Yes, Bitcoin Fans, It’s Debasement

romancoins-20071009100243My 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:

1,000,000.0000001

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?

Advertisements

8 thoughts on “Yes, Bitcoin Fans, It’s Debasement

  1. chromosundrift

    You are horrifically confused, James.

    “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.”

    You are showing here that you have not understood the notion of division. You mention “creation” – we have discussed not addition (which is what happens in an inflating money supply) but division by a power of ten. This is equivalent to moving 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.”

    Do you think anyone has been talking about inserting zeroes into a number in this way? Is that how you think division works? Your example is a nonsensical contrivance. While you’re inserting zeroes, why not put a two either side of the decimal point and maybe sprinkle a few more decimal points around for decoration? You need to study high school mathematics. Division and multiplication by powers of ten.

    “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.”

    How much is enough bitcoin to “stand on its own”, whatever that means?

    Reply
    1. James King Post author

      I’m afraid you are horribly confused. You obviously do not understand division yourself or the concept of currency debasement.

      1) adding a zero to the right of the decimal does indeed create 1/10 of the previous number TO THE RIGHT of the decimal mark, NOT the entire number. I thought I was clear with that point.

      2) It is you who needs help with basic math. Adding a zero immediately to the right of the decimal point is EXACTLY the same thing as moving the decimal point over one space to the left for the purposes of the figure strictly to THE RIGHT of the decimal point, NOT the entire number.

      3) Whatever it is, it isn’t 21 million units. As shown, without a correlation to fiat currency, the purchasing power for everyone on the planet is a fraction of a bitcoin, even less as they are permanently lost.

      This is a simple concept.

      Reply
  2. chromosundrift

    “1) adding a zero to the right of the decimal does indeed create 1/10 of the previous number TO THE RIGHT of the decimal mark, NOT the entire number. I thought I was clear with that point.”

    You were clear on this point in that I understand completely what you mean.

    It’s as if you were saying the moon is made of green cheese. That is an unambiguous statement. It also happens to be an irrelevant fiction.

    When you have a large sequence of digits with a decimal point in the middle as in your example, we call this whole thing a number. Dividing that number by a “power of ten” is equivalent to moving the decimal point. What this means in terms of “adding a zero” (if you insist on calling it that) is that you add a zero on one side of the decimal point and remove a zero from the other side of it.

    That is division.

    If you do not move the decimal point and merely insert a zero just to the right of the decimal point without removing one from the left of the decimal point then what you are doing is not division by 10.

    To explain the consequence of this in terms of “the number to the right of the decimal point” suggests that you have forgotten that the whole thing is one number. We should only be concerned with the whole number. It is the whole number that is being divided and the whole number is indeed going to be 1/10 of the original number if you divide by 10.

    10.1 divided by 10 is 1.01
    10.01 divided by 10 is 1.001
    100.001 divided by 10 is 10.0001

    Do you agree with these? Do you notice that in each case you do not gain or lose zeroes between the 1s? If you do, then we have a glimmer of hope in proceeding to your other topics in agreement. If not, then your definition of division is irreconcilably different to mine and I welcome any guidance from you on reputable sources that I can use to correct my incorrect understanding.

    Reply
    1. James King Post author

      You are being literal for the purposes of invalidating the example when it is clear that I am treating both sides of the decimal point as two SEPARATE numbers for the purpose of the example. The fact that it is all one number is semantics. There are actually TWO numbers there which are juxtaposed with the decimal point. You are being deliberately obtuse.

      In any case, you still haven’t disproven my point. The 21 million units act as a fixed point for which any additional units must be created as a result of division. Bitcoin is considered deflationary because of its fixed supply but RELATIVE TO ITS RELATIONSHIP WITH FIAT CURRENCY that isn’t the case. As its value in fiat currency increases to the point that one BTC is worth too much to exchange efficiently, then it must be divided. This is an inherently INFLATIONARY process that is practically identical to currency debasement.

      As I stated, it’s a simple concept.

      Reply
      1. chromosundrift

        I see you have decided not to answer whether you agree with my divisions! I will give you the benefit of the doubt and assume that since you have focused on other objections that you do not disagree.

