Allen Farrington

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Transcription provided by Podhome.fm
Created: 5/15/2026 12:24:58 AM
Duration: 5540.885
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Alright.
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Welcome back to the Magic Internet Math podcast.
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We have I'm I'm going to say my name this time.
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We're we have Rob Hamilton. I am Brian Hirschfield,
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and we have a very special guest today. By the way, I said that because the last time
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I had said that I'd never said my name on the podcast, and I read these transcripts. And then not just this one, but, like, they attribute, like, my ideas to my cohost and, like, trick really triggers me into insanity.
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But I was reading the AI of last episode, and it they called me Brady.
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And just
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I said I'm like, I gotta start saying my name just because this is, I don't know, unacceptable. So anyway
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Well, I wasn't even sure if you were self doxed or not because it on the little Riverside thing we're all looking at, it says fundamentals.
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Yeah. And when I talk to at Telegram, it's fundamentals. So There you go. I like I wrote It's only LinkedIn, I think, where you I did write a book.
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Wrote add you on LinkedIn. Under my name. I released it under my name.
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It's I'm self docs, but nobody knows or cares who the hell I am. So that's, you know, that's why that works out. We already are friends. Okay. I I I we are connections on LinkedIn. I was like, damn. I have to go add my podcast co host on LinkedIn. Oh, yeah. That's that's
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an important thing to look up during the podcast. Are we Yeah. I know. I know. We have a little friendly banter. I think this is Rob, is this, like, absolutely the first guest. This is first guest. Oh my god. I'm honored. It's all downhill from here. Do you guys do you guys recognize that you guys recognize the voice? That is
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Alan Farrington is our guest today, and we're very, very excited to have him. I feel like this is a long time coming.
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And Well, from from having been the what what was my title?
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I'm I'm on I'm, like, the executive editor or something.
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You you appointed me to something after episode one.
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Well, yeah. Because the first episode of the prior iteration of this podcast, you just kept mocking me with bad math alerts.
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I
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don't think I even I'd had heard the word mock at that point, but that is probably accurate. Yeah. I and we also have to peek a little bit behind,
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the production curtain, the back house operations.
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We started in
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was, like, a month ago before Vegas,
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and I was talking with Alan on Telegram in real time during the taping of the podcast. And then the whole podcast became about Alan,
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but then the audio was so bad that we couldn't release it. Oh, of course. Yeah. So I'm the only one who listened to that one. Yeah. Yeah. Yeah. Those are the lost tapes. I mean, if you thought this podcast was painful with when the sound is good,
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that one
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was really tough. By the way, there's, like, a lot of stories now that I can tell because the word MOG has been invented.
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Like, I just didn't You previously lacked the
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collections.
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Yeah. I lacked the ability to truly describe what is actually happening.
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That's there's some pretty deep
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philosophy of language in there. I'm sure if we if we really, really
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painfully
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torture it, we can start talking about,
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like, model theory or something as well.
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That did you do that on purpose?
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What's going on? I just know it doesn't take much to really trigger something
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trigger something cool in you. So
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we could go there.
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This is magic Internet math, though. So let's
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I don't know. Let's try to get some of this low hanging we got some low hanging math fruit, I feel like.
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I'd like to get out. Maybe like, ask me sums or something. Just
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Yeah. Is
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one plus one equal five? What what do you think about one plus one equals five? Do do sorry. Just do you know the quick math reference?
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I I have this joke all the time with my wife. I feel like both of you guys would appreciate it if you don't know it.
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Go ahead. No. No. Yeah. This doesn't sound familiar. It's some,
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like,
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horribly bad like, so bad. It's funny
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London
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rapper
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who I think is actually I have no idea who he is, but if you Google quick maths, you'll you'll find him. Okay.
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I think he's pretty big on YouTube.
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I'm sure he's big on some other social media thing. I don't Sure. Know anything about it. But he has this one song and this one refrain and this one song where he goes,
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Two plus two is four minus one, that's three. Quick maths.
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That's his rap.
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So there it is. Quick maths.
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That it's like the That's it. That's it. He's loaded up an entire generation with everything they'll ever need to know. Yeah.
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I do want so
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let's
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let's queue you up real quick with,
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you know, the the first episode we ever did and the main kind of the premise of
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how we present math here is as math is a liberal art.
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And if we you know, now that we're getting into linguistics and language
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and all of that, I mean, I'm just like, I'm curious. I I have an idea of, like, where you are. I I know because I've read your books, and I've read your essays, and, like,
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I know you from that. But, like,
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in terms of just you know, what do you think about what do you think about when you think of math as a liberal arts?
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Well,
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I've never thought of that expression until you said it ten seconds ago. So Well, let me let me provide you an opportunity to vamp. Like, I'll vamp for you while you start putting something together.
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This was a a conversation when I first met Brian in person, which is at the John, the the Philly Bitcoin meetup. I had known him for years. He when when we started Anchor Watch, he actually sent me a cold DM, and just like in proper Bitcoin Twitter fashion, his avatar at the time was a Pepe. It just was, like, pointing, saying, not not looking, never selling kind of thing.
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And, he and it turned out that, you know, Brian was an actuary.
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By the way, I stand I stand with Cali now, so that doesn't apply.
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That's right. The Cali the Cali is elite banter.
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Shout out to him. We'll we'll have him on soon enough too and talk about his notes. Yeah. You you should get him on. Yeah. Yeah. We we have, like, a tour of, like, part time amateur mathematician
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Bitcoiners.
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We we have a we have a long after, like as we were planning the first episode, we have, like, a dozen names, and we're like, oh, we're gonna, like, build our way, and we're gonna get to them. And we just started, like, seeing people like, hey. Do wanna do the math podcast? Like, I would love nothing more. You talked to, like, an Andrew Postra or, like, a Jonas Nick who just, their life is, like, the cryptography and the math, and then, like, they go on podcasts to, like, talk about, like whatever new like little product thing is out as opposed to like the thing they're really passionate about.
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So there's a lot of opportunity there. But math is a liberal art.
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Just it'd be interesting too from your perspective because in America math is just kind of like part of this like you know you have to check the box and answer these really crazy word problems that you know and
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they do trigonometry but they do it in such a painful way, there's no beauty and love in it, it's very mechanical and dry
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and
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just as an appreciation of math as part of like being like a well rounded person and having and not everyone has to go you know past even calculus. You don't have to do like crazy like you don't have go into like set theory and like or you know the unreal numbers and like all of these like you don't have to go there But, like, having a strong just appreciation and foundation for, like, math should be part of a well rounded person's education Yeah. And your perspective on that.
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That's super yeah. Okay.
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I appreciate that that setup. I cannot ramble for a very long time. Professional. I'm a as a professional podcaster now. Thank you, Rob. Rob, thank you thank you for that translation. I
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don't know if you guys will be familiar with with this guy. I I recently came across a guy called Joel David Hamkins. Do you know who that is? No.
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He's super interesting. He is a professor
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of I'm not gonna remember exactly. He's a mathematician, basically. He's a set theorist, but he kinda dabbles in philosophy as well. I I think think he's currently at Notre Dame, but he was at Oxford for a long time. He's American, but he's he's backstory in a bunch of different universities. And he's
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he's
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well regarded and well published as a set theorist. He's interestingly
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the
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I forget how you're supposed to, like, qualify this, but the highest ranked or the highest scoring or something to that effect
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ever contributor on math overflow. So that's like a fun little bit of what's introduced with with that. I came across him because he was on
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Lex Friedman's podcast of all places. That was Yes. Fairly recently. That that's how I found him, but I was
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it was clickbait because
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I I mean, if you're looking at it, can probably just tell me right now, Rob. But the the title I think I actually watched an excerpt,
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and then YouTube learned I was interested in that, and it kept feeding me excerpts. And then I just liked them all. I was like, gosh. Shit. I need to just watch all three hours of this now. But, basically, it was that excerpt. I don't even remember what it was, but, like, all of them ended up being exactly what my specialty is, which I'll I'll get into in a second. The reason I'm bringing him up so he's very interesting.
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I I guess I'd say if people are at all interested in my thoughts on anything we're gonna talk about, he's like the professional version of this, so they should go listen to him and go buy his books and so on. And I actually had I had an email exchange with him. He's very he's very, very nice. He was very,
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you know, an entirely unnecessarily
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patient and interested given I'm just some ran I'm not a student. Right? I'm just some crazy Internet person
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emailing him about how everyone's wrong about everything and and had very nice exchange with anyways, I thought of him now because
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I ended up buying his book as a result of this,
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which I I'm not gonna forget the name of it. I think it's he he has a couple of books, as you'd imagine, for someone in his position, but it's like lectures on the philosophy of mathematics, I think. And in the I've only read two chapters of it. But in the first chapter,
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he says
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he thinks that every
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self respecting adult should know a proof that the root the square root of two is irrational.
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So that that's what came to mind just now, Robert. Okay.
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Yeah. This should you know, I'm asked to be a feature. I'm not sure I agree with that necessarily. Don't that'd be nice. I don't think it's realistic.
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You know the lore?
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Yeah. Yeah. It's it's a good it's a good ambition, but I forget exactly how you phrase it, Rob, but something to the effect of,
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you know, it should be a feature of intellectual
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life. Yeah. Like, people Yes. Like, even if you're, like, a a English major, you should understand the basics of that. But sorry, Brian. No. I see. A lot of the I I feel like a a lot of the kind of the instinct there I mean, you can tell me. I don't mean to put words in your mouth, but it's very two cultures esque, if you know the CP Snow essay.
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Does this ring a bell? Nope. No. Okay. Again, I'd encourage readers to readers. Sorry. Listeners. We actually are just bringing you on, Alan, to culture us, really. You're just This is it it's a very, very famous
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essay from, I wanna say, the fifties or the sixties
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where
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CP Snow is
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basically arguing that
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people in the
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sciences more broadly than just math, but people in the sciences are typically well versed in the humanities, but not vice versa. And that that's really sad
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and and kind of bad. It's like a failure of the education system. I I this is an a massive generalization of what that essay argues, but, I mean, it's good enough to address. I I I honestly thought that that's what you were kind of invoking there, Rob. It's like, if anything, that, you know, the two cultures has has got even worse since then.
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But, yeah, I mean, I I I kind of I kind of agree.
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Certainly, from
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my entirely selfish perspective, I
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I get invited on more podcasts. I have more to or like like the like the, you know, the cryptographers that you're mentioning, I'd I'd be able to go on and talk about things that actually interest me rather than, like, what happened on Bitcoin Twitter this week, and where do you stand? Bingo. Bingo. Is it time to excommunicate you yet? Like, we could actually just talk about math instead, which is Exactly.
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It's the dream.
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Okay. So
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that's my preamble. Do should I should I, like, Keep going. Yeah. Let
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me jump in. A little commentary? Yeah. Go for it. Let me jump in. I was gonna ask you, and I can't remember if I've told the story on every single podcast I have, but I don't know if I've told it on this one, and it's a math story. Do you know the lore of the proof of the square root of two being irrational?
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I I'm not sure.
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So okay. I'm gonna tell I'm gonna forgive me, audience, if I told the story, like, seven times here. Seriously, I've I know I've told it on other this is the Pythagoras.
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Yeah. The path so We we last episode. The last episode, we we we just please, yeah, share without. We should tell it again. Okay. Because most people will only listen to this podcast this episode.
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So there was
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in the time of Pythagoras,
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right, there was a group of Pythagoras had a group of followers called the Pythagoreans.
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And
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Pythagoras
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had a
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staunch worldview
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that there only existed rational numbers
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that Mhmm. Basically, it wasn't like he it wasn't like, oh, there's no such thing as an irrational number. It's more like
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any number can be achieved by dividing two integers. Right? That that was his staunch staunch worldview and
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kind of ironic because it only took one of his students to take a Pythagorean triangle with
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the sides of unit sides of one
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to, you know, see that the square root of two being the hypotenuse
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with the simple proof. And this this student whose name is Hephacius.
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He, you know, with a very simple proof, proved that square root of two, it was not possible that could be rational, had to be irrational.
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And this upset the Pythagoreans.
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They were very frightened that Pythagoras might find out about this proof and
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lose his mind and get very upset. And the lore is they they took this guy out to see and drowned Okay.
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Yeah. I knew that. Yeah. Yeah. Now, you know But the truth got out anyway.
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So, like but, like, in math lore in math history lore,
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proving the square root of two is irrational is considered, like, super based.
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It's like the you know?
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I haven't heard that.
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That person has super
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based. It's like your graffiti. You came up with a new proof. It's, like, really stuck sticking it to the man. You get banned from Twitter for proving that. But back in the in the bad old days, you prove that Square is too irrational. It's like a virtue signal almost, right, to, you know It's Russian disinformation.
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Yeah. It's hate speech.
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That I only say that I mean, kind of it from their from their,
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what what would you call it, cosmology. That is pretty hateful speech.
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Yeah.
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How dare you? Yeah.
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But that could be why that why that
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guy think Joel David
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I don't know his name. Joel David Hamkins. Joel David.
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That may be why he thinks this. Right? That every self respecting person should be able to do this proof. Right? And there's so many. It's, like, literally the most proved. Like, it's the one thing that's so the the you know, so many books and That's a nice way about how he says it, by the way. He he doesn't he he's very deliberate in saying a proof because, yeah, there's, like,
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50 plus proofs or something. It's you should have your favorite, and you should be able to prove that.
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Yes. And so I'm
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so where I'm coming from with math as a liberal art is
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you should be nerding out
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over this conversation.
