In his pocket, Joe has an old leather wallet. It contains enough banknotes to buy him a brand new wallet of a better model he saw in a magazine. This buying power is exclusive to him, who alone can use those bills to buy something. Likewise, if he transfers them to another person, then instead of him, only this other person will own their buying power.
However, although Joe's transferring away his banknotes can always transfer along their control, it could never transfer along their entire property, which is not only his. The bills, as possibly distinct from their purchasing power, do not belong to him alone. For example, he has no right to create or destroy them: they are public . What belongs to either him or whoever else controls any such notes is rather their buying power, which is privately owned.
Indeed, by always just privately owning his banknotes, Joe could sell them independently of their purchasing power, which they could not represent. However, selling them in this way would prevent him at least temporarily from using the same bills to buy anything. Then, by recognizing their lost purchasing power as a monetary value , for keeping which they must remain its representations , one can conclude:
- All monetary value must be private.
- All its representations must be public, or unsellable.
Still, if not Joe, then who else can sell, buy, create, or destroy his or any equivalent banknotes? This question should be negligible if what he owns is their monetary value rather than the bills themselves. However, since the purchasing power of each bill can change once people sell, buy, create, or destroy other such bills, the same question becomes critical. Indeed, part of its answer is that now commercial banks create most of the money supply by selling it, in a process called fractional-reserve banking.
According to the Federal Reserve Bank of Chicago,  this is how fractional-reserve banking originated:
Then, bankers discovered that they could make loans merely by giving their promises to pay, or bank notes, to borrowers. In this way, banks began to create money.
Bankers also needed, however – and still need – to keep, at any given time, sufficient money to provide for expected withdrawals: "Enough metallic money had to be kept on hand, of course, to redeem whatever volume of notes was presented for payment. "
Here the name "fractional-reserve banking": commercial banks must hold a fraction of all deposit money as reserves – which legally (since 1971) need no longer be "metallic money" but only a public debt – to meet withdrawal expectations: "Under current regulations, the reserve requirement against most transaction accounts is 10 percent."
In a fractional-reserve banking system, on which most of today's international economy relations, commercial banks create money by loaning it, it is as a private debt .
Transaction deposits are the modern counterpart of bank notes. It was a small step from printing notes to making book entries credit deposits of borrowers, which the borrowers in turn could "spend" by writing checks, thereby "printing" their own money.
For example, once a commercial bank receives a new deposit of $ 10,000.00, 10% of this new deposit becomes the bank's reserves for loaning up to $ 9,000.00 (the 90% in excess of reserves), with interest yet without withdrawing the loaned money from the source account. Likewise, if that maximum loan of $ 9,000.00 does occur and the borrower deposits it into another account, whether in the same bank or not, then again 10% of it becomes the latter bank's reserves for loaning now up to $ 8,100.00 (the 90% now in excess reserves ). As always, the bank charges interest on the loan money since not withdrawing it from the source account. This process could proceed indefinitely, adding $ 90,000.00 to the money supply, valuable only as their borrowers' resulting debt: after countless loans of recursive 90% fractions from the original deposit of $ 10,000.00, that same deposit would have eventually become the 10% reserves for itself as a total of $ 100,000.00. 
Thus through stage after stage of expansion, "money" can grow to a total of 10 times the new reserves provided to the banking system, as the new deposits created by loans at each stage are added to those created at all earlier stages and those provided by the initial reserve-creating action.
Yet how can credit alone create new money? How can a debt retroactively create its owed money? Something else must be happening here, in addition to mere loans. What is it? What else happens in the whole process of commercial banking? First, there is a deposit. Then, there is a loan of up to a fraction (of 90%) of this deposit, at interest yet which the bank never withdraws from the source account. Finally, the borrower can credit that loan to another account, in the same or any other bank. Suddenly, the trillion-dollar question emerges: are these two accounts sharing the same value?
- Regarding deposit money the answer is yes: the loan can still belong to the balance of the source account, which is probably that same deposit money.
