Motivate the Math

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Fundamentals.  @Fundamentals21m
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AverageGary
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Jiimmy Breedlove's nostr post:
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In this episode, we dive into the intricacies of balancing personal and professional life, as the hosts discuss taking a break from podcasting to recharge and manage multiple responsibilities. The conversation transitions into the unique dynamics of working within corporate structures while pursuing personal passions, highlighting the freedom and constraints that come with such arrangements.

The discussion then shifts to the technical realm of Bitcoin and cryptography, exploring the mathematical foundations that underpin these technologies. The hosts delve into the complexities of understanding cryptographic signatures, the importance of modular arithmetic, and the challenges of verifying Bitcoin's cryptography. They also touch on the philosophical aspects of mathematics and its parallels with Austrian economics, emphasizing the need for a deeper understanding and verification of the math behind Bitcoin.

[00:00:22] Unknown:

Okay.   Well, we're here, man. We're here. You know what?   That's what matters most. What matters most is we're here. We're showing up another week. Showing up is the hardest part of anything. Yes. We did take a week off. I took a week off of all of my podcasts. My Yeah. Wife was on spring break and,   did a little traveling.  

[00:00:42] Unknown:

It was the best week to take off because I was spinning even more plates than usual.  

[00:00:47] Unknown:

Yeah. I was telling Gary before the podcast, this is the only podcast I have where my partner has a job.   Yeah.  

[00:00:56] Unknown:

Yeah. All of the other ones were nice and free. Well, when you say job, you mean I'm a wage slave, and Paid job. I work for someone else Yes. To earn a w two.  

[00:01:07] Unknown:

Yes. Somebody pays you to direct your time   in to things other than this podcast.  

[00:01:12] Unknown:

That yes. That is that is true.   But it's nice that I can direct it to this podcast, though. That's one of the nice things about my corporate overlords is they allow me the freedom to   direct my time and energy to things that matter. And that's nice. That's nice. I mean, my first  

[00:01:30] Unknown:

year and a half of rock paper Bitcoin, I had a job,   and I was probably you know, I was that guy. Was that, like, pre s tier rock paper Bitcoin?   I think so. You had a job? I think probably. I think things I mean, I really do think things opened up a lot when I became free. Yeah. Not just because of the freedom. It's because of what I had to go through.   And what it meant to me as a Bitcoiner now to be like, I've,   it's really funny. I'm gonna do this here. It's really kinda funny. I've mentioned these things before, but, like,   there was, I the genesis moment, which I consider the moment I got into Bitcoin.  

Yep. The Exodus moment, which is when I lost my job. And I Yep.   Then I was like, I I I've been into math, and I kinda feel like I know what numbers is gonna be, but what's Leviticus? What is that? And I was asking a bunch of my friends who, like, are better biblical scholars than I. Yeah. And they were saying that Leviticus is when you write the book or when you   come up with a set of rules. It's like, you know, Moses going, getting the 10 commandments and all that.   And so,   like, it may be that actually me writing the book,   which is almost   my book, Bitcoin for Institutions, which is   within a easily within a month of being available and released.  

Yeah. That's my Leviticus.   And this podcast and what we're building with the math academy   is my numbers.   And   then figure out what the fuck Deuteronomy is. What I don't even see this as my lack of  

[00:03:05] Unknown:

biblical knowledge as well. It's like, I don't I don't even know what,  

[00:03:08] Unknown:

Deuteronomy is. I have an actuary's understanding of the Bible, which is I could name the five books.   Is that why is that an actuary's understanding? Very yeah. That's a very inside dig at the actual profession because that's basically, like,   if you ask an actuary   what a group is, you know, he'll say,   oh, it's he'll just name the four x. He'll because he studied that for a test.   He had to study what the thing if he didn't have to study for it for a test, he doesn't know what it is.   Right. Yeah. Never thought any deeper about any of it. Right? But thinks that they understand it. Like, he'll consider himself a scholar.  

[00:03:48] Unknown:

That that's interesting. I've had this,   you you bring up something that I've been thinking about lately, like, in the in the military. They have or in the navy specifically, they have these things called warfare devices, which are like these little badges you get to wear on your uniform. Right? And these are   Yeah. Cool. For the audio listener, I'm showing the three badges I earned. There's, like, the information warfare, fleet marine force, and expeditionary warfare badge. Anyway, the the reason I bring that up and it comes to mind is   to do this, like, to to become qualified, you had to go through a series of,   like, you had to get, like, proof of work, quote unquote, which meant you had to get different sections of the manual   signed off by people that were subject matter expert experts. Right? So when you're going through, like, the medical part, you go down to medical and you have to demonstrate the knowledge of what's in this this JQR, this job qualification requirement. Yeah. You had to demonstrate the knowledge and then somebody would sign off it. Like, you can I'm glad you said what a JQR is because Yeah. Job quality.  

It's like a job qualification requirement thing. It it's a list of, like, topics and or practical application   things   that are, like, the all encompassing for earning this certification, we'll say. Right? So to become a credentialed.   Credentialed. Yeah. PodCom would love this.   But it it's it's it's like to me, though, it was,   because it's the military,   it was it's, like, lowest common denominator. Right? Like, so whatever that might be for this individual badge, like, there's it's very explicitly outlined, like, what you should know, what you should be able to do, etcetera, etcetera. And so you have to go demonstrate, and people will sign off. And then when you get all the signatures,   you filled your book of signatures   with all the different topics and and practical application things. You would then go and say, hey. I'm ready to, like, take a board. And a board is basically just people that are already qualified,   like, four of them or more   would sit there   and, like, okay. We're gonna grill you. And it's like, you know, hour plus, multiple hour long, like, ordeal.  

And sometimes you do it as a group, like, two or three of you together,   but they would sit there and just grill you on everything that's in. Anything that could possibly be covered could come up Yeah. In in the in this in this board.   And prior to the board, you do something called, like, a murder board where it's, like, really, like, we're gonna hit you with everything. And then the final board is sort of, like, a, more of a formality of, like, okay. Like, you you've gone through Real training. The rigor. Yeah. It's actual training. And so   I've been thinking a lot lately   about what that might look like for, like, a a a sovereign individual or  

[00:06:23] Unknown:

a a Bitcoiner or a what whatever you want. Right? Like, there's Reminded me, you know, this reminded me of put like, I haven't had anything like that since I pledged a fraternity.   My friend Exactly. Yeah. And you had to get all of the brothers to sign your note your your little notebook. And in order to do that, you had to basically, like, it's like, here, drink this entire fifth of vodka.   Yeah. And you're not getting my signature until you do it.  

