You touch upon a semantic problem that should be a the head of every political agenda since 2008:
It is possible for money to be created ex nihilo (for example, the federal reserve can create dollars by fiat).
Indeed, while the great majority of the population believe that governments create the money used by their citizens, they fail to realise that private banks (of which the Fed is an example, despite its name) create most new money ex nihilo by lending it against a tiny fractional reserve..
They then proceed to collect interest on all this new money! No wonder the banks are so powerful.
In the UK 97% of money comes into existence this way and circulates throuch bank balances. This brings the banks an income of many billions of pounds each year (depending upon the interest rates being charged) as a reward for a few strokes on their computer keyboards.
No wonder they can fund bubbles of various kinds: dot. com, property, sub-prime, ...
The UK creates the other 3% of new money officially as coins and notes, which can enter into circulation without and interest stream associated with them.
The 'money' has many different meanings. For our society, the 3% of official money-tokens have quite different meanings from the 97% of credit/debt-tokens issued by banks.
That is a really serious semantic problem.
While we worry about semantics on the level of a formal equivalence between one lot of character strings and another, it is a problem we shall never address.
Does any 'ontology' concerning the money system bring this issue to the fore? If it does not, it fails badly.
It is also possible for money to be destroyed. For example, the KLF burning a million quid ( http://en.wikipedia.org/wiki/K_Foundation_Burn_a_Million_Quid ).
This is where the flexibility of being able to view the simple account to account transfer that was the start of the discussion, and which I modeled as a single event, as also being made up of a number of sub-events, which was the analysis that Doug proposed, makes it easier to be able to provide answers at the right level of granularity, and to model source and sink cases like those discussed above.
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