Re: Problem For Physfitfreak (monospace font required)

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.