Is The Bitcoin Power Law Broken? | Matthew Mezinskis

The way that power growth manifests itself is, in the case of Bitcoin, is it has started out higher in the early years. It was, you know, a thousand percent a year, right, on a curve, on a trend. Now it's down to about 40 percent per year on a trend. I think that it's totally plausible that the trend could change. I also think it's plausible that Bitcoin could change other trends in the world. Common sense tells us constant growth is faster than proportional growth. It's going to be good. It's going to be good for Bitcoin holders. On the one hand, the number go up. But on the other hand, this is where you get into the idea of, you know, what does that actually mean? Is TradFi co-opting the system? Can anyone claim any Bitcoins on an ETF? Can you withdraw Bitcoins from exchanges after 10 years? There are a lot of things that could play into this. And by the way, if some of those play out, perhaps as some entrenched players in Bitcoin want, then I think, yeah, Bitcoin could go exponential. It could match. It could mirror the exponential growth rate of the rest of the financial system. Matthew, welcome to the show, man. One of my favorite quarterly interviews that I do. You know what? Last time we were on the show, we were talking about the power law, and we were pretty much at the bottom of the trend. And I think we were kind of calling it the bottom, if not close to the bottom. And then since then, Bitcoin price has gone below the power law trend. And I don't know, does that mean it's broken? Is the power law broken? Yeah, great question, Danny. You know, I come on your show every quarter or so and talk about this stuff a lot. And for old listeners, maybe it's a little bit repetitive, but just very, very briefly. when we're doing trends like this and i've been doing it for a long time you know a little bit less than than giovanni he's kind of got his name to the power law uh he first posted it on reddit in 2018 fall something like that on the price i did it in around december of that year but it's important to remember that we're not trying to model like channels or elliott wave stuff these lines on charts, ABC corrections. If this level of support breaks, then it's over for this amount of months. All of that stuff can be done. I mean, people can definitely do that and they do. And there's no shortage of articles of that on TradingView or YouTube thumbnails. But with the general idea of what I'm trying to do when I look at the price or the money supply is I'm just trying to gauge a relative level of change or the relative growth and see how the asset is sitting, you know, relative to the range of observations in the past. So just looking at the statistical probabilities, it can always be that it sort of goes lower. And we can look at some good charts today to talk about that. But it's not anything where you say, okay, if it goes past this level of support, it's definitely broken or it's over. So another way to look at that is you just have to see if Bitcoin is following this power law. And again, just quick, quick, quick refresher is a power law is not constant growth. Constant growth, like we talk about with our broker, or if you're looking at the stock market or the bond market, you're looking at bond yields, yield to maturity, IRRs, or just returns, right? Those are constant returns that you expect to get every year. So 10% a year, 12% a year. And it's actually getting a little bit faster, which we can talk about on the show as well. But in general, it's constant growth, right, is what we try to achieve in our stock portfolios. With Bitcoin, it's interesting. If you look at the price over a long time, you have a sort of very slightly decelerating rate of growth. So it's not constant. But there is still a relationship here and it's a power relationship. So it's actually the rate of growth is proportional to many things. It's actually proportional to addresses, to hash rate, and it's also proportional to time, to actual existence of time in the system. How long the system has been around. Bitcoin has a proportional relationship, say, till the next doubling, that in this particular case, that proportionality does stay constant. And the number is about 13% a year. So again, I just try to put that broad, broad overview and talk about like the power law breaking. I think it gets people that are even in the space like looking at this from an analytical view of the power law, that kind of wonder, okay, did the Bitcoin gold power law break because that thing looks really skewed? And still the answer is No, because relative to all the other trends that we can judge Bitcoin on, that's an exponential trend, logarithmic, linear. Bitcoin is totally, totally on par with a power curve or a power trend. I know a lot of people get triggered when you say power law, but that's the scientific name for it. But in any event, it's a sustainable growth rate and we can look at it. It's certainly relative to the probabilities, the range of observations in the past, the probability is very, very, it's showing not a lot of likelihood that it breaks too much lower. But again, it can always surprise us to the downside of the upside. So basically, that's my overall disclaimer. No, it's not at all broken. And I can try to show that with some just simple, simple charts here. Okay. But before we do get into the charts, one of the reasons that people have sort of PTSD around a lot of these things like the power law is because of what happened with stock to flow and how people became very dogmatic and never admitted that that whole model broke. What would have to happen for you to say the power law is broken? Is there something that can happen that breaks it, in your opinion? Yep. Good question. Great question. And again, even though I've been tracking this one for a long time, I've also been tracking Bitcoin as base money for a long time, looking at these major sort of macro trends, money supply versus Bitcoin UTXOs, the values of those things. There's going to have to be a lot that would happen to say that it's not a power law anymore. And again, it's totally possible. I'm not at all married to the idea that it needs to stay a power law or a power curve, power regression, however you want to say it. The challenge with throwing a lot of different models out here, and you'll see it, by the way, anytime you see like a straight line, people trying to take a straight line to Bitcoin's trend and the chart is only log linear, all right, that means log scale on the Y, linear, just normal time on the X axis, they're trying to shoehorn it into exponential growth. And it just doesn't do that. So again, I would say that. But if you would look at other types of models like stock to flow, they were also trying to shoehorn in some exponential growth factors into the price when Bitcoin doesn't do that. So it's a bit more confusing with stock-to-flow because in fact, it is a power law. He used the power equation to run through it, but he was running it over the stock-to-flow value over time, which in itself is about a 16% per year negative kegger. If you wanted to average it out, the supply of bitcoins decreases 16% per year. And it's not even average, right? It's not a constant 60%. We know that it halves every four years. So he's trying to shoehorn in a power law over some features of Bitcoin, which are exponential. And that's why it didn't work. Again, it might be a little bit technical there, but I've talked about it a lot as well. It's just, you know, he was trying to compare, say the Bitcoin, like back when he was doing these early models, 2019, 2020, he was trying to compare, say, the growth of gold or the growth of silver to the growth of Bitcoin. That is actually the units that came out of the ground in gold and silver's case or the UTXOs that would come onto the scene every 10 minutes. Everybody knows intuitively that Bitcoin's rate of growth declines, right? It declines there. It actually, again, that might even sound like power law when I said that, but it's an actual exponential rate of growth. The halving every four years, basically, it's a negative 16% per year on average. And he was trying to compare that to something like gold and silver, which when those ounces come out of the ground, 1.8% in gold's case, and actually 1.5% in silver's case, even less, those are exponential factors. They come out every year, about 1.5% for silver, 1.8% for gold. So they're just by nature simply incompatible with what Bitcoin does. And so there was a lot of confusion around that model. And it just, like I said before, you're trying to shoehorn in. He was actually using a power equation, But he was using it with this, a lot of features of Bitcoin that were exponential and it just wouldn't work. Whereas the power law, which we talk about with Bitcoin, we're just taking it purely on the signal that Bitcoin produces, whether it be addresses, whether it be hash rate, whether it be price. we're not even taking into account the having. We're just looking at the way that price grows over time or the way that addresses grow over time. It's like a pure signal, single variable, single unknown variable and running it. And the regression, the relationship is holding up very, very well. So this is kind of, these are some of the answers that I would get there to that question. I don't know if that fully answers it, if you have any more I'm happy to follow up on. If you hold Bitcoin long enough, there's going to come a time when you need some dollars. It might be a tax bill, a business expense, life getting in the way, but whatever it is, it might come at a time when you don't want to sell your Bitcoin. That's where Ledin comes in. Ledin lets you borrow against your Bitcoin instead with tiered rates that go as low as 9.25%. So you don't have to sell your stack if you don't want to. Ledin have operated through every market cycle since 2018 and have originated over $11 billion in loans. 