Motivate the Math

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Fundamentals  @Fundamentals21m
https://xmrchat.com/fundamentals
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AverageGary
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Permutation Groups
https://www.youtube.com/watch?v=VDhy7KXyHF8

In this heartfelt episode of "Motivating the Math," we delve into the personal and professional crossroads faced by one of our hosts. The conversation explores the critical moments in life where one feels like they are on the brink of a breakthrough, akin to Superman facing a wall. We discuss the importance of having a grand goal, such as creating a self-funded math academy, and the challenges of maintaining motivation amidst life's distractions. The episode also touches on the significance of ambition, both in terms of time and money, and how these aspirations shape our lives and relationships.

We also explore the fascinating world of mathematics, specifically focusing on permutation groups and their role in Galois theory. The discussion highlights the importance of understanding mathematical concepts deeply to avoid being intellectually bullied and to stand confidently in one's knowledge. This episode is a blend of personal introspection and mathematical exploration, offering insights into how our personal journeys and professional ambitions intertwine.

[00:00:02] Unknown:

Stop.  

[00:00:28] Unknown:

So we are here. Welcome. Welcome to a very special episode of Motivating the Math.  

[00:00:34] Unknown:

What's up, Gary? What's special about it?  

[00:00:39] Unknown:

Alright. I'm viewing I'm reading,   I'm reading something right now. I'm reading us as being in a pretty critical moment. Okay. Okay.   And I'm not, like so   tell me feel free to edit any of this out, any of it, but I'm gonna just kinda freewheel here. Yeah. And   I'm gonna put you in the in the in the chair   for just a second.   So I'm rating you, Gary,   as   at the edge,   and it's not just of this podcast.   I think you're just at a critical moment where maybe there's a whole like, you know, Superman breaks through the wall, but, like, you don't see you only see you don't see the moment where his, like, fate before he breaks through the wall where his face is up against it, and you're not really sure if the wall is gonna break. And all you see is his face   getting a little mashed up by the wall.  

Mhmm. And,   but it looks like you sort of just had it.   I don't know if it's I don't know if demoralization   is getting to you or   that you're just out of gas with the math podcast   or   there's   you just,   you're maybe at some midlife crisis   where you're not really sure what to do.   And you Okay. And that there's some kind of confluence here.   And maybe it and this is where, like, I could have never done anything like this when I was younger because I didn't have the wisdom to know how to get through these types of moments.   But I'm older.  

And part of   so, like, I have a grand goal. Right? I have a big, big goal that transcends   any of our feelings here. Right? The goal then the big goal is to have,   like, a legit math.   The legit,   like, a legit stood up self funded organization that is educating in math from, like, the context of math being a liberal art.   Okay. And I'm gonna find a better way to say that, but that's, I think, a better way of saying a math academy.   Okay? Because, like, at least to this audience,   that's all getting very   honed for me. But this all came out of that big like, I am   very, very focused   on that end goal even though that end goal is years in the future.  

Right? Yeah.   Years and years.   Sometimes I show up to this podcast   not   sometimes I show up to a lot of my podcasts not having any effing idea what the hell I'm gonna talk about. Right. Right? These aren't these aren't full time jobs.   You like, even though I don't have a job, I'm certainly not gonna make a job   out of I'm not gonna spend hours prepping   for an agenda   for a bunch of podcasts. Sorry, guys. Like, not to rip the illusion off, but most of the time, we come you know, we'll have a loose idea of some topics to talk about, and we hit it. Podcasters with real lives.   Right.  

And I know you're not gonna do that because you're actually   you're busy, man.   You're just busy. You got you're very when I say you're busy, I don't mean just with work. Clearly, you are busy   with a lot of things. Right?   Like, just so you know, I see it in your head and face. Okay. It's   Yeah. And it's And, like Like, yes. The the read is accurate because And it comes through a genuine, like, I care about you. Like, it comes that's how I'm able to see this. I'm seeing it through, like, my care my caring about you. Like, I appreciate you so much, dude. Like, I will never forget that you would reach that you reach out to me at the end of last year wanting to do this.   And then actually did it, and we've shown up for   now 13 episodes, I'm guessing, with this is not strong? Yep. Showing up is the hardest part, though. Right? Like, that's the I will never forget it. I want you to know that. Like, I'll never forget. It means a lot to me. It means a ton that I got to do this. You know? You and I had these comp got to have these conversations. We got to put them out. We got to get feedback. We had guys like Dan and eight Mithrandir   getting engaged with us. Like, we're really building a world. And all of those things for me   made that long term goal look much, much more like it was gonna happen.  

So every time we do this,   it's like, the you've seen Back to the Future?   Yeah. I know it's such a stupid question, but I had a employee once who   he didn't see it, and that was his, like, fucking thing that he thought made him quirky.   Was he hadn't seen Back to the Future? Yeah. It was, like, not, like, that he could show up and, like, I haven't seen it.   You know, thinking that he was absolutely interesting.   So I'm sorry to the audience for having to ask a human being that question, but it comes from a personal experience.   And I didn't read you to be like that, but, you know.  

I've seen it, and the second one. Like, I wanted just to choke this guy every time, like, the movie always comes up, and he always thinks it was like, man, what's the ins like, that's his opportunity to insert himself   as interesting.   That's what I'm saying. Seen that movie. It's like, dude, shut the fuck up and go watch it because,   you know, Jesus Christ.   Anyhow,   you know, the picture   that he that Marty   looks at and, like, when the world is going badly   Yeah. His, like disappearing off of it. Yeah. His siblings disappear. And his Yeah. And then when things start getting back on track,   you know, boom, boom, they reappear back into the picture. Right? Right.  

And, like, I have this goal,   and it's a bit of an empty picture.   Right? It's it's,   like, in a mathematical sense, I would say it is a it is sparse discrete points.   And then every time we do we every time we do this podcast,   a little a little bit more gets, like, it's gets colored in. I start seeing it more clearly. I start   I start interpolating between the dots, between the So so what was it about? Continuity.  

[00:06:43] Unknown:

Yeah. What what was it what was it about today's episode that colored in the dots for you, though? Well, like, what is yeah. Nothing yet. Nothing yet. What I'm trying to tell you is that I  

[00:06:53] Unknown:

I will never forget   what you have done for me   in the last 12 just the last 12 episodes,   and   the picture I am holding of what my goal is is a much more vivid picture Right.   Than it ever would have been. Yeah. So that and that is the   place of caring about you   from which I am coming from  

[00:07:16] Unknown:

Okay.  

[00:07:17] Unknown:

To   maybe   discuss a little bit about you.   I'm seeing you   up against   it. K? Yeah. Little little unsure.   And then with with regards to this podcast, really, but I'm starting like, I see this aura around you, which is like, fuck, dude.   Like like, no. It ain't just this podcast. But, you you know?  

