Invention or Inspiration? – A Conversation With Larry Lesser, PhD

Geoff Mitelman: I’m Rabbi Geoff Mitelman. I’m the Founding Director of Sinai and Synapses, and I’m joined this afternoon by Professor Larry Lesser, who is somebody I’ve gotten to know over the last two years or so – or about 18 months or so, who is a Professor of Mathematics at UTEP, at the University of Texas, El Paso, and also a member of Temple Mount Sinai. Their synagogue, run also by Rabbi Ben Zeidman, proposed a project for our initiative, scientists and synagogues, about Higher Meanings, about the links between Judaism and mathematics. And it was just a really brilliant series of conversations they’ve had, and they’ve looked at so many interesting intersections. And I know that Larry has explored the interplay of mathematics and Judaism. We’ve talked a lot about science and Judaism, but not as much about mathematics and Judaism. So I’m very excited, Larry, to talk with you, especially because my background as a middle schooler, high schooler, and even into college, was mathematics. That is a deep, deep love for that. So it’s nice to be able to talk with you.

Larry Lesser: Thank you. Thank you for having me.

Geoff Mitelman: So I want to start with a question that I grappled with. So I started my college career looking at mathematics, and then I changed from math to Judaism. And one of the things that I still grapple with a lot is that there are a lot of questions in this world, and math very often provides answers – not always, but often, there’s a clearly defined “here’s what the proof is going to be. If you follow these rules, you are going to find something that is always true, eternally true, universally true.” We expect that if we were to find life millions of years away, 1+1 is still going to equal 2. Numbers are still going to be prime. Mathematics is true everywhere.

So, when there are questions, sometimes there are answers, but there are also questions of responses, where truth there is a little bit different. We’ve talked about this on the show, about politics, about religion. Where do you see these questions of truth from a mathematical perspective and from a Jewish perspective?

Larry Lesser: Great question. (Laughs) We’re going big right from the start, I love it.

Geoff Mitelman: Got to start big here. Go big or go home, right?

Larry Lesser: Yeah. So I think people who don’t have a deep background in math or religion overestimate how absolute truth is in either realm in some sense. People may feel like there’s just one answer in Judaism, but then you start seeing all the debates of the rabbis in the Talmud, or you start asking contemporary rabbis and you get different answers, and somehow what you might have thought was black-and-white has a lot of more nuance than you first realized.

It’s actually the same thing in math. Our second speaker in the series that you mentioned – Dr. Kim Jongerius, from Northwestern – made very clear that math involves assumptions. You have certain starting points or axioms, so that it’s not that things are true in some absolute sense, but only within a certain framework that you have set up.

So, even something like arithmetic – 1 + 1 = 2. Well, but that’s true in a certain base, and maybe in another base, something else is true, right? So you always have to ask yourself things like that, and it’s not always obvious. I mean, like Euclidean geometry. The geometry on a flat surface – people thought that that was just true in some absolute sense. For centuries, people just thought that was true. And then in the 1800s, people realize, “Well, actually, if we make a different assumption about whether more than one line or less than one line through a point can be parallel to a given line, we can have a completely, equally valid, alternative geometry” – a non-Euclidean geometry that’s just as valid. And I love that.

There was a Jewish day school – I think it was Keshet – that did a case study where they made like a teaching moment out of that, to say, “And analogously, there’s 70 faces of Torah, not just one.”

I don’t know if that’s the direction you were looking for – but just to complicate math itself even a little bit more, some things in math end up getting so intricate and big and complicated that they’re bigger than one person can verify by hand. It takes a committee of people over years, or maybe it takes a computer to verify, a proof of all possible cases. And that was an issue. People were at one point were like, “Well, does that count as a proof if one person can’t see the whole thing?” And now there’s even things like, there’s things like fuzzy logic as a branch of math, where you can have truth values in between “always true” and “never true.” But that would definitely take us down something too far off the beaten path to get into that. So anyway, it’s more nuanced and complicated than people think in math and in religion.

Geoff Mitelman: Well, I think it also starts with a question of what are your assumptions, what are the axioms? And once you lay out the axioms, and once you lay out the rules of the game, both of them can play themselves out. I think that from a middle-school, high-school, even early-college level of mathematics – I remember studying Euclidean geometry in 8th grade. And you start with these axioms, you start with these assumptions, and you can prove – “bing, bing, bing, bing, bing – this is what the result is going to be.” And I did a lot of stuff of number theory, and that’s if you make these assumptions, know these assumptions – bing, bing, bing, bing, bing.

