 If you have religious conviction that there are completed infinities and you think about it long enough, you might go a little bit crazy. Hello my friends and welcome to the 103rd episode of Patterson in Pursuit. A couple of months ago I was asked by my friend Isaac Morehouse to talk about philosophy of mathematics and why I care so much about it. He's aware I produce a lot of content. I keep harping on some ideas in math. Why is it the case? Most people think that's kind of crazy. So we had a great discussion and I really enjoyed it and got a lot of things off my chest. But the video is behind a paywall. I liked the interview so much I said, hey, could I have this interview and put it on my YouTube channel and my podcast because I think my audience will like it and he kindly agreed. He titled the video, Why is Steve Patterson Mad at Mathematicians? Which I think is the right title for the talk. If you are like me disappointed with the quality of ideas that has come out of the academy and the intellectual paradigm in which we live in the last century plus and you're wondering where these bad ideas came from, I think a lot of the blame should be placed on the shoulders of mathematicians. And I think whenever we get ourselves out of this intellectual malaise that we're currently in, a lot of very deep revision has to be done with regards to philosophy of mathematics. And it's not just an esoteric thing that only affects pure math and geometry. It's something as we discussed in this video that has implications even for things like COVID lockdowns and football. Abuses in the philosophy of mathematics are in a bunch of different disciplines and the stakes are very large. So my anger at mathematicians is because they're dealing with such important concepts that if we get them wrong, the world can be a significantly worse place. So I really hope you enjoy my conversation with Isaac Morehouse. Steve Patterson, sir. Sir. I want to talk about math. Actually, I want to talk about why you're so angry. Why are you so angry, Steve? At infinity. Okay. So I'm shaking my fist at God. No. So here's, here's the story. Unfortunately, Isaac, in the world of ideas, people are very hierarchical. And the world of ideas itself is very hierarchical. People think that, you know, at the peak of the pyramid, you have mathematics. And then you have right below that, maybe physics. And if you talk to some physicists, they might say actually physics is on top. There's a little bit of this debate between those two. But generally, if you've got an economist and a mathematician going into the room, there's some disagreement about the economist's graph from the mathematician. The mathematician's going to win because he's a mathematician. And in my personal pursuit of truth, I find logic to be very, very, very important, as you know, right? Square One Foundation is a knowledge, logic and existence are inseparable. I think this is a really important point. And in making this argument years ago, I had lots of criticism for people who are appealing to math or physics, ironically, saying, no, no, you can have logical contradictions. For example, in mathematics, this has actually happened. I went and interviewed a professor in person in Columbia University who told me that one example of a logical contradiction is an infinite set in mathematics. And he was saying, well, logical contradictions, yeah, they can exist. It's not that big a deal. Look, they're used like in mathematics, and infinite set is a logical contradiction. He said that. He also said that another example would be the pope, because the pope is both married and unmarried at the same time. He's married to the church and unmarried. So this is a professor. Right? I said, oh, why am I angry? So then in physics, for example, people would say, oh, well, of course, there are logical contradictions. You have this thing called superposition. Things could be in two mutually exclusive states at the same time. It's called superposition. So anyway, I started researching physics, a little bit of physics. And some mathematics to figure out where the hell are these ideas coming from. And to my shock and horror, I consider our current mathematical paradigms since the late 1800s to be built on foundations of sand. There are absolutely terrible ideas that are nested in the foundations of higher math, not necessarily talking about arithmetic here, that are wrong. And they have to do with the notion of infinity and the notion of completed infinities. So if you care about the world of ideas, you have to examine the ideas at the peak of the pyramid. And those ideas turn out to be embarrassingly bad, some of them. So the reason that it's a big deal that there's bad ideas in math is essentially that math is the last refuge of scoundrels. That when someone is trying to be pinned against the wall for bad ideas and other areas of life, they will attempt to justify any form of logical contradiction by saying even math, the purest of the pure science that is indisputable, proves that logical contradictions can exist. And that's kind of what makes you find math something you want to tackle because you want to take that argument away. That's one perspective. There's actually two. So the first perspective is sort of from a pure theoretical standpoint. If you're trying to build a worldview to understand reality, you have to have an explanation of what math is and how it relates to the world. And if there are such things as logical contradictions that are inescapable in mathematics, that's actually a very, very big deal. So just from the ideas perspective, you actually got to sort out math a little bit, at least get the foundations more. There's a secondary argument, which is to say that the world of ideas as a social phenomena is very hierarchical. And you have these big shots, these big mathematicians, you can't disagree with the math. The math speaks for itself, you know, right? When the mathematician says X, X is likely to be true. That's also a problem from like this, from a sociological standpoint. There's also a standpoint, which is that in various other domains, there are often abuses of mathematics, appeals to mathematics that are absolutely terrible, that build, that build bad structures of knowledge and also negatively affect our life. Like, oh, I don't know. Maybe, what