# The Questionable Mathematics of Bitcoin

Bitcoin by Sean MacEntee

In The Currency Paradox, I wrote about why Bitcoin is unsuitable as a currency. I included mercifully little math in my essay but, for the purposes of this post, I’m going to have to resort to a little basic math to make my point:

21,000,000 / 7,200,000,000 =

0.002916667

This is the amount of Bitcoin each person on Earth would own if the full allotment of units were divided equally.

21,000,000 / 2,400,000,000 =

0.00875

This is the amount of Bitcoin each working age person on Earth would own if the full allotment of units were divided equally.

21,000,000 / 120,000,000 =

0.175

This is the amount of Bitcoin each working age person in the U.S. would own if the full allotment of units were divided equally.

Right about now it should be dawning on you that there is absolutely no practical way Bitcoin can operate as a currency in its own right. Ever.

So what is the real reason behind the Bitcoin hype? It’s simple: speculation. The Bitcoin scene is more or less a cartel which is selling the convenience of Bitcoin as an exchange and payment mechanism to enrich those who got in on the ground floor.

The math clearly shows that there are far too few units to manage even the most basic economy. However, that scarcity is extremely valuable if Bitcoin is really designed to be a speculative vehicle.

It’s also clear that the only real value in Bitcoin is its exchange rate. Without the ability to exchange it for fiat currency, there is pretty much no true advantage in using Bitcoin as a common currency, at least not if you aren’t exceptionally gifted in fractional accounting.

Don’t get me wrong, I think the blockchain technology on which Bitcoin is built has revolutionary potential. But Bitcoin as a currency is just another exercise in the “greater sucker” theory. Buying Bitcoin won’t make you rich but it will make anyone who already controls a large amount of units very rich.

Caveat emptor.

## 27 thoughts on “The Questionable Mathematics of Bitcoin”

1. chromosundrift

Wow! So you mean if we use a different word and divide bitcoin into smaller units we somehow solve the problem you have with Bitcoin? If we use a unit of microbitcoins (some people are calling them bits but I prefer mics). Then problem solved?

1. James King (@M_Gauche)

Actually, no. The point that I was trying to make is that there are nowhere near enough units for Bitcoin to be practical as a currency in its own right. In order for it to be used practically, it will always have be be attached to a fiat currency. Pricing in fractional amounts, especially the minute ones that would be required for pricing goods and services in Bitcoin, solves absolutely no problem and creates quite a few, one being “infinite denominations.”

The odd thing is that the math I used was the most FAIR way to illuminate the issue. If I had used the current proportion of coinholders, 90% of coinholders would hold far, far less than my worst figure.

Bottom line, Bitcoin’s strength is as a speculative vehicle. If that’s your thing, great. You’ve got 9 million outstanding units and 100 years to make your fortune 🙂

1. chromosundrift

There’s nothing magic about whole bitcoins. Think of it like percentages. When you own USD you own some percentage of all units. You can shift the decimal place around and create a name for that unit. Same goes for gold.

The fact that there are 21 billion millibits. Not enough? Let’s use 21 trillion microbits. We can go on.

The difference between USD and Bitcoin or Gold is that USD is being printed at tens of billions per month, so your percentage is diluting.

2. James King (@M_Gauche)

As a common currency, what problem is Bitcoin solving?

As for your millibits and microbits, are they simply tenths and hundredths of Bitcoins? How is this an improvement on the basic math necessary for accounting with fiat currency?

Let’s look at the last number: 0.175. How would this be denominated in millibits or microbits? It’s already a precise fraction in base 10. How would you shrink this as to make this a whole number? 175 millibits? Then how is this an improvement of the current system? What problem does this solve?

The only supposed advantages of the BTC system is speed and no need for third party trust. But some form of third party trust will still be needed and implemented, especially if it is ever regulated. Think fraud protection or insurance. And then what is the advantage, speed? Cost of transactions? The speed may be nice but transaction costs will rise as the system comes into greater use.

