The Chart that Launched a Thousand Dreams
The purpose of this short note is to analyze a possible basis for the long-term growth pattern — the supertrend — exhibited by Bitcoin, as shown by the chart shared with me by Parabolic Trav, and shown as Figure 1 below.
In the figure, Parabolic Trav shows three distinct cycles drawn from the beginning of the dataset in late 2010, and projected into the future. Each cycle comprises a convex upwards section illustrated in blue; a period of stasis marked in yellow, and a period of decline shown in red. The figure also shows approximations of the positive gradients for each of the convex sections with blue lines, and a set of approximate negative gradients for the sections in red with red lines.
In what follows, I wish to unpack the insights that Parabolic Trav had in mind when he constructed this figure for Bitcoin’s supertrend.
Parabolic Trav, for those who may not have come across his Twitter presence, is the leading proponent of parabolic growth theory for Bitcoin, and his views stand in stark contrast with the bulk of analysts in the Twitter universe.
Through all wince-inducing corrections and through all phases of explosive growth, his view has remained — unflinchingly and unrelentingly — that the trend for Bitcoin is parabolic, and uniquely so when contrasted against just about any other asset. He has been the lightning rod for the angst and anguish of frustrated, disillusioned investors and for non-believers and ‘nocoiners’ alike.
It is hard to argue steadfastly that any asset has parabolic growth, without being labelled a variety of unpleasant things. Among them: ‘deluded’ for thinking that anything grows in that audacious fashion; ‘greedy’ for being blind to the prospect of bubbles and imminent crashes; even ‘unethical’ for foisting staggeringly optimistic views in the public sphere where hordes of investors might actually take you for your word.
In this piece, I would like to examine the case for his theory. I wish to make clear that what follows is not investment advice. Neither is this an ‘advertisement’ for Parabolic Trav. It is a dispassionate assessment of the long-term dynamic of Bitcoin, as identified by him, and shown in Figure 1. The objective is to study what can possibly be driving a parabolic supertrend, if indeed there is one.
How goes the Blockchain Economy?
The argument I wish to offer is two-pronged. The first strand is based on the principles of a Blockchain Economy, and the second is based on an analogy for its manifestations that can perhaps inform our intuition on the Bitcoin supertrend. We can then see whether there is a justifiable correspondence of these explanans with the parabolic supertrend argument.
I offered those thoughts, impelled from a growing unease with the facile manner in which extant models were being applied across the traditional economy, the network economy and the blockchain economy willy-nilly. They seemed to ignore the fact that the blockchain economy represents a fundamental transformation to the manner in which economic organization is occurring. So fundamental, in fact, that in addition to price and directed organization (as with firms), a third category was needed. I called it the cryptographic stigmergy.
In contrast to the network economy, the broad observation I made was that the blockchain economy adds something new that isn’t necessarily an ‘improvement’, but it is unique to it, regardless.
The network economy differs from the traditional economy because value propositions within it are based on network economies: the size, scale, depth and intensity (penetration) of networks are, collectively, an additional source of value to a user, over an above the value the good itself represents.
Networks matter deeply in a network economy. This much is obvious to us, given the world we live in.
But what kind of networks matter? The answer is simple: small-world networks matter most, which is to say that competiton is over centrality within the network. Examples abound of this simple force of logic driving market behavior, including, of course, Google, Apple, Amazon, Netflix, Facebook, and so forth.
What about the blockchain economy? Well, naturally it relies on networks, too. However, the decentralized and trustless-verifiability characteristics of its technology adds back something that was lost in the network economy.
I called it trust economies, but perhaps it is more straightforward to simply see it as a blockchain-version of the benefit to a society from higher social capital. This is not an idle point when you recall that the erosion of social capital has been bemoaned by others, and cited as reason for a detrioration of social outcomes. So, there is, understandably, a strong sense of this promise of Bitcoin to the benefit of global society among some of its proponents.
But, here’s the difference most relevant here: the kind of network Bitcoin seeks to build is antithetical to a small-world network. It seeks to build, (admittedly imperfectly, relative to its ideal-form ambition), a fully connected network — a complete graph that rejects centrality. I know that this isn’t strictly true at present, but the possibility of it remains strong, real, and deeply motivating.
What does this mean more practically then?
This. The growth patterns that Bitcoin will exhibit will necessarily be slower when contrasted to most exemplars from the network economy that have limited scale. Facebook became a global phenomenon in less than a decade. Bitcoin will not. The reason should be obvious, if one ignores price and seeks to understand the nature of Bitcoin. Facebook seeks centrality in building a small-world network. Bitcoin shuns centrality in building a complete graph. A fully connected network…in slow stages. A complete network that strongly exhibits both network and trust economies requires a longer timeframe.