But religion is different than that, right? First of all, you may have different assumptions, but we’ve talked a lot, actually, in these conversations, with Sacred Science, that there’s a difference between – I’m going to phrase it this way – there are what we might call social facts of things that we agree on, because there’s a social agreement that Joe Biden is the president. Those are things that exist only because we agree. There’s what we might call scientific fact, where there are elements of the natural world which we can understand. Vaccines are good. But I think there’s another level of mathematical truth, where mathematical truth is even slightly different than what scientific proof is going to be.

Larry Lesser: Right. Although even there, there’s a nice complication, because what I hear you saying is that math has sort of this deductive essence, and that it’s not really empirical per se. And yet, most working mathematicians use a very empirical process to come up with things to then try to prove deductively, right? They’ll use a computer and explore to see if they can find a counterexample, or to see if something seems to be true for as many cases as the computer can generate easily, but then they still have to prove that their conjecture is true. But how did they come up with the conjecture? Again, that’s more the intuition, that’s more the empirical side. So math really has both aspects – sort of the strict, logical deductive process, but also just the exploratory empirical process.

Geoff Mitelman: And I think one of the dangers that I think has happened over the last however-many years is [that] people will use or frame math as proof, and play that into religion or into politics, when in fact, it’s not a good analogy – where people say, like, “Look, we can prove x or y or z,” and in fact, it’s not as certain as we think it’s going to be.

Larry Lesser: Yeah, absolutely. I mean, the whole process of science [is] that as you gather more information, you continue to update your model, right? And so, if it says “70% chance of no rain tomorrow,” but it rains, it’s not that the science is wrong. It’s still a true fact that 70% of the time, when there have been these atmospheric conditions, it didn’t rain; this just wasn’t one of them, right?

Or you mentioned the vaccine stuff. “How come the CDC says one thing and then a few months later they say something else?” Again, the problem isn’t the scientific process. The process is working as it’s supposed to. It got additional information, so it updated the model, and that had implications for the guidance.

Geoff Mitelman: Well, and I think we’re also – using the word of, I think, John Allen Paulos, we tend to be “innumerate.” We’re not illiterate, but we tend to be enumerate. And it’s hard for us as human beings to understand different probabilities, different statistics. Math is more than just algebra and geometry. There’s a lot of statistics; there’s a lot of exploration, and playing, and trying to be able to see what would happen if. It’s viewed as a level of certainty, when in fact, a lot of mathematics is raising questions and being able to say, “Well, how does this play itself out down the road?”

Larry Lesser: Right. And I hear my statistician friends wanting to push back a little bit, just to say that statistics uses math, but it’s not a branch of math. It’s really its own science. And it’s very different in its nature, because rather than being primarily deductive, as most math is, it’s primarily inductive. You’ve got a sample, you’ve got some data, and from that you’re trying to make some statement about a larger situation or a larger population. But again, there are still assumptions you’re making, right? You’re assuming your inference is only valid if the sample is representative or a random sample, hopefully, and that you’ve checked to make sure that there aren’t confounding variables, and that you’ve looked into what outliers might tell you and just all these other caveats and pitfalls that, again, people who don’t practice statistics regularly may not be aware of, and [that] don’t show up in the newspaper headlines. But it’s a very nuanced process.

Geoff Mitelman: And one that is, I think, is often misunderstood and sometimes misapplied.

Larry Lesser: Yes.

Geoff Mitelman: So you’ve been working on a lot of work on this intersection of Judaism and mathematics. And when we were talking, I remember when you put the application in, that when people think about math and Judaism, I think for a lot of people, they think of Gematria, which is kind of a mystical way of understanding of the world, of “this number means something, and there’s a deep cosmic significance.” And we said, “Yeah, that’s not the direction that we want to go in with our work,” because I think there are some problems of using math to prove things Judaically or using Judaism to prove math.

So, where are some ways in which we can have a better conversation about Judaism and math, so it’s not just, “Well, that’s this mystical number of 8 or 7 or 40.” Math comes up all the time in Judaism in many more ways than just the Gematria.