[00:06:47] Unknown:

Sounds healthy. Yeah.   But the the original intent and this is why I think it's so apropos for,   like, Bitcoin and people that want, like, digital sovereignty and just sovereignty over their lives. It's interesting. Yeah. It's   the original intent of it was when you're on a destroyer or you're on an aircraft carrier or you're on a submarine,   if the if that thing gets hit,   you need as a crew member, you need to know the basic core functionalities   of that vessel   and, like, what needs to happen to keep that thing going. Because, like, a ship can get hit multiple times and keep going. Right? But if a third of the crew dies when it gets hit, you know, like, maybe the engine compartment, like, everybody's dead in there. Well, somebody needs like, you need to have a basic functional,   practical application knowledge and understanding of how the engines work in the ship even if you're just like the radio guy or even if you're just, like, you know, tugging lines and tying up to the pier and stuff. Right? And so the the the concept was you arrive at a ship or whatever platform, and they go, okay. You need to get qualified on this because now you're, like,   a sanction member, a certified   member of this crew, and we can trust you in the event of an emergency   to be able to handle your shit. Right? And maybe it's not your your your day job. Maybe it's not something you're doing all the time. But, like, you have at least gone through the iterations   and done   some proof of work, but also demonstrated that, like, you're capable of doing these things.  

And I wanna I wanna do that with, like, with with with Bitcoin, like, running your own node and, like, doing transactions. You can do it all on, like, ten to four. Perfect. Doing math. Right? It's a perfect setup for what we wanna talk about. Isn't that not?  

[00:08:27] Unknown:

I think there's a reason why it's set. There's an elusive there's an elusive there's something elusive to me that I think would be on the list. Right. So the whole like, the   the reason I'm here   was because I could not verify,   the cryptography. I was Yeah. In my process of verifying Bitcoin. Right. Right? And I go on Bitcoin GitHub and everyone knows story. Everything's great. See the formulas.   Go on set p two fifty six k one and I see the wall of numbers and I'm like, what the fuck? And then Mhmm.   Then I go get this book called understanding cryptography and then that it turns out   there's a whole body of math   and cryptography   behind all of this that I had no idea. Then I got super angry. I said, oh my god. How is this kept from me? And then I got even angrier that I did not,   one of the stories of my life is that when I see a math that I know I have the aptitude for,  

[00:09:26] Unknown:

that Oh, you gotta solve it.  

[00:09:28] Unknown:

I must, like, I must attain it and I get angry. Like, I I get angry and an unstuck like, an insatiable   Yeah.   Ruthless almost yeah. Like, desire to to Yeah. Master it or and then so,   so that's how I got here. Right? And and so now I'm two two plus years into this math thing just from that whole experience.   But like what was the North Star? What was the goal? The goal was to verify Bitcoin. The goal was to understand the cryptography. And I've been having this realization, see, after be going through a few books,   I have to now pick a new, you know.  

I just got through a number theory book. I did Cobblets' book, which is really great. Mhmm.   I'm getting to the end of another abstract algebra book, and I'm like, okay, what am I gonna focus on?   And this thing about   this thing that still eludes me   is,   there's something in cryptography that still eludes me. And it's not because I don't understand Fermat's little theorem or   quotient functions or, you know, what the Euler functions or groups and rings and fields. It's like, I'm pretty good with all like, I'm starting to get pretty good with those things. Yeah. But they haven't they haven't yet gotten me over the hump   of, like, understanding   how to sign a transaction.  

So, like, I feel like if you dropped me in the jungle   with a pen and paper   and,   all of the inputs, I still wouldn't I would struggle   to,   I I would struggle to create a society that use these signatures.   Well, I guess, like, the first question is, like, what, like, what is the a signature? Right? Like like, the thing that is the signature. Yeah. And we're gonna have a very awkward conversation now because, like, I am on one side of the wall of understanding, and you're on the other like, you're on the other side of the wall of understanding. I don't even need to know the math. Like, what the fuck are you talking about? Like, this is really simple stuff. I didn't even need to know any of that math. I just found it interesting, and so I thought maybe it would help me understand it better. But, like, what are you talking about?   Why is this hard for you?  

Right? It is such an interesting thing. Right? Like, why is it hard for me? Like, I think I've demonstrated on I don't know what episode this is, 12 or 13.   I've demonstrated that I have a brain and how to use it. Right? So what is, like, the and so what kind of, like, a re what kind   of not a fucking retarded guy   can, you know, get through all this math and still have this problem?  

[00:11:53] Unknown:

I mean, I don't know if, it's a problem per se. It's just Well, it's a problem. It's your your aperture you you've had your aperture,   like,   very   wide   with because you need to like, you you you're at the beginning   of a rabbit hole of math and stuff.  

[00:12:10] Unknown:

But, like, the you just have to narrow the aperture a little bit. Right? Like, narrowing the velocity. Idiots I feel like the idiots that I managed my whole career. Like, I managed math PhDs who were,   Like, incompetent. Right? They were   they were good weapons to be deployed on certain   tasks. But, like, if you really ask them to   think about something, they'd be like, let me go get a book, and I'll get back to you in a year.   Yeah. That's how I feel. That's literally how I feel about this right now. Yeah.   So you're right. My you know, it it it I guess it's it is an Aperture thing. Right? Because I don't know how to, like,   narrow it enough to just focus on the thing needed for this thing because that feels like an anathema to me.  

It feels like an anathema because   I,   I don't like limiting my views   of things like that.  

[00:13:03] Unknown:

You know what I mean? Yeah. But, like, you you have to   you have to limit in a certain sense because   it's a it's a focus. Yeah. Like, it's just because this won't work.  

[00:13:16] Unknown:

The same way you had to focus on the groups for so long. Right? Like, there was you were excluding other things at the time that you were focused on groups. Yeah. Well, that's, like, the biggest aperture it gets because that that applies to some like, it applies to so many things. And it's, like, really the question is how how long   do I have to do this before I can narrow it so specifically   to the thing I want?   Right. Right? That's   that's really the question. So I don't know. Maybe people listening are like Gary   and or maybe they're   maybe they're like me or, you know, they're like I would like to understand.  

How is there like a is there like a way we is there like a maybe just sort of an academic framework   to start learning signatures? And look, I talked about Jimmy Song's programming Bitcoin book. That's great.   I just I've gone through that. I've I've revisited that book many times. It doesn't really   that Antonopoulos Mastering Bitcoin, I've been through that book several times, but it doesn't it hasn't gotten it to click. Well, to the point where, like, if I was interested in understanding, say, Monero signature scheme or something like that, that I would be like, oh, yeah. You just or even test net. Right? So like, even just test net versus main net. And now there are a lot of things I understand the difference, like, operationally. Actually, I just went through this. Yeah. Yeah. Go ahead. Operationally,   I get   how it's different, but I'm saying, like, where I could with a pen and paper. Right? With a pen and paper and, like, a manageable,   like, a manageable crypto scheme be able to say,   yes, I can kind of, like, manage this whole I can I can I can draw out this whole system?  