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Right? This should, like, touch the part of you that is not like, oh, the math is so elegant. I I get that. Right? Yes. And sometimes the math's really elegant and beautiful, but this is something different. This is more of
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just very humanities
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based. And maybe it is just that it's so you know, we live in a time, and I grew up in a time where it's just so absent from
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like, I don't even like calling it science culture because I don't like referring to math as a science. I really like thinking of it as a liberal art, like blacksmithing or Oh, that's interesting. Yeah. Yeah. Like, where it's you have to dominate the meeting. Agree with that. I I don't I don't think that's even that controversial,
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or that shouldn't be controversial from, like, a philosophical perspective. I see why it might from a cultural perspective.
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Right. Bingo. Philosophical culturally kind of obviously true. It's it's a completely different
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I don't wanna sound too pretentious about it. What what would you call it? Like, the epistemology is completely different. It's a completely different way of deriving knowledge.
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This is a safe space Yes. For being snoopy.
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I mean, like, we we we
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else. We we were, like, we're, like, we're gonna do a whole podcast
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on just the math and basically chiding everyone in Bitcoin
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for as as Brian
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calls it, when you go to the Bitcoin store and you want to speak to the manager and make sure that your Bitcoin is your Bitcoin,
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how do you actually know? Or Mr.
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I don't trust I verify just says, well, the software on the screen has a number, so it's correct. You know what I mean? Like, there is Karens. There's not enough Karens going to the Bitcoin. Going to the Bitcoin. Okay. Yeah. I can throw I can throw a grenade into this, though. I can this is Do it. Yeah. Will hopefully be this is a little bit tongue in cheek, but it's from my perspective, at least, it's funny because it's true. So maybe it kinda triggers you, and we we nudge the conversation along that way. So
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I didn't even get I don't know if your audience knows this. I don't really talk about it that much, but, like, what my
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why I even care about math, like, what my background in math even is.
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I'll skip over it because there's just a funnier point I wanna get to. We can go into more detail later if you want. But I I'm, like, very
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allergic to math that has any actual applications.
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And if I ever learn if I'm studying something and then I learn there's an application, I'm like, ew. No. Get that away from me. I don't wanna so I've I've had these amusing exchanges with Brian. Don't Rob, I don't think we've talked about this, but then, again, that's the point of this podcast. Right? But I've had these I've had these exchanges with Brian where,
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I think because of,
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you know, my being quite
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well educated in some or other area of math that I'm talking to you about, you assume that I am that in everything. And then and then you ask me something that's more basically about, like, cryptography or or number theory even that's underneath the cryptography.
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I was like, oh, I have no idea. Like, I I not only do I not know. I I don't care. I don't like it. It's yucky
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because it makes Bitcoin work, and therefore, it is instantiated in the real world, and I don't like that. Get away from me.
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It's too real. It's too applied. That is hilarious. Exactly. It's way too applied.
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Because it's too like a lot of a lot of cryptography has been ruined by Bitcoin. Like, it's now highly applicable. Well, you can just link link linguistically, the fact that when people talk about crypto now, they're not talking about cryptography, they're talking about cryptocurrencies
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is enough of itself a proof point that that that Bitcoin has ruined cryptography. Absolutely.
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So I don't know what you wanna do with that. You probably I hope that's all the questions. That just won't be applicable because you'll ask me something about numbers. I'll be like, oh, I don't know. I don't like numbers. If I I wanna stay This is actually partly true, by the way, in the in the area of math in which I
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I don't think it's really fair to say I specialize, in which I aspire to one day specialize because as discussed, I think, immediately before recording, Anchor watch a thousand x's, and then I can retire.
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In my area of of interest, let's say, if you see a number, like, you've done something wrong. It's like you're you're you've either made a mistake or, like, your your formalism is poor or whatever. Like, no. Get away. I don't wanna talk about numbers.
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I wanna talk about morphisms.
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That's where it's at.
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I mean, I'm with you, but I I think it's hilar I really am. I and that's
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I I think there's a balance. I think there's a natural tension.
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Right? And I I like the history of this tension between pure math and applied math. My daughter who
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just came home, she is a pure math major. She's Good for her. Three years in. She's doing research this summer on algebraic number theory.
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Good for well, oh, numbers. I don't know. Numbers. Well, she's the only she's the only student that applied that applied for it because all of the other ones applied for, like, you know, physics and shit analysis. You should ask her. I I don't think I actually remember this fully off the top of my head, but are you familiar with
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Bertrand Russell's
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I think maybe other people came up with something similar, but it's attributed to him. His his definition
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of a number
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of of, like, what even is a number. Right? Like, what do numbers mean? What are cardinal numbers? It's something like I wish I could remember off the top my head, but it's like the equivalence
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class
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of
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is it
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by injections
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of is it something something yeah. I can't I'm pretty The equivalent mechanism
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equinumerosity
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where two sets are considered equivalent if there's a bijection between them.
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Yes. Right. Okay. Yeah. So you so you establish equinumerosity
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as a
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bijective
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function an an abstract
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class function on anything,
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and then its numbers
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are the equivalence classes of this equivalence relation
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partitioning
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the class universe. That's numbers. So I'm happy with that. I'm happy with finding numbers in those parts. Fine. No. Actually using. That's right. I I like and, yeah, and, again, I'm with you. Like, when I see a number, I'm like, oh, this isn't math. Yeah.
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It's arithmetic.
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Yeah.
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I wanna see kernels I say that all the time. It's Yeah. I wanna see kernels and cosets. Yeah.
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But
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but there is a there is a tension. You know? So I I think I probably was pretty biased for most of my life and most of the time I raised my daughter in terms of being on the pure math side and pretty much rejecting.
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I just
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what I reject is the notion that it has to
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be a means to an end. That not just the notion, but, like, the Yep. It's like a law. It's a law of the land
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anywhere
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I used to think I was alone in this, right, where, like,
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people just, what the hell? Like, what's the point of studying math if you can't use it for you know, to make nukes,
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to make weapons, or to make Well, I think to do things. That attitude of people who might argue against you is kind of a cell phone or at the very least, it's historically illiterate in the sense that
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almost every
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I mean, probably just every on a long enough time horizon breakthrough
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of applied math of some or other math being found to be useful
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to describe the physical universe
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started
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as someone just dicking around with concepts because it's fun. And had had they not done that, they wouldn't have even had the apparatus
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to then
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to then actually deploy it usefully within physics. And I'm I I hesitate to say this because I don't I don't know anywhere near as much about the history of physics as the history of math, but I I honestly would not be surprised
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if there's literally never been a material
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breakthrough in mathematics that's actually come from physics,
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as in a physical problem
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was
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solved by a physicist inventing new math. I think it's almost always been
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that they are learned enough to deploy
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some or other pure math
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and effectively discover its application?
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I think I think you're probably right. And I think it's interesting. Like, I
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guess the most recent breakthrough would have been
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using, using elliptic curves to solve
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to prove from Matt's last theorem,
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which was a bit of a breakthrough, but it wasn't cryptographers who did that.
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Right?
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Like, it's that's that's actually what algebraic. I mean, I'm pretty sure what
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like, my daughter knows about elliptic curves now, not because of me or any of this. Do you want my do want I have a hot take on this, by the way. You can clip this and then, like, shitpost it as a I don't know how how you advertise this podcast, but
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I so I I looked into this.
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I I I can't even remember why. I just got curious. I guess it's kind of a point. Right? Like, there doesn't even need to be a lie. You just get curious about wiles and for Matt's last theorem and everything. And I I looked into it maybe, like, a year or so ago. And I feel it's important to say I don't at all understand it. Right? I don't I haven't, like, followed Wiles' proof or anything, but I I learned by, like, more the history of how it you know, how we solved it. Mhmm.
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And I decided
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in completely
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uneducated terms
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that I'm kinda pissed off that he gets the credit because what he actually did was prove something called the Tanayama Shimura conjecture.
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And when you look into again, not to, like, downplay that achievement, but it's the it's the Tanayama Shimura conjecture itself
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that is incredibly
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impressive and is the breakthrough. And it's like 90%
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of the way to proving Fermat's last theorem,
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even even, you know, codifying the conjecture.
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All Wiles did was prove the conject like, he didn't really prove Fermat's last like, that's that's silly. That's like the jar was loose. Right? He just did the final little term. What's the chop which chop is the chop that takes the tree down? That's would be the real thing.
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Oh, do want me to answer? Or is this No. Which one? Literally, which one? I want a number. Yeah.
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I told you I'm not I don't deal with numbers. I'm By the way, so every chop of a tree is a group.
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Right? Yeah.
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Exactly.
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But one of them takes the tree down. You
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know? So here's something funny. Everything I know about Fermat's Last Theorem comes
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from a a book
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called,
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brace yourself,
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math girls.
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There's a series a book series. They they're like anime novellas. Like, Shinobi would love this thing. They're like they're like anime novellas
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where these, like, Japanese girls are just they're, you know, they're living their life. You know, like like, you know, a play like High School Musical or something where, like, they show the high school kids that care about being on the basketball team? You know? Like, they so, like, you just
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you get to live through their their view of that because that's what they're into.
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Well, these Japanese girls are just into math, learning math. All their friendships are about, like, who's teaching me better, you know, or who you know, and it's mixed into their little weird romance stuff. And that is how I learned everything about From My Slash Theorem is from one of these books.
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Good for you? Highly recommend it, by the way. Yeah.
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I learned a lot about Japanese
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girls too, probably more than I needed to.
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Which of these was the intention?
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Like, is that is that just your interpretation
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of the books, or was were they actually presented that way? The one on for Matt's Last Theorem is, like, probably one of the best textbooks
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Normie could ever pick up that give that like, if you want the whole curriculum of, like, division algorithm, greatest common divisor, Chinese remainder theorem, like, that whole, like, you know, that whole package,
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this is the this is the book to get. I'll have to put it in the show notes. I'm gonna reveal my big secret.
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It's funny. These these episodes with guests are a little bit different because typically, Alan, what we do, we've spent These episodes. Like, we've Like, the the guest episodes. No. No. That's what I mean. Like, these these are different. Like, I'm already feeling that they're different because typically, Alan, we actually,
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in the fall last year,
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I I was talking to Brian about, like, the power of clogged code in these tools.
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And we I did a like, an hour and a half long call with him over, like, the Christmas holiday.
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And, you could tell, like, his eyes got wide. He's like, okay. I'm I'm this is this is this is the magic right here, like, that I'm gonna go run with. And he's been the magic Internet math website.
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And what he does is he has a whole system of tools and skills now that will take a textbook or take a concept and will actually make it a full interactive educational
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breakdown with quizzes and study guides and all that. And usually what I do is I'll load the study guide up into Claude code and, like, kinda help walk through this whole thing. And now this is just, like, free range. Like, we're just, like, why like, this is, like, this is fully improv jazz as opposed to a concert. Math as a liberal art. Go. This is Exactly.
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Is true. Right?
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Yeah. Yeah. The other ones are lectures. You and I are just I mean, in six episodes, we've just about finished elliptic curves.
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And funny enough, we just finished up elliptic curve, elliptic curves and, like, all of the math behind that. And now we realized that Peter Willa did a whole, like, hyper autistic super detailed drill down of how it all works in Bitcoin. We're like, well, I wish we had this, like, six months ago. So now we're gonna have to just do an encore set and just come on out and just do that again. Part. Not not that I knew all those details, but I had I I suspected as much, and that's why I was insistent on slipping in that I don't like anything remotely applied so you don't try to No. We're not. We're not. That's great. Talk about it. No. We're not. No. That that's that's very much not the vibe here. I think one of the missions, not only just about that being a liberal art, but being able to bring people that are, you know, within the Bitcoin ecosystem to come on a podcast and not, to your point, talk about a single thing related to Twitter or any sort of topic du jour. The closest we get to topic du jour stuff is quantum because No.
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Danger. I Blocked. Blocked.
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Only because
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we wanna make sure people understand, like, the discrete log problem and understand the design space of, like, how Bitcoin is secured. I I honestly I thought you were gonna say something like, we wanna make sure that people understand
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that the people talking about this do not understand it.
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And neither do we, and neither does hardly anybody else.
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There's been a couple of red flag moments. Yeah. Well, there was one other interesting important thing that came out of quantum, which is the
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your person's sense of what a 1% chance is. Because that's like that's been like
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their big argument. It's like, there's even a 1% chance that we have a quantum computer. We must we must act on this now.
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I I have an analogy that I've been working. I've been working an analogy on this. Not that we really wanna talk about quantum, but, like, I just wanna make one. I'm I'm gonna run run it by you guys and run it by the audience, and feel free to
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let me know how shitty this is. But
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the NBA is a
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professional basketball league.
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Heard of it. And so
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there are the NBA has a very big problem coming in the future, which is twelve foot people.
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Twelve foot people are going to ruin the NBA, and we are breeding them now
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because it's obviously in someone's interest. They're gonna make a lot of money if they breed a twelve footer.
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And, you know,
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so we're breeding them, and we show we probably should change the rules now to make sure that it doesn't ruin the game. That's my big That's your metaphor? Perfect. Yeah. Perfect. Perfect. Yeah. We could change the whole thing. We should make the hoops 30 feet. I like that. Yeah. Yeah. Because I can't comment on that, by the way. I feel like this isn't really math so much as, like, philosophy of math, but that's within Perfect. Totally.
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It's I was just encouraged. I was trying to think.
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I have written about this, but I don't think it's in anything that went into Bitcoin is Venice. I think it's in a much earlier essay called
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Cargo Cult Math. Just to actually revisit. I because I've had more thoughts about this kind of thing since then. But
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I feel like you guys would just agree with this immediately. If you don't, it'd be fun, and then we can argue about that.
