Representing Value

rai stone
An 8 foot rai stone used as currency by inhabitants of the Yap islands. Image obtained from Wikipedia under GFDL license.

I start this blog by considering the following very basic question. How can we represent and transact value? A store-of-value asset or currency, whether it is Bitcoin, Ether, the US dollar, gold, or whatever else, has to have and maintain value to be useful. The dictionary definition of the word ‘value’ is not a lot of help: “the regard that something is held to deserve; the importance, worth, or usefulness of something”. This is rather circular. To be useful as a currency, we want an asset to have value but, to have value, it needs to be useful.

Consequently, I will take a slightly different tack. Rather than saying how to make something have value, I consider the bare minimum properties that an asset should have in order to be able to be used to represent value. Whether or not people then want to assign it some value is up to them.

I start with the idea of ownership. This does seem to be central to the ability to represent value. If you cannot exclusively own an asset, then you cannot use it to represent any value that you may want to store. If anyone can just take the asset from you, then can it ever be considered as yours in the first place?

Before anyone complains that this seems a rather individualistic idea of value (property is theft!), let me point a few things out. A public park is valuable, and is a community asset. However, this is a different type of value from that which is represented by money or a store-of-value asset. A park has utility. You can sit in it and enjoy the sun, kick a ball around, or go for a walk. When it comes to paying the park-keeper for cutting the grass, emptying the bins, cleaning out the public toilets, or other tedious tasks, then he or she will probably appreciate being paid in some asset which they can actually own and use to better the lives of themselves and their family. Similarly, the shops in your local high street may be valuable to the community, but if you were to simply pay the shelf-stackers by letting them visit the high street, which they can do anyway, then it would be difficult to find people to do the job. The value that we are interested in here is the more abstract kind, used as a medium of exchange or store-of-value, which can be held by an individual or organization with the aim of exchanging for something with utility when desired.

With the above explanations out of the way, any meaningful idea of ownership of a store-of-value asset or medium of exchange requires the following.

  • The holder of an asset should be able to prove ownership.
  • The holder should be able to transfer ownership to another party.

The second of these properties does imply the first since, transferring ownership will involve proving that you were the owner prior to the transaction. This is only half of the equation though. Just as important as what holding an asset allows you to do, is what not holding the asset stops you from doing.

  • No-one other than the holder of an asset should be able to prove ownership.
  • No-one other than the holder should be able to transfer ownership.
  • Supply of the asset should be limited.

The first two properties are self-explanatory. If you hold an asset, but other parties are able to prove that they own it, or are able to transfer ownership away from you without your permission, then it cannot really be said that you own the asset in any practical way. Implicit in these properties is that, once you have transfered ownership to someone, you no longer own the asset so are not able to change your mind and take it back or transfer it to someone else instead. This is actually an important point, and the solution of this so-called double spend problem in a decentralised way was one of the main factors in the invention of Bitcoin.

The final property, that of limited supply, does require some explanation. Medium of exchange assets such as the US dollar are fungible. One dollar is just the same as any other dollar. You may have $1,000 in a bank account, for example, but few people would care about which dollars are yours and which are not. It is only the amount that matters. When you withdraw money, the bank will not ensure that you receive back the very same dollar bills that you paid in. With that in mind, the dollars would be worthless if anybody could just print as many new dollars as they like, with no way to distinguish these newly printed dollars from the ones that you own. Why would you even care about your bank account if you could just print new dollars yourself anyway?

On the other hand, this does not mean that it has to be impossible for anyone to create new currency for it to have value. Governments or central banks can create new fiat currency, such as printing new US dollars. Yet, the US dollar maintains value over time. It may not hold a fixed amount of value indefinitely. In fact, due to inflation, this is certainly not the case. However, the US dollar maintains value sufficiently well to be useful for commerce, paying salaries, even for saving. So, the ability of governments to print new currency does not remove the usefulness of that currency.

By requiring a limited supply, what we mean is that there are strict restrictions on the creation of new assets. This could mean that creation of new assets should be impossible, or that it is very difficult, that there is a limited quantity of new assets that can be created, or that creation of the assets is restricted to some trusted parties. In the case of Bitcoin, new coins are created only by miners creating new blocks and, furthermore, they can only create a pre-programmed quantity per block. For naturally occurring minerals like gold, the restriction comes from the difficulty of the mining process and, for fiat currencies such as the US dollar, creation of new supply is controlled by the government.