[00:14:53] Unknown:

Yeah.   It's   so the the thing well, first, let me just touch on Testnet because I literally just let's see. A week ago,   I was trying to figure I was like, what what makes Testnet different from, like, from from Bitcoin?   The signatures are the same. Right? So, like, the signatures are the same on test net, but   it's basically it uses different there's a way of encoding   addresses.   It's called Besh 30 2, B E C H 30 2. Yeah.   And it's just it's a way of encoding data where when you look at the data, there's no confusion if it's a one or an I or an l. Right? Because it doesn't actually have l's or i's. It just has ones. And then it has a prefix. You'll see always, like, there's a prefix of, like, b c one something.   Right? And that's that's, like, part of the BESH 30 2. It's like a way of knowing   how did I encode this? Oh, it's BESH 32 with this specific prefix. And you see this, like, cashew tokens and other things. Prefix that makes it different. That's the key. Because Prefix. Yes.  



[00:15:52] Unknown:

Main net uses   best 32 as well. It's just with a different pre it's a different prefix. And so but it's it's not it's not just in signatures. It's the entire,   you know, testnet has its own   protocol.  

[00:16:08] Unknown:

Yeah. Yes and no. And it and it's it is more of and I don't know what this issue is. Right?   It is its own issuance. It it's it's an entirely separate blockchain. Like, it is literally a shitcoin. Like, it it is a copy of Bitcoin,   but it has a different, like, bytes   in the way that it communicates over the network. I think they're referred to as, like, magic bytes.   But that is like an indicator of, like, hey. I'm in test net, whatever. First indicator of a shit coin.   The different bytes? Magic bytes. Magic bytes. Well, no. Mainnet has its own magic bytes as well.   But, yeah, it's a completely separate network, like, different rules.  

It has different so one of the other things that, like, when you're running a Bitcoin node is,   there's, like, pre there's seed nodes that are in there. So, like, you need to go know where to go look   for like, if you're just bootstrapping a Bitcoin node from nowhere and you have nowhere else to point it to, like, get attached to a node, they're actually seed nodes hard coded in a Bitcoin core,   that I think you might be able to configure, but it'll go out and look for those. Right? So test f four why I've I've lost two I have two nodes that were got lost in in the Internet. They got lost in the Internet? What do you mean? Yeah. They just stopped connecting. You know, they just stopped connecting to anything.   That's kinda weird. We can unpack that another day though. Yes. That's Yeah.  



[00:17:26] Unknown:

I I'm you've triggered it of curiosity within me. Now this is a nine that seems to still be humming. But like I had an umbrella and I built a Raspi bolt both.   The Raspi Bolt was actually resurrected the Umbrel because it found finally found something on the Internet, but then they both got lost.  

[00:17:44] Unknown:

I'm so curious to look at those logs. But that's we're not here to dissect Bitcoin core logs today. Yep.  

[00:17:51] Unknown:

Interesting,  

[00:17:52] Unknown:

man. Yeah. So test set's not any different. The signatures are all the same. Right? And Yep. And the the crazy thing so Nasr   is also the same signatures.   Right? It's it's a matter of, like, what are you signing?   And generally speaking,   when you go to sign something,   it's it's you you usually referred to as the message. Right? You have because when you go to validate a signature, it's you have, like, a signature, a pub key, and a message.   And then you put   it through the equation of, like,   I am checking the signature against this message for this specific pub key. Right?   So a Nasr event is the same thing. You we we when we sign the Nasr events, it's the same exact algorithm   or formula   for signing a Bitcoin transaction.  

It's just what is the message that you're signing.   Right? And that's the key component.   So in   and then also in Bitcoin   Bitcoin land, you have like, post Segwit,   the thing that Segwit like, the witness part, like, the segregated witness, the witness thing.   And and this is, I think there's yeah. Learn me a Bitcoin. There's a quote from Peter Willow. Witness is just another word for the signatures in transactions. So they literally they they created this new   transactions. So they literally they they created this new data structure. Signature. Right? You're talking about the structure of a transaction.   Yeah. Yeah. Right. But but what you sign though at the end is just  

[00:19:14] Unknown:

Is this hash of that whole thing? I Right. That I understand.  

[00:19:18] Unknown:

Okay.  

[00:19:19] Unknown:

The the question is I'm thinking more of so, like, from my brain is in,   programming Bitcoin.   Mhmm. And you have these parameters r and s. Right?   How do you connect that to the   the transaction hex of that whole,   you know, the whole where is the when you have that when you have a transaction,   right, where you have   call it let's say it's a p two s h transaction and you have your witness and you have your witness and you have your you don't have a script. You know, you have your transaction ID and your   index and your, you know, those inputs and then you have your outputs,   your pub keys, and then you take the you know, your lock time and blah blah blah. Right? A to z. Then you take the you take the hex of all you you take the hash, sorry, of that   concatenation.  

Right.   Right?   Where does where does   the where does the signature enter?   Where does the signature enter? Where does the signature enter? Like, where does the like, where in other words, where does   like, what's the action   that actually verifies   that somebody So you're the keys to unlock to move that   transaction?   Maybe I have to redo  

[00:20:39] Unknown:

my base 58 class to reconnect with this. Probably. But you're you're you're doing point comparisons. Right? And so   there are   that that r value, right, like, that that is an important piece of the signature,  

[00:20:52] Unknown:

and then there's the s value that's also an important piece of the signature. What do these represent what are the r and the like, the r and the s   seem like they're abstractions of, like, a Cartesian x y.  

[00:21:05] Unknown:

Yes. So so r, like the capital r, it it specifically in Schnorr signatures   is referred to as the public nonce.   Right? And and you arrive   by basically   taking   a  

[00:21:22] Unknown:

Let's pretend it's a p two s h.  

[00:21:25] Unknown:

P two SH. Like an yeah. Like that script. So no no Schnorr.  

[00:21:30] Unknown:

Yeah. Like a typical pre Schnorr, but post segway.  

[00:21:35] Unknown:

P okay. Alright. So that's, like, with e c d s a. Yes. That is that is actually different in the way that you   because ultimately, you end up with a message. Right? And that message is is like a hash.  

[00:21:48] Unknown:

But arriving at what that message is I mean, I basically I mean, I think I like, in layman's turn, this isn't a mathematical this isn't a mathematical question. The question is can you just recreate that? And if you need the secret, you need the secret puzzle piece   to recreate that. That's not so, like, you know what I'm like, I get, like, that that's clear to me. Okay. It's clear to me that no one on earth without knowing the you know, without being able to plug in that secret   Yeah. Yeah. Puzzle piece can recreate the hash. Okay. That's not a that's not a problem.   The problem is is actually   understanding that puzzle piece.  



