{ "episodeId": "SLP621", "speakers": { "stephan": { "name": "Stephan Livera", "role": "host", "tag": "STEPHAN" }, "planc": { "name": "PlanC", "role": "guest", "tag": "PLANC" }, "sminston": { "name": "Sminston", "role": "guest", "tag": "SMINSTON" } }, "segments": [ { "speaker": "stephan", "time": "00:11", "start": 11.09, "text": "Hi everyone and welcome back to Stephan Livera podcast brought to you by Bold, the place where you can buy and sell Bitcoin over at getbold.io, that's for the American listeners. Now joining me today are Plan C and Sminston. Now Plan C and Sminston have been impressing me with some of their work they've been doing and putting out some interesting analysis. Analysis on power law and, micro strategy and various aspects of, Bitcoin and how it applies. So, first of all, welcome to the show." }, { "speaker": "planc", "time": "00:39", "start": 39.15, "text": "Yeah, appreciate you having us. It's a pleasure. definitely a fan of your show, definitely a fan of you in general in the space, and, yeah, looking forward to the conversation here. it's always something to talk about in Bitcoin and with Bitcoin, and it's just, yeah, it's just exciting times to be in the space, so looking forward to it." }, { "speaker": "sminston", "time": "00:56", "start": 55.5, "text": "Yep. I" }, { "speaker": "sminston", "time": "01:00", "start": 60.0, "text": "Expand the, the community, I think, from the quantitative analysis side, something we've been working on, hope we get to touch on, is, we're trying to really connect with people on X, obviously, and in social media, and try to, you know, bring some of the quantitative analysis and the data across the board, which is really, I think, what's inspiring us about the space, is increasing our confidence, and I'm excited to get into it with you, Stefan." }, { "speaker": "stephan", "time": "01:21", "start": 81.45, "text": "Yeah, of course. And, so as you guys both know, I have recently" }, { "speaker": "stephan", "time": "01:30", "start": 90.0, "text": "At the top, power law is gonna obviously come up as a theme, so it would be good to, I guess, define and maybe explain a little bit or at least how would you explain, power law, power curve as it applies to Bitcoin. So, Plan C, do you wanna start?" }, { "speaker": "planc", "time": "01:46", "start": 106.15, "text": "Yeah, I'll do the non-technical, version of it just for the people that wanna hear like kind of from somebody who's not, not like personally myself, I don't have like the, the background in, in like super in depth statistics or anything. So let's, Spence and handle that, but I'll just, explain it from a very simple standpoint, for people that aren't technical. So, in my understanding of the power law is simply, it's a log of time, you know, versus a log of price" }, { "speaker": "planc", "time": "02:16", "start": 135.83, "text": "Best curve to com-- to combine, you know, a log of price versus a log of time, but a simple way of looking at it is does, essentially requires more time to have an equivalent increase in price throughout the, throughout the, as Bitcoin grows. So naturally, you know, Bitcoin becomes a higher market cap asset over time, so it's just a little bit, takes a little bit more time to essentially get the same gains. And so some people would say, okay, that sounds like diminishing returns. I, it is technically diminishing returns. So, From a statistical standpoint, the volatility, if you look at Bitcoin, through the lens of volatility, the volatility has actually been coming down since the beginning of Bitcoin in a very, systematic way. And so that pattern could break. I mean, everything's possible. I mean, we, we're always open-minded. We don't get dogmatic with the data. We, we like to look at all the possibilities. But the trend is very clear. With the, the, the volatility is diminishing over time, up until this point. So we just follow what the data says. And, Is, you know, right now we're averaging about a, forty-five percent Kager per year. So, currently that's the compound annual growth rate, right, Kager for, Bitcoin, based on the power law, it's about forty-five percent. So the power law says that'll, based on the current trajectory of the power law That would diminish over the next ten years, roughly speaking, to about twenty-five percent. And so it's actually very in line with, some of the, the stuff that Saylor said publicly. Saylor doesn't ever say specifically the power law, but when you compare the power law projections, over, over, from now until like twenty forty-five, it's, his, his projections are kind of like a ballpark power law, somewhat. he, he uses a different model to get to this kind of a similar ballpark range. He talk-- he's more looking at it Standpoint of like the total addressable market in the world, for Bitcoin, so that's kind of how he gets to his numbers based on different saturation levels, but, based on the power law, it would still show that we're, you know, forty-five percent to twenty-five percent over the next ten years. So, and that's compounding growth rate, it, some people might say that doesn't sound like much, but those numbers get very high, very quick when you're compounding those kind of, those kind of levels, and that By quite a bit. So that's the very simple way of looking at the power law, you know, it's, there's a range of probabilities is another way of looking at it, so it kind of gives you this, this range of probable prices, and, yeah, we can get into it more detail, but I'll let, Steph share the technical side of it." }, { "speaker": "stephan", "time": "04:49", "start": 289.42, "text": "Steph, Steph, let's hear from you." }, { "speaker": "sminston", "time": "04:51", "start": 291.24, "text": "Yeah, that, that was an awesome, background there, Plan C. I think, from my perspective, so coming," }, { "speaker": "sminston", "time": "05:03", "start": 302.79, "text": "Any means before I came into the space, and it's really the math and the, and the data and power law being a kind of a, a key part of what, what drew me deep, more deeply into the space and doing more of my own analysis. But the power law in its essence, what really different-- the, the difference between a power law and you hear people talk about exponentials or exponential growth is that you're essentially flipping the, the coefficient, which is the exponent, in like a very simple, simp-- simple math explanation is like what's in, what lives in versus what's being taken to the power of, you kind of switch those, right? So for an exponential, what's, for an exponential, what's, what's being set as a constant is the growth rate. for a power law, there's actually a changing growth rate, and so there, that coefficient lives in the exponent itself. So for example, we can get down into the weeds later, but, w- What that, the difference is in terms of what it implies about a system, like the underlying system, which I knew a little bit about, is that typically when things are exponential, they're not something that are-- something that's, that long-term sustainable or something that's gonna have the fuel to grow itself into, much larger, larger orders of magnitude. inherently, what's typical about, physical systems, there's a lot of literature out there, there's books out there, there's work from Geovanni Money on, on social media, can explain that, it typically implies something resilient, robust and something that's going to have almost a fractal nature to it. So a power law implies that something is going to be carried up in scale by several orders of magnitude. and it also comes with it a feature that, it's not gonna have a constant growth rate. So the growth rate actually changes over time. So a power law, by definition, because You know, the scaling factor lives in the exponent, it's gonna continue to grow much longer and, and to much greater orders of magnitude, but it's gonna slow the, the, the rate of growth is gonna slow to some degree over time, and that kind of comes, kind of comes with the territory. so there are, those are a couple key differences, and I think once you understand that this is a true power law, that something can be modeled Extremely well with extremely high accuracy, you know, ninety-six percent R squared with the power law. It's a very simple model actually, and the fact that it explains so much about this asset's price over its entire history was the most compelling thing to me. And so that's the math aspect of the power law and kind of, some-- when something really clicked for me, once I moved beyond, you know, when I first saw stock to flow early on, saw a couple of other kind of basic-looking models, and then I saw power law, and I had kind of aha A, a lot more substantially on my own, in terms of my own investment. So." }, { "speaker": "stephan", "time": "07:50", "start": 470.36, "text": "Fantastic. Well, thank you for that explanation. And I think in simple terms, as you, as you were saying, it-- people sometimes speak about Bitcoin and they wanna say it's going up really fast, and so that's where people kind of say this, \"Oh, it's exponential.