A corollary of the properties outlined above is that, if we want to get our hands on some of the asset, then we need to do one of two things. First, we can persuade someone to transfer ownership of their asset to us. This is likely to be accomplished by transferring something of equal or greater value to the existing owner, such as by purchasing it directly from them or by them using the asset to purchase some item from us. Once this occurs, then the asset is already being used as a medium of exchange. The second method is to directly create new supply that we own, such as mining for gold or Bitcoin but, by the requirements, there should be limited ability for us to do this, or should at least require some expenditure from us to create this supply.



As an example, consider gold. This has been used as money for millenia and is still used as a store-of-value. Ownership of gold is easy to understand. You just need to have it in your possession. Maybe you carry it in your wallet in the form of gold coins, or have gold bars stored away in a safe to which only you or a trusted friend has the key. If someone wants to transfer ownership to themselves without your permission, they need to steal it by taking your wallet, breaking into your safe, or get past whatever other security you may have. Transferring ownership is straightforward for the owner. You simply take some coins from your wallet, or unlock your safe and remove a bar, then hand it to the other party.

The final point concerning the supply is also easy to understand. Creating brand new gold is almost impossible. Although it has been created from other elements using nuclear reactions, this is a very expensive way to create tiny quantities of gold. More likely, if you wanted to create more supply, you need to mine it. This is still expensive, and it is only economical to increase mining activity when the gold price is high enough. It is estimated that about 1,500-2,000 tonnes of gold are mined per year, which is about 1% to 2% of the total above-ground stocks.

The properties of gold are what many people will instinctively think of when the idea of ownership or exchange of an asset is considered. That is, ownership corresponds to physically having the item in their possession, and exchange of ownership is performed by giving the physical item to another party. This is misleading though, as many assets used as a currency are not like this. We may hand over dollar bills to someone in a shop to pay for an item but, just as likely, we would use a payment card which does not involve exchanging anything physical, even if we have a mental image of such an exchange taking place. Even gold itself is mainly traded as paper gold. This could be in the form of an ETF (exchange traded fund) which is backed up by some gold held in a vault somewhere. We trust that the gold does really exist corresponding to the ETF, but no physical gold changes hands or is affected in any way when units of the ETF are bought and sold between parties. Most of the time, the gold backing up its value does not play any direct part in the trading of the paper gold.

Rai Stones

rai stones

A very interesting form of money has been created by the native inhabitants of the Yap islands in Micronesia. These rai stones are sometimes used as an example demonstrating how value can be created through a shared belief in that value. As such, they are often compared to Bitcoin. In this sense, rai stones represent a rather abstract form of value even though the stones themselves are physical objects. Very physical. If one hit you on the head, you would know about it.

Rai stones were mined on certain Micronesian islands, mainly Palau, then transported back across the ocean to Yap. They are roughly circular discs of stone, with a hole through the center. Although sizes varied, large rai stones could be over 3 meters in diameter, so their transportation was very difficult. The whole procedure of mining and transporting these stones was an arduous process which could take years, result in deaths of those involved, and it was common for stones to be lost due to capsizing of the boats or rafts on the return journey. Once delivered to the Yap islands however, they were highly prized.

An interesting aspect of all this is that, once put in place in Yap, the stones were rarely moved. For the largest stones, moving them would have been a difficult task anyway, and they were mostly left in place. Even so, it was agreed as to who the owner of each stone is. The stones would be used in financial transactions, even though they would not be moved. So long as the Yapese society is in agreement as to who the owner is, then this ownership can be transferred without any physical movement of the stones themselves. Wikipedia mentions that they were, and still are, used in rare important social transactions, such as marriage, inheritance, political deals, sign of an alliance, ransom of the battle dead, or, rarely, in exchange for food.

Taking things a logical step further, there are cases where large rai stones were lost at sea, never to be seen again. However, the fact that they could agree that the stone still exists, even at the bottom of the ocean, still allowed the Yap inhabitants to use the lost stones as a store of value.

Ownership of a rai stone would not seem to offer any direct utility, not even the ability to display it proudly to visitors at your home. The stone just stays in its location regardless. There is only the societal agreement that you are the owner, and that it has value. In fact, we could wonder whether the stones even really needed to physically exist in the first place, especially since some were lost at sea but were still able to be used in their physical absence for their intended purpose. However, the difficulty in obtaining the stones seems to be a large factor in determining their value, which would not be the case for purely imaginary items. It has been suggested that obtaining rai stones was the original ‘proof of work’ protocol.

US Dollars


Once upon a time, the value of a US dollar was tied to the value of gold. Although the quantity of gold backing a single dollar changed over time, this link was dropped altogether in 1971 with the ending of the gold standard. The US dollar is now a fiat currency whose value freely floats on the currency markets according to supply and demand.