[00:22:26] Unknown:

Okay.   So so the r value in this is actually   the x coordinate   of this thing   called like, it's a random point on the curve. Right? This is, like, the randomness that you point because you have your private key, and then you need some, like, random thing random point that that you arrive at.   Yeah. So they call that The r value is the x value of   capital r, which is just   an e c d s a. It's your private key times the generator point.   Right? So you're multiplying the private key times the generator point, and you arrive at this, like, r value. I see.  

[00:22:58] Unknown:

I see.   Okay.   Okay. And so connecting it to the math is that the private key, the generator point, the it's like the first of all, the elliptic curve, the points on the elliptic curve form an abelian group.   Right. We know that. And it's it's also cyclic.   And when it's cyclic being cyclic means that you have a generator that,  

[00:23:22] Unknown:

under addition I'm sorry. I hold on. I misspoke.   It is not your private key. It is a random number.  

[00:23:29] Unknown:

But times the generator. So that's the It's a random number times the generator. Right? And anytime you here's one of the things I think might help is Let me just complete the sentence here though because the the key of it being a cyclic group is that the generator can is multiplied by   all of the   numbers   in, like, in a finite field. In other words, if, like, you had a finite field of 11 elements,   all the numbers zero through 10, you can multiply by that. That generates the multiplying it by your generator creates the group.   Right. So in other words, the generator times every   you know, all of the   members   of the finite field, I. E. Zero through your modulus minus one. Right. Right?  

Creates all of the points on the elliptic curve.   So if you multiply by the generator, you're guaranteed to still arrive on that curve. That's right. That's the key. The key is so generator times any number, and that's why so now it's making sense. Like, you can take the generator times some random number Yep. To get a random point.   A point that you will some random point that you know will be on that elliptic curve. Well, and  

[00:24:37] Unknown:

correct. And it's   Yes. That's the start. This is the start of connecting the dots here.   Well, and the the,   like, just basic and and I don't wanna misspeak   necessarily, but, like, I'm I'm fairly confident that also   the private key times the generator gives you your public key.   And and, hopefully, I did not screw that up. I do think that's the case. Yes. Yeah. Yeah. The generator point multiplied by the private key is a public key. So you're almost, like, generating another public key   as part of it, and the x value of that public key is the r part of the signature.  

[00:25:14] Unknown:

And for people who don't know, there are you can go onto the Bitcoin GitHub and see what the generator point is. It's under g, like, g equals, and it's   Yeah. What is it? A 64 character number or 64 character string? I have no idea.   It's great. It's all hex, so, yeah, probably 64. It's something I think on one of these episodes, I suggested that we need some people in the community to memorize it just in case at all. You did suggest that. Yeah.   That should be on the that You get a tattoo of it. That should be something you need to do to get your notebook signed.   Memorize the number? Yeah. Memorize the g.  



[00:25:48] Unknown:

That   that would be pretty interesting.   Maybe. Maybe for, like, a gold gilded version of the of the of the badge.  

[00:25:57] Unknown:

That would that's, That'd be be I mean, I would I would do that over drinking a fifth of vodka.   And I would do it earlier. I would I would definitely it would take me less time.  

[00:26:09] Unknown:

I don't there's a lot of people that would probably just take the the fifth of vodka, though. And I would peel it.   Okay. So you have the r value, right, which is just the x of the random number that you picked   times the generator. So random number   k   times the generator gives you this public   value, which is now, like, part of your signature, the r. And then the actual signature,  

[00:26:34] Unknown:

the s part of it So you in order to prove I have my key, I have to be able to get to that I need to be able to arrive at that point   using the known name or But that random point. Right? Because you're essentially it's if you take the the random number I have to be able to arrive at the public key. If if I can get to the public key   on my own, it's only because I know the private key.  

[00:26:59] Unknown:

Right. Yeah. Yeah. Yeah. Yeah. Because you you know the private key, you can multiply it by the generator, and you arrive at the public key. Yeah.   Well, what I'm saying is that that r so you you create this random point  

[00:27:11] Unknown:

Mhmm. On the curve. Yeah. So what's the point of a random point? What is the object of a rand of doing a randomized   point?  

[00:27:18] Unknown:

Because when you're   when you have a random point,   I I think if you didn't use a random point because the next part of it. Right? So the s part that's the r part. The Yeah. R is the random point. The s part of it is the actual signature,   and you're using,   your private key in this equation. You're using the message hash, and you're using this random point. So it's a way of, like, obfuscating   your private key. Right? Because you don't wanna necessarily, like,  

[00:27:46] Unknown:

Yeah. Got it. Because you can pack in if you yeah. You need it's it's a Right.   It's an indirect way,  

[00:27:54] Unknown:

I guess. Well, I don't know. Maybe I'm not I'm not sure. This is one of the things I think with nonce, it's called, like, nonce reuse is is an issue with some signature schemas. Because if you reuse the same random number for the signature scheme,   then you you risk sort of explosion. Because now the equation   it's  

[00:28:13] Unknown:

Jimmy's I hate   Jimmy's son drives me crazy, by the way. But yeah. But it's kinda like like he did write this book, and it was important. I mean, it Yes. Jimmy Son is like a slightly better version of Nassim Taleb.   We wrote Taleb wrote a great book in 1995,   and, like, he wrote a okay book in 02/2002.   And   but, you know, he's just done nothing but be a fool since. Jimmy Son is not on that level. He's just more of a,   he doesn't operate on the level of the guy that wrote that book. And so I feel awkward continuing to refer to this book, but   he does such a good job. He does such a good job on this one page of explaining why reusing that knots will expose your cake.  



[00:28:59] Unknown:

One is because the s like, the equation to arrive at s. Right? So the two parts of the signatures r and s.   R is just the x value of a random point on the curve, and then the s is the actual equation where you input   the message hash,   which, you know or or just the message, but it's usually hashed,   plus   your private key times the ran the the little r. So your private key multiplies itself by the x value of this random point.   And then that value   is then,   multiplied by  

[00:29:34] Unknown:

this random number to the negative one power. The I the identity value of this random So you're talking inverse. Yes. Yes. I'm sorry. That's the inverse. I mean, that is the inverse is a way of saying something to the negative one power.   Right. Yeah.   Wait. Let me see. Here here. Oh, by the way, I hope that my book is so good that people   say I could never that I stopped living up to the quality of the book and then I just am normal.  

