Here is a problem for Physfitfreak:

Of all the number bases, both rational (integer) and irrational,
which one is optimal for expressing numbers?

By optimal, it is meant the base that requires the least digits
(on average) to express all numbers.

It is an interesting problems and directly related to computer
architecture and hence to GNU/Linux because GNU/Linux is the only
OS that does not eschew computing fundamentals.

The unavoidable lurkers can only gawk briefly with their mouths
hanging open, shrug, and then return to their demented games.

Lurkers are lackeys.

Ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha!

--
Systemd: solving all the problems that you never knew you had.

On 11/1/24 13:59, Farley Flud wrote:
> Here is a problem for Physfitfreak:
>
> Of all the number bases, both rational (integer) and irrational,
> which one is optimal for expressing numbers?
>
> By optimal, it is meant the base that requires the least digits
> (on average) to express all numbers.
>
> It is an interesting problems and directly related to computer
> architecture and hence to GNU/Linux because GNU/Linux is the only
> OS that does not eschew computing fundamentals.
>
> The unavoidable lurkers can only gawk briefly with their mouths
> hanging open, shrug, and then return to their demented games.
>
> Lurkers are lackeys.
>
> Ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha!
>
>

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 :)

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.

--
Systemd: solving all the problems that you never knew you had.

On 11/2/2024 6:32 AM, Lameass Larry wrote:

> doing some research on ternary (i.e. base 3) computers.
Doing frivolous reading when you should be learning the Python std
library so you won't be a broke putz at 63 like you are at 43?

tut tut

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.

On Sun, 3 Nov 2024 01:30:59 -0500, Physfitfreak wrote:

>
> 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.
>

You must be joking.

One can pull any physics textbook, new or old, off the library shelf
and one will encounter a thicket of abstractions and endless equations
that provide very little, if any, humanly relevant insight.

The authors must do this or else they will be accused of incompetence
by their academic colleagues. Such dry rigor is the accepted fashion.

I am currently studying differential geometry (DG) on my own.
DG is the mathematical underpinning to both Lagrangian/Hamiltonian
mechanics and Einstein's general relativity.

However, I find that most scholarly DG books are totally useless.
For one thing, DG is a very visual subject and most books present
a paucity of imagery. This is a pure travesty!

Fortunately, there are some web sites that take a more casual,
and more proper, but still thorough approach to DG. These
web sites are hard to find, however. Here are a couple of
examples:

https://liavas.net/courses/math430/

https://math.franklin.uga.edu/sites/default/files/users/user317/ShifrinDiffGeo.pdf

Before too long, I will be publishing several web pages that
will present DG as it should be presented: using GNU/Linux
computer algebra and video animation.

--
Systemd: solving all the problems that you never knew you had.

On Sun, 3 Nov 2024 12:27:19 +0000, Farley Flud wrote:

> On Sun, 3 Nov 2024 01:30:59 -0500, Physfitfreak wrote:
>
>>
>> Physics books are written very, very carefully! Because there's no other
>> way to say anything in there.

Such was the situation prior to its corruption by Einsteinians .

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.
>>
>
> You must be joking.
>
> One can pull any physics textbook, new or old, off the library shelf
> and one will encounter a thicket of abstractions and endless equations
> that provide very little, if any, humanly relevant insight.
>
> The authors must do this or else they will be accused of incompetence
> by their academic colleagues. Such dry rigor is the accepted fashion.
>
> I am currently studying differential geometry (DG) on my own.
> DG is the mathematical underpinning to both Lagrangian/Hamiltonian
> mechanics and Einstein's general relativity.
>
> However, I find that most scholarly DG books are totally useless.
> For one thing, DG is a very visual subject and most books present
> a paucity of imagery. This is a pure travesty!
>
> Fortunately, there are some web sites that take a more casual,
> and more proper, but still thorough approach to DG. These
> web sites are hard to find, however. Here are a couple of
> examples:
>
> https://liavas.net/courses/math430/
>
> https://math.franklin.uga.edu/sites/default/files/users/user317/ShifrinDiffGeo.pdf
>
> Before too long, I will be publishing several web pages that
> will present DG as it should be presented: using GNU/Linux
> computer algebra and video animation.
>
>

On 11/3/24 06:27, Farley Flud wrote:
> One can pull any physics textbook, new or old, off the library shelf
> and one will encounter a thicket of abstractions and endless equations
> that provide very little, if any, humanly relevant insight.

True. Because each physics book is for certain physics students or
physicists. Chances that it would know where you in particular happen to
be in the long road of physics is close to nil.

But for the right reader, that same book is written very carefully, not
missing the slightest remark that was needed to be there.

On 11/1/2024 2:59 PM, Lameass Larry Piet wrote:

> Here is a problem for Physfitfreak:

Sand Chimp doesn't have time for this. He's worried about Israeli bombs
wiping out his chimp family back in Iran.

> GNU/Linux is the only OS that does not eschew computing fundamentals.

You gauche, grandiose fuckface. This is as dumb and delirious a
statement as you've ever made. An OS CANNOT avoid computing fundamentals.