- Regarding account balances the answer is no: the loan can also belong to the balance of the target account, potentially being additional deposit money.
However, if the partial balances of both accounts must represent the same deposit money, then how can they duplicate it?
Privately Public Money
Distinguishing the letter "a" from its verbal sound would prevent this visual representation of that word. Likewise, distinguishing a banknote from its exchange value as money would prevent this concrete representation of that value.
The resulting discrimination between a representing entity and what it represents must happen to all representations of something dependent on them by something independent from them. Indeed, the letter "a" does not depend on its dependent word, or a banknote on its dependent trade value as money. Likewise, bank accounts do not depend on their dependent balance, nor precious metals on their dependent buying power. Anything that depends on being represented by something independent from representing it becomes indistinguishable from that representing entity.
Besides, only by being concrete can objects remain independent from what they represent, which they always do. Here, each alphabet letter, banknote, precious metal, bank account, or other self-independent representation, even if just imagined, must be concretely objective. While conversely, because money depends on its own representation, all its concrete representations must remain indistinguishable from their monetary value, despite this value and those representations being always respectably private and public.
So letting money concretely represent its own exchange value is inherently problematic: the resulting indistinction between this concrete money and that privately owned value must privatize its other public representation of the same value. Consequently, all such purely objective representations of money will require an impossibly privatized control of their still necessarily public, unsellable selves, whether by their private owners publicly selling, buying, creating, or destroying them.
Even so, Joe still privately controls the exchange value of his always public banknotes. Indeed, people have long expressed that value concretely, with not only banknotes but also countless other objects, including precious metals and bank accounts. Yet how could they do it? How did they solve the ownership conflict inherent in any such private public representations of money? How could each concrete representation of money be both private and public? The solution was to delegate its privatized ownership to a public monetary authority.
People had no other choice: any privatized ownership of a still necessarily public entity can only consist in the privatizing delegation of its public ownership. Then, all resulting delegates will institute one same body administrating or governing this public entity: the state or government , part of which must private control any object that concretely representations money.
However, the private and public ownership of one same thing are still mutually exclusive. Here, the public authority that results from privately controlling all concrete representations of money must rather be private. Occasionally, this conflict will segregate all administration of money by Governments into a privatized part of their public selves: a central bank. Indeed, any privatized power could only remain public as long as just part of it became private. So the same governments will become private by delegating all their control over money to that private part of themselves, which conversely will remain public just by relating to them.
Finally, regardless of government structure, concrete objects can only represent money by remaining privately public , although while privately owned by the public part of governments, even if also by their central banks. For which to be possible, any government already privatized into its own central bank must create this always privately public money by borrowing it from that bank. Then, this government not only buys the created money from its privatized inner self, as which it reciprocally sells it to its public whole, but also destroys that money by paying it back to its lender bank, if ever. While conversely, that central bank becomes the original creditor of all this privately created, publicly loaned money, of which it must create ever more to enable paying its interest. As that, with the resulting inflation and recursive interest payments, the same bank owns an ever-increasing fraction of the exchange value of all its issued money.
Still, even in the absence of any central bank, once commercial banks create money by loaning it to people who then use that money to buy public debt, or even just pay taxes, governments already borrow their money from the banking system, respectively indirectly. Then, the partial privatization of those governments only lacks a formal, institutional expression.
So bank accounts must be as indistinguishable from their deposited money as any such represent representations are indistinguishable from the money they represent. There are two deposits in different accounts being always different money, even if one is just a loan of money from the other: when depositing money borrowed from one account into another, people must duplicate that money, by mistaking it for both accounts.
Additionally, since all money created by commercial banks remains as just balance fractions borrowed from their client accounts, that money must be worth only as credit , or as the corresponding debt principal . This way, except for money regardless in reserves nor loans – and possibly not even in bank accounts, so not being excess reserves – but not from loans, bank loans are the only money supply left for paying their own interest. Consequently, such an interest-paying, self-indented money supply must grow at least at its own interest rate less any other money also excluded from bank reserves: historically, whether as loans or not, the total money supply must increase exponentially.
