Double-entry bookkeeping as a directed graph

Something that makes this simpler to think about from a modern perspective is that accounting is older than the popular use of negative numbers. By a lot. If we were to invent accounting today, we'd probably use positive and negative accounts instead of debit and credit accounts.

Algebra over addition is second nature to us at this point, but it would not have been obvious to the average merchant in 1604, and even then, negative numbers were viewed quite poorly.

What is important is that there are always two sides to a transaction and that they are inverses of each other. This is all a credit and debit are. Inverse operations on a number.

Therefore, we can make a rule that a transaction balances when credit = debit. (aka we didn't invent money as debit + credit = 0, but remember that we didn't like negative numbers when this system was invented, so this last fact is more of a happy coincidence that happens to ALWAYS WORK, for some reason, rather than the goal).

What is then reasonable is to consider literal cash on hand to be the most positive (debit) kind of account there can be, and work backwards from there. If I want to handle an expense, then I need to invert the cash account somehow (credit it) and therefore have the opposite kind of entry for where the money went (debit it). So an expense account must have a generally debit (or positive) balance.

But where did the cash come from? Well that comes from income and I want the cash to be debit-ey so the place it came from must be credit-ey otherwise I risk writing a transaction that doesn't balance (equal zero). So then income accounts must generally be credit accounts rather than debit account (aka they hold a typically negative balance or are "credit normal").

What is really killer about this system, is it just so happens that every mundane transaction you could ever write will end up as balanced transactions and each of these possible transaction accounts end up having the same usual balance of credit or debit (negative or positive). I think that is just so elegant.

This has nothing to do with labeling transactions so that the labels conform to the common meanings of English words. When an account representing assets has its balance go up, that's a credit. When an account representing a liability has its balance go up, that's a debit. And vice versa. If I, say, draw down a line of credit for $100 and deposit the funds in my checking account, then from my point of view, my LoC should debited by $100 and my checking account should be credited for $100.

This makes sense regardless of how you think about the LoC. If you think of the available credit as an asset, then when you draw down the LoC the available credit balance goes down and it's a debit. If you think of the amount owed on the LoC as a liability, then when you draw down the LoC the amount owed goes up and it's still a debit.

> CREDIT mhink's account $100 (increasing liability)

No. This transaction does not increase liability in any absolute sense. It increases liability only from the bank's perspective. From your perspective, it increases assets.

If I understand your comment correctly, where you're getting confused is, you're reading Current Account (Assets) to mean your inventory of lemonade. What they actually mean in this case is money moved from Income to your Assets (e.g. your cash register). That's why assets went up in this example.

Of course for your lemonade business you might keep track of your lemonade as well (which I think is what you're talking about when you refer to assets). The lemonade sale would then lead to a decrease in your lemonade asset and and an increase in your expenses (cost of goods sold), so the right hand side of the equation balances.

So when selling lemonade there are actually 2 things happening:

1. Your income and your assets (your amount of cash) both increased. Income and Assets are on different sides of the =, so the equation still balances

2. Your lemonade assets decrease and you incurred the cost of that lemonade as an increase of your expenses. Those are both on the same side of the =, so the equation still balances.