Fundamentals. @Fundamentals21m
Book: https://zeuspay.com/btc-for-institutions
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AverageGary
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Pascal's Triangle
https://en.wikipedia.org/wiki/Pascal's_triangle
In this episode, we delve into the fascinating world of probability distributions and their relevance to Bitcoin's security and mining processes. We start by discussing the concept of probability distributions, such as binomial and Poisson distributions, and how they help us understand the likelihood of different outcomes in various scenarios. This understanding is crucial for modeling events like coin flips or mining block rewards, where knowing the average payout and the necessary capital to sustain operations over time is essential. We also touch on the importance of randomness and entropy in cryptographic applications, emphasizing the need for truly random variables to ensure security. The conversation then shifts to the adversarial nature of Bitcoin's network, highlighting the importance of understanding potential attack vectors, such as a 51% attack. We explore how the Poisson distribution is used to model the probability of mining success over a given period, and why it's vital for the network to be tested through both simulated and real-world attacks. The episode underscores the necessity of open-source software in creating robust systems that can withstand various threats, and the role of probability in ensuring the resilience and security of Bitcoin's decentralized network.
[00:00:02]
Unknown:
Stop. You thought you were gonna get math, and we're just gonna we're gonna discuss something that I think I think the framing we can put around this, though, will be evergreen.
[00:00:35] Unknown:
Well, it's let's just preface real quick Sure. That, episode 19. The math podcast has had an interesting trajectory up to this point. I think we started out with a lot of ideas, and we start we were doing regular episodes probably either every week or every other week. Yeah. We're sort of at the point now where we're not on that cadence, but whenever we start thinking of a math idea, we're like, alright. It's time to rip. Yeah. And, so, like, I think I forgot who the last one that came up was the, the Quantum FUD. Right? And that just that Yeah. Yeah. That just came up and we were like, yeah, dude. We need to do an episode about that. Let's it's time to rip. And then I heard you I heard you mention the name Poisson way too many times for me to then not make that connection and say, wait wait a second. That's math. Why are we why am I not why are we not doing it? Then not only is it math, it's like literally the math in the white paper.
The only math. I think I think you've I've you've stated as much. Yeah. There are Bitcoiners that think, like, a page number is math. You know? Well, I've I've been one of those. Well, it's more like Are they wrong, though? Can I tell a quick oh, absolutely not? Last up here is just shout out. So shout out to Solex, regular listener, and I'm sure he's eagerly awaiting this conversation. I don't know. It's great to find out It's just great to find out people are, like, marathoning this show, and that's what kinda keeps it going. You know? That's what keeps me going.
[00:02:13] Unknown:
I mean, something has to fill the psychopathic void inside of all of us. And, when you run out of macro and when you run out of, the bugle, come to the math.
[00:02:22] Unknown:
Can I give you my
[00:02:24] Unknown:
my version of page number numerology? This is like everyone's gonna stop listening forever when they hear this. Your version of page number numerology. Okay. You have it your own way of do yeah. I'm like, I'm trying to hack.
[00:02:36] Unknown:
No. It's just words in my head. It's just so stupid, and this is just why I'm such a fucking retard. Okay? But if you read, Eric Caisson's crypto sovereignty
[00:02:49] Unknown:
Yeah. K. I've not finished it, but I've begun.
[00:02:52] Unknown:
Did you get to page one zero three by any chance? Oh, we can check right now. It's one of those book oh, you know what? I actually took it out of my book bag. It's like, I don't know why my brain does this stuff. I just don't know. I wish it didn't. But, like Okay. You know what's on page one zero three. I'm going from one zero two to one zero three, and I'm reading something that really he is very passionately now talking about the I haven't read this book in two years. Okay. So this just paraphrasing my brain in my head, though. But, like, he's very he's making a very strong case about, you know, how powerful a NIM can be and why it matters so much to Satoshi.
Correct? Yeah. And I'm just noticing page one zero three, and I just my brain said, oh, Jan three. This is What? Okay. Stupid and, you know, it's not worth it's not even worth the minute I just spent talking about it. I just thought it was hilarious and funny, and I've I've been telling people, like, it matters.
[00:03:49] Unknown:
Like, check the number every once in a while. You rearrange the numbers. Right? Like, if you use, like, the the British people, they do, like, a different ordering in the numbers. It's like the month is first. Europeans do it. And that's why by the way, that's why,
[00:04:02] Unknown:
you know how everyone celebrates Pi Day in The US on March 14? Well, not everyone. But, yes, I understand some people do. It's a great sign you're like a math larp. Like, oh, I love pie. Pie day. You know? I'm I'm a pie guy. Hey. The public school celebrated. Okay. Like, all the math teachers in public school get all excited on March 14. Something I've always said that's fallen on deaf ears is that really worldwide, it should be, July 22 because and and it's so much better than March 14, so much better because they put the day first, the slash, then the month.
And so July 22 is twenty two slash seven, and that's famously pi. That's, like, the closest approximation to pi. That's the closest approximation to pi. 22 divided by seven is the closest approximation to pi. That you're gonna get from rational numbers. Like Really? From rational numbers under a 100 or under a fucking trillion. You know? Like, that's the best approximation you can get without without, like, really breaking out
[00:05:09] Unknown:
advanced calculators. But do they, like, the do the Brits have, like, a different name for, like, pies, though?
[00:05:15] Unknown:
No. Okay. Bangers? No. Because I know they call, like, cookies biscuits or whatever. But it's not that's not such a British thing. It's more of a extended EU type. Rothschild empire. Do it. I feel like in Canada, Australia,
[00:05:30] Unknown:
all over Europe, New Zealand, that this is a custom. You know, and it makes me question whether America should do that because the metric system is right. Like, base using base 10 for for the the base unit of, like, measuring things is just,
[00:05:46] Unknown:
easier to reason about. Yeah. But we have guns, and we can be ungovernable. And so we can have stupid fuck Yeah. I have a nine millimeter.
[00:05:53] Unknown:
It's a fucking nine mill even the guns figured it out. It's still the metric system. It's true. It's true. We can't escape it. We can't escape our destiny. Nope. We can't. Metric metric maximalism, and, we should just move completely off of the, what is the calendar we use? A caesarean calendar or whatever? Gregorian? Gregorian? I don't know. I don't I don't fucking branch Davidian?
[00:06:17] Unknown:
We almost we almost ended up on the Branch Davidian calendar. We we hadn't gotten that guy.
[00:06:25] Unknown:
Jesus Christ. We were talking about adversarial thinking. We started recording because we,
[00:06:30] Unknown:
like, started talking a lot and forgot we were talking and said, why aren't we recording?
[00:06:35] Unknown:
Yeah.
[00:06:36] Unknown:
I think even though we intend to talk about Poisson distribution at some point in time, we were because everything we say is pure gold. Valuable for its utility. Pure gold. Pure gold. Valuable only for its utility. Slight amount of maybe some tungsten in there. But, we were talking a little bit about the issue of the day, which
[00:06:57] Unknown:
we tend not to I tend not to bring it apart. But we can frame it around an evergreen topic, which is adversarial conditions. Yes. Antifragility.
[00:07:07] Unknown:
So we're here episode 19, and it just so happened this past weekend. Bit of a watershed event. And, you know, there's been there's been to me what's been a very I've covered I've said this publicly on the show. I feel like the the nots the cannots debate has been just sort of a childish demonstration of really a lack of ability for Bitcoiners to communicate effectively.
[00:07:31] Unknown:
Yeah. Yeah. Wow. That's yep. Well, and that's been it's very obvious on, like, both sides of the of the debate too. I forgot what side what I forgot what episode we covered this, but we
[00:07:42] Unknown:
did. We definitely had this conversation. I got a lot of shit for it. I'm great. I'm happy to for the fucking tennis nurse. Piece of shit like you for breakfast. You eat shit for breakfast?
[00:07:51] Unknown:
Sorry. Happy Gilmore quote. Keep going.
[00:07:56] Unknown:
Yeah. We have, like it's so funny when you have a podcast that has so few listeners and that you still catch a lot of shit for from people who really wouldn't be in the target demographic at all. Right? Most people, I think, who listen to this are, like, think Nas is gay. My guess. It's my guess. Maybe. Maybe. I don't know. It doesn't like, it We had running the same consensus engine, that's fine with me. Interpreter That's TP. Yeah. Like, we had that we had that conversation already, so we're not gonna but, basically, what happened in the over the past weekend was that, a guy named Portland Hoddle who has been you know, he this guy has done some things in the past. I wanna say
[00:08:37] Unknown:
Well, he gave a talk about, like, how you could slow down a block. Like, you put a shit ton of signature checks, and there was, like, some special structure, and you had to tee it up with a bunch of other transactions before you actually executed it. But he gave a talk and did a live demo of, like, a twenty five minute block validation,
[00:08:54] Unknown:
which is Yeah. I consider I consider him a good follow because he basically will every I don't know. Every once every three or four months, he'll have some Twitter thread on some just something he was fucking around with that Yeah. He kinda he kinda broke on somebody. Yep. Maybe one one of the times was the Moon Wallet situation. I can't No. I don't know. I wasn't paying attention at that point if it was You know, he's a good pretty good follow in terms of, you know, he's out there he's out there trying to break shit. When I've met him personally, he's also, like, he's also a very intelligent individual as well. Like, he he knows
[00:09:27] Unknown:
he knows what he's doing. You know, you can't you can't find some of these like, to figure out a twenty five minute block validation, you have to know how the scripting engine works. You have to know what will potentially delay that scripting engine and, like, a number of other things. And then to, like, recreate that in a reg test environment, right, is, like, you know, you have to know what the fuck you're doing with the note.
[00:09:50] Unknown:
So I think from a certain point of view, this fake nots debate I call it fake. I really think it's fake. I I do think it's, like, some type of influencer capture shit. About consensus. So, like But so at some level, I believe this debate is a blight and a pro potentially problematic. I've, again, talked about it on all my podcasts. Potentially problematic to the Bitcoin network in terms of I I think it just dem it demonstrates to our attackers how bad we are at actually solving problems. And I'm not saying don't do that. I'm saying, hey. Let's let it run its course, but it is what it like, don't go virtue signaling and tell me you're, like, doing god's work by doing this shit. Right? You're not you're not doing god's work by running knots. I mean, you're free to do so, but, like, don't try to claim some superior position. It's absolutely insane. In fact, the more you try to argue and defend that position, the more the wider you open the door to our attackers because they see how retarded,
[00:10:53] Unknown:
like Well, and it's prominent people here are. And the interesting thing too is this this quote, unquote, like, attack or and and just to lay it out. So Portland Huddl figured out that Comcast, the the ISP, Internet service provider, has, like, data cap limits on, I think, upload side of things. And so if you are running a node behind a Comcast IP and you are, uploading a bunch of like, if a bunch of nodes come to you that wanna do IBD or initial block download Yep. And start hitting you, like, hey. Give me blocks. Hit me. Give me you will run out of that limit, whatever that limit is. And there's a configuration within Bitcoin Core and nots that enables you to put, like, a cap on that upload. So, eventually, you're just, like you'll stop, like, giving blocks to people. Right? Yeah. Or, like I I can't remember the the technical specifics of how that configuration limit works, but it prevents you from, like, getting throttled
[00:11:48] Unknown:
from a bunch of people connecting to core. There's an actual switch in Bitcoin core. There's a Yeah. An option. So correct me then if I'm wrong. This wasn't, like, explicitly this isn't wasn't even really targeting the nots things. This is targeting anybody running running a note, really, to say, hey. This is this is an issue you may wanna understand if you run a note. It just happened to really blow up. It's the the, virtue signal of the nots people is I run a note and I protect the network. I mean, that's that's so that's really why they got particularly they got particularly blown up and why it got particularly funny to to many good people. Many good people, got caught up laughing with, got caught up laughing with Portland Huddl, and, I find it, I find it reprehensible, the attacks on the laughers.
God, this is not gonna age well, but, like Well, no. It it people get no. People get what I'm saying. There's a duality to this. Right? Because, like, is it fucked up to attack somebody running a node at home and, like, basically, DoSing their node? Never okay. Sorry. Sorry. I'm getting caught up in the world. Kind of a dick mood. But, like, if you're gonna participate in this thing called Yeah. Bitcoin. Dick yeah. It's kind of a dick move to be, iron to be an iron sharpening iron. Okay? Right? Absolutely. Yeah. So, like, we accept people out of jujitsu all the time. It's a dick move to fucking choke somebody out, but guess what? Like, you're gonna learn a lesson. Did you wanna build your citadel with nice guys, or do you wanna build your citadel with the kind of dangerous men that will actually you might be you know, you wanna keep close and you may fear, but actually are gonna give you a shot at Yeah. Just a shot, right, at defending your life against the state. Right? I mean, you have to basically cast your lot with the dangerous men. You have to.
Am I wrong?
[00:13:40] Unknown:
No. I don't think it's it's not, peaceful men, ideally. And, like, looking at Portland Huddl's
[00:13:46] Unknown:
avatar on Twitter, it doesn't look very dangerous. But he is, you know, he is iron sharpening iron.
[00:13:54] Unknown:
The the danger is the the knowledge. Right? And and, again, this is like I made the assertion before we started recording. I am glad that more people understand node configuration, this one piece of node configuration than they did before. Because otherwise, they would have floated through the rest of their node running career, never thinking about, like, what do you what do you like, what is this configuration thing? Right? Like, not a lot myself myself included, I couldn't tell you all the different configuration options in a Bitcoin core node. No. That's not a problem. I could tell you right now the ones you can are because you had some fucking problem or some worry or something didn't work. And that's the only re it's the only way
[00:14:29] Unknown:
you ever learn of a configuration option. Yeah. And he gave he basically gave everyone the keys, so to speak, the, the solution. He gave everyone the solution. Right? And yet everyone still wants to kill the messenger.