\" And I guess to the point you were making, exponential implies this sort of- Constant growth rate as opposed to power law, which implies, let's say, a diminishing returns over time, right? We're gonna see this kind of tapering down over time, Aspect. That's like one key difference you would make there, right?" }, { "speaker": "sminston", "time": "08:22", "start": 502.23, "text": "Yeah, absolutely. And I think, you know, people really, who are just, discovering this on the, through whatever, whatever means, hear diminishing returns, I think it's a very scary term. But I think, once you understand systems like city growth, for example, or, you know, organismal, you know, growth, or, you know, there's all kinds of physical systems. I mean, there's even astronomical systems that, that follow power laws. You realize Which also follow a constant, a constant rate of diminishing returns to make it really go the distance and make it long term resilient and kind of, to, to borrow a term, anti fragile, right? And so, whereas we wanna stay away from things, things-- those of us who are not sort of- want to stay away from short term trading or don't have very confidence in what the short term pri-price action, that long term, y-you know, model trajectory is really important, and so we kind of, we accept the diminishing returns, and even with the diminishing returns, you know, and you can look at the projections for this, the Kager going out into future decades will continue outperform pretty much anything else out there. So, yeah." }, { "speaker": "stephan", "time": "09:27", "start": 567.0, "text": "Yeah, certainly. I think it's a, it's a way to be realistic and grounded while, you know, everyone's throwing I think one topic that would be great if you guys could expand on this is, is it just an opinion? You know, is it just drawing charts on a line or is there something objective? As an example, the h-high R squared or can you explain a little bit about why it's not just TA drawing a line, it's not just guys drawing random lines on charts?" }, { "speaker": "planc", "time": "09:54", "start": 594.5, "text": "Yeah, I, I can speak to, to that a bit, and then Spencer, if you wanna get into, like from a technical side, just some, like, answer the same question, I Let's say I believe there's something a lot deeper here than, than just a regression fit, and the reason why is there's solid theory behind the power law and why Bitcoin should follow or does follow a power law, and it's not real-- it's not just price versus time, there's actually power laws, patterns found throughout Bitcoin, so it's actually the hash rate growth is also follow-following a power law, and also the growth of the addresses, and, and there's other, even other components that, it's quite detailed, but there's other things following it. So Straight, pretty much twenty four seven just investigating it once I found out about it, 'cause I've looked into unchained data for years and other, other models for Bitcoin, but the parallel just stood out right away. I actually talked to the, the guy that discovered it, Giovanni. I spent, I got on a nine hour phone call with him over Zoom and, and got like the full download from him, so it was quite interesting, yeah, it was so, such an interesting conversation, we like talked for nine hours straight. And so, I mean," }, { "speaker": "planc", "time": "11:04", "start": 664.48, "text": "More fundamental to Bitcoin, and, and the interesting thing is, to give an analogy, you know, like, like you talked about before, people think they want an exponential, but the problem with an exponential, and why it can be confusing and it might, people might, think that Bitcoin falls an exponential, is because technically speaking, I believe Bitcoin does fall an exponential, but it's only for very brief periods. So it's actually only during the absolute peaks of the bull market that Bitcoin actually does somewhat shift, and we've actually modeled this, me and Sminston, we During Bitcoin's, market cycles where it does actually go exponential temporarily, but that's always the unsustainable part of the cycle, and then what happens is it grows and collapses, it, it kind of goes exponential and then it's not sustainable, then the price rolls over and then it actually crashes back down to power law support. And so the support is the bottom, we'll get into the charts in the, later on in the show, but the bottom is the power law support, and so Bitcoin goes exponential and then crashes back to that support line. And so, exponential, Apple, like, what would you rather have, a, a flash in a pan, which is more like these meme coins and these sorts of like low quality coins that follow an exponential, or would you rather have Bitcoin, which is more like a, a big log burning on a fire, right? That's sustainable, kind of like, you know, it's, it's long term, right? It's like, you can put kindling on a fire, yes, the fire looks great, for very short term, or you can put a big log in the fire, and now you have," }, { "speaker": "planc", "time": "12:34", "start": 754.5, "text": "Anyways, that, that's kind of the point. I mean, exponential is, it sounds appealing, but really, the power law, you know, I, I believe, it just, it just follows that pattern, it, it's very clear, and the, and the R squared is getting stronger, so that's one way of looking at it. We actually have a chart for that, but, it shows over time, that might be actually a good time to show that one. Spencer can get into it as well, but, basically the This is the chart here. So, I might as well quickly talk about this one actually. Sure, yeah, let's get into it now. Yeah, so, so this one's really, shows it very well, and this was actually created by Spencer, so, it's his chart, he, he's the one that first posted this on X, it's a great chart. And so the bottom there, and, and correct me if I say anything wrong, Spencer, but the bottom, kind of chart there shows the fit of the data, pretty much eight years, and it's been trending higher. And so it's up to, it's at the highest it's ever been right now. It's, actually getting close to ninety-six per- ninety-six R squared or zero point nine six R squared or ninety-six percent of the data, you know, is fitting the power law. And then the top chart there is, is the, showing the slope. So every power law has a different slope, just like, an exponential would have different rates of constant growth, right? You can have an" }, { "speaker": "planc", "time": "14:05", "start": 845.32, "text": "yeah, gold is an exponential, I believe. Or you can use like M2 money supply or something that has constant growth, right? And then you can have something that has, you know, a higher percentage of, of an exponential that's kind of that consistent growth. But with the power law, the slope, right? It's been, it's been stable now for, really going back about eight years. And so it's, it's not-- this pattern, I mean, if you, if you, didn't change the power" }, { "speaker": "planc", "time": "14:35", "start": 874.86, "text": "Basically the same slope as two thousand and sixteen, or say two thousand and eighteen, right? If you took the same, and you just stop the data, right? And actually we've done this, we've actually shown this. Essentially, like a back test kind of thing, yeah. Yeah, exactly. Or more like a forward" }, { "speaker": "stephan", "time": "14:50", "start": 890.29, "text": "test, I guess, but yeah, go on. We" }, { "speaker": "planc", "time": "14:51", "start": 891.42, "text": "did for-- we actually did, yeah, forward and backward. Sina actually did backwards as well, so I believe Sina took like the last, four years. He, he did it both directions. He" }, { "speaker": "planc", "time": "15:05", "start": 905.22, "text": "but, but, if you stop it in, so I actually ran it where I stopped all the data at the third happening, so I believe it was twenty twenty, and I essentially, stopped all the data there. And then what I did is I said, okay, using the power law, using the power law slope, I'm gonna try and, get the average, price for the next four years. And so what I did, and we actually have a chart of this, Vince, if you wanna pull it up, we might" }, { "speaker": "planc", "time": "15:34", "start": 934.5, "text": "Bitcoin price, between the third and the fourth halving. So this is, this shows it so well, and this actually compares it to Stock to Flow, and there's actually a huge difference in the accuracy. So Stock to Flow, I think it's worth mentioning as well, Stock to Flow, Plan B created, three models actually. And so when you have three models, it's a lot easier to kind of be accurate 'cause you can jump between models, you know? So he created three models. One that showed between the third and the fourth halving, the average price Price would be, I believe, around two hundred and eighty-eight K. So he had kind of three models for that window of time between the third halving and the fourth halving, right? So between like around twenty twenty and twenty twenty-four, and this is the average price. So if you take all the, all the days between that window and you average them out, he, he had three models predicting a fifty K average, a hundred K average, and a two eighty-eight average. Well, the actual average for that range of time was actually thirty-two thousand, or say thirty-three thousand to keep it Look at the slope, and you take, you take the power law's kind of slope for every single day, and you average out that same window, you actually get within four point five percent of what occurred. So when you stopped the testing in twenty twenty, the power law predicted the next four years, when you, when you look at the average price, within four point five percent accuracy, which is just incredible. and so people say, \"Well, this can't predict the future.