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So if you own a Bitcoin ETF, especially if it's GBTC, you need to talk to Swan Private about RBX today. Head over to swan.com forward slash wbd and booking a call with one of their team that's swan.com forward slash wbd so the question that i would have around that is i guess two things let's start on what would actually have to happen for you to say yes this is broken yeah it's gonna break or not be a model that is applicable if another traditional basic scientific regression fits the price the address growth the hash rate better um now there is a grand theory that i have around a lot of this stuff uh it primarily resolves around uh revolves around exponential growth and power growth mostly because those are the two types of growth that uh well really it's just exponential growth that is most prevalent in the financial world. And that's primarily driven by the interest rates. So your bank loan, your mortgage, whatever you are paying on capital that you borrow to acquire assets, whether it be a house, car, something for your business, that's exponential growth. So when you have a bank loan that's 5%, that's fixed constant growth that you got to pay per year, that's your cost, that's the bank's income. And of course, there are spreads on that. And yes, the rates can go up and down. That's true. They do change with the market. But as time goes on, whether it's a little bit up, a little bit down, you're still paying this sort of constant fixed rate of capital. And so it is hard to imagine. And I don't want to go too far off on this tangent with the answer, but it is hard to imagine if Bitcoin's growth right now. So basically, the way that power growth manifests itself is, in the case of Bitcoin, is it has started out higher in the early years. It was, you know, a thousand percent a year, right, on a curve, on a trend. Now it's down to about 40 percent per year on a trend. There will come a point, and this plays into something that, you know, Michael Saylor talks about, is we all know basically Saylor's cost of capital. we've seen that the market's trying to liquidate Saylor in the last couple weeks, right? With Stretch really being stretched as far as keeping the buck. And his cost of capital is 10%, 11%, whatever it is, right? But that's a fixed cost of capital. And as long as Bitcoin on a trend grows more than that, Saylor is fine. His shareholders are fine. Strategy is fine. But if Bitcoin ever started to grow less than 10%, percent, Saylor's going to have to shrink the cost of his capital, or he would start to have to shed some coins and he would have some liquidity problems. He's a long way from that. And I cannot just, just to back of the envelope, even though Bitcoin on a trend is growing about 40% per year and declining, that means it's doubling every two years, 40% per year is doubling every two years. But that, that growth is declining in a, in a, in a compound fashion, like the rate is shrinking and the doubling time is increasing, right? But it takes a long time to get to that 10% as we're all modeling it in the power curve space at the moment. It's going to take to about 2070 to get there. The fireworks are going to happen much sooner. I think probably in the 2030s up to 2040 for a variety of reasons. We could talk about this, but I'm already... When you say fireworks, what do you mean? Yeah. So I'm already getting ahead of myself sort of in the grand theory. And, you know, we can look at some charts to illustrate this. But should we come back to that then? Because I have some other questions that maybe a bit more of the groundwork before we get to that. Yeah, yeah, we can do that. But again, just to let me make sure I answer your question, though, because about breaking or not, whatever, if it stops being a power law visually on the chart, if the R squared starts to shrink, if something like an exponential trend looks better over the curve, over the price action of Bitcoin or the address growth or anything, then Bitcoin would stop to be a power law. But we're nowhere near that right now. Nowhere near that right now. So the one thing that I want to try and get to the bottom of, because we've spoken about this before, but I don't know if I fully understand the reasoning, is you say that Bitcoin can't follow an exponential trend, whereas like traditional financial assets do follow an exponential trend. Why is that? Yeah, well, I haven't said it can't i just said that it is not okay and that's the interesting thing so again giovanni's been following this since about um fall of 2018 myself uh at the end of the year 2018 and at the time that was the best looking trend uh that would fit it wasn't even hard to really find that you just you know you can plot it on excel and and look at the trend uh automatically on the curve right or Google Sheets. In the early days, like 2014, 2013 on Bitcoin Talk, there was this kind of relatively well-known account called Trollolo Lo. And he was doing the same thing. I was trying to sort of update the work that he was doing, but he was actually finding a logarithmic trend, which is actually more explosive at the beginning and usually more gradual growth at the later periods of the observations. It's a little bit different than power law. But brass taxes, Bitcoin at the early, early days kind of did look like that with the explosive growth. And then from about 2016, 2017, it started to settle into this trend, which is very sustainable, sort of gradually decelerating growth every year, but still very high growth for anybody. And by the way, if you catch the bottoms and then it gets back to trend, you can get well over that, which we can look at just for fun, some scenarios. That's an example already right there where Bitcoin seemed to be following one trend, and it actually turned out it was following another, which is power trend. And I'm totally open, by the way, that it could follow an exponential trend in the future. And by the way, that is a very plausible scenario in my view, considering the rest of the financial world follows exponential trends. We have all of our interest rates on our credit, which are exponential trends. And it really, it does come, you know, Sailor has this 10% across the capital that everybody knows about. It does play into sort of my grand theory about how it could all work out, which again, we can table towards the end of the episode once we look at some charts. I think that it's totally plausible that the trend could change. I also think it's plausible that Bitcoin could change other trends in the world, which would probably be the more cypherpunk interesting view but bottom line of all this is i'm just trying to look at this through the lens of more uh statistics and math rather than kind of you know one-off blog posts or whatever youtube thumbnails um because i've been i've been charting this stuff for a long time and i and trust me i'll tell you if i notice that it's it's breaking i like the idea of uh bitcoin pulling the financial world like that i guess that is bitcoin eating the financial system is it pulling everything into its time time preference yeah and and i can explain that via the math so i think let's get into the chart can you pull up and we'll go through it yeah absolutely so here's a simple one i've shown this in a variety of uh ways before this is just even simpler because i've also shown this with stock to flow um but i sort of redoing my system so i don't have at the moment so here i'm showing you the price of Bitcoin up until today as we speak. Everybody knows this chart, log linear. This is log linear, right? And as you can see, it looks kind of like a rainbow, right? It doesn't look like a straight line, but I'm showing you, I'm shoehorning in an exponential trend. So the exponential trend, for those that remember, right? It's a straight line on log linear. So here's the exponential. And I put it on straight line, but this curved line is the power curve. And yes, we are well below it. We are well below it. All right. In the past, we've also been well below it. We've also been well above it. But if you just look, just use your eyes. You don't even look at the map. You can see the nice rainbow power trend looks much better on Bitcoin's price. And when we say Bitcoin's price, it doesn't just mean price. It means supply, demand, the interaction of actors in the market. You know, it can be a proxy for adoption itself. So it's a lot. There's a lot going on when we look at price versus if I put on exponential and let's just even take the power curve off. Do you think that looks better or worse? Definitely worse. And you can see it. You really can't like you can just use the eye test for a lot of this stuff. So so we can shoehorn in exponential trends. The key is to not get too married, I would say, to to any of them. But yeah, If we just look at the exponential trend here, Bitcoin hasn't hit it since 2022. I mean, it just clearly doesn't work. Yeah, exactly four years ago. And by the way, stock to flow gives a very similar effect, which, again, I was trying to sort of verbosely go through that earlier. But there are aspects of Bitcoin's system that are exponential, which, by the way, the 50 Bitcoins having every four years, that is. It's a negative 16% per year. That is what happens. It just happens in a weird way. Regardless, if you try to model that in and then stick a power law on it, which is what he did, it's shoehorning and it's not fully scale invariant. What a power law is, it's scale invariant. Anywhere on the curve that you pick it, the growth will be proportional relative to where it is at that point in time. So you can just see it doesn't work. And now let's look at the overall CAGR here. All right. I'm going to show you down here. It's a great CAGR if we were still on it. It's 108% per year. See it? 108% per year. Okay. And what this is saying is any point on the exponential curve that we would pick, it doesn't matter where, you would grow at 108%. If you do that present value, future value calculation that finance people know how to do, it will be 108. It just doesn't do that. So a much better model is a very simple power curve. So if we take off exponential now, we can see it tracks it. And we'll go into the details here. But if I go down to my very simple calculations here, now CAGR of power is actually higher, but that's irrelevant. It's just taking the first point on the power curve. and I go back to Bitcoin P today, May 2022 till today, which the power curve is about 140,000 at the moment, $140,000. So you can see how far under we are, right? At 62. It doesn't make sense, right? Because it's not, that is not a, it's not a constant growth rate. What it is is scale invariant, which we just have to look at the trailing 12 month in the power, you see 40.2% right there, 40.2%. that's the power laws growth rate at the moment but that declines every year and just to see as well what does power growth look like in log log which means we took take all the dates which are numbers not dates you have to take the actual numbers and starts with genesis block of one back in january 2009 you see it starts to become almost self-evident that it's growing according to power. You see, it fits very well. Yes, we're under, but we've also been under there in the past. It fits really well, but you would have to say probably the last 18 months, two years is the least well it's fit in its history by the looks of it. Right. Because it has not exploded above. But this is where, again, not to toot my own horn, Danny, but I mean, people got to be modest here. They got it. You know, I was all right, let's just go in. Let's go into the to the to the detail. Here's here's one I do all the time on my stream. This is quantile regression. Okay, so we're moving to just showing the one curve, the OLS, which is the main. Think of it as the mean regression. It basically just yeah it it it analogous to the mean Now we looking at something that is analogous actually to the median but it trying to find all different levels of a certain level of price, like what would be a 10th percentile, zero percentile, 20th percentile. And the 50th percentile is actually the median. So they are slightly different. It's a slightly different analysis. It's called a quantile regression or a percentile quantile regression. There's two. now i'm showing you the mean and the median there's just two different ways to do it they're both power they're well statistically significant within uh you know each other i mean the statistically uh um well the relationship is actually statistically insignificant they're so close together