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People have a very
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ill like, people in general have a very ill conceived idea of what
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probabilities
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mean
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even in, like, a well defined context. And I think the problem is that because they don't understand what makes such a context well defined,
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they then use it in a purely like, they just extrapolate it to where it makes absolutely no sense. And I think the example you just gave is is one of them.
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That basically,
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a probability only means something
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in a
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in a space
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where
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the outcomes
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are all
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known
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and
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definable.
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Mhmm. And
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you can you can kind of sort of depends on what the exact physical scenario is, but you can run
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it
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independent. You can run independent trials.
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Right.
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Right. Yeah.
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And getting a full house in poker. Extend that to just
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you're not actually talking about probability. You're talking about something like likelihood, right, which is just
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psychological.
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It's not mathematical.
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It it's interesting because you you can do it in meaningful ways. You just have to be very careful how you're doing it. So the the only way that I would so something like exactly what you just suggested,
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you know, 1% chance of quantum or or whatever, x percent chance of anything in the real world.
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The only sane
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meaningful way to interpret that is as an indication of what you think is a fair bet,
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which is interesting. Right? Like, you can follow-up on that, and you can push that in interesting in kind of interesting directions.
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But
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you can't
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treat it as a scientific question because it's it's simply not. It's it's entirely a psychological question
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that you can maybe help your understanding with these mathematical
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I mean, they're not even really mathematic. It's like arithmetic to Rob's earlier point, Tools. Right? You can you can quantify your psychology in interesting ways, but that doesn't mean you're doing science. You're just talking shit.
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Right. It's almost like,
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when you
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they're almost like it's like wearing math as a skin suit. You're like, oh, yes. See, there's numbers on the screen. You have to I'm I'm I'm I'm this is scientific now. This is this is not me kinda do a sleight of hand of putting numbers on a screen. I'm I'm embezzling my opinion and making it seem legitimate because I threw some numbers on the screen. And whenever you get immediately
368
00:34:17.815 --> 00:34:23.895
you're you're you're you're put the moment you have to apply any of these things in the real world, you have to make a list of assumptions,
369
00:34:24.135 --> 00:34:29.110
and that's where people embed all of their political biases or their emotional like tendencies
370
00:34:29.270 --> 00:34:30.150
immediately.
371
00:34:30.470 --> 00:34:34.790
You could say like, oh, well, know, the two thousand and eight financial crisis, those were mathematically
372
00:34:34.790 --> 00:34:35.590
rigorously
373
00:34:35.590 --> 00:34:42.950
modeled. How could you say you could never go wrong? We had math, right? Or you know, long term capital management. You had all the world's best mathematicians.
374
00:34:43.235 --> 00:34:45.155
How how could you go wrong? Right?
375
00:34:45.555 --> 00:34:51.715
And I think that's a good point. Winning blacks about black and shoals were on that team for Christ's sake. Right. Right.
376
00:34:52.035 --> 00:34:57.235
Right. By the way And so the the person with the skin suit definitely celebrates pie day, like, really hard.
377
00:34:58.880 --> 00:35:05.680
It it's the I fucking love science of, you know, the like, you know, you're like, oh, I'm a nerd. Right. Exactly.
378
00:35:07.280 --> 00:35:13.200
Exactly. No. That it's actually as I'm pulling up this article now, Brian, you and I should read this before the next episode because
379
00:35:13.985 --> 00:35:21.505
looking at this, of course, I did what everyone does in 2026 and just dumped us some asked for a summary from GTT. This is the cargo cult math article?
380
00:35:21.745 --> 00:35:28.870
Yeah. Oh, like Oh, nice. I I found it. No. I found it immediately. Yeah. Found it immediately. Great job on the SEO there. First hit.
381
00:35:29.270 --> 00:35:31.510
Yeah. It was right there. Immediately right there.
382
00:35:32.870 --> 00:35:35.990
And false precision and misplaced significance,
383
00:35:36.390 --> 00:35:44.415
and you use exactly statistics and all this stuff. And I think that's a really good, thing. I mean, what's really Do know what's interesting there, though? I don't know if your little summary has told you this.
384
00:35:44.815 --> 00:35:49.775
That all comes from like, I as an in the essay, I heavily cite this book.
385
00:35:50.575 --> 00:35:53.775
What's it called? It's called the cult of statistical significance,
386
00:35:54.260 --> 00:36:03.940
which you guys would both love if you haven't heard it. I don't wanna go, like, I read this ten years ago, and I wrote this five years ago. So I can't opine on it too much too intelligently,
387
00:36:03.940 --> 00:36:06.900
but, like, we should all go read it, and then we can come back and talk about it in a month.
388
00:36:07.695 --> 00:36:20.655
Perfect. I I'm I'm I'm using our group chat as, like, the meeting notes aggregator for this Nice. Nice. For the for the podcast. This is this is gonna be good. And you get full credit because in 2019, you talk about artificial intelligence in this
389
00:36:21.430 --> 00:36:24.390
article. Oh, yeah. So you get you get you get full think boyfriends.
390
00:36:24.390 --> 00:36:31.910
That whole so early. That whole argument is just as applicable now. I mean, it I don't think I mentioned the following because I think it actually came out later, but there's a single meme
391
00:36:32.070 --> 00:36:40.485
that captures this perfectly, which I'm pretty sure you guys all know about. But if if not, this will be fun that I'm introducing it to you. It's like a
392
00:36:41.125 --> 00:36:42.405
it's it's a
393
00:36:42.485 --> 00:36:44.085
a picture of
394
00:36:44.325 --> 00:36:45.445
a ship
395
00:36:45.445 --> 00:36:48.805
in the foreground and then, like, a huge demon
396
00:36:49.089 --> 00:36:50.530
in does this ring a bell?
397
00:36:51.410 --> 00:37:00.130
Nope. Give me a little bit more. It's like when I say picture, obviously, it's it's like a cartoon. Right? So, like, a ship like, an ancient sort of trireme type, you know, Greek naval vessel.
398
00:37:00.450 --> 00:37:11.895
Like, clearly very old looking ship. Yep. And then a huge I guess the implication is it's I don't know the right, you know, Greek mythology terminology for this, but, you know, Greek demigod or whatever that's out to destroy it. And
399
00:37:12.535 --> 00:37:14.295
and then the the the
400
00:37:14.615 --> 00:37:19.360
caption, I guess, is over it is oh, so over the ship, it's
401
00:37:19.600 --> 00:37:34.855
sometimes it says supercomputer. Sometimes it says AI. I'll just say AI to fit the theme. And the AI that plans the economy one year in advance. Right? And then the huge demon monster thing is, I like broccoli now. I know I know I do yeah. I I remember that. Yeah. Like
402
00:37:35.415 --> 00:37:37.015
Yeah. That's basically
403
00:37:37.255 --> 00:37:45.495
the argument about AI that I make in '20 With the punchline with the punchline with the punchline, I remember the meme. I typed in Yeah. Meme monster ship,
404
00:37:45.830 --> 00:38:09.434
and it's now giving me fan fictions of women falling in love with demon monsters at sea and shipping for romantic relationships between the woman and the demon. So I'd I I also like that. That's hilarious. But to your point, yeah, like the I've seen this I think it was, like, Mark Andreess and a couple of people were retweeting it a while ago. But just the idea of you have these ridic rigorous we have all of the science and credentials. And this is where I do as a as a small, like, philosophical,
405
00:38:09.434 --> 00:38:24.370
political aside, people are like, ah, if only the Soviets had AI, they would have figured it out. And then, like, I like broccoli is the thing that destroys the entire yeah. Perfectly said. Yeah. That that's another perfect example of had AI. The AI would have told them to read nieces, and then they would have stopped.
406
00:38:27.970 --> 00:38:31.410
They would have cut that shit out. Yeah. That's right. That's right.
407
00:38:32.505 --> 00:38:35.384
No. This is this is good, though, because I
408
00:38:36.105 --> 00:38:36.665
this
409
00:38:37.065 --> 00:38:41.145
is something that in Bitcoin as I was getting into Bitcoin when I first got into Bitcoin,
410
00:38:41.785 --> 00:38:57.050
in 2013 going to BitDevs, I felt a closer kinship and connection to this. And just as the culture grows naturally as it scales, you kinda have to map onto the culture that exists. And since most people don't value math, you start straying away a little bit from, like, the mathematical anchors of what we find interesting.
411
00:38:57.210 --> 00:39:03.175
And I think Brian and I's goal of this is trying to, you know, make math fun and interesting and not intimidating.
412
00:39:03.415 --> 00:39:03.975
And
413
00:39:04.775 --> 00:39:09.655
Oh, my goal is very much to make it intimidating, so I we're gonna we're gonna clash on this.
414
00:39:09.895 --> 00:39:13.415
Well Do you remember how I define number thirty minutes? I don't even remember.
415
00:39:15.440 --> 00:39:17.280
No. I I think intimidating
416
00:39:17.440 --> 00:39:44.010
it could be intimidating, but the journey of learning, you should just lean into it and just embrace the pain. And people in Bitcoin are like, oh, price volatility. I don't care. It's like, okay. I don't understand set theory. I don't care. You should just still lean into it and, like, start digging into it deeper. I care more something I wanted to mention, by the way. This this came to me after we kinda moved on, but it's right back to the way you teed up the the the opening, Rob Yeah. By math as a as a liberal art. There's one other thing I wanted to mention that I'm sure will prompt some interesting thoughts from you guys that
417
00:39:45.130 --> 00:40:01.645
I'm not sure I'd go quite as far as you went in terms of I mean, maybe you were just being rhetorical. I don't know. But, like, oh, everyone should love math, and it's beautiful and whatever. Sure. I I do I do hesitate a little bit because I have I have in the back of my mind kind of a worry that if you push that attitude too far,
418
00:40:02.285 --> 00:40:02.845
you
419
00:40:03.565 --> 00:40:17.390
you you essentially become like I don't actually know who the math version of this would be, but, like, I fucking love science. Right? It's like that. Yes. And, like, Neil deGrasse Tyson is who I had in mind. And I don't if you guys know Brian Cox, not the actor, but he's, like, the British Neil deGrasse Tyson. Yeah.
420
00:40:18.030 --> 00:40:19.790
And and you kinda horrible.
421
00:40:19.950 --> 00:40:21.485
I don't yes. It's the worst.
422
00:40:21.645 --> 00:40:26.365
I totally His his his summary in Google is physicist and musician.
423
00:40:26.525 --> 00:40:33.165
Uh-huh. God. So, yeah, I'm wary of, like, nudging people in that direction. I do think you need to
424
00:40:33.530 --> 00:40:35.849
you need to stay rigorous,
425
00:40:35.849 --> 00:40:36.970
and you need to
426
00:40:37.450 --> 00:40:40.490
insist on real understanding as opposed to just, like,
427
00:40:41.050 --> 00:40:41.770
juggling
428
00:40:42.010 --> 00:40:47.175
I don't know the right metaphor is, but, like, not doing it seriously, basically. Right. That said,
429
00:40:47.735 --> 00:40:55.495
I see that as and, actually, come come the thing that you can make exactly this argument about probably anything in the humanities as well, which maybe is a very nice link.
430
00:40:55.735 --> 00:40:57.815
I see that constraint
431
00:40:58.295 --> 00:40:59.015
as
432
00:40:59.175 --> 00:41:00.215
empowering
433
00:41:00.295 --> 00:41:01.815
rather than debilitating
434
00:41:02.440 --> 00:41:05.960
in that it forces you to be
435
00:41:06.520 --> 00:41:07.400
creative
436
00:41:07.400 --> 00:41:09.160
in a genuinely useful
437
00:41:09.240 --> 00:41:10.040
direction.
438
00:41:10.040 --> 00:41:11.800
Right? It it it channels
439
00:41:11.800 --> 00:41:14.680
the creativity that you do need to do it well
440
00:41:14.925 --> 00:41:16.045
towards
441
00:41:16.685 --> 00:41:25.485
much more profound understanding of the material. And there's the sorry. I'm jumping all around because I'm I'm all these links are coming to me, I don't know how to tie them together necessarily.
442
00:41:25.645 --> 00:41:38.010
But just on the on the math is liberal art. There there's I forget who this I mean, Rob, you can you can just find this out immediately. You're obviously quite quite good at sourcing stuff this way. There's a quote from a I believe it's a poet, but I can't remember who,
443
00:41:38.330 --> 00:41:38.890
that
444
00:41:39.930 --> 00:41:43.575
writing in free verse is like playing tennis with the net done.
445
00:41:43.895 --> 00:41:49.015
I think that's basically exactly the instinct that I'm driving at here with with math that
446
00:41:49.575 --> 00:42:00.120
and sorry. The what the original thought I had that I wanna get back to the That's Robert Frost writing free versus, like, playing tennis with the net done. Remember that. Okay. Yeah. I should know that. I or I should if I'm gonna recite that, I should be able to remember it.
447
00:42:01.800 --> 00:42:05.240
The the original thought I had was, you know, that aside,
448
00:42:05.960 --> 00:42:06.600
I
449
00:42:07.000 --> 00:42:08.520
do get very
450
00:42:09.319 --> 00:42:13.080
I guess I used to. I haven't really thought about this in long time. But when I was studying math
451
00:42:13.319 --> 00:42:14.765
as an undergrad, I
452
00:42:15.165 --> 00:42:15.805
got
453
00:42:15.965 --> 00:42:17.325
irritated
454
00:42:17.885 --> 00:42:18.605
at
455
00:42:19.245 --> 00:42:25.165
basically how I I think math is almost always very poorly taught, and especially in
456
00:42:25.965 --> 00:42:27.085
younger and younger
457
00:42:27.890 --> 00:42:32.210
just ages, I guess. Never it doesn't the class doesn't matter necessarily.