\" Well, it already has predicted the future already, right? Like it, we, we-- 'Cause, ' Or, or sorry, twenty eighteen. I mean, it's, it's already shown, predictive potential, like it has worked, basically is the point. Doesn't mean it's gonna work going forward, but it already has worked, so it's kind of a proven model. So I'll let Spencer go talk there for quite a while, but, but yeah, this is-- I don't know if you, well, your thoughts on this, but as far as the accuracy, I mean, at least historically, at least for the last four years, I mean," }, { "speaker": "planc", "time": "17:34", "start": 1054.4, "text": "Analysis at Q4, and they said, \"Okay, well, what's the average price gonna be for the next four years?\" And it came out with, I believe, one thirty or one thirty-three, I can't remember off the top of my head, but it's basically saying the average price is gonna be one thirty or one thirty-three in that range between the, the halving we just, you know, started, right? Or just had, and then the next one. So" }, { "speaker": "stephan", "time": "17:54", "start": 1074.36, "text": "the twenty-eight halving, yeah." }, { "speaker": "planc", "time": "17:56", "start": 1075.76, "text": "Exactly, like twenty twenty-four to twenty twenty-eight, that window, it's Holds. Now, stock to flow says five hundred K, so there's a big difference there, right? And, so the stock to flow it gets exponential, right? Then the next happening window, stock to flow says five million, right? So there's a big difference between the parallel and stock to flow. it hasn't been as apparent up until this point, but they're gonna diverge quite a bit. So, oh, let's focus on the out of sample. Yeah, so the, so the" }, { "speaker": "sminston", "time": "18:23", "start": 1102.64, "text": "out of sample clearly kind of starts to fall apart when you," }, { "speaker": "sminston", "time": "18:29", "start": 1108.94, "text": "when you" }, { "speaker": "sminston", "time": "18:34", "start": 1114.38, "text": "Kind of, you know, doing chicken scratches, a million chicken scratches on a chart, to try to see what fits, but it is a good example of something that is just not, you know, when backtested, it really falls apart. When out-of-sample testing or, or modeling is done, it falls apart and it has to be, you know, adjusted and, and the model itself doesn't really make sense. the power law and- Rather is very elegant, it only has a couple of key parameters in it, it avoids the problem of the pitfall of overfitting, which, you know, folks, folks, in the financial world and, and outside the financial world would try to come up with very complex models with a lot of parameters, and they come up with a beautiful-looking model that fits the data perfectly, but has absolutely zero predictive power. That's another problem. The power law, the power law, so kind of to go back to your question, Stefan, the power law is it a Power opinion, you know, people, some people really take issue with the term power law, and, and I think a misconception there is that it just kind of comes out of a conventional term from, from mathematics. it's-- and I, I think you talked about this with Sina a bit in your last episode. I, I have no issues calling it a power function, power curve. It's just a very simple math equation is all it's referring to, so it's not an iron law of the universe that everything has to always follow power law all the time. but Elegant model that you don't have to worry about the issue of overfitting. It's something that explains the model in its entirety without having to do a lot of fine-tuning, a lot of adjusting over its life. it's, it's something that explains the, the network growth pretty beautifully in a fundamental sense. So you've got the Metcalf, Metcalf's Law Sort, sort of effect, right, where you've got the value of the network, exponenitiating, on top of the growth of the network. so hopefully that kind of answers your question, but I think this, you guys were, you guys were segwaying into this chart just to speak. a minute on this. I think this is one of the, my favorite charts I've ever put together 'cause for me, again, it was another solidifying, look at the entire life of, of Bitcoin. You can actually see the evolution of, or the stabilization of that, that exponent. Or if you look at it in log-log space for the power law, it's the slope, right? It's a linear slope. And so that top plot, is that slope, right? Or it's that scaling, it's that exponent. The bottom plot is the R squared Squared, so it says essentially the accuracy, right? It's how much of the data, what percent of the data is explained by the model. This is all power law. And so this, this I think would connect with a general audience, I think in an intuitive way, and for me it does as well. It almost looks like a ringing of a bell, you know, you could like imagine of, sort of a physical analog there, or you could imagine a thermostat that's trying to, reach equilibrium. So there's clearly, like a, a value of pretty close to six, maybe five point seven, five point eight, for the slope that it's been converging at, like Plan C said for the last over eight years. The interesting thing is Somebody could have, picked this up as early as maybe like twenty sixteen, twenty seventeen, and put together a pretty, pretty darn accurate, future projection of the price based on the power law using that, that scaling coefficient in two thousand sixteen, especially given that the R squared was like ninety per ninety percent almost. And the first time we saw somebody actually do it, I think there were a couple people, but, you know, Plan G, or Plan G, we call him Giovanni, was definitely, the first to kind of like, post about it. I think it was two thousand eighteen. and so there were a few years there where it was like kind of ripe for discovering, you know, and, and, and they would have been, proven to, to be very accurate, for years into the future. So I think this is pretty cool." }, { "speaker": "stephan", "time": "22:32", "start": 1352.44, "text": "Yeah, it is fascinating. I, I think the obvious question people will have in their minds is, what would it take to break this thing? Like, could there be something at a fundamental level that changes, whether that is, you know, a new outside source of capital coming in or maybe something goes wrong with Bitcoin that there's some- Unknown bug in the cryptography or the implementation or something like this. What are the things that it would, you know, in your mind, what would it take for it to, quote unquote, break?" }, { "speaker": "sminston", "time": "23:02", "start": 1382.17, "text": "From my perspective, so from, I think that the, the B value here, the scale co- the exponent here, this is clearly showing a strong stabilization effect, and so if I started at this stage in the, I mean, the, the asset's quite mature at this point, right? We've got a market cap of just, you know, like two trillion or something like that, and we've got, an ever-growing, accuracy of the same model that's been explaining it for most of, most of its life. I think if I, the, the thing I always- Go to is if the R squared and/or the scale coefficient here, being the exponent, started to, have a persistent change away from its, its stabilization Point here, which looks like it's five, five, five point seven. there are different factors that could start to drive that, that I think over time because it does follow a, a, a resilient kind of anti-fragile Network growth that has those in underpinnings, therefore it's a power law. I think the more it exists, the less likely any of those things are kind of, going to happen actually, because I think it's gonna be robust against black swan events, for example, like COVID, governments trying to shut it down, you know, over regulation. I mean, I, you know, to be a little bit hyperbolic, I almost feel like it would take something like an act of God to start to take this thing offline. It's just the, Computer network that's, that's supporting the most pristine, you know, and perfect money that there is, to borrow a term from Saylor. So anyway, to more simply answer your question, I think if I started to see a persistent dive, or change in the downward direction for the scale coefficient for the power law, just following the data, that, that's what would do it for me. I think it's the power law makes it such that the longer that it exists, the less likely it is for something that to, for that to occur. Also, as the exponential bubbles- Don't really have an impact on this whatsoever. So, tem-small temporary fluctuations to the upside aren't concerning to me whatsoever." }, { "speaker": "stephan", "time": "25:09", "start": 1509.28, "text": "Back to the show in a moment. 