that you know you could say one or the other is the best way to do it basically the same thing yeah right so can i ask you a question on this because like the reason i said the last 18 months, two years or whatever looks the worst it's looked is because like, if you go back to that 2017 one, sure, there's loads of time that it's well above that median line, but there's also plenty of time that it's below. And it cuts through just by eyeballing it, what you would imagine to be roughly the middle. Whereas this time it's like at our highs, we just got above it. Like it looks like that line needs to be pulled down in the last two years. Right. So this is where, again, I would say people need to be sort of modest when you're talking about YouTube thumbnails or whoever's predicting a million dollar Bitcoin, which by the way, plan B predicted in the fall of 2025. He predicted that the price would be that way in the fall of 2025. He did it like two years prior. People got to sort of not think about the clicks and think about the statistics and sort of just at the time, adaptively adjusting your view to what you see. So this is what I was doing. I was looking at exactly the analysis that you said, let's look at the Q80, Q90. So what these quantiles will do, they try to find their own median, kind of. They try to take a range, which would give us to the point where the median is precisely 50-50. All right. So 50% observations will be below the line, 50% above. And what they're doing is trying to find their own, I'm using the word median, but it's basically their own baseline to the percentage you tell it. So I say to the software, again, I'm an applied statistics guy, so I don't try to... I used to do a lot of this stuff by hand, actually, the power law, but anyway, AI makes it too easy now. So I say, give me the Q80. Give me the quantile approximately where I can look at this, all right? And I'm just going to show you the Q80 versus, let's say, the median, all right? So I only have the median, I only have the Q80. So that red line slices through the data according to a power law and and it it is showing you that basically 20 of the observations are above the line 80 below that's q80 the q50 median 50 50 and the ols by the way is more you think of it more like to me it's slightly different like i said it's statistically almost the same thing as the q50 over the long term but anyway so here we go. This is what I mean by people need to have some modesty. I was fully expecting on my stream. I was talking to people. My streams are there for everybody to see. I was saying, all right, we know about the four-year cycle, which by the way, we haven't talked about. We can get into that because that's another triggering point for people. But we know about the four-year cycle. We know about the power law. We know about Bitcoin's adoption. I'm looking forward to on my stream, counting the days. You can find all these episodes I did. Let's count the days that Bitcoin was above the Q80, right? Back in 2021, 2017, 2013. Let's imagine that there's a way to sort of, you know, get ahead of the market and do that because I fully expect it to be similar like that. Things like hyper-Bitcoinization, all that stuff, it's nice to talk about, but the data suggests differently. It suggests a more gradual approach. When that did not happen, when that did not happen in the fall, right? We barely got to Q80, you see here. And Q90, Q100 is like, just forget about. But when we were in October, so here's August, by the way. And here's October. When we started to not hit those levels and really fall down, and then Giovanni had a very interesting cycle analysis, which he has pointed, and we can talk about this as well briefly. But it's basically trying to look at, so the power law here, this is looking at the main wiggle, the main trend, right? Putting it in these straight lines on log-log. Of course, we can also look at the cycles, the wiggle within the main wiggle. Giovanni in the spring, he made me want to try to do this analysis myself. He did sort of a cycle analysis where you look at the returns in log space, which you can't see them unless you look at log space. And you look at, you try to extract some cycles still using a power law underlying math. He found that there was a cycle about 4.2 years apart. All right. And to me, that even further validated it. But again, he did that in like March or February of this year. Let's still put ourselves in the mind of fall of 2020. He still had that analysis. He was talking about it. He said there'd be a drop in November. He was right. I was listening to him. And so I was very cautious to people. First of all, because the power law is strong the way that it shows its bans about relative risk. Second of all, because the cycles are a strong signal as well. And people were very, very quick to dismiss both of those things. How many times did we hear the four-year cycle was over in the fall of 2025, right? I think I said it a thousand times. Right. Because we had this stable, nice growth and everything. When really, I think in reality, what happened, if you just look at this is, notice how quickly we got back to the median here. This was already in 2024, all right, early 2024. What I think was really happening was ETFs. ETFs were onto the scene, right? It came out in January, 2024. And I think Wall Street started to front run this idea. Of course, Wall Street knows about the parallel. They know about every other model that they do with their quants. So they started to think, all right, well, this has obviously been a powder keg of 10 years, you know, politically suppressed idea, Bitcoin ETFs. We got to front run it. You saw that there's a lot of growth and it cooled off. And then again, a lot of growth at the end of 2024. All right. Both of which, by the way, are above the median. Let's just take, just only show the median. Which was really elevated growth compared to, say, the last four year cycles. Just keeping it simple, keeping it simple. In 2017, right, we didn't get to the median until 2017. Right. In 2021, we didn't get to the median until December of 2020. I remember those days as well. And COVID, everybody's locked down. And all of a sudden, Bitcoin prices exploding and meme stocks and everything. But notice how the explosion comes very quickly above the median. All right. In 2013 as well as the year of 2013, we got back to the median. So usually, and particularly that crypto winter, as it's called, the, you know, from 2013 top to 2017 top, spent a long time under the median, under the power law. And here we went deep. And when I say here, for those that are maybe it's harder to listen to this podcast unless you're not watching. But for those in that, remember the 2022, you know, SBF gift to us all of, you know, puking really, really bad in in November 2022. to Peter Zion is saying, you know, it's $17,000 overvalued on Joe Rogan when the price is $16,000. Very, very deep, deep depths of depression. It only took, you know, a year, basically a year, basically 2023. And all of a sudden, 2024 is kicking off and we're back to the median. That was a different trend. That was a different sort of cycle within the cycle. So you need to adapt a little bit. And what I saw was, and Giovanni also solidified this further for me, was with, it's still the overall scheme seems to be a four-year trend, which we can get to, but we were just, we couldn't stay above that very strong OLS or the median, however you want to look at it. The OLS was even breaking down further. And so I was just cautious. You can find it on my streams. I was saying, guys, like, look, I was hoping by this time, October and November, we were going to be counting the days above these Q90 bans and just, you know, just having fun with this, seeing, okay, how repeatable is this trend? How strong is this trend? You know, is this something that we can sort of really, really find some signaling? And the point was, we didn't. And there's just, there was a lot of people that were super bullish October, November saying the four-year cycle was over. It's just completely ignoring reality. And then all of a sudden, you know, November, we broke down below the trend itself. And then the start of the year, you know, metals are on tear as well. We just, we broke down very, very fast. So yeah, it's not, no four-year cycle is repeatable in Bitcoin, but there is a four-year cycle. And if the thing is not doing exactly as you think it will, just be cautious. That's all I can say is be cautious. So look that's my view and it turned out to be it turned out to be the right way to look at this in the fall the thing that keeps me up at night with bitcoin cold storage isn't bitcoin failing it's my setup failing and this is where anchor watch comes in with anchor watch your bitcoin's insured with your own a plus rated lloyds of london insurance policy and all bitcoins held in their time-locked multi-sig vaults so you have the peace of mind knowing your bitcoin's insured while not giving up custody so whether you're worried about inheritance planning wrench attacks natural disasters, or just your own silly mistakes, you're protected by AnchorWatch. 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It's simple, secure self-custody without the stress. Go to bitkey.world today and use the code WBD to get 10% off the new BitKey. that's bitkey.world and use the code wbd the the thing that i can't get my head around on the four year cycle is is why it would exist like i mean you can observe it and it clearly does like i thought it was going to be broken um but i just don't understand what's driving it because you can't really say that the cut-in subsidy is is really a leading driver of the four-year cycle anymore like i don't know what the the sort of driver of that is anymore i think you can i think you can, Danny. Why? It's such like a small amount of supply coming onto the market compared to... That's the reason that people give on the why not, right? I've interviewed these people, I know you have, and there's plenty of people that have talked about it. Again, it's not a big deal. Everybody has their opinion on Bitcoin, but look, the gold market... Let me put some of my applied statistics, and I'm interested in financial history and stuff as well. Mining in general is a huge game for the monetary system of any society, right? We have the famous case of Spaniards, Cortes and such, you know, just stealing a lot of Aztec gold and other gold in the new world in like, you know, Bolivia, Peru. Now today, there was this silver mountain that when that got back to Europe, that can cause great carnage, right? If you overmind, if you flood the supply. But generally speaking, if you are running a mine or close to the state, the polity, whoever is running the system, it's a pretty good business and it's pretty good for the state. Again, we don't have to judge on if the state is good or bad or what becomes good in the state. I'm just saying mining is a strong business in the history of monetary, monetary, the civilization that, the civilizations that arise around money usually have to be very close to a mine. Of course, they can overmine it. They can have problems. But this is the origins of the Cantillon effect, by the way, the Cantillon effect, or you want to say it, is that those that are closest to the mine have the most power. It's important. Now, gold. Before this huge surge in gold to $5,000 at the start of this year plus, right? 