From the article:

Similarily, a currency system using balanced ternary would save visits to the bank - customers would be likely to have exact change, or be able to get a small number of coins in change, and sellers would just occasionally need to deposit a large coin or two

My question: Who is going to want to carry around coins that indicate negative amounts of money. I would quickly throw away (or conveniently lose) any such coins.

---

Update. I see that Pakaran has deleted my sentence in the article "While mathematically appealing, such a system [using balanced ternary as a monetary system] would require the existance of coins representing negative amounts of money, which would be impractical." This was added to a sentence that Pakaran wrote here (see above "Similarily, a currency system using balanced ternary...").

Here is my understanding of a balanced ternary monetary system. In balanced ternary, you have digits that represent postive number, and digits that represent negative numbers. For example, 5 is represented "+--": 9 - 3 - 1. To represent five dollars in a balanced ternary system, one would have a nine dollar bill, a negative three dollar bill, and a negative one dollar bill. It's not balanced ternary unless we have some way of representing negative amounts. Well, if I had five dollars from having a positive nine dollar bill, and two negative bills, well I would just throw out the two negative bills and have nine dollars!

So, yes, either I'm hopelessly confused about this, or we will need to keep the above sentence in the article. Please clarify if I am mistaken somehow. Samboy 14:07, 23 Dec 2004 (UTC)

The point is that with balanced coin sizes, it's convenient for people to pay in exact change, which counts down on the number of bank visits by customers to turn in rolled coin, and by sellers to get more small coins. That reasoning is taken from a website, I forget which. Pakaran (ark a pan) 14:11, 23 Dec 2004 (UTC)

Oh, and you don't need negative coins for this to work, any more than you need a negative mass for the balance to work. Pakaran (ark a pan) 14:13, 23 Dec 2004 (UTC)

OK, I found something here. I can't read ps documents right now (!@#$ xmas vacation and no real internet for my Linux laptop), but the Google text version of the document says this:

A Currency System based on Balanced Ternary All currency systems use a set of tokens, usually called coins and notes. Suppose we choose the value of the tokens (let us call them coins), to be multiples of 3 : 1, 3, 9, 27, 81 and so on. Further suppose that we want to pay the sum of x units. Representing x in ordinary ternary with digits 0, 1 and 2 gives a means of representing and hence of paying x units using no more than 2 coins of each denomination. However, if we express x in balanced ternary with digits -1, 0 and 1, this represents a transaction where the customer pays x units by exchanging coins with the shopkeeper. Every 1 represents a coin that the customer gives the shopkeeper and every -1 represents a coin that the shopkeeper gives the customer. Each need have only one coin of each denomination in order to make any transaction possible. This system has a pleasing symmetry to it. Since -1 and 1 digits are equally likely, the exchanges will tend to balance out so that no particular denomination tends to run out or build up (assuming a uniform distribution of prices). Thus the customer will keep a supply of each denomination, having to withdraw high denomination tokens periodically and only rarely having to either split a coin into 3 of the next denomination down or exchange 3 of one denomination for one of the next denomination up

So it looks like I was mistaken. I will reword a clarification taking this information in to account. Samboy 14:19, 23 Dec 2004 (UTC)

Update: Description fixed. Samboy 14:22, 23 Dec 2004 (UTC)