No matter how you cut it, Bitcoin as a currency doesn’t solve a problem.

1. chromosundrift

You seem to be arguing against Bitcoin based on trust and regulation now. I’ll discuss those points with you if you consider the matter of “the questionable mathematics of bitcoin” resolved in my favour.

The main argument in your article is that there is some kind of obvious problem with having 0.175 as the average share of Bitcoins. I see no obvious problem with this because the currency is so divisible and we can use smaller units.

1. James King (@M_Gauche)

“I see no obvious problem with this because the currency is so divisible and we can use smaller units.” – chromosundrift

This is how a “satoshi” is denominated:

0.00000001 BTC

This is how I broke down my fractions:

0.002916667
0.00875
0.175

Do you see a difference?

No matter how you cut it, you are dealing with fractions of a fixed amount. Once again, what problem does that solve?

Every currency is transacted in its base unit. If the “satoshi” was the base unit, I wouldn’t have even written the post. However, that isn’t the case. The base unit is the BTC, which only has relative value in comparison to fiat currency. The value of BTC could crash and end up being worth less than a dollar. Then breaking it down into smaller units is a worthless exercise.

We could consider 50cent pieces dollars;
We could consider quarters to be dollars;
We could consider dimes to be dollars;
We could consider nickels to be dollars;
We could consider pennies to be dollars;
We could consoder half-pennies to be dollars;
to infinity.

The problem is that you actually can’t expand a money supply in that fashion, it’s instant debasement.

When the satoshi is the base unit of BTC exchange, I will concede the point. But then, I won’t have to.

No concession. You’re welcome to address the other points, though.

3. James King (@M_Gauche)

I understand your point perfectly well. The problem is that attempting to expand BTC in the fashion you suggest will result in instant debasement.

Let’s say you go from Bitcoin (1 BTC) to microbits (.1 BTC) in order to produce more units for distribution. The only way this will work is if everyone who has priced their goods in BTC converts to offering their goods in microbits. Otherwise, the purchasing power of the money will decrease by 90%, eliminating the value of having “expanded” the money supply. Even if all merchants and others agreed to move from BTC to microbits, the value of everything would still drop 90% relative to transacting in Bitcoin.

No matter how you cut it, you are dealing in fractions of a fixed amount. By nature, the money supply will NEVER expand, regardless of how many decimal places to the right you move.

The metaphor that I used in my essay is using an eye dropper to distribute a bucket of water rather than a cup. You may get more servings of water from an eye dropper but you’ll still distribute the same amount of water.

No matter how you cut it, the proportions are the same. .175 BTC is the exact same thing as 175 microbits.

1. Max Kaye

It doesn’t result in debasement because the proportion of the total supply controled by each individual doesn’t change.

We’re not actually suggesting redefining what a ‘bitcoin’ is. By definition a Bitcoin is 1/21,000,000th of the eventual total supply.

When you say “Right about now it should be dawning on you that there is absolutely no practical way Bitcoin can operate as a currency in its own right. Ever.” I *presume* (because it is not obvious) that you’re making the claim there are *physically not enough units* to allow Bitcoin to act as an effective currency (I say effective because you can easily have a currency where each fundamental unit is worth something crazy like a house, it’s just going to be a pain to use).

The physical number of units is currently measured in satoshis, however, if we were to modify the protocol we could make the fundamental unit the microsatoshi (10^-6 satoshis) and the fundamental value proposition does not change because we have simply increased the divisibility of each coin.

When you say “As for your millibits and microbits, are they simply tenths and hundredths of Bitcoins? How is this an improvement on the basic math necessary for accounting with fiat currency?” there are two comments to be made.