5,200 bucks, 5,300 bucks in February, January, February of this year. And say two years ago, the gold mining market in totality in the whole world was about $100 billion. And again, gold's different from Bitcoin. Sailors made this observation. Many people have, I have as well. Gold mining is not like it used to be, right? People don't try to save some of the gold. They just want to shed the gold. It's a revenue profit center, but it's also a cost, right? So they shed the gold to cover their costs, and that's it. That's just how the gold market is. Bitcoin is totally different. A lot of miners hodl Bitcoin. It's much easier to do. It's not easier to do in the fact of mining, but I mean, it's easier, obviously, to transfer around. Bitcoin is changing the economics of mining in general, just because mining is a general concept. So this is also interesting. but still still to this day uh mining can always be disrupted by price and when the gold price and silver price went up to four or five thousand dollars an ounce on a trailing 12 month basis the gold mining industry went from being a hundred billion dollar industry to over the last couple years being a 400 billion dollar industry and still at the moment it's over you know on a trailing 12-month basis, if that $5,000 would hold, it'd get up to a $500 billion industry. The oil, just for people's, another way to understand the comparison, the oil markets are a trillion dollar industry a year. Trillion dollars in revenue, sometimes it'd be a trillion five, super volatile, super political. These are huge industries, right? And all of a sudden, because of a 20-year spike in the gold price, gold is now a $400 billion, $500 billion, industry. That's going to matter. It affects everybody politically, economically, geopolitically. Now, with all that little background, imagine applying that 20 years from now into the Bitcoin mining space. Imagine that we have whatever, $400, $500 billion of Bitcoin mining revenue, and then it gets halved in a day. It's going to matter. It's going to matter. It's not going to not matter. This is just a feature of the Bitcoin system that everybody, I think, kind of wants to forget. But Satoshi built it in and it's what we have. It won't necessarily have though. If we're talking that far out, the percentage of the minor revenue coming from fees will be much higher than the percentage of revenue coming from fees today. Today, it's largely subsidy. At some point in the The fee percentage can and will be higher for sure. But the inflation or whatever you want to call it, the issuance, the subsidy, the block reward, it's still going to be a meaningful. It's still going to be a meaningful number when we're talking about Bitcoin being, you know, 5 million, 10 million a coin. So I get all the arguments against it. I get the fact that, you know, many more times a volume and dollar amount of Bitcoins flow between miner wallets and or ETF wallets or exchange wallets. Right. I get the the whole premise of the idea. The bottom line is mining is an important topic in the realm of monetary finance, monetary history. Satoshi specifically designed mining for that reason. and he decided to have it every four years. It's a shelling point. It's a shock. So I am, again, I'm just trying to be modest about this. I would not discount mining as quickly as many people are apt to do in the space just because nominally right now, right, it's much smaller than, say, 50 Bitcoins a block, which it used to be, right? It still can be a huge amount of money in the future, and I expect it will be, and I expect that it will... also provide a lot of fireworks and shocks to the system. But that's how it is. That's how it's designed. So if we go back to the power law, if you think the four-year cycle is still real, and are we about as low as we've ever been compared to the median on the power law? Like how far from a bottom do you think we are? Right. So I'll just show you very quickly the worst and the best. And then I'll also show you another way I'm looking at this now. So this is all time data, right? And the reason I'm getting these nice smooth lines is I'm extending, I'm taking the all time data, how I find the coefficients, don't worry about it, whatever, running the math and then extending the line back and extending forward. All we can do in the future is extend it forward. But in the past, I'm sort of creating lines that actually didn't exist at the time. This is a small caveat here. So there's another way to look at this, which I think will be more helpful. But basically, if you can imagine, if you look here, you see how we had this big drop here at the start of June. and now we're basically setting our own new bottom here. Okay, and we're off it, but this is way too early for me to predict. Like, you know, we're going up from here. I'm sure YouTube thumbnail will do that for you. But I would just be cautious about the levels that we're at. But as you notice, if we paint this line backward, we go back to the SPF levels. There's a huge amount of gap here. At the time, the zero was actually here. So another way I'm looking at this chart now is I'm showing the evolving trend. All right, I also have the shades of the bears here. If these charts are constantly evolving, does that actually mean that they're useful going forward? I'd be really interested to see what this chart looked like as the sort of statistics were back in, say, the SPF crash, like how this cycle would have looked since then. Right, right. So that's something I'm trying to show more on my streams now because precisely to your question, you get the nice smooth lines when you just draw the math based on the all-time data, right? But the question would be, what did the data show, say, in 2013 or 2017 or 2021? So that's why I'm now, when we look forward, okay, we have the same projection of the lines, right? The percentile, quantile bands, basically. For simple language, I'm just calling them the lines. But here's how it would actually look over time. And I think this is even more helpful to show people how, you know, trends can change, They can evolve, but still overall, we're still in a power function. So here's every band, but actually how it would look at the time. And every new day's worth of data, we change the band. So I'm not projecting backward, which I'm actually doing here to get the nice smooth lines. I'm just showing you how they would look at the time. So this goes back to what I was talking about with Trollolo. If you look at the early days here, this 2011 pop, I'm going to start my pricing about Bitcoin P today. sub penny um i think i used 35 pounds uh for those 10 000 bitcoins because remember it was a it was a sterling to dollar transaction yeah uh but in any event um notice how these gaps are larger kind of wild the lines are trying to figure themselves out and no one in the world was thinking that bitcoin was was running like a power power trend at this time all right not even here and you would see this thing, which is the Q100, which is like the realm of possibilities of Bitcoin's price. It's fantastic, right? Like, let's just look at what the number says. Q100, when we were at December 2013, that $1,000, you know, $1,200 top, right? November, December, is saying $350,000 for Bitcoin at the time is theoretically possible. Obviously, you know, we needed some more time to work out and the price never got close to that. But because of the action that occurred in 2011, that's what the math said. All right. So let's even take off Q100 just because, again, it sort of distracts, I'd say. But I'll come back to it because you can find some interesting things here. Anyway, as particularly as we get into 2016, 2017, and this is where, you know, Giovanni and myself, if we started into 2018 looking at how this was forming, notice how the lines get A, closer together, and B, straighter on log-log. They're not perfectly straight, but they get pretty good. You can clearly see from 2017 top, they get, you know, there's a pattern. And so this is another way to see the power lock. Now, look, let's look at the worst examples, the worst offenders where we form new bottoms in this. We were at, say, a Q0 of $281 in December 2014. But as that crypto winter, as it's called, I'm not using that word to trigger anybody, went down to $200 at the lows in 2015, that Q0 turned into, well, this is log-log, so it actually kind of stayed the same. But at the worst case, it got to $190. And you can just see, for those watching the video, you can see it's obviously dropping quite consistently. 2018, interestingly, that dropped to $3,000. Nominally, we know that $3,000 was well over the $1,200 top of the prior cycle. That's also an interesting thing to look at. We didn't really puncture there, right? That was kind of a nice support. And then 2020, we did. And notice here in 2020, the pandemic briefly, we punctured below. and let's actually look at what happened. So the Q0 line is coming down and it's setting a new bottom of, you know, and if we look at the way that that came down, and by the way, this also shows you that this has nothing to do with are they parallel to each other? You see the Q0 is actually slightly above the Q10, which is interesting, at the time in 2020. But it comes down to fully... you know, be in the current position that is today. And it took about from 2020 February to, you know, to 2020 late March, obviously during the just extreme craziness of the pandemic and scared a lot of people. And then so that's sort of the new bottom relative to this, like I said, for lack of a better word, like setting these bands, these individual sort of thresholds of where the price can possibly be. And we just we set a new low and that's it. So you just have to imagine that that's going to be not imagine, like just understand this is the probability of reaching this level is lower. And then, look, we set a new low as well with Scam Bankman Fraud's gift to us all after, of course, the just DeFi summer of madness in 2022, all that stuff, Terra, Celsius. And so it took us again a couple months. We set a new low, but as Peter Zion was again saying Bitcoin was $17,000 overvalued at 16,000, we were already sort of forming that bottom. And then it took until January of 2021 to get out. And once you see, just notice here, once you see the price start to rise off of the Q0 level and when I say Q0 it actually Q0 It finding the least probable event relative to the power law And once it starts to move away from that usually that bottom holds through the next cycle. It doesn't always go lower. Notice in 2018, it didn't go lower, but it did briefly in 2020. It did briefly in 2022. And now we're setting a new low. So from this June fall, we went to a low of Q0 of 67,000. Now our Q0 is 59,000. So here you can see it actually as it evolves. And brass tacks, bottom line, when you do this type of analysis, which is not lines on charts, I'm not just connecting dots. These are actual scientific functions here. And when you see there more white space between each band, it just means the range of probabilities is expanding. It means our range of uncertainties based on prior observations is unfortunately a little bit wider. Risk is possibly a little bit more. But if past is prologue, it doesn't last that long. And generally, these are screaming by opportunities. And frankly, statistically, relative to the power law or the power curve, this is as cheap as Bitcoin has ever been. In fact. Yeah. So who knows when the bottom will be, but statistically, this is deep, deep value, as good value as you get. Deep value, as good as you can get for the brass tacks listener here. But also, like you said, you don't know the bottom. I'm not saying this is the bottom. There's nothing here that tells me, you know, in August, we're not going to dip lower or whatever. U.S. legislation fails miserably, this Clarity Act, and then, you know, people try to, you know, Trump gets impeached or whatever. and his crypto businesses. He becomes the next SPF, which I've, by the way, said that could even happen like two years ago, just thinking about the four-year cycle. I'm not at all saying that. I have no idea what will happen. But, you know, these are interesting little nuggets that line up with the four-year cycle. And as far as I can tell here, the four-year cycle is perfectly intact. it's shallower than prior cycles. We've only been through nine months of this. It's 53% drop. 2020, we got to a 77% drop. Sorry, 2022. 