From pycyn@aol.com Tue Oct 02 08:25:03 2001 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_4_1); 2 Oct 2001 15:23:09 -0000 Received: (qmail 77063 invoked from network); 2 Oct 2001 15:23:08 -0000 Received: from unknown (10.1.10.142) by 10.1.1.221 with QMQP; 2 Oct 2001 15:23:08 -0000 Received: from unknown (HELO imo-r10.mx.aol.com) (152.163.225.106) by mta3 with SMTP; 2 Oct 2001 15:25:02 -0000 Received: from Pycyn@aol.com by imo-r10.mx.aol.com (mail_out_v31_r1.7.) id r.f4.102a6f2c (2617) for ; Tue, 2 Oct 2001 11:24:54 -0400 (EDT) Message-ID: Date: Tue, 2 Oct 2001 11:24:54 EDT Subject: Re: [lojban] Re: possible A-F... To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_f4.102a6f2c.28eb3646_boundary" X-Mailer: AOL 6.0 for Windows US sub 10535 From: pycyn@aol.com --part1_f4.102a6f2c.28eb3646_boundary Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable In a message dated 10/2/2001 9:39:54 AM Central Daylight Time,=20 thinkit8@lycos.com writes: > hmm, a 7-bit number would be much more efficient. >=20 I agree. I think the problem was with deciding how the bits were assigned.= =20=20 Clearly a calculator or a clock or whatever actually carries these displays= =20 as 7-bit numbers and there is a rule for assigning the bars to the bits. I= =20 don't know whether all displays use the same assignment or not (my=20 experiences with computers favors "not"). Anyway, I don't know the=20 assignment and I do know the other system, so I go with what I have. In an= y=20 case it is better than attempted visual displays across unreliable media. Which is one of its chief defects. I have -- as I said earlier -- not had = to=20 say anything because others were spewing out my lines (see earlier go-round= s=20 on this topic) for me.=20=20 There are two questions here: what would be the most rational base for the= =20 number system, given the sorts of things we use numbers for? and what syste= m=20 could actually be adopted? For the second of these, I'm afraid that habit is an enormous obstacle to=20 overcome. When it is backed up, as decimalism is, but physiology, I don't= =20 see any chance of any new idea working -- certainly in our lifetimes and, I= =20 think, ever until we grow the extra digits. For the first, a long series of studies have suggested that the most=20 important uses of numbers are simple counting, for which all the major=20 contending bases are roughly equal -- small enough to have memorable digits= =20 (60 is out), large enough to give small=20 numbers for ordinary counts (2 and 4 and probably 8 out); fractions, the=20 most common of which are half, quarter, third, fifth, eighth, and then the= =20 rest pretty much in a lump (fifth -- and tenth -- seem to be phenomena of=20 decimalization, since they do't correspond to real-world cases except in=20 those kinds of contexts); phone numbers and addresses, which may even take= =20 precedence over fractions but are neutral among bases except as in counting= .=20=20 Hex does actually have a small technical advantage in phone numbers in that= =20 it might allow a more efficient use of switches (at enormous cost -- a fact= or=20 in "habit" affecting what changes can actually be made) in the phone syste= m=20 (which is already set up for duodecimal, note). So, it is fractions that=20 count most and there duodecimal does better than hex, even though 3 of the= =20 top five fractions are powers of 2. The mess that is 1/3 cancels the=20 advantages of 2 and 4 and is not nullified by the minor mess of 1/8=20 duodecimal. In fact, hex loses out even to decimal on this. (Of course, y= ou=20 can argue with the weightings, though these have been pretty consistent ove= r=20 years of studies). I have left out time, since it is so obviously a=20 duodecimal win, with decimal close behind and hex nowhere in sight.=20=20 --part1_f4.102a6f2c.28eb3646_boundary Content-Type: text/html; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable In a message dated 10/2/2001 9:39:54 AM Central Daylight Time, thinkit8@l= ycos.com 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 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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