Larry Lesser: Absolutely. I’m really glad you said that. And even some of the rabbis of the past have warned of dangers of relying on Gematria for that way – that they were probably using it more as like a teaching aid, as a mnemonic, to help you remember that two concepts are connected because they have that numerical thing that they happen to find. I can understand why that’s the first kind of connection that comes to a lot of people’s minds, because it’s probably the example of math and Judaism that’s the most prominent in everyday culture. Like, we’re always being asked to give tzedaka in multiples of 18. Why is that? Well, because chai, the Hebrew word for life, has the numerical equivalent of 18. Or why is 15, whether it’s a page number or in the name Tu B’shvat, like a day of the month – why is that written tetv instead of yudhe? Well, because we’re trying to avoid God’s name.

So I get why that’s… but I think that’s probably part of a larger thing, that the general public kind of reduces math to just arithmetic. In general, it’s like, “Well, if I can balance my checkbook, I don’t need, or ever, I don’t need to know, or I’ll never use algebra and geometry and pre-calculus,” and so on. And I could push back against that way of thinking, too, if you want.

The paper I wrote in 2006, because I was teaching full-time at a Jewish day school in Houston for two years, and high school students are not shy about letting you know if they’re not into a subject – a lot of them were like, “Well, I’m just here because it’s required, and because I have to do well in the SAT, but I’m never going to use math.” And they wouldn’t even try to hide their feelings about it.

And so I thought, “Well, let me try make this – let me to help.” Like, I mean, a lot of times Jewish day schools will make Judaic integrations or connections to other subjects, but it’s usually just in the humanities, like with literature or history. It’s like, well, why not math? Why not math too? And so I started looking around for what I could find, and there was no one source that kind of had everything I wanted, but I found bits here, bits there, and I made up some stuff of my own, and I put it together in an article in the Journal of Mathematics and Culture that was published in 2006, and that was really, like, the first comprehensive look at connecting math and Judaism for classroom purposes.

Like we say, yes, I found some more Gematria things, but I found so much more. Most of the article has lots of other things in it, like the way we count in Judaism – the mathematics of counting in Judaism, whether you’re marking time or counting people, or permutations, and geometry and pi – mathematical modeling. There are examples of that, there are examples of logic. The Jewish Talmudic reasoning of kal v’chomer has a counterpart of the secular reasoning technique of a fortiori – you could go on and on. To me, it’s just always cool when you find that the first written or known example of a particular math topic sometimes happens to be in Jewish text, right? Like, the first written fair division problem was in the Talmud – three creditors, how do you divide up the estate right? And no one could figure out the Talmud solution for centuries, until just, like, a couple of decades ago by someone who I think won the Nobel Prize in economics.

So, anyway, it made it fun for me. I mean, I’m sure it realistically only made a difference for some of my students, but I was having a good time finding those connections. And what really was moving to me, though, was (and by the way, if I ever got some foundation funding, I’d love to sort of write up a textbook or supplement with all the major math topics illustrated with Jewish context, but that’s another project down the road, perhaps), but it’s one thing just to make connections between the two, but it’s yet another when sometimes learning the math actually helps you understand what you might have assumed was just hyperbole on the religion side. And then suddenly it’s like, “Well, that’s actually plausible. That’s actually consistent with the math. That’s kind of cool.” Because, as you know, as a rabbi, just as there are a lot of people who aren’t shy about saying, “Oh, I had these uninspiring early experiences with math, that’s why I’m turned off now,” I’m sure you have people that come to you saying, “Yeah, I wasn’t that inspired by the religious education I received, and so once I had my bar mitzvah, that was it.”

And of course, what happens is 20 years later, when they have their own kids, now they realize, “Well, maybe I threw it out too soon. Maybe there’s more to learn than the sort of juvenile, pediatric version that I still have.”

Geoff Mitelman: Well, what’s fascinating is looking at how many times Numbers – I mean, look at Numbers. That’s a translation of the fourth book of the Torah. Bamidbar is what it is in Hebrew, “in the wilderness.” But it’s called Numbers. It starts as a census, of counting. And people talk about the sixth day of creation and the seventh day of resting. and how divisible the number six is, and why 12 becomes so important, because I think it’s so divisible there as well. And we don’t even realize how integral – if you will, if I can use a little pun – how integral mathematics is into Jewish text and Jewish thought. And logic also, as well – being able to say, if it works in this lesser case, how much more – so is it going to be the case for a larger thing?

And that comes up all the time in rabbinic literature. If it’s true that Texas is big, how much bigger would it be true about Alaska? Whatever analogy that we have there, that comes up all the time, I know, in both mathematics and in Judaism.

Larry Lesser: Absolutely.