[00:30:00] Unknown:

I wouldn't mind that. I hope nobody ever thinks I'm normal.  

[00:30:04] Unknown:

I'm just saying I I wouldn't mind that if ten years from now, people are like, yeah. That book was really good, but he hasn't really done much since.  

[00:30:12] Unknown:

Yeah.   But the the like oh, and here it says modular inverse of the number.   But that's it. So so at the end, you have these two values. It's probably the thing that it's the thing that  

[00:30:24] Unknown:

abstracts out, and that's why the signature itself could be closed. Right. Yeah. ECDSA does not have  

[00:30:31] Unknown:

modular multiplicative  

[00:30:32] Unknown:

inverse. Now not to do too much, like, housekeeping here, but I was I was thinking before the episode.   I don't know how you feel about this, but we might have to make this video. We might have to do a video podcast. And and it we don't have to show our faces if we don't want to, but we're always   I mean, more often than not, we're sharing screen with each other. We are. Yeah. I don't care about sharing my face. That's fine. Like we should   do this   it just feels like we should do this in a video format.   At least it should be available   because I think it's really it's hard enough.  

Right? Right. It's, like, hard enough to figure out the hell we're talking about. I'm so glad this is this is so much easier. It's easier, we'll just say, when you have this stuff casted.  

[00:31:18] Unknown:

Absolutely. As long as we don't do it live.   I don't think live is worth it.  

[00:31:23] Unknown:

What do you mean?  

[00:31:26] Unknown:

Doing   live broadcasts  

[00:31:29] Unknown:

because then No. No. Yeah. No. I know what you mean. Yeah. Yeah. Yeah. Yeah. Yeah. No. No. We're not, like, streaming. Not when they're doing live streams or anything. Like, of course, it's live. We're here. Right? No. Yeah. Yeah. Yeah. Not not asynch it's still synchronous, but I meant, like, a live broadcast. Like, I don't I don't ever wanna be beholden to a live broadcast because that's what it feels like. It feels like you would be become beholden. Yeah. No. I don't I'm just saying I think that it's,   it's almost cruel to do this without the video aids, but the visual aids.  



[00:31:58] Unknown:

Right. But there's a level of masochism you have to enjoy   if you're gonna be We don't wanna kill our nation. You know?   So go to learn [email protected].   Look at the ECESA signature page. That's what we're that's what I've been referencing.   Yes. Because I don't have this stuff memorized.  

[00:32:16] Unknown:

Okay. So let's okay. So now let's assume everyone's with us here.   Okay. Right now.  

[00:32:23] Unknown:

I know Piazza's.  

[00:32:27] Unknown:

Alright.   Well But the but the but the opposite, right He's he's listening to, like, 10 different podcasts at the same time.  

[00:32:35] Unknown:

The opposite side of this, right, the verification piece of it, is you're just checking if the values   match.   Right? So, like, once once you've provided the signature,   there there's this s and r value.   Right? So and and then everybody knows the data or the the message, Right? The actual data that's being signed. So that that should be consistent. Right? So in the in the case of Nasr, it's the whole Nasr event. In the case of Bitcoin, there's actually and this is where, like, the   technicalities   of Bitcoin get pretty interesting   is there's this thing called a sig hash   Yes. Which tells you what part of the transactions you're actually, like, signing for.  

And that's probably just, like, even that's probably too rudimentary of an explanation to give it justice.   But the the the sig hash fields are quite,   nuanced and complicated as it pertains to, like, Bitcoin scripting and transaction.  

[00:33:31] Unknown:

Fully understand the SIG hash options.   That's   you know, that took me a a lot of repetition   in   mastering Bitcoin.  

[00:33:40] Unknown:

Yeah.  

[00:33:41] Unknown:

And I don't like, that never clicked with me either. Not saying we have to do that now, but, like, it's like that is maybe something we hit at some point. Like,   what the what the purpose is of  

[00:33:55] Unknown:

So let me let me just re this is this is one that I found,   and I just   we'll cover it just base like, very, very quickly. But there's, like, SIG hash all,   which means   that you're signing every input and every output in any change that will And where does this sorry. Where does  

[00:34:14] Unknown:

remind me where this flag is found. It's not is this this flag in the transaction?   It's in the transaction. Yes. Where? What in what, like, Poof. In what field?   Let me I don't know. It's part of the dirt. It's it's part of the part of the dir signature.   Dir well, it's dir encoding. Sorry. The dir encoding. Right? And it's yeah. Got it.  

[00:34:36] Unknown:

I think that's different, though. But it's,   it's a great question where where it's at. It's some bytes. Right? Like, it's it's like I gotta read this in my base CTA class. Two, three, 80 one, 80 two, or 83. And these are all hexadecimal values. And so it's like some part of the trans well, let's let's look at a transaction, and we can, like and this is where it would be better to have   it on have it on video.   But we don't, so you all suffer with us.  

[00:35:03] Unknown:

I I know what a der   encoding looks like by eyesight just from   harshing so many of these things. Yeah.  

[00:35:12] Unknown:

I mean, that's more impressive than I I can't I can't recognize der.   So Anyway, they're flags that you find the transaction,  

[00:35:21] Unknown:

and it's just are you signing transactions class, but, like, it is part of it. You have to kinda we have to get in there at some point in time.  

[00:35:28] Unknown:

Well, it's this is more of   what is the message that we're signing. Right? And this is why I'm I was saying it's the same signature algorithm   for Bitcoin using Shor   as it is for Nasr. It's just what is being actually signed. Right? Because in Nasr, you're signing a hash   of the entire note.   Right? And that's that's specified in, I think, like,   zero one or something like that.   And then in in Bitcoin,   there's actually a flag that tells   you and everyone else   what part   of   the transaction you're signing.   Right? So   it's, it's a little   it's just interesting, and that's because you can sign any data.  

Right? Like, I can this is something that,   Right. Like, PGP tried to to enable   more broadly back in the day,   but they didn't have, you know, shitposting on Nostril like we do today. Like, we're bootstrapping   a key network on Nostril   because we can sign and exchange messages.   The only people that used to do this back in the day were, like, you know, Cypherpunks and nerds and, like, a lot of other stuff. But now it's become so prolific and easy to use, these signatures and the verification of the signatures, that, like, everybody can just do it. Right? And that's   it it it's gathering a network effect.  

But signing the data, I can take a Bitcoin key or a Noster key because they're the same curve, sec p two v d six k one, and I can use those keys   to create a signature over any message that I want. It just so happens that Bitcoin is a very specific message   that it's using to sign, and you have to know that. Right? Because to validate the signature,   you need to have the same message.   Because any change and this is one of the things around   signatures   is there's this I wanna say it's called nonrepudiation,   but it's basically it's like, if I provide the signature on this,   there's no way for me to,   like, refute that I did this   because   This is where, like, HMAX   and,  

[00:37:37] Unknown:

you know,   other   other information is attached to the message to ensure that it's coming from the place   that it's What is what is HMAAC? That that was intended.  