1. Not tenths and hundreths but thousanths and millionths (since we’re talking SI units)
2. Fiat currency involves a reasonable constant value per unit and expanding supply. Bitcoin involves a non-constant value per unit but fixed supply. We don’t need a continually expanding supply if we can become more precise with our measurements (more significant figures). This is because the fundamental requirement as demand for a money supply grows is the ability of that supply to adequately represent value on a useful scale. Bitcoin deals with this differently than inflationary fiat.

I don’t know why I wasted 15 minutes typing this to you. Just sit down and think about a supply without thinking about units. Think about it in terms of proportion of that supply that each person controls and how that changes and is manipulated over time, either by trade or inflation or mining.

1. James King (@M_Gauche)

“It doesn’t result in debasement because the proportion of the total supply controled by each individual doesn’t change.

We’re not actually suggesting redefining what a ‘bitcoin’ is. By definition a Bitcoin is 1/21,000,000th of the eventual total supply.” – Max Kaye

This is exactly the point I made.

“The physical number of units is currently measured in satoshis, however, if we were to modify the protocol we could make the fundamental unit the microsatoshi (10^-6 satoshis) and the fundamental value proposition does not change because we have simply increased the divisibility of each coin.” – Max Kaye

But you actually haven’t increased supply, it is simply a math trick. You instantly destroy the purchasing power of the money by dividing it more.

Think of how gold used to be debased … the coins would be DIVIDED and a cheaper base metal would be added. The results was MORE COINS but not MORE GOLD.

You are doing the same thing digitally, just without the cheaper metal.

“1. Not tenths and hundreths but thousanths and millionths (since we’re talking SI units)” – Max Kaye

Doesn’t matter how you divide it. Supply doesn’t increase, each unit become worth less in CURRENT PRICING.

“2. Fiat currency involves a reasonable constant value per unit and expanding supply. Bitcoin involves a non-constant value per unit but fixed supply. We don’t need a continually expanding supply if we can become more precise with our measurements (more significant figures). This is because the fundamental requirement as demand for a money supply grows is the ability of that supply to adequately represent value on a useful scale. Bitcoin deals with this differently than inflationary fiat.” – Max Kaye

That is my point. There aren’t enough units to viably represent a modern economic system. Bitcoin is the equivalent of locking everyone in a box and expecting them to shrink in order for everyone to have room.

“I don’t know why I wasted 15 minutes typing this to you. Just sit down and think about a supply without thinking about units. Think about it in terms of proportion of that supply that each person controls and how that changes and is manipulated over time, either by trade or inflation or mining.” – Max Kaye

The worst part is that you do not seem to have read your own response with a critical eye. You’ve more or less supported everything I’ve stated.

1. James King (@M_Gauche)

Read my response above. No matter how you cut it, it’s debasement. Supply doesn’t increase, you are just redistributing smaller pieces. Whatever current pricing is set at, the value of the money drops every time you divide it.

Debasement is when you increase the supply, not divide it. Gold is debased by the addition of other metals, not the use of smaller amounts of gold.

You have things backwards.

Bitcoin is not debased, it is divided into, say, the percentage of the total supply that is enough to buy a coffee. Today that may be a few millibits. If it becomes a few micro it’s then it is because relative to coffee, bitcoin has increased in value, like gold has in the past and exactly like the USD has NOT.

1. James King Post author

Debasement is when you lower the value of a currency. This was done with gold coins through dilution with cheaper base metals.

The reasons Bitcoin has increased in value RELATIVE to the dollar is its scarcity, perceived utility, and the increase in dollar supply.

I’ve written a post re: this thread. It’ll be up Thursday.

Debasement is the reduction in value yes, by the increase in supply of coins without an increase in gold. You are right to call it dilution, also inflation. In the case of gold coins it is fraud, in the case of USD it is called monetary policy and in the case of Bitcoin it cannot happen.

So now do you understand why Bitcoin has a fixed money supply?

2. James King Post author

I never debated this point. I stated that it is not enough to manage an economy and it isn’t.

As for Bitcoin not being able to be debased, you are incorrect. More this Thursday.