[00:07:42] Unknown:

Yeah. And now you're completely right.  

[00:07:44] Unknown:

See you in this frame, the more I see you as we're doing this, it's the more it's validating for me. And it's not a great It's more like, I just want you to know I get you. I get it. And I'm like, I am and I got you. Like, when I say I got you, like, I got this. Like, dude, I'll put you on my fucking back   and carry you have however fucking long I have to.   Okay?   Yeah. And it's not to keep this podcast going because we could end this podcast right now. Yeah. You say the fucking word, and I will have no hard feelings whatsoever.   You say the word, I will hit stop,   and you and I will just be friends forever.  

I okay. So I want you to know that it's not I'm not invested   in keeping this going. It's for you, I'm gonna carry it's like, I just wanna carry you through the next level. And mostly, it's because of like, the reason I agreed to do this with you to begin with is because of my view of you. Like, I view you as just kind of huge   high energy guy that contributes a lot.   And, like, the look on your face right now implies, like, that you don't see yourself that way.  

[00:08:46] Unknown:

Or you don't feel like you're doing that right now maybe in the world. I don't know. No. No. Yeah. Definitely the latter. Definitely the latter. Like, I I know I've got a lot of energy and and   the,   it's been a lot of distractions lately. It's probably what it's come down to.  

[00:09:03] Unknown:

Fiat, you know, family, that's a distraction. Anything specific. Yeah. Yeah.   This is like I wanna say, like, you know, I do think this will be an interesting podcast.   And it's not like we're we're not gonna focus on this for forty minutes. We're gonna you know?  

[00:09:20] Unknown:

We will talk about math? We'll talk about math. Yes.  

[00:09:23] Unknown:

I will always find a way. K? We will we will we will find a way. K? Well, we showed up kinda like, you know,   you stalled our our intro conversation. You stalled longer than usual.   It was just like That was the first sell. Yeah. You're just not ready to get on on mic and get you know, it's okay, dude. It's like, I just I want you to know, make no mistake, I fucking got you. Yeah. Yeah. Yeah. Regardless of where we end up here. Okay. K.   Now,   having said that,   there is something I had in my mind that I did wanna discuss a little bit. I wanna spend a little bit time on before we got into anything technical.   Okay. So it's an insight I had this week.  

It's an insight I had about studying math. I mean, I you know, if if nothing else, right, I do you know, I spend three to four hours every day Mhmm. Working on that. And,   so I'm, you know, I'm always kinda introspective about what it why the fuck am I doing this? It's kind of important.  

[00:10:25] Unknown:

Right? You're right. Why would I do this? Do you ever consider, like, the how of you're doing it? It?  

[00:10:30] Unknown:

Do I consider the how if I'm like,   consider the how? That sounds like a Malcolm Gladwell book.  

[00:10:36] Unknown:

I don't know who Malcolm Gladwell is, but I've seen Back to the Future.  

[00:10:40] Unknown:

Yes. Credit to you for seeing having seen Back to the Future and getting the references.   Credit to how. Well,   credit to how. Question to how.   Yeah. Well, before I get in before I don't know. Before I would address that,   I wanna   just give the listeners   and you   a little bit of this insight that I   that I had. And it's not very eloquent because it's not very well formed, but I think it's valuable.   Studying math so you all know why I got into this rabbit hole, at least   this current version that I'm in, which is the most persistent version of the math rabbit hole I've ever been in in my life. Mhmm.   I've studied math pretty,   you know, pretty intensely   before Bitcoin.  



[00:11:30] Unknown:

I had Just a different variety of math.  

[00:11:32] Unknown:

Well,   I had what I did in college. I struggled and Right. And ended up I had then I always had periods where I when I changed careers, when I left, like, being an actuary and became a,   like, a derivative   Mhmm. Portfolio manager or market risk manager, I had this I felt very inadequate   mathematically,   and I felt like I had to level up, and I went pretty deep, like, with, at least for my ability   in,   stochastic calculus, differential equations, the kind   the kinds of things financial engineers   use on standard.   Thing and then so, like, this is long this is I'm talking decades ago. Right. I would be in a meeting, let's say, and my boss and somebody else   would have this discussion and say, we should use, Lebesgue equations to model   to model this And you didn't know a Lebesgue equation. It doesn't matter. It doesn't matter. Right? It's just what   I would sit there and hear that and say, I don't know what the fuck that is. Yeah. And then two year rabbit hole.  

Right. You see what I'm saying? Like and, like, when it wasn't even easy to find math books,   but, like,   let alone be be able to crack open, see the table of contents and see if it eventually gets to LaBecca Coacheus.  

[00:12:52] Unknown:

Okay? Right.  

[00:12:53] Unknown:

And,   that's the kind of thing that would throw me into   a a one to two year rabbit hole. But usually   but usually the way those ended,   I can tell you right now, I don't know what the fuck Lebesgue equations are right now.   Okay. So they like, I petered out of the rabbit hole before   probably accomplishing the main mission. So the rabbit hole I'm in now was validating cryptography,   led me to that understanding cryptography   book, which   which made Galois theory the North Star because that was the thing that just I don't know. That's what I walked away from. Now do I understand Galois theory? A little bit now.   I mean, you go through all these abstract algebra textbooks. It's usually the last chapter.  

So it's, like, months and months and months, and then you get to this thing called Galois theory. And now I'm thinking, you know what? Galois theory is not that critical to understanding cryptography, but it's still my white whale.   It's still, like, my motivator.  

[00:13:52] Unknown:

Why is it not like, what was the   epiphany of making that not critical? Like, you you believed it so before third book I the third abstract algebra  

[00:14:01] Unknown:

book I decided to use just really told me that,   Galois groups   are another name for a finite field, and it turns out that really finite fields are really what but in the understanding cryptography book, they call them Galoisomers.   Okay.   Okay. So it took a it was right. But you like, if I hadn't dove into the rabbit hole and found myself three fucking textbooks later,   I would not have known that. But so now it, like, doesn't matter.   Right? Because my white whale is actually cryptography. And, like, the stuff we talked about last week of, like, really feeling like I can   feeling like,   I'm living up to the aptitude I should have around this.  



[00:14:44] Unknown:

Right? Like, you you feel   you feel comfortable now with the subject of cryptographic math   that you could teach it  

[00:14:53] Unknown:

or develop curriculum for it. I think Is that what you're saying? I think I I at least can become that person.   Mhmm. You see what I mean? Like, I Mhmm. I have the ability to become that person   because   so   when you go through   it's when you go through math, it's such a journey. Right? There are things that you just learn because all you think about is the future,   and you learn a fact that   opens up the future. Right? Mhmm. But then there's a lot of things that   you   learn that you've already known.   But then you see   like, there's a lot of things you know and you have no ability to explain.  