does it mean to say there is an exponential graph of infections of COVID? Yeah, because when somebody says, oh, no, you don't understand. We must lock the world down. It's an exponential graph. That's an, that doesn't appeal to the weight of mathematics to try to justify some type of outcome or what just happened in Bitcoin cash. You have the brilliant mathematician who did very well, who made a point. Amerisyshe made a point of saying he did very well in math and his French school. And when he talks about game theory, he says, hey, listen, Bitcoin, ABC is a shelling point. And what that means is, in other words, we're very, very important. And that means you should essentially make sure that you give us money because we are the shelling point. Do you know what a shelling point is? If you don't know what a shelling point is, that means you're kind of stupid. And that means you should really shut up and do what I tell you to do because I'm the mathematician guy and I'm telling you that Bitcoin, ABC is a shelling point. So suddenly we have an appeal to mathematical concepts in something like Bitcoin and something like industry and something like COVID. It just comes up in economics, as you well know, there are all kinds of appeals to mathematics that don't actually port onto the world. So it's very important to have a clear philosophy of mathematics. So you want to bring math down a notch in a way as well so that people, you know, it's funny, I found this any area that I've gone into in any depth and I never have in math. But recently I have started to in health before COVID for my own health, particularly like virology and understanding of blood-borne infections, bacteria, you know, I'm not going to pretend I'm an expert, but you go deep enough and you realize we don't know what the fuck we're doing. And if the common view could just be there are way more things we don't understand in health than those we do or in math or in astronomy or in whatever that alone would be really, really powerful. Check against some of the abuses. So let me see if I can explain because you shared a video. This is what prompted me to call you. Yeah. And at risk of going on one of my things where I talk for too long, which I definitely have a problem with. You get a lot of criticism for that, Isaac. I think it's all right. I think some people talk more than others. It's okay. Well, look, the reason that I care about it and I normally don't listen to very much criticism is because my, in my family, we all are talkers and I have, I have been the victim of my own relatives inability to contain the self-defense mechanism. Yes. And in the older I get, the more I realize I'm going to be less and less aware of other people's social cues. And I don't want to be an old guy who like everyone's like, oh my God, you know, I sort of have the same thing here, except with nose hairs. So I remember when I was really young, my grandfather had some nose hairs sticking out and I was like, never, never shall it. And now every once and I'm like, you know, it's there. I'm just going to let it be. You just got to meld it into the mustache beard. Yeah, you know, it's not, it's really not worth it. So you, this is what got me on it. Cause I mean, I've heard you talk about math and we've chatted a little bit about infinity stuff and whatever, but you posted a really great video. It was like 40 minutes long. And I saw you on Twitch with some people saying, hey, go check this out. And the video was basically why the concept of real numbers is fake, why real numbers are fake. And he essentially says, and I thought it was a great video made perfect sense to me. And I didn't disagree with anything he says, look, take something like pie, which is a number that you can't define because it has an infinite number of, of, you know, decimals that keeps going. There's the practical use of pie and he's not arguing against that. It's a useful hack. What pie is, is a hack. It's basically an admission that we don't know exactly how the hell to figure out the area of a circle, but we found a hack that works good enough. And for whatever your application, you can just keep extending the number of decimals to get it accurate enough for that particular application. So for practical mathematics, there's all kinds of hacks like this and they're great in pure mathematics rather than just saying, we don't know what pie is and we can't actually prove that this is some actual existing number that is used in these arithmetical functions. We just, we just discovered that it works. We can't really tell you why the hell it works and we can't actually use it in a verifiable way, theoretically. Instead of just saying that, which would be the honest thing to say, the pure mathematicians just basically define themselves out of the problem by saying, well, no, we can do all these things because it's a, it's a repeating set and then we can multiply that by another, you know, infinite set and we can do all these things and they basically just create new symbols that are essentially self-referential and that in order to try to justify. So I get all that and I think that's silly. But why does it really matter that the few people in the world who are doing pure mathematics are arrogant enough or stupid enough to pretend that they can get away from the fact that these infinite numbers can't be multiplied by each other and given, and give an answer that makes sense? Like, why does that matter to the rest of the world? What, what, what is the negative implication that that's going to have? Sorry, several, several different things I want to say before I answer that question. I'll say pie is, you know, one of the most important foundational, practical concepts in mathematics. So when people are critical of the conceiving of pie, it's usually very subtle and important points, but it does not translate into saying, you know, we can't use pie anymore. That's not what a lot of people are or who are critics would, would argue for. There's, there's a, so I'll answer your second part of the question. The reason it's important is many fold. So first of all, because we have a, a sociological hierarchy and generally an intellectual hierarchy in terms of how important we think various disciplines are, I, I, it's the same thing as if philosophers were making a huge