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You can use Visa, Ledger, or Coldcard hardware wallets to spin up a Bold Vault in just a few minutes, and the Bold Vault is the only collaborative custody vault available with zero monthly fees. They're also offering zero fees on your first ten thousand dollars of Bitcoin buys and twenty-five dollars of free Bitcoin when you buy a hundred dollars of Bitcoin or more. Try Bold today and upgrade your stacking experience over at getbold.io. And now back to the show. I see. So in your view, then it's essentially if the R squared dropped really low or, you know, hypothetically- Exactly. Then you would start to question, okay, maybe it's no longer valid. And in, in your, in the framework we're working with here, it-- you can still have these kind of big bubbles up and crashes down where there'll be times where it's above the line and times where it's below the line, but the point is, is the average price over the cycle still in that range? Then it sort of indicates, okay, it has a high R squared and it still has a good fit. Is that roughly what you're saying?" }, { "speaker": "sminston", "time": "27:54", "start": 1673.59, "text": "Yeah, it's kind of like a health--" }, { "speaker": "sminston", "time": "27:59", "start": 1679.02, "text": "I was looking, quote unquote, unhealthy, you know, and I, I think it would be near impossible to see that kind of thing happen overnight. It would be something that you're kind of seeing a persistent, phase change with, which is, you know, it's always like possible, but I think it's, it's becoming ever less likely that something like that would happen. But I think what you said is, is correct." }, { "speaker": "stephan", "time": "28:17", "start": 1697.1, "text": "One other question, just on this, I'd love to hear your thoughts, and I know you guys probably have thoughts on this as well. There's a lot of people in Bitcoin who are talking about, \"Oh, well, it's an S curve. There's gonna be this S curve moment, right? And we're just at the knee of the curve, and eventually there's gonna come a moment where, you know, the masses come in to Bitcoin, and maybe that's, in internet terms, maybe that's like the equivalent of the AOL moment, right? The moment that all these households" }, { "speaker": "stephan", "time": "28:47", "start": 1727.32, "text": "Believe that, you know, basically the power law is still gonna stay intact even if such a, an event were to occur?" }, { "speaker": "planc", "time": "28:54", "start": 1734.15, "text": "Yeah, I mean, I would say, so to, yeah, to speak to that and to quickly also answer the last question, from my standpoint as far as the, the power law, because it is a very common question, like what would actually invalidate or, or cause the power law to cut, quote unquote, break. From my perspective, it's, it's somewhat similar to Spen's, I would say, you know, technically speaking, the R" }, { "speaker": "planc", "time": "29:17", "start": 1756.7, "text": "Fit to the power law. At a certain point, I don't know, you could, you could draw like an arbitrary line in the sand and say if it goes below zero point eight five, then no longer gonna use it or something. But, I mean, for me, if it goes below ninety, then that would be kind of like, okay, what's something might be shifting here, because it's been trending up and, you know, been at ninety five, for quite a while. the other way is if it broke below power law support. So at the bottom of And kind of stayed there for a while. if that was the case, the, the bottom bound there, that's the blue line, so that's essentially the, the bottom five percent of the distribution of the power law using a, a quantile regression, you can also kind of call it a percentile. So it's just showing the, the probabilities of the distribution range of the, of the dataset. And so that bottom five percent, right? Which means five percent of the data points have ever gone that low, you know, that we've only gone there during COVID" }, { "speaker": "planc", "time": "30:17", "start": 1816.7, "text": "The, the FTX slash Luna collapse, we actually went down to the bottom of that blue band again. So if we've broke significantly below that, and we stayed there for a bit, that would be start to be concerning on my end, probably more so than, than anything, 'cause that would show a pretty significant deviation to the downside. And I don't think that, I don't see that happening unless there's something fundamentally wrong with the network. from a network standpoint, or not network standpoint, from a network effect standpoint, I don't When it comes to, network effects, right? Within the crypto space, within digital asset space, at two trillion dollar asset, network effects are there, and just, just everything about Bitcoin has already reached the network effect, in my, from my opinion, in my opinion. now, like, see, Spencer said, an act of God pretty much, like it, it, in order to break below, 'cause I think there's something fundamental about that parallel support, potentially connected to the mining side of things. So I Perfect. I, I don't even want to really speculate, on the technical side with that, but there's, it would take something really, really significant in my opinion to break Bitcoin, the power law to the downside, and then to the upside, I mean, as far as, the denominator goes, the denominator we typically use is USD, so it can kind of be misleading where the power law could appear to be breaking to the upside, but really it's just the, you know, the US dollar essentially collapsing or failing or no longer being a useful, you know Also look at Bitcoin versus, you know, gold as, as a more stable way of looking at it. You could even chart-- and actually, Spencer's done this. He actually charted, he has a chart for this. I'm not sure if he's gonna show it today, but, he charted, Bitcoin versus oil, Bitcoin versus real estate, Bitcoin versus gold, so like more stable, quote-unquote stable, asset classes. So, yeah, I mean, as far as Janser's question though specifically," }, { "speaker": "planc", "time": "32:17", "start": 1936.74, "text": "Of adoption, all of a sudden, you know, Bitcoin's gonna just go to this S curve. Now, of course, that's possible, everything is possible, of course. It's kind of all probabilities. I look at everything more in the, in the side of probabilities, but I don't think that's gonna be the case for Bitcoin, I'll tell you why. Other technologies, you know, like, you know, you could use, like a social media app or something like this, it's so easy to a-adopt these things as far as you're clicking" }, { "speaker": "planc", "time": "32:47", "start": 1966.72, "text": "Putting their life savings into this asset class, even though Bitcoin is spreading as kind of a mind virus, I look at it as there's buffers against that. And so I'm sure you've encountered this, like when people first hear about Bitcoin, there's this natural process where they're not over-- they're not gonna overnight just throw all their money into Bitcoin. There's essentially a, a, like a, a period of time where you need to kind of learn about it, understand it, and so everyone's gonna go through that, that kind of cycle themselves. But what I'm trying to say is it Because we're talking about literally people's accumulated time, that's a great way of showing it. You can measure Bitcoin as a power law versus other things other than US dollars. and so as long as the US dollar remains stable as an asset or as a, a currency, I don't see the power law breaking or going into like an S curve, myself. and essentially, the essence of what I'm saying is, it just comes down to, yeah, I mean, it, it's just at this point, I It's reached escape velocity, so, yeah, I mean, it would take, it would take a lot, oh, the main point of what I was saying is simply that, people aren't, like I said already, people aren't gonna throw all their life savings in overnight. I know some people do, but on the aggregate, on the average, you know, there's a, there's a period of time where people have to kinda understand it, they're gonna put a little bit in, a little bit more, and so that's naturally gonna have this adoption that," }, { "speaker": "stephan", "time": "34:17", "start": 2057.28, "text": "go back to the power law probability analysis. I think this would be a really interesting chart for listeners to check out. And, yeah, Plan C, if you could just explain a bit about what's going