> From a mathematical perspective, abnormal balances are essentially negative balances, though in accounting negative numbers should never be used or allowed.
This seems like a bad legacy passed down unwittingly. I am not trained in accounting, but been keeping my books for several years now. I have written a ledger-cli clone and have been using it for the last three years for both personal and company accounts. Using signed numbers works perfectly fine during book keeping. I use the Debit/Credit lingo only when I need to show reports to the pesky accountants. (Fortunately, my main accountant doesn't bother me with formalities).
Yeah, the "should" is editorializing. The avoidance of negatives is pretty easy to explain as a simple mistake. From the article:
> Luca Pacioli, often referred to as "The Father of Accounting," wrote, printed and distributed the first complete description of double-entry accounting in 1494.
> In 1545, Cardano in his Ars Magna did not allow negative numbers in his consideration of cubic equations, so he had to treat, for example, x^3 + ax = b separately from x^3 = ax + b (with a,b > 0 in both cases). In all, Cardano was driven to the study of thirteen different types of cubic equations, each expressed purely in terms of positive numbers.
> In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple".
Bookkeeping uses a different reasoning system than you are accustom. I think of it as vectors in a 2-dimensional space (asset/liability, income/expense) -- where each vector has a magnitude and a direction (debit/credit). You can think of "debit" being the head of the vector (where value is going), and the "credit" as being the tail (where it comes from). Transactions are paired, complementary movements in this space -- not plus/minus movement along a single line.
Visually, it's much easier to distinguish between a debit and a credit if they are in different columns. A tiny little minus sign won't do it. Of course, you could use color, but, that's not always printable. Parenthesis are OK, but, it makes sanity checks in your head difficult. Of course you could do this transformation a report if you wanted, but really, how often does that happen?
Logically, these are actually very different activities. When you debit an asset account, it's representing a kind-of-activity that happens (retained value accumulating). Once you view credit/debit as just plus/minus, you're tempted to neglect the other dimensions of the interaction. To a beginner, debit/credit affect on asset/liability/expense/income accounts seem like an unnecessary distiction, however, the interactions are inverted in their affect. Is minus good or bad? It completely depends upon your perspective.
Redundancy is a feature not a defect; it's a checksum. There's always a tendency to simplify the model and elminate the balancing interaction and check. This is possible, of course, and it does simplify the recordkeeping. However, it means that logical classification errors are harder to discover. When (perhaps big) money is at stake, why take the risk? By having 2 complementary transitions in a more complex space, you cause the person making the entry to think... and that's very useful (even if it's tedious or exhausting).
Pratically, you have convention/tradition. You're making a choice to use plus/minus for credit/debit is one of the distinctions, you could just have easily use it for asset/liability or income/expense. Why favor credit/debit? While this may not be the best way to solve these concerns, the approach is the incumbant -- most financial people expect this kind of problem to be this way, regardless of the extra complexity involved. Tradition here reduces communication overhead.
Even so, the rules arn't passed down unwittingly, they form an approach known to work. I think each generation is welcome to challenge (and they often do challenge) tradition, however, new approaches need significant justification.
> Transactions are paired, complementary movements in this space -- not plus/minus movement along a single line.
Sure, transactions are pairs (or balanced sets) of entries. Entries however, are exactly plus/minus movements along a single line in a single account. Sign (+/-) reflects that much better than debit/credit labeling does.
> There's always a tendency to simplify the model and elminate the balancing interaction and check.
Using +/- in place of credit/debit does not eliminate the balancing interaction. In fact, it makes exactly what is done in the balancing interaction more explicit.
> You're making a choice to use plus/minus for credit/debit is one of the distinctions, you could just have easily use it for asset/liability or income/expense. Why favor credit/debit?
Because income, expense, asset, and liability, are all kinds of accounts, and credit and debit are not, they are descriptors of whether an entry (or balance) is a flow (or accumulation of flow) of value into (debit) or out of (credit) an account.
> Pratically, you have convention/tradition. You're making a choice to use plus/minus for credit/debit is one of the distinctions, you could just have easily use it for asset/liability or income/expense. Why favor credit/debit?
The answer is that people intuitively understand what an asset, liability, income and expense is. People don't understand what a debit and credit is. If I deposit money in to my bank, should the 'bank account' in my accounting system be credited or debited? Most people would (incorrectly) say 'credited'.
It isn't that complicated. They key to unlocking double-entry accounting is the accounting equation and the (8?) or so rules mapping debits and credits to transactions. As for a bank deposit, it needs to be understood that the statement is produced from the bank's perspective. I don't think that the average person, given a few hours of learning, would struggle with this.
This rules are in place due to over centuries of accounting experience. It may seem unintelligent or silly to the untrained eye, "debito and credito" , exclusion of negatives or many other are in fact in existence because they work.
This seems like a bad legacy passed down unwittingly. I am not trained in accounting, but been keeping my books for several years now. I have written a ledger-cli clone and have been using it for the last three years for both personal and company accounts. Using signed numbers works perfectly fine during book keeping. I use the Debit/Credit lingo only when I need to show reports to the pesky accountants. (Fortunately, my main accountant doesn't bother me with formalities).