This is a long extract from my response to Martin.
The penny finally dropped just now with your reference to resolving currency account balances into Left and Right handed. While credit is necessarily involved, it is not widely understood, but currency is not actually necessary to create and clear what I term people-based credit, of which more below.
Tally sticks represented One Dimensional accounting; double entry book-keeping represents Two Dimensional accounting, and what you have identified as Three Dimensional accounting represents an advance on the existing approaches to Triple Entry Book-keeping taken by Todd Boyle, Ian Grigg and Satoshi of Bitcoin fame.
In order to create a coherent 3-Dimensional accounting system, it is important to correctly describe what exactly the units of account represent; in what context; and the relationship between Value, Credit and Currency.
Value is not definable, or rather it is definable only in relative terms by reference to a standard unit of measure for Value or 'Unit of Account'.
There are many types of Value, of which only one - Energy - is tangible, and in my analysis there are two other intangible/immaterial sources of value (aka in economic-speak, factors of production): Location (3D Space) and Intellect (Subjective Knowhow and Objective Knowledge) which have a use value over time (which I term utility) which may be priced by reference to a unit of energy as a standard unit of measure for Value.
The key issue in a monetary/fiscal system is, what does the Unit of Account actually represent?
In my analysis, the conventional fiat currency Unit of Account symbols: £, $ or - represent a negative - because bank promissory notes in the modern monetary system do not represent claims over positive Value (as they did in the days of free banking and Real Bills), but rather a claim over a claim over Value asserted ex nihilo by a credit intermediary aka a bank.
The misrepresentation at the Dark Heart of modern money is the creation of a false positive from a double negative, and the reality is that the $, £ and unit actually represents a negative value.
Bitcoin and its wave of clones more or less represent a nullity (although some argue that Bitcoin represents a net drain of energy). These coins represent claims over past energy production (Proof of Work), rather than future energy production (Promise of Work). Since the work expended in producing the coin was for the account of the Issuer, then it represents no more value to the coin holder than would (say) a Mars Bar receipt compared to a Mars Bar voucher.
But I digress down a topical byway.
I think we are agreed that a unit of energy represents a positive. I believe that the move to the 'least energy cost' principle which I advocate for energy policy, based upon Denmark's pioneering approach, may be spread virally by using an energy unit of account; creating energy currencies of different types; and using 'energy loans' denominated in energy to invest in renewable energy (Mega Watts) and the lowest hanging fruit - Nega Therms and Nega Barrels of carbon fuel savings.
Credit and Currency
Credit may be defined as a promise by an issuer to provide Value in exchange at a future - uncertain - point in time.
As stated above, there are three types of value which are relevant to the use of a unit of energy as a metric:
Energy - in static (material) and dynamic (immaterial) forms;
Location - which is immaterial 3-Dimensional Space;
Intellect - in subjective form (knowhow and everything else between our ears); and objective form (data patterns or representations in material or immaterial forms).
The Value created by people over time (aka Labour) may be de-constructed into two types:
Energy - which is unqualified Labour or 'Manpower'; and
Intellect - the subjective value which qualifies Labour: this dies with us, but includes knowhow, knowledge, skills, contacts, experience, intuition and much else.
There are other people-based types of Value such as spiritual and emotional value which are measurable with metrics other than energy, but that is another story.
When people issue credit (promissory notes or Real Bills) it is based upon their individual or collective (eg within a corporate constitution/protocol) capacity to provide goods and services in the future.
Now, as I point out here:
The Community is the Currency
such credit is created directly on a Peer to Peer basis by reference to a standard unit of measure for value (unit of account) and may be settled in one of two ways:
Chain Settlement - existing open P2P obligations eg A to B; B to C; C to D; and D to A are settled by the identification and generation of a chain A>B>C>D>A. This credit clearing requires a combination of a framework of trust and a technical/messaging platform which when combined constitute a Clearing Union.
Currency Settlement - other asset-based (Peer to Asset) credit instruments acceptable to the holder of the promissory note are presented in payment and accepted to settle the obligation.
The point I am getting to is that your two Left and Right Handed pairs represent undated people-based credit.....but not currency. Pricing of undated people-based creditary claims over Value is purely subjective - often involving emotional and even spiritual considerations....some might say irrational albeit not in the accepted mathematical sense.
In my analysis, the use of location over time and the use of energy over time are locally and generally valuable in exchange respectively, and this makes them both good candidates for currency. Indeed, fiat currencies are largely land-backed, but deficit/debt based.
However, these currencies, being based upon Commons, will in my view be issued by a custodian holding productive assets in common, and they represent a positive with no negative.
Here, I believe, the four Chiralkine objective/rational? number pairs represent the four possible states of 'ownership' of units of asset-based currency which are positives without a negative:
(0,0) neither mine nor yours;
(1,0) mine not yours
(0,1) yours not mine
(1,1) both mine and yours
Both (0,0) and (1,1) represent Zero - ie in logical terms neither/nor & both/and
System users don't need to know how the sausage is made, and chiralkine accounting must be put into effect in a way that is invisible to the user. This requires the consensual protocols/framework agreements - I call them the Guarantee Society (people-based credit) and Capital Partnership (asset-based credit) which share risk and reward - which frame the mechanisms of credit creation, exchange and settlement of both people-based credits and asset-based currencies.
These are the consensual protocols which I have been developing for a decade, while the necessary generic credit 'prepay'/promissory instrument is a close relation to Ian Grigg's Ricardian Contract.
I envisage for people-based credit mobile phone personal operating systems/payment devices, which generate encrypted promissory notes Bitcoin style. For asset based credit/currency I think we will see local 'energy treasuries' which broadcast encrypted promissory notes as energy dividends and land dividends.