Geoff Mitelman: So one of the things that I know that you mentioned, if I’m remembering the paper that you talked about, comes from a phrase, actually, in Numbers, of mah tovu ohalecha Ya’akov, which translates as, “How goodly are your tents, o Jacob, how beautiful your dwelling places, o Israel.” It’s the first thing that Jews say when we enter the sanctuary. Jews need to have a minimum of 10 to be able to say certain communal prayers. Bcause of a little thing you don’t say “1-2-3-4-5,” they will say, “not one, not two, not three.” Sometimes they’ll go, “mah tovu ohalecha Ya’akov.” So they’ll use those as as they count to 10. But you also did something about the spatial arrangements of the Israelites’ tents as well, because the rabbis say that “it was so good” because there was privacy. So can you talk a little bit about that paper that you worked on?

Larry Lesser: So, first, for clarification, that paper was written by the fourth speaker of our series – not by me, but by my UTEP colleagues, Olga Koshaleva and Vladik Krenovich.

Geoff Mitelman: Yes.

Larry Lesser: And so, I wouldn’t try to recapture their whole paper, but it was a really nice example where they examine the connections between the geometrical placement and what would optimize privacy. And what was further cool was, they did a follow-up paper, because the first paper was just visual privacy – “What arrangement makes it where it’s hardest for anyone to see anyone else?” But then they did a follow up paper on audio privacy. “What will make it hard to hear anyone else?” So that they have audio privacy also, in case something’s going on in the tent that no one else should hear. So, yeah, it was really cool.

We have posted the papers that all six of our talks have speakers who have written either books or articles or both in this area. And we have a bibliography that we have posted. In fact, right now I have a demo version of it, at larrylesser.com/speakerreferences, I think it is. Anyway, I can get that to you later.

Geoff Mitelman: What’s interesting is that there are several elements of linking the math and the Judaism. One is just the text itself. Then how the rabbis talk about “ Why are the Israelites’ tents so good?” Because there’s privacy. And Victor and Olga – thank you for giving them credit for that paper, because they should absolutely get the credit for that wonderful work that they did – of being able to say, “Here’s how it would have been laid out.”

But as we’re thinking about privacy, our world is now based on zeros and ones, and privacy happening through Facebook – we’ve had all these conversations about Facebook and privacy here – facial recognition, that privacy and math actually are very closely intertwined, much more so in the last 15-20 years than what we would have seen previously.

Larry Lesser: Absolutely. People going through statistics, or, actually, the big buzz now is data science is its own field now. And there’s a big part of data science that focuses on data ethics. Just because you can easily capture a whole bunch of data doesn’t mean you should. The discussions about what does privacy mean now, especially if you’re just harvesting data off web pages or things, there are lot of important discussions that need to be happening.

Geoff Mitelman: And probably some optimization also as well, of “What is going to be the optimal way to be able to protect your privacy?”, which is something that we’ve had to deal with as human beings for hundreds of thousands of years. How do we be part of a community and protect our own individual selves?

Larry Lesser: Absolutely. We have one more speaker left in our series. It’s December 16 – David Novick, the title of his talk is, “Will Computers Make Religion Obsolete?” (Laughs) And of course, I don’t think it’s a spoiler to say the answer is “no.”

And one example that’s come up recently that is just really fascinating is, just like you have all this new technology with social media, this whole thing with autonomous self-driving cars – they have to be programmed with some ethics, right? Because what if the car detects that, if it keeps going where it’s going, it’s going to hit someone – but if it swerves onto the curb, it’s going to maybe kill three pedestrians? Well, which is worse? And so you’ve got the trolley problem all over again now.

Geoff Mitelman: Right, and with a certain amount of mathematics, that you’ve got to factor in what is going to be the trade-off, because there’s got to be a tripwire of, “It’s a yes or a no.” On some level, you’ve got to make a binary decision, or the car has got to make a binary decision of “What is it going to do? Is it going to move forward or stop?” And how do you square that circle, if you will?

Larry Lesser: Yeah.

Geoff Mitelman: And what’s interesting – we’ve had a couple of speakers through Scientists in Synagogues, actually drawing the analogy of self-driving cars with a whole conversation that happens in the book of Exodus and then later in the Talmud about the ox that gores. Because if you have an ox, if you own something that is supposed to make your life easier, whether that’s a self-driving car or an ox, there is going to be some percentage of damage that’s going to be done and/or may kill people. So the trade-off is, “how much value does it bring?” versus “what is the detriment to society?” And we do make calculations of saying “it is worth x number of people dying each year in a car accident to be able to drive,” right? It’s a horrible calculation, but that is what the world is. And so the Talmud says, “Well, then, who’s going to be responsible?” When something bad happens, people are responsible. So, who ultimately becomes responsible for a self-driving car killing somebody? Who is ultimately responsible if the ox gores? Because the ox and the self-driving car don’t have a level of autonomy; they are programmed and/or thinking in a way that is not what a human is thinking.