[00:37:50] Unknown:

Yeah. Yeah. Yeah. There's a combination   of   okay. Message authentication code.   There there's a couple different like, signatures are not like the end all be all. Signatures are just like one aspect  

[00:38:02] Unknown:

of it. Right? Because you can Yes. I've been using the word signature  

[00:38:06] Unknown:

as a, like, a way to validate everything, and that that that's not how it works out. Point. Right? Like, it's just a number. You you you're you're doing point   arithmetic again.   Like, when you when you would send a PGP email, a common practice and you see this even so when I was working in when I was in the navy, we had this PKI. Like, on my my identification card,   I had, like, I had a secret key.   Right? And I could when I plugged it in the computer,   I could sign my emails. And there was, like, a big push at it ebbed and flowed of, like, hey. You make sure you sign this email so they know it's, like, from you, blah blah blah.   Well, you could also encrypt using those same keys.  

But what you would do is you could encrypt the email with the key. Right? And that's a whole different, like,   algorithm, a whole different function, but it's using this this these these,   you know, same keys,   and then you would sign   that encrypted file or rather a hash of the encrypted file.   Right? So you'd encrypt the contents,   and then you would hash the contents, the encrypted, the the, ciphertext.   You'd hash that, and then you would create a digital signature   over that ciphertext that is hashed.   And so Yes. You have, like, two things here. Right? You have one And layers upon layers of needing secrets to  

[00:39:23] Unknown:

unpack. Yep.   You know, which is   kinda awesome.   Right? It's beautiful to and it's very rich way to think about   how to keep secret.  

[00:39:34] Unknown:

Right. Well, and we can have a shared secret. Right? Like, that's the Diffie helmet key exchange where we can exchange public information between each other and then use I use your public information, use my public information   to combine with our respective secret information to arrive at a say at a same point again that is now an asymmetric key for encryption and stuff like that.  

[00:39:56] Unknown:

So, like Yeah. And if I'm making a curriculum, I think that's the first that's probably the first endpoint I would wanna get to whereas   do people understand why that works? And that's   you do have to you do have to get   from Hat's little theorem or a little function   Chinese remainder. You have to get that basic there's this basic stack. This is what we talked about originally. Just to get to   Diffie Hellman.   Just to you know, why that why that works.  

[00:40:26] Unknown:

Oh, and it works because of the properties of all those things. Right? Like, all those things define the properties that are applicable   It's does to these numbers that we're using. Straight up algebra  

[00:40:36] Unknown:

on that at that level.   But it takes a it,   it takes   it takes some work to get there. Like and,   you know, one of the problems   I have to say and one of   the reasons I'm I like doing this podcast   is that   maybe it's something I noticed this morning that,   we don't   modular arithmetic is not a way we think natively,   and it's really hard actually to   understand   something like how two times three could equal one   and to think like that.   It's very hard to think like that in, you know, in a mod five. It does, right? Two times three equals one in a mod five. Yep. But when you're when you're looking at algebra and you're looking at, like, the properties of rings and fields,   it's very   non native   to think   from a world of congruence.  

But if you learned it as a child   oh, and one of the reasons why it's so non native is because when you go to like, if you study math in college, you're gonna   you're gonna go through calculus   and then analysis, and you're gonna get just   so   your mind will be taken over completely   by,   continuous   and infinite   non you know, thing things that are not congruent with congruence, Things that are just really, like,   totally contra. So what then it becomes time   to learn this stuff in this world, and it's so foreign   to,   it's so foreign to the thinking. So I think, like, you can start learning   these basic, like,   modular arithmetic   these basic concepts of modular arithmetic. I think it's,   you have a big head start.  

And if you're a Bitcoiner and you understand why Diffie Hellman works, why the algebra works, and I think every Bitcoiner has the aptitude to do that. I don't think there's a single   you better, by the way. Like, otherwise,   how can you really   I don't know. How do you really feel good about it. But, I mean, I think everyone   who has the aptitude to figure out that Bitcoin is good has the aptitude to understand   that algebra.  

[00:42:56] Unknown:

That maybe that that's interesting.   That that gave me an interesting thought, and   I wonder,   like,   you're basically highlighting,   like, a different way of thinking.   And that is, like, at its core, what Bitcoin sort of enables.   It was always sort of innate, but,   like, humans have always been able to, like,   change the way they think about the world as opposed to,   like, what   you know, what the whatever   the current society   frames everything. Right? Like, you always have these, like, out of the box thinkers or people that, thought in a different way. What's that Jimmy Son post that you sent me yesterday that got me thinking about all of this?   One and you're gonna hold on. You're gonna have to take a few minutes to explain that to me because I didn't quite get it. But   but I guess it it's interesting that, like, at the fundamental   mathematical   level   that enables this thing called Bitcoin, like, this this thing called cryptography really because cryptography is like, Bitcoin is just one very large aspect of cryptography that is, like, enabled,   but there's, like, so much more to it. And so it's interesting to see   the entire mind shift of these people that have adopted   cryptography   as, like, the basis for their   value system,   for their money like, as for their money. Right? Like, that's I I think that's pretty all encompassing by saying that.  

Like, it's so radically different   from the way that other,   mathematical   disciplines at work, I guess. Right? Because you're you're just saying, like, you you go and you learn all these, like, esoteric infinite bounds, like, things. That would  

[00:44:43] Unknown:

that's only true now in the like, in our world because Right. We focus on   we seem to focus on the math of weapons and   physics and stuff like that,   continuous,   calculus and analysis. But then it's also those things are really important, by the way. You don't like, those that is the essence of mathematics. So, like, you know, I'm not saying   that shouldn't be taught. It's just very different.   It's very different to then think in   a discrete   context.   I think like in China, the Chinese   have a big advantage because   they just start thinking about this from a much earlier age. Like, we are   like, you have whatever you did as a child. Like, sometimes maybe you memorize the timetables. Maybe you did more than that. And then that's kinda what you have to cling back to when you go back to discrete math is your whatever it is that you developed as a maybe as a child. Because there's no avoiding the continuous   there's no avoiding analysis, this field of analysis. That's   like, that is really the rich   the rich treasure trove of what   what mathematics   has to offer. Okay? Yeah.  

Right? So you have, like, analysis   and algebra are, like, two opposed   no. Not opposed, but they're parallel tracks, and they're both, like, really important, obviously, but you can't avoid them. You can't avoid analysis,   and it   it's a way it they're they're diametrically opposed ways of thinking,   which is why you it's such a powerful thing to be a mathematician.  