Okay. The difference between a teacher and just a practitioner.   Right? A teacher's   somebody who really goes who goes through the material at   a variety of angles. That's why five different textbooks has now helped me.   Also, with number theory, I've done, you know, three to four textbooks on number theory,   which has allowed me now to, you know, it's like then you find it's like once it something really clicks, you this desire awakens inside of you to want to now explain it. It's like, oh my god. I think I can explain this. Right. And then you want to.  

[00:16:07] Unknown:

Right?  

[00:16:08] Unknown:

So the videos I've done that are on the YouTube side right now or on satellite earth are   definitely things that have clicked for me that I felt, at least, that I've found a unique   way to,   in my when I say unique, it's just the way I understand   it to present it. But   the thing   so the insight, though, back to the insight   That you have to do I talked about my past. I talked about my past to to   say that I have always it it   there are always situations that would kick me into a math rabbit hole. Okay?   The one I'm in now happens to be the most persistent one I've ever been in. There's no end in sight.   There really is no end. Like, in my old life,   a fight with my wife would be enough to get me out of a rabbit hole.  

Right? Right. Like, you know, I might just ignore a problem in my marriage for a year,   and then so one big fight about it would be enough to be like, oh, shit. I can't be in this rabbit hole anymore. Yeah. Yeah. Yeah. Can't do it. You know? There's no it's either the that   or   my marriage.   Right. You know, I choose.   Right? I totally understand that. Understand that. Right? And Absolutely.   So in the past, that's typically how it would go. Now   what makes this persistent?   For one is my own interest in it, obviously. So, like, it's not like I'm not having problems with you know? I think,   discovering Bitcoin   is a,   horrific,   horrific   vector of problems in a relationship.  

Okay?   Yeah. Discovering Bitcoin is like detonating a bomb in a relationship,   especially if it's a long like, if you're older and the relationship   has much more history without Bitcoin.  

[00:17:56] Unknown:

Well, that's because the the it's a fundamental shift in your understanding of  

[00:18:02] Unknown:

reality. But it brings up issues of value of Right. Yeah. Standards,   ideals, and what you might be might you think you're entitled to. And, like, it brings up all of the shit that you could've kinda, like, skated over forever.  

[00:18:17] Unknown:

Right. Or just outsourced to your  

[00:18:19] Unknown:

insert, you know, streaming media news outlet. And, like, I worked this job, and I made a lot of money, and it made I made enough money that none of that shit mattered. Right. Right. Yeah. Yeah. If I didn't care deeply about it. And then all of a sudden, I started caring deeply about these value things.   Yeah. Right? And said, no. I'm not entitled to x y z. I'm not entitled to that. And guess what? You aren't either.   Yeah.   Grenade in relationship. Right?  

[00:18:46] Unknown:

It's a I think it's a it's an inflation of quality of life.  

[00:18:50] Unknown:

In some way. Yeah. Well,   it's just it's like, you know, a lot of things you can just sweep under the rug, you just no longer can because   your that your bell has been rung. Right? And so, you know, you're in a relationship. So what happens to you in some ways happens to the whole relationship? I don't know. Anyone Man, can you imagine someone who can, like, have a   a real epiphany about Bitcoin and about themselves   and about their own freedom and all that and have it not affect their relationship? What kind of psychotic relationship would that be?  

[00:19:23] Unknown:

I can't I can't imagine that because, again, like, you're   yeah. You're you're you're the   like, the   base level of your understanding   changes.   Because I always think I've had   the the the values,   of a two degree, like, we'll call them chivalrous values because I think that's, like Noble values. I would call them values and things like that, but with   largely misguided, right? Like that's what got me into the military. It was like, oh, freedom and democracy.   This is great. And then you get there and it's giant fraud, waste and abuse and murder.  

[00:19:59] Unknown:

So,  

[00:20:01] Unknown:

so it's like it's it's like mis misdirected, misguided. And then   the   imperativeness   of   like, once you learn it, like, the evangelism that takes over and then the the the rabbit hole that you're in, it's like it's an it's like a moral imperative,   especially if you have kids.  

[00:20:23] Unknown:

Yeah. So now your standards and ideals as so, like, I I went   so my oldest child,   at the time I discovered Bitcoin, my oldest child was 17 years old.   So I went seventeen Seventeen. Yeah. Went seventeen years   under a certain   under a certain set of standards and ideals. Under a fiat standard? No. Not I wouldn't say they were antithetical   in any way Right.   To what they are now. It's just that there are things I didn't know was possible.   You understand? It's a lens. It's a lens that you would have to be it was a limited lens   because I didn't know certain things were possible. I didn't know it was possible   for, Lexa, I was always raising a mathematician   Mhmm. Under a liberal arts context, and I was always giving my middle finger to anybody who tried to vocationalize   math.  

Okay? People already you know, people have known this. That's something that's not a problem because people Yeah. People already know not to ask What are you gonna do? Oh, what are you gonna do with that? You know, like, people already know. Like, I've been beating people up   for, you know,   the last nineteen years overshoot. But   I didn't   re like, I just kind of trusted   that something would work out. I didn't really know there was a way to cause   that outcome.   You see what I mean? Like, I had no idea. I just thought, like, you know what? I'm gonna make enough money that if it all fails,   I will provide a cushion somehow. And then, you know, it's like that got completely debunked. I'm like, no, that's never gonna happen,   obviously,   because that money is disintegrating.  

Yeah. And,   right. So, you know, it's like two you know, there's two sides of the coin. One side is, oh, well, that plan is dead.   Right?   There's no fucking way. You can't make enough money to   support somebody who Not anymore. Who doesn't have a clear idea of how to, like, add value to them. Right? There's just no fucking way to do that. Okay. You're talking about patronage.   Well, I'm talk I mean, I'm saying, like, I can't I that's a ridiculous standard or ideal that   my child could just ignore,   you know, could could ignore vocation entirely.   Mhmm. Right?  

But, also,   the vocations   didn't exist.   None of these things so that's why I I was, like, shunning all any vocation, because, like,   you know, those were all   bad ideas for me. And then I real you know, I didn't know I could create the vocation myself.   See, I didn't know I could build this. You know you could just do things?   Yeah. I you know what I mean? I had no idea.   Yeah. So, a, I didn't know I didn't realize my money was no good, and then, b, I didn't realize I could just   pivot.   Yeah. You know, like, when my dad was my age, he wanted to do this. He couldn't   he felt he couldn't. He wanted to pivot.  



[00:23:18] Unknown:

You get to a point where   you're like, oh, I can step off this wheel that I've been running on.  