The Crucible of Bitcoin
The second point I wish to make is a derivative of the fact that Bitcoin is the quintessential blockchain, and it’s evolutionary pattern can, therefore, inform views on the Blockchain Economy (and, indeed, the society) that it seeks to build.
The social network properties of Bitcoin lend themselves rather well to a comparison with the growth properties of bacteria in a Petri dish.
The growth path of the organism passes through distinct phases. During the lag phase, the bacteria are acclimatizing to the environment, with little or no growth in their numbers. The exponential phase occurs when the bacteria begin propagating by cell doubling, and their growth becomes proportional to the number of bacteria present in the Petri dish. When the bacteria exhaust the resources available to them in the Petri dish, they then enter a phase of stagnation. Collectively, the three phases describe a sigmoidal pattern of growth, not uncommon to the growth patterns of several organisms, including the length and mass of humans and potatoes. If the Petri dish is then left untended, the bacteria eventually enter a death phase.
What did you just call me?!
Yes, I realize that Bitcoin is neither a bacterium, nor is it a potato. A node in the network isn’t meaningfully doubling in any given period. However, the network structures that the overarching processes exhibit do make this setting an exceedingly apt analogy.
Over a network of given size, Bitcoin goes through several stages of adoption, from the early adopters and innovators at one end of the Bell curve to the laggards, comprising the other end. Eventually, and once all the adopters have been added to the ecosystem, the network is, in a manner of speaking, completed.
However, networks are constantly being added to the Bitcoin ecosystem in discrete episodes, and there are many more potentials networks that are yet to be added than there are already with access to it. The imagery is assisted by considering the number of participants in the Bitcoin community as a proxy for the size of the Petri dish for the bacteria.
Consider Figure 2 below. Each section of the curve is marked by a different color, introducing a different sized ‘Petri dish’, and subtly different factors that influence the environment that each provides for the growth path feasible within it.
The lag (L), exponential (E) and stagnation (S) phases are all marked out at the start, middle and end of each section of the overall curve.
At this stage, it is worthwhile re-examining Parabolic Trav’s chart from Figure 1, and contrasting the components of the supertrend it depicts with Figure 2.
Here again, is Figure 1:
Note that, while there are essential similarities in the dynamic paths of the repeated sections it shows to those in Figure 2, Parabolic Trav’s chart additionally shows the periods during which Bitcoin experienced noticeable corrections. These include: June 2011, when Biticoin went through a decline that exceeded 90%; the crash of 2013, courtesy of the MtGox, that saw the price take a nosedive from over $260 to under $55; and, the most recent decline that began in December last year.
To explain these declines — and the negatively-sloped red lines in Parabolic Trav’s chart — clearly, the death phase of the bacterial growth model also needs to be considered for the case of Bitcoin.
The Many Deaths of Bitcoin & the Antifragility Ladder
Figure 3 shows the effect of adding the beginnings of a death phase to the process. One can readily imagine a curtailed death phase at the end of each of the sections of the overall curve, replicating the many deaths of Bitcoin that are routinely documented in the popular press.
Doing this, now yields a curve with an uncanny resemblance to the supertrend in Parabolic Trav’s chart.
However, why must these death phases be curtailed, and what, if anything, can we say about the increasing gradients represented by the successive red lines of the death phases he illustrates in the chart?
The intuitive explanation is a sense that the bacteria learn with each successive iteration how to cope with the characteristics of the environment.
With a growing resilience in the Bitcoin blockchain alongside the length of the supertrend, the steepness of each successive death phase should indeed be expected to become less pronounced.
The decreasing slopes of the red lines in Parabolic Trav’s chart, therefore, represent an antifragility ladder for Bitcoin.
Here’s to a tougher future!
Bitcoin has faced a fair few ‘near-death’ phases in its own history. The larger the episodic FUD event, the larger the entry into a seemingly terminal death phase. And there will doubtless be several more death phases that Bitcoin will be plunged into. As a matter of fact, if the view that this note presents on the growth dynamic of the supertrend has any merit, it stands to reason that, indeed, it must.
However, the death phases cannot endure long; this, indeed, is a key insight we can draw from the antifragility ladded in Parabolic Trav’s chart.
The nature of Bitcoin, rooted in its blockchain, prevents the death phases from reaching a criticality that plunges the growth path into oblivion. The phase adds to its toughness and enables successive additions of networks to the ecosystem. The next lag phase inevitably ensues once the network adjusts to a new environment, and the sigmoidal path upwards resumes.