result; it will always be one, no problem, that’s how I defined it. Fine? But on the other side, I’m looking for the theory; that’s not the practical goal, the goal is theoretical. From the standpoint of searching for the theory, every such theory will speak in a slightly different language, or at least in a slightly different basis. But my assumption is that every basis is a rotation of the previous basis, so it’s a linear combination—or perhaps non-linear, it doesn’t matter—of the parameters of the previous basis. If it’s convenient for you to use this, use it. It doesn’t matter. It could be that cold, heat, white, and black can be written as combinations of dust, wind, water, and fire. And cold in one combination, heat in another combination—if the determinant is not zero, then that’s fine, and it’s possible—then it’s only a rotation. Fine? Okay. Now what basically remains for us to do is to complete the process back into the results. Right? Until now I said that in order to identify the parameters—we haven’t finished the theoretical work yet, we’re only halfway there. In order to identify the parameters, we look at the acts, because the acts are what we know, what we understand. If I were looking for something shared by marriage, betrothal, and redemption, I wouldn’t know how to look for that; those are halakhic / of Jewish law concepts. Therefore I look at the acts, because the acts I know: intercourse, money, document—I know what those are, so I look for what characterizes those things. Therefore I do the search, the identification, through the acts. In this case, I’m not saying there is always necessarily a preferable state, but if the rows or the columns are preferable—there may be cases where one can do it with both, I don’t know, I haven’t thought about that. But in this case it certainly is so. Now, however, I take the results of my inquiry and try to explain things with them. How will I explain things with them? Let’s see. After all, I have already reached the conclusion that this is the solution I choose, right? So I immediately erase the complicated solution and this as well. And now I ask myself what the interpretation of the results will be, not of the acts. So look, betrothal is something that in order to apply it you really need only a minimal requirement—some ability to impose halakhic / of Jewish law effectations; there doesn’t need to be pleasure in it, there doesn’t need to be connection in it, value, nothing. What is needed is an act that has some minimal halakhic force. I’m speaking in general language now. An expression of will? Expression of will, according to your interpretation, whatever. Is there nothing of connection in betrothal?
[Speaker D] What? But in betrothal isn’t there something…
[Rabbi Michael Abraham] One second, one second, one second. I’ll get to that in just a moment. I’m trying to show where we now gain from this whole matter even when we return to the yeshiva-style analytical learning. We’ll see that soon. That’s the theoretical gain in the halakhic / of Jewish law context. So in betrothal we say: all that is needed is some act with a force that can impose halakhic effectations or bring about halakhic results minimally, or express will, whatever. Against her will—I don’t know, that’s some sort of artificial thing written there; it’s hard to talk about. But divorce is the same thing: you need only the ability to impose halakhic results, but at a greater intensity. That’s all that’s needed there. So money doesn’t have enough intensity, therefore it can’t effect divorce; a document has that, so it can effect divorce. But money and document both basically work here because they have alpha, okay?
[Speaker B] Maybe that’s why in Islam you have to say “divorced” three times? What? Because it’s three alphas. Something like that.
