Talk:Ternary numeral system

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This article just had an edit (which I undid) which only added the line: "Currently there is a private project underway to develop ternary logic into a usable programming language.". No facts, nothing that could be checked. Without knowing who is allegedly attempting to do this, there is no way to tell if this is a legitimate project, or another scam to get people to support a new startup. I also question the semantics... Has binary logic been built into a usable programming language? What would that mean? I can't think of any language feature (other than the list of possible operators) that cares if the underlying logic is binary or ternary. Nahaj 02:45:39, 2005-09-06 (UTC) [addendum: Fortran back in the 1960's had three way if statements... (Positive, negative, zero). (: What's the ternary version of "foreach" ? :)

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)


The argument that all digits (-1,0,-1) are "equally likely" is suspect. The American Mathematical Society has had papers explaining why (back in the days that log tables were still used) the pages with numbers starting with "1" were more warn than those starting with "9". Wouldn't that same idea apply here?

Benford's law doesn't really apply to the initial digits here, since every positive number starts with 1 and every negative number with -1. For second and later digits, however, we should see the exact same sort of bias: for the second digit of positive numbers, for instance, -1 is commoner than 0 which is commoner than 1 (in the ratios .4649735206 : .3062702279 : .2287562514).
I'm not sure what consequences this has for the original point about the symmetry of a balanced ternary system. I don't think the poster was talking about a scenario in which one's equally likely to be on the buying as the selling end of a transaction, for instance... 4pq1injbok 03:44, 2 August 2005 (UTC)

The balanced ternary section badly needs to be wikified and cleaned up, I think. 4pq1injbok 03:24, 2 August 2005 (UTC)

Contents

[edit] Balanced Ternary math

I have a short tutorial on balanaced ternary (and the math tables) here: http://www.eoti.org/~malachi/tutorials/ternary.html

I was going to add the tables in where the current multiplication one is, but I don't have the time right now to learn the Wiki table format. If anyone would like to convert the tables over for use here, feel free.

[edit] Balanced Ternary math algorithms?

Should there be a section on ternary or balanced ternary math tricks? (Such as the "'repeatedly add up the digits until you get a one digit number' trick to test for even in BT?" [If the resulting digit is zero, it is even))

Should there be a section of random ternary facts (Such as "Multiply by 3^n+1 in balanced ternary leaves the last n digits intact")

Should there be a section on ternary math algorithms? (Is BT shift and add or shift and exponentiate enough different from the binary versions to be worth showing? (Or even mentioning?)

Should there be some actual examples of arithmetic in the system?

[edit] History

There is a pointer to the Russian machines, but not to Thomas Fowler's 1840 ternary calculator. ("The Ternary Calculating Machine of Thomas Fowler", in the IEEE journal "Annals of the History of Computing, Vol. 27, No. 3, p 4-22 at IEEE Explore) This leaves one with the missconception (promoted by the Russian pages) that there was nothing in ternary before the Russian machines. Nahaj 14:57, 8 November 2005 (UTC) Addendum: There is now a link in the article. Nahaj 02:15, 25 May 2006 (UTC)

[edit] Use

I don't recognise this system as a computing student, is it really that commonly used?

Is is not that commonly used. But it has interestinging theoretical advantages (Such as [as Knuth points out] rounding and trunctation being the same operation. And there have been machines built using it. (Since the 1800's !!!) I encountered it as a computer science student, so some "computing students" do. Nahaj 03:01, 3 January 2006 (UTC)

[edit] Move

I moved the article to Ternary numeral system, for consistency and also because "ternary" can mean ternary operation, which is used frequently in several programming languages. Ternary has been turned into a disambiguation page. æle ✆ 19:13, 16 January 2006 (UTC)

[edit] Cantor set

Should the article mention the Cantor set which consists of the elements of [0,1] whose ternary expansion does not contain any 1s? —Tobias Bergemann 10:45, 19 January 2006 (UTC)

[edit] The size of a tryte

From the article:

"Ternary also has a unit similar to a byte, the tryte, which is six ternary digits."

This is heavily (or at least somewhat) disputed: some would consider it to be nine trits, and I would go so far as to include 27 as a possibility. --Ihope127 20:34, 19 January 2006 (UTC)

[edit] Balanced Ternary move.

Balanced ternary was move to its own separate article, but all the balanced ternary talk was left here.... Anyone object to a move of the talk to follow the article? (: I wouldn't mind, of course, if someone just moved it. :) Nahaj 02:13, 25 May 2006 (UTC)

[edit] Strange fonts

On my machine, the symbols ⅓ and ⅔ appear as thirds when editing, but as halves when reading. A glyph for two halves--how strange! I would think then it would be better to avoid them anywhere. Davilla 22:49, 22 August 2006 (UTC)

[edit] More (not quite so) practical uses of trinary

Trinary has appeared in a few esoteric programming languages, like Malbolge and TriINTERCAL. 129.67.18.148 09:39, 15 October 2007 (UTC)

[edit] Gideon Frieder's replacement ternary numeral system is not explained

Gideon Frieder's replacement ternary numeral system called Ternac (different from the one used in the Setun)is not explained