2018, we got to an 84% drop. 2014, we got to an 85% drop. So each drop is less than before, but I have no idea if it's going to be 53% this time, 60%. But what we do see so far is actually relative to the drops, relative to the trends, the cycle is, you know, the deviations from regression are shallower. They're shallower this time. It's interesting that it's the smallest drop in any of these bear markets, but probably the worst sentiment we've had. You know the next question I'm going to ask, though. So let's just assume that the four-year cycle is real. um what would the median line be for the top of the next cycle right now so if we assume that the four-year cycle is uh is real that means it's going to be uh 2029 right and let's just say somewhere 2029 uh november all right the ols there you can see 386 000 median 365 000 uh on a low case q0 184 000 and on a really fun case which is put that q100 back which is really looking uh like you know by the way those things are technically possible but We got a million dollar Bitcoin. Million dollar Bitcoin, but let's look at the Q90 there, $500,000 Bitcoin. Another interesting thing is to look at the multiple over under the curve itself. That's what you see in the parentheses there in Stooltip. So a 3x multiple used to be more popular. It used to happen, let's say it was more prevalent. Now, I think that's less rare, but getting to a 1.4x, 1.5x, totally possible. uh and by the way notice how those deviations uh i'm talking about the multiples over under the trend so so my ols let me put this chart back in just so you can see it clear what i'm talking about the ols is is is one right q0 q100 here notice how back in the day right when we're when we're establishing this trend, trying to work out the math, the Q100 could be 20x, right? The trend, 10x, the trend. Q0 could be 0.16, 0.09, the trend, right? Q0, wherever it was painted. Today, Q100 is 3.3x, Q0 is 0.42. And as we go in the future, these actually converge. So you actually get less extremes to the upside, less extremes to the downside, which is in itself a very nice visual of that scale, scale invariant sort of power law nature where it's a sustainable growth with, yes, not as much upside, but also not as much downside. and in general, a more stable type of a growth is actually what power growth represents. Yeah, I'm here for that. That sounds good. If you're trying to take into account like official market hypothesis, is there an argument that as this sort of model ingests more data, it will stop breaking to the downside every couple of years like it is doing now because it will have seen enough previous market moves that it can sort of price in the future? Or is that is that too far out there probably no i mean uh and again this gets back to the grand theory which we can talk about um i'm trying to think if we need more charts to show you in response to uh what you're talking about here but i would say you know how i said the power law is projected to slow to a 10 growth rate in 2070 that's still that's nice to project out that far and i do it for fun and i show people what the price would be and what the growth rate is on my streams all the time with this. But I think that that's more just trying to give us a flavor of how the thing will grow. And I do think, I don't want to say there comes a time when, like, I'm using this term a lot like fireworks, right? Often in financial markets, we try to say there comes a point when this stuff breaks or whatever. That so far hasn't happened. And I could be wrong, though. Like, we could be geopolitically worldwide. We don't have to get into it, right? We're in sort of a realignment now, whether it's NATO, whether it's China, whether it's Russia, whatever. We're in a realignment of sort of the world order. It's possible that the dollar loses status and Bitcoin ascends rapidly there. And that's why I use this term sort of fireworks. I do see something like that happening in the 2030s simply because of the way a lot of numbers are lining up, right? So the power law is going to be about, it's going to fall to, you know, 25%, 20% by 2040. That's going to happen to match, I think, what the stock market is probably doing around then. And also the market cap of Bitcoin, you will be around 5 million per coin at that time. So that's going to be about $100 trillion market cap. The monetary base is also going to be about $100 trillion. Again, I don't want to be drawn in by these round numbers. Because even when Bitcoin's $100 trillion in the monetary base is $100 trillion, that's still that 50-50 market share. And it probably will be the case that maybe some central banks are backing, major central banks are backing their balance sheets with Bitcoin at the time. so it's it's hard to predict i would say like exactly how this uh plays out but what i do think is a we're on a collision course is bitcoin's value is going to grow to a number and also the growth rate of the asset itself is going to shrink to another that's comparable to the rest of sort of the world trad fi and then at that point and again that point could be many many years it could be a decade um the world's gonna have to see do they want to like lend out bitcoin or let's say they lend out fiat units maybe some of them are backed by bitcoin uh to try to get a good return where we're still using like dollars euros yen as the base underlying currency or do we move to the sort of numeraire where it's satoshis and then in that case do you want to lend out those precious Satoshis at a rate that is actually probably either too hard to pay back for the borrower because they're getting the Satoshis continue to get stronger or do we go to something like totally different like an equity-based system or a system where there's just maybe some very short short-term debt but if a bitcoin world where people are investing in projects and trying to you know just develop the world maybe there's some sort of a different model obviously with technology and everything where it can be on more of like an equity-based system but that's that's part and parcel of the grand theory that i'm thinking about because i think in 10 years you're gonna a lot of these numbers are going to collide the the financial system and the Bitcoin system. And I'm not exactly sure how it plays out, but I do, for anyone listening to this show or watching the show in the back of their mind wondering, okay, well, how does this work if Bitcoin's growth rate declines, but the stock market stays at like 15, 20% per year, what happens? I agree. There's going to have to be a decision that's made there by people of all kinds and all sorts of governments. Are you just going to have Bitcoin sort of locked in some component of the economy like gold? Withdrawals are almost impossible in the TradFi world and just exponentially more fiat units are lent out at interest, just like the system we have? Or do we move into this system where Bitcoin actually as a stable, scalable asset that grows at a power regression will actually pull the rest of the world into their system and then maybe the system will start growing power. But the key here is, if it's not clear, if you grow in power, an interest rate won't work there. A fixed interest rate won't work. At some point, Bitcoin's enviable UTXOs, they're going to accrete in value, but relative to, I don't know, the dollar or Apple stock, they actually might fall below that. So then what happens at that point? see i think that's really interesting it's one of the things that i've always really struggled with because clearly if we went to a bitcoin standard you're not going to get rid of credit like credit is always going to exist in some capacity and if if there's like a business opportunity or an investment that looks tempting enough people will part with satoshis to invest in that and and some people will be able to make enough money on those business decisions or whatever to pay back those loans but not everyone and i get that in this fiat world we have tons of malinvestment because it's very easy to get your hands on on credit but if you do you have the opposite where people are unwilling to lend unless you have an absolute killer idea and there's actually lack of investment yeah that's the that's the old like it's almost keynesian central banker like right i mean fear the deflation and um look i i don't have a full answer i'm more thinking about it mathematically and I would say it would depend on the system. It would depend on the monopoly of the system, who's in control of the system. And if we're on a decentralized system where everybody's individual demand is stronger than the government's actions to compel them and they're just going to want Satoshi's, they're going to want it in their wallet or they're going to want to use Lightning, then I think such a system could work just fine But actually, due to the nature of Bitcoin's power growth in this case, and just the nature of, you know, we know that the supply is extremely limited here, unlike gold, unlike silver, where, again, it exponentially produces 1.8% a year more gold, 1.5% a year more silver. the system could change we could have like sort of the best way i could describe it is is uh you know either very short-term factoring type debt or people people are just going to have to take uh more equity contracts in their endeavors and everyone becomes a vc yeah yeah exactly and you might not be sure the exact, you'll have a range of your return. Maybe there's like some preferred return that you try to get, but if you don't get it and you split the profits or whatever, technically nothing is impossible to do here, but it's just, it's not exponential growth. So we're, we're already going into my sort of the grand theory and I have so many different charts, but I don't know where you might want to take this, but I can show you. I think the most interesting and most relevant right now is probably talking about the treasury companies because