Subject: Re: [lojban] Re: possible A-F...

From: [email-masked]
Date: Tue, 2 Oct 2001 11:24:54 EDT

In a message dated 10/2/2001 9:39:54 AM Central Daylight Time, 
[email-masked] writes:

> hmm, a 7-bit number would be much more efficient.
> 

I agree. I think the problem was with deciding how the bits were assigned.  
Clearly a calculator or a clock or whatever actually carries these displays 
as 7-bit numbers and there is a rule for assigning the bars to the bits. I 
don't know whether all displays use the same assignment or not (my 
experiences with computers favors "not"). Anyway, I don't know the 
assignment and I do know the other system, so I go with what I have. In any 
case it is better than attempted visual displays across unreliable media.

<you give no reason for decimal other than tradition, which is such a 
lazy and meaningless defense.  i've given the reason for hexadecimal--
it is a power of 2.>

Which is one of its chief defects. I have -- as I said earlier -- not had to 
say anything because others were spewing out my lines (see earlier go-rounds 
on this topic) for me.  
There are two questions here: what would be the most rational base for the 
number system, given the sorts of things we use numbers for? and what system 
could actually be adopted?
For the second of these, I'm afraid that habit is an enormous obstacle to 
overcome. When it is backed up, as decimalism is, but physiology, I don't 
see any chance of any new idea working -- certainly in our lifetimes and, I 
think, ever until we grow the extra digits.
For the first, a long series of studies have suggested that the most 
important uses of numbers are simple counting, for which all the major 
contending bases are roughly equal -- small enough to have memorable digits 
(60 is out), large enough to give small 
numbers for ordinary counts (2 and 4 and probably 8 out); fractions, the 
most common of which are half, quarter, third, fifth, eighth, and then the 
rest pretty much in a lump (fifth -- and tenth -- seem to be phenomena of 
decimalization, since they do't correspond to real-world cases except in 
those kinds of contexts); phone numbers and addresses, which may even take 
precedence over fractions but are neutral among bases except as in counting.  
Hex does actually have a small technical advantage in phone numbers in that 
it might allow a more efficient use of switches (at enormous cost -- a factor 
in "habit" affecting what changes can actually be made) in the phone system 
(which is already set up for duodecimal, note). So, it is fractions that 
count most and there duodecimal does better than hex, even though 3 of the 
top five fractions are powers of 2. The mess that is 1/3 cancels the 
advantages of 2 and 4 and is not nullified by the minor mess of 1/8 
duodecimal. In fact, hex loses out even to decimal on this. (Of course, you 
can argue with the weightings, though these have been pretty consistent over 
years of studies). I have left out time, since it is so obviously a 
duodecimal win, with decimal close behind and hex nowhere in sight.