Larry Lesser: Yeah, that’s a great example. And again, a nice example where you’re connecting something contemporary, like the self-driving car, to the story from Jewish text about the ox. So that’s just been really a neat thing, where you see things from the past and things from the present, because too often people go to one extreme or the other. They either live in the past and they shut out anything modern, or they embrace everything modern, but assume anything that’s old has nothing to teach us now. And that’s a false dichotomy.

Geoff Mitelman: Right. I think that’s a lot of what we aim to try to be able to do, of trying to say we need both. Why I so enjoy some of the programs that you all have done, is that there is a perception in American society, right – there are lots of letters to the school board or to the politicians that used to be, “don’t teach evolution by natural selection.” There’s now, “don’t vaccinate my kids. Don’t put a mask mandate.” There was an article in the New York Times just earlier this week about how COVID has accelerated the science and religion [divide]. But I don’t know anybody who’s writing letters to their school board saying, “Let’s not teach Euclidean geometry, because Euclidean geometry is going to corrupt our children.” The math and the science, they’re linked, but I see them viewed differently, the way that people perceive mathematics versus [how] they perceive science. And I’m curious, as somebody who is a working mathematician, do you feel the same sort of concern and vitriol that you may experience if you were a biologist or somebody in public health?

Larry Lesser: Great question. You know, it’s kind of funny, because it is true that people who teach math are a bit more insulated from the political kind of stuff. In fact, I have a colleague – it’s really funny. He is a political science professor. And when he’s traveling, and some stranger makes small talk with him and asks, “Well, what do you do?” and he says, “I teach political science,” that just seems to open up floodgates – “Oh, well, then what do you think about what Trump did?”, and all this kind of stuff. And he doesn’t always want to get into conversations with strangers. So what he tells them is, “I teach math.” and that stops the conversation right away. (Laughs)

But just to push back on something that an assumption you’re making, even though we are more sheltered from these kinds of controversies of the day, we are not totally sheltered, because, for example, even something as simple as, like, long division – it could become politicized. “Should we teach long division in the schools, or just let people use calculators?” And somehow that gets politicized with the back-to-basics movement versus the technology people.

And even the algorithms by hand have cultural differences. If a student moved here from Mexico, for example, as a lot of our students at UTEP do, they actually have a different physical layout for writing out the long-division algorithm. It gets the right answer, it’s equally valid, but it looks different because the numbers are in different places, not all the numbers are written down. And so, a teacher who doesn’t know that might say, “That’s wrong, do it the right way.” And so, you get political things coming out of that.

And there are a number of people who, in trying to make math more engaging and more relevant, have developed curriculum where math is taught often using examples or contexts that come from justice issues – racial justice, or climate change, or whatever. And again, you can imagine that there are always going to be those few people in the class, or their parents, who are going to say, “You’re politicizing math, and you’re propagandizing my kid, and stop it.” There are some things to have to navigate.

Geoff Mitelman: And obviously, I’m a big believer in STEM education, and that sometimes there are barriers for people with STEM education. I think there are gender perceptions that happen – [with] the leaky pipeline, of ensuring people of color, women, come through and be involved in the STEM field. And that’s trying to shift that to a more equal playing field of thinking about science and technology and engineering and mathematics. And there probably are pieces that I’m not even aware of, of cultural sensitivity.

Larry Lesser: Absolutely. I mean, you just mentioned gender, and we’ve been taking the concept of gender for granted for decades. But now it’s become clear that gender identity is more complex than a binary. And so, you’ve got all these math and statistics textbooks that have been written with examples of “males” and “females,” as if that covers all the options. Now STEM people are having to come up with more nuanced ways of conducting surveys and doing analyses that acknowledge that there are more than two possibilities, and even when there isn’t data in one of the other categories, to at least acknowledge that there could have been data – that’s a big step.

And again, here’s another example where we’re talking about this new contemporary awareness we have, and yet, when you go back to the Talmud, there are, like, a half-dozen different gender identities in the Talmud. People’s minds are blown when they hear that. So, this is not new. But here’s another connection, that science and religion are not so far apart.