obviously sailors had a rough couple of weeks ever since they sold that first 32 bitcoin i don't know what was that a month a month or so ago um they've kind of been in a mess it looks like they've recovered it now they've sold bitcoin to pay dividends which makes total sense to me i think that's what they should do i think that's good um but like you said earlier in the show their cost of capital right now is 12 13 whatever it is that's fine as long as the caga stays at around 40 but as you said that's not going to continue forever and just as like a complete vibe gut check it's clearly not going to exist forever like bitcoin is not going to go up at 40 forever yeah the question is when does that date come and what do they do in that situation because it's funny that they've gone from basically a zero percent cost of capital when they were doing converts at zero percent to now paying 13 i don't i don't know what the market is like why the markets forced them to do that but i mean 13 is pretty high the trade-off is probably the preferred aspect of it so it's very very difficult for him to get liquidated because yeah it's a perpetual instrument which is smart on his part is very smart to do it that way but that yeah there is a higher uh hurdle rate there that he has to make um let me show you this this this is uh the s&p i don't know if i showed you this last time but this is the s&p over a couple hundred years i I showed this actually at the cheat code conference, a variant of this chart. So exponential growth, again, I'm not going to go through all this, but this is S&P 500 back calculated. There's people that do this back to like the 1800s. Bottom line is it's very slow growth in the 1800s. The 1900s got a little bit faster. I do these as a little monetary epoch. So when the Federal Reserve was founded, then when we went off of gold, Bretton Woods ended and we went to 1971, ended the Bretton Woods standard. And then from 2008, when basically banks got bailed out all the time by central banks, we have this monetary easing sort of pattern. And notice that the treadmills get faster and faster, and the treadmills are actually the growth rate. I'm going to take the growth rates off. But here's the, this is log linear, exponential growth. But what is actually here is Jeffrey West, the physicist, he's got a great book called Scale, talks about this as well. There's others that talk about this. He calls it super exponential. So it is constant growth, but it actually grows even faster over time, right? If you just take these sort of long enough horizons. And that's my question about actually how the Bitcoin system marries with this idea. And I do think it's going to be a part of it. So when Jeffrey Ress wrote his book, just to summarize, try to summarize a physics book in 30 seconds here, he was talking about this very interesting idea of the singularity, but he wasn't using like the Ray Kurzweil, he was just using a mathematical singularity. But if we can see that with our world, our fast growing world of technology, and we know that we grow faster and faster and faster over these epochs, but notice that the time periods are shorter and shorter and shorter. We still have some time. We have some time. But presumably, there'll be another crash, probably a deep crash, more monetary inflation. But also, also, there is technological development, which causes the stock market to grow faster. AI is a prime example right now. Okay. there will come a point where we reach what this mathematical singularity which basically there's one point and you know we can't grow any faster what happens there that's the question he poses in his book he leaves it open and he wrote this book i think the first draft was 2014 or maybe 2017 i'm not even sure uh he was not mentioning bitcoin he did not think about bitcoin here so i've sort of overlaid bitcoin as an idea of what could take over the mathematical singularity It's just another data point. And I think by the mid-2030s, you'll see these fireworks. So again, exponential growth. Let's take off these trends. Let's show you in percentage term what these mean. So now you have these. This is the treadmills, right? While you're pulling that up, can I ask you a quick question on this? Does it have to stay exponential? Yes. All financial markets have always been exponential. primarily, in my opinion, I don't have like vast amounts of underlying research here, but it's as ancient as, you know, the oldest contracts that we have is basically the interest rate. It's an ancient thing and interest by definition, applying an interest rate to an asset, to a debt, to a mortgage, whatever, to a company, cost of capital, that's an exponential function. So it will always be exponential. And what's even, let's say, even scarier or wilder for our time, is we have massive amounts of technology and faster and faster growth rates. So this is the super exponential. So again, just very basic here. I'm sorry, I'm being an idiot here, but I want to know why. Why does putting an interest rate on it make it exponential? Is it because of compounding? Yeah, yeah, yeah. So that is compound interest is the same thing as exponential growth. Okay. Geometric growth, continuous compounding, exponential growth. They're all essentially the same function. And that is, by the way, a straight line on log scale. So when you grow, you get a trend that looks, let's just say I'll grow from 2008. I split up the trends here. But from 2008, I have a line going through this. You can clearly see this is exponential. Log linear. And in my opinion, the reason for this is credit. It's credit. It's the interest rate. Yes, the money supply is a part of it and everything. but the stock market is way more valuable than the money supply. So it's credit actually that does it. And notice, by the way, this is another small tangent. The markets are negatively skewed. You see that how we have like huge dips to the downside and then we sort of slowly go up, but then we always have these stairs up, elevator down. Right, right. That is different than Bitcoin. If we go back to Bitcoin, this is sort of a different topic. Notice how the crazy spikes are the opposite. We surprise ourselves to the upside, which is why, by the way, I still think we can do that. It might not be hyper-Bitcoinization all in one day, but I think we can easily go to $250,000 or $300,000, whatever. You probably saw this as well. One of these ideas, maybe Trump buys strategy, and we have a $250,000 God candle or something. All this stuff is possible, and Bitcoin actually surprises to the upside, so you never know. But that's sort of a small I'll change it. Back to the idea of the stair steps, which I got to find. There's too many charts for you here, Danny. Where did I put it? Here it is. The stock market over a long, long, long period. The other trend, which is wild, is it's actually faster exponential trends. That is also appears to happen in markets. And maybe it happened in old times as well. Maybe that was why Rome collapsed. Maybe that was, you know, people blame it on money printing. They blame it on this, a bit on that, but it could have been a situation like this. Now, again, we always want to think this time is different. I hope that with technology and with Bitcoin and with everything else in our modern world, we're not going to go back to Mesopotamia or anything, we're going to have a major crash. And I also think that there are release valves, primarily Bitcoin, that could get us out of such a crash. But this is part of the grand theory. So there's this physicist Sornet, there's Jeffrey West. They are posing these ideas that we get to this super exponential growth. And it happens to be, by the way, late 2030s, where they think that we could get at this faster and faster point where it's just like, well, what happens next? I mean, and that does fit in with the whole AI narrative so well. It does. It does. It does. So mathematically, what I'm trying to show you here is faster and faster growth. And so now, again, I'll show you the growth rates. this is exponential growth. This is what I was saying about the interest rate. Like you can think of this as the interest rate. Think of it as the growth rate of the stock market, whatever. It is the growth rate of the stock market, but also think about interest rate. 2% in the 1800s is how the stock market grew. When the Fed was founded until 1971, 4.73%. Straight line, compound growth. Take out the noise. Yes, we had the Great Depression, a lot of volatility, whatever. Brass tax, 5% in the early 1900s. Late 1900s, 9.5%. This is when I was studying finance. We would talk, you know, getting a 10% return was extreme in the stock market. Now, from 2009 till today, we're at a 12% per year compounded growth rate. So basically, so again, I know I'm going through a lot here, Danny, but the bottom line is, I'm trying to visualize, and Jeffrey West actually uses this phrase in the book. He says, faster and faster treadmills of growth. You can even see it in the stock market if you go far enough back and look, the dollar is, there are many currencies in the currency graveyard, right? Thousands of currencies. I'm not saying, I'm not predicting a collapse of the dollar or whatever imminent. I have no idea. But what we do see with the US stock market, with the dollar, with many currencies, is faster and faster growth rates of debt, faster and faster growth rates of the stock market. And then there's a question, how does that work with Bitcoin's interestingly novel model of being a new digital currency that's not controlled by anybody? But the market is showing a sort of actually declining growth rate, still growing quite fast, but it's scaling in a different way. It's a curious, I think it's a very curious overlay to this question of what could happen with the singularity. So if I put on Bitcoin now, back to our beautiful power curve, hopefully you start to see where I'm going. I don't even know how you meant to read this. Right. So it's the same power curve, but on the right axis, I'm showing trailing 12 month growth. Now the noisy one is here, right? Trailing 12 month growth. Obviously, you can get thousands of percent, hundreds of percent, whatever. this is, you know, and then it can go negative. Let's just take that off, take the noise off. This is actually a curve trailing 12 month. It's just the trailing 12 month return on the OLS, right? On the average power curve. So now we can start to see the smooth curve of Bitcoin. And then here's, you see, we're at that 40% right there, right? As of today, July 2026, 40% return, $62,000 Bitcoin. If I back this out, I used to have this go out to like $2,100. I told you that it when it will hit 10 but let just look at when it will hit other levels So it hits 30 on a curve Bitcoin power curve in 2031 In 2041 it hits 20 And in 2070, it hits 10%. So actually that gives you a scale that it's not linear. It's not constant, right? It slows. And even the rate of this slowing, right, can take longer. Right? So 2031, 30%. Right now, 40% per year. By 2031, it's projected to slow to 30% a year. By 2041, it's projected to be 20% per year. If we match that up with this idea of faster and faster treadmills. And who's to say what's going to happen in the next 10 years of the stock market? But we're at 