[Rabbi Michael Abraham] Now look: in marriage, for example, what is required is alpha and beta. Alpha and beta—that is not high intensity, the ability to impose effectations is not high, that’s alpha—but it is colored, it is colored by what? By connection. Meaning that marriage essentially requires some power of connection; betrothal does not. Now this leads us into various investigations by later authorities (Acharonim); one really can branch out here into investigations of later authorities (Acharonim). Because basically the question always is: what is the relation between marriage and betrothal? And in quite a few places one can indeed see that betrothal—after all, what does the Talmud / Talmudic text itself say? “For it prohibited her to the whole world like consecrated property.” Meaning, the kiddushin and betrothal are to prohibit her to the world. Marriage is to bring her into his house and connect her to him. And then what emerges here is that kiddushin means the imposition of a halakhic effectation, in this case a prohibition effectation, like consecrated property, like a vow, where I prohibit her to the world. Therefore alpha is this transparent parameter whose whole function is to impose halakhic results. Where is the bond created between husband and wife? In marriage. I’m already beginning to feel like a preacher. But I think what’s beautiful here is that these theoretical results bring us back into the study hall. Meaning, I can now take these results and go to the study-hall analyst and tell him: listen, I got such-and-such. First, identify for me who alpha is, who beta is, who gamma and delta are—you know the halakhic reality, identify them for me. After that, explain why indeed in the results too these are the things that are at play, and what the conceptual-yeshiva significance of that is. For example, that betrothal is prohibition to the world and marriage is bringing into his domain—various things of this kind. There are also halakhic ramifications to it, all kinds of things, investigations of later authorities (Acharonim). Meaning, these things reveal to us something of what actually governs all these processes, the depth of what is really happening. We only see the phenomena. This works, this doesn’t work, this happens, this doesn’t happen. Suddenly we discover what stands behind the phenomena, what the theory is. Here pleasure operates, here it’s only making a connection, here you don’t even need to make a connection, it’s just the imposition of an effectation. You see, alpha here is even in divorce; divorce doesn’t connect, divorce disconnects, right? Meaning, clearly alpha cannot be related to connection, because otherwise what is it doing in divorce? Fine? So there are all kinds of substantive hints here—this time it’s no longer empty formalism but substantive hints that will help us understand the halakhic concepts in a way that cannot be understood otherwise. Meaning, this model overall takes us step by step to understand the halakhic concepts we are dealing with. Meaning, now I understand what is actually operating in every halakhic act—what in principle, not which acts do it, but what truly brings this thing about. Why indeed money or intercourse or something like that does something—because there pleasure is transmitted, and pleasure is what imposes the thing. Now one can think what that does—I don’t know, maybe in Kabbalah, I have no idea—but it’s a tremendous opening for trying to understand what in the study hall they don’t actually know how to do. How to understand what actually stands behind it—nobody ever thought what causes kiddushin or marriage to take effect: is it pleasure or a capacity for connection? Those are not study-hall concepts, but from here it emerges quite naturally. Let’s continue. Look what happens here.
[Speaker B] Wait a second—in marriage it says alpha and beta; does that mean you need both? Both expression of will and…?
[Rabbi Michael Abraham] Yes, of course. That’s why I say that one can even relate to it as a kind of coloring. I color the ability to impose halakhic results with the color of connection. It is basically the ability to place a halakhic result that is connection. That is called alpha and beta. Fine? Now what happens here? Here and here we already know: the yevamah and redemption—that was our constraint—require pleasure, that’s gamma. Right? We already saw that. And redemption of course also requires—what is delta? Value. That doesn’t surprise us, right? When we redeem something, obviously what is needed there is value. That’s what redemption means: to redeem is to give its value and receive in exchange for that value the object being redeemed. So we are not surprised to discover delta here. Right? That value is actually what effects redemption. Meaning, look—it fits our simple intuitions not badly. And with the yevamah this means: in the yevamah there is connection—a very interesting point—there is connection, and pleasure is required, and an intensity of two alphas is required. The ability to perform halakhic acts—two alphas. It is harder to create connection with a yevamah than to create the connection of marriage—notice, marriage which is already after kiddushin. But marriage without kiddushin is harder to accomplish than yevamah, I think.
[Speaker C] And also, in the yevamah that pleasure is required—that’s something that goes against the concept.
[Rabbi Michael Abraham] What, the yevamah needs what?
[Speaker C] Pleasure goes against the concept. Why? Because with a yevamah it can be against her will. Yevamah is not—now we can begin contradictions here—but the intuition doesn’t fit so well. Okay, thanks for the comment, truly, I don’t know.