[00:23:24] Unknown:

Well, yeah. The thing is, like, what I'm really committed to   actually is much more has I have much more tools, like,   tools. I don't like that term, but I have more ability than I had ever realized   in fulfilling this. Yep. You see what I mean? So I I much I didn't realize.   And I don't know. I mean, I think a lot of people get into Bitcoin and are like, oh, good. I'm can retire now. But it's, you know, for me, dude, this is like coloring in the picture.  

[00:23:52] Unknown:

Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah.  

[00:23:57] Unknown:

Yeah. Yeah   And,   you know, because I was definitely not interested in them. I always felt like if they had to go into some vocation   that currently   had existed with a math degree, I would all be for naught.   Right. But she can't sit on her ass and do nothing. Right?   So it's gonna be like the uncertainty with the uncertainty would be would be filled in with urgent learning until we figured out what we could do, which is now   now   we can do that knowing that, like, she knows   that she's gonna be okay.  

[00:24:38] Unknown:

But, yeah, there's an avenue.   All the hard work and what a relief to know that your hard work and dedication to something   is is is is can pay off.  

[00:24:51] Unknown:

Yeah.  

[00:24:52] Unknown:

So   that is all  

[00:24:55] Unknown:

why did I even go into all that? Right? Because I haven't even gotten through the insight yet.   This is classic fundamentals podcasting right here.   That's what we show up for. Classic. So, the reason I went into that was to give you the background   of   because the insight isn't gonna seem that interesting unless you understand that,   like,   I've been living this life   Mhmm. For   decades.   It's not that different, but it isn't the most subtle things make the biggest difference. You see that? Yep. You see what I mean? Like, the most subtle things. So  

[00:25:31] Unknown:

Especially over the longer time frame. No. So  

[00:25:33] Unknown:

I I don't know why I started thinking about this and what it has to do. It's not it has to do with math, but, like,   this this thing about who the fuck like, what kind of person are you? Right? Like, you know, are you, like, you know, noble values and what kind of person are you?   I started thinking a lot about,   what good, you know, what good is   having a lot of money. That's one it's one thing to have a lot of money, but I judge a person, and I think most wealthy people judge others on what   what they are,   what they aspire to spend their money on.  

Okay. Yeah. I'm not saying I don't I don't judge people like that per se, but that's because they solve the problem of having the money   in the first place already. So they yeah. So, like, you're either you know, you're worthy in wealthy circles by what you aspire to spend your money on, and that's why most of those people have great stories about what they wanna do with their money. And, you know, like, in corporate America, there's   people are very good at articulating their ambition   because it's really important   to be   like, if you're not aspiring to, like, own a jet or do if you're not aspiring for something that's completely outside of your reach, you're not that useful.  



[00:26:41] Unknown:

Yeah.  

[00:26:42] Unknown:

Right. Interesting. So they want you   to aspire   for something, but it's so it's something that they could provide by printing money. Right? Well and and that like, my mind as you're as you're talking about this, like, aspiring the insight yet. This is still something.  

[00:26:57] Unknown:

But, like, the the aspirations of, like, what to spend the money on,   it's interesting because, you know, there I I do have the daydreams occasionally of, like, five to ten years down the road. It's like, what do you do what do you do with this newfound wealth sort of thing? And it's not a fucking jet. That's for sure. Like, I don't want a jet.   I want long lasting positive impact on the community and the world if that's possible.   And   it's like now now now it is somewhat like, there is   a way forward with that.  

[00:27:27] Unknown:

I think yeah. And I I think it's nihilistic   to not have to to not   have anything,   to, you know, to not have that ambition or to not have things.   What are we doing this for? Right? So I do think it's important. We just don't you just don't wanna be doing it for what they're doing it for.   Right. Right? And so   I would encourage people. And so, again, this is I haven't yet   I'm I've delivered half the insight, which is more like I'm standing on the other side of saying, what are you spending your money on? That's important. That's, like, an important thing to consider. And then the other one is, what are you spending your time on? What or what do you what do you aspire   to spend your time on? And I like, I guess I've always looked at,   like, my stack of books   as my retirement instead of my my four one k. I looked at my stack of books as, like, if I ever get   imprisoned   or gulagued  

[00:28:21] Unknown:

Yeah.  

[00:28:22] Unknown:

I can still go into   the last stage of my life   with my books   and Right. Have something to do.   Yeah. And so it's the question of like, it's the same question of, like, what would you do if you had your own time? And I've   I am one day away from the one year anniversary   of being Of having your time. Of being granted the gift of my own time.   And it's pretty wild. A really wild ride.  

[00:28:50] Unknown:

Is this insight do you think do you feel like this insight that you're you've half shared, is this, like, a culmination of having that much time to to figure it out? I think so in some ways. It's like, you know,  

[00:29:04] Unknown:

for the first,   like, six months,   I was, like,   I was really driven to do things I feel like I never had the opportunity to do and never would again.   Okay. Yeah. And then at some point, I realized,   no, this is how it is,   Like, forever.   It could like, if I can find a way,   right, if I can find a way to reinvent   a career,   right,   and reinvent my earning ability  

[00:29:34] Unknown:

Mhmm.  

[00:29:34] Unknown:

Then it's always like this. And there's I never have to live like I'm never gonna have this time again.   And then the question is, so so   now that I'm a year in, I'm still   what am I I'm still studying I'm still studying math with the same intensity.   Yeah. That tells me   that   I'm probably going   to fulfill,   like, my goals at the end of my life, which would be to be study.   Yeah.   And   so it's more you know, you   you don't just create time   for no reason. You create time because you have an ambition of  

[00:30:13] Unknown:

using that time to an end.  

[00:30:16] Unknown:

Yeah. Same with money. Yeah.   Same   with money, same with time. I think it's useful to ask what are you aspiring   to do.   And, you know, look, when you work a job, it's hard, really hard to do. And it's really hard for,   it's a hard exercise for young people   because you feel like you have all the time in the world anyway.   Even though if you're working a job and you're like, well, you know, I can't spend enough time with my kids, so, you know, I don't have enough time to do this and this and that, but you don't have that   end of your life type of like   Existential crisis?  

You know, like my two grandfathers,   one of them worked he was an accountant and just worked on his friend's taxes till the day he died. And my other one my other grandfather was,   he was doing every class in a community college  

[00:31:11] Unknown:

until Just for fun.  

[00:31:13] Unknown:

Yeah. And that that's how like, he was like a legend because he was,   you know, everybody knew who he was. And Yeah.   I think up until he started losing it, like, at 90. He died at 99. He died at 99, so he didn't go to, like, the end of his life   studying.  

[00:31:29] Unknown:

He he did. He was close enough.  