[00:14:46] Unknown:
Well, in the in the it's a solution not to the node problem, whether you're core or you're not. Right? It's the same issue. It's an a limit on the ISP. Right? And this highlights something,
[00:14:58] Unknown:
so running your own node, and yet you can't you you're, like, subjected to a data Can't keep it on my ISP that you don't understand. I mean, it's so pathetic. Right? That's I'll I'm so glad this is was brought to light because now I mean, we want people to we like, it's ideal. That's a narrative that doesn't have substance. We want that narrative to actually have substance. Yeah. Otherwise, you're just a you're just a larv. Right? And then you'll kill the messenger for killing the narrative if that's the way you are. Right? We wanna like, what I so I feel like he's providing substance by find you know? And it's just there's probably 20 more of these that need to be done before we really have run robust nodes.
[00:15:42] Unknown:
Well, it's it's operating in adversarial environment is what it is. Right? Because, like, this happens to somebody using Comcast in The United States or whatever. Right? So, like, now replace yourself running a node and put yourself in some, like, despotic regime, right, that is, like, even more authoritarian or even more, like, tuned into the knobs that they can push and pull on on the network.
[00:16:08] Unknown:
Right. They know the configuration options of their control grids. We need to know the configuration options as many as possible. And you know what? Maybe this is just a good segue into the episode because learning math is not something you have to do. You never wake up saying, fuck. I don't know if I know enough math. Most people don't. Right? Most people don't wake up saying shit. Don't know if I know enough math to get through the day. And yet Yeah. We study it anyway. We do the work because it's important. The same way it's imp like, you know, it's like knowing the configuration options on your node, nobody really wakes up says, oh, shit. I wonder if I understand all that, if I can really get through. But you know what? That could today could be the day that that fucks you up. This you actually reminded me of another topic that I don't know if we'll wanna dig into today,
[00:16:56] Unknown:
but it was something that did make give me pause. And and I I thought about reaching out to you, but I just, I had not because I hadn't done any of the due diligence. But recently went on a couple podcasts talking about simplicity, which is like a new scripting engine essentially for Bitcoin. But the way I'm trying to figure out remember the way that he described it. But it's like the way he described it was there's, like, some very, very, like, core fundamental primitives within there that then you can, like, build on top of, and then they have these things called jets, which are, like, predefined combinations of these primitives.
[00:17:32] Unknown:
I feel like reading about I would feel like I spent when we first started this podcast, I feel like this was, like, January
[00:17:40] Unknown:
Yeah. Where
[00:17:41] Unknown:
this came out, maybe the paper or the abstract. Well, Simplicity's been around a while because I remember hearing about it at BitDevs. Like We started before I ran it. We started talking about it. I this is back. I I ran it. I think I ran this through, like, the Google notebook thing to get to to get a a digestible podcast on the actual white paper.
[00:18:03] Unknown:
And The Simplicity white paper or the Yeah. Bitcoin white paper? Simplicity, I think think it was. Well, it's live on on Liquid now. That's like the that was like the big thing was, like, this is Symplicity is now a feature of the Liquid Federation Network. Wow. Yeah. Like, they're I mean, if you're serious about a project, you need to go put it somewhere that it can actually be used. And and that's sort of what and if you hear the podcast and sort of alludes to this is, like, he as, like, the lead r and d at Blockstream, right, which is, like, nothing to shake a stick at, but, like, he sees liquid as sort of, like, a testing ground. Like, he's a Bitcoin maximalist. Right? Like Yeah. But he sees liquid as his testing ground for, like, all these other cryptographic things. What are these different things that you can do with the math in in a scripting engine or with confidential transactions or whatever else? There's a bunch of other stuff that's on liquid that is, like, it could be on Bitcoin, like the main net.
But, you know, you need like, as we've seen, you need a lot of buy in.
[00:19:05] Unknown:
Yeah. Because test net's too many times to like, test net's hard
[00:19:09] Unknown:
to do anything else. Oh, yeah. Test net four. Well, test net four is is constantly under, quote, unquote attack. If you go to a fork observer
[00:19:19] Unknown:
So liquid is an is a sandbox for Bitcoin that Absolutely. It's a different kind of sandbox for Bitcoin.
[00:19:26] Unknown:
Yeah. Yeah. Right. And it just happens to be, like, the big one of the big sandboxes that's doing real world, like, transactions.
[00:19:34] Unknown:
It's funny, though. So liquid I mean, it's interesting and funny too, but because, Blockstream at one point were giving away a lot of sats to hand out at meetups Oh, yeah. To do, just, like, a little bit of a demonstration on Liquid. And the funny part of it was, like, if they gave, like, if they gave, say, you know, 500,000 sats to give to, you know, 20 people, The thing, it has to clear every minute. You you can't, like, you can't just go boom, boom, boom, boom, boom, boom, boom. You actually need to you can't just get you can't put them all into one transaction. Yeah. It's got a one minute block time. I I mean, I've I've used liquidity That's that that was the big lesson we all walked away with. Oh, really? Yeah. That's because that's what we experienced.
[00:20:17] Unknown:
Well, there's a way you you can do, like, atomic swaps with liquid. It does have the one minute block time. And I remember when the fees were spiking around, like, the initial ordinal craze and stuff like that, like, the super high, you know, hundreds of sats per e byte. A lot of people were like, oh, hey. Like, just go go use liquid because it has interop with lightning. It has and that's the other thing that I think was interesting, is it's all this interop. Right? Like, it's the it's the interop. And at the the core of the like, this interoperability is the math.
Right? Like, you you you go from one chain to another with these swaps. I think generally using something called, like, an adapter signature, which again is like a way of structuring a math equation in special signatures where it's like, I can encumber this transaction. And then once you provide a signature for it, then that reveals another secret that I can use to, like, unencumber
[00:21:10] Unknown:
this other transaction. Unpacking that at the next episode. Let's now put that on the calendar because I feel like that's the like, it's I feel I suspect that the work we did on group theory will explain why that's the case. I suspect interoperability has to do with, isomorphisms.
[00:21:30] Unknown:
Here's some here's some homework.
[00:21:32] Unknown:
Alright. Yeah. I will. I will break put that on, and maybe that's the next stage of where we go here. Or maybe Yeah. Right? And we we're finally gonna cover, I feel like I I'm glad for this episode 19. We're gonna cover some probability. We're gonna, you know, we're gonna cover what's in the white not specifically, maybe what's in the white paper, but the fact that it's probability. I thought a little bit about how to approach this.
[00:21:59] Unknown:
Well, that's good. Because I just say the word,
[00:22:03] Unknown:
and I don't You said you said you exactly. Few times. And so I'm like, okay. Why aren't we why aren't we doing an episode on so let's do it. Let's let's let's do you wanna are we ready to move off, or do we wanna do you have anything more to
[00:22:17] Unknown:
No. That's it. I I think, just the last caveat or last, like, little, like, tangent is if you go to fork.observer and you click little drop down and go to test net four, you can see what a highly forked network looks like visualized. Yeah. There's a there's a great dev out there that does a lot of monitoring tooling. Put that in the show notes. Yeah.
[00:22:38] Unknown:
Yeah. And just like embrace, adversarialness. Don't be gay. You know, like, don't get all, awoke because people are laughing. Yeah. A lot of good people.
[00:22:53] Unknown:
It's like, why are they laughing, though? Right? Like, they're not they're not laughing at the the misery of some node runner in their house. Yeah. Like, it's That node runner can still get their transaction out.
[00:23:05] Unknown:
Again, man, like, I I these people are just lost, in my opinion. Just absolutely lost. You know?
[00:23:13] Unknown:
They're I mean, they're on the right track. Right? They're still big like, everybody's a Bitcoin. Like, people thinking and caring about this are Bitcoiners, so it's like, are they paying attention to the right thing? Maybe, maybe
[00:23:24] Unknown:
not. But, like, if you're hung up on a narrative with no you're hung up on a narrative with no substance, you will kill then you will kill the messenger who tries to actually put substance in behind the narrative. Right? So if you're if you're unwilling now to have the substance put in and you just wanna kill the messenger, go eat a dick. Okay. But make sure you fry it in tallow, not seed oil. But you know what? You require Bitcoin asks for no no forgiveness whatsoever. You're always fucking welcome. You're always welcome to accept the protocol whenever you want. You know? It's like it's so funny. I I don't wanna get too more into too much more into this.
But, these people are like the anti shitcoiners, and yet the they are they're kinda shitcoiners. Right? It's just just interesting. That's gonna get taken out of context, and no one's gonna understand what I meant by that, and I'm gonna get the last Okay. Whatever. Whatever. It's out there. I'm a podcaster. I say shit. It happens.
[00:24:20] Unknown:
It's it's funny. Recently, like, making comments in one of the group chats I have, this guy put the you know, it's like this mass figure with the hand up, and it's like silence,
[00:24:30] Unknown:
insert name. Yeah. Pod comp name is talking or whatever. Yeah. Yeah. Yeah. And it's like silence dev, podcasters talking. I was like, wait. I have a podcast too. But they don't mean, like, our podcast. They meant pod comp complex, podcast that really pumped ocean. That's what I was that that's that's my interpretation is that they, you know, the PodConv complex pumped Ocean.
[00:24:49] Unknown:
And I'm a fan of Ocean, though. Right? Like, I love what the Ocean team is doing. Yeah. This isn't even like an Ocean project. It's just so it's just the insane person. They
[00:24:58] Unknown:
they the the insane person they decided to have to be their CEO. This was like a side project for him, and it became you know? But but it's still in, like, the loudspeaker of that of, like, the PodCon complex. Yeah. Right? So it's just you know, you don't get to they're they're like antibiotics, dude. You don't you don't get to decide which of these narratives are the ones that stick. They all they all get pumped out, and that's just the way it is. PodConf doesn't discriminate.
[00:25:24] Unknown:
That's true. That's fair.
[00:25:26] Unknown:
Oh, man. Alright. Let's get into math before we, before this gets even more off the rails. Shall we? Shall we talk a little math?
[00:25:35] Unknown:
Well, first of all, bring up your white paper. Turn to page six.
[00:25:40] Unknown:
Yeah. I wanna get I wanna prep I'm actually excited about how I'm gonna lead into this because I know we this is gonna be about Poisson, but I'm actually gonna make this a little bit more general because we've never done this on Motivate the Math. So episode 19, we're gonna do this now. I want I'm excited to talk about, like, probability. Oh, yep. Things of a probabilistic nature, things like random variables, random processes. And I wanna just I think, Gary, we should talk about that a little bit in general because then it's like, okay. What does it matter to know the word versus normal versus binomial versus like, why does it matter or versus a negative binomial versus, you know, you name it. Okay. So, like, we sometimes we like to say we like to think we understand, the probabilistic nature of something.
So for example, if I flip the coin, now that's I know that's a foreign concept to most people because they don't there's no more coins. Right? We have Bitcoins that you can't flip. That's, like, my biggest criticism of a Bitcoin would be you can't flip it.
[00:26:52] Unknown:
You gotta go with, like, challenge coins. Right? And the military has a strong culture of challenge coins. That's what the world is moving towards. I've got a Bitcoin better one. I've got a I've got one for my employer. Coin. Nice. Challenge coin. If I was a boomer,
[00:27:05] Unknown:
I would be on, like, CNBC right now saying, if you can't flip the coin, it's not a real coin.
[00:27:13] Unknown:
There's so many it's it's interesting because the, the dual, like, you know, flipping something, right, in the nature of, like, a house or, like, a a trade or or something like that. It's like, oh, I flipped this. Right? So that's a it's an interesting They've they've co opted all of the ways
[00:27:26] Unknown:
we that kids naturally learn about probability. Okay? Okay. They've co opted. They got rid of the coins, and now these kids don't understand risk. They they you don't flip any you you don't flip to for, chance anymore. Yeah. You flip for profit. Oh.
[00:27:46] Unknown:
There's a sound bite. Okay.
[00:27:48] Unknown:
Yeah. Okay. Podcast is over. So but okay. But let's go back to just imagine imagine there's a thing called a coin with two sides. Mhmm. And then you can flip it. On one side is a head of some Fiat lizard piece of shit, and on the other side is some structure that you lived in Yeah. Where you built. Okay? And imagine that you when you flip it, it lands on either the head or the tail with equal chance. Right?
[00:28:16] Unknown:
Yep.
[00:28:21] Unknown:
So how would you like, if you basically were running a game of coin flipping, right, and you said I'm gonna pay $2 per head and I'm gonna pay $1 per tail, what would be the price I would charge per flip in order to not you know? And and or and and how much capital would I need to hold to run that game to to make sure I don't go broke? Like, there's a certain amount I need to charge Yeah. So that I make money over time because there's this then thing called the law of large numbers that applies to certain probability distributions.
Okay? So the distribution I'm talking about happens to have a name called binomial.
[00:29:06] Unknown:
But it's like random walk?
[00:29:08] Unknown:
Yeah. Well, yeah. It's just binomial. Meaning, there's there binomial just means that there's two outcomes. Heads Right. There's there's two outcomes, and it doesn't have to be equal probability. You could have, like, a weighted coin. Like, if we were back in the wild West and, these guys walked around with weighted coin. You ever hear the term loaded dice?
[00:29:27] Unknown:
Yep. Yeah. So, like, the Well, my frame of reference for probability is dice because
[00:29:33] Unknown:
Dungeons and Dragons. Yeah. So dice is the dice is still in existence. They haven't come for the dice yet.
[00:29:39] Unknown:
Not yet. I'm coming for it, though. They will.