[Rabbi Michael Abraham] The yevamah actually is a huge novelty. What? It’s a huge novelty, but he says that the fact that it can be against her will—
[Speaker C] it’s not likely that pleasure here would play the role. And ah—in the yevamah, where intercourse is against her will, even though there is pleasure. Why? All those who go shopping enjoy it very much. The shopping experience.
[Rabbi Michael Abraham] If you hadn’t called
[Speaker D] it connection, you would have called it…
[Rabbi Michael Abraham] You said connection with regard to house, you called it house, and then it came out zero.
[Speaker C] And then someone suggested earlier first of all
[Speaker D] calling this connection “dwelling,” which here is intercourse, and then it came out zero. So what? How does that improve our situation?
[Rabbi Michael Abraham] No, I don’t understand how that works out, but perhaps really
[Speaker D] it’s better to call it connection.
[Rabbi Michael Abraham] I’m saying again, this is a suggestion. I don’t know how to decide here, but I’m showing a direction that opens very interesting possibilities, and I think it’s not an implausible direction to propose an interpretation of these parameters. Now this is a process that is essentially a mathematical process in the same way.
[Speaker B] If we were taking a system of experiments in which forces and accelerations are measured, and we discovered there the parameter that links them linearly, and afterward attached to it the label “mass,” F equals ma, which links acceleration and force. And afterward we identified it intuitively with what we are used to recognizing in the world as heavy and light—not inertial mass but
[Speaker C] gravitational mass.
[Speaker B] I think that what we’re doing here is basically a similar process. Meaning, there are certain concepts here, similar to gravitational mass, that we know from the world of our intuitive human concepts—namely value, pleasure, and connection. We made a model here, found various coefficients supposedly, just as inertial mass is a coefficient between acceleration and force. And now we’re doing the matching, the correspondence.
[Rabbi Michael Abraham] The matching here really is matching between two parameters, not between a parameter and a meaning. Gravitational mass and inertial mass—that’s matching between the two of them.
[Speaker B] Right, those are two precise physical definitions. But let’s say, if we didn’t have measurements that measure gravitational mass, then ordinarily we know concepts of light and heavy from time immemorial. Before we entered the laboratory at all, we already feel that—more or less like pleasure, connection, and value are intuitive things at the first stage.
[Rabbi Michael Abraham] Fine, in any case, this is just to try to understand in broad outline how this thing can work on the theoretical plane too and not only on the plane of reading the information. How it can actually build for us the scientific generalization, such that if we now take a table that does not deal with Jewish law but a table that deals with…
[Speaker C] Rav Ashi said in the teaching that when there is pleasure, when there is pleasure it does count, because he does derive benefit. And here too, where it is against his will and there is no intention to do it, once there is pleasure…
[Rabbi Michael Abraham] Ah, so actually that is a proof that pleasure is involved, because the fact that it works against his will means that he nevertheless benefits. Okay, fine. These are things one can think about. I am of course only proposing an initial suggestion here, but yes.
[Speaker C] We’ve returned not on the halakhic plane
[Rabbi Michael Abraham] but on the plane where we’re talking about a table we are trying to fill on the scientific plane. So on the scientific plane, basically we are supposed to do exactly the same work. We have a collection of data, as I said earlier with mass and attraction to the earth and so on. And we fill it in with the same technique, discover parameters, try to identify the parameters according to the characteristics of the objects of course, not the physical results that we don’t know or the physical forces, but in terms of the objects, which we do know. That parallels the acts here in place of the results. And then after we decipher or identify the parameters, now we also understand the results. We also understand, say, that the “charge” of gravitational force, the thing on which it acts, is mass. From the objects, from the identification of the objects—what component or what components characterize the objects—we can identify what the components or characteristics of the physical result are, of the physical force in this case. So it’s exactly the same process. Meaning, in the end this is just a mechanization of the process of generalization. That’s what there is here.