458
00:42:32.770 --> 00:42:47.085
Even here, you do need a little bit of a caveat that, like, I don't think this is well well before my time. So, I mean, it's well before all of our times, but, like, I'm aware of the whole new math disaster. I don't think you should be teaching five year old set theory. That that is not the point I'm making, that everything should just be ultimate creative
459
00:42:47.085 --> 00:42:56.910
and, like, foundational or whatever. You do need people to wrote learn kids rather. You do need kids to wrote learn timetables. Like, that's fine. Mhmm. You need them to wrote learn some stuff.
460
00:42:57.230 --> 00:42:57.790
But
461
00:42:58.030 --> 00:43:00.990
I would argue as quickly as possible,
462
00:43:01.550 --> 00:43:05.790
you you should be encouraging an appreciation of creativity
463
00:43:05.950 --> 00:43:07.070
rather than
464
00:43:07.390 --> 00:43:12.915
just extending wrote learning to everything. Like, math is a bunch of facts about numbers
465
00:43:12.995 --> 00:43:14.915
that mean absolutely nothing to you,
466
00:43:16.195 --> 00:43:28.460
but you just gotta learn them, and then you gotta put them on the test. And then or, Rob, you said something that in February right at the start that it's like a checkbox thing that you just you just need to know how to do this, and then you do it, and then you never do it again. And you wonder why you ever learned how to do it.
467
00:43:28.860 --> 00:43:30.220
If I were the
468
00:43:31.100 --> 00:43:35.740
math education czar or or something, whatever whatever would be applicable,
469
00:43:37.365 --> 00:43:39.685
Yeah. I would I would push for
470
00:43:40.325 --> 00:43:41.125
much
471
00:43:41.205 --> 00:43:41.925
more
472
00:43:43.285 --> 00:43:45.045
much more understanding,
473
00:43:45.045 --> 00:43:46.245
much more
474
00:43:46.805 --> 00:43:47.685
education
475
00:43:47.685 --> 00:43:51.445
with understanding as the goal rather than mechanical
476
00:43:51.445 --> 00:43:52.165
reproduction.
477
00:43:53.079 --> 00:43:58.840
And so I guess in that sense, math is a liberal art. The end. We're done. There you go.
478
00:43:59.480 --> 00:44:01.800
Yeah. The the other thing here is
479
00:44:03.079 --> 00:44:11.895
so a lot of what I draw on here is this essay called the mathematician's lament. Definitely check that out. Oh, that's yeah. I I read that a long, long time, but I know that one. Yeah.
480
00:44:13.015 --> 00:44:20.295
And it like, you just really did a good job of explaining what happens if you take an art, any art, and you make it mandatory.
481
00:44:21.130 --> 00:44:21.770
Mhmm.
482
00:44:22.250 --> 00:44:31.690
It then becomes kind of perverted in the way you have to teach it because it becomes a mandatory thing. And this is sort of why it's sort of become what it's become and why people hate it so much because
483
00:44:32.250 --> 00:44:38.705
it'd be like, you know, oil it's like the oil painting or blacksmithing was in, like, some kind of mandatory class,
484
00:44:39.985 --> 00:44:40.785
people
485
00:44:40.785 --> 00:44:44.945
would hate it. Yeah. And, you know, you wouldn't you completely lose
486
00:44:45.105 --> 00:44:49.265
like, what happens when you learn an art, it's like you're building you're
487
00:44:49.265 --> 00:44:50.305
building will.
488
00:44:50.385 --> 00:44:52.065
Like, when you're trying to dominate a medium,
489
00:44:52.839 --> 00:44:54.680
let's just say, like, blacksmithing.
490
00:44:54.680 --> 00:45:01.720
You you are trying to dominate a medium. Like, you you don't go from a hunk of metal to a bracelet unless you
491
00:45:02.200 --> 00:45:03.000
somehow,
492
00:45:03.559 --> 00:45:05.559
you know, you transcend
493
00:45:05.559 --> 00:45:13.295
something and you you dominate the medium enough to transcend it. And you either do it or you don't. And I think in math,
494
00:45:13.615 --> 00:45:15.295
that domain is,
495
00:45:15.535 --> 00:45:20.895
like, your sense of your own ability to reason, your sense of yourself, your strength of conviction.
496
00:45:22.550 --> 00:45:26.310
And I think that's the in order to that's like the meet that's the end.
497
00:45:26.550 --> 00:45:30.150
To me, that's the end of learning math. You're learning it to learn yourself,
498
00:45:30.470 --> 00:45:38.935
to become to have conviction in your own reasoning. And I don't think everyone has to do it, but I don't think also don't think you can really live a self determined life unless
499
00:45:39.095 --> 00:45:42.455
you're on that path. I'd I'd I'd go further as well that I think
500
00:45:42.935 --> 00:45:44.215
a lot of people
501
00:45:44.695 --> 00:45:50.855
would do it or at least would appreciate being made to do it if they're if they're in school and they're being made to do it.
502
00:45:51.760 --> 00:45:52.400
If
503
00:45:53.440 --> 00:45:58.960
the way I suggested it be presented were the norm such that there was some kind of
504
00:45:59.440 --> 00:46:07.115
excitement in the discovery and and even I go Rob said it's a safe space, I don't have caveats. But some No. Some appreciation
505
00:46:07.115 --> 00:46:14.875
of of the beauty of what it is you're doing. Because I feel like the three of us, I'm sure this doesn't need explanation.
506
00:46:15.035 --> 00:46:24.410
Mhmm. But to the, you know, a normie on the street, it this would all just be or, like, a. It wouldn't even be it'd be like, they they just think we're taking the piss. They think we're hitting by this.
507
00:46:24.810 --> 00:46:27.290
What I one other thing I wanted to mention actually just because
508
00:46:27.690 --> 00:46:31.930
I realized everything I said before maybe sounded a bit like my theory about this is
509
00:46:32.205 --> 00:46:35.005
as presented there was very theoretical,
510
00:46:35.325 --> 00:47:01.285
but it's it's derived from my actual experience, which I I kind of regret in hindsight. Not not in the sense of, like, I regret my decisions, but I regret it was this way, and I wonder how much better it could have been. I was funny. I I don't even remember when we've been recording for so long. I said, I'll I'll eventually tell you my background, we can get into some questions based on that. I don't know. How long do you guys even wanna go for? Like, I can go past the hour if you want. I can stay on. I have no job. I can do a little bit longer. I can do a bit Yeah.
511
00:47:02.565 --> 00:47:04.645
Have I have nothing. So we'll stop whenever you want.
512
00:47:05.765 --> 00:47:06.405
So
513
00:47:06.725 --> 00:47:07.365
I
514
00:47:07.845 --> 00:47:10.005
I think I only really appreciated
515
00:47:10.005 --> 00:47:18.190
or or started to appreciate anything that we've talked about now probably in second year of undergrad. So all the way through primary school,
516
00:47:18.510 --> 00:47:22.270
all the way through secondary school sorry. This is, UK lingo.
517
00:47:22.430 --> 00:47:23.870
I'm I'm sure you understand.
518
00:47:24.750 --> 00:47:28.190
And and then even first year of of uni where I studied math,
519
00:47:28.855 --> 00:47:35.335
I was just I was, like, good at it, and so I passed the test, but, otherwise, I didn't really care. Mhmm. And it was only
520
00:47:35.815 --> 00:47:51.850
I think it was it was partly that I finally hit on material that was genuinely interesting to me. So this is basically when Brian, you brought this up a long time ago. This is when it was broken out that there is such a thing as pure math. Right? And so it was this specific class called algebra and analysis.
521
00:47:52.170 --> 00:47:55.690
And then also the two teachers of this class, the one guy did algebra, the other did analysis,
522
00:47:56.285 --> 00:48:07.805
who were very, very good. I think the university did it on a purpose. Like, they knew that that's how that class was how they were gonna hook people who were maybe on the fence about continuing with it. Because also in in I don't know if you guys know this, but UK university
523
00:48:08.170 --> 00:48:11.370
or sorry. No. Scottish university because you do four years.
524
00:48:11.690 --> 00:48:13.850
After the first two years, you decide
525
00:48:14.170 --> 00:48:24.225
what you're gonna do for the third and fourth years. Mhmm. And so there's a lot of people who just, who do math classes for credit, but then they'll never like, a lot of my friends did that, actually. They ended up majoring in something else.
526
00:48:25.184 --> 00:48:27.505
And so it was that class that made me appreciate
527
00:48:27.984 --> 00:48:36.945
that there even is such a thing at pure math, that I'm interested in it, that I'm even better at it than all the other stuff I've just been memorizing and, you know, reproducing
528
00:48:37.105 --> 00:48:37.345
wrote.
529
00:48:39.089 --> 00:48:42.609
And then the final push after that wasn't until
530
00:48:42.849 --> 00:48:43.890
third year
531
00:48:44.210 --> 00:48:45.010
when
532
00:48:45.010 --> 00:48:46.450
I got introduced
533
00:48:46.450 --> 00:48:56.195
to basically logic as, like, an extension of this line of thinking. And and the way when I'm saying, like, I kinda regret this that I ended up graduating
534
00:48:56.755 --> 00:49:04.035
the most interested in math that I'd ever been and be like, oh, shit. I need to go and be an adult now. Like, if I'd if I'd known this
535
00:49:04.435 --> 00:49:21.690
four years ago or ten years ago even, like, who knows what I could have You're And not not even that me achieving anything is relevant, but, like, I I would have enjoyed it. Well, this is you're you're pulling on a key thread, because, without going too long, I had a very similar story where I actually was struggling through math all throughout collie high school.
536
00:49:22.635 --> 00:49:23.195
And
537
00:49:23.915 --> 00:49:41.020
then I went to college as a business major, and then I became a math and econ double major because I started getting into math courses and the structure of the environment and the materials were much more conducive for me learning. And this is like the missed opportunity of how education is handled at those lower levels where math is treated as this
538
00:49:41.900 --> 00:49:48.780
very, like so intensely applied because it's always like in The States, it's always a word problem and you have to memorize
539
00:49:49.715 --> 00:50:01.235
sine and cosine and tangent. Like SOHCAHTOA is what, you know, is trying to be the opposite over the hypothesis. Like, and it's all like rigorous. Like, I think to your point earlier, like, like multiplication tables, yeah, that just requires
540
00:50:01.869 --> 00:50:06.110
rapid iteration to be able to function in society for those basic things. But
541
00:50:07.310 --> 00:50:16.030
none of those really interesting things are ever really exposed until you get into those higher levels. I think it's a huge disservice because there's many people where if they, at the start of their educational journey,
542
00:50:16.665 --> 00:50:18.985
were provided these more open free form
543
00:50:19.465 --> 00:50:23.065
beautiful things about math, you'd have a lot more people that are mathematicians.
544
00:50:23.385 --> 00:50:35.080
And downstream from that I think just a general better more productive society from that too. Yeah. Well, actually, I can one one thing I'd add to that, I I make the same case even more strongly. And this sort of echoes something I talked about before
545
00:50:35.240 --> 00:50:39.560
in the development of the the history of the subject that I think
546
00:50:39.880 --> 00:50:43.965
it's it's kind of a cell phone focusing so much on,
547
00:50:44.285 --> 00:50:45.005
like,
548
00:50:45.245 --> 00:50:56.205
nailing what you're learning down to an application because for exactly the reasons you just outlined, Rob, if you gave people that or kids, really, that's more the point. People in earlier education, if you gave them that freedom,
549
00:50:57.130 --> 00:50:59.130
they would become
550
00:50:59.290 --> 00:51:00.410
more interested
551
00:51:00.490 --> 00:51:10.410
in the process of learning itself and then actually end up better able to apply it. So even if your goal is that they should be applying this all day long every day, right,
552
00:51:11.175 --> 00:51:17.735
They do that better if you stop drilling application into their heads. If you if you let them actually explore,
553
00:51:18.055 --> 00:51:18.855
I guess,
554
00:51:19.415 --> 00:51:29.150
why they ought to be applying it, then they actually find on their own. They're like, oh, I I I know why I'm supposed to be applying this now. As as the kids say nowadays, let them cook.
555
00:51:29.549 --> 00:51:30.190
Yes.
556
00:51:30.589 --> 00:51:33.390
The kids do say that. That's so Indeed.
557
00:51:34.030 --> 00:51:36.190
Did you guys ever read this book called range?
558
00:51:37.390 --> 00:51:39.630
No. I've heard good
559
00:51:39.965 --> 00:51:45.245
good reports. It's like one of these fan read. It was once one of these old, like, airport bestseller types. Yeah.
560
00:51:45.805 --> 00:51:46.605
There was a
561
00:51:47.165 --> 00:51:58.680
But it's a good airport bestseller. It was. And now it's because well Though I gather. Well, it's really about, like, the notion of being a generalist versus specialist. That's what it focuses. So there's a lot of this, like, pure versus applied
562
00:51:58.920 --> 00:51:59.720
tension.
563
00:51:59.880 --> 00:52:00.119
But
564
00:52:00.760 --> 00:52:04.600
right? Because pure versus applied is kinda like being a generalist versus a specialist.
565
00:52:05.015 --> 00:52:09.895
Mhmm. But there's a chapter in the book where they described an experiment,
566
00:52:10.215 --> 00:52:12.135
a very longitudinal
567
00:52:12.215 --> 00:52:13.655
experiment over,
568
00:52:14.295 --> 00:52:20.060
say, I think it was five years where they went into, I think it was American colleges calculus
569
00:52:20.060 --> 00:52:20.860
classes,
570
00:52:20.860 --> 00:52:22.780
like entry level calculus. Right?
