XPost: comp.os.linux.advocacy   
   From: physfitfreak@gmail.com   
      
   On 11/2/24 05:32, Farley Flud wrote:   
   > On Sat, 2 Nov 2024 00:15:11 -0500, Physfitfreak wrote:   
   >   
   >>   
   >> In an absolute way? Disregarding unrelated limitations?   
   >>   
   >> Then that base would be infinity :) Then any real and complex number   
   >> will be expressed in just one digit :)   
   >>   
   >   
   > Good guess.   
   >   
   > This stuff is quite new to me.  I just stumbled upon it when   
   > doing some research on ternary (i.e. base 3) computers.   
   >   
   > It's all explained here:   
   >   
   > https://en.wikipedia.org/wiki/Optimal_radix_choice   
   >   
   > The "cost" of representing a number N in base b is (monospace   
   > font required):   
   >   
   >            log(N)   
   > b * floor(------ + 1)   
   >            log(b)   
   >   
   >   
   > Letting N --> inf we get the asymptotic cost:   
   >   
   >     b   
   >   ------   
   >   log(b)   
   >   
   >   
   > Here is an image of the plot of this relation:   
   >   
   > https://i.postimg.cc/CLwHyyzP/asymptotic-cost.png   
   >   
   > The minimum of this curve will give the lowest "cost"   
   > of expression.   
   >   
   > Take the derivative, set it equal to zero, and solve.   
   >   
   > Using Maxima:   
   >   
   > diff(b/log(b),b);   
   >   
   >      1         1   
   >   ------ - -------   
   >   log(b)      2   
   >            log (b)   
   >   
   >   
   > Set equal to zero and solve:   
   >   
   > solve(diff(b/log(b),b) = 0, b);   
   >   
   > [b = %e]   
   >   
   > There it is!  The most efficient number base is e, Euler's   
   > constant.   
   >   
   > But since irrational bases are not practical, we use the closest   
   > integer base which is 3.   
   >   
   > Thus, ternary (base 3) computers are the most efficient in   
   > storing numbers.   
   >   
   >   
   >   
      
      
   I'll go over that later (it is very late now). I read an article about   
   early Soviet computers built using a ternary number base when I was   
   beginning the third year of undergraduate physics. The department had   
   created an optional "computer programming" course that year for physics   
   students, or so I heard. This was early 1970s. I took that course and   
   attended the first two class sessions, then dropped the course right   
   away when I found out it was designed and created by the engineering   
   school, not the physics or math departments. I had a bad experience with   
   another optional course, "statics", a couple years earlier which had   
   caused us physics students grief and much anger in the way the material   
   were exposed to students and how strangely absurd the treatment we got   
   felt to us. That course was also an engineering school course. Both text   
   and the instructor were from the engineering school.   
      
   In that second session of the computer programming course, the   
   instructor gave us a handout about binary and ternary systems. Evidently   
   back then they were still thinking the choice Soviets had made (or had   
   tried at least) could be the one that become common.   
      
   Even that handout smelled of an engineer behind it creating it. For   
   instance, I remember I went back and forth in it to see where they   
   mention _which_ three numbers the Soviets had chosen. In binary of   
   course 0 and 1 had been chosen but in ternary that damn shit of a   
   handout would not say which three numbers were chosen! 0, 1, and 2? -1,   
   0, and 1? Even -2, -1, and 0? The creater of the handout was oblivious   
   to the significance of which set to choose and which one the Soviets   
   chose...   
      
   It disgusted me just like that "Statics" text had done, and I dropped   
   the course right after reading that handout.   
      
   Physics books are written very, very carefully! Because there's no other   
   way to say anything in there. They're not discussing things for   
   technicians. They're not discussing things for "engineers" or   
   "managers." They're discussing them for human, and for the sake of   
   _only_ finding stuff about nature; nothing else.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)