[Speaker C] Now what
[Rabbi Michael Abraham] I want to do now is actually move on to additional examples and see the potential this has—not just as an example. There are a few arguments here after all; I hope I’ll finish today, we’ll see. I’ll take a few examples and try to show why this is equivalent. I’m not going to solve it on the board; whoever wants can do it. The book on this has come out. There’s material here from what we learned during the year, so for now it has only reached chapter one, but eventually it will all come out. In any case, here it is: the logical hermeneutical rules, logical-deductive inferences in the Talmud. In any case—well, goodbye to you. What? A few days ago, a week.
[Speaker B] Thank you. What is this? Will it also come to Midah Tovah, to the internet? To the online course?
[Rabbi Michael Abraham] What, the file?
[Speaker B] No, the content of this course—will you also stream it through Midah Tovah?
[Rabbi Michael Abraham] Because my partners here in the book matter to me too, but I don’t know if—fine. Come on, time is short. Fine. In any case, look: we have, for example, several examples that we show there. One example: the fellow I worked with took a table of cameras from the internet. Data on cameras from the internet. The zoom, I don’t know how many flash modes, whether one can process images in memory, all kinds of camera properties, its price, response speed, all kinds of things, doesn’t matter, all kinds of such things. We have a table with a set of several cameras; for each of them we have a collection of data—what its zoom is, what this is, every datum, yes, for each camera—and overall it’s just a table. Okay? In that table one datum is missing. Let’s say one datum is missing there, just one missing datum. And the question is whether we can fill in that datum with this technique. Now what is the idea behind it—why should that be implementable there at all? It will be implementable there exactly as I say regarding scientific inference. I have a collection of facts; I build a theory of what the parameters are that are responsible for price, for zoom, for however many batteries it has, all the camera’s properties. If I take, say, all of them for purposes of the theoretical discussion, then basically the claim is that there are some parameters that govern these properties. These are functional properties; these are properties we encounter. The question is what in the structure of the camera or in the structure of the designer’s mind—it doesn’t matter for now what influences it—caused these properties, and whether there is a connection among the properties. And there is. Usually a camera with better performance will be more expensive, an inverse relation between price and weight, a direct relation between price and performance usually. Right? Meaning, even on that technical level, before getting into physics. Just on that technical level I can try to infer—for example to make an a fortiori inference in a simple two-by-two table. If that camera, which is cheaper, has such-and-such zoom, then this camera, which is more expensive, certainly will have at least such-and-such zoom, if not more than that. Then someone will tell me: what about that camera that has a more expensive battery, so who says maybe its zoom is worse? Then we’ll check the battery too, add another column, and continue. After we collect all the data, one can do the entire tractate of Kiddushin on it, and overall fill in the data. And of course I can fill in those data by building a theoretical model, alphas betas gammas and deltas. And those alphas betas gammas and deltas can be of several kinds. One kind, for example, is technical constraints of the camera. Sometimes the zoom interferes with, I don’t know, the…
[Speaker C] resolution?
[Rabbi Michael Abraham] the resolution or whatever it may be. So because of the technical constraints, I discover a correlation without even knowing how cameras work. I identify it through the data. My model will show me that connection. Fine? Sometimes it’s just that cameras designed with high zoom are probably intended for professional photographers, so they also give them sophisticated flash. Not because there is something in the structure of the camera, but in the structure of the designer’s tendency, of the manufacturer. It doesn’t matter—the parameters can be of one type or another, but in the end there is no reason I shouldn’t be able to fill in that datum too. So by the way, he did try to fill it in, and meanwhile he still hasn’t found what the real datum is. So we’re checking whether we filled it in correctly. We put in a table with diagrams and everything, and we know how to work this way. Now he is trying to check whether it is in fact correct.
[Speaker B] The year of manufacture also has to go in there. What? From experience, the year of manufacture also has to go in there. Why? In the first years there’s a rapid price drop; afterward it reaches saturation because you can’t go below production cost. Okay. Fine. Let’s say the brand—if it’s Leica or Samsung—there are also products ten years old that you won’t see for twenty-five dollars even if it’s second generation. Right.