error in the fundamentals of the way that they approach philosophy. So it's sort of the same phenomenon sociologically. That would be a problem because philosophers are actually very important and they should, well, philosophers should be more important, maybe not academic philosophers, but in terms of like those who are actually contributing to the world of ideas and my opinion, philosophy is the inescapable foundation. You can't get below philosophy because you're just doing more philosophy and mathematics, I think is actually sort of subservient. It's definitely subservient to philosophy because you can ask philosophical questions about mathematical constructs and most mathematicians don't. So there's the sociological component and there's the, there's again the worldview component. If you have somebody, it's, it's sort of like, imagine we were talking about theology a few centuries ago and theology is actually an important discipline, especially if you ever try to have a rational conception of God, we're not just talking pure faith based stuff, but you're trying to understand the properties of God and like in like a 16th century context. If all the theologians are making some elementary error and are incredibly dogmatic and unable to see the errors and the theories they're constructing, that's a big deal. Like ideas matter and, and it's especially important for me because I'm very partial to axiomatic deductive reasoning when it can be done carefully. Like humans have this unbelievable ability to identify truth and then use careful logical deduction to figure out other strains of truth based on that one truth. And that is like a sacred method. That is a sacred process. When that gets screwed up. I don't disagree with you, but, but you're still kind of up in the sky. It's like it's dangerous to have wrong ideas that can have bad implications. Fair. Can you give me a concrete example of how the errors in pure mathematics have made the world worse besides, oh, you can't get academic tenure unless you agree with that. So I would say that it is definitely the case that in physics, for example, there have been bad ideas that have been perpetuated for decades, for 50 years where sound minds in the domain of physics have wasted away working with shitty concepts that don't actually port on to the world because they don't make logical sense. So I would say there was a huge amount of intellectual horsepower and IQ points that are all spinning their wheels or going in the opposite direction because the framework for thinking about math they've inherited is definitely wrong. And it's like, you know, engineer. There's also a relation between physics and engineering here. If you have, if in your, if in the educational system, your engineers all are getting taught bad methods of reasoning or bad ideas about what structures can withstand hurricanes and what structures can't, that concretely affects the world. So I'd say the same thing, like with infinity and the amount of space that has been wasted and mental cycles that have been spent in the debates with thinking mathematicians and physicists debating people who are talking about really bad ideas and math physics is huge. It's a huge amount of time. So maybe like you feel like the theoretical component, say pure mathematics, errors there slow the progress of applied mathematics, which slows the progress of computer science and physics and engineering, which slows the progress of actual material world. That's one problem. And then there's also the problem you started with, which is that the belief culturally that mathematicians are like these gods that know everything leads to a lot of deference to authority and academia having an undue influence over the world. And lockdowns. I mean, I would personally pour a connection between a mistaken understanding of the philosophy of math and global lockdowns. And here's an unseen consequence of this. I occasionally get emails from people who say to me something along these lines. Wow, Steve, I really enjoyed your commentary or your articles on infinite sets or some mathematical thing. They say, I was debating this with my teacher in high school or in college. And I thought I was so stupid that I said, Oh, I'm not cut out for higher math, even though I enjoyed mathematics and I pursued something else. So that's an unseen cost. Maybe the world does not have those excellent minds who could have gone into engineering or some other thing because they thought, Oh, I'm stupid because I can't make sense of these concepts that actually turn out not to make sense. Yeah, that's funny. I'm not like I wasn't like in love with math to begin with. But when when math got to basically the the irrational numbers or whatever, all this, you know, bullshit of, you know, you know, cosine of whatever. I just remember being like, this just seems stupid to me. I'm not interested. I don't want to sit here and debate with people about all these imaginary things. Yeah. Like, I don't get why that's interesting to them. So I just kind of decided, I decided I just didn't understand it well enough. And maybe that's true. I'm not claiming I have a good understanding of math. But the more that I've learned about other disciplines, the more I realized like, it's often the case when you get to a point where you think, huh, I miss, I must not just be smart enough to get it. It's because you've hit a point where the obfuscation level has gotten yes. And what you have is a fracturing. You have a fracturing of students who go, Oh, yeah, I understand these concepts. These check out. I'm a smart guy who's learning the smart thing. And those are actually the people who are so dumb, that they're not asking the questions that they know they should be asking or good heavens. They're too stupid. They don't even know they should be asking questions. Breakthroughs and disciplines often come from somebody in a different discipline that comes in sort of orthogonal. That's a thing you bring in some some external mind who doesn't have the same framework as everybody else who's trying to approach a problem. And sure enough, they can think of the problem in a different way. And this is and I like normal Wild Burgers, one of my heroes, I think he's doing incredibly important work. It's funny. So I started, I started walking down this entire