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Topic: is it true that the hindus educate the world i math?
Replies: 25   Last Post: Aug 19, 2007 3:57 AM

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 Ben Rudiak-Gould Posts: 210 Registered: 2/2/05
Re: is it true that the hindus educate the world i math?
Posted: Aug 17, 2007 6:56 PM

[newsgroups trimmed]

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 arm-balance 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's-complement 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

Date Subject Author
8/17/07 harmony
8/17/07 M. Ranjit Mathews
8/17/07 markwh04@yahoo.com
8/17/07 Ben Rudiak-Gould
8/17/07 Harlan Messinger
8/17/07 ,hari.kumar@indero.com
8/17/07 markwh04@yahoo.com
8/17/07 Androcles
8/18/07 Androcles
8/18/07 Androcles
8/18/07 Androcles
8/19/07 Androcles
8/17/07 mb
8/17/07 hari.kumar@indero.com
8/17/07 M. Ranjit Mathews
8/17/07 mb
8/18/07 hari.kumar@indero.com