[Speaker D] True. Can I add—is that because of some kind of obsession some manufacturer has?
[Rabbi Michael Abraham] No, heaven forbid. “Obsession” isn’t accurate. If you take all the data—take all the cameras with all the manufacturers with all the data on every camera, on every model—then you’ll discover all the obsessions. Because there is no crazy person with only one isolated obsession, unless he produces only one camera of only one type only one time and with one obsession. Then maybe it really would be pathological. But if he’s a camera manufacturer, then even if he has an obsession you’ll discover it. So you’ll discover the crazy basis in his case; it doesn’t matter. And you’ll be able to infer conclusions from it. So that’s why I say: obviously, when we focus on only part of the data, that has a price in reliability. But theoretically this model can describe generalization in any field, or generalization in another field, for example. Tornadoes too—again just a table we found on the internet. Various storms of various kinds—Katrina, Ivan, Hugo—they have lists for all these, after all. For each one there is the number of vortices, the speed, the diameter of the core, suction power, doesn’t matter, there are some parameters I know nothing about, not important. A collection of parameters about this tornado. I assume it has some connection to the physics of the storm, without knowing the physics at all. And if one datum were missing for one of the storms, I think I could complete it. In one way or another.
[Speaker C] If the model deals with this issue in quantitative terms, then with great difficulty there’s barely anything here.
[Rabbi Michael Abraham] No, no, now I’m getting to that. Now I’m getting to that. That’s a good comment, I’m getting to that now. Actually, in many very—another example, maybe one more example before that, because that’s where I got stuck. I tried to make a prediction model for companies that collapsed. That’s something worth a lot of money. If I can predict whether a company will collapse. So I take companies that collapsed in the past and companies that didn’t collapse in the past, and I build a table, and I collect the relevant data—whatever experts claim is relevant; I don’t understand any of this at all. Okay? And I can start talking now about debt repayment relative to annual turnover, or to some unit of time, doesn’t matter. How many layoffs there were each year. What the size of the factory is, I don’t know, how many employees, what the assets are, the value of the assets relative to turnover. All kinds of data that are economically relevant, without understanding anything about economics, without understanding anything about what’s going on there. In my humble opinion, this ought to give results. Meaning, it has to predict—I don’t know, again, maybe you need a huge amount of data and it would be impractical, but on the principled level, if I take all the relevant data without understanding economics—that’s the point.
[Speaker C] You need to understand economics in order to know what the relevant data are.
[Rabbi Michael Abraham] Obviously, but that’s always true; it’s like that in Jewish law too. That’s why the classification is always like that. But I’m saying, leave it—I’m saying theoretically, I don’t even need the relevant ones. Take all the data. And the model itself will do the mapping.
[Speaker C] And that’s theoretical. Obviously.
[Rabbi Michael Abraham] I’m just—I’m talking here about theory right now. Now there, really, that’s where we got stuck because of the issue you mentioned. I tried playing with it a bit and seeing whether I could predict companies that had already collapsed. Meaning, to try to look at the data, extract the company’s data from a year earlier—let’s say it collapsed two years ago, so take its data from three years ago—and compare that to the data of other companies that did collapse and didn’t collapse, and see whether I can predict that it will collapse or not. I can check whether my model works or not on companies that already collapsed. Okay? Never mind, we didn’t really manage to do the—
[Speaker C] That’s because—
[Rabbi Michael Abraham] We were stuck on what?
[Speaker B] Collapse is very strongly tied to the global situation.
[Rabbi Michael Abraham] Everything—so put everything in. Put that in too, all the more so.
[Speaker C] Put in whether it’s a Jewish company or not.
[Rabbi Michael Abraham] Okay. In any case, where we got stuck here, where we got stuck, is the obvious limitation you mentioned earlier.