Geoff Mitelman: That’s also because they’re dealing with human questions and mathematics. I’m a believer that – and this is a whole discussion that I remember in high school and college – of, “Is math invented or discovered?” I am more of a believer that it is discovered more than it’s invented, but I could be convinced otherwise. But still, when we’re trying to discover it, there are human foibles and human questions and challenges, and math may be something that is discovered, but mathematics is done by human beings in a community. And that’s an important aspect that’s often overlooked.

Larry Lesser: Absolutely. I mean, human beings – the society of mathematicians – have to decide what constitutes proof, what constitutes someone being able to teach the course. They have to come up with their own definitions, their own standards, for this sort of thing. I mean, even something as basic as a number system – that came from a culture and a time, right. So why are Japanese or Chinese numbers written vertically? Well, they had these bamboo strips available to write them. And the Babylonians had stylus tablets with these things, and so their numbers look like these marks. People just kind of assume that math was just sort of found on tablets, so to speak, one day, and that’s it. And the truth is that, like you say, they evolve out of human communities as well.

And what’s sad is that most people don’t take enough math to sort of get a glimpse of that, because it’s not covered in sort of the high school curriculum, usually. When they get to college that maybe they’ll take a history of math class – they have those now. Or maybe they will take a “math for liberal arts” kind of class that brings in fascinating topics like infinity – that doesn’t otherwise get covered in any of the “usual” math classes. And I just love the approach. I’m at a research university, but I have sort of a liberal-arts sensibility to how I view math and statistics.

Geoff Mitelman: Well, you used a word that I want to talk about for a few minutes, which is “infinity,” because it’s a fascinating topic, and it’s one that leads to religion. And this was something I was thinking a lot about in March of 2020, because I was in New York. I was five miles from New Rochelle, which is where the epicenter was at the end of February, beginning of March, of 2020. But the line that kept coming up, as COVID was starting to spread all over North America, and particularly in New York, was that “every life has infinite value” – that’s a line that’s said religiously – or that “God is infinite.” And when we say every life has infinite value, that’s a wonderful statement to say. But what was happening with COVID was there were only a certain number of ventilators. There were only a certain number of ICU beds. For most of the last 30, 40, 50 years, we didn’t have to deal with overcapacity of ventilators and beds, and stretching the healthcare system. So everyone’s life was more valuable than what was actually available to the healthcare system. When it stretched to the breaking point, it became a question of, “is our people’s life really infinitely valuable?” And how do you compare infinite value of one person on a ventilator versus another person who is losing their job and is going to be out on the street and hungry? And what’s their value? It’s hard to compare. You can’t compare infinities, almost by definition. And so, I know this is something that you and everybody at Temple Mount Sinai talked about as well, of the role of infinity in both Judaism and in mathematics.

Larry Lesser: Yeah, thanks for bringing that up. That was the opening talk. And even though I’m the co-organizer of this series, I just had to give that first talk myself, and I love doing it. And I believe you attended the talk, so thank you again for attending. Infinity turns out to have its own rules and its own arithmetic. But what’s not obvious, until you start exploring, is that some of the ways in which the rules are different actually illuminate a lot of very profound ideas in Judaism that I hadn’t really – I [was] just like, “Okay, yeah, the rabbi said this,” but that it’s really completely consistent with it.” So, when it comes to life, we have the famous thing in the Talmud of “saving one life can equal saving a whole world,” right? And it turns out that is absolutely true in the arithmetic of infinite numbers in mathematics, that one infinity equals 6 billion infinities. I mean, that is absolutely true.

Of course, the converse direction of that is that many lives is therefore not worth more than just one life. And so, you have the trolley problem. We can’t kill one person to save 10 people. We’re not allowed to do that. And again, this is very different from – I mean, there’s some secular philosophy, like Mill’s utilitarianism, that would say, “Well, of course, five lives is better than one.” But not in Judaism – Judaism really maintains that distinction.

Even the infinite value of just one life is played out in other ways – such as when we count people up, as you mentioned, we don’t say, “you, you’re one, you’re two, you’re three.” We count in an indirect way to respect the infinite value of human lives. And that’s not just to see if we have a minyan, a prayer quorum, but also, when we’re doing a census. In the Bible, there’d be a proxy of counting coins or counting lambs or something. And even Israel today uses an indirect method, in certain aspects, in tabulating their census.

