Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: Physfitfreak <physfitfreak@gmail.com>
Newsgroups: comp.os.linux.advocacy,sci.physics
Subject: Re: Problem For Physfitfreak (monospace font required)
Date: Sun, 3 Nov 2024 01:30:59 -0500
Organization: Modern Human
Message-ID: <vg75b3$3mcv$1@solani.org>
References: <pan$1e274$4cabc85a$bdc256fd$f948ec9b@linux.rocks>
 <vg4cgv$br8c$2@solani.org> <pan$a57c0$4c040b81$8dcb6976$beba7258@linux.rocks>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 3 Nov 2024 06:30:59 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="121247"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:7NMReCDQxnWHuqRuhqPXKSNbXS8=
X-User-ID: eJwNyMkRACAIBLCW5FjEcnCV/kvQXyawkOD0QDgaXdJKLnQQPF4wZu5SzVgFuo0PkT/p+15ViUE1uB3NnHxY+xT7
In-Reply-To: <pan$a57c0$4c040b81$8dcb6976$beba7258@linux.rocks>
Content-Language: en-US
Bytes: 4791
Lines: 111

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.