The Bitcoin Power Law is Falsified by Inflationary Currencies is a Bad Reason Fallacy

A common criticism raised against the Bitcoin Power Law Theory (BPLT) is that it doesn’t hold up when applied to economically unstable, hyperinflationary currencies like the Argentinian peso, Turkish lira, or Lebanese pound. Some argue that because millions of people use these currencies, the Bitcoin Power Law is invalidated on a global scale. This argument, while provocative, fundamentally misunderstands both the nature of power laws and the purpose of the theory.

1. Hyperinflationary Currencies are Outliers, Not the Rule

The first point to clarify is that hyperinflationary currencies are not representative of global economic systems. Currencies like the Argentinian peso and Turkish lira are economic outliers, experiencing extreme levels of inflation due to a complex set of factors including poor fiscal policy, political instability, and loss of confidence in the government. In such environments, economic fundamentals break down, and price signals become distorted. This is why these currencies cannot be used as reliable units of measurement for long-term analysis.

In the same way that extreme weather conditions like tornadoes temporarily disrupt the effects of gravity (even cows can fly in these conditions), hyperinflationary environments temporarily distort the behavior of currencies. This doesn’t mean that the underlying laws of gravity are invalid; it simply means that extreme forces are at play. The same is true of Bitcoin’s power law behavior — it remains valid in stable economic conditions, but hyperinflation introduces extreme forces that distort short-term price behavior.

2. Bitcoin’s Power Law Holds Across Stable Systems

The Bitcoin Power Law has been observed over 12 years and across multiple orders of magnitude. It holds up not only against the US dollar but also against other major, relatively stable currencies like the euro, yen, and gold. The power law also holds true when Bitcoin is compared against real assets like real estate or commodities. Here is a beautiful graph by another power law researcher @sminston_with showing how several assets lose value following an inverted power law (that is similar to the more known power law in time) with a similar exponent.

We can use almost any asset that is relatively stable to show the evolution of the price of Bitcoin in the last 15 years, in this case cleverly the power law is shown as a decreasing phenomenon because the graph intends to illustrate how these assets lost value relative to Bitcoin.

We can use almost any asset that is relatively stable to show the evolution of the price of Bitcoin in the last 15 years, in this case cleverly the power law is shown as a decreasing phenomenon because the graph intends to illustrate how these assets lost value relative to Bitcoin.

This consistency is because power laws describe long-term behavior that emerges from feedback loops and interactions in complex systems. Bitcoin’s price, adoption, hash rate, and security are interdependent, forming a system that self-regulates over time. When external forces (such as economic stability) are present, this system behaves predictably according to the power law. A graph showing how the Bitcoin Power Law holds with several relatively stable currencies. Even a factor of a few in total inflation over the last few years is considered stable in comparison with the one million x growth of Bitcoin since 2010.

We can use several stable currencies to show that the power law holds. The power law curves in the log-log space are all parallel but not on top of each other because they are expressed in the relative value (the y-axis) of each currency. However, they are all the same power law with slightly different slopes, showing the overall growth pattern.

3. Hyperinflation is a Temporary Disruption, Not a Permanent Condition

Hyperinflationary currencies are not stable and are not reflective of Bitcoin’s global behavior. Instead, they represent temporary disruptions where other forces, such as poor government policy or rapid devaluation, temporarily overwhelm the typical market forces. Hyperinflation is not a normal state for most currencies, and it’s essential to recognize that it doesn’t represent the global economic norm.

If Bitcoin is being measured in a currency like the Argentinian peso, it’s not that the power law fails; rather, the currency itself is failing. In such cases, Bitcoin becomes the store of value that people turn to as a hedge against the collapsing local currency. The very fact that Bitcoin holds its value during these crises reinforces its strength as a global asset, one whose long-term trends remain predictable even when measured in terms of stable currencies.

4. Bitcoin as a Hedge Against Hyperinflation

Ironically, Bitcoin’s role in hyperinflationary environments supports the idea that it behaves according to a predictable power law over time. When people in countries with unstable currencies see their purchasing power evaporate, they often turn to Bitcoin to escape this rapid devaluation. The flight to Bitcoin during hyperinflationary periods demonstrates that Bitcoin offers long-term stability in a world of unstable currencies.