Or the idea in Judaism that there’s a hierarchy of infinities, that there are different levels of spiritual worlds, the world of action and formation and creation and emanation and the ein sof. It turns out math has different sizes of infinity also. It’s not just either “you’re finite” or “you’re infinite.” There are different sizes of infinity. That’s kind of mind-blowing. And so, in the talk, it was a lot for people to take in, I’m sure – it’s the proverbial drinking from the fire hose, because they were learning for the first time that mathematical infinity is much more complex than they realize. But then seeing that those things illuminated, things they had heard in Judaism…

Or another example even, is the value of the mitzvot, the commandments – because sometimes there’s a few commandments that are singled out, as “this one is so special, it’s equal to all of the others combined.” “Well,” you might think, “okay, that’s just a rabbi’s hyperbole.” But it turns out if you assume that a commandment has infinite value, then it’s perfectly consistent with mathematics to say that. So, anyway, it was just fascinating to really bring out all those connections and put them together in a talk that was still accessible for general audiences.

Geoff Mitelman: And what’s fascinating to me, and what I always love, is that a lot of the language that’s used religiously will use the word – we’ll say “infinity” or “infinite,” “endless” or “eternal.” But in my mind, it’s shorthand for a really, really big number. I don’t think that when they were writing the Torah or rabbinic literature or liturgy, of a level of what infinity truly meant. Because we will say that when we look at the stars, and you’ve got your background of this wonderful astronomical background, we say, like, “it’s an infinite number of stars.” Well, it’s not an infinite number of stars. It’s billions and billions and billions and billions of stars. And we are small human beings looking up at the sky, and we can’t really process the difference between 800 billion versus 400,000 versus infinity. It’s all just sort of like, “a big number.” And I think that’s being able to say, “Well, let’s define what is this infinity that we’re talking about? And is that the appropriate word to use?” And I think sometimes the answer is yes, and sometimes the answer is no.

Larry Lesser: Right. I mean, the term ein sof literally means “without end.” And so that’s a qualitative way of describing infinity, right? So, in math, we have two ways of talking about infinity. We have sort of infinity as a process versus a completed object. And the process is what people are more thinking of, because it’s like, “Well, no matter how many objects you have, you can always add one more.” Or if it’s easier to visualize going in the other direction, you start with a cookie. You eat half the cookie, now you eat half of what’s left, and now half of what’s left and half of what’s left. And you, quote, “never would finish.”

But there’s another way of thinking about infinity, which, in effect, says, ultimately, you do eat the whole cookie, and ultimately, there is this completed thing that contains everything, and that takes a little more time to get your head around. And, yeah, that would be fascinating to go back through all the examples in Jewish texts. And I’m sure we would find that in some cases, yeah, they just meant “a really big number,” and in other cases, they really meant something beyond that.

Geoff Mitelman: Well, and I’m thinking about – there’s a website that I love called “Wait, But Why?” And I come back to this link all the time, of a number called Graham’s number, which I’m sure you know about. I don’t know if our listeners know much about Graham’s number. But the way that he described it is that it’s like asking, “What’s the biggest number you can think of?” And he would say, like, “A Googolplex to a Googolplex power.” And he said, “Graham’s number makes that look me like asking a kid ‘What’s the biggest number you can think of?’ And they say, 100 + 100.” I mean, Graham’s number is so mind-blowingly huge. And what he said, at the end, was that it reminded him that ultimately, he does want to die. He does not want to live forever, because it would be so difficult to be living in a place that where nothing would – where something would live forever, that we don’t really understand what the level of eternity actually means if we really think about that.\

Larry Lesser: Wow.

Geoff Mitelman: And with Judaism, as we use the word olam, which sometimes means “universe,” and sometimes means “eternity” – is that a completed infinity? Is it something that is self-contained, or is it something that is beyond what we’re able to understand? And is it something of just, like, whatever it is, it is more complicated than we can realize as finite human beings?

Larry Lesser: Yeah. And there was an interesting thing with the history of this, because Georg Cantor was doing a lot of looking into the nature of infinity, and there were some people that gave him a hard time about, “What’s this talk of actual completed infinities?” It felt heretical to them. And in his mind, it was actually leaving even more room for God, because it’s like, if infinity is even more complex and big than we had previously imagined, and God must be even beyond that, aren’t we saying, if anything, this is consistent with really supporting the idea of God being beyond everything?