[Speaker C] Fine, in any case—
[Rabbi Michael Abraham] There are two—the problem we got stuck on is that in a large majority of cases, these are not binary problems. Not zero-or-one problems. Just as you asked, actually. The problems are really—what does it mean for a company to collapse? It’s a question of degree. How severe a problem will it have? Because “collapse” is not a sharp definition. Every company decides to collapse under slightly different conditions. Of course, compared to storms—not to mention when I want to know what the diameter of the storm’s center is—what diameter is, that’s a continuous parameter. It could be one meter, two meters, three meters, two centimeters, or a kilometer. That’s infinitely many values. So in my table I don’t just have zero or one; I need to look for an algorithm that works on tables where the values, the entries of the matrix, are not zero or one.
[Speaker C] We had something like that once. Exactly.
[Rabbi Michael Abraham] So we had something that already starts moving a little in the direction of zero, half, or one. The question is whether I know how to do something continuous. And for now we still haven’t worked on that; that’s a question we still need to deal with. You can make an initial approximation to this by giving an intelligent but more primitive definition of the question. I can ask: will the company enter a deficit greater than half its assets? That’s a yes-no question. Meaning, yes or no. I’m not asking how large a deficit it will enter, but whether it will enter one of more than half its assets. And then I check across all the companies, and it will be zero or one—either it’s above half or it’s not above half. So I can translate any continuous question into a zero-or-one question, except that then the answer I get will of course be at a very coarse resolution. I won’t get how large the deficit will be; I’ll get whether the deficit will be above half or below half. But now notice: I’ll run it again. And now I’ll ask the question: if I discovered that it’s less than half, now I’ll ask whether it’s less than a quarter—lion in the desert, yes—I’ll close in on this thing, I’ll ask again, and basically that’s the way to build a continuous model.
[Speaker B] Binary. Right, to turn it into parametric.
[Rabbi Michael Abraham] Alpha times x plus beta—there are all kinds of techniques, we thought about that too. There are all kinds of techniques you can try here. I think this is something one can think about; it is definitely feasible, to build a model that will solve continuous problems, not binary problems. And then, for example—just one more second, I’ll give just one more example. For instance, a traffic judge—also an example we discuss in the article, by the way. A traffic judge has all kinds of offenses brought before him. One person drove without a license, another drove under drugs, alcohol, I don’t know. There are also different outcomes. One ran over a person, one was just caught without a license and with no victims. One only hit someone, one hit another car, all sorts of things like that. And what did the judge rule? There are several punishments. There is prison, and again, prison is continuous—it could be a year, two years, three years—but let’s say: was there prison or wasn’t there prison? A binary question, okay? Was there license suspension, a fine, all kinds of—fine, suspended sentence, all kinds of things like that. Build a table and try to see whether in the next case that comes before that judge, a lawyer—the lawyer is now standing there, he comes before him with a client who drove under such-and-such conditions, and he appears before Judge So-and-so. And I have data on that Judge So-and-so. The question is whether this judge will put him inside or not.
[Speaker D] What mood is he in that morning?
[Rabbi Michael Abraham] What?
[Speaker C] No, that’s not a problem.
[Speaker D] First of all, why not?
[Rabbi Michael Abraham] Does he tend to moods? Exactly. Maybe according to the weather? I’ll put that in too, it doesn’t matter. Theoretically everything can be included. Again, obviously in practice this would be very limited, because I won’t be able to take that much data. But an intelligent choice of the rows and columns can also give practical results that are better than—
[Speaker B] What’s the difference between this and probabilities, game theory? What’s the difference?
[Speaker C] No, there are things here—also in game theory they often use zero-one in order to solve a problem of a continuous variable. That concludes the lecture of Rabbi Michael Abraham, Thursday, the 29th of Iyar, leading into the 1st of Sivan, 5770, May 13, 2010. A full picture—they’re continuous.
[Rabbi Michael Abraham] So then you have to write a function for each one, and you have lots of functions. And calculations of all kinds of multiple integrals and all kinds of things of that sort, yes. What fun.