12% right now. By the way, that's without dividends. So if you reinvest dividends, you got another 2% on there at least. So you're getting close to 15% as it is in the stock market. But say we have another crisis, then we have another round of money printing. It does seem like the late 2030s, 2040s, we're going to have some fireworks because based on the models that we have with Bitcoin versus the numeraire, the dollar, this is the growth rate that it's tracking. And it's going to cross with a faster and faster stock market probably by late 2030s, maybe early 2040s. Yeah. The idea of being able to buy like an S&P index and get more returns than buying Bitcoin is weird. And I don't know what it means. right likewise uh what it would mean is if if what it would mean is is that bitcoin has been co-opted into an exponential asset sailor has this other sort of way too cheeky way that he describes what he thinks is going to happen have you heard him say basically uh that basically bitcoin's going to settle into a 21 return i don't know if you've heard him say this what does What does he mean? Well, he means that it's going to go exponential. And by the way, he's never, I'll give you a little inside baseball on this. I know that he's talked to Giovanni a little bit. He said, hey, congrats on the power law. Giovanni met him at some event. And then at these things, you can't really talk quickly, right? And, you know, Saylor's obviously an in-demand fella at these conferences. And he tried to get into it a little bit, but Saylor basically said, you know, I think it's at the end of the day, Bitcoin's an exponential asset. It's going to grow exponentially. to be clear, none of us that have been studying this for a long time see it right now going exponentially. It could in the future. But what does that mean if it goes exponential? First of all, this growth rate turns into a straight line. So by the way, if you hold Bitcoin, I'm not saying this will be like a bad thing number go up wise, right? It actually would portend, if we go back to this chart, right? The original chart I showed you, exponential versus power, take off log, log, just look at log linear. If we get back on exponential growth, which is the straight line, common sense tells us constant growth is faster than proportional growth. It's going to be good, right? It's going to be good for Bitcoin holders. On the one hand, the number go up. But on the other hand, this is where you get into the idea of, you know, what does that actually mean? Is TradFi co-opting the system? are can anyone claim any bitcoins on an ETF? Can you withdraw bitcoins from exchanges after 10 years? There are a lot of things that could play into this. And by the way, if some of those play out perhaps as some entrance players in Bitcoin want, then I think, yeah, Bitcoin could go exponential. It could match, it could mirror the exponential growth rate of the rest of the financial system. One of my favorite quotes was from Thomas Pacquiao from PubKey. He said on a show we did years ago, we're all going to be rich and depressed because the project failed. And that seems like the example where we're all rich and depressed. I actually remember that show. Thomas is a great dude. And what he is saying is 100% what I am saying here. I'm just trying to show you the math of it. I'm trying to show you the math of it. So this is my grand theory is basically a lot of people that are in the system have a lot of fiat interest that they need to pay back. In order to pay that back, they have to stay above the level of interest. To do that, you have to be exponential. To be exponential, it could require some sacrifices. It could require a lot of fiat interest. It could require you not holding your keys. It could require an overbearing state on here. There's a lot of things that could go into that factor. It also might be a totally different scenario, which is Bitcoin turning the system power. But again, that's a different scenario. Yeah, but I want to know what that scenario is. Because if Bitcoin going exponential is essentially, if we simplify it to that being Bitcoin being co-opted by the financial system as we know it today, what's the inverse of that? What is Bitcoin co-opting the financial system into power? What does that mean? I think it means, we started to get into it a little bit, but I think it means we're free. There might be some sort of money monopoly. You know, I always say the dollar is the best looking horse in the glue factory, right? It's around for now. It's been around for a long time. There's still thousands and thousands of currencies in the graveyard. I'm not saying the dollar definitely avoids it or definitely doesn't. But if Bitcoin persists globally, and by the way, if mining is free globally, where people can mine, people can trade, people can send, you can withdraw your keys. You know, you got things like Fetty Mints, super popular or Chalmian Mints or whatever, whether that's a layered system, which it's going to have to be obviously, but the layered system is also very, very easy to sort of get back in the castle and get back to on-chain Bitcoins. If all of those things persist, then I think there's a real possibility that we stay in that free cypherpunk Bitcoin world where Bitcoin keeps growing as it is. And then once we do have that crossing point, right, which I also think about a lot, people will start to say, look, I'm not I don't want to do it. I don't want to put my capital at risk, hope that I get 20 percent in the S&P or whatever. I just rather hold Bitcoin. I'll invest in some projects. I'll pay for, you know, employees. or whatever, but the model might look a little bit different. The model might be more equity. It might be very, very short-term debt, factoring, invoicing type debt. Short-term is the best way I can say it. Because imagine putting these together now. Sorry, not this one, but the stair stepper, right? Where we 12%, 50%, and then the declining interest rate. The only way that this system holds, which is the power, this mathematical relationship holds, is if people sort of say, okay, I don't feel like I need to chase Apple at 20% CAGR. I'd rather hold Bitcoin. I'd rather do it a different way. And by the way, I'm not sold on either. Like to me, it's 50-50. It's just 50-50. I see this is why I'm not married that Bitcoin stays power. I think Bitcoin could lose its power function, turn into an exponential like Saylor wants So back to what he said, he has said this sort of cheeky number like, oh, it just settles under 21% per year. That's a total number pulled out of thin air. It just obviously has the number 21 in it. And it happens to be 11 percentage points higher than his cost of capital. So it sounds good. There's no evidence in the Bitcoin power curve that it's going to stop at 21% per year. By the way, 20% is right out here. 2041. wait where is it there it is 2040 get 2040 2041 so this is why this is this is part of my grand theories basically this is why i think late 2030s early 2040s we're lining up with the jeffrey west sornette singularity idea ray kerswell by the way says the same thing uh late 2030s. We're lining up with probably $100 trillion valuation in Bitcoin, $100 trillion valuation in base money, and anything goes. By the way, to throw one more chart at you, here's the monetary base. We talk about this a lot, right? I haven't updated this for the third quarter. Sorry, for the first quarter yet, even. I have broad money and base money as of 2020. These things move slower. We can look at Fed balance sheets if you want after this. We can leave much more updated. uh here's the monetary base over 50 years i don't want to change too many topics but basically this is the money supply that's comparable with bitcoin it's world central bank money all right it's about 26.4 trillion dollars as of 2025 year and 26.4 if you run these same regressions notice how we're you're an expert now danny on exponential versus power you see straight lines on log linear base money is an x it's an exponential function notice where are we in the realm of probabilities way low, way low, right? We need more of the crazy. Right. We're at the bottom end. And again, I'm not saying it's going to happen tomorrow. Fed is being a little bit cagey with their minutes. Warsh is, you know, the sort of hawk dove, Griffin sort of, you know, amalgamation. We're not quite sure where he's going to be. But basically, as John Tamney, who has a great book on money long ago, said presidents usually get the Federal Reserve chairman they want. and we know what Trump wants. So lower interest rates, more money printing. But anyway, we are at the lower end of the curve globally. We were at the higher end of the curve at 30 trillion in 2021. So here's the point. This is another wrench in the scenario. Sorry, that's further back data, which is not really comparable. At 50-year data, you look at this CAGR. This is the CAGR of the exponential OLS right there. CAGR 10.2% per year. 10.2% per year. It's actually more than that. It's interesting there that, so when you pulled up the other chart of the S&P, it was 2% way back. It's essentially still 2% at 12% today. No, no. No, you mean it's essentially growing the way that it was in the 1800s? Yeah. No, it's not. Here's the interesting kick. It's another wrench in the formula. Money supply is actually growing slower since 2008. So is U.S. debt. So here, you might think that it's growing faster. We had all this money printing in 2008. And yes, it does kind of depend on where your starting date when you do these regressions. But I started year-end 2008, by the way, same time that Bitcoin started. So this is 1971 trend. So you see the trend here, 10.2% CAGR. Here's another chart where I started in 2008. Notice, first chart, second chart, first chart, second chart. when you start the regression later, it's actually shallower growth. And I'll show you the Kager, 7.7. So in the last 15, 20 years, I believe that the powers that be, the whatever, the central banks, they realize how bad they screwed the pooch in 2006, seven and eight with low interest rates and everything else and the bailouts now. So they're very cautious actually about extending. How is that possible? How is it lower? When we know they're printed trillions and trillions of dollars over the last, especially over the last like six years, 2020, 2021. Right. The bottom line is they don't always print money. They print more, they print less. You know, the Federal Reserve wasn't printing money from 2014 until 2020. Yeah. A lot of people don't sort of know that. Now, other currencies were. You see, it was generally going up. And there's a huge spike in 2020, 2021. But since, you know, this is a long five years now where we've taken the money supply back from $30 trillion down to $26 trillion. And if you just run the math from 2008 when Bitcoin started until today, this is the actual CAGR. It's only like 8%. So let's just round it. 8%, 7.7%, 8% versus 10%. over the 50 years, all in dollar terms. By the way, not to throw another wrench in it, but it's actually probably, both are probably faster than that. Because if you measure, if you do these regressions all in their native currency and then take the average, it looks different than if you do it in dollar terms. It's showing dollar