[00:29:44] Unknown:
I I I I used to walk around with my little baggie of I think I bought it from CoinKite one of these days, one of these times. It's like a little baggy. It's a little baggy with tiny dice. Mhmm. And, it looks like a bag of drugs. You know? But it's got tiny dice, and you it's called, like, entropy. You know? It's kinda funny. Right? It's like, oh, yeah. It's true. Right? You wipe you have this fucking
[00:30:08] Unknown:
little time full of dice. Dungeons and Dragons player that was like a caster, like a wizard with magic, had that bag of dice already because there's one specific spell in the realm called fireball. It's like a very iconic thing. And as you level up, you just get more and more of these six sided dice because because it's six sided dice in your bag. Right? Yeah. Yeah. You get more and more of these six sided dice because as your level goes up, like, that's how many how many the more dice you roll for, like, damage. And so it's because I already had a shit ton of six sided dice, so I didn't need to buy mine from Koincite. I already had them from, you know, past activities.
[00:30:43] Unknown:
Yeah. It's cool the way they come in a little baggy, I gotta say. And it's just like you actually do line put them in lines. It's very strange. It's very illicit, because you're put you're creating by you're creating a binary numbers. Yeah. That's how you you know, that's one of the ways you can make your own key with your own dice.
[00:31:01] Unknown:
It's one of these sources just a bunch of dice. Recommended source of entropy Yeah. For creating a key. Yeah. That's right. And there's a minimum number of dice that you want in that, and this is, like, a very, very key. And you maybe you can explain the math on this, but it's like there's a very, very specific
[00:31:21] Unknown:
minimum that you want. Otherwise, you will have something called low entropy. Yes. Meaning We won't do that this episode, but there is a the quest so it's a matter of, there's a couple things. One is, if the law of large numbers basically is, I mean, I wouldn't call it a law, but people call it a law. Mhmm. It's that, like, you know, how do you how confident are you that if you flip the coin enough times that it actually converges to, a probability distribution that you can actually model and feel comfortable that it'll converge to?
Right? So it said that the, Well, and that's in relation to, like, a security assumption. Right? Well, not well, it's more, like, how do I know if okay. Look. How do I know? How do I feel comfortable? How would I run this game if it was just coin flips? Right? How would I run this game if I again, I pay out, again, $5 for a head and I pay out $1 for a tail. How much do I charge per flip, and how much capital do I need on hand? Let's and then that's where you're what's called big n. Big n is, like, the number of it's like, what's the number before I Go broke.
Well, you know, I need to hold capital for a certain amount of loss. Right? Right. Like, so if I'm gonna pay $5 on a head, how do I know how do I really know it's not gonna be head 500 times? And I'll you know, that would mean I have to hold $2,500 in capital. But I probably don't. I can probably rely on the law of large numbers and say that, well, much more reasonably on in two if if my big n is 200, it's more likely I can I I can hold a lot less than that because the the very it's very likely they're not all gonna be heads?
[00:33:19] Unknown:
You're describing, like, mining pool
[00:33:22] Unknown:
Well, that's quote. That so Poisson distribution, not that we're getting into it yet. I just not quite ready yet. But it does it is a, it is one of the distributions that, like, a binomial distribution can converge to. So, like, in other words, you can use the binomial distribution, meaning, okay, one if there's by is two. That's it. And I have two outcomes, a or b, heads or tails. Right? One or zero. And it's very convenient to think of it as fifty fifty. You don't have to. But let's just, for the sake of this conversation, say it's fifty fifty.
[00:34:00] Unknown:
Right? Okay.
[00:34:04] Unknown:
There are things we understand now about a binomial distribution that if we knowing that it's binomial, it's like, remember when we had the conversation about groups and said, well, what is why does it matter that we know it's a group? Because then it, like, allows us to know a lot about the system. You know the box that you're playing in? Yes. So so knowing a coin flip is a binomial distribution with a certain probability allows us to say, okay. What's the average? Mhmm. Right? What is the average, what is my average payout if these are my you know, if I'm paying out, what is gonna be my what is gonna be the average payout, which is gonna help me decide the break even for what I charge for that game? So for example, 5 if I pay $5, I should have really written this out and figured this out before I started talking about it because I'm already, like, losing my concentration on it. It's probably gonna it might this might be wrong. But if I if I pay a $5 for a head and $1 for a tail, my average payout will be should be $3.
[00:35:10] Unknown:
Right. That's what that's what my gut told me. Like, this whole time when you were saying, like, $1 for one $2, I was like, oh, a buck 50 is, like, kinda where you wanna fall in the base assumption due to 50. So in that, if it's if it's five and one, five plus one is six divided by two is three. So the average and that's what you would call the mean. The mean of that distribution
[00:35:29] Unknown:
is three, which means if I charge less than $3 for that for that flip, I'm sis I'm gonna systematically lose money. Okay? But if I charge $3.01 for that flip, I systematically make money over a long period of time, but the question then becomes, what is the big end that's required for that to happen? What is the big n required for the law of large numbers to kick in such that I am just scalping one cent per toss as opposed to really being at this risk of variance?
[00:36:07] Unknown:
Yeah. Right? Yeah. Yeah. Yeah.
[00:36:11] Unknown:
Yeah. That's how you think about it. And so and so what so what is the big n? And then I and, you know, you know if you know, now you you wanna extend this into a mining pool. Right? It's the same I absolute well, there's one thing that I'll say that
[00:36:26] Unknown:
there's a parallel here that I think we've talked about previously is, like, you boil it down to a binomial. But in in our previous talks and stuff, I remember being able to take polynomials and boiling it down to a binomial equation where it's like, you boil it down to a binary representation.
[00:36:42] Unknown:
So Binomial is a is a so okay. Maybe I'm using the words wrong. No. It's fine. It's it's based off of a polynomial. Mhmm. So there's something called the binomial theorem, which tells you that any two numb if you square any two numbers, just gives you the formula. Just get you know, there there's a formula. There's a theorem that says this is what it this is what you end up with. And it matters if, this is back now. This is where where you need group theory because if, if you have a, like, a modulus, right, a lot of those terms are gonna zero out. And so in other words and when you have a modulus in math, you call it a characteristic. If it has a characteristic of, like, two, then then basically, all of your numbers are gonna be zero or one, and so a lot of the terms of the binomial expansion are gonna zero out.
Incidentally incidentally, here's a fun fact. Half the terms. Right? Yeah. Well, possibly. Oh. Here's a fun fact. Do you do you know what Pascal's triangle is? No. Well, we're gonna attach that to the show notes. It's one of the greatest things ever discovered by Blaise Pascal. Pascal's triangle. Shout out, Blaise. Another French mathematician, I I guess, like, like Poisson. But, Pascal's triangle, maybe we'll just I'll just save this for another maybe I'll save this. I'll do a video on it. But Pascal's triangle, every row gives you the binomial coefficients.
It's kinda cool of the it gives you all the every row gives you the coefficients of the binomial expansion. It's very, very cool. Also, every row sums to to the end.
[00:38:34] Unknown:
This yeah. Okay. I I pulled up I pulled up a website, and it's it's worth going to visualize. It's a an a tool for visualization.
[00:38:42] Unknown:
Yes. Because you can build this triangle structure. It's also if you're bored, if you ever, like, have hours where you must sit somewhere and not do anything Mhmm. You could just sit there and write out every row. You can go as far as far as you can on Pascal's triangle. Okay. So there is a binomial, which is like the simplest version of a well, not the simplest version. There's a monomial, and then there's a constant. But there's a binomial, which is a simpler version. It's a simplified sort of version of a polynomial. Mhmm. Okay?
But the binomial distribution as a probability distribution like, there's no polynomial distribution necessarily. There's not because we don't know it's too general. We just don't know enough. And unless we can get it to, like, two outcomes. Right? Mhmm. Okay. Really get to that. We don't really get that, we don't really get that sense of maybe we know something.
[00:39:40] Unknown:
Like, it it would expand beyond, our
[00:39:45] Unknown:
does it expand beyond our ability to, like, reason about? Is that Yeah. It's just we just don't we just don't know. Like, there's certain things. Like, there's there's a class of random variable that's just random that we literally know nothing about. Mhmm. Right? Like, it's literally it's so it's genuinely random. Right? Like, it's genuine and then there's, like, those sometimes are those are really desirable to try to construct, obviously, for obvious reasons. Right? Yeah. In cryptography. And so you want like, sometimes you actually want to know the properties of a truly random variable, and you wanna be able to maybe test if you generated a 100,000 of them, you wanna be able to test to for that randomness.
Right? You wanna And is that, I mean, is that a a way of that can't be abstracted into a into a or modeled into a distribution.
[00:40:37] Unknown:
Is that a way of measuring, like, entropy? Yeah. Right? That's, like, a way of measuring to that you have enough entropy.
[00:40:45] Unknown:
Yeah. Like, you want you really want, like, perfect randomness. Right? And it's and, you know, when we talk about randomness, what we usually have with random variables is pseudo random variables, not truly random variables. So, for example, the like, when you the classic example is, like, the shuffle on your iPod. Yeah. Right? Where it's it's not truly random because if it was truly random, there'd be pretty reasonable probability that the same song would play four or five times in a row. So they make it's right? They make sure that that doesn't happen.
Right. Right? So it's it's
[00:41:25] Unknown:
pseudo random. What it that makes me, on some, like, developer stuff. Like, you have these things called seeds into your random number generator. Yep. So it's like you can have a, deterministic randomness where it's like, hey. This is a random number, but, like, if I give it the seed of five, all the variables and the inputs and everything like that, like, are deterministic. And that's that's useful for, like, testing
[00:41:52] Unknown:
certain things. It's vital. It's not just useful. Right? Yeah. Yeah. That's true. Yeah. Yeah. Because, otherwise, you
[00:41:58] Unknown:
if you're testing anything without Boolean logic, true or false, Like, you have to have a way of knowing the inputs predicting the inputs to verify that the outputs are what you think they are when you're when you're running it through. But then on the the opposite side of that, it's like you don't. Your seed, whatever it is, like, you don't want that to be consistent. But there's also
[00:42:22] Unknown:
When you're at when your outcomes are ordered, it's vital because it's the only way to replicate your outcomes being ordered. If all you're trying to do is take an average, you might get away with not having a random seed because your average should still convert everything should converge to that average. So this the random seed is really important when your outcomes are ordered. You need random out you need you need you need random outcomes, and you need them to be ordered, which you see that a lot in risk where, you know, you'd look at you'd look you'd look at the tail. You look at the ordering, or is it the like, when and when you say ordering, I order. In other words, so so in risk, a lot there's a concept of, conditional tail expectation where what you'll do is you'll study the just the lowest tail. So in a if you have a thousand, scenarios, you'll look at the 20 worst ones. And in order to look at the 20 worst ones, you need to know you said there's no way to there's no way to replicate those without either having all your scenarios be super deterministic, which is how a lot of companies do it, or, having a random seed that, you know, that you you know I mean, having a random seed is not that different from the hierarchical, key structure.
[00:43:40] Unknown:
Well, that's what I was thinking because if you take a message and a signature, the same message and the same signature will result or the same message and the same, signature algorithm will result in the same signature on the other side. Right? Yeah. But you don't know what that signature is until you run that that equation. But once you've run that equation, you know what the inputs are, and now you can deterministically arrive at the output even though that output is not known to you without, like, doing the math.
[00:44:08] Unknown:
Yeah.
[00:44:09] Unknown:
Yes. So Oh, man. I've been okay.
[00:44:13] Unknown:
Yeah. So this is good. Like, we're we're actually creating runway for future episodes again. This is good. I've been vibe coding an app that is directly applicable to this. Dude, we're gonna talk about that when Okay. Okay. So, definitely, we're just gonna we're gonna put that on the schedule. Guys, we're creating runway. I feel like we have 10 more episodes in us easy just on what just on what we're discussing. Bearish. This is good. No. I'm just saying easily. E easily. Yeah. Yeah. Yeah. Without the world without the world giving us more material from now. Right? Mhmm. So, again, I wanna focus just again on probability distributions because I feel like if it's hard for that was the hardest thing for me to understand. Like, why do I care if something is a binomial distribution versus a, uniform distribution, which is what, a dice roll would be?
A roll of a dice would be a uniform distribution. Every outcome has the same probability. Right? If it's a six sided dot that's not you know, it's equally weighted. It's one
[00:45:15] Unknown:
sixth. The output of a sha, if it's, like fit should be uniform. Right. That's right. And and that's why every hash your ASIC makes has the same chance of winning a block as anyone else's. But if you have more hashes, then you have more chance. So you the uniform distribution is a good distribution to
[00:45:36] Unknown:
Okay. Yeah. Alright. Now it and then there's a question of, does a uniform distribution converge over time into, like, you know, to a Poisson? And I'm sure there are smarter people that that got met that I think and I think that's the case. I think, like, a uniform I think it's the classic I think that's actually classically how what Poisson distribution models is the largeness of, the uniform, you know, the uniform distribution, which is then now what you have in a mining pool. Right? You wanna know now, like so one is what's the probability of the event happening? Right?
Then the question is, if I know that and it's and then and they're equal or they're behind you know, I understand the probability of the event. Right? Right. One in a fucking billion or whatever it is. Right? Mhmm. As if, welcome to 2010. You know, when the probability of winning a block was, like, one in a billion. No. But, whatever it is. Right? What a Poisson distribution then asks or measures is given a big n, given the number, I I know I'm gonna do a numb a certain number of trials. What is the distribute what's the probability of one success zero successes, one success, two successes, three successes, etcetera? Right? What's the in other words, what's the probability to hit zero blocks, one block, two blocks, three all the way up to big n, whatever big n is? Right.
Right? So if I wanna say over a day, that's big n is one forty four. So over over a day, how many times out of a 144 am I gonna hit a block? Or in a difficulty period, which is two weeks, is what? Twenty one sixty?