[00:46:15] Unknown:

Right? One is that because, like, analysis is you're you're almost trying to make sense of something   that is infinite,   but then   in in, like, algebra, you can have, like, very   concrete   like, you you you remove the infinite possibilities   to a degree.  

[00:46:34] Unknown:

Well, yeah. Like, even in time, like, you know, there's this idea of continuous time because,   you know, we do experience   life   continuously,   but you can't measure anything continuously.   Right? You can only measure something in discrete  

[00:46:50] Unknown:

units. At a given point in time.  

[00:46:52] Unknown:

Yeah.   It's more of the measurement of something.   Yeah.  

[00:47:02] Unknown:

Alright. Tell me about this Jimmy Song post.  

[00:47:05] Unknown:

You know, if there was anybody other if, like, if this guy hadn't written a book that I really respect, I would roll my eyes at this thing completely, you know. Why is that?   I don't know. It because it kinda it reads like a it reads like a Breedlove post in a certain way. Oh.   Except the fact that except Jimmy Sean wrote a really,   good book on the subject kind of.   So I, you know, he has I'll give him a pass. He has the latitude.   He has the latitude to do things like this.   Right? And you you,   you tipped me to this.   I did. And I you know what? I added you. I have to tell you, you know what I like about Jimmy Song's Nostr profile?  

What's that? He goes by Jimmy Song at programming bitcoin dot com. So he plays to his strength.   Yeah. Okay. That's   gonna give him credit there.   Okay.   Here's what he wrote. Here's what he wrote. I'm reading papers about rational trigonometry.   This is already sounding like pretentious. What is rational trigonometry?   I'm going to guess that it's trigonometry strictly with rational numbers.  

[00:48:10] Unknown:

Okay. Alright.  

[00:48:11] Unknown:

Right? And rational numbers are, you know, fractions p over q.  

[00:48:16] Unknown:

Okay.  

[00:48:17] Unknown:

Which is, you know, typical trigonometry, you have irrationals like pie,   all over it. Right? So that is kind of an interesting   thing to think about.  

[00:48:27] Unknown:

Okay.  

[00:48:28] Unknown:

Right?   Okay. So I'm reading papers about rational trigonometry   and not basing math on set theory.  

[00:48:36] Unknown:

Okay. What is set theory?  

[00:48:42] Unknown:

Set theory is a field.   It's a pretty   evergreen field of math   that   you you probably use it all the time but don't call it set theory.   Okay.   For me, I'm most familiar with it in the probability context.   Okay. But it's more of like with unions and intersections   and, you know, we have   members of sets and you think of unions, intersections.   Anyway, and he says, Rejecting   This thing doesn't it's not going to make any sense. We'll have to put it in the show notes. But anyway, so I'm reading papers about rational trigonometry and not basing math on set theory, comma,   rejecting infinite sets and real numbers   using Cauchy's category of converging sequences   and my mind is blown. It's like I'm reading Austrian economics of the math world. Now that last sentence is like Breedlove wrote that for him, so forget it.  

Okay. But like, I'm going to read that last piece again. It says rejecting infinite sets and real numbers using Cauchy's category of convergent sequences.   Yeah. Which is like,   this thing, if you study analysis and I'm not   like an analysis expert. I've been through a couple of textbooks in the last year, so I have   a little bit of knowledge, but my daughter is like   neck deep   neck deep in analysis.  

[00:50:05] Unknown:

Okay.  

[00:50:07] Unknown:

Her answer pretty much to everything in life is that,   it's,   no because it's because of Cauchy or no because of Lipschitz.   So, like, there's these certain overriding   it's like a way of thinking in analysis where you can pretty much you can reject certain   it's   it's like in modular arithmetic when you have a zero and you just you can ignore it. Mhmm. Right? So if, like, if you had a base if you had   a finite field   modulo   modulo two.   Right?   Mhmm.   And then you had this big   polynomial that was like x squared   plus   sorry, x to the tenth plus   two x to the eighth plus four x to anything with an even   anything with an even coefficient gets eliminated,   right? Because it's modulo   two. So it's   zero. Right? It's equivalent to zero.  

So using this concept of using Cauchy is like a way of eliminating   certain things. It means it's bounded. There's like these tests of   if you look at a sequence, is it bounded? Is it convergent?   Is it continuous?   Is it uniformly? You have you're asking all these questions and then there's you just apply one word, Cauchy, who happens to be a mathematician who   studied a lot of this. And if it's Cauchy, it just it's a category. Like, it's then this it's this type of sequence. And I can't and and again, I'm not even strong enough to tell you what it all what it actually means. But,   this is what he's saying. Like,   if something is Cauchy,   it just implies that it's usable. It's almost like saying in abstract algebra, it's like saying something's a group.  

Okay. It means that there's now a field.   There's like a field of math that can be performed on it because   you know of   certain essential properties of it.   Okay.   And so   for Cauchy's category of converging sequences, it just means that,   it means something   that it Right. That puts it in a category. Usually, may   like, in analysis, you wanna know, can it be, is it continuous? Can it be different? Can you take a derivative? Right?   These are the can it be integrated? These are, like, the important questions in analysis.  

[00:52:31] Unknown:

Right? So why did it get,   analogized   to Austrian economics?  

[00:52:37] Unknown:

Like, what is what is it? Why Why did he let Breedlove write this line? Let's let me let's try to think about it for a second. Well, his mind is blown. And I think anytime you or I or anybody in this   space, anytime our mind is blown,   we start feeling like we were when we started reading Austrian economics.   That's at least how I Okay. Maybe that's how I would read it. Right? Like,   the but But when Yeah. When I entered the Bitcoin space and I started   you know, I did read human action, which was not easy.   Kudos to you. I read a couple of like Rothbard books. I did not read Man Economy instead. I started it, but I just was like, My brain was like, Nah, this is too much.  

But, like, it was mind blowing that it was a mind blowing renaissance.   And anytime I feel like my mind is blown, sometimes I am taken back to that time.  

[00:53:29] Unknown:

Because it it puts   and to me, it's   to me, I read this as   Jimmy is reading something   that puts a framing around the world that makes   sense   and is hard to sort of, I guess, refute   or to to, like,   like, you you might be able to,   like,   somehow   pseudo intelligence, you know, like,   explain it   away. But, like, at the core of it, like, no. This is this is, like, the truth of the way things work. Right? And that was that was one of the things for me in Austrian economics was, like, the human the idea of human action   and and meaning,   like, it's either even inaction is an action of itself. Right? Like, humans all are doing these things. Like, this is like a Yeah. A fundamental truth of the reality we live in. And so that's why I was curious why what this thing meant because,   if that's, you know, if that's the what he's supposing is saying. To me, it's saying, there's this math world, and here's now this, like,   almost irrefutable   explanation for the way that things work.  



