Re: measuring systems (was: Selenites)

Nik Taylor wrote:
>Carlos Thompson wrote:
>> in older text, even with the Arabic/Indian notation, parts of units where
>> given as fractions, then 1/5 was nothing complicated as 0.249724972497...,
>> but 1/5.
>
>True, but with fractions, the base doesn't really matter, now does it?
>So as far as a "basal notation", duodecimal is easier with common
>fractions, while with fractions both are equally easy.
I want to say something about this fraction issue here. It's true that
fractions are equally easy no matter the base. But I wonder if you know
what happens with rational numbers when you try to translate them into
a different base. This came up to me some time ago when I was trying to
devise a binary system for some conculture (I think).

In base ten, you have 1/10, 1/100, 1/1000, etc. These fractions are the
basic ones to form the digits after the decimal point. But there's
*no way* to write exactly 1/1000 = 0.001 by using a reasonable number of
binary digits. (May a number be irrational in one base and rational in
another one? Math teachers/students out there?). Your fractional digits
in binary (the equivalents of 0.1, 0.01, 0.001 in decimal) would be
(in decimal) 0.5, 0.25, 0.125, etc. And you can't use any of them twice.

I know this is a bit off-topic and probably not a concern in everyday
life, but I had to point it out and perhaps someone has a good idea about
it. If you don't ever have to convert between bases, there's no problem.

>P.S., how did the Romans do multiplication with Roman numerals?  I can't
>imagine trying to multiply XXIII by XIV without converting into Arabic
>numberals.
I wonder what the Mayas did. Either they had to learn a 20x20 multiplication
table, or they could multiply dots and lines separatedly and then add them.
The system is quite wieldy -- I've tried and I could!