571
00:52:23.100 --> 00:52:29.820
And they basically told the professors they can teach it as easy as hard as they want, but they have to basically stick to a certain certain curriculum.
572
00:52:30.460 --> 00:52:30.780
And
573
00:52:31.464 --> 00:52:37.225
yada yada yada, the bottom line was they found out that the professors that taught it the easiest,
574
00:52:37.545 --> 00:52:41.065
their kids got the better grades, and the professors were ranked higher,
575
00:52:41.625 --> 00:52:52.850
but the kids were not doing the kids weren't doing anything in math five years later. Whereas the ones that taught at the hardest, the kids got worse grades, the professors got poorly rated, and all the kids were in math somehow five years later.
576
00:52:53.330 --> 00:52:54.770
That's a generalization.
577
00:52:54.770 --> 00:52:56.290
But, like, that's essentially
578
00:52:56.530 --> 00:53:04.335
what like, it has to be hard. True. Yeah. Yeah. That actually that maps directly onto my experience just to flesh it out a bit that, you know, when I was saying primary
579
00:53:04.815 --> 00:53:07.135
school, secondary school, first year of uni,
580
00:53:07.454 --> 00:53:10.015
I just did it. I was good at it. I passed. Whatever.
581
00:53:10.494 --> 00:53:19.310
I think I don't know if it was this class exactly, but it was that kind of shift in the the the subject matter to some extent, the way it was taught to some extent.
582
00:53:19.550 --> 00:53:22.270
That was the first time I ever actually found it difficult,
583
00:53:22.589 --> 00:53:38.485
which was, like, a weird experience, but in hindsight was obviously incredibly valuable because prior to finding it difficult, I just didn't really care. I just say, okay. I'll just do it, and then we'll just get on with my day. Whereas now I was like, oh, shit. I actually, like, have to think about this. Like, I have to try to understand this,
584
00:53:38.885 --> 00:53:40.085
and that's much healthier.
585
00:53:40.165 --> 00:53:41.925
Why didn't they do that when I was five?
586
00:53:43.490 --> 00:53:55.490
Well and I think it's another part of the problem, like, asked this I think a big part of the problem in the way education is done, it's very linear and gated. Meaning you know? And it's like, you have to do step one before you do step two.
587
00:53:56.255 --> 00:54:04.015
And I just remember, like, I hated high school. I really didn't go for, like, two years till I got caught. I just caught school.
588
00:54:04.975 --> 00:54:16.020
But for some reason in high school, I've told a story before. I I couldn't figure out what a logarithm was or did. And I just it was like one of those things I accepted. I guess I'm never gonna know what this thing is. It's fine. Whatever.
589
00:54:16.180 --> 00:54:23.300
And then, you know, I go to college and I take physics and I take calculus and I'm like, what? Wait. Wait a second. This makes total sense.
590
00:54:23.700 --> 00:54:33.395
You know, why didn't they teach it? And, you know, why didn't they let me why didn't they let me do this when I was in high school? Or why didn't you know? And I feel like a lot of even now with the AI
591
00:54:33.555 --> 00:54:36.275
math platforms, they're all very gated.
592
00:54:36.435 --> 00:54:45.060
Like, that's the whole value that they provide is that they don't unlock the next level until you gain mastery over the certain thing. And I'm kinda not into that. I kinda
593
00:54:45.460 --> 00:54:47.380
like offering every class
594
00:54:47.460 --> 00:54:52.260
and because you never know, again, what shop's gonna take that tree down or what's gonna make it make sense.
595
00:54:53.140 --> 00:54:55.060
So curious your thoughts on that one.
596
00:54:56.035 --> 00:54:58.915
I mean, I disagree. I'm sorry. I don't have anything in there.
597
00:55:00.115 --> 00:55:00.755
That
598
00:55:01.475 --> 00:55:03.395
is my experience. Yes.
599
00:55:04.835 --> 00:55:05.875
Yeah. As
600
00:55:06.355 --> 00:55:14.450
I build the Math Academy, it's something I think about a lot, which is like making everything available. It not it's really hard to do to teach nonlinear
601
00:55:14.450 --> 00:55:18.610
and nonlinear. You know, it's much easier obviously to say I value because,
602
00:55:19.330 --> 00:55:25.255
you know Yeah. I'm not gonna let you into the I'm not gonna let you into the deep end until you can do the doggy battle. Right?
603
00:55:26.295 --> 00:55:27.015
Yeah. Absolutely.
604
00:55:27.575 --> 00:55:28.295
Yeah. I
605
00:55:29.255 --> 00:55:30.615
as a brief tangent,
606
00:55:31.015 --> 00:55:32.935
have you heard guys heard of Alpha School?
607
00:55:33.415 --> 00:55:35.735
Nope. No. So long and short,
608
00:55:37.290 --> 00:55:39.530
I I this is top of mind because,
609
00:55:39.850 --> 00:55:43.370
the principal, but basically the founder of it,
610
00:55:44.090 --> 00:55:45.290
was a successful
611
00:55:45.450 --> 00:55:47.130
b to b SaaS entrepreneur,
612
00:55:47.210 --> 00:55:48.410
you know, multibillionaire,
613
00:55:48.410 --> 00:55:56.495
took a billion dollars out of the company. It was all bootstrapped. So he took a billion dollars out and put it into this company called, Alpha School. And it was they had this one campus in Austin,
614
00:55:56.895 --> 00:56:01.535
and they do two hours a day of AI structured learn like learning.
615
00:56:01.695 --> 00:56:09.490
And then you get four hours of doing whatever you want to where the kids are, like, making food trucks or they're becoming elite competitive athletes or they're doing whatever.
616
00:56:09.809 --> 00:56:10.930
And they
617
00:56:11.250 --> 00:56:12.690
had this brilliant strategy
618
00:56:13.730 --> 00:56:25.135
of how they recruit people. Like for students is they ask you to go to your all these private charter schools. People are paying $50,000 a year for their kids to go. And you say, hey. Can I see the school's standardized test results?
619
00:56:25.615 --> 00:56:39.390
And they wouldn't give them. Almost no one does that. But they would, and they would be like, well, we're top 1% of everything. And they're talking about, like, the nature of learning. But the way they and they now have, like, dozens of campuses in The United States. They're looking to open one up in Nashville, so we went to just like see what it is.
620
00:56:40.830 --> 00:56:41.550
They
621
00:56:41.710 --> 00:56:44.270
find this sweet spot for kids
622
00:56:44.510 --> 00:56:46.590
that they need to when you're structuring
623
00:56:46.830 --> 00:56:54.155
education and you're testing them, they need to get answers correct between 7580%
624
00:56:54.155 --> 00:56:56.555
of the time. If it's higher than 80%,
625
00:56:56.635 --> 00:56:58.875
the students start to disengage from the material.
626
00:56:59.355 --> 00:57:01.835
And if it's lower than that, they get demoralized.
627
00:57:02.315 --> 00:57:05.435
So you want to be in this constant steady state of friction
628
00:57:06.039 --> 00:57:06.839
where
629
00:57:06.920 --> 00:57:13.000
they're not gonna know, like, I know every answer, so I'm not gonna apply myself or I can't get any of these right, so I'm going to fail.
630
00:57:13.240 --> 00:57:15.320
And what they're doing now, they're
631
00:57:16.039 --> 00:57:26.185
they've been massively successful. They're always, like, top 1% test scores, like and they've been totally mocking the educational institute. And then what they did is they went to all of basically the Silicon Valley
632
00:57:26.424 --> 00:57:30.505
founders and got their kids to go. And then they made it like this really sexy brand
633
00:57:30.905 --> 00:57:31.944
to pull everyone in.
634
00:57:32.930 --> 00:57:36.930
But I think it just goes to this, like, the the point of learning and structuring things where,
635
00:57:37.490 --> 00:57:38.769
you wanna constantly
636
00:57:39.009 --> 00:57:55.015
like, and Brian talking about, like, the Math Academy, letting people self explore and figure these things out. But if you I I massively looking back on it, I massively disengaged from math, not because I didn't understand it, because I was bored. And I was able to half wing it. I was able to, like, without applying myself, wing it.
637
00:57:55.415 --> 00:58:00.770
And then you have deficiency gaps because since you're kind of winging it, you never solidify those core foundations.
638
00:58:00.930 --> 00:58:05.010
But that's what changed when I got to college. Since it was all much more self directed,
639
00:58:05.250 --> 00:58:18.095
it was a better environment for me to be able to excel and learn and find passion. And you you you briefly touched on this, Alan, and we moved past it. The idea of having passion in what you do and its ability to remove friction.
640
00:58:18.655 --> 00:58:20.895
When you're passionate about an idea in a subject,
641
00:58:21.055 --> 00:58:30.220
you are no longer doing work, you're doing play. And when you're doing play, you're actually self amusing, and you're gonna have infinite more stamina because you're not taxing like your reserves.
642
00:58:30.380 --> 00:58:37.500
And that is something I think that's generally lost. And I think the the way math works in education in general is it's just constant friction.
643
00:58:37.740 --> 00:58:47.465
Either friction because you get it and you're bored, so then you stop applying yourself and then you're kind of like trying to figure your way out as you go along, or it's just so hard you'll never figure it out.
644
00:58:47.945 --> 00:58:51.545
Mhmm. Just a a random thing to drain your will.
645
00:58:51.945 --> 00:59:03.359
Right? And and, Brian, this is more to your point too. Like, they just want a bunch of obedient people. And that, like, for powers that be in power structures that exist in the world, if peep of a a lot more people were just genuinely passionate about math
646
00:59:03.920 --> 00:59:05.840
in an end of itself.
647
00:59:06.079 --> 00:59:19.325
Not I need a math degree because I'm gonna be an engineer or I need to pass this math exam with a good score so I can get into a good college. Right? If it was actually the end of with of itself that you would have a much more, you know, prosperous society. They're
648
00:59:19.325 --> 00:59:24.205
just training us to be obedient factory workers, man. It's not fair.
649
00:59:24.810 --> 00:59:25.530
Yeah.
650
00:59:26.650 --> 00:59:27.290
Yeah.
651
00:59:29.210 --> 00:59:32.810
But it is I would say having a lot of people who have
652
00:59:33.210 --> 00:59:36.330
high conviction in their own abilities to reason is
653
00:59:36.970 --> 00:59:37.370
probably,
654
00:59:38.335 --> 00:59:39.055
you know,
655
00:59:40.095 --> 00:59:41.055
dangerous.
656
00:59:41.295 --> 00:59:43.455
You know? Sure. Some people that's
657
00:59:43.855 --> 00:59:58.869
you know, I do think that's a a motivation. Although, I don't know that they have to do anything intentionally to stop it because people naturally don't wanna do the work. You know? It's it's not I don't know. Like, it's one of those things. It's kinda like you don't have to stop people from learning to be black belts either. Right?
658
00:59:59.109 --> 01:00:00.630
You don't need an artificial
659
01:00:00.869 --> 01:00:05.750
like, nobody in power is like, oh, there's too many black belts running around. We have to do something about this. Right.
660
01:00:06.605 --> 01:00:09.405
I I don't think they need to do anything necessarily,
661
01:00:09.405 --> 01:00:14.285
but I think that the way it's evolved the way math education evolved does have that effect.
662
01:00:14.525 --> 01:00:15.885
Gentle nudging.
663
01:00:15.885 --> 01:00:18.605
Yeah. And let and let inertia take over the rest.
664
01:00:21.250 --> 01:00:22.690
It's not fair, man.
665
01:00:24.130 --> 01:00:27.730
That's like every Bitcoin book, by the way. Right? Well,
666
01:00:29.170 --> 01:00:42.715
Alan, speaking of Bitcoin books, why wasn't there Bitcoin is math section of Bitcoin is Venice? It's just that Bitcoin is math. There's some math trickled in there, but I that's why I was saying before, I couldn't remember if the probability stuff was in there or not. And then I remembered I re pulled it out into the other one.
667
01:00:43.275 --> 01:00:47.435
That's right. Why isn't there I know you're asking as a joke, but I'm now tempted to give a serious answer.
668
01:00:49.490 --> 01:00:50.210
Because
669
01:00:50.530 --> 01:00:52.930
the point of Bitcoin is Venice
670
01:00:53.010 --> 01:00:56.050
is to trick people into recognizing
671
01:00:56.050 --> 01:00:56.690
that
672
01:00:56.850 --> 01:00:57.570
they
673
01:00:57.730 --> 01:00:59.410
understand economics
674
01:00:59.410 --> 01:01:00.370
enough
675
01:01:00.609 --> 01:01:03.410
to like Bitcoin without knowing it.
676
01:01:04.125 --> 01:01:04.685
And
677
01:01:05.725 --> 01:01:07.405
there's occasionally
678
01:01:07.405 --> 01:01:10.445
a point where math can nudge that along. But,
679
01:01:10.765 --> 01:01:12.285
again, I don't wanna become
680
01:01:12.605 --> 01:01:14.045
Neil deGrasse Tyson.
681
01:01:14.205 --> 01:01:18.925
I don't wanna be, oh, I fucking love math. Here's some math that is irrelevant.
682
01:01:19.350 --> 01:01:29.830
And how Bitcoin is hides like, Bitcoin enforces math. That's one of those things I guess, I think I was really just triggered into being here right now by all the Bitcoin books I read when I got into Bitcoin. Because
683
01:01:30.550 --> 01:01:33.190
I don't get it, like, oh, it solves a math problem.
684
01:01:33.670 --> 01:01:43.835
Yeah. Yeah. I do believe, like, the the phrase sovereignty through mathematics to me is evokes this really beautiful thing, and I think that is a lot of what I focus on here. Right?