[00:31:33] Unknown:

Yeah. If I'm lucky Those can grow it to the end of life. If I'm lucky, I'll go at   the time when it's when it's up. Right? Right.   But I do have this aspiration to, and I think that's something you have to build your whole life. You have to just build it,   know, because not not everybody's gonna be able to do something like that.   So, like, between this math academy,   which is like an invention  

[00:31:59] Unknown:

Mhmm.  

[00:32:00] Unknown:

In a certain way, it's an invention.   You know, that's where that's   so I need to raise the money. So that's where I I need to work   and figure out how to earn   Right. And add value.   Right? So it's gonna be a trade where I, you know, add value, earn money,   fund the building of this and   my time and effort, and then also my legacy would be that this would be what my children run.   Yeah.   Hopefully, take it further   and maybe actually make a difference with it.  

[00:32:36] Unknown:

Well, it's interesting. I can't remember where   I heard it, but it was like   the this idea of,   families in an area or or in a community that have long standing like, they're they're the family that runs the math academy.   Right?   And and, like, that's the   it it's like a,   the the time, energy, and focus of of the family unit as a whole   are is sort of, like, dedicated to that.   Right? And it's like, in my area, it's like, there's, like, one family does all, like, the the waste treatment for your, like, septic units and stuff. It's like that's what the it's a family branded, you know, combs, waste, and septic. We got one of those.   So it's like that   having that sort of,   Combs.  

Generational.  

[00:33:25] Unknown:

Yeah. Like P. Diddy.  

[00:33:29] Unknown:

Wrong skin tone for this family, but maybe there's some distant relation. You never know with Genghis Khan. I think he meant different skin tone.  

[00:33:36] Unknown:

Yeah.   Yeah.  

[00:33:42] Unknown:

Who knows though? You know? I mean Genghis Khan was very prolific. So who knows? Indeed.  

[00:33:48] Unknown:

So the Combs family does all the waste management.   Yep.   Yeah. Yep. It's funny. They're not allowed to have they're not allowed to have, like, thick Italian names anymore.   Oh. They have selfies.  

[00:34:01] Unknown:

Thick Italian like, the thick Italian names aren't are very prolific in this in this   geographic area. Mhmm. At least not that I've encountered. So Not yet.   Not yet. That's true. One day. One day when I become important enough, I suppose.   So what was it like if you had to put it into a a sentence, what was the insight?  

[00:34:23] Unknown:

So the okay. Well, the so then the, you know,   the insight was,   your ambition matters.   Your your forward looking ambition as to what you want to spend your time and what you wanna spend your money on does matter. I guess I used to think it didn't matter. I wanted so when I worked,   I used to say, oh, I don't have I don't wanna I don't wanna jet. I don't want you know, I wanna be self sufficient and I used to think that and I think I was right, but I used to think that that idea hurt me   in my professional life. That was limiting. And I think, actually, the thing that drove   me over the edge, the thing that drove them over the edge to actually fire me,   I believe was revealing to them that I had no interest in even advancing   a level. You were no longer a pawn in their game. I basically because I I told them I had no interest in my boss' job. And I actually felt bad. I felt bad for him that he so revealed himself to be so naive and stupid   to think, not only to think that I did, but to actually strategize around it. And   I I   told his boss that I told his boss I said, like, I feel bad for him. Like, he's really kind of naive and stupid   that he thinks that. I don't I have no interest in it. Yeah. And that was the beginning of that was then the beginning of, you   know,   beginning of the end. The beginning of the beginning.  

Yeah. But And that's like,  

[00:35:51] Unknown:

it's a machine. Right? Like, you were in a machine,   and the old pieces age out, and then they need to be replaced with a different cog.   And so the machine   self interested   would, of course, reject the cog that's not gonna fit in in the old one's place.  

[00:36:08] Unknown:

Yeah. Well, this cog,   the cog that is me Yeah.   I was generating myself like, myself, I was generating over a hundred million dollars a year for the company. Yeah. Yeah. So, like and so, like, I I it's almost like I needed to prove to myself that enough that, like, that didn't matter   to them. I had to prove to myself that only the forward looking ambition is what mattered,   and it was worth more than literally hundreds of millions of dollars.   And to to be so that from so that I would have no illusion of going back.  

[00:36:45] Unknown:

Right.  

[00:36:45] Unknown:

You know, I think it's very easy to talk yourself into going back and saying, well, that company happened to be stupid, but they not they aren't all stupid.   You know what I mean? Because that that paycheck is   not nothing. Right? It's definitely   so I needed to basically be told under under no uncertain terms, I don't care how much money you're bringing in. I don't fucking care how much it is. Right?   And the irony of it was, like, my whole ethos and the way I have made all this money was by undoing bad math.  

[00:37:18] Unknown:

Right.  

[00:37:19] Unknown:

So and saying, you know what? All your illusions about all this math is bullshit.   I'm actually gonna, like, unwind it and not do any math here and just do what a stupid person would do, and I literally and the hundred million was legit. Like, we paid a dividend on it. Like, it was, like   Yeah. It's fucking for real.   You know? And, like, it just destroyed these people. Like, like, what? Like, it's not complicated. It's not mathematical. I don't need to hire a fucking PhD to understand it. It's like, no. It's like, you know what? Well, then we don't need you. I said, well, that's true. I gave this I gave this hundred million of you as a gift. Mhmm. Okay. But,   like, if you want it to be 300,000,000,   you may want to let me focus on it. Right. Instead of all this other bullshit.  

And by the way, I'm not interested in   I'm only like, I only want to focus on this. I don't even care about promotions or anything. Like, just focus on this. I wasn't even asking for   money. Right? Yeah. I was ask I was demanding what I wanted to spend my time doing, and they wouldn't have it.   And so they made it clear under no uncertain terms that it was not.   And by the way, I know for a fact now they're not making a hundred million dollars. They're not they're not even doing it. Yikes.   So, having that conviction   inside of yourself   on what you know what I mean? What your ambitions are. You think like, I I guess, again, I I had a perverted idea that, like, almost, like, being ambitious was wrong. Like, being ambitious was stupid,   lame, and for gay people.  

Like like it That's the target of that ambition, I think. That's how you got in trouble. Like, that's how you ended up in positions you shouldn't be in,   and   I'm thinking now   that's not the case. It's actually you really want   only losers lack it. Like, you know, you have no ambition font. You're a nihilistic loser.   You have to have ambition. You wanna know but you wanna be very close   to, like, yourself. You wanna you wanna have a, like, you know, you want it to be to really accurately reflect   you who you are.  

[00:39:19] Unknown:

Well, and and perhaps all the energy you have.   It's not so much the the lack or presence of ambition, but it's, like,   the value of ambition   and the the lens that   Bitcoin puts, the filter that Bitcoin puts over the world for you allows you to more accurately discern what that ambition   could or should be   for yourself.  