[00:47:25] Unknown:
Two thousand sixteen blocks? Sorry. 2,016.
[00:47:28] Unknown:
I'm sorry. So right then, your big end would be 2,016 blocks. How many which is actually much that's a more relevant question than a day because what happens in 20 in 2,016 blocks is, my hash just gets devalued and debased into the next period Maybe. Difficulty adjustment usually. Over time, it's if you're if we're if we're, like, transporting our brains into this law of large numbers world. Right? Yeah. You you know, you over time, your hash gets debased by, like, 30, you know, 30% a year. Like but, you know, by one by one ish percent every time every two weeks. Right?
[00:48:08] Unknown:
Yeah. Yeah. That's probably I don't know what the exact measurement of this. But and that goes to the acceleration of the block's arrival. Right? Because it's like, if you go back to block zero and measure to today, on average, I think it's been less than ten minutes per block Yeah. Because we've had this ever increasing hash rate. Yeah. Which has ruined a lot of having parties. My having party was spot on. Like, it happened at the party. We all celebrated. It was a wonderful time.
[00:48:37] Unknown:
But, again, once it just I wanna Yeah. Keep this fairly evergreen and understand like, from the mindset of what is a probability distribution and why does that you know what I mean? How does that help me? How does the knowledge of a probability distribution help me? So Mhmm. Like, when Satoshi tried to spell out in the white paper and it's so funny, dude, when people are like, it's just math. Nobody talks about this math ever. Yeah. They think that the math is, you know, the sum of the blocks over 21,000,000 or what you know, or, you know, that's the thing. You know, like, that equation and they've you ever see these memes, you know, where they're like, oh, the Pythagorean theorem and then there's the sum of the sum of the blocks.
Right. This is Yeah. The having equals 21,000,000. It's like, that's the math. It's ridiculous. Like, this is the math, actually. Well, at least as as far as why a decentralized proof of work concept is going to, you know, why is it why why can't it work? Right? So the math here is what happens when, you know, what happens when everybody competes for a block. Right?
[00:49:54] Unknown:
It's framed in the in so it's it's section 11 of the white paper. And the the first sentence and and this is interesting just because Good thing it's not chapter 11. The lead into.
[00:50:04] Unknown:
Although that's how a lot of miners went bankrupt. Oh, but
[00:50:09] Unknown:
I missed that on the first one. But the the the it's section 11 calculations. And the first sentence is we consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. So, like, it's framing in, like, this calculation is critical when you have to look at attacks on the network. That's right. So, like, adversarial thinking was a great segue into this topic.
[00:50:34] Unknown:
There's no way to deterministically really, like, deterministically attack the network. Right? And then so, like, even if you can do a 51% attack, right, you're still subject to the law of large numbers. And, you you know, if you're big in it, then that's why, like, you know look. Big end for confirmation six.
[00:50:55] Unknown:
Right? Right now. Big end big end to sustain I mean and that's, like, enormously expensive as it is. I would raise that just given the number of consecutive blocks that we've seen from these big mining pools.
[00:51:06] Unknown:
Oh, fuck. Yeah. But, like, if you think about you know, so you think about somebody who does wanna attack the network, and they wanna they wanna like, let's just say they have the intention to mine 10 to 20 blocks Mhmm. Backwards. Right? Yep. Probabilistically, that the the cost you know, 51% attack doesn't mean you're getting you're gonna win 51% of the blocks. Right. Certainly, especially if your big n is 20. You may win zero still even by you know, you still may win zero. Yep. Right? There's like a, you know, there's a non zero probability. You you actually win zero blocks with a 51% attack. That's just like so in other words, this to me, I would say this is straight math.
You know? And, it's unlikely, but it is you know? The other distribution that might be relevant for people to know is called the negative binomial distribution, which is in a binomial distribution. In other words, what's the probability, if I did 10 tries, what's the bit probability of some number of failures before success? So, like, what would be if you know, what's the probability of nine tails before I get my head?
[00:52:23] Unknown:
Right. And that when the end value goes up, it's that, like well, I guess it doesn't the end value could go up, but your your Well, the end target for success could remain the same and the outcome is now different.
[00:52:38] Unknown:
I mean, yeah, the answer is it should, you know, you should it shouldn't be more than, you know you're in a binomial distribution. It shouldn't be too much more than two. Right? But it could be. It could be 10. It could be a 100. You could it's like, again, it's not impossible. This is what people need to understand. Right? It's definitely not an especially, like, people who are gonna put capital behind a probabilistic attack Yeah. Do need to understand that you could go a 100 blocks before you get that
[00:53:08] Unknown:
before you win your block in a 51% attack. Well, now it's interesting to flip that on the the opposite side of things too is, not necessarily being attacked, but being the one that is being censored or attacked. Right? Like, your your chance of success at breaking through whatever is, like, preventing you from hitting a block or for preventing you from broadcasting your transaction is the same calculation.
[00:53:34] Unknown:
Yeah. And but then there's this missing piece that maybe you can help with, which is that I think the other the part of the fifth there's a part of the 51% attack, which is the probability of winning the block. There's the other part of the fifth the one, you know, the 1%, which is that you're doing more work. You can't. So if you do win the block, you'll win. If you do win the block and there's, like, any dispute, you will have more work done because you did 51 you know, you will have done more work than anyone else. Right? So So maybe there's this piece that I'm missing around that that
[00:54:03] Unknown:
Well, it yeah. The the the the the tip of the chain is the most work, and so you could have it. And you can see this. This is what happens when a chain split occurs is if two blocks are found at roughly the same time, and now you have a chain split on the network, which happens I don't wanna say, infrequently, but, like, frequent enough that you can go again forked out observer. It will let you go But you're gonna be the one if you if you did 51 of the work, you're pretty much you're guaranteed to win that dispute. Correct? I don't know if guarantee the guarantee might be a strong
[00:54:36] Unknown:
strong You're not guaranteed to win a block with that hat with that, you know, with that amount of hash. You're not guaranteed to get one block in a day or a week even. Well, it's not just one block, though. It's a consecutive block because
[00:54:47] Unknown:
the the 51% attack is targeting, you're trying to orphan a chain. Right? Which means you're trying to accumulate a new chain without, you know, the the censored transaction in it or the censored block in it Mhmm. With enough work for the rest of the network to go, oh, this guy has the most proof of work. Because you see this commonly where there's a chain split where there's two different blocks. Like, the last one, was, you know, 1,700 blocks ago or so according to Forked Out observer at the time of this recording. And it was via BTC hit a block and Brainspool hit a block. And so, essentially, the race then becomes like, well, who's gonna get the block after that? And that goes into, some game theory things about, like, peering your node and getting your block to as many people as possible for them to start building on as a valid tip of the chain. Yeah. And by the way, as you're speaking, man,
[00:55:41] Unknown:
shout out to the base 58 LARP because you actually get to do this in real time. I need I I have to do this. You get to play this game and do this in real time
[00:55:52] Unknown:
and get to really send Oh, like, you try to get your block out to the rest of the network so they start building on it in real time. And, yeah, you have you you know, you're sitting in a room with other
[00:56:02] Unknown:
people creating you know, doing mining and, you know, you have chain splits and you have to at some point, it does you do it, you know, it does come together and figure to reconcile. Yeah. At some point, you do figure out who actually did win the block, and you have to keep a couple of different records and, you know, keep a couple different chains. Yeah. Very cool.
[00:56:21] Unknown:
Oh, wow. That is cool.
[00:56:24] Unknown:
So, like, if I and if I hadn't done that, I would just like, I wouldn't have the visual sense of what you're saying right now.
[00:56:29] Unknown:
Well, and in the larp, right, like and you can kinda it's like each table with its own node. Right? And then you're Yep. You're literally connecting your node to other tables via, like, string and, like, passing messages across the string. Yep. And so in the case that we're talking about, it's like when you find the block, you have to, like, pass it along the string to as many nodes as possible so they start using your block to build on. But if somebody on the other side of the room also has a block at roughly the same time, they're gonna be doing the same thing. And now you, if you're in the middle of that, have to decide, okay. Well, like, which one you know, is it the first one I see? What if I see both of them at the same time? In that situation, the the 51
[00:57:04] Unknown:
attacker, I think, you know, pretty much has the trump card because they've done they have done they will always have done more of the work.
[00:57:13] Unknown:
Well, they will be con they will be able to continue to do more work to build on whatever block they deem to be the the That's right. The winner. That's that's right. To
[00:57:23] Unknown:
show it. But I think the what I wanna distinguish here and, again, I'm not, like, super expert. Right? Mhmm. I'm just a math guy,
[00:57:31] Unknown:
amateur math guy. Yep. Amateur Bitcoin guy. Or math influencers. You can say it. I'm
[00:57:39] Unknown:
as of now as of now, I'm an amateur Bitcoin guy too because no no one's paying me. But, the the when people think of a 51% attack, they think I think that typically people will think about it as the probability of winning a block. A sequence of blocks, though. Yes. But it's also but it's also the fact that you're demonstrating work.
[00:58:02] Unknown:
Yep. There's a cost to it.
[00:58:05] Unknown:
Yeah. Right. I mean, I think we could probably do a better job of teasing this out, but we weren't prepared to discuss this.
[00:58:14] Unknown:
I mean, I think we did a pretty good like, I don't know. I I learned a lot, so I assume that the listeners will learn a lot,
[00:58:22] Unknown:
even though we have a lot of listeners. This is great for me. I had a great personal experience. So okay. So let's get back to then it's so interesting. Right? So when the white paper positions this Poisson distribution as an attack, we started the episode on, you know, Portland Huddl's. You know? It's, again, iron sharpening iron. Mhmm. It's almost like we want people to attack the network. Right? It's almost like we would want a 51% attack. I've always said, like, yeah. Like, shit coins are a good are like a like, why do people Well are people sold the money at them when they're just they they demon you know, they're they're the attack that is needed. That's just part of the evolution of this thing. Right? We don't want it, but we should be prepared for it, and we should understand what it is. Maybe we maybe we do it correctly model it. Maybe we if we're really putting our life savings behind this thing, maybe we want it to be attacked a lot.
[00:59:17] Unknown:
Yeah. I no. I no. You never wanna be attacked. Right? So, like, just like putting on, like, my military hat. It's like you never wanna be attacked. You would always rather know the attack vector and then fortify a position to where you cannot be attacked. You're you're unassailable. Right? And this is why I have, like, I have two bid access in the car. I have to take to UPS after this. Thousands of years into military,
[00:59:40] Unknown:
intelligence. Right? We're fifteen years into this war, and the only way to know these things is for the attacks to happen. Yeah. Well, and I'm not saying, hey. Please attack us or anything. But, yeah, it's I mean, you'd have to be a giant pussy and, like, real Pollyanna to, like, think that, there's any other way, honestly, for this thing to get robust fast. Right? Yeah.
[01:00:08] Unknown:
Yep. Well and, also, it's like if you can if you can be attacked, if your position is a saleable by a single individual with some, like, AWS credits, like, that, you know, that's not a nation state. Yeah. That is that is not a That's right. That is not the, Apex predator that could be attacking you.
[01:00:32] Unknown:
The key you we have to see every attack possible. That's and that is you know, that's why it's open source. Yep. Right? And that's why open source software will always be the most robust over time because it will see the most attacks. And, you know, there's no the hope is not a strategy. Yeah. You have to be you have to test in battle. Simulated or real as well. Yeah. Simulated or real. If if some dipshit is a you know, if some dipshit from behind his computer is able to fuck your node over. I'm not saying portal is a dipshit, but he could have been. Any dipshit like, if I mean, if he did it, any dipshit could do it. Right? Well, I think the dipshit would be do it and then go sell it to some Yeah. Intelligence agency. If any dipshit can attack the nodes on the network, then you don't have much of it.
You don't have much. You know? Like, your Bitcoin isn't worth that much if it's that easily attacked.
[01:01:41] Unknown:
Well, that's that's the other thing that, you know, thinking about is, like, they there's always, people always allude to the economic relevance of a given note as well for, like, if it's being attacked. Right? Because, like, somebody could attack my note at home, and, like, I'm not doing, like, I just don't do a lot of transactions through that node. So, like No. I get it. Right. It's like they but then you can attack, like, River's node, and you can really put a substantial impact. And these, like, I But River doesn't have Comcast ISP. Like, that's that's the other thing. It's like the River is not going to have a a a throttleable throttle throttleable connection.
And if they do, they will probably have some other redundancy built in. Node. You can prob you know, you can attack SupertestNite's
[01:02:25] Unknown:
node. And, he might be under Comcast. I don't know. The point being, right, like, these these there are people that we share our network with that think that, the fact that it's illegal to do a denial of service attack on somebody means that it won't happen, and we don't have to worry about it.
[01:02:44] Unknown:
Yeah. Well, here's the other here's here's here's a bullish scenario too that could result in the same thing. It's like everybody So no suddenly decides to run a node, and you have thousands of new new nodes doing IBD or or millions of new nodes. Right? The whole world is suddenly like, oh, shit. I gotta do this Bitcoin thing. And so they start IBD. Right? Is it likely scenario? No. But, like, that same scenario would have resulted in the same end result of, like, your Comcast ISP upload limits being breached, and your node is now offline. Oh, wait. You're saying, oh, the prop the likelihood of all, like, of a lot of nodes doing IBD at one time? Yeah. Yeah. That's what I'm saying. Like, you if a million nodes went up come. Don't you think that day will come when, you know,
[01:03:27] Unknown:
when there's, like, there's 9,000,000,000 people in the world. They're not all gonna run nodes, but there's, like, gonna be more than, like, 15,000 nodes at some point. Probably, we'll get a day where, like, 10,000 people all spin up a node.
