[lisper]

You're right, I did leave that out. But you also left something out: equity. The real equation is that ∆ State = ∆ Change = ∆ Equity. So there are really three things that need to balance (or four or six if you consider the counterparty's books and depending on how you count). But the income/expense really has nothing to do with the actual transactions, they have to do with the arcane rules around paying your taxes as a business entity, where you can be taxed on income you haven't actually received yet, and deduct expenses you haven't actually paid yet, or not be allowed to deduct expenses you have paid until long after you've actually paid them (depreciation). This is generally not applicable to individuals running lemonade stands. This is (and I know you know this) the difference between cash and accrual accounting. Those terms hide the fact that the difference between these two is mostly a reflection of tax law.

Accrual is also a way of doing implicit projections into the future, which made sense back when accounting was done with pen and paper, and payments could not be initiated by the payee. In that world, there was no such thing as (for example) an automatically renewable subscription. Today there is. How would you account for signing up for such a subscription? Theoretically, an open-ended automtically renewable subscription is an infinite liability (unless you start taking interest rates into account, but of course no one does that because no one knows what interest rates are going to be in the future). The Right Way to do this is to keep track of it as an infinite series of transactions with time stamps, which would be impossible to do with pen and ink, but is trivial for a computer.