Paciolo got it wrong and why it doesn't matter.

After doing a worked example of trading using normal accounting conventions with graphs and it just seem wrong and a bit abitrary as Tiger Beatle puts it in their documentation. Luca Pacioli’s wrote the textbook in 1494 Pacioli 1494 and everyone has copied the conventions since.

I think it is wrong rather than just a matter of convention. There are other good examples in Science where for instance the electron has a negative charge so the flow of electrons is in the opposite sent to which current is meant to flow. The negative charge was discovered in 1987 by JJ Thompson

I am theorising that there are two problems which lead to this:

• Not using negative numbers
• Starting with a going concern rather than a fresh one

Negative numbers

The Chinese first invented and used negative numbers and they used the same convention as Pacioli, with amount sold as positive and amount purchased as negative.
However as it seems to be a single entry system a sale corresponds to an increase in cash rather than a movement.

Srinivasa Ramanujan was an Indian genius. One of the amazing things about him is that he created and taught himself mathematics with intellectual leaps. So much so that we are still catching up with him. What this means is it is very possible for an individual genius to reinvent things rather than assume the transfer of knowledge from the Chinese to the Indian hindu culture. Both routes could be possible.

The problem comes in the transmission of Hindu mathematics to Italy via the Arabs. The Hindus had negative numbers which they used for debts. Along the way the Hindu/Arabic numerals were transmitted but negative numbers were dropped.

The use of negative numbers with the direction gives the graph representation meaning. Without negative numbers you move in Paciolo’s language from shall give in dare and shall receive “in habere” and by “per” and to “a” in the journal. In the ledger you have the left and right hand side which substitute for positive and negative numbers.

There is an advantage of separating out the positive and negative numbers in that it becomes easier to error check your balances. Making simple errors is very easy however you do it espeically if writing all the numbers out 4 times by hand.

At least two people who have used graph theory have both swapped the convention as it just makes more sense. So perhaps Kleppmann 2011 did it and he just said

Now, by convention, accountants flip the sign on all of the blue and pink nodes’ balances, which means that the two sums end up being equal. And that’s why it’s called a balance sheet.```

## Going concern

I think the reason Paciolo went for his interpretation is that he started with an inventory of a going
concern.  The first movement is cash to equity and once you have made that choice everything has to 
follow. If he had started with an empty balance sheet I think he might have gone in a different
direction.


In the end it becomes a matter of presentation and computers are adept at reformatting and
redisplaying in your own personal choice.