Double-entry bookkeeping as a directed graph

And then crypto-sign each transaction with an enormously expensive proof-of-work function because you don't trust anyone wearing a suit and then blindly go all-in on this new "blockchain" being the solution to every problem and then get scammed all the way up your own asshole by believing your own bullshit, and then beg those people in suits to fix it for you like a housecat begging for food from their owner they just scratched the shit out of, and be confused that they can't fix everything for you this time because you intentionally cut them out of the system. It's foolproof!

> The common English use of 'credit' and 'debit' is correct,

Yes, by definition.

> The mistake is that we talk about them as "our" accounts.

No. The mistake is the failure to recognize that every account is actually two different accounts, one for each party to a transaction. A bank account looks different to the bank than it does to a depositor or to a borrower. To a depositor, a positive balance is an asset -- quite literally "money in the bank". To the bank, a positive balance in a deposit account is a liability, a loan that it has taken from the depositor on which it must pay interest (at least sometimes) and which it must eventually pay back. To a borrower, a positive balance on a loan is a liability, to the bank it's an asset. Every financial asset is a liability to some counterparty. Even cash is a liability to society at large. So whether something is an asset or a liability depends entirely on your point of view, and so if both parties are going to use the same number to represent an account balance, it is an arbitrary choice what the sign represents. A positive number is always going to be an asset to one party and a liability to the other. Which is which is totally arbitrary, except that there are some deeply entrenched conventions: a positive balance on a deposit account at a bank represents an asset to the depositor, a liability to the bank. A positive balance on a loan represents an asset to the lender, a liability to the borrower. A positive balance on an invoice represents an asset to the seller and a liability to the buyer. But there is no inherent reason why it has to be that way, it's just tradition.

Likewise, whether "credit" means "increase" or "decrease" is also simply a matter of convention. A "credit" to a deposit account means the balance goes up. A "credit" to a loan account (i.e. a loan payment) means the balance goes down. The thing that unifies these things is that a "credit" is either an increase in an asset or a decrease in a liability since both assets and liabilities are recorded by convention as positive numbers. So in isolation (i.e. without a balancing double-entry transaction), a (positive) credit increases your net worth and a (positive) debit decreases it.

Cash might be an account, and a bank account might be another one. So if Alice buys with cash, it'd be $20 debit in the books account [1] and $20 credit in the cash account. Or if she paid for the book with something that directly takes the money from the bank account, the credit would be to the bank account.

Note that "credit" in double-entry bookkeeping means a transfer from that account and debit means a transfer to that account. So the debit side of buying the book goes into the books account. The credit entry is for whatever account value is transferred from in the transaction.

I'm not sure I'd say that Alice's net worth goes down by $20 when she buys the book since the financial value of the book would technically also be part of her net worth.

I also wouldn't consider "net worth" to be a single account.

Technically net worth would be the sum of all of Alice's assets in cash, bank accounts, real estate, books and other non-financial assets etc., minus all her liabilities. Each of those might be a separate account in the bookkeeping.

Disclaimer: I'm not an accountant.

[1] There might not be a separate account for books unless Alice is a real books aficionado and a meticulous bookkeeper, so the account might also be "books, movies & music", "entertainment & culture", or just "personal items" depending on what granularity is desired/needed.

It might also be that such items are not considered to have financial value in the system (which would probably be the correct unless Alice collects books) and the debit ("to") would actually go in some kind of an (abstract) expenses account instead. Either way, both the value leaving cash/bank and the value "entering" some other account would be entered.

Might be the slight fever talking, but wouldn't the debit and credit be exactly the other way around? When you get paid by your employer, in your books the money enters your bank account ("debit") and is coming from an (abstract) employment income account ("credit").

When you pay your power company, the money leaves your bank account ("credit") and enters the (abstract) power company expenses, utilities expenses, or whatever account ("debit").

Are you, perhaps, confusing money with currency?

Money is just a promise. Anyone can create those. Which should be quite obvious. When you go to work to, as we literally say, make money, your employer is making a promise that in exchange for you work you can take something of some defined value later. Later, you will take that promise and turn it into something of value, such as food. Once spent, the money is destroyed. The promise is no longer valid. The deal is done.

Currency is a promise to a particular entity, such as a central bank. A central bank will loan you something of some value, you equally promise to give them something of equal value (we'll ignore interest for simplicity) back at a later date. Indeed, only the central bank can accept promises made to the central bank. If you accepted a promise on behalf of the central bank, without explicit authority, then you are quite right that trouble is coming your way.

Because there is a trust component required in promises, often promises made – such as the promise of your employer to feed you later – will be backed by a promise to the central bank. The central bank has a military to send if someone really tries to play nasty with promises made, so that carries a lot more trust than if you and I wrote up our own 'IOU'. This may be why you see money and currency as being one and the same. Often they are, but not necessarily so.

Accounting is simply for keeping track of promises. That's why we invented it. You don't need accounting for barter. It is the promises that necessitate accounting in order to keep track of what promises are outstanding and what are fulfilled. A bookkeeper doesn't create money per se, but they certainly account for money created and destroyed by the entity they are bookkeeping for.