video. It was super simple. Yes. So the funny thing is right. Those if you go online Wild Burgers, God bless the man. Okay, a couple of stories. First of all, I started walking down this road of math heresy several years ago now. And at the time I didn't know of normal Wild Burger. And I had I was I'm not interested in mathematics in terms of like applied math, like what the actual formulas I don't give a shit, I care about the philosophy of mathematics, but I don't really care about the mathematics itself. But I thought, All right, well, I'm definitely onto something with the fact that they're that the idea of a completed infinity is nonsense. You cannot get an output out of an infinite process. You don't reach to the end of something that has no end and withdraw some meaningful content. That's a logical contradiction. So for some period of time, I was like, well, shit, maybe I need to be doing some math. So I developed these very laughably elementary intuitions about, okay, like what is it exactly an irrational number? What's the skirt or two? How does it really, really hard? It was fun. It was a good exercise. But I was sort of, I thought I was the only person in the world to raise. Well, I had created some video on it. And one of one of my listeners said, Hey, you should check out this normal wild work ground. It was like, Oh, my gosh, this guy, I was working, you know, in terms of the scale, I had got to like square one or two. And he's like square 10,000 for developing the new mathematical theory on not exactly the same foundations, but far superior foundations. We overlap probably like 95 percent when he's talking about things. I'm like, Okay, this actually makes logical sense. It's funny, because I interviewed him on my show. And he hates philosophy. He thinks he's like, Oh, we he actually, for some good reason, philosophy video. I know he doesn't think of it that way, though, because because the actual relationship of academic philosophy to math has been a shitty one. Part of the people, the people that established a lot of these terrible ideas in the turn of the 20th century, were also philosophers, people like Bertrand Russell, people like Georg Cantor, a theologian, slash philosopher, slash math. So in his mind, he's thinking, The last thing we need is philosophy. And then I talked to him, I'm like, Oh, you can think of it that way. But you are doing philosophy. Yeah, like the whole your whole way of approach is a different philosophical woman. You don't you're not a Platonist. You don't think there are there are numbers out there with that are unknown quantities that we can never really concretely access, but we only approximate. And you're saying no, no, the numbers are the things that are constructed by a particular particular method. What your computer generates is actually you're creating a number rather than an existing out there in the ether prior to its construction. He just didn't think of it that way. Anyway, that was that was yeah, that was multiple stories. What how does you ask me a question? And then I went on the story part. I'm trying to remember the brother. We were talking about the real world. Now I know that when I meet a business owner, whose company went under because of lockdowns, I will tell them the real reason it went under is because because people think infinite sets exist. There is there is a connection there. Yeah, I guess. Yeah, go ahead, go ahead. It was something along the lines of a wild burger. You were talking about the wild burger video and throughout his work, he is trying to be honest. He's trying to say, okay, actually, the theory of real numbers doesn't check out. If you're just being intellectually honest, then you you can't assume that your conclusions are true. So like there's different ways of trying to define real numbers and has changed over time. And our current attempts at defining it sound nice and can please undergrad students and grad students, but they're not actually they don't check out. They're not logically rigorous. There's there's a bunch of mush here and he just acknowledges it. And I swear he is he is a tiny he has a tiny glimmer of hope in a just total garbage heap of supposed thinkers. These are the people with the highest IQs in the world. And I'm telling you of all the different disciplines that I have investigated and all the different professionals that I have spoken with who are professors and supposed intellectuals, mathematicians are the most dogmatic of all of them, more so that the religious. I have not met a religious person as dogmatic as somebody's mathematicians who have literally never conceived of a single alternative way of thinking about mathematics than that which they were taught in high school. I would not have believed that Steve, because it sounds so absurd on its face, given the number of dogmatists I've met in other areas, until I started seeing you dive into this territory and I started seeing what would happen to your Facebook comments, your YouTube comments. I mean, and even people that I knew that I didn't even know were like really into math, like friends of mine or colleagues, I would see them just become the worst versions of themselves. I could imagine just ripping on you and hate for things that I was like, how can you get emotional over this? Like I can see getting emotional over politics or religion or even sports for God's sake. But like what circles? Okay, here's what it is. This is such a fascinating phenomenon. Here's what it is. Math is the domain that in our intellectual religion and in the West, why I think it's actually a global thing. We think that this is the special place for smart people. Would you do something correct in mathematics and you get approval from mathematicians and you mathematically prove something that is supposed to be outside of criticism from non mathematicians or who is or conceived non mathematicians? Yeah, that is supposed to be like you have reached a level of true pure intellect and brilliance when you're talking math and they say Oh, someone's really smart. Being really good at math is like usually the thing that matters the most when that word is used. You know what I mean? Yes. And it matters most to those who are mathematically skilled because psychologically they are approaching the world with this unflappable belief