[01:03:38] Unknown:
How probable is it?
[01:03:40] Unknown:
That's that is a well, that's a that's a great place to fucking end this end this thing. But, yeah, that's a that would be a, a good Poisson calculation, I think.
[01:04:22] Unknown:
Where is my mind? Where is my mind? Where is my mind? Where is my mind? Mind? Where is my mind?
Stop. You thought you were gonna get math, and we're just gonna we're gonna discuss something that I think I think the framing we can put around this, though, will be evergreen.
[00:00:35] Unknown:
Well, it's let's just preface real quick Sure. That, episode 19. The math podcast has had an interesting trajectory up to this point. I think we started out with a lot of ideas, and we start we were doing regular episodes probably either every week or every other week. Yeah. We're sort of at the point now where we're not on that cadence, but whenever we start thinking of a math idea, we're like, alright. It's time to rip. Yeah. And, so, like, I think I forgot who the last one that came up was the, the Quantum FUD. Right? And that just that Yeah. Yeah. That just came up and we were like, yeah, dude. We need to do an episode about that. Let's it's time to rip. And then I heard you I heard you mention the name Poisson way too many times for me to then not make that connection and say, wait wait a second. That's math. Why are we why am I not why are we not doing it? Then not only is it math, it's like literally the math in the white paper.
The only math. I think I think you've I've you've stated as much. Yeah. There are Bitcoiners that think, like, a page number is math. You know? Well, I've I've been one of those. Well, it's more like Are they wrong, though? Can I tell a quick oh, absolutely not? Last up here is just shout out. So shout out to Solex, regular listener, and I'm sure he's eagerly awaiting this conversation. I don't know. It's great to find out It's just great to find out people are, like, marathoning this show, and that's what kinda keeps it going. You know? That's what keeps me going.
[00:02:13] Unknown:
I mean, something has to fill the psychopathic void inside of all of us. And, when you run out of macro and when you run out of, the bugle, come to the math.
[00:02:22] Unknown:
Can I give you my
[00:02:24] Unknown:
my version of page number numerology? This is like everyone's gonna stop listening forever when they hear this. Your version of page number numerology. Okay. You have it your own way of do yeah. I'm like, I'm trying to hack.
[00:02:36] Unknown:
No. It's just words in my head. It's just so stupid, and this is just why I'm such a fucking retard. Okay? But if you read, Eric Caisson's crypto sovereignty
[00:02:49] Unknown:
Yeah. K. I've not finished it, but I've begun.
[00:02:52] Unknown:
Did you get to page one zero three by any chance? Oh, we can check right now. It's one of those book oh, you know what? I actually took it out of my book bag. It's like, I don't know why my brain does this stuff. I just don't know. I wish it didn't. But, like Okay. You know what's on page one zero three. I'm going from one zero two to one zero three, and I'm reading something that really he is very passionately now talking about the I haven't read this book in two years. Okay. So this just paraphrasing my brain in my head, though. But, like, he's very he's making a very strong case about, you know, how powerful a NIM can be and why it matters so much to Satoshi.
Correct? Yeah. And I'm just noticing page one zero three, and I just my brain said, oh, Jan three. This is What? Okay. Stupid and, you know, it's not worth it's not even worth the minute I just spent talking about it. I just thought it was hilarious and funny, and I've I've been telling people, like, it matters.
[00:03:49] Unknown:
Like, check the number every once in a while. You rearrange the numbers. Right? Like, if you use, like, the the British people, they do, like, a different ordering in the numbers. It's like the month is first. Europeans do it. And that's why by the way, that's why,
[00:04:02] Unknown:
you know how everyone celebrates Pi Day in The US on March 14? Well, not everyone. But, yes, I understand some people do. It's a great sign you're like a math larp. Like, oh, I love pie. Pie day. You know? I'm I'm a pie guy. Hey. The public school celebrated. Okay. Like, all the math teachers in public school get all excited on March 14. Something I've always said that's fallen on deaf ears is that really worldwide, it should be, July 22 because and and it's so much better than March 14, so much better because they put the day first, the slash, then the month.
And so July 22 is twenty two slash seven, and that's famously pi. That's, like, the closest approximation to pi. That's the closest approximation to pi. 22 divided by seven is the closest approximation to pi. That you're gonna get from rational numbers. Like Really? From rational numbers under a 100 or under a fucking trillion. You know? Like, that's the best approximation you can get without without, like, really breaking out
[00:05:09] Unknown:
advanced calculators. But do they, like, the do the Brits have, like, a different name for, like, pies, though?
[00:05:15] Unknown:
No. Okay. Bangers? No. Because I know they call, like, cookies biscuits or whatever. But it's not that's not such a British thing. It's more of a extended EU type. Rothschild empire. Do it. I feel like in Canada, Australia,
[00:05:30] Unknown:
all over Europe, New Zealand, that this is a custom. You know, and it makes me question whether America should do that because the metric system is right. Like, base using base 10 for for the the base unit of, like, measuring things is just,
[00:05:46] Unknown:
easier to reason about. Yeah. But we have guns, and we can be ungovernable. And so we can have stupid fuck Yeah. I have a nine millimeter.
[00:05:53] Unknown:
It's a fucking nine mill even the guns figured it out. It's still the metric system. It's true. It's true. We can't escape it. We can't escape our destiny. Nope. We can't. Metric metric maximalism, and, we should just move completely off of the, what is the calendar we use? A caesarean calendar or whatever? Gregorian? Gregorian? I don't know. I don't I don't fucking branch Davidian?
[00:06:17] Unknown:
We almost we almost ended up on the Branch Davidian calendar. We we hadn't gotten that guy.
[00:06:25] Unknown:
Jesus Christ. We were talking about adversarial thinking. We started recording because we,
[00:06:30] Unknown:
like, started talking a lot and forgot we were talking and said, why aren't we recording?
[00:06:35] Unknown:
Yeah.
[00:06:36] Unknown:
I think even though we intend to talk about Poisson distribution at some point in time, we were because everything we say is pure gold. Valuable for its utility. Pure gold. Pure gold. Valuable only for its utility. Slight amount of maybe some tungsten in there. But, we were talking a little bit about the issue of the day, which
[00:06:57] Unknown:
we tend not to I tend not to bring it apart. But we can frame it around an evergreen topic, which is adversarial conditions. Yes. Antifragility.
[00:07:07] Unknown:
So we're here episode 19, and it just so happened this past weekend. Bit of a watershed event. And, you know, there's been there's been to me what's been a very I've covered I've said this publicly on the show. I feel like the the nots the cannots debate has been just sort of a childish demonstration of really a lack of ability for Bitcoiners to communicate effectively.
[00:07:31] Unknown:
Yeah. Yeah. Wow. That's yep. Well, and that's been it's very obvious on, like, both sides of the of the debate too. I forgot what side what I forgot what episode we covered this, but we
[00:07:42] Unknown:
did. We definitely had this conversation. I got a lot of shit for it. I'm great. I'm happy to for the fucking tennis nurse. Piece of shit like you for breakfast. You eat shit for breakfast?
[00:07:51] Unknown:
Sorry. Happy Gilmore quote. Keep going.
[00:07:56] Unknown:
Yeah. We have, like it's so funny when you have a podcast that has so few listeners and that you still catch a lot of shit for from people who really wouldn't be in the target demographic at all. Right? Most people, I think, who listen to this are, like, think Nas is gay. My guess. It's my guess. Maybe. Maybe. I don't know. It doesn't like, it We had running the same consensus engine, that's fine with me. Interpreter That's TP. Yeah. Like, we had that we had that conversation already, so we're not gonna but, basically, what happened in the over the past weekend was that, a guy named Portland Hoddle who has been you know, he this guy has done some things in the past. I wanna say
[00:08:37] Unknown:
Well, he gave a talk about, like, how you could slow down a block. Like, you put a shit ton of signature checks, and there was, like, some special structure, and you had to tee it up with a bunch of other transactions before you actually executed it. But he gave a talk and did a live demo of, like, a twenty five minute block validation,
[00:08:54] Unknown:
which is Yeah. I consider I consider him a good follow because he basically will every I don't know. Every once every three or four months, he'll have some Twitter thread on some just something he was fucking around with that Yeah. He kinda he kinda broke on somebody. Yep. Maybe one one of the times was the Moon Wallet situation. I can't No. I don't know. I wasn't paying attention at that point if it was You know, he's a good pretty good follow in terms of, you know, he's out there he's out there trying to break shit. When I've met him personally, he's also, like, he's also a very intelligent individual as well. Like, he he knows
[00:09:27] Unknown:
he knows what he's doing. You know, you can't you can't find some of these like, to figure out a twenty five minute block validation, you have to know how the scripting engine works. You have to know what will potentially delay that scripting engine and, like, a number of other things. And then to, like, recreate that in a reg test environment, right, is, like, you know, you have to know what the fuck you're doing with the note.
[00:09:50] Unknown:
So I think from a certain point of view, this fake nots debate I call it fake. I really think it's fake. I I do think it's, like, some type of influencer capture shit. About consensus. So, like But so at some level, I believe this debate is a blight and a pro potentially problematic. I've, again, talked about it on all my podcasts. Potentially problematic to the Bitcoin network in terms of I I think it just dem it demonstrates to our attackers how bad we are at actually solving problems. And I'm not saying don't do that. I'm saying, hey. Let's let it run its course, but it is what it like, don't go virtue signaling and tell me you're, like, doing god's work by doing this shit. Right? You're not you're not doing god's work by running knots. I mean, you're free to do so, but, like, don't try to claim some superior position. It's absolutely insane. In fact, the more you try to argue and defend that position, the more the wider you open the door to our attackers because they see how retarded,
[00:10:53] Unknown:
like Well, and it's prominent people here are. And the interesting thing too is this this quote, unquote, like, attack or and and just to lay it out. So Portland Huddl figured out that Comcast, the the ISP, Internet service provider, has, like, data cap limits on, I think, upload side of things. And so if you are running a node behind a Comcast IP and you are, uploading a bunch of like, if a bunch of nodes come to you that wanna do IBD or initial block download Yep. And start hitting you, like, hey. Give me blocks. Hit me. Give me you will run out of that limit, whatever that limit is. And there's a configuration within Bitcoin Core and nots that enables you to put, like, a cap on that upload. So, eventually, you're just, like you'll stop, like, giving blocks to people. Right? Yeah. Or, like I I can't remember the the technical specifics of how that configuration limit works, but it prevents you from, like, getting throttled
[00:11:48] Unknown:
from a bunch of people connecting to core. There's an actual switch in Bitcoin core. There's a Yeah. An option. So correct me then if I'm wrong. This wasn't, like, explicitly this isn't wasn't even really targeting the nots things. This is targeting anybody running running a note, really, to say, hey. This is this is an issue you may wanna understand if you run a note. It just happened to really blow up. It's the the, virtue signal of the nots people is I run a note and I protect the network. I mean, that's that's so that's really why they got particularly they got particularly blown up and why it got particularly funny to to many good people. Many good people, got caught up laughing with, got caught up laughing with Portland Huddl, and, I find it, I find it reprehensible, the attacks on the laughers.
God, this is not gonna age well, but, like Well, no. It it people get no. People get what I'm saying. There's a duality to this. Right? Because, like, is it fucked up to attack somebody running a node at home and, like, basically, DoSing their node? Never okay. Sorry. Sorry. I'm getting caught up in the world. Kind of a dick mood. But, like, if you're gonna participate in this thing called Yeah. Bitcoin. Dick yeah. It's kind of a dick move to be, iron to be an iron sharpening iron. Okay? Right? Absolutely. Yeah. So, like, we accept people out of jujitsu all the time. It's a dick move to fucking choke somebody out, but guess what? Like, you're gonna learn a lesson. Did you wanna build your citadel with nice guys, or do you wanna build your citadel with the kind of dangerous men that will actually you might be you know, you wanna keep close and you may fear, but actually are gonna give you a shot at Yeah. Just a shot, right, at defending your life against the state. Right? I mean, you have to basically cast your lot with the dangerous men. You have to.
Am I wrong?
[00:13:40] Unknown:
No. I don't think it's it's not, peaceful men, ideally. And, like, looking at Portland Huddl's
[00:13:46] Unknown:
avatar on Twitter, it doesn't look very dangerous. But he is, you know, he is iron sharpening iron.
[00:13:54] Unknown:
The the danger is the the knowledge. Right? And and, again, this is like I made the assertion before we started recording. I am glad that more people understand node configuration, this one piece of node configuration than they did before. Because otherwise, they would have floated through the rest of their node running career, never thinking about, like, what do you what do you like, what is this configuration thing? Right? Like, not a lot myself myself included, I couldn't tell you all the different configuration options in a Bitcoin core node. No. That's not a problem. I could tell you right now the ones you can are because you had some fucking problem or some worry or something didn't work. And that's the only re it's the only way
[00:14:29] Unknown:
you ever learn of a configuration option. Yeah. And he gave he basically gave everyone the keys, so to speak, the, the solution. He gave everyone the solution. Right? And yet everyone still wants to kill the messenger.
[00:14:46] Unknown:
Well, in the in the it's a solution not to the node problem, whether you're core or you're not. Right? It's the same issue. It's an a limit on the ISP. Right? And this highlights something,
[00:14:58] Unknown:
so running your own node, and yet you can't you you're, like, subjected to a data Can't keep it on my ISP that you don't understand. I mean, it's so pathetic. Right? That's I'll I'm so glad this is was brought to light because now I mean, we want people to we like, it's ideal. That's a narrative that doesn't have substance. We want that narrative to actually have substance. Yeah. Otherwise, you're just a you're just a larv. Right? And then you'll kill the messenger for killing the narrative if that's the way you are. Right? We wanna like, what I so I feel like he's providing substance by find you know? And it's just there's probably 20 more of these that need to be done before we really have run robust nodes.