        Also, I can see you are getting frustrated. I hope you see by my tone, that while I may also be frustrated that we are not achieving a common understanding, I am communicating in good faith and attempting to be as clear and correct as I can. Hopefully you are also.

        “You are being literal for the purposes of invalidating the example when it is clear that I am treating both sides of the decimal point as two SEPARATE numbers for the purpose of the example. ”

        It’s clear that you are doing this. What’s not clear is why. Why on earth would you cook up your own concept of numbers? Does your argument depend on it? If not, perhaps you could consider an example that uses normal decimal numbers. The example you are giving is unrelated to the question of whether there are enough currency units and the fact that you are inventing your own exotic numeric operations suggests that you have misunderstood the explanation given to you why 21 million Bitcoins can be sufficient.

        As for “invalidating the example” I certainly consider it utterly invalidated. The point your example is supposed to make is hopelessly absent. I posited (several times) that because bitcoin can be divided, the distribution is plentiful. In several cases you have expressed some doubt that merchants have the ability to handle changing from BTC to mBTC but this is demonstrably false since it has already happened. It is expected to happen again (see the debate on the naming of the “bit” as an alias for one millionth of a bitcoin). I’m not seeing you pursue this point but this argument of yours is certainly coherent. It’s still not convincing, but only because the facts show that it’s not an obstacle in practice, but at least the theory was clearly stated in terms that are not under contention.

        “Bitcoin is considered deflationary because of its fixed supply but RELATIVE TO ITS RELATIONSHIP WITH FIAT CURRENCY that isn’t the case.”

        What is the relationship between fiat currency and Bitcoin? I see you are EMPHASISING this key phrase, but the phrase has an utterly opaque meaning. It’s not only vague, it’s ambiguously phrased and it’s unsupported by evidence or explanation. Are you referring to an “exchange rate” between one specific fiat currency and Bitcoin? If you are, the sentence presumably should be interpreted as “relative to its exchange rate, bitcoin is inflationary”. I can’t imagine what you might mean by this. How can something be inflationary “relative to” an exchange rate? Do you just mean that the exchange rate is changing over time? That’s not the same thing as inflation. Inflation is the degradation in purchasing power of money, not the mere increase in prices due to changes in demand.

        “As its value in fiat currency increases to the point that one BTC is worth too much to exchange efficiently, then it must be divided. This is an inherently INFLATIONARY process that is practically identical to currency debasement.”

        No. Both inflationary processes and debasement involve an *addition* of new supply, not a division of a fixed supply into smaller subunits. This is your fundamental error. It’s precisely the difference between addition and division. It’s also a difference of price movement based solely on a change in demand as opposed to one based on a change in supply. Inflation requires increased total supply.

        At risk of derailment, if you have a half-cup of milk and you tip it equally into two other cups, you have divided the milk into two quarter cups. Two quarter cups are equal to one half cup. The supply has remained fixed. Debasement is if you water down your cups of milk such that you have, say, two half-cups of “watery milk”. Note the defining difference here is the *addition* of water.

        In this metaphor, the milk represents the value and the cup volumes represent the units. Water in this case, represents an increased supply, but without the addition of actual value (nourishing milk). Inflation is the increase in supply and the consequent commensurate decrease in demand.

        Bitcoin subunit division is like the separation of milk into more vessels, not the addition of water. Inflation and debasement are like the addition of water. It’s an important difference.

        Considering gold for a moment, if we came up with a way of turning lead into gold, it would be as if we had a cow that can create new supply. Of course, if you have a cow, you could flood the market with milk (literally!) If you did this, the amount of milk you can trade for a dollar, or for bacon, gold or, anything else, this amount would go down. Milk would be everywhere and nobody would pay a high price for it. Likewise, if the supply of milk is fixed (as is the supply of gold or Bitcoin), the market will not be flooded. Assuming everyone knows the milk supply is fixed, milk is a scarce commodity, and assuming there’s a desire for the milky nourishment (the features of the asset) then the price can go up. People with only a dollar might only be able to buy a thimble full of pure milk. This is the process of “price discovery” that all free markets demonstrate. Being a fixed supply, milk was divided to accommodate the limited purchasing power of the people, but milk was never debased. Milk can of course be debased with water but that’s not possible with Bitcoin, it’s always 100% pure, so in my milk metaphor, that’s why I draw attention to the consequences of the typically traded units being of 100% pure milk only.