of them being the smart ones. They think and they think that means well that generally as it applies to most things in the world, I am part of the intelligent group and I have special knowledge that cannot be wrong. I am presented with the sacred knowledge of mathematics in various domains and they have never encountered any criticism or challenge of their mathematical ideas. So when they do their heads explode, they go, you know, it's like it is a personal, deep psychological attack on their self conception. If it's the case that they're wrong about the things that they they reserved as sacred truths that all the smart people share and those are wrong and maybe even wrong for elementary reasons. That is just that in people make inferences to their own intelligence and they go, Oh, gosh, I must not be very smart or they do the converse of this, which is also funny to go steep. If you were right, you would have to be a genius. That's the only way you are not a genius. Therefore, you are not right. And I'm like, first of all, I don't accept that framework, because if you're saying in order for me to be right, that I'm a genius, that makes me very uncomfortable. Because my claim is actually much more damning than that. I'm saying that it does not take a genius to see that what I'm saying is true. And I mean that literally, I mean, if you have a honest 15 year old who who is listening to what I'm saying, they're trying to honestly compare it to what their their calculus professor is saying, they're going to go, you know, actually Steve makes a good point. I sort of see what he's saying. So I'm saying, I'm not saying it takes a genius. I'm saying take somebody that's honest. And I think most disciplines get to this level, certainly philosophy or the philosophy of any discipline, how do you know this? You get to a point where you can only go further. If you ignore your common sense, where it's like, well, that doesn't make any sense. Oh, well, it does. If you just throw common sense out the window and then you can go further, right? Like, yes. Yeah. And when you do that, here's what the intellectual class does. They play these games where they go, okay, well, we're just assuming that all of these fundamental errors are sorted out. And they spend the rest of their careers and intellectual energies building on top of those dubious assumptions that they never took enough time to challenge. And then the whole game that they're playing is based on bad assumptions. So the papers that they write the sophisticated conversations they have around the water cooler, it's all based on these assumptions that they never took the time to challenge. It is identical to what happens with religion. I remember seeing that in economics and having the realization that like, almost every sort of sub discipline of economics is utterly like the entirety of welfare economics, right? The minute you accept it, interpersonal utility calculations are impossible. The entire discipline in every paper ever written becomes utterly useless and pointless, but there are just like tons of people doing it all the time. Yeah. So okay. Here's it. I'm thinking of a way to because I keep coming back to this accepting and acknowledging that there are things that I don't want to say unknowable, but at least unknown. So you don't have to be a genius to understand that this stuff is incorrect. Now maybe you have to be a genius to come up with a correct theory like Wilder. Yeah, exactly. That can rebuild these things on new foundations. But there's sort of two, like my question is, do we even necessarily need that? Right? Because there's kind of two things that happen when you when you run into a this the spot where you say there's there's the practical and applied person who says, I have no clue what the hell pie is, or if it's real, I just know that it actually works when I'm trying to get the area of a circle. So I use it. And it's a mystery. That's almost like the faith based approach. Look, I don't know why the hell this works, but it does. And it's because it works because God gave us miraculous golden, you know, numbers that we can use and whatever, right? Whatever it is, you just sort of have faith because it's worked in the past and you use it. And you just sort of say, I don't need to know, like some things are unknowable. That and then the other is, I want to know what it is, I'm going to keep pursuing it. That's the person that tends to either go crazy, lose their mind, like literally, and I've heard, I don't know if this is true that in higher mathematics is like the highest rate of insanity of any discipline. Yeah, it's a thing. It's a thing. Yeah, it's like a real I think Ted Chang has like a short story I read about, which is great. They either go crazy, or they have to either say, I've studied my whole life and I still can't give you the answer. Or they just have to at some point throw in the towel and pretend they have the answer. And I think that's the most dangerous of all pretending to know something that we don't know is what you're railing against. My question is, is it better to just not try to find the answer and just use the thing that works practically, rather than trying to find the answer? So let a thousand flowers bloom, like some people are going to be interested in the application. Some people are going to be interested in the theory. I tend to be more on the theoretical end. And so that's what I'm that's what I'm railing against. You said something I wanted to something really good. I wanted to comment. Oh, they and sanity thing. So I actually have some theories on on what's going on here. So I think part of the reason that mathematicians go crazier or are crazier than other disciplines is partly because of autism. And autism, I think, has a connection with brain inflammation, nervous system inflammation, and it also sort of gives people superpowers. Autism can ask burgers, whatever you want to call it, the people who are your stereotypical computer scientists, mathematicians, they have the ability to hyper, hyper, hyper, hyper focus on one specific thing, deal with one variable at a time, but like, take it to its, you know, super magnified level. And that is awesome for math. That's not awesome for a lot of other things. But I think what happens is because people have this mindset, and