[00:15:42] Unknown:
Well, it's it's operating in adversarial environment is what it is. Right? Because, like, this happens to somebody using Comcast in The United States or whatever. Right? So, like, now replace yourself running a node and put yourself in some, like, despotic regime, right, that is, like, even more authoritarian or even more, like, tuned into the knobs that they can push and pull on on the network.
[00:16:08] Unknown:
Right. They know the configuration options of their control grids. We need to know the configuration options as many as possible. And you know what? Maybe this is just a good segue into the episode because learning math is not something you have to do. You never wake up saying, fuck. I don't know if I know enough math. Most people don't. Right? Most people don't wake up saying shit. Don't know if I know enough math to get through the day. And yet Yeah. We study it anyway. We do the work because it's important. The same way it's imp like, you know, it's like knowing the configuration options on your node, nobody really wakes up says, oh, shit. I wonder if I understand all that, if I can really get through. But you know what? That could today could be the day that that fucks you up. This you actually reminded me of another topic that I don't know if we'll wanna dig into today,
[00:16:56] Unknown:
but it was something that did make give me pause. And and I I thought about reaching out to you, but I just, I had not because I hadn't done any of the due diligence. But recently went on a couple podcasts talking about simplicity, which is like a new scripting engine essentially for Bitcoin. But the way I'm trying to figure out remember the way that he described it. But it's like the way he described it was there's, like, some very, very, like, core fundamental primitives within there that then you can, like, build on top of, and then they have these things called jets, which are, like, predefined combinations of these primitives.
[00:17:32] Unknown:
I feel like reading about I would feel like I spent when we first started this podcast, I feel like this was, like, January
[00:17:40] Unknown:
Yeah. Where
[00:17:41] Unknown:
this came out, maybe the paper or the abstract. Well, Simplicity's been around a while because I remember hearing about it at BitDevs. Like We started before I ran it. We started talking about it. I this is back. I I ran it. I think I ran this through, like, the Google notebook thing to get to to get a a digestible podcast on the actual white paper.
[00:18:03] Unknown:
And The Simplicity white paper or the Yeah. Bitcoin white paper? Simplicity, I think think it was. Well, it's live on on Liquid now. That's like the that was like the big thing was, like, this is Symplicity is now a feature of the Liquid Federation Network. Wow. Yeah. Like, they're I mean, if you're serious about a project, you need to go put it somewhere that it can actually be used. And and that's sort of what and if you hear the podcast and sort of alludes to this is, like, he as, like, the lead r and d at Blockstream, right, which is, like, nothing to shake a stick at, but, like, he sees liquid as sort of, like, a testing ground. Like, he's a Bitcoin maximalist. Right? Like Yeah. But he sees liquid as his testing ground for, like, all these other cryptographic things. What are these different things that you can do with the math in in a scripting engine or with confidential transactions or whatever else? There's a bunch of other stuff that's on liquid that is, like, it could be on Bitcoin, like the main net.
But, you know, you need like, as we've seen, you need a lot of buy in.
[00:19:05] Unknown:
Yeah. Because test net's too many times to like, test net's hard
[00:19:09] Unknown:
to do anything else. Oh, yeah. Test net four. Well, test net four is is constantly under, quote, unquote attack. If you go to a fork observer
[00:19:19] Unknown:
So liquid is an is a sandbox for Bitcoin that Absolutely. It's a different kind of sandbox for Bitcoin.
[00:19:26] Unknown:
Yeah. Yeah. Right. And it just happens to be, like, the big one of the big sandboxes that's doing real world, like, transactions.
[00:19:34] Unknown:
It's funny, though. So liquid I mean, it's interesting and funny too, but because, Blockstream at one point were giving away a lot of sats to hand out at meetups Oh, yeah. To do, just, like, a little bit of a demonstration on Liquid. And the funny part of it was, like, if they gave, like, if they gave, say, you know, 500,000 sats to give to, you know, 20 people, The thing, it has to clear every minute. You you can't, like, you can't just go boom, boom, boom, boom, boom, boom, boom. You actually need to you can't just get you can't put them all into one transaction. Yeah. It's got a one minute block time. I I mean, I've I've used liquidity That's that that was the big lesson we all walked away with. Oh, really? Yeah. That's because that's what we experienced.
[00:20:17] Unknown:
Well, there's a way you you can do, like, atomic swaps with liquid. It does have the one minute block time. And I remember when the fees were spiking around, like, the initial ordinal craze and stuff like that, like, the super high, you know, hundreds of sats per e byte. A lot of people were like, oh, hey. Like, just go go use liquid because it has interop with lightning. It has and that's the other thing that I think was interesting, is it's all this interop. Right? Like, it's the it's the interop. And at the the core of the like, this interoperability is the math.
Right? Like, you you you go from one chain to another with these swaps. I think generally using something called, like, an adapter signature, which again is like a way of structuring a math equation in special signatures where it's like, I can encumber this transaction. And then once you provide a signature for it, then that reveals another secret that I can use to, like, unencumber
[00:21:10] Unknown:
this other transaction. Unpacking that at the next episode. Let's now put that on the calendar because I feel like that's the like, it's I feel I suspect that the work we did on group theory will explain why that's the case. I suspect interoperability has to do with, isomorphisms.
[00:21:30] Unknown:
Here's some here's some homework.
[00:21:32] Unknown:
Alright. Yeah. I will. I will break put that on, and maybe that's the next stage of where we go here. Or maybe Yeah. Right? And we we're finally gonna cover, I feel like I I'm glad for this episode 19. We're gonna cover some probability. We're gonna, you know, we're gonna cover what's in the white not specifically, maybe what's in the white paper, but the fact that it's probability. I thought a little bit about how to approach this.
[00:21:59] Unknown:
Well, that's good. Because I just say the word,
[00:22:03] Unknown:
and I don't You said you said you exactly. Few times. And so I'm like, okay. Why aren't we why aren't we doing an episode on so let's do it. Let's let's let's do you wanna are we ready to move off, or do we wanna do you have anything more to
[00:22:17] Unknown:
No. That's it. I I think, just the last caveat or last, like, little, like, tangent is if you go to fork.observer and you click little drop down and go to test net four, you can see what a highly forked network looks like visualized. Yeah. There's a there's a great dev out there that does a lot of monitoring tooling. Put that in the show notes. Yeah.
[00:22:38] Unknown:
Yeah. And just like embrace, adversarialness. Don't be gay. You know, like, don't get all, awoke because people are laughing. Yeah. A lot of good people.
[00:22:53] Unknown:
It's like, why are they laughing, though? Right? Like, they're not they're not laughing at the the misery of some node runner in their house. Yeah. Like, it's That node runner can still get their transaction out.
[00:23:05] Unknown:
Again, man, like, I I these people are just lost, in my opinion. Just absolutely lost. You know?
[00:23:13] Unknown:
They're I mean, they're on the right track. Right? They're still big like, everybody's a Bitcoin. Like, people thinking and caring about this are Bitcoiners, so it's like, are they paying attention to the right thing? Maybe, maybe
[00:23:24] Unknown:
not. But, like, if you're hung up on a narrative with no you're hung up on a narrative with no substance, you will kill then you will kill the messenger who tries to actually put substance in behind the narrative. Right? So if you're if you're unwilling now to have the substance put in and you just wanna kill the messenger, go eat a dick. Okay. But make sure you fry it in tallow, not seed oil. But you know what? You require Bitcoin asks for no no forgiveness whatsoever. You're always fucking welcome. You're always welcome to accept the protocol whenever you want. You know? It's like it's so funny. I I don't wanna get too more into too much more into this.
But, these people are like the anti shitcoiners, and yet the they are they're kinda shitcoiners. Right? It's just just interesting. That's gonna get taken out of context, and no one's gonna understand what I meant by that, and I'm gonna get the last Okay. Whatever. Whatever. It's out there. I'm a podcaster. I say shit. It happens.
[00:24:20] Unknown:
It's it's funny. Recently, like, making comments in one of the group chats I have, this guy put the you know, it's like this mass figure with the hand up, and it's like silence,
[00:24:30] Unknown:
insert name. Yeah. Pod comp name is talking or whatever. Yeah. Yeah. Yeah. And it's like silence dev, podcasters talking. I was like, wait. I have a podcast too. But they don't mean, like, our podcast. They meant pod comp complex, podcast that really pumped ocean. That's what I was that that's that's my interpretation is that they, you know, the PodConv complex pumped Ocean.
[00:24:49] Unknown:
And I'm a fan of Ocean, though. Right? Like, I love what the Ocean team is doing. Yeah. This isn't even like an Ocean project. It's just so it's just the insane person. They
[00:24:58] Unknown:
they the the insane person they decided to have to be their CEO. This was like a side project for him, and it became you know? But but it's still in, like, the loudspeaker of that of, like, the PodCon complex. Yeah. Right? So it's just you know, you don't get to they're they're like antibiotics, dude. You don't you don't get to decide which of these narratives are the ones that stick. They all they all get pumped out, and that's just the way it is. PodConf doesn't discriminate.
[00:25:24] Unknown:
That's true. That's fair.
[00:25:26] Unknown:
Oh, man. Alright. Let's get into math before we, before this gets even more off the rails. Shall we? Shall we talk a little math?
[00:25:35] Unknown:
Well, first of all, bring up your white paper. Turn to page six.
[00:25:40] Unknown:
Yeah. I wanna get I wanna prep I'm actually excited about how I'm gonna lead into this because I know we this is gonna be about Poisson, but I'm actually gonna make this a little bit more general because we've never done this on Motivate the Math. So episode 19, we're gonna do this now. I want I'm excited to talk about, like, probability. Oh, yep. Things of a probabilistic nature, things like random variables, random processes. And I wanna just I think, Gary, we should talk about that a little bit in general because then it's like, okay. What does it matter to know the word versus normal versus binomial versus like, why does it matter or versus a negative binomial versus, you know, you name it. Okay. So, like, we sometimes we like to say we like to think we understand, the probabilistic nature of something.
So for example, if I flip the coin, now that's I know that's a foreign concept to most people because they don't there's no more coins. Right? We have Bitcoins that you can't flip. That's, like, my biggest criticism of a Bitcoin would be you can't flip it.
[00:26:52] Unknown:
You gotta go with, like, challenge coins. Right? And the military has a strong culture of challenge coins. That's what the world is moving towards. I've got a Bitcoin better one. I've got a I've got one for my employer. Coin. Nice. Challenge coin. If I was a boomer,
[00:27:05] Unknown:
I would be on, like, CNBC right now saying, if you can't flip the coin, it's not a real coin.
[00:27:13] Unknown:
There's so many it's it's interesting because the, the dual, like, you know, flipping something, right, in the nature of, like, a house or, like, a a trade or or something like that. It's like, oh, I flipped this. Right? So that's a it's an interesting They've they've co opted all of the ways
[00:27:26] Unknown:
we that kids naturally learn about probability. Okay? Okay. They've co opted. They got rid of the coins, and now these kids don't understand risk. They they you don't flip any you you don't flip to for, chance anymore. Yeah. You flip for profit. Oh.
[00:27:46] Unknown:
There's a sound bite. Okay.
[00:27:48] Unknown:
Yeah. Okay. Podcast is over. So but okay. But let's go back to just imagine imagine there's a thing called a coin with two sides. Mhmm. And then you can flip it. On one side is a head of some Fiat lizard piece of shit, and on the other side is some structure that you lived in Yeah. Where you built. Okay? And imagine that you when you flip it, it lands on either the head or the tail with equal chance. Right?
[00:28:16] Unknown:
Yep.
[00:28:21] Unknown:
So how would you like, if you basically were running a game of coin flipping, right, and you said I'm gonna pay $2 per head and I'm gonna pay $1 per tail, what would be the price I would charge per flip in order to not you know? And and or and and how much capital would I need to hold to run that game to to make sure I don't go broke? Like, there's a certain amount I need to charge Yeah. So that I make money over time because there's this then thing called the law of large numbers that applies to certain probability distributions.
Okay? So the distribution I'm talking about happens to have a name called binomial.
[00:29:06] Unknown:
But it's like random walk?
[00:29:08] Unknown:
Yeah. Well, yeah. It's just binomial. Meaning, there's there binomial just means that there's two outcomes. Heads Right. There's there's two outcomes, and it doesn't have to be equal probability. You could have, like, a weighted coin. Like, if we were back in the wild West and, these guys walked around with weighted coin. You ever hear the term loaded dice?
[00:29:27] Unknown:
Yep. Yeah. So, like, the Well, my frame of reference for probability is dice because
[00:29:33] Unknown:
Dungeons and Dragons. Yeah. So dice is the dice is still in existence. They haven't come for the dice yet.
[00:29:39] Unknown:
Not yet. I'm coming for it, though. They will.
[00:29:44] Unknown:
I I I I used to walk around with my little baggie of I think I bought it from CoinKite one of these days, one of these times. It's like a little baggy. It's a little baggy with tiny dice. Mhmm. And, it looks like a bag of drugs. You know? But it's got tiny dice, and you it's called, like, entropy. You know? It's kinda funny. Right? It's like, oh, yeah. It's true. Right? You wipe you have this fucking
[00:30:08] Unknown:
little time full of dice. Dungeons and Dragons player that was like a caster, like a wizard with magic, had that bag of dice already because there's one specific spell in the realm called fireball. It's like a very iconic thing. And as you level up, you just get more and more of these six sided dice because because it's six sided dice in your bag. Right? Yeah. Yeah. You get more and more of these six sided dice because as your level goes up, like, that's how many how many the more dice you roll for, like, damage. And so it's because I already had a shit ton of six sided dice, so I didn't need to buy mine from Koincite. I already had them from, you know, past activities.