5. joefish75

This one is simple. There are a million “bits” (also called microbits in a bitcoin). Each ‘bit’ can be dived into a hundred ‘satoshis’. This means there are max 21,000,000,000,000 bits (21 trillion) available, or 2.1 quadrillion satoshis. I am personally pushing for the usage of ‘bits’ instead of BTC in most software to avoid exactly the confusion you’re talking about.

Dividing the currency also is not debasement/inflation – it’s not _creating_ new currency, it’s splitting the amount down for more exact measures. This is just like splitting gold down into ounces instead of pounds, or counting fractions of a cent (like some mobile providers do).

The amount of currency actually created is consistent and levels off in the Bitcoin network, which is one of its attractions

1. James King Post author

This doesn’t matter as I’ve pointed out. I can split a dollar into 100 pennies. That has no meaning if there are not enough dollars. More on Thursday.

1. James King Post author

There are only 21 million possible Bitcoin and roughly 13 million in circulation. My point was that it doesn’t matter how many satoshi there are as it doesn’t matter how many pennies are in 3.9 trillion USD.

2. chromosundrift

James you are wrong. Many people have tried to explain the same thing to you.

Dividing a currency unit into sub parts solves the “problem” you were originally talking about. Please just convert everything into percentages and you will see.

Of course, it’s not actually a problem because the solution is so obvious (except to you).

The only currency distinction actually worth discussing is the difference between fixed supply and expanding supply. If you are not talking about this, then you have a simple mathematical confusion going on.

If Bitcoin goes up in value then we will all happily use smaller divisions of Bitcoin to buy things and this has already happened several times.

What you are missing is the supply and demand side of currency exchange.

If everyone in the world was simultaneously determined to get enough Bitcoin to buy a house, then, although as you point out they will only be able to get 0.175 Bitcoins (or 175,000 “bits”), the value of this much Bitcoin will be pushed up until either it is enough to buy a house or people change their minds. Scarcity and demand produce an increase in prices.

This is high school maths and economics. If you are writing essays at this level then you should do more research and pay attention to your commenters more carefully. You should look up milli and micro before you post. You should understand the economics of supply and demand, the meanings of inflation and deflation and monetary policy. The people commenting here know what that stuff means and you are yet to learn it.

3. James King Post author

I clearly wrote that the only real value in Bitcoin is the EXCHANGE RATE. Bitcoin only makes sense because it can be exchanged with fiat currency.

But imagine if you COULDN’T exchange it. Then the fundamental flaws become clear. Its debasement is a matter of mathematics. It would be impossible to run an economy with Bitcoin in its own right.

You look at a BTC and immediately associate it with its exchange value. But that value is subjective. Remove the exchange rate as a factor and its apparent that Bitcoin is fundamentally flawed. Those flaws will play out even relative to its exchange rate over time. It’s a matter of mathematics.

What you and your friends are not taking into account is market pricing. How will going from one denomination to another affect market pricing? When you move down to smaller denomination how does this affect market pricing? Once you understand that, you’ll get my point. Think of how such a change would be reflected in purchasing power related to prices WITHOUT considering exchange rate, just Bitcoin itself.

4. James King Post author

Ironically I have been incorrect about something. What I haven’t understood is that the exchange rate acts as the “cheaper base metal” in Bitcoin debasement. It’s what allows the divisibility without penalty. But this proves my point that Bitcoin cannot stand on its own as a currency. It’s tied forever to fiat currency.

6. chromosundrift

I’m sorry James, the “fundamental flaws” are not clear enough for me.

“I clearly wrote that the only real value in Bitcoin is the EXCHANGE RATE.”

That’s an incredibly strange sentence. Reading further, you seem to be saying that if Bitcoin was on its own without another currency to exchange with then there would be some kind of mathematical problem that the economy could not survive.

You also appear to believe that you have explained this problem but if you have then I have not understood it at all.

Maybe it’s my fault.