Geoff Mitelman: And this brings it back to a whole circle. I didn’t even realize how many mathematical languages and frames and metaphors we use. But this brings us back full circle, because mathematics can’t prove God’s existence or disprove God’s existence. And I think that’s something that theologians tried to do in the Middle Ages, and I think some people even try to do now. And for some, they will say, “Axiomatically, God exists,” and that’s where they start. But it’s a recognition that that’s an axiom, that’s a statement of faith, that you are starting in this way. But mathematics cannot prove or disprove God. I don’t think science can either. And I think that’s an important distinction of – it’s trying to place something in a realm where it’s using the wrong language to talk about these kinds of questions.

Larry Lesser: Absolutely. One thing came up about a decade ago. The Aish Discovery Project came through El Paso, and one of their sort of modules is they bring up the Bible codes as sort of proof of the divine authorship of the Torah. And first of all, almost no one on the planet knows mathematics deeply enough – and at the same time, Judaism deeply enough – to really have an informed opinion about this, in my opinion. I mean, it’s beyond what I know in both realms, too. But just to oversimplify – well, I don’t want to try to recreate the whole thing, but there was a mathematician, Barry Simon, who identifies as an Orthodox Jew, who wrote in Jewish Action, the OU Journal, how he felt that the analysis was problematic as a Jew, as well as as a scientist.

But what made this tricky was that originally, a statistical journal published an article saying, “The Bible codes are true, basically.” And years later, they published another article that basically – I don’t know if it was a retraction, but it rebutted it, that they had not been careful about defining. Again, it comes back to defining what you’re starting from, right? If you define in advance, “Here are the names we’re going to be looking for, and here are our rules for deciding what spelling to use of the names when there’s choices of how to spell the names,” if you define all that clearly in advance, and then you start looking, that’s one thing. But if you don’t, then all bets are off. But that’s a really subtle point, and a lot of people.

So I don’t want my faith hinging on whether or not someone finds a Bible code, or whether or not someone finds some particular piece of archaeological evidence for a particular biblical event. I think faith needs to be bigger than that. But I also think that sometimes belief is overrated in this sense, that even in traditional Judaism, you have a lot of things where what matters more is that you act as if something is true than whether you personally believe it’s true. In other words, if you’re the kind of person who acts as if you are personally delivered from Egypt, then you will have so much more empathy for other people, and you will be a better person, right? Or if you act as if your sins and your merits are equally balanced, and the next one is going to tip the scale, whether or not you believe that’s literally true, if you act as if it’s true – again, you’re going to be a more thoughtful, careful person, and that’s good. So, sometimes I think we make too big a deal about what we’ve proven true and what we believe is true. How we act is ultimately what matters the most.

Geoff Mitelman: That’s – you couldn’t have said it better. So, Larry, thank you for both the time this afternoon and the wonderful work that you are doing at UTEP and at Temple Mount Sinai. And if people want to find more, they can go to larrylesser.com, right? That’s where they can find your writings and some of your music and some of the programs that you’ve run, correct?

Larry Lesser: Correct. The stuff on connecting math and Judaism I’ve put on larrylesser.com/Judaism. And as you mentioned, I also have music. I have larrylesser.com/sparks, which is the album I just released last year. And actually, there’s even one song on that album that relates to this theme. This song is called Rowboat, and it basically takes the midrash that everyone’s familiar with, of interdependence, of the guy who’s drilling only under his own seat – what’s the problem, right? But it extends that to the current situation of climate change, where we need to recognize we’re interdependent on each other right now, and what people do in other countries around the world is going to affect the water level here as well. And of course, there’s interdependence going on with how we approach the pandemic. I mean, we could go on and on. So again, another example of how ancient wisdom has a lot to teach us about how to handle our contemporary challenges that we have in the science world.

Geoff Mitelman: Absolutely. And I think that’s being able to find that wisdom is so valuable. So I really appreciate the time, and people can find all the other talks at Temple Mount Sinai, of all the conversations about Higher Meanings and the conversations and the papers that we reference there, you can find those I know on your website – you can also find them at our website at sinaiandsynapses.org. You can find me, I’m at  @RabbiMitelman at Twitter, or you can find us on Facebook and Twitter at @SinaiSynapses.

And our conversation next week is going to be with Professor Lisa Miller at Columbia University, who talks about children’s spirituality and has a new book out called The Awakened Brain, about the interplay of science and spirituality for children, which is something that’s very close to my heart, with two young kids. You can join us every week, Tuesdays at 2:00 p.m. Eastern for more conversations. But for now, Larry, thank you for taking the time, and thank you all for joining us here today.

Larry Lesser: Thank you for having me.