
Re: is it true that the hindus educate the world i math?
Posted:
Aug 17, 2007 6:56 PM


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Rock Brentwood wrote: > The Untold Story of the Signary Machine (3 digit base 3 for *signed* > integers) > http://federation.g3z.com/Mathematics/Signary.htm
Er, not exactly untold. This system is called balanced ternary and it's very widely taught; at least, I've heard of it many times from independent sources. If you reinvented it then good for you, but you should be aware that it already has a standard name that's different from yours.
I don't know how long ago it was invented, but according to this article one Thomas Fowler designed and built a balanced ternary calculating machine in 1840:
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4215923 http://ieeexplore.ieee.org/iel5/85/32187/01498715.pdf?isnumber=&arnumber=1498715
The article also mentions Claude Bachet's observation in the early 1600s that single weights of 1, 3, 9, ... units could be used to balance any integral number of units on an armbalance scale.
A more advanced machine was built in 1958:
http://en.wikipedia.org/wiki/Setun
The use of binary in modern machines has nothing to do with lack of vision and everything to do with the physics of transistors.
Also, your whole article suffers from a confusion of levels. The bits in a "binary" computer don't mean anything. The meaning comes from how they're used. Sometimes they're treated as unsigned numbers, sometimes as two'scomplement signed numbers, sometimes as elements of Z_{2^32}, sometimes as vectors of boolean values, sometimes as coefficients of polynomials over Z_2. Microprocessors have hardware support for some operations on some of these interpretations, while others have to be implemented by hand in terms of generic bit operations. Your statement that "in most binary machines one needs to make a distinction between signed and unsigned quantities" is ludicrous. It's not a necessity, it's a convenience. People *want* to be able to use the full range of a machine word for unsigned quantities, where half the range would not be enough. Bits or trits, it doesn't matter; if your machine instructions can only interpret trytes as integers from 121 to 121 then you will merely be inconveniencing programmers, forcing them to write inefficient code for the other operations that they need.
 Ben