I used to have more of it than I do now, I'm sort of working out of it. I was never like super autistic. But I mean, that's like definitely a case of it. And that's okay. What happens is they because they're not good at philosophy, they build these long streams of deduction. And the idea that the, you know, every single step along the way, they're certain. This I know this, I know this, and I know that I know this. So then when you start evaluating the foundations, you go, Oh my gosh, every single thing that I thought I knew is possibly wrong and get this poor people. They even go because they're not good philosophers and they're not good critical thinkers, they go, Oh my gosh, mathematics might internally contain contradictions. But this is a thing. This is a thing that was discussed in the first part of the 20th century, especially, is mathematics complete? Is it provably complete? Are there nested contradictions in it? And some people are seriously entertaining the idea that there are inescapable contradictions and structures of mathematics. So for them, that's the only way they know how to think is sort of in that mathematical logical deductive sense. And they go, I cannot know anything. It is impossible for me to know anything. There are contradictions, everything I've built everything on top of just gets just kind of collapses. And it's no surprise that insanity is the result. The famous example, one of the famous examples is Gayard Cantor, the guy who I think part of me talked about before. This is the guy who developed a theory of infinite sets around the turn of the 20th century. I can't tell you I didn't know anything about him until you started talking about math because every friend I told about you and was like, Oh, check out this guy's book on Bitcoin or this interview about Ross Albrecht, they would come back and be like, Oh, I saw that guy. He's crazy because he hasn't read Cantor. Or no, wait, not Cantor. Maybe it's Gertl. Is Cantor the one that you hate? Cantor is one of the ones that I hate. Yeah, I think it was Cantor. The one I all these people kept being like, Oh, well, Cantor explained all that Steve just doesn't understand. I mean, it could be Gertl. I don't know. Those are the two was Gertl. I think it was. I think it was actually. Well, that's a separate thing. Yeah, they don't know what to talk about. But with Cantor. So he's the guy that came up with the theory of the infinite set that he called trans finite set. And I kid you not he he the reason he developed this theory is because he thought God talked to him and told him it was the glory of God was the trans finite and the infinite personally kind of talked to him and told him this theory. And I'm not saying that God can't speak to people. I'm just saying it should be a red flag. Yeah, like it should be a red flag, though, if one is to be very hierarchical and say, Okay, this is the this is a critical breakthrough in the story of the philosophy and mathematics, the history of mathematics, the foundations of mathematics. The guy that was first talking about infinite sets did say that God spoke to him and it was the glory of the trans finite that was telling him his theories. And he did end up in an asylum and kind of went crazy. And it's also not a surprise to me because if you're trying if you if you have this, this type of mindset, and you're meditating on the concept of the completed infinity and you're absolutely convinced there's such a thing as a completed infinity, you're going to go crazy. Because there is a logical contradiction, the idea that there is a completed infinity. And for me, like I have a specific definition for insanity, right? So there's a lot a lot of parts when people are talking about insanity, they're talking about some social thing, if you believe something that lots of other people don't believe, I don't care about that. I think there is such a thing as insanity, but just something like believing in the existence of logical contradictions or thinking a logical contradiction is true. It's like the only constraints I'm putting on insanity. I mean, it'll break your brain. It'll yeah, if you're a mystic, okay, like you say all is one, I am part of God, I've seen the whole thing, great, it's possible. But if you say there's a logical contradiction, that's the only barrier I'm saying I'm sorry, you're nuts. So it's not again, it's not a surprise. You meditate on if you deeply believe you have religious conviction that there are completed infinities and you think about it long enough, you might go a little bit crazy. And that's where I almost think like the, you know, the sort of religious take for lack of a better word or the woo woo take of like you encounter something like that that you can't explain and you say, wow, there are mysteries in the world. And I'm in awe of the mysteries. And I'm going to just ponder them and be in awe of them and just let them be and not make me uncomfortable. That can get silly and woo woo as well. But there's something about that that's maybe safer, maybe preferable in some instances, then I must figure this out until it makes me go crazy. Well, and also I don't think there needs to be attention here. So I'm totally open to spiritual experience. I've had a spiritual experience totally changed my life. Like, yep, that is a that a part of the a part of God told you that what he told Cantor was actually wrong. Exactly. Craziness imminent. No. God told me that as much as I love my wife, Julia, that's how much he loves me. The most powerful realization that belief that I could have. Now, I don't think I don't have to segment that in my brain and be like, I shan't ever think about this. I shan't make sense of it. If there's a logical contradiction, so be it. It's like, no, it's just a part of my experiences. I'm trying to explain in the most rational way possible. And I think there's also something here like you can be you can be a tolerant theoretician. So so the if you are a strict theoretician, then you say Cantor was an idiot and his existence was damaging to the world of ideas and a little bit favorable to that. But if you want to be if you want to be tolerant, you could say, look, the concept of the completed infinity has been very useful in mathematics. We can say as a as a good theoretical point, actually we have to clean up this