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 carrie= s these displays as 7-bit numbers and there is a rule for assigning the bar= s to the bits. I don't know whether all displays use the same assignm= ent or not (my experiences with computers favors "not"). Anyway, I do= n'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=20

lazy and meaningless defense.=A0 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 earl= ier 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 s= ystem 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 lifetime= s and, I think, ever until we grow the extra digits.

For the first, a long series of studies have suggested that the most im= portant uses of numbers are simple counting, for which all the major conten= ding bases are roughly equal -- small enough to have memorable digits (60 i= s out), large enough to give small=20

numbers for ordinary counts (2 and 4 and probably 8 out); fractio= ns, the most common of which are half, quarter, third, fifth, eighth, and t= hen the rest pretty much in a lump (fifth -- and tenth -- seem to be phenom= ena of decimalization, since they do't correspond to real-world cases excep= t in those kinds of contexts); phone numbers and addresses, which may even = take precedence over fractions but are neutral among bases except as in cou= nting. Hex does actually have a small technical advantage in phone nu= mbers 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). &nb= sp;So, it is fractions that count most and there duodecimal does better tha= n hex, even though 3 of the top five fractions are powers of 2. The m= ess that is 1/3 cancels the advantages of 2 and 4 and is not nullified by t= he minor mess of 1/8 duodecimal. In fact, hex loses out even to decim= al on this. (Of course, you can argue with the weightings, though the= se have been pretty consistent over years of studies). I have left ou= t time, since it is so obviously a duodecimal win, with decimal close behin= d and hex nowhere in sight.

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