[00:39:42] Unknown:

Yes. And that's what caught that's what detonates grenades in relationships,  

[00:39:46] Unknown:

by the way. Because Yeah. Because if they're not seeing the same thing.  

[00:39:49] Unknown:

Well, you know, your partner saw you as somebody with a certain ambition or with a certain  

[00:39:55] Unknown:

way of going out. Their life. They enlisted e five in the navy.   At some point,   she saw something, and and I think she was right, and, thank god for it. So  

[00:40:07] Unknown:

So it's all very you know, like, it's all a very interesting journey, and, you know, the ups   are great, and the downs are   legit. Like, there are legit problems to deal with. Right? Yeah. Especially in   relationships. And so my job was like, no. We're not having   your little epiphany about ambition is not working for us, but,   credit to my wife. Like, we're still you know, we're we're still trying to figure that shit out.   Right?   Yeah. You know, like,   any my parents   can barely deal with talking to me.   Ah. Right? Because, like, I you know, well, they're they're not even boomers. They're older than boomers. Right.   And, like, you know, my insistence,   them accepting that the world they live in is not the world they grew up in.  

It's a a lot for them to deal with.   Yeah. Right? It's   so, you know, I've alienated a lot of people.  

[00:41:06] Unknown:

Yeah.   And that's an interesting topic too because the   it's like the the alienation.   I think as long as it's on their end, if they choose it,   you can't you can't do anything. Right? Like, they still want to  

[00:41:24] Unknown:

have a relationship with me. So there's a but, like,   I didn't know that I can literally demand capitulation   if I was really, you know,   super grounded.  

[00:41:36] Unknown:

Yeah. Yeah. Yeah. You know?   Demand capitulation. That's a good term.  

[00:41:41] Unknown:

Yeah.  

[00:41:42] Unknown:

Yeah. That yeah.   Water on rock. Like, that's   to me, that's, like, the,   I don't know.   That reminds me of  

[00:41:52] Unknown:

what's that? It's called also having a frame. Like, look, I'm not gonna accept certain   ideas. I'm not gonna accept   certain you know what I mean? I'm just not gonna accept certain things   that,   you know,  

[00:42:05] Unknown:

that maybe I'm gonna have to accept that. Understand.  

[00:42:09] Unknown:

Yeah. So, like, that's you know,   I don't like, the whole Bitcoin fixes this thing, like, it's not true with relationships.   If it fixes them, then it definitely breaks them first.   And it's definitely, if Bitcoin breaks things before they fix them and then the things that are worth fixing get fixed.   And the things that aren't worth fixing just go away   broken   forever.  

[00:42:36] Unknown:

Yeah. And that's a that's a sobering thought.   That's a lot. And if you're not, like I think it's a lot Especially if you hold on to the things that are broken. Like, if if there's a a strong   desire to maintain a frame   that that is broken.  

[00:42:51] Unknown:

Well, yeah. I think it's a very difficult   concept for   the average age   group   that   participates in Bitcoin.   And I think that's what's I find it so interesting, like, being a Gen X, which is, like, I'm in the minority. There aren't many of us here. But, like,   I accept the consensus   is   younger.   Right. Right? The consensus is much younger   and much less,   worldly,   although   more than their age suggests, but certainly less than me.   Yeah. Right?   So, like, my role here   is not to,   try to dominate as though I'm a consensus determiner. It's more of, like, okay. How can I help   the dominant group?  

Right. And so they're using my wisdom   and experience.  

[00:43:48] Unknown:

Well, and you Right. Made for a claim before that anybody that is alongside you levels up.  

[00:43:53] Unknown:

I believe that to be and that that's always been the case. And I think I would say that was my biggest strength in Fiat as well.   Okay. You know, the management team that   left   that I you know, the management team were all people that trained under me.   So it's like,   that is a quality that I've always had. Yeah. You know, people will level up and because you like you know?   Let's assuming I care about you. Even the guy that didn't see Back to the Future   He leveled up. He leveled up and he's on yeah. He leveled up big time.   Not enough to go watch the movie or anything.  



[00:44:33] Unknown:

Yeah.   But level up, how what's the what does a level up look like? How do you how do you proceed that? He turned into he was,  

[00:44:41] Unknown:

I mean, this guy was just   a destined to be the 40 year old virgin   and ended up getting married. He married another person who worked for me. They both leveled up into marrying each other.  

[00:44:55] Unknown:

Good. And,  

[00:44:58] Unknown:

I don't know if they'll find this insulting if they ever hear this. I doubt they will. But,   you know, I mean, I I I cared for them and all that, and I   spent a lot of time   on seeing to it that they leveled up.   I didn't know they were gonna level up into each other   Right. And start a family and all this stuff. You know? I'm pretty sure she didn't see back to the future either. That's probably a requirement. Common connection that bound them. I'm sure.   Right. But, like, yeah, I mean, these guy over here always looks at me some way when I say I haven't seen back to the future. That wasn't gonna be possible, and I'm not taking sole credit for it. But, I mean, I was definitely you know? Yeah. You're involved. You're in proximity.   You know, there's enough success stories,   people who,   I'd say, worked under me. You know? I mean, for   not to get into me or anything like that, but I mean, it's like even my one of my what was considered my biggest weakness was I gave too much,   like, I gave too much,   like, authority   and responsibility   to the people in my like, who work for me.  

Was it who said that was your weakness? Everybody who like, all of my management was like, you gotta be the guy.   You know? You gotta be the guy like that. And, you know, in some ways, they were like, they were I think they were right in their game.  

[00:46:16] Unknown:

Right? Yeah. Because I see that.  

[00:46:19] Unknown:

But if they knew I didn't give a shit,   like, do you be you have what you guys don't understand is I don't care   about   being the guy. Yeah. I don't care about that. I care about making everything better.   The way I make everything better is by giving the junior guys airtime and developing them and giving them a chance and all that, you know, giving them my stage.  

[00:46:42] Unknown:

Well, it's like there was a saying it's like,   in the military, it's like you give give somebody just enough rope to hang themselves.   And it's like you give them the leeway to go do what they need to do,   but,  

[00:46:54] Unknown:

you know, they're Yeah. I give them their own everybody else too, though. In corporate America, that's the thing. Like, I'll also use these people as, like, my pit bulls on everybody else.   Mhmm. And then that sort of,   I have to give them   the stage   at that point because they're you know,   we've gone a field a little bit on the math podcast   here, but, you know,   I think, like, I I you know, maybe this is just the episode where we deal with, like, not wanting to fucking do it.  

[00:47:24] Unknown:

Which is part of motivation. Right? Like, if there was nothing that was deterring us from it, we why would you need motivation?  