on here." }, { "speaker": "planc", "time": "34:28", "start": 2067.83, "text": "Yeah, I, I really like this because it's, it's a very agnostic model. So it's basically not saying like there's a specific peak. It's, I'm not trying to say like, okay, the peak's gonna happen at any, any one point in time. It's just showing, what it's showing is essentially taking the power law and Dash line, you'll see there kind of towards more the bottom third of the dataset. So that, that line there exactly, that's, quote unquote fair value. You can look at fair value in a couple different ways with the power law, but this is using, the fiftieth percentile. So what it's saying is half the data points are below that line, half the data points are above that line. And so, yeah, essentially half the time we spend above and half the time we spend below that line. And so that's actually at seventy-one That line, as you can see, right now we're about thirty-two percent above that, fair value line, but that doesn't mean, of course, you should sell your Bitcoin. You know, I don't advocate trading the cycles, I don't advocate really selling Bitcoin in general. I think the only time you wanna sell is if, in my opinion, anyways, is if, you know, take a little bit off the table to change your life in a meaningful way and basically enjoy more memories with your loved ones, because time is the most important asset, even above Bitcoin, in my I'd like to look at it. So, but don't expect to get back in, you know, at a lower point. Anytime you sell your Bitcoin, don't assume you get back in at a lower price. Simply sell if you feel like, so that's where this model comes in handy, 'cause you're, you can kind of assess, historically speaking, where we are in the dataset, and if we're at one of the higher quantiles or higher percentiles, you can say, \"Well, if I do wanna sell a little bit of my Bitcoin to Actually kind of perfect. It shows on the chart that we're at the sixty-six point seventh percentile. So what does that mean? It means a third of the time exactly we were above this point. So people think we're overheated right now or they feel like we're in this euphoric, place in the cycle. Well, we're-- we've actually been above this, level of euphoria or deviation from the power law to the upside, a third of the time. So we're still have tons of room above us, and that last third is actually where a lot of the, most of the gains, really are. And so, yeah, we're at a very healthy level. you know, that top band, the red band there is the top, three percent of the dataset. So we're only there three percent of the time, that's the ninety-seventh to ninety-nine point nine nine, quantile. so based on today, one thing people should understand, th-these numbers increase every day, because essentially over time, you know, with the way the parallel works" }, { "speaker": "planc", "time": "37:12", "start": 2232.14, "text": "Growth rate. And so just so people see these numbers on the chart, don't, that's not predicting the peak of the cycle, that's not predicting, you know, ultimately where we'll be. That's just based on today. So if, if the price today was at over a hundred and ninety-five thousand, we would actually be in that red band, right? So there's tons of room still, the bottom band, you know, thirty-five to forty-three, that's showing kind of the, the worst case scenario band. So if we had like some crazy black swan, Going down to kind of like thirty-five to forty-five K range, maybe going below thirty-five just very, very briefly. I mean, you can see on the chart there, we went down slightly below the blue band during COVID, but, but if you actually-- this is a ten-minute chart, this chart updates every ten minutes, so we actually only spent about half an hour below that blue band. So it wasn't-- it was just the very bottom of that crash. It looks like we were there, but, we went below it, but really it was so short-lived, right? It can be anywhere kind of in that range and, yeah, that orange band. So we don't know for sure how high we'll go, obviously. If you look at the pattern in the past, you know, twenty thirteen, we got to the very top of the, of the distribution, we got to the ninety-nine point nine nine. In twenty, seventeen, we got to the same, we got to ninety-nine point nine nine. Last cycle, we actually only got to ninety-nine point five, for the percentile. So we don't know how high we'll get this" }, { "speaker": "planc", "time": "38:42", "start": 2322.14, "text": "But, that's, that's essentially the, I look at as a useful, useful tool, to kind of like zoom out and be like, okay, where are we, right? 'Cause, i-i-it's, it's not, like a daily trading model or a monthly model or even, even really a cycle trading model, although someone could use it if they did want to do that. I look at it more as just assessing kind of where we are and, and what value you would theoretically get if you sold your Bitcoin, right? And you wanna" }, { "speaker": "stephan", "time": "39:12", "start": 2351.76, "text": "This show brought to you by mempool.space, the world's leading Bitcoin visualizer, and now they've got an accelerator program. So if you have a transaction that you sent at a fee that was too low to get confirmed, now you can fix this at, with the mempool accelerator. The way it works, you can go and search your transaction, scroll down, click accelerator, and you don't need an account, you can pay with Lightning, and then it'll show you it's now in the process of being accelerated, and then after a few minutes, it's confirmed. And so this is a" }, { "speaker": "stephan", "time": "39:42", "start": 2381.5, "text": "And this can happen where maybe your wallet doesn't have RBF or CPFP, or it might help you in situations where it's impractical to go and re-sign, so for example, multisig with keys in different locations. And thirdly, even in some Lightning scenarios, perhaps a forced close, you might not be able to use RBF, and so in this case, the mempool accelerator can help you out. So keep it in mind, and you can find out more over at mempool.space/excelerator. Yeah, I like the idea of thinking about getting good value for your Sats, right? If you're thinking about, okay, you know, I, I need to, whatever, you know, if you have a life event coming up, you know, you're getting married or you're buying a house for the family, this kind of thing, then, yeah, maybe timing it towards those events. It, it certainly, kind of makes sense, I guess, the way I'm thinking about it at least. I'm curious if you were to sort of expand it out, Will the numbers really change a lot based on, you know, where Bitcoin goes, or do you think now, you know, because it's been, whatever, fifteen or sixteen years now, that, i-it's gonna be sort of, the path is relatively set?" }, { "speaker": "planc", "time": "40:51", "start": 2451.19, "text": "Yeah, so I think it's relatively set. So you could actually do this in a couple different ways, and the way Sina would say is you should actually stop updating, the model. You should actually take a kind of a snapshot of where we're at, and you should basically continue on with the, the, mathematical equation for the slopes, right? Of, of the different, of the different quantiles. You should basically maintain that slope and just put it out for a year or a couple years or however long you wanna go, and just take a snapshot so nothing changes. The other approach is you go a dynamic approach where you are updating it every ten minutes, which is the approach I'm doing with this currently, where it's updating every ten minutes. But the actual stability of the model, you know, there's probably rooms for slight movements, as far as, still kind of stabilizing things, but I think it's ninety-five percent or more the way there already. And I don't think the, in my opinion, Spencer can tell me if he thinks otherwise, there's, you know, probably not massive fluctuations at this point Yeah, to answer your question though, the numbers that it's projecting out, especially when you only project out like one year, if you project out ten years, yes, I think they're still, you know, when you're using a dynamic model and you're projecting out ten years, yeah, I think the numbers for ten years from now would fluctuate probably pretty, pretty significantly. But if you're only projecting out a year, I don't see it fluctuating, that much. Actually, Spencer did run a little bit analysis on this, if he wants to speak Yeah, yeah, but that's basically- I guess" }, { "speaker": "sminston", "time": "42:19", "start": 2539.35, "text": "my, my, my, two cents on that is that, it depends on what percentiles of the data you're talking about. So right now, while we're looking at Plan C's, if you look at all the data that's closer to his bottom band there, kind of the support level, blue. everything. So I do have a-- I don't have the chart prepared, so apologies, but I did an analysis a few months back where I looked at the data percentiles, meaning, you know, the, the lowest percentiles