Way back in the 1980s, Yuji Ijiri came up with the idea of momentum accounting, which he also called triple entry bookeeping. This is a distinct idea to the triple entry we typically talk about in our circles, and indeed pre-dates the work of Todd Boyle, Gary Howland and myself.
The collision in names was unfortunate and unintended, I only found out about Ijiri's idea when someone pointed me to it much later. Which leaves us and many others wondering - are they the same? Connected? Aligned? Unconnected? and other outrage...
I see a connection, so I'll try and draw it out.
As I understand it, Ijiri's third entry is a derivative of two successive accounting entries, making it like momentum in physics. Therefore, he suggests, we could in effect use this 'calculus' technique on accounting records to predict the future direction of activity.
A summary of what Yuji believes can be illustrated in the following analogy. The profits of a company are like a motor trip. Sometimes the car is driving forwards, sometimes backwards, and sometimes sitting still. The Balance sheet tells the precise location of the vehicle. The Income statement tells how fast the vehicle is traveling. The speed of the vehicle describes to investors information that can be used to estimate the future only as long as the vehicle travels the same speed. The question of whether the car is accelerating or decelerating can only be determined by using past information to estimate. What if the new triple-entry method allowed for the calculation of acceleration, or the momentum of the company, as Yuji defines it.
Everyone wants to know the future, indeed there are entire departments in companies and topics at business school just for that - using data to predict the future. Ijiri's is a very neat idea, but I have a doubt.
To be frank, I am not comfortable with the notion that you can measure momentum by doing a 'calculus' over accounting records. "These methods are complicated and not free from problems and errors. Yuji acknowledges that there are many fallacies in this procedure..." As his third entry is derivative information, I suspect that its conceptual value (use) is limited by fraud / deception.
This is to emphasise the Bill Black school of accounting rather than the Yuji Ijiri school. Because accounting records are used (relied upon) by many people for many things, once someone starts doing 'derivative' processing and relying upon those results, the opportunity for gaming that player’s outcomes rises.
This concern is analogous to say Enron pumping the results at the end of quarter, or the sales department cutting corners at end of month to 'make the numbers.' Momentum accounting would create a new measurement to game, like a Heisenbergian effect or Goodhart’s Law, as soon as you stress a controversial measurement it becomes useless for the task at hand. Computer scientists will also recognise a sense of GIGO here - garbage in, garbage out.
(I’m not enough of an accountant to think beyond that concern, and I haven’t read Ijiri’s books; I await like others the attention of serious accountants.)
Now, switching to the idea of cryptographic receipts, our triple entry. The goal is to make the accounting records so reliable, they can be the money. The notion that the record alone is strong enough to be the trade led us to say "the receipt is the transaction." This is what Gary and I built in 1995-96, and what Todd Boyle theorised about in the late 1990s; once the transaction has been rendered into a cryptographically sealed record, and shared amongst the three, it becomes the entries. It dominates other data, to use CS lingo, and therefore replaces it or leads it, whether it be other records or other systems like double entry.
Hence triple entry.
At a knowledge level, this leads to a new phenomena: "I know that what you see is what I see" as @gendal captured it. Now, there is a meta message here such that where you can merge the accounting system with the reality it accounts for - the receipt is the transaction, or the smart contract is the trade, if you are blockchain oriented - we improve the quality of the base layer to the point where it isn't a representation, it's the reality.
Entries become the foundational facts, rather than just representing other facts.
Back to momentum accounting, the point about fraud & gaming is that (IMHO) you will never be able to rely on it if both the momentum calculations are simply observations from which anyone can draw conclusions, and the underlying records are subject to error.
But combined, momentum accounting over the top of cryptographic receipts, the former might work. In a sense, this is to suggest that cryptographic receipts are necessary for momentum accounting, and this might be one of the reasons why Ijiri’s ideas never took off: layering observations over uncertainty sounds risky, and the market wasn't ready to take it on.
That's the relationship I see - with the newer blockchain generation systems as an accounting layer, we now have a factual base where momentum accounting might take off. (To see the how, look at the paper on AI & blockchain.)