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From: ir230@sdcc6.ucsd.edu (john wavrik)
Newsgroups: comp.lang.forth
Subject: Re: Standard systems vs. standard programs
Message-ID: <11977@sdcc6.ucsd.edu>
Date: 22 Jul 90 21:18:07 GMT
References: <9007201343.AA14784@ucbvax.Berkeley.EDU>
Organization: University of California, San Diego
Lines: 46



Let's imagine a time in which people around the the world have reached 
the stage where, for world commerce, it would be desirable to produce 
a Standard for arithmetic.

The state of affairs:  In Babylon a numeration system with base 60 is 
     in use, Arabia has used a base 10 system, the Hexians have used 
     base 16 while their neighbors, the Booleans, have used base 2. 
     [Historical note: the small nations of Hexia and Boolea were 
     eventually annexed by Latvia] 

Please note that "10" is used in each of these countries -- but it has 
a different meaning in each.

What to do?  Here are some possibilities:

1.  They could notice that 0 is the only number which is written in
    the same way in all their systems (fortunately the Romans did not 
    attend). They make 0 their standard and declare that "Arithmetic 
    is broken -- but we feel it is useful for everyone to know what 
    they must avoid if they want portability." 

2.  They set about producing an international standard which has all 
    the best features. In particular they choose a common base, common 
    symbols for digits and arithmetic operations, etc. To sooth those
    current users at home who do not plan to engage in world commerce, 
    they agree to continue to provide support for the next few years 
    for their customers' current numeration systems as well as the new 
    international system. 

3.  They decide to devise a complex numeration system which will allow 
    everyone to continue to use their current base -- but which will 
    also work with all other bases.

It would take the best mathematical minds in the world to pursue
approach 3 -- it would probably take them well over 3 years to come 
up with something, and whatever they came up with would be far less 
satisfactory than any of the existing systems.  As for approach 1, it 
is hard to believe that anyone would be perverse enough to suggest it --
but, in some respects, the world never changes. 

                                                  John J Wavrik 
             jjwavrik@ucsd.edu                    Dept of Math  C-012 
                                                  Univ of Calif - San Diego 
                                                  La Jolla, CA  92093