Pacioli’s Equality, a better name for double entry accounting

Euclid, Pythagoras, Newton, Einstein, Heisenberg, Planck. These names conjure a sense of elegance, of fundamental knowledge, of natural order. They have each contributed foundation stones to our understanding of the natural world. Together, theirs and many other ideas act as first principles upon which we lean as we build spacecraft, cure disease, and create art.

The association of a name with a theory or theorem is not just administrative. We do not use the name ‘Newton’s Third Law’ as a database reference, an abstracted name with which to retrieve associated knowledge inside our brains. Instead, the name ‘Newton’ carries emotion. An emotion that is collectively understood across society.

Newton’s name lends an energy above and beyond the phrase ‘the third law of motion in classical mechanics’. That energy matters: It excites the mind, invites inquiry, provokes the imagination. Present a child with the phrase: ‘A theory on the fundamental limit of precision in measurement of pairs of properties of a physical particle’, and they may well give up on studying physics.

Present them with: ‘Heisenberg’s Uncertainty Principle’, and you might well spark their curiosity. This phenomena is visible beyond ideas describing the natural world: We don’t name brands ‘Very Fast And Good Looking Cars’, we name them ‘Tesla’.

Absolutely zero curiosity, energy, or wonder is sparked by the phrase ‘Double Entry Accounting.’ It is more likely to spark the gag reflex.

This is a crying shame. Such a shame, and such a waste, that I won’t refer to the above mentioned idea in those terms again. Instead, I will refer to it as ‘Pacioli’s Equality’.

This name is not quite fair. Luca Pacioli, an Italian of 15th century vintage, did not invent the accounting principles to which I am lending his name. Instead, his is the first known work to codify them: Summa de arithmetica  geometria, Proportioni et proportionalita, published in Venice in 1494.

Many artefacts predate Summa. Records kept in France in the 13th century, authored by Amatino Manucci, are the earliest surviving example of Pacioli’s Equality. But we must pick a name, and the author of the first known textbook on the topic is as good as any. Pacioli it is.

In the most general terms, Pacioli’s Equality could be described as: ‘Every change has an equal and observable origin.’ Which sounds idiotically simplistic. No less simplistic, I say, than ‘an object that is at rest will stay at rest unless a force acts upon it.’ These phrases are deceptively simple, for they act as foundations upon which immensely valuable paradigms can be constructed.

In the world of money, where Pacioli’s Equality is most often applied, but which is certainly not the only domain in which it can be applied, we could re-word the description as: ‘Everything you have is equal to everything you have received.’ Or, as a very formal equation:

Everything I Have = Stuff People Gave Me

Of course, we might also have some stuff that might not belong to us. Say, ‘everything you have is equal to everything you have received, plus what you have borrowed.’ Formally:

Everything I Have = Stuff I Borrowed + Stuff People Gave Me

Any increase on the left side (what I have), must be balanced by an increase on the right side (I must have either borrowed it, or someone must have given it to me). That blindingly, but deceptively, obvious equality is presented to first-year accounting students as the ‘double-entry accounting equation’:

Assets = Liabilities + Equity

At which point their eyes glaze over, Instagram is opened, and somewhere, an adorable kitten dies.

This is where the shame lies. Pacioli’s Equality is the basis for arbitrarily complex information storage systems. By recording both the origin and destination of a resource, we can construct, for any point in time, both the current state of an entity and every quantum of change that led to that state.

In other words, Pacioli’s Equality allows us to observe both the position and performance of an entity, measured in some arbitrary unit. That unit is most often money: The common names for a measurement of position is a ‘Balance Sheet.’ The common name for a measure of performance is an ‘Income Statement’.

The fundamental elegance of Pacioli’s Equality is utterly absent from modern accounting practice. Load any piece of accounting software, and you will be presented with ‘invoices, customers, credit cards, bank accounts, trial balances’: These are domain-specific objects, each of which is an implementation of the equality, rather than a window onto it.

Sometimes, software might open an interface to ‘journals’, or allow direct manipulation of ‘ledgers’. These are edging closer to a fundamental expression of Pacioli’s Equality, but they are treated as second class citizens. Interacting with them, especially programmatically, is generally painful.

We have combined computers and fundamental knowledge to create wonderful outcomes. Program Einstein’s theories into a computer system and you can model the position of a space probe orbiting Saturn to pinpoint accuracy. Build on Euclid’s theorem and a computer can create nigh-unbreakable cryptographic constructs that allow distributed virtual currencies.

Where is the fundamental computerised expression of Pacioli’s Equality? It is surely not manifest in the current accounting software landscape. That is a shame. We are poorer for it. We can make a baby step towards encouraging innovation by replacing the awful name. Exit double-entry accounting. Enter Pacioli’s Equality.