685
01:01:44.235 --> 01:01:54.120
So it because that's really being con you know, having conviction in yourself. To me, that's like the final boss of really if you'd are you really gonna huddle your stack forever or for how long you need to?
686
01:01:54.760 --> 01:01:58.600
The space between your ears is really gonna be the the big boss
687
01:01:59.000 --> 01:01:59.640
of
688
01:01:59.880 --> 01:02:07.605
you know? Because, you know, and you just see it, these FUD attacks. They come on fast. They come on furious. And the next thing you know, you're a former Bitcoiner.
689
01:02:08.565 --> 01:02:09.285
Yeah.
690
01:02:10.484 --> 01:02:17.365
Well, I there's a fun link here to something that we've talked about offline, Ryan. I don't know what extent you wanna go into. Although you're kinda doing it now. Like, I'm just,
691
01:02:18.540 --> 01:02:29.660
you know, daydreaming about one day doing it that when Bitcoin moons and we all retire and we can just think for for I was gonna say think for a living, but not just think to pass the time. That that I had this idea of
692
01:02:30.234 --> 01:02:32.315
really wanting to write a textbook.
693
01:02:32.714 --> 01:02:33.755
And it's like,
694
01:02:33.915 --> 01:02:40.795
I was just stopping myself writing because this won't happen for at least five or ten years and maybe just never. This is massive, massive endeavor.
695
01:02:40.795 --> 01:02:42.555
But, nonetheless, I would like to,
696
01:02:42.795 --> 01:02:44.860
at one point, have the time to,
697
01:02:45.180 --> 01:02:47.180
to write the textbook, which is basically
698
01:02:48.140 --> 01:02:49.420
explaining
699
01:02:50.540 --> 01:02:53.660
all of the math you need to understand
700
01:02:53.820 --> 01:02:54.540
Bitcoin,
701
01:02:55.180 --> 01:02:56.700
but with a very similar,
702
01:02:57.975 --> 01:03:00.855
what's the best way of putting this, a similar attitude
703
01:03:01.175 --> 01:03:05.575
to the goal of Bitcoin as Venice, but obviously written in a completely different way.
704
01:03:06.455 --> 01:03:16.150
So nothing to do with economics and none of the, like, rhetorical flourishes or whatever. It's like a real text. Right? Like, a proper you know, you could have you could build a class around it if you wanted to. But the point being,
705
01:03:16.390 --> 01:03:21.670
it's aimed at people, basically mathematicians or or or at least people who
706
01:03:21.910 --> 01:03:25.109
have a pretty solid academic grounding
707
01:03:25.109 --> 01:03:25.829
in
708
01:03:26.465 --> 01:03:34.065
probably pure math because it's all not all. It's, like, mostly rooted in number theory, let's say. But the but the way it's presented is just like,
709
01:03:34.465 --> 01:03:36.065
these are the building blocks.
710
01:03:36.305 --> 01:03:38.545
Now you understand them mathematically.
711
01:03:38.545 --> 01:04:02.295
Here's how they plug into Bitcoin. And, actually, I can imagine it going the other way too. I would want it to be written in such a way that interested Bitcoiners would also read it because they're like, oh, well, I know the coal, but, like, I wanna know the nuts and bolts of it now too. This is So, yeah, one day I'll do that. This is this is why we've done probably eight hours on just elliptic curves. We've done eight hours just on elliptic curves. We the the first episode,
712
01:04:02.375 --> 01:04:04.375
Alan, was modulo arithmetic
713
01:04:04.535 --> 01:04:11.300
with with modulo seven and just making a modulo table and then being like, okay. Now we're gonna take a really, really, really, really big number,
714
01:04:11.780 --> 01:04:15.300
and and that is doing modulo the Mersenne prime.
715
01:04:15.859 --> 01:04:25.734
Two to the two fifty six minus two to the two thirty two minus two to the six. Like, the exact the exact module of field Bitcoin uses. Yeah. Of course. Of course. Yeah. Of course. Yeah. Yeah.
716
01:04:27.015 --> 01:04:31.734
Yeah. And so, like, this is a Bitcoin truly was in many ways like this beautiful
717
01:04:32.535 --> 01:04:33.414
intersection
718
01:04:33.414 --> 01:04:43.870
of these very heavy mathematical concepts into a way that could actually sigh up people into caring about how it works. Because it's no longer a textbook thing. It's the math is the money.
719
01:04:44.350 --> 01:04:56.975
I I I when I stuff in Acrobat, I say, like, the code is the money. So, like, for the rigor of, like, deploying software, but the code is just a representation of the math. And so the the math being the money that you wanna get people interested in this stuff because
720
01:04:57.295 --> 01:04:59.935
how could you not want to be interested in
721
01:05:00.015 --> 01:05:12.310
how the whole thing works if you have your wealth stored in it? I can give you a really fun teaser here actually, and I might shoot myself in the foot in the sense that I'm not sure how much of this I actually remember even though I'm I'm gonna introduce the topic. But have I ever talked to either of you about
722
01:05:13.190 --> 01:05:14.150
hash functions?
723
01:05:14.230 --> 01:05:36.319
Just just as a I'll I'll give you more detail, obviously, but does this say, like, I'll need to help myself. I'm I'm buckled in because that's where actually where we're going to next so you can help do the we'll look for the next part of the course. Well, then you'll you'll have intelligent things to say to Finally. Intelligent things to It's a good change. Well, we have nothing intelligent. Maybe I thought I maybe spoken to Brian about this. I guess not, though. I I've spoken to James O'Byrne at enormous
724
01:05:36.319 --> 01:05:41.440
length about this. You should get him on, by the way, when you're doing your He's on the list. Oh, sorry. He's a friendly. Yeah.
725
01:05:42.880 --> 01:05:54.194
So you can ask him about it. He he he probably remembers. Although, he's just been, like, a word of I just throw 10 dumb ideas at him, and he tells me one of them is actually quite good. I'm like, yes. Yes. That's what I'm gonna go with. It was DLCVM.
726
01:05:54.194 --> 01:05:55.315
That was the good idea.
727
01:05:55.555 --> 01:05:56.435
Exactly.
728
01:05:58.115 --> 01:05:59.075
And I've spoken to
729
01:06:00.480 --> 01:06:02.720
Nifty a little bit about it as well.
730
01:06:03.600 --> 01:06:05.600
And I thought I'd maybe spoken to Brian. But, anyway,
731
01:06:06.960 --> 01:06:07.600
I
732
01:06:08.000 --> 01:06:09.600
in digging into it,
733
01:06:10.080 --> 01:06:13.119
I really don't think that people understand
734
01:06:13.119 --> 01:06:21.235
that much about hash functions. And I'll I'll I'll set up, like, what I mean by that because it's not very well defined the way I've just put it. So,
735
01:06:23.954 --> 01:06:40.870
actually, I'll back I'll backtrack just a second. But my my goal in terms of, like, where I wanna go this is I'd originally I wanna, like, write something on this. I'd I'd originally thought maybe actually a video would be the coolest output because a lot of it's kinda visual, and so sort of apologizing in advance if I don't explain it very well because, like, I have the picture in my head, but I would really need to draw some of it.
736
01:06:42.875 --> 01:06:49.035
But that content, whatever that is, would would address the following. Right? Like, this is the problem I'm I'm saying how to address. That if
737
01:06:49.515 --> 01:06:55.674
you ask someone and and, like, especially a Bitcoiner because, you know, they'll have a firmer grinding of, like, what the point of it even is.
738
01:06:57.320 --> 01:07:11.000
I think there's, like, two basic ways of sort of, quote, unquote, teaching someone what a hash function is. I would just say, like, chat two fifty six. It doesn't really matter which one because they all kind of have the same they work in different ways, but they do kind of the same thing in terms of the purpose of them.
739
01:07:12.515 --> 01:07:15.315
There's two basic ways of addressing it. So one is that
740
01:07:15.555 --> 01:07:16.195
you
741
01:07:16.755 --> 01:07:24.115
you you sort of literally describe what it does. Like, you specify the function. Right? And there's good videos for this on YouTube. Think
742
01:07:24.720 --> 01:07:37.440
what's the name of the learn me a bitcoin has a really good Yep. Do you guys remember him from Yep. A while ago. He he has a great one of, like, literally just running through what's happening inside a hash function, and you sort of see it working.
743
01:07:38.035 --> 01:07:43.075
And so that's cool. Right? So that's one way of approaching. It's like, okay. Well, you do the following, and that's what the function does.
744
01:07:43.315 --> 01:07:46.355
Another way of answering what is the hash function is
745
01:07:46.915 --> 01:07:48.995
the the characteristics
746
01:07:48.995 --> 01:07:53.960
that a worthwhile hash function embodies. Right? So it's like
747
01:07:55.480 --> 01:08:02.040
well, I mean, you guys know them. I don't need to run through it. But, like, what what the purpose of it is, you know, you get you get the output that it's it's nonreversible,
748
01:08:02.040 --> 01:08:12.855
and, ideally, there's no collisions. And Mhmm. You therefore can and you kinda quickly slip into more of the application rather than just the math. It's like, therefore, it achieves these things for you, and you can use it in mining, and you can use it in Mhmm.
749
01:08:13.175 --> 01:08:14.855
Know, whatever however else you wanna use it.
750
01:08:16.135 --> 01:08:20.455
Those are both good. And I think output, by the way, standard output is a real underrated
751
01:08:21.320 --> 01:08:22.920
property of hash functions.
752
01:08:23.080 --> 01:08:31.639
A standard Yep. Yeah. Exactly. Yeah. It's it's deterministic, so it's not like it's not just spewing random nonsense. And it but there's there's only there's, don't know, like, three or four of these properties.
753
01:08:32.120 --> 01:08:39.545
And I I I'd be surprised if you guys disagree with this that both of these, more so the second one, but I think to some extent the first one,
754
01:08:40.025 --> 01:08:42.344
you need to understand them to understand Bitcoin.
755
01:08:42.585 --> 01:08:56.400
Like, I I realize understand Bitcoin isn't very well specified, but whatever your minimum threshold for it is Absolutely. You need to be able to explain these things by hash. Yeah. Okay. So that's all well and good. But I started wondering,
756
01:08:57.440 --> 01:09:00.320
effectively, a third way of probing this, which is like, okay.
757
01:09:00.720 --> 01:09:02.560
I get that it
758
01:09:02.800 --> 01:09:04.400
has these characteristics.
759
01:09:05.095 --> 01:09:06.935
Right? And I get that
760
01:09:07.335 --> 01:09:10.534
doing these things, so the first explanation,
761
01:09:11.255 --> 01:09:14.135
gives rise to these characteristics.
762
01:09:14.535 --> 01:09:19.575
But why does it have these characteristics? Like, what is it about doing these things
763
01:09:20.110 --> 01:09:22.510
that creates these properties?
764
01:09:22.670 --> 01:09:23.710
So almost like
765
01:09:24.030 --> 01:09:40.704
I don't know if this is really all that helpful. This might be more confusing, but it's like, this is the this is the input, and, like, that's well understood. And, like, this is the output, and that's also well understood. But what's the throughput? Like, when you when you do these things and you get these things, why do you get these things? And
766
01:09:41.265 --> 01:09:52.230
I don't think anyone really knows. Like, honestly, this sounds hyperbolic, but I've done a lot of research into this, and I don't think there is a good explanation of this anywhere.
767
01:09:52.790 --> 01:09:54.390
Like, why the hash function
768
01:09:54.470 --> 01:09:56.790
does what it does? Like, how does it does it do it?
769
01:09:57.030 --> 01:10:05.275
Do it do it? How do it well, it's it's hard it's quite difficult to even specify the question. Like, this was this is probably the main help that James
770
01:10:05.675 --> 01:10:10.555
gave me when I was first outlining this was and and I'm now forgetting what he said, but but
771
01:10:11.195 --> 01:10:20.500
but in terms of, like, being specific in what it is I'm even asking so this is kind of addressing what you're getting at, Rob. I'll I'll try to articulate this as clearly as I can,
772
01:10:22.420 --> 01:10:26.500
and I'll probably fail. This is what I apologize for at the start because I haven't thought about this in a while.
773
01:10:30.835 --> 01:10:31.554
Why
774
01:10:32.915 --> 01:10:38.114
you do these things. Right? You have the inputs or you have answer number one. You do all of these things.
775
01:10:38.915 --> 01:10:42.275
Why do you get answer number two and not
776
01:10:42.850 --> 01:10:43.650
say
777
01:10:43.730 --> 01:10:57.330
answer number three? Or another here's another way of thinking about it. Say your goal is to get answer number two. Right? But you don't actually know about answer number one. How would you go about constructing such a thing that gives you answer number two?
778
01:10:58.715 --> 01:11:05.675
And, again, this isn't, like, very this is still not very well specified, but I feel like I have a good intuition of this that I'm still failing
779
01:11:05.835 --> 01:11:08.795
to articulate well. But it's it's basically,
780
01:11:08.795 --> 01:11:09.274
like,
781
01:11:09.675 --> 01:11:11.755
I don't think this is what I started off saying.
782
01:11:12.310 --> 01:11:16.469
I'm convinced that no one really understands
783
01:11:16.469 --> 01:11:21.269
this. And the caveat I was gonna make, this is really important because I don't want this to sound horrifically arrogant.
784
01:11:21.350 --> 01:11:28.385
When I say no one really understands, I think almost everyone I mean, certainly, cryptographers, like professional or academic cryptographers
785
01:11:28.385 --> 01:11:29.185
for sure
786
01:11:30.305 --> 01:11:36.705
are not confused about this. It's not like it's an open problem. Right? Like, they understand how hash functions work.