like that blue band all the way up to the top, the full spectrum, right? Kind of every single quantile, zero to a hundred, and I wanted to see from the power law kind of perspective, how does the slope change if you, if you break, if you kind of isolate each of those different percentile? And what I found was that, if you look at everything between kind of zero or not exactly zero, but one to third percentile up to like the fiftieth percentile, which is that fair value fiftieth percentile, this is interesting, the, the slope of the power law actually doesn't really change appreciably at all. So it's, it's, it's virtually the same, no matter what, what percent, percentile you model i-in that bottom fifty percent As you start to go to the top 50th percentile, you can see above that fair value line, that's where you start to see a lot of the bubble action, right? And these kind of come and go, they're much greater magnitude, you know, exponential growth, exponential decay. but the data, the closer you get to the top, the less the data tends to spend, at those high of those deviations. But I guess the point there being that, in terms of the long-term stable price projections, like the trajectory of that fiftieth percentile line, the support line I'm way more confident in the long-term stability of those projections, in that bottom 50th percentile band kind of no matter, you know, whatever, whether it's the fifth percentile, thirty-third percentile, 50th percentile. But it's, I think a lot less-- I think what we're still trying to learn more about and gather more data. is, is when you start to go to the, the higher deviations, right? The, the, the, the tops of the bubbles, for example, is kind of like the least certain territory. So that's kind of maybe how I'd answer that question. Yeah." }, { "speaker": "planc", "time": "44:25", "start": 2664.67, "text": "Yeah. So, Spencer's chart, maybe can speak to exactly, Like the, this, this kind of stabilization, 'cause it's similar to the, the, this, we talked about the power law stabilization of that slope. Well, it's actually similar with this model. He was showing, I think he, he took different parts of the dataset and he kind of projected out the price for the end of this year and was seeing like how stable that price was based on using all sorts of s- kind of snip, snippets of the dataset. And essentially, I believe, it's showing like more and more stabilization over time" }, { "speaker": "planc", "time": "44:59", "start": 2698.91, "text": "Q4 of next year, those projections were starting to get fairly stable, but it's still uncertain how, if it's completely stable. So right now, I mean, that blue or the, the red band is basically for people that are interested. It's, it shows like quite a range naturally, and the reason why it shows quite a range is because, you know, at those peaks, I mean, the Bitcoin goes so exponential, that, that, there's quite, quite extremes at the, at the tops, right? So it, it does allow kind of range of, of, of, of, of that top to occur. so yeah, anyways, it, it sh- it really shows with the red band that we could be anywhere between, if you look at the very end of next year, upwards of four hundred thousand. So i-if we had the same level of a peak as twenty seventeen, which was the ninety-nine point nine nine percentile, so like the very, very top of the dataset, if we, if we match that-" }, { "speaker": "stephan", "time": "45:54", "start": 2754.11, "text": "Yeah, no, let's talk Equivalent to twenty seventeen." }, { "speaker": "planc", "time": "46:01", "start": 2761.07, "text": "Yeah, if, if it, if it hit the exact, level of, percentile, right, of the dataset as twenty seventeen and, and twenty thirteen, right? Both of those peaks, we got to that point. If we match that for this cycle and, and, we peaked at the very end, say December, we'd basically be almost at four hundred thousand. So that's kind of the upper, upper limits of, of, in my opinion, within the range of what we've seen since Bitcoin. We, I mean, and if that was the case, it'd be the first time we ever went there. But, anything like four hundred or less, is within the distribution, and that red band is essentially between three hundred to four hundred K for that, for the, the end of next year, and then the orange band would be, you know, I can't, off top of my head, maybe two to three hundred kind of range or something. So, but this is, he, yeah, he can speak to this as far as the stabilization of this model." }, { "speaker": "sminston", "time": "46:53", "start": 2813.37, "text": "Yeah, there's On this, all I'm doing here, to my point there about the higher percentiles, like once you go to the orange band, red band, this is trying to model the, the, the using quantile regression, which we haven't really, we might, I don't know if we'll have time to dive into that, but the quantile regression method for the power law, I'm looking at the specifically ninety-ninth percentile, of the data, which if you remember back to Plan C's previous chart, that's like up, very high up in the red band. So if you look at the bottom plot here, there's a trajectory here, there's kind of like a decay and a stabilization of, and a change, importantly, there's a change in what you would predict the, November twenty twenty-five Ninety-ninth percentile price to be, if the, if the bubble top were to happen around that time, right? And so that, so that's why I'm saying, if you're using just the quantile regression method for the very tops, of the data, things tend to become a lot more certain, I guess, the closer you get to your kind of target point, like the, the point at which you expect there to actually be a bubble. Does that make sense? Can you show, can" }, { "speaker": "planc", "time": "48:05", "start": 2885.12, "text": "you explain the bottom charts, Vincent, what exactly you're showing there? 'Cause The first year of data, and he's trying to predict the price for, for like, you know, November of, of next year. And if you use only the first year of data, it would have said we'd gone to a million, million dollars, right? Or, or one point two million." }, { "speaker": "sminston", "time": "48:24", "start": 2903.57, "text": "Yeah, this is like, all of this is trying to predict if the bubble top happens in November of next year, of twenty twenty-five, that bottom, all that bottom chart is showing that if you were to try to do that using the ninety-ninth percentile quantile model," }, { "speaker": "sminston", "time": "48:40", "start": 2920.21, "text": "July of twenty thirteen. the point here is that people have kind of like way overestimated it, right? And then once you start running that in kind of, you know, there's a tr-- there's a trajectory right there, right? And so once you start doing it in twenty twenty, you're kind of like estimating around four hundred thousand, and now we're in July, we're, we're kind of like a little above two hundred thousand or two hundred or like two hundred and seventy-four thousand, ran-- last time I ran this is what we're kind of projecting The change isn't, as, as, large in recent months, right? In recent years. So it's probably gonna be, so we're much closer to what it's actually gonna be, but that's, that's the difficulty with trying to predict the actual bubble tops. But I do have a different model that I think may hold some weight, if, if we have time to get into that. But, yeah." }, { "speaker": "stephan", "time": "49:31", "start": 2970.84, "text": "Yeah. Okay, well, one other thing I'm curious to get your guys' thoughts on, I think PlanC, you were talking about this idea as well of a possible extended cycle. could you explain a bit about what you mean there? What, what could that look like?" }, { "speaker": "planc", "time": "49:44", "start": 2983.67, "text": "Yeah, I mean, the, the theory here is, I mean, a lot of people, because, I guess they're almost have PTSD because, you know, previous, cycles we go into the bull run and, and some people have said, okay, the super cycle, this extended cycle," }, { "speaker": "planc", "time": "50:00", "start": 3000.44, "text": "We've just kinda stuck with this four-year cycle. people are somewhat opposed to the idea. I ran a poll on X, and it got a few thousand, people, and so it was a decent sample, and I think it was three-quarters of people, from off the top of my head, three-quarters of people expected the four-year cycle to continue, and there was about a third, a, a, a quarter that said, \"Okay, yeah, I'm open to the idea of an extended cycle.