        Bitcoin may be divided to ensure there are enough pieces so that everyone can buy, say, a coffee with a couple of units. Today the name of that unit is the millibit and is equal to 1/1000th of one Bitcoin (there’s no need for you to borrow the term q-bit from quantum computing). One day we may need to go down to microbits which are millionths of one Bitcoin. This has already been explained to you, but it doesn’t affect the supply of Bitcoin and there is no “relationship to fiat” to speak of.

        In the case of most fiat currencies and also of gold coins that are debased by “base” metals (which you mentioned), something is *added* to the supply. The amount of fiat increases because new fiat is printed. This is addition, not division. In the case of the debasement of gold coins, base metals are added so that there are more coins. The coins have less gold in them and if you value the coin through only the gold content, each coin is worth less because of this. You must be aware, however, debasement causes a reduction in value per unit only because of this addition, as the introduction of coins without as much gold is an increase in the supply of coins. This should not be confused with the division of gold as a decreasing proportion of a larger number of coins. Gold supply is fixed and any use of pure gold is, by definition, not debased. Again, the debasement depends critically on *addition*.

        If you have a money supply of 21 million Bitcoin and you want everyone to have some, you are right in concluding that there will not be enough for everyone to have a whole Bitcoin each. This is obvious, but it’s not a problem. Because while there are 21 million Bitcoins there are 21 BILLION millibits. If that’s not enough then there are 21 TRILLION microbits. If that’s not enough you can continue to divide them until there are enough (minor protocol changes are necessary at some point).

        Bitcoin does not get debased because there is no base “metal” introduced to the “coins”. There is no digital equivalent of copper or whatever metal was traditionally used to cut the purity of gold coinage. Division of Bitcoin is not debasement, it’s more like using gold dust. Gold dust is just as pure as gold nuggets, but smaller pieces. The only reason to divide gold or bitcoin into such small pieces is if the value goes up. If it doesn’t go up, you don’t need to bother. If gold was about the same value per ounce as coffee, perhaps you could exchange a nugget for a coffee? As it is I think you’d need dust amounts.

        Note the value I’m talking about here is purchasing power – relative to all goods, not specifically to fiat. If the value of Bitcoin does not go up, then no problem, because this implies that people do not desire it much. The world population will not compete to get the currency if it is not valuable. It will therefore not need to be divided. When the Bitcoin economy was smaller, whole bitcoins were worth less than a cent and many thousands were necessary to buy a pizza. Was your argument stronger then? If people see value in Bitcoin (because it has utility after all) then they will try to acquire it and this “demand” as it is called in economics will drive the price up. This is the “law of supply and demand”. In this rising price scenario, the increased price prompts us to subdivide the currency such that we speak in units which are convenient for coffee purchases.

        Fiat currency does not have some kind of primary “relationship” with Bitcoin. Your repeated insistence that there is a relationship which somehow confines the purpose and definition of Bitcoin is unsubstantiated and unexplained – yet it is a recurring assertion. Ask yourself if the same arguments apply to pure gold as traded on the world’s gold exchanges. Bitcoin and fiat, bitcoin and gold, gold and fiat or AUD and USD are just asset pairs that have an exchange rate (otherwise called a price) but that is the only “relationship”. The price of Bitcoin could just as well be measured in t-shirts, and in fact on sites that sell t-shirts for Bitcoin, it is.

        The root of your problem here is that I think you forget that prices are fundamentally affected by the denomination of the majority of one’s costs. If a t-shirt manufacturer sells t-shirts to a printer for dollars, then the price at which the Bitcoin t-shirt shop must sell them for a fixed profit margin will depend on the exchange rate between dollars and bitcoin. This is true today when we buy things from other countries. The USD is a widely held “reserve currency” which makes things a bit confusing, because it may lead you to believe that this status is a permanent fixture of global economics. It’s not. We see that BRIC countries are increasingly distancing themselves from the USD as a reserve and this exposes increasingly, the fact that the USD is just another currency.