idea there. We can extract value from the concept of completed infinity without actually committing logical errors. That's great as well. It's just when people people are absolutely committed, they're devoted, they are religious devotees of the idea that in a literal sense, there are actualized completed infinities in the world and the concept checks out. And that's what I have the problem with a big problem with. I want to say one other thing. I actually wrote this because I didn't forget it. I've been watching more football this season. And on to I know, right? I used to be really into the NFL and I kind of gave it up. But now I'm enjoying it a little bit more. There's a couple of occasions which have made me quite angry, which I think it was like two two point conversions. And one of them was a two point conversion. And one was a going on it for on fourth down, instead of like kicking a field ball. And both occasions, you know, the part that when they went for it for two, they failed. And when they tried to convert the fourth down they failed. And I was like, you dummies, obviously you did the wrong thing here. And some of the commentators said, Well, you know, you know, Brett, they have the statisticians over there and the math checks out. You have to check the math says in this circumstance, you're supposed to kick the field goal. I'm going you absolute idiots math does not work that way. And the reason math doesn't work that way is because there are too many variables for you to plug into your little formula. If you're going to make good decisions in the football field, you have to say, Okay, what's the momentum like? Is it raining? Do I have any relevant injuries? There's even a political dimension. If I if I don't go for it here. And I defer to the statistician, the other people don't like the statistician than they don't like them. So even if we make it, is it long term a bad decision for the quality of my team before political reason? Are you gonna you're telling me that the little statisticians have the formula for the probabilities? Give me a break. Yeah, it's funny. I I've always been interested in that in sports. And there's like some high school coach that always goes for it on fourth down, always goes for two and always kicks an onside kick. And his team is like really good. And when you look at it, statistically, the number of times it's successful and the payoff for success ends up averting out to where like that is a rational position to take. And so people will argue from that. And I'm like, you got to think, not all two point conversions are equal, not all onside kick recoveries are equal. If you're a head coach, and you're in a conference championship game about to go to the Super Bowl, and you're up by seven and your defense is playing great. And you do your onside kick. And the other team gets it with a short field and goes down in scores. You're going to get fired. And rightly so. No, no, no, you could make it to the NFL. If what I'm listening to is true, because even the commentators were like, well, you know, you can't argue with the math. So this is interesting. This is interesting. This is where I think realizing trying to be more pragmatist and I've become this way more and more over my life with ideas, seeing them, not that there aren't, you know, absolute truth, nothing like that, but seeing them more as a toolkit that's useful in certain circumstances. So this all started with baseball. It started with Billy Bean at the Oakland days and the book Moneyball, the movie Moneyball is all about this. And he with a lot of success saw how the old school guys, the old school scouts were kind of like he's a he's a five tool player and I've got gut feel and I'm gonna bring him on. And he saw how he kind of used all the statistical analysis to see how certain things were actually more important than other things. Now there's criticisms of his method. And I think it can go too far in baseball for sure. But he's had a lot of success. I think what's interesting to me is that the statistical approach is way more relevant in baseball than any other sport. They play 162 games. They have like three, four at bats every game. Every at bat is like six, seven pitches. And so when you start to look at the sheer quantity, individual games don't matter that much. In terms of your total, you know, ability to make the playoffs and whatever. And like, it's way more useful in baseball, you move to basketball. And it's less useful than in baseball, but way more than football. They play 82 games. They have, you know, they shoot them. They have 50, 100 possessions a game. And so you look at the difference between a two pointer and a three pointer statistical analysis. It's like it's taken the three pointer a long time because of cultural factors to get to its logical end, which is that you should be shooting three pointers way, way, way, way more than the originally was happening when the three point line was introduced, you should be shooting more three pointers, you know, than anything other than layups, right? Those things make sense. You move it to football. It applies even less. They play 16 games. There's hardly there's like 40 snaps on offense. The players, the same player is, you know, players play maybe 2010 to 20 plays in an entire game oftentimes, the injuries that the home field away, the emotional ups and downs, those things are all all those other factors are elevated even more. And the statistical component is even less relevant. So it's just interesting to see it applied universally when like there's something valuable to it, right? Just like when you play poker, you can have an advantage if you have a good understanding of statistics by realizing something that may feel wrong in your gut is actually like probabilistically a good move to make. But you also need to understand that sometimes that's not what you want to do, right? Like not all situations are equal. And if you can read the emotion, if the guy across from you is drunk and you know he's going to go all in no matter what, because you've seen him drunk before, then you going, you know, trying to bluff is not a good thing, even though the statistics would tell you to. Exactly. But and even then in each one of those case cases that you're bringing up in the different sports, the more you zoom