[00:47:32] Unknown:

Well, yes. It's motivation isn't just like, why do I wanna study this particular one thing? And, oh, and I guess the thing I missed on the insight was that I feel like cryptography is a big enough it seems to become a big enough thing for me to persist this rabbit hole. So I was gonna say that I think you do need   a North Star, and I think, like, we're lucky to have cryptography because I think that could be a good one for everybody   if you care about it. And I want to get people to I want people to care about   the mathematical cryptography.  

Right. You know, and whether you never use it, whether you ever use it or not,   most people, like, you know, you are going to go, you are going to do your entire career and never think about Fermat's love here. Right? Yes. Correct. However,   if you're somebody who goes through all that, you're just so much more capable and you're more confident and you're much less likely to get rooked   by   a grifter.   You're much less likely to be impressed by somebody who says, I feel like I'm   experiencing the Austrian economics of math.   Yeah.  

And that's like   I told you when I changed careers, I became a financial engineer. I became obsessed with, like,   stochastic calculus and differential equations, and the reason was that,   I would get bullied by traders   intellectually, and   I was like, That's bullshit. These people are stupid. I'm not letting them I'm not going to let them bully me. They would and I'm like, I'm going to be able to read any paper   and be able to say, no.   You may have cited this paper, but I'm citing this paper, which debunks your paper,   and I needed to learn the math. I needed to really learn the math. Academic sparring?  

Would you consider that to be academic sparring? Yeah. But it's more of a it's like   in trading   when you work for investment banks,   it's big time larping.   You're you're   you're a pretend academic. You know? Yeah.   But,   but the but but for me, it was about not being not being able to be bullied.   And Right. The core, that's just what I want people to   I want people to feel that. I want people to not be okay with being bullied by stupid by stupider people.   And like the, you know, the couple of hundred people that listen to this,   I want like, that's what I want them to hear is, like, you guys are all better than being bullied by losers   who don't really know what the fuck they're talking about.  

And all it takes is a little bit of work every day or every other day or just staying in the game and not getting demoralized.   And, you know, you could be someone who stands on your two feet and says to,   somebody, no, that's, like, stupid.   Yeah. Just to somebody who, like, you know, wants to impress you with their little   math insights.   You can kick the tires on these people.  

[00:50:29] Unknown:

Or you can come up with an entirely new idea.  

[00:50:33] Unknown:

Yeah.   Yeah. Or just you know, I mean   so that that, you know, that's the motivation   I'm looking for.   And I want you to know that, dude, we don't have to it's you know, you don't have to come in every week and   deliver a math sermon.  

[00:50:54] Unknown:

Yeah.   Right? It's Right. You know, the  

[00:50:58] Unknown:

I want you know, whatever it is you're going through,   I want you to know there's no pressure here.   So if you're if part of what's weighing you down is feeling like you're letting this podcast down or any ideas like that, get rid of part of it. Yeah. I I get it. I get it. Like, I know how that feels. I understand completely. You know?   So this is the,   you know, I mean, if you want, if you want, do anything mathematical, we got   we got a few minutes.  

[00:51:27] Unknown:

I mean, did you have anything math?   This is the thing. I haven't looked at it math in a long time.   In a long time being, probably a lot less time than most people, though.  

[00:51:39] Unknown:

I I I guess yeah. I've become I in the last week,   I've been obsessed with,   permutation groups.   Permutation groups. Yeah. So, you know, we know what groups are, right? Groups are,   we know they satisfy the four axioms and maybe five. Right. Right?   So permutation,   they're called symmetric groups.   Whereas, like so imagine a group being   the number one the numbers one, two, and three.   The only difference is the order,   right?   So you have a group one, two, three, you have a one, three, two, a two, one, three, a two, three, one, a three, one, a three, one, two and a three, two, one.   So you have six elements in the group   and the operation of this group is called   composition,   meaning   god, I'm gonna have to do a video now. You really wrote me in the last minute. I'm not Keep going, dude. No. No. Keep going. Keep with the words. Is called the operation is called composition, meaning,   the permute the actual permutation is called composition is called composition. Boy, I'm not gonna be able to explain this. I'm gonna try.  

Yeah. So if I have one   one,   element that goes one that maps one two three to one two three, of which, by the way, that's the identity element.   Okay.   Why is it the identity element? Because if I apply one if I map one, two and three to one so one goes to one, two goes to two, three goes to three. Mhmm. Because it never changes.   So   applying that   applying   that   map   keeps so if I had the if I had the element   three two one   Mhmm. And I applied this map of one goes to one, two goes to two, three goes to three to it, I end up with 321.   Right?  

I still I end up with the same order.   K. That's why that that's what so there's an identity element.   Okay? Right?   And,   that's what comp so what composition is is this operation that applies this mapping.  

[00:53:59] Unknown:

Okay. So, like, if I did I guess, how are you selecting the identity element?   It's  

[00:54:05] Unknown:

the same way I would ever do it in any group, which is the one if I take any element   and multiply the identity element, I get that element.   It leaves the element unchanged   when the operation is applied.   Okay.   So like in   the integers with addition, I know the identity element is zero because   any integer plus zero is itself. That's zero. Right.   And in multiplication,   I know the identity element is one because   any of those   elements times one is itself.   Mhmm. So in a in a symmetric group,   any   of the any of any permutation   that   gets composed with   one two one going to one, two going to two, three going to three is just going to be itself. I know this When you do identity, when you explain things around the identity, it always sounds very trivial.  



[00:55:00] Unknown:

Right. Except  

[00:55:03] Unknown:

except when you turn it around and say, Well,   why does identity matter? Identity matters because of the next because   of the next property, which is the inverse.   Identity matters   because knowing what the inverse is   is really important.   You can't do a signature,   as we know, without an inverse. You can't   right?   The inverse is dividing.   Yeah.   And so you need to know the identity   to know the inverse,   because the inverse Okay. Is what you operate on to get the identity.  

[00:55:42] Unknown:

The inverse. Yes. Yes. Yes. Okay. Yep.   Right.  

[00:55:47] Unknown:

Yep. So, again, in in the, finite field modulo five. Right?   Mhmm.   Of integers, finite field of integers modulo five,   I know that the identity   is one,   correct? Because any number   times one is itself, right? Right.   So then what is the inverse of two   in that field? It's the thing I multiply it by to get one,   which is  

[00:56:21] Unknown:

four.  

[00:56:22] Unknown:

Well, two times four modulo five  

[00:56:25] Unknown:

gets three. Three. I'm sorry. Two times three is mod two times three is six mod five is one. That's right. So three,  

[00:56:32] Unknown:

you we know so, like,   how do you think of the inverse in a finite field modulo five? It's it's I know because I know what the identity is. If I didn't know what the identity was  

[00:56:43] Unknown:

I wouldn't be able to do it. Identity with the inverse. I wouldn't be able to do it. Right. Exactly. And so  

[00:56:48] Unknown:

why does the inverse matter? It's because you have equations   like,   you   know, 2x plus one equals zero.   How do you get the two off of the x? You divide by two. Well, you don't really divide by two. You multiply by the inverse of two. Right.   Right? Which would be in traditional   in the reals or the rationals, it'd be one half. But in this finite field, it happens to be the number three.   So this all goes back to,   you know I can't, like, repeat it enough. Right? You want the like, those fundamentals   of group theory   Keep coming up over and over. Yeah. They keep coming up, and they keep, like like   So what are it's the same story over and over. Permutation groups used for then?  