supremacy because they get weaker against the dollar. I don't want to throw too much wrench in that, but they are printing a little bit faster than this in their native term. It's true, weighted globally. let's forget that for now 10% versus 8% 10% 50 year trend 8% 2008 trend in the money supply that's another wrench in the curve or another wrench in the uh the calculation where I think uh I think they are well aware of the damage that they have done in uh in intervening in the market so much they think that they have all these tools like paying interest on reserves and And, you know, they're just more cautious, so on and so forth. And actually, the data shows it like U.S. federal debt has the same trend since until 2008. U.S. federal debt was growing faster than it has been since 2008. It still grows. It's still huge. Right. I mean, this is the nature of compounding. But that that exponential trend over the epoch is slightly slower. So again, it's a little bit of a wrench in the thesis of this one, where the stock market for sure is growing faster. But does it matter if they're aware of the issues with that trend? Because when push comes to shove, if they need to, they're still going to print money. Sure, they will. We can be sure that that's the main thing that they know how to do. And that's how they deal with crises is to add liquidity or basically add zeros to banks' accounts with them at their master account. So it's a digital money print that they do as opposed to a physical. They also do physical money print. And they have started that too, right? The Fed balance sheet is growing again after a few years of doing nothing but drop, essentially. Right. Here's the Fed balance sheet. You see it has been growing since November of last year, ever so slightly, and maybe even cresting a little bit. And then we have, you know, sort of hawkish-dove-ish mixed signals from the new Fed group. They're not really, they're very, they just released their minutes this week and they're very cagey, but some people think they might even hike in September. We'll see. But I think I have one of the ECB as well. No, this is the ECB balance sheet. Okay. So it's about 6.12 trillion euros. Again, when I say balance sheet for people that are new to this, it's the monetary base. This is the asset side. The liability side is mostly the monetary base. There's a little bit of other things sometimes, but just keep it simple. ECB, since it's been founded in 1999, has grown its balance sheet at a K-grade of 10.6%. So notice that's actually similar to the 50-year curve. But they as well are at the bottom end. The bottom end of the analysis. Time to short fiat and buy Bitcoin. Yeah. Yeah. So it all looks good, I would say, if we assume that money printing is good for Bitcoin, if we assume there might be some more instability in a very unstable, exponentially growing system. And we assume that Bitcoin is a sort of more stable power asset that is still growing tremendously at 40% per year and, by the way, discounted to its lowest percentile quantiles. All that looks good. but the grand theory as we've sort of been touching on and off in this episode is i think it's you know late 2030s maybe even a little bit later as i said they can push if they really want to they can take off the gas and they did that last five years so um it's just the nature all i do is measure this stuff danny i try to give people the best way to look at this stuff just by measuring rather than talking, but I'm giving you hard facts, hard data. Stock markets growing faster, exponentially growing, sort of stair-stepper, super exponential growth. Base money is actually, it's growing fast, but it's over the last 15, 20 years, it's actually growing at a slower rate of return. US debt as well. So there's a mix there. But if we want to come back and just think about Bitcoin as this asset, we try to grow it, measure it, how it's growing and everything. It's looking pretty good. Never financial advice always. And one more thing just to show you here. If we take the lows, let's say you bought in the low here. Let's actually even show you the evolving exponential trend, which is here, right? Which we talked about this one. Like, let's say in 2022, when Peter Zion was saying it was overvalued, you held it just until here, we got back to trend. Okay, this window is 2022, December, until we got here. The window is a little bit wider, but what you see, I'll just show you the dates. What I just zoomed in was 2022, December 7th, holding until 2024, March. That's actually when the price got from it's low to trend. Let's look at the actual Kager that you could have earned right there. 176%, 176%. When the trend itself, um, well, this is a little bit different because it's evolving. Let me go back to this one just to show you the trend at the time. Uh, here we go. Roughly here to there. I said, you know, it could have even gotten 197%, right? If you bought whatever, or it's going to be slightly off. 180, 190% CAGR. The trend itself at the time was 48%. 48% was the power curve trend. Now we're down to 40. So you can still in Bitcoin make many multiples over the trend. Even though I tell you again and again and again, I tell people it's doubling every two years, but that doubling time will increase. The rate of growth will decrease. You can still, if you pick the right moments, and by the way, now seems to be a right moment, and six months from now could still be the right moment. I'm not saying we're out of this bearish period, but if you have the whole encompassing view, you understand statistics, you understand how this stuff is working, statistically, we're in a very good place for a bullish Bitcoin hodler. Yeah, who knows if it's the bottom, but it's not an area you're probably going to regret buying. The interesting thing to me is this, whatever happens mid to late 2030s, it's like perfectly in the first turning two worlds bitcoin and the financial system collide who knows what happens but that's exciting i can't wait to see it yeah it really is like we'll be here for it right danny i think it's uh it's it there if you look for it you will find all sorts of crazy numbers conspiracies thoughts about you know if gold's coming back or whatever but you know if we can measure the bitcoin system measure the trad fi system there's a lot of interesting things happen in late 2030. So I think that's pretty cool. Another thing, just one more here, or we can go longer if you want, but there's another chart, there's UTXOs. I like to show against, so let's say Bitcoin's the benchmark now. How strong are different currencies within that? And actually Bitcoin is going to become that true measuring stick. So here now, this is the same power curve, but I'm using it. I'm starting everything at one on Bitcoin Pizza Day, May 22nd, 2010. So it's the same exact curve, but the numbers aren't really going to make sense. It's just you can see the power curve. Bitcoin itself is up 15 million times. So good on the person that bought them from Lazlo, right? Since Bitcoin Pizza Day, 15.5 million times. And the power curve is up 34 million times. So you see the discount on the power curve there. We're at 45% under the curve. So this is the dollar. Is there a currency that I found that is actually stronger? Stronger would be lower than the dollar. There is. Happens to be the Swiss franc. Just slightly. Just slightly. All right. So the Swiss franc is only up 10 million. Only. You're only up 10.6 million in Swiss franc terms since Bitcoin pizza day. All right. But it's very similar, right? It's almost identical, but it's just we can say that relative to Bitcoin, the Swiss franc is the strongest. Dollar's next. But then here's something cool. Let's look at weaker currencies, like way weaker. Let's look at Turkey, Turkish lira. They had the right idea of actually lowering interest rates during massive inflation. That was their sort of policy a few years ago. So here you see Bitcoin is doing very well against the Turkish lira. If you are denominated in lira, you need to save your purchasing power. You'd have 459 million more times Turkish lira if you had bought those bitcoins in 2010. Again, the number is not important. It's the level of these colors, basically, or the currencies. And now look at this. Let's do the power curve on that. Talk about the power curve breaking, Danny. The Turkish lira hasn't even broken. It's above its power curve, its power regression, which I think is pretty interesting. Now, it's probably going to go under it, and if passes, prologue it. Notice how in the last cycle, it was under its power curve much shorter than the more dominant global currencies of the dollar and the franc. So that's interesting. Now, let's look at the Argentine peso. Just one more. Let me find it for you. BTCRs. There we go. And this, by the way, is the official bank rate. It's even worse in reality. This is not the black market rate, but just to show you. So there you'd have 5.8 billion times more Argentine pesos if you bought the Bitcoin with those pesos back in the day in 2010. And then let's look at the power curve on that. It's not even close to the curve. It's never coming back. So that shows you, by the way, this idea of breaking. Is the power curve breaking? Actually, in all currencies, it's a power curve. There's a little bit different slopes. There's different levels. None of them have broken. And in fact, in two of these currencies out of four that I'm showing you in this chart, the price of those currencies relative to the curve that they manifest themselves in the Bitcoin market, it's actually above. It's above trend. Probably going to go below soon in the case of Turkey, if we have a couple more months of bearishness, but that's how it looks man matt this has been awesome i love that we've done like an hour and a half on the power curve i i initially thought this would be like 15 minutes of the conversation but it's been awesome um but we'll just have to do it again at some point thank you uh thank you for sticking with us i know you've got a sick kid over there but um appreciate you guys for dealing again at some point with the takes and uh i appreciate it tell everyone why they can go and check out your youtube channel book up list everything you do yeah you can find me at uh all the platforms at one base money so the number one base money um podcasts streams whatever you just go there on twitter or youtube and you'll find uh my account and yeah this is a lot of what i'm doing now every day is just trying to dig into the numbers of how these trends work in the bitcoin world and in the trad file world trying to reconcile them and uh like you said it's going to be It's going to be an interesting next few years. I'm glad to be sharing it with you and others in the space, man. So happy to do it anytime. When are you going to open this up so I can use these charts? Soon. Hopefully by the fall. Hopefully by the fall. You'll be ready to go. It's about time, man. Ready to go. I know. I know. It's an effort. Like I said, I'm more an applied statistics guy. So I don't want to just go only this. I want to get you some economic data, some money supply data, some other things. I'm trying to get it all together here. I will be a subscriber when you do it. Appreciate you, man. Thank you. No problem, Danny.