in, the more you realize actually it's not the math itself that implies anything. Should you be shooting more three pointers? Well, it depends. Who do you have on your team? If your players, if they happen to have spent their lives not practicing the three pointer, then in that time in circumstance, they should be shooting the three pointers. If you're coming from if somebody's got a background and like it turns out their personal story is the pull the way that they set up their hoop. There was a bunch of like rocks in the middle area they didn't want to step on. So they just practice over and over shooting the three pointers, they could be like, okay, I don't really care what the statistics say in this particular this individual circumstance, the variables are such that it makes more sense to shoot the three pointer. And that's the case in every domain. Every domain outside of mathematics, and maybe a little bit in physics and definitely a bit in engineering, when you're trying to play the pure math game, you're going to fail because you're simply not taking enough variables into account. And this is it really did burn me when I'm watching the football because I'm like, the only reason I'm hearing these commentators talking about this bad decision as it was a good decision is the social aspect. And they were laughing about that. Like, I don't understand the numbers. I wouldn't have done that. But I mean, if the math says to do it, say stuff like oh, they got they got a real smart guy up in the booth there and they'll call down and tell them whether or not the math tells them to do this. Exactly. And it's like it. So for me, I'm going at this is the same at the same intellectual cancer and the philosophy of mathematics can be seen when you're talking about interpretations of quantum mechanics and you're talking about it on the freaking football field. Yeah, we should let a computer coach an NFL team. Yeah, yeah, soft. Do that as well as it can play chess or Oh, oh my gosh. Okay. So I just have to say something about this. Okay. So this is so this is also infuriating. So in chess, this is one of the things I love chess player happened for many years. I love it. I'm actually doing a chess tournament this weekend, which I'm excited about having to do that in a while because of COVID. But so Alpha zero is this program that Google came up with. And they have a different approach to playing chess than other pre existing computer programs. And it's actually the way they do it is brilliant. And there's all kinds of lessons that can be learned about the learning process because alpha zero doesn't have the biases of humans. Doesn't have the inputs of grandmasters and established theory. So like when alpha zero just came on the market, people like, I played this crazy ridiculous move that's definitely wrong, then it ends up winning. Because because it doesn't have those biases it's really fascinating. But anyway, people think that that alpha zero is and in its success in chess and go is reflection of the inevitability of computers making all of our decisions for us in the world. And it's like guys, you have to understand the chess board is an eight by eight grid of black and white squares with a finite number of pieces on it, all the which have a finite number of moves. And you can literally it's the perfect information game. This is a raw could be a raw calculation game. The world, any part of the actual world that is not a constructed game by humans is a billion times more complex. Well, and humans took what like a thousand years to teach a machine to be able to play that eight by eight by eight grid. It's like it's there's no creativity. There's no there's no outside of the box creativity on the chessboard. Like there's all kinds of creativity within because it's so complex for humans. You can have creative play, but it's not like you're going to see the bishop moving sideways. Like that type of thing. There's no there's not really empirical wonder that can be found on the chessboard. If you play with my kids, there will be all of a sudden, you know, pieces can be thrown and everything will run over my king. You know, well, exactly. Like there's no there's no there's no shock of discovery in a radical sense on the chessboard. But there is in the most every little piece of the world that we live in, there is material shock and awe that a computer is not suited. Does I'm not even sure if it has the capacity to learn about. It's an open question in my mind, but yes. Anyway, you got me going. Yeah, no, I feel like we could go for a long time. We're going to wrap it up on for this time. We'll have to do another discussion. But now I have a new life goal, which is to watch football with you because I feel that you would be equally as angry as me, but about totally different things. Right. We would compliment, you know, yeah. Well, remember, as you're a Detroit Lions fan, so I don't know. That makes me a little uncomfortable. I don't know if I want to be with losers. The nice thing about Lions fans is that we know that we're losers. So we're we're OK, easy to be or we're self-deppered. We hate ourselves. We don't know why we're Lions. Fair enough. Fair enough. You know where you stand in the hierarchy. Aren't you from like upstate New York? Yeah, anyway, are you a Buffalo fan? Well, I grew up in the proximity of Buffalo and Buffalo fans. So technically, hey, this year, though, Buffalo is doing well. Yeah. Last, I mean, it did take 20 years to get there, but or 30 years to go to the Super Bowl and lose all the time, which was yeah, four times in a row. I hear. Yeah. And like, you know, people say how hard that must be as a Lions fan. I'm like, that sounds like heaven to me. I love to sniff greatness. I don't have any. I can't say I have any any teams that I'm like a super. We've been moving so much that I just can't invest and say I'm a Cardinals fan because I'm in Arizona, you know, I guess I'm rooting for the Bills. You know, just given the history, they've sucked for so long. It's a good story. Well, you know, if you know Bills fans, then I fully expect if they win this week for you to get hammered and dive off the roof of an RV onto a folding table. That's how I like to party for sure. I thought so. Hey, thanks, Steve. We'll talk to you soon. All right. Good talking with you.