The power law behavior of Bitcoin, when measured in more stable currencies like the dollar or euro, reflects Bitcoin’s growing role as a global hedge. It doesn’t matter if a local currency collapses — Bitcoin’s power law behavior remains intact for the long-term, global perspective.

5. Hyperinflationary Systems as Special Cases

To go back to the flying cow analogy, let’s reconsider the argument. Imagine you’re observing how gravity works, and you know that objects fall toward the Earth at a predictable rate. Now, picture someone pointing to a cow flying through the air in a tornado and saying, “See! Gravity doesn’t work! The cow is flying!” This claim is clearly absurd because gravity hasn’t failed; rather, an extreme and rare external force (the tornado’s winds) has temporarily lifted the cow into the air.

A post I made some time ago to address this common criticism. When we teach in introductory physics classes how gravity works (by the way the distance covered by a falling object is also a power law) we exclude confounding factors such as the drag due to air because it is a complicated phenomenon and because it is usually a very small correction and can be ignored at first approximation. In extreme cases, air drag could be dominant and even make a cow fly (like during a tornado) but this doesn’t mean “gravity is broken” it means that the forces that before were negligible are dominant. These are extreme cases and scenarios and we can still study them scientifically but then we are studying tornado physics and not gravity any longer.

The same logic applies to hyperinflationary currencies. The power law of Bitcoin remains valid but in special cases like hyperinflation, extreme economic forces are temporarily dominating, distorting the picture. The fact that these currencies are outliers does not invalidate the global power law behavior that Bitcoin consistently demonstrates against more stable currencies. It’s also crucial to highlight that Bitcoin is primarily traded in major currencies like the US dollar, euro, and other stable global currencies. The hyperinflationary economies often cited in critiques, such as the Argentinian peso or Turkish lira, represent tiny economies in comparison to the overall global economy. These countries’ economic instabilities, while serious for those affected, are a small fraction of the global trading volume in Bitcoin.

To address these concerns comprehensively, we developed a weighted power law model using cumulative growth data over 15 years of Bitcoin. This model incorporated in almost a dozen global currencies, including both stable and hyperinflationary currencies, weighted by their relative GDP. Remarkably, this weighted power law provided an even better fit than the power law expressed purely in dollars. This demonstrates that Bitcoin’s power law behavior is even more robust when viewed in a broader, more globally representative context.

A power law model expressed in the y-axis as cumulative gains (so we can compare different currencies with different denominations) that is the weighted average of several currencies (USD, CAD, JPY, CNY, AUS, ARS, TRY, ZWO, PKR) both stable and hyperinflationary. There are several methods one could average the relative contribution of each currency but we used the GDP of the relative currency nations in this example.

The previous graph shows a power law model expressed in the y-axis as cumulative gains (so we can compare different currencies with different denominations) that is the weighted average of several currencies (USD, CAD, JPY, CNY, AUS, ARS, TRY, ZWO, PKR) both stable and hyperinflationary. There are several methods one could average the relative contribution of each currency but we used the GDP of the relative currency nations in this example.

Conclusion: Power Laws Still Hold

The argument that Bitcoin’s power law is broken for people using hyperinflationary currencies ignores the broader context of Bitcoin’s behavior on a global scale. Hyperinflationary environments are special cases, not the rule. They do not represent the global behavior of Bitcoin’s price, adoption, or other key metrics.

In fact, the power law theory becomes even more significant when you consider Bitcoin’s role as a store of value in these environments. People turn to Bitcoin as a hedge when local currencies fail, proving that Bitcoin’s long-term predictability is valuable even during extreme economic instability.

The core point remains: Bitcoin’s power law behavior has been observed across multiple stable currencies and over long time horizons. Hyperinflationary systems are exceptions, not the rule, and their failure doesn’t invalidate the underlying principles governing Bitcoin’s long-term growth and adoption.