[00:54:42] Unknown:

Yeah. I one of my pet peeves with Austrian economics  

[00:54:46] Unknown:

Okay.  

[00:54:47] Unknown:

Is   its conflation   its attempt to conflate with   the sciences.   And,   you know, the book that   got me really close to this   was,   Hape,   it's called Economic Science and the Austrian Method.   I don't think it is a science though. Well, I know. And so, like, the arguments I got   with people about that book was that economic science should have been in quotes.   Right. Honestly,   and he will never listen to this podcast, But, my   like, one of my favorite authors and my favorite people to this day in big leagues, the person who I consider an absolute role model for me is Canute Pfannal.   Like, I view him as, like, two cycles ahead of me. Like, I wanna be where he I I would definitely see myself, like, where he is in, like, two cycles or something like that. Like, hopefully, written a few books and, like, still have a good head on my shoulders.  

But,   the one thing that he, like, he hits on his pet peeve with the axiom of action and saying, like, well, if you try to refute it, you're only proving it.   And,   like, that's the kind of stuff that I feel like I just feel like it's dangerous   to and, you know, in this   you know, people who listen to this podcast, right, motivate the math, part of it is also making sure that we have the right   structure,   right frame   to view things in the world and that we're rigorous.   Now I think you can be   so rigorous,   right, that you start thinking you're dunking on people   and it's that just gets very dangerous. You know, it start it like, it starts to look like you like the smell of your own farts.  

Mhmm.   Or you're trying too much to valid you really, really need to validate   this field,   because Austrian economics is not like   math.  

[00:56:45] Unknown:

Right?  

[00:56:47] Unknown:

And math is not irrefutable   either.   Right? Math is not some irrefutable   thing.   It doesn't like make your It's just a way of framing it. Yeah. I hate to do the math. I hate that I hate that,   saying. Like, let's do the math. No. It's not   that's Yeah. I mean, that's people should do that, and you should help maybe help people do that. But, like, that's   not like,   math isn't gonna make your case.   You know? It's just gonna like, math is to just make people   better and deeper thinkers and frankly, more annoying.   Math should make everybody, like, more annoying and more annoying to argue with because   there's no stand there's no great standard of argumentation.  



[00:57:32] Unknown:

Right? It's just   Yeah.   Well,   math is like the stand one standard of argumentation. Right? Because you if you can reduce the the argument down to,   like, equations  

[00:57:44] Unknown:

It's just math, bro.  

[00:57:45] Unknown:

Just set parameters around it. Now we're all talking about the same thing. Right? And this goes back this goes back to   the math is a language. Yeah. Yeah. We're not all  

[00:57:54] Unknown:

saying the same thing, but we are at least we know we're talking about the same thing. Yeah.  

[00:57:58] Unknown:

That's so true.  

[00:58:00] Unknown:

And this is again why I fear   I like, my fear,   my concern   is that   we understand   math so little or we believe in it like a religion,   and,   you know, we lose the ability to actually verify. We lose the desire. We lose the idea we even have to verify.   Like, you know, I don't know how many people thought they needed to verify the cryptography of Bitcoin. I don't know. I don't know the answer to that question. I'm sure I'm not the only one. I think the number has gotten  

[00:58:32] Unknown:

smaller  

[00:58:33] Unknown:

over time. I'm I'm sure I'm not the only one who felt the need to do that. Right? Right. But then the question is   who wants to verify the math too? And then that number gets even smaller.   Right.   And   that's the one where, I mean, I feel like I'm sounding the alarm, and I'm now   doing this work because I feel like more people   need to feel the need to verify the math and they have the aptitude for it. Eric, like, I do believe people have the aptitude for it. I might need I might need to help them a little bit.   Right? We might we might need to help motivate it, and then we might need to do some videos or have a class to Some explaining. Teach how it work teach how these some of these basic things work. But, like,   I think that because people don't think they have the aptitude for it, they don't think they've convinced themselves that they don't need to validate it. They think math is some type of thing that stands on its own from God.  



[00:59:29] Unknown:

Well and,   you know,   like,   change,   unknowns   are all, like, things that humans fear.   And so   you're you're we're telling everybody, it's like, hey. All that math you learned, yeah, throw it out the window. Not all of it, but, like, here's this new way of doing math. And I think that's probably intimidate. It's just I think it's just flat out to be. I don't think it's fair at the window. I think what we're saying is  

[00:59:55] Unknown:

what if you actually   What if we don't let What if you couldn't get let off the hook because you did actually know What if you had the aptitude to do this verification? You   know,   And what if it was actually really easy?   What if it really was actually easy?   Right? Mhmm. When I say, you know, like easy, like,   you know, you spend a half hour a day for, like, a couple of months,   maybe,   and you are, like, now in the position to,   like, be really sovereign, you know, like, that type of   and not you know what I mean? Not it's not like it's not a lot if it was so easy, everybody would do it. But there's something you know, it's just beyond the elusiveness.   Right?  

But what if it was easy enough   that, you know, most people now would take the responsibility   and would do it, would be interested in verifying   the math   because they can they understand you know, and it's like if they don't even   so that you know, once again, that's why we do this. I feel like that's why we were here and why we want we just have these conversations   to to demystify   a lot of these,  

[01:01:13] Unknown:

just this whole idea. Well, and also to shame people into taking responsibility. Right? Because if you don't actively pursue   increased responsibility   and then you suddenly   are burdened with responsibility,   You know? Like, that's it's it's like the fitness thing. Right? If you suddenly have to run a marathon without training for it, you're gonna suffer. You might you'll probably still finish the marathon,   but you're gonna suffer. I think responsibility   and taking responsibility is one of those things, and Bitcoin is is nothing if it's not a radical   a a movement of radical personal responsibility.  



[01:01:46] Unknown:

If I knew there were a thousand people like me in the world, like, in the world, I would be like, well, you'll run into one of those people, and you'll be okay.   Yeah. That's true. And yeah. So, like, when I I just my experience is that that's I've I've had so few people who really think this is important   that it becomes an it becomes a responsibility   on my part   to,   sound the alarm and try to do something about it.  

[01:02:15] Unknown:

Well,   let's, let's keep doing something about it because I think I think what we're doing is working, and there's a very, very clear mathematical indicator.   It's   working.  

[01:02:52] Unknown:

Because everyone comes to look.   Don't wanna be anything   where my life's an open book.   A dream   that's true.   But I'd see   it through.   If I could be here,   I'd   Thanks, everybody.   Couple of doosols.