That's   they're used in Galois theory   as it happens.   Okay. Like, big time for, like so when you wanna do a field extension or so what what permutation groups are so cool, I mean, it's it's so the one, two,   three, those six elements   is what's called the symmetric group of order three.   Okay. And it has six elements, actually three factorials   and the number of elements, three times two.   Then there's an order four. The what I mean,   the short answer Or would have 16?   Actually, it would have,   Oh. No. 24.   Four factorial.   Oh, yeah. Factorial is different. Okay. Yeah. So four times three times two.  

The reese so it's, like, literally, like, the key to Galois theory and the get the the big   of Galois theory to, if you don't feel like spending ten years in a rabbit hole,   it's that fifth degree polynomials ensemble.   This is what Galois figured out, but he had to basically reorganize   all of abstract, all of, like, what people knew about group strings and fields. He had to reorganize it   to be able to,   be able to definitively   say that fifth what's called a quintic is unsolvable.  

[00:58:58] Unknown:

Fifth degree polynomial.  

[00:59:00] Unknown:

In other words, like, yeah. So, like, we know we can solve a quadratic. We have the quadratic equation. So   to,   solve something like,   x squared minus two equals zero or three x squared plus five x plus seven.   We know how to solve for x. We have the quadratic equation. We know   how to solve When we say solve for x, what's the x that makes the whole thing zero?   Okay. So we all we we know those we know that a general quadratic is solvable. We know certain we know specific ones are solvable, like, okay, x squared minus one, x is either plus or minus one.   Mhmm. X squared plus one, we go in the complex fields and say we can extend it to complex fields and say it's plus or minus I   for x squared plus one.  

But we know a general quadratic is solvable.   We just happen to know that. I'm sure there are people I'm sure April Mithrandir can tell us exactly why that's the case,   why we know that. We also know that for cubics and for cortex.   This is like we're talking thousands of years of proof of work.   Okay.   Okay. That's behind this. And then one of, like, those open questions was what about   Quintech? I can   x to the fifth minus one equals zero. I can solve that. That's the fifth root of   one. One clearly solves that. So, like, there   are quintics that are solvable, but   in general, it's not. Like, you can't say that you can't say it generally.  

In other words, generally, either in in other words, they do there   exists quintics that are unsolvable.   He used the symmetric groups and this property of isomorphisms.   Remember   how I said,   if the reason why it matters to identify something as a group is because we could make   equivalences between things that don't look like each other?  

[01:00:57] Unknown:

Yeah.   There's a dog that just ran in. I'm sorry.  

[01:01:02] Unknown:

That's okay. Dude, my dog ran in a hundred times.   There you go.   Yeah. He really likes being picked up like that.   So you remember when I said like, Oh, why does it matter if something's a group? Because two things that don't look like each other can be considered actually equal.  

[01:01:22] Unknown:

Congruent, you mean?  

[01:01:24] Unknown:

Well, equivalent. It's technically an equivalence relationship. Okay. What's an equivalence relationship? An equivalence relationship is a relationship that has the three properties, reflexivity, symmetric and transmittance.   Okay. Conruence is an equivalence relation and that gets proved. You can prove that. You prove it in   groups, rings, and field. You can prove it in integers.   You prove it everywhere.   Congruence   is   an example of an equivalence relation.   Okay. Because it has those three properties. It has those three properties. Right? Yeah.   And isomorphism,   which means when you say two groups are essentially equal to each other, they just   they don't look like they're equal, but they are. Okay? And,   that   Galois used this fact of a symmetric group with order five being   Okay.  

Equal   being   and to prove that this Quintic had no solution. And that's like   again, dude, it's fucking multi, multi, multi year rabbit hole to really   be able to back that up. I'm probably set it all wrong, but I'm pretty sure, like, this is where I am is that that's my statement   as to why,   really why do those symmetric groups really matter.  

[01:02:40] Unknown:

It's because it's proof of the the quintic.  

[01:02:43] Unknown:

Well, that's one of the main that's, like, one of the key ways it was used.   Okay. There's a lot of other really cool shit about it. Mainly, it's it's in how you fix. It's just like when you want to extend a field   and add like one element to it.   So like   take the equation x squared minus two equals zero.   Okay?   Okay. If you are using real numbers, you would say the square root of two is a solution to that.   Right. But if you were in rational numbers, you would say there is no solution.   If you wanted to use a domain that   minimized how big it could be, you would say, I just want to extend the rationals to this one element. I'm going to take all my rationals,   but I'm going to say all the rationals plus the square root of two is going to be my domain.  

Instead of saying all the reals because now you're not using a massive   The way, though, presumably you would save space   is   I have a field that's the rationals, and the reason why that works out is because you can actually do just a permutation   on   the rationals.   You can basically fix   the things you want to fix and then add the things you want to add.   Add the elements you want to add to it. So you know how, like Does it still allow you to maintain certain properties then?   Yes. Because it's like you know how a number is a product of primes, but the only difference is the order?   Right. Same idea.  

And   same idea with a group. With these groups, it's like the consists of these elements. All that changes is the order, so it's the same   elements,   just in different order.   That's what symmetric group is. Same elements, different order.   Yes.   I'm gonna I'll look for some examples I can attach to the show notes.   But you know what?  

[01:04:39] Unknown:

We got some math in here. We did. That was good math too.   I'm still, like You made it a real nightmare. I still ponder the application. But if you if you made it this long, thank you for for sticking with us. You guys are the best. Did anyone I mean,  

[01:04:54] Unknown:

make yourselves known. If you guys are, like, listening to, make yourselves known to me. You guys have no idea. Like, you guys will be, like, my g's for life. Make yourself known if you're still   Listening.   Still on this.   Alright. Yeah.   Any any parting words, Gary?  

[01:05:12] Unknown:

No. No parting words right now.   Be peaceful, not harmless.  

[01:05:18] Unknown:

I have, well, okay. It's good. I have parting words for you and for anyone who's in anyone who can relate to Gary right now   is, you know, you guys   are perfect the way you are. You're you're exactly where you're supposed to be.   It's not wrong to feel this way. Mhmm. It's totally appropriate.   Don't fight it   and keep showing up.  

[01:06:42] Unknown:

My.   Bye.