However, who does then create all needed new money? Before central banks, governments would have done it. Later, each new central bank has created ever-increasing amounts of that money on behalf of its government. Indeed, since the source account of any bank loan could have been the target account of other such loans, from which it would be then indistinguishable, banks can always replace that source account by debt instruments, including some representing a public debt. So by becoming central banks, they can create a new account money in exchange for promises from their governments of paying it back with interest, essentially the same way that they replicate part of that money in exchange for promises from their commercial clients of paying it back with interest . However, paying the additional interest on this new money, now created as a public debt will demand still more money. Then, the same banks will – as they always did – create ever more money from new public debt for paying interest on both private and old public such self-indented money. This way, all new money created as a private or public, interest-paying debt must recursively amplify any deficiency of itself initially solved by central banks creating still more of it.
The result is an exponential growth both of the money supply and the debt it represents, then a proportional, ever larger transfer of exchange value to the banks through inflation and interest payments, respectably, which must collide with social-resource limits. Constructively delaying this collision depends on a corresponding increase in the social production of wealth, which must rather collide with natural-resource limits.
Are there any alternatives to such an unsustainable economic system?
Abstractly Represented Money
Unlike the symbol for a verbal sound, its audible self can not become indistinguishable from what it means. For example, the sound of the word "everything" can not already be everything and still mean it. Unlike its visual representation, that sound is not recognizable independently of meaning something else, which which it must always be distinguishable.
Still, verbal sounds are not the only meaningful entities always necessarily distinguishable from their meaning. There are also public representations of a privately known entity. For example, the number three could represent a single, just possible number to every person while representing the actual number five only to Joe.
Then, people could publicize a number (like five) as referring another, private one (like three) without ever publicizing this private (the five-like) number as conversely referencing that public (the three-like) one. Public-key cryptography does specifically that: it uses two numbers or keys of which, although either number means the other, only the private key can reveal its corresponding public key. This way:
- Any content encrypted using the public key can only be decrypted by someone who also knows the private key.
- Any content signed using the private key can still be authenticated by someone who only knows the public key.
Using public-key cryptography, people can finally avoid privatizing their public representations of money, by representing any exchange value as a private key then representing this private key, or metarepresenting its represented value as the corresponding public key. For example, the Bitcoin decentralized network uses public-key cryptography to build signature chains , each link of which represents a balance transfer , or transaction . In Bitcoin, transferring the balance of one public key to another consists in combining the target key with the transfer that triggered in that balance, then signing this combination with the source private key. After which, any holder of the source public key can authenticate this new transfer as originating from whoever could sign it – necessarily by holding the source private key.
Then, money becomes a privately-signed yet public transaction chain despite never becoming itself public. For the first time in history, representing an exchange value (as a private key) does not require privatizing its publicly representing object (the corresponding public key). With such a metarepresented money, or metamoney , a public abstraction (a public key) can represent an exchange value (that of a private key) without ever becoming itself private – which makes its privatized control by any public authority not only unnecessary but also impossible.
Indeed, publicly expropriating money, whether by selling, buying, creating, or destroying it, requires privately controlling its public representing object, which then must be concrete. On the contrary, abstractly representing that money prevents all privately public entities from having any control of its representing object, then from necessarily expropriating an increasing fraction of its exchange value. While conversely, to avoid this privately public, though increasing expropriating control, each object representing money must be abstract – like a public key.
Finally, to be centralized – in a government or central bank – a public monetary authority must privately control what represent money, which then must be a concrete object. While conversely, to control an abstract representation of that money, this public authority must become decentralized – in a metamonetary system, like Bitcoin.
- Dorothy M. Nichols. Modern Money Mechanics. 1994. Written in 1961. Revised in 1968, 1975 and 1992.
- After twelve recursive loans of 0.9 excess in reserves each, a $ 10,000.00 deposit would have already become $ 10,000.00 × (1 – 0.9 12 ) ((1 – 0.9) = $ 71,757.0463519.