[00:30:43] Unknown:
Yeah. It's cool the way they come in a little baggy, I gotta say. And it's just like you actually do line put them in lines. It's very strange. It's very illicit, because you're put you're creating by you're creating a binary numbers. Yeah. That's how you you know, that's one of the ways you can make your own key with your own dice.
[00:31:01] Unknown:
It's one of these sources just a bunch of dice. Recommended source of entropy Yeah. For creating a key. Yeah. That's right. And there's a minimum number of dice that you want in that, and this is, like, a very, very key. And you maybe you can explain the math on this, but it's like there's a very, very specific
[00:31:21] Unknown:
minimum that you want. Otherwise, you will have something called low entropy. Yes. Meaning We won't do that this episode, but there is a the quest so it's a matter of, there's a couple things. One is, if the law of large numbers basically is, I mean, I wouldn't call it a law, but people call it a law. Mhmm. It's that, like, you know, how do you how confident are you that if you flip the coin enough times that it actually converges to, a probability distribution that you can actually model and feel comfortable that it'll converge to?
Right? So it said that the, Well, and that's in relation to, like, a security assumption. Right? Well, not well, it's more, like, how do I know if okay. Look. How do I know? How do I feel comfortable? How would I run this game if it was just coin flips? Right? How would I run this game if I again, I pay out, again, $5 for a head and I pay out $1 for a tail. How much do I charge per flip, and how much capital do I need on hand? Let's and then that's where you're what's called big n. Big n is, like, the number of it's like, what's the number before I Go broke.
Well, you know, I need to hold capital for a certain amount of loss. Right? Right. Like, so if I'm gonna pay $5 on a head, how do I know how do I really know it's not gonna be head 500 times? And I'll you know, that would mean I have to hold $2,500 in capital. But I probably don't. I can probably rely on the law of large numbers and say that, well, much more reasonably on in two if if my big n is 200, it's more likely I can I I can hold a lot less than that because the the very it's very likely they're not all gonna be heads?
[00:33:19] Unknown:
You're describing, like, mining pool
[00:33:22] Unknown:
Well, that's quote. That so Poisson distribution, not that we're getting into it yet. I just not quite ready yet. But it does it is a, it is one of the distributions that, like, a binomial distribution can converge to. So, like, in other words, you can use the binomial distribution, meaning, okay, one if there's by is two. That's it. And I have two outcomes, a or b, heads or tails. Right? One or zero. And it's very convenient to think of it as fifty fifty. You don't have to. But let's just, for the sake of this conversation, say it's fifty fifty.
[00:34:00] Unknown:
Right? Okay.
[00:34:04] Unknown:
There are things we understand now about a binomial distribution that if we knowing that it's binomial, it's like, remember when we had the conversation about groups and said, well, what is why does it matter that we know it's a group? Because then it, like, allows us to know a lot about the system. You know the box that you're playing in? Yes. So so knowing a coin flip is a binomial distribution with a certain probability allows us to say, okay. What's the average? Mhmm. Right? What is the average, what is my average payout if these are my you know, if I'm paying out, what is gonna be my what is gonna be the average payout, which is gonna help me decide the break even for what I charge for that game? So for example, 5 if I pay $5, I should have really written this out and figured this out before I started talking about it because I'm already, like, losing my concentration on it. It's probably gonna it might this might be wrong. But if I if I pay a $5 for a head and $1 for a tail, my average payout will be should be $3.
[00:35:10] Unknown:
Right. That's what that's what my gut told me. Like, this whole time when you were saying, like, $1 for one $2, I was like, oh, a buck 50 is, like, kinda where you wanna fall in the base assumption due to 50. So in that, if it's if it's five and one, five plus one is six divided by two is three. So the average and that's what you would call the mean. The mean of that distribution
[00:35:29] Unknown:
is three, which means if I charge less than $3 for that for that flip, I'm sis I'm gonna systematically lose money. Okay? But if I charge $3.01 for that flip, I systematically make money over a long period of time, but the question then becomes, what is the big end that's required for that to happen? What is the big n required for the law of large numbers to kick in such that I am just scalping one cent per toss as opposed to really being at this risk of variance?
[00:36:07] Unknown:
Yeah. Right? Yeah. Yeah. Yeah.
[00:36:11] Unknown:
Yeah. That's how you think about it. And so and so what so what is the big n? And then I and, you know, you know if you know, now you you wanna extend this into a mining pool. Right? It's the same I absolute well, there's one thing that I'll say that
[00:36:26] Unknown:
there's a parallel here that I think we've talked about previously is, like, you boil it down to a binomial. But in in our previous talks and stuff, I remember being able to take polynomials and boiling it down to a binomial equation where it's like, you boil it down to a binary representation.
[00:36:42] Unknown:
So Binomial is a is a so okay. Maybe I'm using the words wrong. No. It's fine. It's it's based off of a polynomial. Mhmm. So there's something called the binomial theorem, which tells you that any two numb if you square any two numbers, just gives you the formula. Just get you know, there there's a formula. There's a theorem that says this is what it this is what you end up with. And it matters if, this is back now. This is where where you need group theory because if, if you have a, like, a modulus, right, a lot of those terms are gonna zero out. And so in other words and when you have a modulus in math, you call it a characteristic. If it has a characteristic of, like, two, then then basically, all of your numbers are gonna be zero or one, and so a lot of the terms of the binomial expansion are gonna zero out.
Incidentally incidentally, here's a fun fact. Half the terms. Right? Yeah. Well, possibly. Oh. Here's a fun fact. Do you do you know what Pascal's triangle is? No. Well, we're gonna attach that to the show notes. It's one of the greatest things ever discovered by Blaise Pascal. Pascal's triangle. Shout out, Blaise. Another French mathematician, I I guess, like, like Poisson. But, Pascal's triangle, maybe we'll just I'll just save this for another maybe I'll save this. I'll do a video on it. But Pascal's triangle, every row gives you the binomial coefficients.
It's kinda cool of the it gives you all the every row gives you the coefficients of the binomial expansion. It's very, very cool. Also, every row sums to to the end.
[00:38:34] Unknown:
This yeah. Okay. I I pulled up I pulled up a website, and it's it's worth going to visualize. It's a an a tool for visualization.
[00:38:42] Unknown:
Yes. Because you can build this triangle structure. It's also if you're bored, if you ever, like, have hours where you must sit somewhere and not do anything Mhmm. You could just sit there and write out every row. You can go as far as far as you can on Pascal's triangle. Okay. So there is a binomial, which is like the simplest version of a well, not the simplest version. There's a monomial, and then there's a constant. But there's a binomial, which is a simpler version. It's a simplified sort of version of a polynomial. Mhmm. Okay?
But the binomial distribution as a probability distribution like, there's no polynomial distribution necessarily. There's not because we don't know it's too general. We just don't know enough. And unless we can get it to, like, two outcomes. Right? Mhmm. Okay. Really get to that. We don't really get that, we don't really get that sense of maybe we know something.
[00:39:40] Unknown:
Like, it it would expand beyond, our
[00:39:45] Unknown:
does it expand beyond our ability to, like, reason about? Is that Yeah. It's just we just don't we just don't know. Like, there's certain things. Like, there's there's a class of random variable that's just random that we literally know nothing about. Mhmm. Right? Like, it's literally it's so it's genuinely random. Right? Like, it's genuine and then there's, like, those sometimes are those are really desirable to try to construct, obviously, for obvious reasons. Right? Yeah. In cryptography. And so you want like, sometimes you actually want to know the properties of a truly random variable, and you wanna be able to maybe test if you generated a 100,000 of them, you wanna be able to test to for that randomness.
Right? You wanna And is that, I mean, is that a a way of that can't be abstracted into a into a or modeled into a distribution.
[00:40:37] Unknown:
Is that a way of measuring, like, entropy? Yeah. Right? That's, like, a way of measuring to that you have enough entropy.
[00:40:45] Unknown:
Yeah. Like, you want you really want, like, perfect randomness. Right? And it's and, you know, when we talk about randomness, what we usually have with random variables is pseudo random variables, not truly random variables. So, for example, the like, when you the classic example is, like, the shuffle on your iPod. Yeah. Right? Where it's it's not truly random because if it was truly random, there'd be pretty reasonable probability that the same song would play four or five times in a row. So they make it's right? They make sure that that doesn't happen.
Right. Right? So it's it's
[00:41:25] Unknown:
pseudo random. What it that makes me, on some, like, developer stuff. Like, you have these things called seeds into your random number generator. Yep. So it's like you can have a, deterministic randomness where it's like, hey. This is a random number, but, like, if I give it the seed of five, all the variables and the inputs and everything like that, like, are deterministic. And that's that's useful for, like, testing
[00:41:52] Unknown:
certain things. It's vital. It's not just useful. Right? Yeah. Yeah. That's true. Yeah. Yeah. Because, otherwise, you
[00:41:58] Unknown:
if you're testing anything without Boolean logic, true or false, Like, you have to have a way of knowing the inputs predicting the inputs to verify that the outputs are what you think they are when you're when you're running it through. But then on the the opposite side of that, it's like you don't. Your seed, whatever it is, like, you don't want that to be consistent. But there's also
[00:42:22] Unknown:
When you're at when your outcomes are ordered, it's vital because it's the only way to replicate your outcomes being ordered. If all you're trying to do is take an average, you might get away with not having a random seed because your average should still convert everything should converge to that average. So this the random seed is really important when your outcomes are ordered. You need random out you need you need you need random outcomes, and you need them to be ordered, which you see that a lot in risk where, you know, you'd look at you'd look you'd look at the tail. You look at the ordering, or is it the like, when and when you say ordering, I order. In other words, so so in risk, a lot there's a concept of, conditional tail expectation where what you'll do is you'll study the just the lowest tail. So in a if you have a thousand, scenarios, you'll look at the 20 worst ones. And in order to look at the 20 worst ones, you need to know you said there's no way to there's no way to replicate those without either having all your scenarios be super deterministic, which is how a lot of companies do it, or, having a random seed that, you know, that you you know I mean, having a random seed is not that different from the hierarchical, key structure.
[00:43:40] Unknown:
Well, that's what I was thinking because if you take a message and a signature, the same message and the same signature will result or the same message and the same, signature algorithm will result in the same signature on the other side. Right? Yeah. But you don't know what that signature is until you run that that equation. But once you've run that equation, you know what the inputs are, and now you can deterministically arrive at the output even though that output is not known to you without, like, doing the math.
[00:44:08] Unknown:
Yeah.
[00:44:09] Unknown:
Yes. So Oh, man. I've been okay.
[00:44:13] Unknown:
Yeah. So this is good. Like, we're we're actually creating runway for future episodes again. This is good. I've been vibe coding an app that is directly applicable to this. Dude, we're gonna talk about that when Okay. Okay. So, definitely, we're just gonna we're gonna put that on the schedule. Guys, we're creating runway. I feel like we have 10 more episodes in us easy just on what just on what we're discussing. Bearish. This is good. No. I'm just saying easily. E easily. Yeah. Yeah. Yeah. Without the world without the world giving us more material from now. Right? Mhmm. So, again, I wanna focus just again on probability distributions because I feel like if it's hard for that was the hardest thing for me to understand. Like, why do I care if something is a binomial distribution versus a, uniform distribution, which is what, a dice roll would be?
A roll of a dice would be a uniform distribution. Every outcome has the same probability. Right? If it's a six sided dot that's not you know, it's equally weighted. It's one
[00:45:15] Unknown:
sixth. The output of a sha, if it's, like fit should be uniform. Right. That's right. And and that's why every hash your ASIC makes has the same chance of winning a block as anyone else's. But if you have more hashes, then you have more chance. So you the uniform distribution is a good distribution to
[00:45:36] Unknown:
Okay. Yeah. Alright. Now it and then there's a question of, does a uniform distribution converge over time into, like, you know, to a Poisson? And I'm sure there are smarter people that that got met that I think and I think that's the case. I think, like, a uniform I think it's the classic I think that's actually classically how what Poisson distribution models is the largeness of, the uniform, you know, the uniform distribution, which is then now what you have in a mining pool. Right? You wanna know now, like so one is what's the probability of the event happening? Right?
Then the question is, if I know that and it's and then and they're equal or they're behind you know, I understand the probability of the event. Right? Right. One in a fucking billion or whatever it is. Right? Mhmm. As if, welcome to 2010. You know, when the probability of winning a block was, like, one in a billion. No. But, whatever it is. Right? What a Poisson distribution then asks or measures is given a big n, given the number, I I know I'm gonna do a numb a certain number of trials. What is the distribute what's the probability of one success zero successes, one success, two successes, three successes, etcetera? Right? What's the in other words, what's the probability to hit zero blocks, one block, two blocks, three all the way up to big n, whatever big n is? Right.
Right? So if I wanna say over a day, that's big n is one forty four. So over over a day, how many times out of a 144 am I gonna hit a block? Or in a difficulty period, which is two weeks, is what? Twenty one sixty?
[00:47:25] Unknown:
Two thousand sixteen blocks? Sorry. 2,016.
[00:47:28] Unknown:
I'm sorry. So right then, your big end would be 2,016 blocks. How many which is actually much that's a more relevant question than a day because what happens in 20 in 2,016 blocks is, my hash just gets devalued and debased into the next period Maybe. Difficulty adjustment usually. Over time, it's if you're if we're if we're, like, transporting our brains into this law of large numbers world. Right? Yeah. You you know, you over time, your hash gets debased by, like, 30, you know, 30% a year. Like but, you know, by one by one ish percent every time every two weeks. Right?