\" So, still the majority, at least on that small, Been maybe the first couple, maybe really early on, it was about the happenings, but I, I do think at this point it's not anything to do with the happenings. I think it's, basically, a combination of adoption and then it's, it's more to do with the liquidity cycles, which are closer to four, like around four years. So I think it's mostly the cycles of Bitcoin are, are more so driven by liquidity and adoption. And so assuming a relatively stable, growth of, amount of adoption," }, { "speaker": "planc", "time": "51:00", "start": 3060.04, "text": "you Option in, in the cycle and the liquidity cycle plays out the same, then under that, under, under those conditions, you would expect kind of the four-year cycle to continue. That's, that's basically my point. now there are some caveats though because I believe, okay, that, so we'll, we'll go with that. So it's essentially, yeah, if, if, but if we pull forward a lot of adoption, meaning if we have like nation states, you know, all of a sudden overnight, like game theory kicks in and they're all competing for Bitcoin, well" }, { "speaker": "planc", "time": "51:30", "start": 3090.42, "text": "Doing could pull forward a ton of adoption. So if we kind of, and also just the fact that we have kind of a crypto, friendly regime in, that could pull, pull forward quite a bit of adoption as well. So if we pull forward a lot of adoption, and we have a, and, and yeah, in that case, maybe that adoption is enough to essentially create a, a head, tailwind that, i-is strong enough to counteract the, the, the headwind that would be the liquidity cycle. So the normal liquidity cycle Overcome by the, the crazy degree of adoption, not to mention the ETFs and all these other things as well. So if there's enough adoption, put forward is the m-my main thesis, we could essentially have a bit of an extended cycle where we're able to overcome the liquidity cycle to some degree, or the liquidity cycle might play out slightly differently, it might be slightly extended, there's, you know, always a little bit of that possibility. but even if we don't get an extended cycle, I think the other possibility is we have a bit of a, a muted bear" }, { "speaker": "planc", "time": "52:30", "start": 3150.4, "text": "I believe at this point the, the discount of Bitcoin going to zero is essentially gone. So in previous bear markets, during the, you know, the fear part of the cycle where people are panic selling and, and we're kind of capitulating in the bear markets, there's always been in the past this like back of the mind, okay, could Bitcoin really just go to zero here? And I think that's always created a bit of a discount. I mean, obviously the OGs and, and people that have held Bitcoin for a while, that are really versed in it, they" }, { "speaker": "planc", "time": "53:00", "start": 3180.42, "text": "Okay, we could go to zero moment, and in that case, I think it's caused, it's been a large part of the reason why we've had these like eighty percent drawdowns, right? Eighty-five even. I don't think that's, in my opinion, I don't see that happening anymore. I think, if anything, we have a muted bear market where maybe we drop down anywhere between like forty to sixty percent." }, { "speaker": "planc", "time": "53:22", "start": 3201.83, "text": "so, yeah, I mean, it, it, I kind of see it the one of those two Don't, don't think Saylor by himself is enough, he would have to be buying just tremendous amounts. I mean, he's, he's put this, forty-two billion out for the next three years, I think he's gonna go through that way, way quicker and he's, he's gonna buy a lot more. But even under those situation, under the circumstances, I still don't think it's enough by himself. It's gonna require multiple players, you know. So, anyways, I'll let Spencer go, I wanna give him a chance to," }, { "speaker": "sminston", "time": "54:00", "start": 3240.44, "text": "I'd say that I totally buy into the thesis that we're shifting from, significantly shifting from more retail to more of the institutional," }, { "speaker": "sminston", "time": "54:11", "start": 3250.89, "text": "market movement here, and that's what's kind of like defining-- we're going into what's defining this cycle. So I don't know, I don't really have a strong opinion on that. I tend-- I too kind of go back to sort of the, the laws of scale here, and I think that it takes, much more, money inflows and, and market moving To move a, a similar amount, to move the needle a similar amount in these bubbles for this next one, and I think that's part of like what we kind of expect here. So it might all come out in the wash, and we'll get like a pretty predictable bubble size, but I'm, I'm really, I don't know about market timing, I think Plan C is actually much more read and expert on that, so I'm just gonna go with what he said." }, { "speaker": "stephan", "time": "54:53", "start": 3292.53, "text": "Yeah. Well, I think, I think you're right about the, I mean, it Over time, it kind of implies this anyway, right? Right." }, { "speaker": "sminston", "time": "55:04", "start": 3303.52, "text": "Yep, exactly, exactly. That's my thinking. So," }, { "speaker": "stephan", "time": "55:07", "start": 3306.66, "text": "yep. Yeah. Okay. so any other charts you wanted to show us that we haven't got to yet?" }, { "speaker": "sminston", "time": "55:12", "start": 3311.79, "text": "Well, if you don't mind, 'cause we were on the topic of sort of bubble tops, and the cycles here, I could do a quick explainer here, but ask any questions and we can stop anytime. But Something I've been really focused on and sort of, I guess, I think, I'd like to think I made some headway on is exploring, I'm, so I made this decay channel oscillator, and so I've started doing semi-routine updates on this, and so you can see this is all normalized from zero to a hundred percent, and this is meant to be something that's, it's all based on the fundamental power law support, right? So that's the zero percent, and, I think it looks pretty nice, for various reasons, but quantitatively it Which I'll get to. But what it's doing is it's telling us basically where we are, at any given point in time for all of its history, including today, between that zero percent power law support, like as low as you can go to to maxed out, not in terms of price, but in terms of percentage, between that channel. And so the channel, specific-- So a lot of people ask, well, 'cause they weren't there in the earlier history when I was developing this, it's like, \"How does this made exactly? \" And what does this mean that we're today, you know, we're not exactly at fifty percent, we're a little bit lower now 'cause we're at ninety-three thousand, but this is from, you know, a few days ago. But what does fifty The difference between the cycle price top and the, and the possible price bottom, which, which is set by that power law. So it forms a channel. this is the twenty twenty-four snapshot. maybe I'll come back to that So this is the way, that I basically constructed it, and I'm-- this is, I put this together as an illustrative tool. So the bottom left is that oscillator that we're kind of tracking, and right now we're like hovering around forty, fifty percent heated. kind of like right in the middle zone, right? So we've got about fifty percent of the way to go. So how do I build this? So the hundred percent mark is actually, if you go to the top left quadrant, it's that upper bound, the dash line. And the way I form that upper bound dash line is I take the cycle top data points from every single cycle, so you can kind of see them in red here, one, two, three, four. There's four, really four data points. And then there's the power loss support line, which is the fifth percentile power loss, that's the solid white line. The dash line is simply, taking the deviations to those maximum points in every single cycle And then measuring the exponential decay that's formed by that, and then you do a little, you do kind of a math trick, which is you multiply that exponential function with the power law function, and what you get is, you basically get an exponential decay that's overlaid onto a power law, and so you can see it's decaying at a certain rate in that window or that channel starts to close over as the further you go out in time, that volatility, it's projecting that that volatility gets smaller and smaller, which is like the diminishing returns that, that you mentioned, Stephan. So another way to look at it. so I'm, I'm just trying to create like an upper and lower bound here, that- The freaky thing about it, and I did some analysis on this before, is that it's, it's a small amount of data points, but the, the fit of that exponential function is like ninety-nine point nine or ninety-nine point eight R squared, with a very low P value. So it's, it's- You know, it's not a lot of data, and so like, I don't, I wanna take all of this with a grain of salt, but I'm, I'm-- it's compelling enough to where I'm tracking and developing it. It's kind of my point, and I think it's also-- happen to think it's conservative. But anyway, this is log-log space, so it's kind of the line that you can't unsee, that we see with the parallel. and then if you transform that to log, in the y-axis and then linear in the x-axis, you get another chart that looks pretty, pretty familiar, and that's kind of what it looks like in log-linear. that-- this is, this would be more like what Plan C's, chart is, right? Like a log-linear chart. and