787
01:11:37.185 --> 01:11:40.465
It's more like it's more a problem of education.
788
01:11:40.465 --> 01:11:42.760
It's that I am not
789
01:11:44.360 --> 01:11:46.280
I am convinced this understanding
790
01:11:46.280 --> 01:11:49.320
is out there, but it's entirely
791
01:11:53.000 --> 01:11:57.954
I don't I actually have no idea what the right way of describing this is. It's only in people's heads.
792
01:11:58.195 --> 01:12:02.034
Right? Like, everyone who's worked with this stuff Gaussian. Gets this,
793
01:12:02.355 --> 01:12:13.699
but they've never had to explain it. And so the explanation is not in writing anywhere. And so I wanna write it. Like, the the exact properties of how these functions work and the the
794
01:12:14.020 --> 01:12:16.099
actual application of making these things
795
01:12:16.659 --> 01:12:17.939
these hash functions
796
01:12:18.020 --> 01:12:21.780
correctly work in the expected format being Yeah. I like, well document.
797
01:12:22.305 --> 01:12:29.905
I I think I think a nice way of because this is the way I arrived at it. Like, this is literally what I was asking myself and trying to find an answer to is
798
01:12:30.705 --> 01:12:45.430
there's no good written answer for why does it do that. So not does it do that or even how does it do that. Because how does it do it is part one. Right? It's, answer for one. You do is do this. Mathematical proof of why the things we do in these hash functions
799
01:12:46.070 --> 01:12:47.670
obtain all of these properties
800
01:12:47.845 --> 01:13:15.380
that So this is really interesting. I talked to James a lot about this. I have no idea. Like, I'm completely on the fence because I haven't done enough work on it yet as to whether an actual mathematical proof could even exist. Well, so the there is no mathematical proof for elliptic curve like what we use for LIBSEC p. There it's it's just a brute force of the the space of how many numbers in this modular prime field we're operating on is so vast that we're kind of operating in a security assumption of obscurity.
801
01:13:15.755 --> 01:13:19.434
Not a formal security proof being like this is perfect and this works.
802
01:13:20.395 --> 01:13:43.280
Maybe hash functions are in the same way where we're just throwing so much entropy into the system that we're like good luck reverse engineering this as opposed to a rigorous mathematical proof as to why it has these properties. That's not quite what I mean. I wanna push it a little bit. It's on the right track, but I wanna push it a little bit. It's more of the hand waving. It's more like you kinda start off assuming it does work. Like, it's it's sort of feels like it certainly works.
803
01:13:43.885 --> 01:13:45.405
And it's just driving
804
01:13:45.405 --> 01:13:46.125
at
805
01:13:46.765 --> 01:13:47.725
giving
806
01:13:47.725 --> 01:13:48.364
a
807
01:13:49.005 --> 01:13:50.685
this, I think, is the
808
01:13:51.325 --> 01:13:55.565
the security proof for for elliptic curves is is is a great comparison here
809
01:13:56.205 --> 01:14:02.950
because I think, actually, in that realm, essentially, you you understand this a lot better than I do, Rob, but I've I've looked into this a little bit years and years ago.
810
01:14:03.670 --> 01:14:09.510
It's it's sort of the parameters of the problem are well understood even though there's no, like, there's no proof,
811
01:14:09.830 --> 01:14:23.175
but you can say you can very intelligently say quite a lot about why there's no proof or, like, what a proof would look like if there were such a thing or why there might not be like, it's sort of it's understood as a problem even though the answer isn't known.
812
01:14:23.895 --> 01:14:25.574
As far as I'm aware,
813
01:14:26.215 --> 01:14:36.800
for hash functions, what it is I'm driving at is just again, I gotta be careful how I say it. It's not that no one understands this. It's it's almost like the opposite. It's like, because everyone understands it,
814
01:14:37.120 --> 01:14:54.324
no one bothers explaining it. So there's no way to there's no way to, like, effectively learn this. This is actually kind of an interesting link back to all the educational stuff that the only way to learn it is to just become an expert by kind of brute force of using it. I But there's no good theoretical explanation.
815
01:14:54.325 --> 01:15:07.720
Alan, I think what you're doing is you're charging Brian and I with a mission for our next eight episodes when we go into HUD functions to answer this question for you. Well, no. This You're sniping my future content. This is I'll do in five years to never. Consider yourself sniped, but, like,
816
01:15:08.360 --> 01:15:11.244
this is of great interest. This is of great interest.
817
01:15:11.485 --> 01:15:16.284
And I like, if I'm understanding you, you know, you'd say, like, maybe nobody
818
01:15:17.085 --> 01:15:24.124
everyone understands what a hash function does, but, like, if you were asked the SHA two fifty six versus RipeMD
819
01:15:24.125 --> 01:15:24.844
one sixty,
820
01:15:25.929 --> 01:15:38.409
You know? A good one would be why is MD five and SHA one now insecure, Brian? That's a perfect example because MD five, which was, like, the hash function of, like, the early two thousands and SHA one are now both insecure.
821
01:15:39.055 --> 01:15:54.335
And so, like, what happened that made those specifically insecure? Mhmm. Like, why why is SHA two okay? Yeah. Yeah. Like, why is SHA two fine, but why is SHA one now busted? Like, that's perfect. Yeah. So but the ultimate tease, though. Right? So that's biggest tease because I don't see how we can possibly cover it on this podcast.
822
01:15:55.850 --> 01:15:59.770
I having thought about this quite a lot and having spoken to the handful of people I mentioned,
823
01:16:00.090 --> 01:16:06.810
I feel like I kind of know the answer. It's just very difficult to articulate it.
824
01:16:07.130 --> 01:16:07.850
And
825
01:16:08.844 --> 01:16:12.925
pretty much every aspect of it is, for me at least, is much
826
01:16:13.244 --> 01:16:20.124
more easy easily conveyed visually. So, like, I could draw you a picture and hold it up to the camera, but I'm really not sure I could explain it verbally.
827
01:16:21.165 --> 01:16:24.590
So that's why I'm excited that it doesn't feel, like, completely intractable.
828
01:16:24.590 --> 01:16:28.030
It's like, I've thought about it enough to say something intelligent.
829
01:16:28.270 --> 01:16:45.754
I just need a lot more time than I have. I need Bitcoin to moon so we can all retire, and I can do all these vanity math projects once again. We're gonna do our part by we're gonna do subpar versions of this and just have you angrily angrily come out and just do it. You know? Nice.
830
01:16:46.074 --> 01:16:50.900
You know, one of the first things I ever wrote when I came into the Bitcoin space was
831
01:16:51.140 --> 01:16:56.260
I had done nifty's base 58. I was completely enamored by the base 58 curriculum.
832
01:16:56.740 --> 01:17:09.614
And I wrote this thing called highway to hex, which is like a play on the song highway to hell. And I thought it was so cool that, like, ACDC was, like, about power and electrical power and, you know, that Bitcoin miners to do all this hashing.
833
01:17:10.094 --> 01:17:22.619
And in the song itself, highway to hell, they have lyric, like season ticket on a one way ride. Like they have like, it's like you know, the song itself is like, you're going to hell. It's a one way function. You're you can never come back.
834
01:17:23.340 --> 01:17:23.979
Lovely.
835
01:17:24.380 --> 01:17:27.260
And I thought that was so freaking cool. I just thought that whole
836
01:17:27.500 --> 01:17:30.780
I don't know. Like, I just thought it was so cool. And, like, let's like,
837
01:17:31.485 --> 01:17:54.389
in the blog post, I had a, like, a one of those embedded just like, oh, type in an input and do the hash function just so you could see, like, how, you know, how different and what actually comes out of it. But I really like this. Like, now you really triggered me really because now that we have the AI, we can really, I think, do a really detailed Oh, oh, this is super interesting, actually.
838
01:17:54.950 --> 01:17:56.950
No. I don't think you will be able to. So that this is
839
01:17:57.830 --> 01:17:59.990
that this is another good five, ten minute tangent.
840
01:18:00.765 --> 01:18:01.965
What got me
841
01:18:02.605 --> 01:18:05.245
completely convinced that this is a worthwhile problem
842
01:18:05.405 --> 01:18:06.125
is
843
01:18:06.605 --> 01:18:14.125
AI's inability to give me a good answer. And, actually, I ended up having I got completely sidetracked in my discussion with James about this
844
01:18:14.530 --> 01:18:20.050
because we ended up veering off into a, like, philosophy of LLMs conversation
845
01:18:20.050 --> 01:18:25.170
instead, which I can now spring on you and and hijack even more of of this discussion,
846
01:18:25.650 --> 01:18:31.465
that we we came up with this this kind of amusing heuristic, which I'm sure a lot of people have stumbled into independently.
847
01:18:31.545 --> 01:18:37.065
Like, you guys I know you you've both mentioned even on this podcast how much you use it. I'm sure you've you've encountered this.
848
01:18:37.465 --> 01:18:38.025
That,
849
01:18:39.065 --> 01:18:40.745
basically, if you can
850
01:18:41.380 --> 01:18:43.059
get given how
851
01:18:43.700 --> 01:18:44.660
LLMs
852
01:18:44.660 --> 01:18:51.300
are are are trained effectively, like how they arrive at the, you know, the the knowledge they have, if that doesn't trigger you too much,
853
01:18:53.085 --> 01:18:54.284
It's
854
01:18:54.364 --> 01:18:55.645
a reasonable
855
01:18:55.645 --> 01:18:58.925
assumption. It's not a proof, but it's a decent heuristic
856
01:18:59.085 --> 01:18:59.804
that
857
01:19:00.045 --> 01:19:01.804
if you can
858
01:19:02.045 --> 01:19:03.085
repeatedly
859
01:19:03.085 --> 01:19:04.925
prompt it about
860
01:19:05.485 --> 01:19:07.565
something that you suspect is
861
01:19:07.850 --> 01:19:11.530
a worthwhile problem, right, and an open problem, more importantly.
862
01:19:12.170 --> 01:19:16.810
And no matter how hard you try, it just gives you nonsense back. Right.
863
01:19:16.970 --> 01:19:29.574
That is the confirmation that it is in fact an open problem. Right. And so that's so that's how I so I don't think this is gonna work. Right? If you do this, tell me what happens because Interesting. I didn't take this that seriously
864
01:19:29.815 --> 01:19:41.730
until I did my little prompting exercise. And then I was like, oh, shit. Like, really no one knows this. So I was talking with, Jesse Posner in Vegas about this and someone who's a classic
865
01:19:42.290 --> 01:19:56.314
like, with a lawyer and philosopher, but then also just started, like he was explaining to me his educational background in math was they were all primary sources. There was no hand wave. You had to start from he never even got the set theory in his math education because it was all foundational stuff.
866
01:19:56.635 --> 01:20:01.994
And he was talking about casually his idea of these large language models and how they know knowledge.
867
01:20:02.510 --> 01:20:06.670
He got very philosophical in that there is probably a universal abstract
868
01:20:07.310 --> 01:20:10.750
platonic sense of weights and biases of the world,
869
01:20:11.310 --> 01:20:13.550
of a knowledge map of everything.
870
01:20:14.030 --> 01:20:22.244
And the domain in which we understand is where it works. And this would go to your point, Alan, that, like, the moment you step outside its box of, what it's trained in understanding,
871
01:20:22.485 --> 01:20:25.124
it's like stepping off into a cliff. It's pure gibberish.
872
01:20:25.284 --> 01:20:40.379
And you have to kinda, like Yeah. Yeah. Re pull it back in. And and the examples of what people have done so far with discovering or proving new things that are outside the knowledge with LLMs is they basically provide this very rigorous scaffolding of like, these concepts are true.
873
01:20:40.699 --> 01:20:55.125
Now I need you to instead of tell me the answer, I need you to iteratively go through the scaffolding to try and get like one step further out into the unknown to try and build a bridge of knowledge with these things. Yeah. Oh, and actually, there's one there's a final really fun link I can make here.
874
01:20:55.605 --> 01:21:02.659
I'm not sure how much time you have, how willing you are for this to continue to be hijacked. But this will ring a bell for Brian that
875
01:21:03.219 --> 01:21:10.739
when this is actually the exact order in which this happened. When I then it was this problem. It was the hash function thing that gave rise to this heuristic
876
01:21:10.900 --> 01:21:15.780
and this realization of how interesting this is. As much about LLMs as about
877
01:21:15.495 --> 01:21:16.534
the given topic.
878
01:21:16.775 --> 01:21:18.854
But that then I
879
01:21:19.335 --> 01:21:28.374
didn't grasp this immediately, but once it kinda sank in and I talked to James about it for a bit, what it was we were witnessing and what the implication of this was. I then went back
880
01:21:28.695 --> 01:21:29.655
and did
881
01:21:29.975 --> 01:21:30.455
the
882
01:21:31.330 --> 01:21:33.330
basically, the the problem
883
01:21:33.489 --> 01:21:35.809
this is tying really fun loose ends together.
884
01:21:36.770 --> 01:21:58.165
A while ago, I was saying, you know, I I by the very end of undergrad, I was the most interested in math I'd ever been, and then I just had to stop and go get a real job. Right? The problem that I had narrowed in on that I've said to you, Ryan, you know, one day, we just we will retire, and I go and do a PhD on this. I fed that in as well, and the same thing happened. And I was like, yes. Yes. This is real. Like, this is actually worth going
885
01:21:58.165 --> 01:22:05.510
and learning about. And And then the even funnier thing, I don't know if you guys have experience with this, but I so I use three LLMs,
886
01:22:05.910 --> 01:22:07.750
and I have
887
01:22:08.710 --> 01:22:12.710
I don't even know. Like, I've actually never asked anyone about this. I don't know if this is consensus or
888
01:22:13.045 --> 01:22:14.165
I I have,
889
01:22:14.485 --> 01:22:17.045
for me, at least discovered that they're good at different things.