[00:48:08] Unknown:
Yeah. Yeah. That's probably I don't know what the exact measurement of this. But and that goes to the acceleration of the block's arrival. Right? Because it's like, if you go back to block zero and measure to today, on average, I think it's been less than ten minutes per block Yeah. Because we've had this ever increasing hash rate. Yeah. Which has ruined a lot of having parties. My having party was spot on. Like, it happened at the party. We all celebrated. It was a wonderful time.
[00:48:37] Unknown:
But, again, once it just I wanna Yeah. Keep this fairly evergreen and understand like, from the mindset of what is a probability distribution and why does that you know what I mean? How does that help me? How does the knowledge of a probability distribution help me? So Mhmm. Like, when Satoshi tried to spell out in the white paper and it's so funny, dude, when people are like, it's just math. Nobody talks about this math ever. Yeah. They think that the math is, you know, the sum of the blocks over 21,000,000 or what you know, or, you know, that's the thing. You know, like, that equation and they've you ever see these memes, you know, where they're like, oh, the Pythagorean theorem and then there's the sum of the sum of the blocks.
Right. This is Yeah. The having equals 21,000,000. It's like, that's the math. It's ridiculous. Like, this is the math, actually. Well, at least as as far as why a decentralized proof of work concept is going to, you know, why is it why why can't it work? Right? So the math here is what happens when, you know, what happens when everybody competes for a block. Right?
[00:49:54] Unknown:
It's framed in the in so it's it's section 11 of the white paper. And the the first sentence and and this is interesting just because Good thing it's not chapter 11. The lead into.
[00:50:04] Unknown:
Although that's how a lot of miners went bankrupt. Oh, but
[00:50:09] Unknown:
I missed that on the first one. But the the the it's section 11 calculations. And the first sentence is we consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. So, like, it's framing in, like, this calculation is critical when you have to look at attacks on the network. That's right. So, like, adversarial thinking was a great segue into this topic.
[00:50:34] Unknown:
There's no way to deterministically really, like, deterministically attack the network. Right? And then so, like, even if you can do a 51% attack, right, you're still subject to the law of large numbers. And, you you know, if you're big in it, then that's why, like, you know look. Big end for confirmation six.
[00:50:55] Unknown:
Right? Right now. Big end big end to sustain I mean and that's, like, enormously expensive as it is. I would raise that just given the number of consecutive blocks that we've seen from these big mining pools.
[00:51:06] Unknown:
Oh, fuck. Yeah. But, like, if you think about you know, so you think about somebody who does wanna attack the network, and they wanna they wanna like, let's just say they have the intention to mine 10 to 20 blocks Mhmm. Backwards. Right? Yep. Probabilistically, that the the cost you know, 51% attack doesn't mean you're getting you're gonna win 51% of the blocks. Right. Certainly, especially if your big n is 20. You may win zero still even by you know, you still may win zero. Yep. Right? There's like a, you know, there's a non zero probability. You you actually win zero blocks with a 51% attack. That's just like so in other words, this to me, I would say this is straight math.
You know? And, it's unlikely, but it is you know? The other distribution that might be relevant for people to know is called the negative binomial distribution, which is in a binomial distribution. In other words, what's the probability, if I did 10 tries, what's the bit probability of some number of failures before success? So, like, what would be if you know, what's the probability of nine tails before I get my head?
[00:52:23] Unknown:
Right. And that when the end value goes up, it's that, like well, I guess it doesn't the end value could go up, but your your Well, the end target for success could remain the same and the outcome is now different.
[00:52:38] Unknown:
I mean, yeah, the answer is it should, you know, you should it shouldn't be more than, you know you're in a binomial distribution. It shouldn't be too much more than two. Right? But it could be. It could be 10. It could be a 100. You could it's like, again, it's not impossible. This is what people need to understand. Right? It's definitely not an especially, like, people who are gonna put capital behind a probabilistic attack Yeah. Do need to understand that you could go a 100 blocks before you get that
[00:53:08] Unknown:
before you win your block in a 51% attack. Well, now it's interesting to flip that on the the opposite side of things too is, not necessarily being attacked, but being the one that is being censored or attacked. Right? Like, your your chance of success at breaking through whatever is, like, preventing you from hitting a block or for preventing you from broadcasting your transaction is the same calculation.
[00:53:34] Unknown:
Yeah. And but then there's this missing piece that maybe you can help with, which is that I think the other the part of the fifth there's a part of the 51% attack, which is the probability of winning the block. There's the other part of the fifth the one, you know, the 1%, which is that you're doing more work. You can't. So if you do win the block, you'll win. If you do win the block and there's, like, any dispute, you will have more work done because you did 51 you know, you will have done more work than anyone else. Right? So So maybe there's this piece that I'm missing around that that
[00:54:03] Unknown:
Well, it yeah. The the the the the tip of the chain is the most work, and so you could have it. And you can see this. This is what happens when a chain split occurs is if two blocks are found at roughly the same time, and now you have a chain split on the network, which happens I don't wanna say, infrequently, but, like, frequent enough that you can go again forked out observer. It will let you go But you're gonna be the one if you if you did 51 of the work, you're pretty much you're guaranteed to win that dispute. Correct? I don't know if guarantee the guarantee might be a strong
[00:54:36] Unknown:
strong You're not guaranteed to win a block with that hat with that, you know, with that amount of hash. You're not guaranteed to get one block in a day or a week even. Well, it's not just one block, though. It's a consecutive block because
[00:54:47] Unknown:
the the 51% attack is targeting, you're trying to orphan a chain. Right? Which means you're trying to accumulate a new chain without, you know, the the censored transaction in it or the censored block in it Mhmm. With enough work for the rest of the network to go, oh, this guy has the most proof of work. Because you see this commonly where there's a chain split where there's two different blocks. Like, the last one, was, you know, 1,700 blocks ago or so according to Forked Out observer at the time of this recording. And it was via BTC hit a block and Brainspool hit a block. And so, essentially, the race then becomes like, well, who's gonna get the block after that? And that goes into, some game theory things about, like, peering your node and getting your block to as many people as possible for them to start building on as a valid tip of the chain. Yeah. And by the way, as you're speaking, man,
[00:55:41] Unknown:
shout out to the base 58 LARP because you actually get to do this in real time. I need I I have to do this. You get to play this game and do this in real time
[00:55:52] Unknown:
and get to really send Oh, like, you try to get your block out to the rest of the network so they start building on it in real time. And, yeah, you have you you know, you're sitting in a room with other
[00:56:02] Unknown:
people creating you know, doing mining and, you know, you have chain splits and you have to at some point, it does you do it, you know, it does come together and figure to reconcile. Yeah. At some point, you do figure out who actually did win the block, and you have to keep a couple of different records and, you know, keep a couple different chains. Yeah. Very cool.
[00:56:21] Unknown:
Oh, wow. That is cool.
[00:56:24] Unknown:
So, like, if I and if I hadn't done that, I would just like, I wouldn't have the visual sense of what you're saying right now.
[00:56:29] Unknown:
Well, and in the larp, right, like and you can kinda it's like each table with its own node. Right? And then you're Yep. You're literally connecting your node to other tables via, like, string and, like, passing messages across the string. Yep. And so in the case that we're talking about, it's like when you find the block, you have to, like, pass it along the string to as many nodes as possible so they start using your block to build on. But if somebody on the other side of the room also has a block at roughly the same time, they're gonna be doing the same thing. And now you, if you're in the middle of that, have to decide, okay. Well, like, which one you know, is it the first one I see? What if I see both of them at the same time? In that situation, the the 51
[00:57:04] Unknown:
attacker, I think, you know, pretty much has the trump card because they've done they have done they will always have done more of the work.
[00:57:13] Unknown:
Well, they will be con they will be able to continue to do more work to build on whatever block they deem to be the the That's right. The winner. That's that's right. To
[00:57:23] Unknown:
show it. But I think the what I wanna distinguish here and, again, I'm not, like, super expert. Right? Mhmm. I'm just a math guy,
[00:57:31] Unknown:
amateur math guy. Yep. Amateur Bitcoin guy. Or math influencers. You can say it. I'm
[00:57:39] Unknown:
as of now as of now, I'm an amateur Bitcoin guy too because no no one's paying me. But, the the when people think of a 51% attack, they think I think that typically people will think about it as the probability of winning a block. A sequence of blocks, though. Yes. But it's also but it's also the fact that you're demonstrating work.
[00:58:02] Unknown:
Yep. There's a cost to it.
[00:58:05] Unknown:
Yeah. Right. I mean, I think we could probably do a better job of teasing this out, but we weren't prepared to discuss this.
[00:58:14] Unknown:
I mean, I think we did a pretty good like, I don't know. I I learned a lot, so I assume that the listeners will learn a lot,
[00:58:22] Unknown:
even though we have a lot of listeners. This is great for me. I had a great personal experience. So okay. So let's get back to then it's so interesting. Right? So when the white paper positions this Poisson distribution as an attack, we started the episode on, you know, Portland Huddl's. You know? It's, again, iron sharpening iron. Mhmm. It's almost like we want people to attack the network. Right? It's almost like we would want a 51% attack. I've always said, like, yeah. Like, shit coins are a good are like a like, why do people Well are people sold the money at them when they're just they they demon you know, they're they're the attack that is needed. That's just part of the evolution of this thing. Right? We don't want it, but we should be prepared for it, and we should understand what it is. Maybe we maybe we do it correctly model it. Maybe we if we're really putting our life savings behind this thing, maybe we want it to be attacked a lot.
[00:59:17] Unknown:
Yeah. I no. I no. You never wanna be attacked. Right? So, like, just like putting on, like, my military hat. It's like you never wanna be attacked. You would always rather know the attack vector and then fortify a position to where you cannot be attacked. You're you're unassailable. Right? And this is why I have, like, I have two bid access in the car. I have to take to UPS after this. Thousands of years into military,
[00:59:40] Unknown:
intelligence. Right? We're fifteen years into this war, and the only way to know these things is for the attacks to happen. Yeah. Well, and I'm not saying, hey. Please attack us or anything. But, yeah, it's I mean, you'd have to be a giant pussy and, like, real Pollyanna to, like, think that, there's any other way, honestly, for this thing to get robust fast. Right? Yeah.
[01:00:08] Unknown:
Yep. Well and, also, it's like if you can if you can be attacked, if your position is a saleable by a single individual with some, like, AWS credits, like, that, you know, that's not a nation state. Yeah. That is that is not a That's right. That is not the, Apex predator that could be attacking you.
[01:00:32] Unknown:
The key you we have to see every attack possible. That's and that is you know, that's why it's open source. Yep. Right? And that's why open source software will always be the most robust over time because it will see the most attacks. And, you know, there's no the hope is not a strategy. Yeah. You have to be you have to test in battle. Simulated or real as well. Yeah. Simulated or real. If if some dipshit is a you know, if some dipshit from behind his computer is able to fuck your node over. I'm not saying portal is a dipshit, but he could have been. Any dipshit like, if I mean, if he did it, any dipshit could do it. Right? Well, I think the dipshit would be do it and then go sell it to some Yeah. Intelligence agency. If any dipshit can attack the nodes on the network, then you don't have much of it.
You don't have much. You know? Like, your Bitcoin isn't worth that much if it's that easily attacked.
[01:01:41] Unknown:
Well, that's that's the other thing that, you know, thinking about is, like, they there's always, people always allude to the economic relevance of a given note as well for, like, if it's being attacked. Right? Because, like, somebody could attack my note at home, and, like, I'm not doing, like, I just don't do a lot of transactions through that node. So, like No. I get it. Right. It's like they but then you can attack, like, River's node, and you can really put a substantial impact. And these, like, I But River doesn't have Comcast ISP. Like, that's that's the other thing. It's like the River is not going to have a a a throttleable throttle throttleable connection.
And if they do, they will probably have some other redundancy built in. Node. You can prob you know, you can attack SupertestNite's
[01:02:25] Unknown:
node. And, he might be under Comcast. I don't know. The point being, right, like, these these there are people that we share our network with that think that, the fact that it's illegal to do a denial of service attack on somebody means that it won't happen, and we don't have to worry about it.
[01:02:44] Unknown:
Yeah. Well, here's the other here's here's here's a bullish scenario too that could result in the same thing. It's like everybody So no suddenly decides to run a node, and you have thousands of new new nodes doing IBD or or millions of new nodes. Right? The whole world is suddenly like, oh, shit. I gotta do this Bitcoin thing. And so they start IBD. Right? Is it likely scenario? No. But, like, that same scenario would have resulted in the same end result of, like, your Comcast ISP upload limits being breached, and your node is now offline. Oh, wait. You're saying, oh, the prop the likelihood of all, like, of a lot of nodes doing IBD at one time? Yeah. Yeah. That's what I'm saying. Like, you if a million nodes went up come. Don't you think that day will come when, you know,
[01:03:27] Unknown:
when there's, like, there's 9,000,000,000 people in the world. They're not all gonna run nodes, but there's, like, gonna be more than, like, 15,000 nodes at some point. Probably, we'll get a day where, like, 10,000 people all spin up a node.
[01:03:38] Unknown:
How probable is it?
[01:03:40] Unknown:
That's that is a well, that's a that's a great place to fucking end this end this thing. But, yeah, that's a that would be a, a good Poisson calculation, I think.
[01:04:22] Unknown:
Where is my mind? Where is my mind? Where is my mind? Where is my mind? Mind? Where is my mind?
Introduction and Podcast Trajectory
The Math Behind Bitcoin
Page Number Numerology
Pi Day and Metric System
Adversarial Thinking and Bitcoin
Node Configuration and ISP Limits
Probability Distributions and Randomness
Understanding Probability in Games
Binomial Distribution and Law of Large Numbers
Uniform Distribution and Mining Pools
Poisson Distribution and Bitcoin Security
51% Attack and Network Security
Open Source and Network Robustness