        The price of T-Shirts in dollars depends on the “exchange rate” (again, just another name for “price”) between cotton and dollars. If crops are ruined, and supply is reduced, we might expect the dollar price of cotton to go up. This will affect the dollar price of t-shirts. It can just as easily be seen to affect the bitcoin price of t-shirts without reference to dollars, but if the cotton is not available for sale in Bitcoin, then the importance of the Bitcoin-dollar exchange rate is forced. This is, hopefully, quite clearly a function of the cotton producer’s inclination to accept Bitcoin. There’s no less reason for her to accept bitcoin than for the t-shirt shop.

        If both sides of the Bitcoin transactional economy grow, we will see an increase in Bitcoin’s value and a growing necessity for dividing Bitcoin into smaller units. But the money supply of Bitcoin will not be increased, and therefore nor will it be debased. No new bitcoin will be added after 21 million BTC. It will be pure like gold dust or thimbles of milk. US Dollars, if they are continually printed, will continue to lose their value as they have for a century, currently standing at around 2% of their original value (when compared to a CPI basket) and when compared to gold, the ratio is way higher.

        So I reject fully your repeated statement that Bitcoin is inflationary due to it’s “relationship with fiat”. Bitcoin has no relationship to fiat beyond its exchange rate with it. This rate is determined by a free market through a price discovery process of an (ultimately) fixed supply of 21MBTC but a changing demand. The need to divide bitcoin is therefore a function only of its purchasing power which is in turn driven by demand for it.

  3. James King (@M_Gauche)

    So the basic premise of Bitcoin is that ALL resources that will EVER be produced, discovered or created will have a total value of 21 million units.

    More resources means each Bitcoin will increase in value. To accomodate the increase in value of Bitcoin relative to resources IN GENERAL, Bitcoin are divided to more finely match determined values for specific items, etc.

    OK.

    Now, what does a house cost in Bitcoin?

    What does a car cost?

    What do a pair of shoes cost?

    None of these items are priced purely in Bitcoin.

    The point that I’ve been trying to make is that, by having an exchange rate with fiat currency, Bitcoin is indelibly tied to the fiat currency system.

    Under THOSE circumstances, I’m 100% correct that Bitcoin is simply debased currency.

    You are assuming a transition at some point to PURE Bitcoin pricing. I will concede that such a thing is possible and that, in theory, 21 million units is more than enough.

    However…

    How do we get to that point? Why would people choose to invest in the Bitcoin system? What does it offer to those who are ALREADY RICH? What benefit is there for them to upend the system?

    Why would central banks or governments abandon their fiat currency monopolies? For that matter, how will things be priced purely in Bitcoin? What is fair value for anything in Bitcoin?

    You’re confusing what is theoretically possible for what is likely.

    And the main problem is that the total value of Bitcoin doesn’t actually encapsulate the value of ALL resources at this point but roughly 7 billion dollars worth of resources in FIAT CURRENCY.

    The long-term issue with Bitcoin is that it requires almost EVERYONE on the planet to PURCHASE them and THEN abandon any relative relationship Bitcoin has with fiat currency. The ones who will benefit the most are the creators and early adopters and investors in Bitcoin, sowing the seeds of a new financial elite.

    Again, why in the hell would the entrenched elites buy into that? For that matter, anyone who can do basic math can see that Bitcoin would make global inequality even MORE of a problem as the relationship to fiat currency has made them very easy for people who already control a shitload of fiat currency to acquire them in far greater proportion to their supply.

    I think I more clearly understand what you are getting at but the confusion was created because Bitcoin doesn’t work like that RIGHT NOW. What gives Bitcoin value RIGHT NOW is fiat currency. Otherwise, it is a worthless mathematical exercise AS A CURRENCY.

    I didn’t even address creating a global economic system that would be crippled or destroyed by anything that threatens global electrical power. The Earth recently was almost hit by a massive solar flare that would have disrupted elctrical power on a global scale.

    You’ve convinced me that it is theoretically possible to manage an entire economy on 21 million Bitcoin. You have not convinced me that it is practical.

    Reply
  4. Pingback: What Satoshi Got Wrong | The Currency Paradox

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s