then you can convert that to linear-linear, which is like, kind of what the old-school financial analysts are used to looking at other assets in. So it's just linear time, linear year, and then linear price. And so it's all the same channel that's formed in every single one of these, and the oscillator is just showing what percentage between the top and the bottom you are at any interesting point." }, { "speaker": "stephan", "time": "59:29", "start": 3569.01, "text": "And I will point out actually, for people who are fans of the whole S-curve adoption, if you look at linear, linear, and you zoom out, it kinda can look like an S-curve, but just, you know, on a zoomed-out way, right?" }, { "speaker": "sminston", "time": "59:40", "start": 3579.54, "text": "Yeah, it has some Siness to it. Yeah, I think that the- Yeah, I, it, for the tops at least, and I don't know what exactly to make of that. I think it's more of a decay on top of a power law. Going back to your earlier question, I don't know what's gonna happen to the power law in the future in five, ten, twenty years. Right. I, I tend to take, and, take a page from Giovanni's philosophy, which is like, we have the data that we have, we don't have any indication of things turning into a Weibull or sort of" }, { "speaker": "sminston", "time": "01:00:12", "start": 3612.72, "text": "Don't see any fundamental reasons why we're, we're looking that we'd be going to that territory, but we, we could. Hey, Spencer," }, { "speaker": "planc", "time": "01:00:18", "start": 3618.26, "text": "do you wanna share, roughly speaking, the price if you feel comfortable, like kind of Q4 of next year, what is the decay channel, kind of happening for, for the tops? 'Cause some people might find that interesting." }, { "speaker": "sminston", "time": "01:00:30", "start": 3630.13, "text": "So this is, This is, so I just ran this again. So, this is the same thing. I'm showing the inset is the oscillator view, which I up-update, you know, semi-regularly, once or twice a week. And then this is just the linear-linear view, on the bottom, right? So this is showing- what it implies, and it's, it's not really important the difference, it's not too important at least the difference between the blue and the white tops there, it's sort of, within error, but basically what we're showing is that sometime later in twenty twenty-five, it implies, the potential to break out beyond, two hundred thousand. And so just, just throwing out the caveat that, yes, w- the, the work that I do around here tends to be a lit-on a little bit more conservative side than what a lot of the, kind of the moon-mooning, work, a lot of other models that are out there. But it's kinda hard to model the tops, you know? And it's, it's hard to walk that line of like, do I wanna be over-conservative or do I wanna be over, over-optimistic? It's like You know, so I think I, I just try to be really transparent, and I try to be, slightly on the conservative side if I can, and, you know, I, I'd love to be proven wrong, and I'd love the bubble top to here to explode past this to three, four hundred thousand. I wouldn't be angry at that at all, from a financial perspective, and it wouldn't shake my confidence importantly in the fundamental power law, which is really mostly defined by, by the kind of the support" }, { "speaker": "stephan", "time": "01:01:54", "start": 3714.31, "text": "line. Right. Because the average" }, { "speaker": "sminston", "time": "01:02:01", "start": 3721.19, "text": "I do, and I will put one more asterisk, is that another development in the next week, and I just gave a preview of it yesterday, is that there's some assumptions with this model. Like, one of the assumptions is that over enough time, the volatility diminishes to, I mean, basically the tops converge to but never quite touch the bottom. So intuitively, some folks might think that, \"Well, that doesn't really make sense, even if it's fifty years from now.\" So I actually have a sensitivity analysis coming up, just a quick preview, I guess. Which shows a little bit more of a bullish case, so now you're talking about being more comfortably in the two hundred thousand range if you assume that like the volatility drops to half of that or a third of that or something like that. So there, there are a couple of knobs there to turn, so just wanted to give that caveat. Interesting. Okay." }, { "speaker": "stephan", "time": "01:02:49", "start": 3769.58, "text": "Yeah. Yeah. So I, I guess let's try to summarize a few things. As we've mentioned, there are some interesting implications here of power law or power curve applied to things like the number of Bitcoin addresses, Bitcoin's hash rate, and of course, Bitcoin price, like we've spoken about, might be some interesting implications for people in the world of finance, whether they are advocating or, you know, helping, educate customer, Customers about Bitcoin, maybe even for the builders in the space, they may be thinking, \"Well, maybe, the number of users or the number of addresses, maybe that in, influences the way they build or develop something in the space also.\" So maybe those are some interesting implications. So just any, you know, final closing thoughts from, both of you guys. I," }, { "speaker": "planc", "time": "01:03:34", "start": 3814.81, "text": "I would just say that, you know, I think people, the fact that, that up until this point, you know, Bitcoin has followed a power law, growth pattern, Give people a lot of confidence, that this is a, it's a very stable, at this point, a very stable asset. you know, it might not feel that way day to day, right? Sometimes the price can move up and down quite a bit, although the volatility does appear to be coming down, or has, is coming down really. I would say, yeah, I mean, it's, it's, it's a very healthy growth pattern, it's a very long-term growth pattern, and, yeah, I mean, It's, it's great for anyone building the space 'cause they can be, be very confident that Bitcoin's not going anywhere. I mean, obviously people know that, that it's been steady Bitcoin and all the reasons why it's, you know, it's very, a very amazing, venture and asset class. But, yeah, I mean, it, that's basically it from my perspective. I mean, I, I just love following the data, just, just seeing where things go, but, there's no signs that this is, is gonna break anytime soon. and if it does, I'll be the first person to be posting about it, that's for sure. So, yeah, that's pretty much" }, { "speaker": "stephan", "time": "01:04:46", "start": 3886.59, "text": "it. Oh, thanks, Steph." }, { "speaker": "sminston", "time": "01:04:46", "start": 3886.93, "text": "Stephan. Yeah, great, PlanC. thanks again for having us on, Stephan. This has been awesome to come on your platform. Thank you. my closing would be, you know, I think, And that it's, it, it's following laws of scale here, that it has more orders of magnitude to cover, and I think it implies that we have like a five to ten year window here ahead of us where I think that it's, it's, it's an asymmetric, opportunity unlike anything that will probably ever happen in our life, for most, in most of our lives. if you track the, the, the power law of the Kager, which goes along with this, right, compound annual growth rate is doing sort of an inverse power law. So if you imagine it That is measurable, it's accurate, it's the same, it's just a translation of the power law, but, like a couple data points here is that, it won't diminish to the same kagur of say an S&P five hundred until somewhere around the year twenty-one, or sorry, twenty seventy-one, thereabouts. Oh, wow. And it won't diminish to what we're having as the average rate of, monetary inflation in the US until about the year twenty-one o five. And so, you know, the, you still wanna be doing significantly better than that, and I think if you, if you take a look at the math behind this, especially over the next five to ten years, it's probably one of the best, yeah, best side ups, best asymmetrical opportunities. And certainly I feel like that personally based on the math. So, yeah, thanks, thanks for hearing us out, Stephane. This has been awesome." }, { "speaker": "stephan", "time": "01:06:22", "start": 3982.73, "text": "Fantastic. Well, yeah, so listeners, check, check Plan C We're called Best Bitcoin Data Family, so guys go and join that, and, you also have the Best Bitcoin Data Show, so links will all be in the show notes. And, yeah, once again, thank you Plan C and Sminston for joining me. It's been, really great, discussion and, fascinating to see w-where things go, you know, whether the power wall stays intact or not." }, { "speaker": "planc", "time": "01:06:49", "start": 4009.0, "text": "Yeah, I definitely appreciate you having us on. we're huge fans of you and just your work and, and, yeah, being Conversation" }, { "speaker": "sminston", "time": "01:07:01", "start": 4021.91, "text": "going. Likewise for me. Yeah, it's an honor, Stephan. Thanks, thanks for all you do in the space. Thank you." } ] }