890
01:22:17.605 --> 01:22:23.925
So I use Grok for anything that's like it's basically just a substitute for Google. It's like, can you Google this for me? Grok. I
891
01:22:24.805 --> 01:22:31.889
use Claude for anything that's, like, vibe coding. I don't do any remotely serious vibe coding. I'm just, like, pissing around.
892
01:22:32.610 --> 01:22:33.409
Or
893
01:22:34.050 --> 01:22:36.369
real, like, quote, quote, real research,
894
01:22:36.849 --> 01:22:37.329
but
895
01:22:37.650 --> 01:22:39.249
provided it's
896
01:22:39.250 --> 01:22:40.050
in English,
897
01:22:40.614 --> 01:22:43.175
at which I'm making that qualification
898
01:22:43.175 --> 01:22:45.735
to then set up perplexity
899
01:22:45.735 --> 01:22:47.415
for math. Perplexity
900
01:22:47.415 --> 01:22:50.775
is by far the best for exactly this kind of stuff in my experience.
901
01:22:51.175 --> 01:22:53.574
And but even that, I didn't fully
902
01:22:54.130 --> 01:22:57.170
realize. I kind of hacked my way to this understanding
903
01:22:57.170 --> 01:22:57.810
because
904
01:22:58.370 --> 01:23:01.570
with the my eventual PhD question,
905
01:23:02.290 --> 01:23:04.370
what happened with Grok was
906
01:23:04.450 --> 01:23:11.434
I pushed it far enough that it was just giving me no. It's funny. You said gibberish a minute ago, Rob. It wasn't exactly gibberish. It was just like
907
01:23:12.554 --> 01:23:14.074
it was coherent,
908
01:23:14.715 --> 01:23:15.114
but
909
01:23:15.515 --> 01:23:16.874
consistently
910
01:23:17.435 --> 01:23:25.130
like, not even wrong, just, like, almost refusing to understand what I'm saying. That's like what it felt like in terms of if you're, you know,
911
01:23:26.250 --> 01:23:27.850
what's the word, like anthropomorphizing
912
01:23:27.850 --> 01:23:33.850
its response. It's like, you wanna just shake it and be like, no. That's not what I that's not what I asked you. Right? Whereas
913
01:23:34.105 --> 01:23:35.145
perplexity
914
01:23:35.145 --> 01:23:40.104
pretty quickly was like, no. You're right. That's a good question. I'm like, thank you. It is a good question.
915
01:23:41.465 --> 01:23:47.465
I really thought so. I found perplexity to be really good at, like, surprised me the most in terms of its
916
01:23:48.390 --> 01:23:50.310
feels like its ability to reason.
917
01:23:52.230 --> 01:23:55.910
I've so I've actually I've only really tried it for this kind of thing.
918
01:23:56.710 --> 01:24:06.045
If you have recommendations for other ways of using it, hoping to Yeah. I've I've used it more in my It's really good on that side. Professional life. But, like, yeah, like, I thought Claude was pretty good, though, at
919
01:24:06.925 --> 01:24:17.485
like, on the website, when I brought in these textbooks, a lot of them left proofs to the reader, but I wanted the proofs to be clickable Mhmm. On the sites, and I had it. So I've said, if there's no proof, just create one. And,
920
01:24:18.300 --> 01:24:28.699
I think one day my daughter will go through and check all of them to make sure they're right. No. Just be complete nonsense. But my spot checking of them is like, well, yeah, did a reasonable job of creating these things.
921
01:24:30.140 --> 01:24:31.980
I mean, that's where we are right now at least,
922
01:24:32.985 --> 01:24:38.025
which is a far cry from where we were two years. Two years ago, I remember doing this experiment
923
01:24:38.185 --> 01:24:45.305
with a long division in chat GPT. I gave it, like, a 100 long division problems, and it got, like, 20 of them. Right? Right.
924
01:24:46.620 --> 01:24:49.100
Yeah. Yeah. They've they've all recently,
925
01:24:49.260 --> 01:24:49.980
I think what they
926
01:24:51.020 --> 01:25:01.205
Claude, like, Alan, your point about, like, anything vibe coding Claude. I would say over the past two months, OpenAI's codex is now the better one because what happened was six months ago So
927
01:25:01.765 --> 01:25:06.965
for Claude. Come on. No. Claude's good. No. No. Claude's still good. But, like, as the observation here,
928
01:25:07.285 --> 01:25:11.365
Anthropic was, like, extremely narrowly focused on just doing code things.
929
01:25:11.940 --> 01:25:27.620
And OpenAI was like, oh, we're gonna make boomer video generated slop, like like the Sora model. And, like, they got distracted and they realized, Hey. Like, what are we doing here? We're a tech company. Obviously, the software piece, you can just write the software scaffolding to do all of the other fun things later, make the software really, really good.
930
01:25:28.655 --> 01:25:31.775
And I think to your point, Brian, about like long division,
931
01:25:31.935 --> 01:25:41.695
this is like the classic, like, you know, how many hours are there in strawberry? And like up until maybe three months ago, we couldn't answer that question because it didn't have the rigor. It was just doing the token piece.
932
01:25:43.080 --> 01:25:44.280
All that to say,
933
01:25:45.719 --> 01:26:06.565
I'm keeping a close eye on all of it. Like, the rate of acceleration has been very impressive. The the the just in general. Just the the rate of the compounding growth and acceleration of all this stuff and its ability to be productive is just You reminded me of another really funny meme there, though, Rob, the Go for with the whole that, like, the this is what I actually thought you were gonna say, the realization that if you if you just nail
934
01:26:06.805 --> 01:26:28.515
software, then actually everything else kinda follows from that. Yes. But then but then all the tech bros, like, extrapolating that to be like, well, that's because the universe clearly is code. Like, that's what we Right. But then but then the meme is, like, putting this in the historical context of, you know, five minutes after have you seen this one? It's five minutes after inventing the wheel. Like, guys, what if the universe is all just like revolutions?
935
01:26:28.515 --> 01:26:44.410
Right? And then five minutes after inventing the mechanical clock, guys, what if the universe is all just a Newtonian machine? And it's like right. And then I forget I think there's another one, but then now it's five minutes after inventing the LLM. Guys, what is the universe? It's just like a language model.
936
01:26:44.730 --> 01:26:48.810
So you're saying Bitcoin podcasts have existed for all time.
937
01:26:49.850 --> 01:26:51.930
That's right. Basically,
938
01:26:51.930 --> 01:26:53.930
the universe is a big one big Bitcoin podcast.
939
01:26:55.105 --> 01:26:57.744
That's what it is. Exactly. I
940
01:26:58.784 --> 01:26:59.344
mean,
941
01:26:59.665 --> 01:27:00.304
I
942
01:27:00.864 --> 01:27:24.534
I hate to end this party, but I need to start No. Winding it down. Stay on for another hour and a half, Rob. That's right. And and then I'll I'll tell Becca that I had to create shareholder value by talking to my investor about math. She'll love that. She'll love what what you tell her, right, is that it's only by going pointlessly deep on pure subject matter that we inadvertently
943
01:27:24.534 --> 01:27:28.454
create the tools for practical value. And so that is why
944
01:27:28.775 --> 01:27:43.609
So that's actually with Alan this whole time. That is genuinely true, though. The whole building Trident Vault was me autistically spiraling about how to make more secure Bitcoin vaults. And then like so that is actually earnestly, like, people think innovation happens in, like,
945
01:27:44.250 --> 01:27:48.809
10 person collaborative, like, meetings. Right now. Look. Rob and I are creating shareholder value.
946
01:27:51.525 --> 01:27:54.325
But to the point though that, like, it really is,
947
01:27:54.965 --> 01:28:12.210
I think, mutual friend of all of us, Steven Lebka, just going on walks and pondering in the sun is actually where the shareholder value is made, where you're just like, I need to I need to wrestle these big ideas and just get blood flowing. And then you have these epiphany moments, and then you just go sprinting from there. It's it's it's seldom, if ever,
948
01:28:12.370 --> 01:28:13.090
you know,
949
01:28:13.570 --> 01:28:20.864
large corporate meetings of everyone exchanging ideas. Like, it's it's like, the the true big bang, like, pop stuff is
950
01:28:21.105 --> 01:28:28.704
someone autistically spiraling over a narrow domain until they figure out all the pieces. Steven's my second podcast today later today.
951
01:28:29.344 --> 01:28:35.010
Funny you should bring him up. And by the way, I've just decided I'm gonna title this episode creating shareholder value.
952
01:28:38.370 --> 01:28:39.570
Perfect. Perfect.
953
01:28:40.130 --> 01:28:41.489
Yes. I
954
01:28:41.810 --> 01:29:14.120
mean, Alan, like, I think you you charge us with a good mission. We were already teeing up hash functions. We'll start playing around for a little bit, and all we will do is provide you scaffolding for you to do your next big leap when you become a full time player. I recommend, right, is entirely selfishly. Feel free doing all this. When I say recommend, I mean, Well, you're on the board. You're you're on the board of the math, whatever, whatever your title is. You start You're on board. Start with you start with the second answer, which is what are the properties you want to achieve in creating this function. Right? So then people have like, they understand why you're doing it at all. Then you do the second answer.
955
01:29:14.280 --> 01:29:22.425
No. Sorry. The I think the first answer is the way I Mhmm. Gave it originally. Then you have the first answer of, okay. This is how it works. Like, this is what you're doing,
956
01:29:22.744 --> 01:29:27.144
and then you can try to answer what I want and
957
01:29:27.704 --> 01:29:28.824
probably fail.
958
01:29:29.144 --> 01:29:30.264
But who knows?
959
01:29:31.144 --> 01:29:33.550
I'm a try. We'll give it a crack.
960
01:29:34.910 --> 01:29:41.309
And and now It's especially funny that you insisted on this. Like, we are recording video, but you only do audio because
961
01:29:41.469 --> 01:29:45.630
I swear to god this isn't the the knowing the subject matter, it's impossible
962
01:29:46.125 --> 01:29:53.164
to explain verbally, or it's at least very, very difficult. We've we've done multiple times. Send you pictures I have taken of doodles
963
01:29:53.405 --> 01:29:55.244
to explain all of this way better.
964
01:29:55.485 --> 01:30:21.414
Plea one, please do too. There's multiple times Brian and I have done this podcast, and we're like, oh, we're just real, like, masochists because we're explaining all of these, like, elliptic curve operations. And and I'm I'm, like, gesturing with my hand. I'm like, what I'm actually just pantomiming for Brian. No one else. Curve with his hands. You know? Like that. And then I'm doing, like, the the linear transformations for double point edition, and I'm like, what am I doing? Like I do aspire to get to video. What about, like, side effects? What if you're like,
965
01:30:23.175 --> 01:30:28.540
I mean, what you should right. If you wanna, you could just you have a YouTube channel, right, you could just throw this one up. Emergency podcast.
966
01:30:29.260 --> 01:30:30.860
You got the soundboard.
967
01:30:30.940 --> 01:30:49.265
Yeah. I mean, if you wanna throw this up on YouTube, that's fine. I'm not Okay. I might. Not I I'm not in my office. I'm not in my office right now, so it'd be perfect if one thinks that this is where I do all my work, not normally. Oh, that'd be great. And then people will appreciate I'm wearing an ankle watch hat. Bingo. Yeah. Brand placements. So we really are creating shareholder value now. We are. Yeah. We are.
968
01:30:49.985 --> 01:30:50.705
Excellent.
969
01:30:51.105 --> 01:30:51.824
Amazing,
970
01:30:52.705 --> 01:30:53.185
guys.
971
01:30:53.825 --> 01:30:56.225
This has been a lot of fun. This has been a really good,
972
01:30:56.945 --> 01:30:58.545
jump off into the
973
01:31:00.200 --> 01:31:18.235
having a guest on. And and this is like this is the Amous Bouche or the dessert depending on how you view the order of the courses of where we're just trying to, like after eight episodes of chewing through all of the elliptic curve math, we can just have a little bit of fun as a breather before we torture everyone with hash functions.
974
01:31:18.555 --> 01:31:24.635
Nice. It's good. You you go on too many dinners with the Lloyd's boys. That's right. Yeah. That's right.
975
01:31:25.755 --> 01:31:26.315
That's right.
976
01:31:27.940 --> 01:31:36.499
Wonderful. Thank you so much, Alan. Thank you so much for coming on. Thank you, Alan. Great time. Long time long time coming. We'll have to do it again soon.
977
01:31:36.980 --> 01:31:45.005
Well, you've just teed up perfectly when we'll do it again. Right? You go on to chapter whatever on hash functions. Yeah. Let's do hash functions. Material.
978
01:31:45.005 --> 01:32:10.820
We'll bring you back. Guest appearance where we debrief on me telling you it's all impossible anyway. So how did you do? When you can Yeah. That's right. More. When you cannot tolerate Yeah. Watching this I actually anymore. I actually like this format of Alan throws out big, crazy, abstract ideas. You and I toil away for three months, and then we come back. And then and then we come back, and then Alan's like, that's okay, I guess. You know? Right? Like, you can Yeah. I don't I don't even care about that anymore. I've moved on. This is what I want you guys to do. Exactly.
979
01:32:10.995 --> 01:32:14.355
Like, oh, that's old news. Let's do the next one. Yeah. Exactly.
980
01:32:14.915 --> 01:32:15.635
Exactly.
981
01:32:16.275 --> 01:32:18.515
Excellent. This is in the books.
982
01:32:20.355 --> 01:32:22.195
Now let's