--Pablo Flores

begin 600 WINMAIL.DAT
M>)\^(@X/`0:0" `$```````!``$``0>0!@`(````Y 0```````#H``$-@ 0`
M`@````(``@`!!) &`#P!```!````# ````,``# #````"P`/#@`````"`?\/
M`0```%(`````````@2L?I+ZC$!F=;@#=`0]4`@````!#;VYS=')U8W1E9"!,
M86YG=6%G97,@3&ES= !33510`$-/3DQ!3D= 0E)/5TY632Y"4D]73BY%1%4`
M```>``(P`0````4```!33510`````!X``S !````&@```$-/3DQ!3D= 0E)/
M5TY632Y"4D]73BY%1%4````#`!4,`0````,`_@\&````'@`!, $````=````
M)T-O;G-T<G5C=&5D($QA;F=U86=E<R!,:7-T)P`````"`0LP`0```!\```!3
M3510.D-/3DQ!3D= 0E)/5TY632Y"4D]73BY%1%4```,``#D`````"P! .@$`
M```"`?8/`0````0````````#DSD!"( '`!@```!)4$TN36EC<F]S;V9T($UA
M:6PN3F]T90`Q" $$@ $`)P```%)%.B!M96%S=7)I;F<@<WES=&5M<R H=V%S
M.B!396QE;FET97,I`+8-`06 `P`.````S@<)`!T`"@`T``X``@!)`0$@@ ,`
M#@```,X'"0`=``H`)P`D``(`4@$!"8 !`"$```!%1#5%-T,P0C@V-3=$,C$Q
M.4,R.30T-#4U,S4T,# P, #J!@$#D 8`8 <``!(````+`",```````,`)@``
M````"P`I```````#`#8``````$ `.0# @?M<L.N]`1X`< `!````)P```%)%
M.B!M96%S=7)I;F<@<WES=&5M<R H=V%S.B!396QE;FET97,I```"`7$``0``
M`!8````!O>NP7/L+?%[N5X81TIPI1$535 `````>`!X,`0````4```!33510
M`````!X`'PP!````&P```&9F;&]R97- =&%U+G=A;6%N:2YA<&,N;W)G```#
M``80I"?"XP,`!Q"U!0``'@`($ $```!E````3DE+5$%93$]25U)/5$4Z0T%2
M3$]35$A/35!33TY74D]413I)3D],1$525$585"Q%5D5.5TE42%1(14%204))
M0R])3D1)04Y.3U1!5$E/3BQ005)44T]&54Y)5%-72$5214=)5@`````"`0D0
M`0```,\%``#+!0``P@H``$Q:1G433TP,_P`*`0\"%0*D`^0%ZP*#`% 3`U0"
M`&-H"L!S971N,@8`!L,"@S($1@(`<'!R<3$@"%4'L@* ?7\*@ C/"=D"@ J!
M#;$+8&Y@9S$P,S0*^Q+Q<VPQ. J@`V!T!9 %0$[ :6L@5&%Y%3$8#.@@('<9
M`CH8#QD4"H_M&F@^&W\9%$,*P!4P!"#D5&@#<'!S`B ;!1SGIQW/'M\903X@
M"X @!O %!($@&2!X="P@949V"? ;`&ET:"3P: QE( <0`:!I8R])+&YD!S #
MH&X9$&%T+FD"("5 '1%T!"!O9NP@=0,`)_%W)A 5H"%_TR*/(YQG:25R800@
M`U [`- G8G,E0"8!`Z Q+RXU&P`L82<A: N 9R![!: @L&PF@"=0"8 L4C"P
M+C(T.0' +[4N,&#.+"D/*A\CG&)U!4 MD7XN,*\QOQPO-'\UCQD%5/YR"E E
M0#.B);,LG#.0+&#))B!D;P>0;B<%0!6@\0= ;'D@`, "0 20)4#/)R 'X#P2
M)&!T/S</.!\Y&+I3;RQ3"L$L86$@+B([P0= )Q<B)4!D=?T$<6,'<$)1! `E
M4"Q@%#+W);,ND01@;CY//U\8NBR9_RBP`Q F(#J,,Y N(2Q0%:#9)5!Q=3RS
M1!%Y-!\:I/T<Y4DMP0(P)/!!,$) /.#_(- '@"XT`: (8$V1+D L>%5#T7,*
M4" HPBY-,'3Z)P0@=#GQ)?$G4!SE27C?2FXG$3SU.W=0H$(SL4U!)P(@),(&
MD"!Y"& @:Q\]@1SE*+ G4%!087!POPGP*)$EPB90)V)"4G4&T/\$D"B3`Z!6
M`E$0/.!-L5$0[P!Q"V 9("7R;21A3; <Y?]!\";0#= HT4V!5*0@@$/A]R[P
M!X H0'!-HEU13B(D\'L'<2Q09T$P62--0E#R>?<N4ELW#;!V! !>D3.0"X#S
M"L!.`7ES&2!:\ (0!<"#7A,%H&YC=6QT"'#-)B H34 N,FLI2V9,UO\#H#O#
M&2 GD58"$< E<"V!OQ=P)4!F,F9F9F$2`&-<PO\'D"8@4APF`1SE.\$F@"20
M_FX'D4VQ8A%:\"8")M L`)TG\6$!@%0U0V9P;UL1WU3D)@$5H%#@'.4J4\$M
MT+QY*DVB&Q EP$J!>"RQ<SS19P0@/2]Q9L 3T&+]/.!U`)!.DCR"(-$!H$CQ
M/UBD*!%I1F%$:R10H"A-WTWQ0?!R-5C0)&!R6!<D<O]J(#NT`' O,'596U8N
M$G)R_6H@/P70)U EX3R@$;!8X7HO8<!U#; ","@!;38_^6/0(%D(82R'0E%K
M)!SE^R1Q834H)@)*H2P0!T!Y]/LH,"^ ,25 <'%^Y'"A)'%]0V4I55%BX"\P
M6- <Y2BK?]HO@#5^\C*"<S&"POUG@T%VL58"+O \4G$`=H+7/. H(5K#= /P
M8U"08_T_5C-/%$/A81(%0"@@9BW]3;!P:>%VHACQ.\ "8%.B?P5 0?!BH@22
M)'$E85G 9/\9P!SE+M!<$#HD34 1P"\P_TVQ;+,^`7HSB-,$D%=!!"#_3B)V
M$A' 0=)>P 1P)& -L.]!\$[#?'9L\4E5Y#P0/%)_BK)EU$VQ8J&*P5QA$@!W
M?PGA.[,M%&V24[*)$DCP;<=C[4:?&050+E,P@%!0_SV2CY E\P@#!" \$#SP
M8N'_!2 NTT_");,(`UB2!) '0/YS>+!-,81#2W]&3QBZ0Y$?+ !V(5^GF38\
MX%A82?>@L'#"H*!6):-.XI*%+E+_6Q(F-9P/G1\8NEBDFS%+;_],?E5T5O,F
M`G0Q+&&8(5"@_D4EP50T/.",94CP"L L0?H@`=!X`="9/1SE`9%(\/\E0 6Q
MJM,%H("RH <\$&MB_W:Q+M!J(A'P'1$O`CS1=J+_+4.,<)A#E0=GT6&60^%]
MX9M:D0/P922P/. M+4TP?B>2(@B!+S%VL9N1@*(AMV/\'.6TD%!QX4$P1A4Q
M%P>0'.44P0"Y$ `#`! 0``````,`$1 `````0 `',.!.*9FNZ[T!0 `(,.!.
<*9FNZ[T!'@`]``$````%````4D4Z( ````#-<@`'
`
end