We could think of dollars in terms of the physical items of dollar bills, quarters, etc. These notes and coins can be held and physically passed between the parties of a transaction, much as can be done with physical gold. This is misleading though. Although dollar bills can be used in this way, the majority of US dollars do not exist in this form. Banks hold dollars in the form of federal reserve deposits, which do not exist as actual dollar bills, but can be converted to such physical money if required.

Next, consumers hold US dollars in the form of bank accounts. Due to fractional reserve banking, there is no requirement for the bank to actually have this money available either in the form of physical dollar bills or as federal reserve deposits. Only a fraction of the money in their customers accounts is required to actually be held by the bank. Really, then, most dollars only exist as numbers in the databases of the banks, and are assigned to the individual accounts. These represent liabilities for the bank, since they are owed to the account holders.

When a payment of dollars is made using a payment card or other virtual payment method, then the banks involved will subtract the amount from the account of one party and add it to the account of another. Numbers are being updated in databases, but no immediate physical exchange is occurring. From this perspective, US dollars and other fiat currencies have a lot in common with purely digital forms of money.

Digital Money


Although it is a relatively recent invention, digital money is becoming more well known in the form of Bitcoin and other cryptocurrencies. These are largely decentralised, with no individual entities entrusted with the control of the currency. Centralised digital currencies such as CBDCs (central bank digital currencies) are also under development by various countries.

What is a bitcoin though? Or, for that matter, what is any digital currency? Whatever it is, we should be able to make transactions purely using computers connected via the internet. As computers deal in data, and the internet is used to transfer data, some common depictions of digital money seem to suggest that it some kind of data like a computer file. A transaction would then presumably be performed by sending this file to someone else. This is entirely false though, and computer files are wholly unsuitable as store-of-value assets or as a medium of exchange. This is because they can be duplicated indefinitely, so the requirement of a limited supply could not be enforced in any way. Furthermore, if I was to send a file that I own to another person, then they have no way of knowing whether I have retained a copy for myself. In fact, transferring data digitally necessarily involves making a copy of that data, rendering it useless as a form of money.

To understand how a store-of-value or medium of exchange asset can exist in a purely digital world, we should go back to the properties outlined above. Namely, ownership. To own a bitcoin, it is only necessary for all parties to be able to agree that you are indeed the owner. Then, if you transfer ownership to someone else as part of a transaction, everyone should be able to agree that this transfer has occurred, and that the other person is now the owner.

For digital assets, where only information is being moved around, we are going to need a database. This is just an online ledger recording all transactions that have occurred in the asset.

  • The holder of an asset should be able to query the database to prove ownership.
  • The holder of the asset, and no-one else, should be able to update the database to transfer ownership to another party.

One method of achieving such a ledger is to entrust its upkeep to a specific entity, much as is done with banks holding a database of the accounts of their customers. In that case, making a transaction involves contacting the bank and requesting the transfer to be made. Proof of identity will be needed, which can take the form of just possessing the payment card, remembering a password, or even presenting yourself physically at the bank. Trust is required that the entity maintaining the ledger will be responsible and only update it in the way expected, and that if its upkeep is passed on to another party then they will also maintain it in the same way.

Decentralised finance, on the other hand, is peer-to-peer and does not hand the upkeep of the database to a single entity. This requires a distributed ledger which is held by multiple parties (or nodes) across the internet. Blockchains are precisely such distributed ledgers, and anyone can perform the duties of a node, so no trust is placed in a single party. However, such decentralisation does raise two issues.

First, only the holder of an asset should be able to submit a transaction to the ledger to move ownership to someone else. As mentioned above for a centralised system, this can involve proving your identity to the bank before being able to transact, which will likely involve giving the bank some potentially sensitive information. For a distributed system, we need to be able to prove ownership and restrict transactions of an asset to those approved by the holder in a purely algorithmic way, and without revealing sensitive information. This is done using public-key cryptography, whereby only the owner of the asset is able to sign transactions using his private key, but the public key is sufficient for nodes to be able to validate the transaction in the ledger.

The next problem is that, if many nodes each keep a copy of the ledger then how can we ensure that they are consistent? If two nodes did have different versions, then how can we decide which is correct? In particular, if I was to pay some bitcoin to another person, then what is to stop a third party who sees a different or outdated version of the ledger thinking that I am still the holder. This could result in me being able to spend the same coins twice. A major achievement of Satoshi Nakamoto was the solution to this problem, by using a proof of work protocol for the Bitcoin blockchain.

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