My recent article “The Questionable Mathematics of Bitcoin” sparked a little bit of controversy in the Bitcoin community. A few of its members decided to educate me on the “fallacy” of being unable to expand Bitcoin over an extended economy. Their claim was that, because Bitcoin is infinitely divisible, enough units can be produced for everyone who wants them.
My counter-claim is that dividing Bitcoin will definitely produce more units, but it will also debase the currency. Here’s my case:
Lets start with a simple numerical premise:
The above number has an equal amount of zeros before and after the decimal point. Bitcoin proponents would have you believe that, for the purposes of a currency, it doesn’t matter whether the number of units created happens before or after the decimal point.
There’s just one problem with that … the number on the left of the decimal point increases if I add a zero directly to the left of the point. If I add a zero directly to the right of the point, the numerical value on the right side of the decimal point decreases.
It’s apparent even from a mathematical basis that, while there can be theoretically infinite variations of expansion and contraction on either side of the decimal point, they are by no means the same thing. This holds true in reality as well. Classical Mechanics plays out in the visible world, but the rules change when things get really small. Then Quantum Mechanics takes over.
So, no, dividing a currency and expanding a currency are not fundamentally the same thing. In the world of Bitcoin, creating more units by dividing its base units produces new fractional units. In fiat currency, creating more units by expanding the money supply produces new whole units. Without the expansionary component of the exchange rate between Bitcoin and fiat money, the method for creating more units for distribution would have a huge inflationary impact relative to pricing. As the proportion of Bitcoin relative to its supply is constant for every person, redistribution of units would have to take place as a result, a zero-sum exercise in which some would accumulate greater proportions of Bitcoin at the expense of others. It is the ultimate in scarcity economics.
As further proof, let’s look at how gold coins have been debased in the past. They were divided and then the pieces were melted down. A cheaper base metal was then added to the gold to create a coin of similar volume. In the end, more coins could be produced that looked like and had the same economic value of the original pure gold coins. A particularly enterprising person (or government) could just melt down a whole bunch of gold coins, add in some cheaper base metal, and mint a larger bunch of new coins. But the premise is the same.
In this circumstance, while the number of coins increases, the amount of gold does not. The total purchasing power has increased, but only as a result of adding the cheaper base metal. It was a method of increasing a money supply without compromising its purchasing power. However, inflation is the natural result of such a practice.
For Bitcoin, fiat money acts as the “cheaper base metal” component in its debasement. While the supply of Bitcoin is static, its value increases as a result of demand translated into fiat currency. So, the expansionary component of Bitcoin is not its actual divisibility, but only its divisibility in relation to its value in fiat currency. Breaking Bitcoin down into smaller denominations doesn’t increase the amount of it. Indeed, just like a debased coin, the amount of Bitcoin per unit in relation to total BTC supply shrinks as it’s divided. However, its value is preserved as a function of its scarcity and demand, exactly like gold. In other words, the Bitcoin system acts as an additive to the fiat currency system, not a competitor. Bitcoin and fiat currency are inextricably “mixed together”; a component that is valuable only because it is scarce with an expansionary component that is abundant and cheap.
However, what happens if Bitcoin doesn’t have an exchange value in fiat currency? Its purchasing power evaporates as it’s divided. That’s simply a matter of mathematics. A fraction of something is always less than the whole. Here’s an example:
A salesman is offering a doll for 1 BTC and you have 1 BTC. Let’s say that the Bitcoin Foundation, in order to produce more units, decides that instead of BTC, it recognizes the base unit of Bitcoin as a “q-bit” or .1 BTC (I don’t know if a “q-bit” is an actual thing, I’m just using the term for demonstration purposes).
Two scenarios are possible:
- either all 1 BTC units become 1 q-bit units. This allows a 90% increase in total units but their purchasing power relative to current pricing is decreased by 90% thereby requiring 10x the number of units to purchase that same doll; or
- all BTC units become 10 q-bits and, because the total money supply is fixed at 21 million units, the change has absolutely no impact whatsoever.
What should be obvious is that the 21 million unit cap acts as an absolute wall around an economy. Think of it as a decimal point. Nothing can ever practically increase in value, only decrease. Once you divide Bitcoin and distribute the units, any attempt to multiply them back together becomes impractical. When you expand a money supply on the left side of the decimal point, contraction is a simple matter of subtraction. However, division of a money supply on the right side of the decimal point isn’t simply a matter of multiplication to “contract” it. Indeed, it’s much easier to continue to divide, creating smaller and smaller fractions resulting in lower and lower value.
To summarize, the divisibility of Bitcoin is only important relative to Bitcoin’s ability to be exchanged with expansionary fiat money. In its own right, such divisibility degrades the purchasing power of each unit in relation to current pricing or becomes a completely arbitrary exercise.
I made my original point to show that Bitcoin in its own right is unsuitable as a currency. It was never designed to replace or disrupt fiat currency and could never stand on its own. There simply isn’t enough of it. The design of the Bitcoin system makes it clear that it was meant to take advantage of the very system that many Bitcoin supporters want it to replace: fiat currency.
In other words, the collapse of the fiat currency system would also guarantee the collapse of Bitcoin. Bitcoin cannot practically exist without the fiat currency system.
With this understanding, it became clear to me that Bitcoin is simply a speculative vehicle designed to enrich its creators and early investors. It’s connection to fiat currency makes its use largely redundant. As I pointed out, it is not truly solving a problem. As a matter of regulation, third party trust elements will need to be implemented into the overall system. As for low transaction costs, those will likely rise and gain at or near parity with current money transfer and exchange offerings as the system is used more. The only truly enduring benefit of the Bitcoin system is transaction speed, but this would also likely degrade significantly as more people utilize it.
Here’s the heart of the matter: the proportion of Bitcoin in regard to everyone’s share of the total money pool never changes. On its own and without any exchange relationship with fiat currency, this translates into a fraction of a Bitcoin. This isn’t so much of a problem when Bitcoin is high in value, but definitely will have impact when its value in relation to fiat currencies is very low.
Would you really want to figure out how to live on a fraction of a Bitcoin?