There are three basic reports that businesses produce regularly: the balance 
sheet, income statement, and statement of cash flows. A=L+E describes the 
balance sheet. The equation that describes the income statement is profit (or 
change in assets) = Income-Expenses, except remember, accountants prefer to 
add, so they think of this as dA+X=I.  (I'm using dA to mean profits, a change 
in assets.) We're skipping the cash flow statement for now.

Another equation accountants are fond of, since they don't like subtraction, is 
debits=credits. If we substitute in the balance sheet equation, we get that 
debits=A, and credits=L+E.  For the income statement that means debits=dA+X, 
and credits=I.

Now accountants hate to subtract, so how do they deal with things like paying 
down a credit card from a bank account?  Well, some accountant long ago figured 
out that if you subtract debits and credits from both sides of debits=credits 
you get -credits=-debits, or -credits=A and -debits=L+E, and -credits=dA+E and 
-debits=I. So instead of subtracting from an asset, we can just add a credit. 
And instead of subtracting from liability by paying it down, we can just add a 
debit to it.

So along comes Ledger, written by a computer scientist, not an accountant. 
Computer scientists don't have anything against subtraction since it's really 
just 2's complement addition, and they hate added complexity, so they do away 
with credits and debits entirely by just moving everything to one side of the 
equation. Debits+-Debits=0. What are debits? A. What are -debits? L+E. 
Substituting in we get A+L+E=0, and we remember that if we want to add to a 
liability or an equity, we add a negative number. For the income statement this 
becomes dA+X+I=0, and remember that adding to income means adding negative 
numbers.  (Thinking of income as negative is certainly counterintuitive, but if 
you think of depositing your paycheck, income, in your checking account, an 
asset, you can see it makes sense. I think there's a Ledger variant that gets 
around this counterintuitive result by allowing you to declare accounts as 
credit accounts and flipping the minus sign for you.)

Accountants have something they call a trial balance, which basically just adds 
the balance sheet equation and the income equation together. A+X=L+E+I.  This 
is called a trial balance because the books can be verified at any time against 
this equation 

Computer scientists like the reduced complexity of using just one equation, so 
that's what ledger uses. Ledger moves everything to one side of the equation, 
A+X-(L+E+I)=0, and gets rid of the minus sign by remembering that L, E, and I 
are negative balances.

That's pretty much all I know about accounting, along with how I apply it to 
Ledger. I only have those five top level accounts. Everything else is a 
subdivision of one of those five accounts, and I only subdivide accounts if I 
absolutely have to. If I can accomplish something with tags rather than by 
subdividing an account, that's what I do. And if I can get the job done without 
adding a tag, then I won't even do that. There's a lot of things you can 
account for. I could track the serial numbers of the bills I use in a 
transaction, for example, but if that information isn't going to be worth more 
to me in making some future decision than the time it's going to cost me right 
now, I don't bother.

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