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Hidden dimensions could explain where mass comes from

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  Hidden dimensions could explain where mass comes from Anthk NM <anthk@disroot.org> - 2026-01-04 14:47 +0000
    Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-04 15:41 +0000
      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 17:06 +0100
      Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-04 15:08 -0800
        Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 10:47 +0100
          Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-05 07:59 -0800
            Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-05 08:22 -0800
            Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:43 +0100
              Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 00:00 -0800
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 09:28 -0800
                  Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 10:04 -0800
              Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 10:43 +0100
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 06:51 -0800
            Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:22 +0100
          Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 14:10 -0800
            Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:36 +0100
            Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:45 +0100
            Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:49 +0100
              Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 15:09 -0800
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 15:14 -0800
                  Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 00:47 +0100
                    Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 19:40 -0800
                      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 17:29 +0100
                        Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 08:48 -0800
                        Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-06 17:29 -0800
                          Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-06 19:20 -0800
                        Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-08 23:20 -0800
                          Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-09 00:03 -0800
                    Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-07 08:47 +0100
                      Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-07 11:46 -0800
                        Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-08 09:03 +0100
                          Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 08:16 -0800
                            Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-09 02:55 +0100
                              Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 19:55 -0800
                                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 22:34 -0800
                                  Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:24 +0100
                                Lagrangian mechanics (was: Hidden dimensions could explain where mass comes from) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-09 12:13 +0100
                                  Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 08:37 -0800
                                    Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 09:03 -0800
                                      Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-12 07:58 -0800
                                  Re: Lagrangian mechanics nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-09 21:17 +0100
                                    Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 13:23 -0800
                            Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:13 +0100
                          Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-08 20:13 -0800
                            Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:19 +0100
                              Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-10 13:08 -0800
                                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-11 10:13 +0100
                Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 00:45 +0100
                  Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-10 13:12 -0800
    Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-04 17:07 +0000
      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 18:39 +0100
      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 18:41 +0100
      Re: Hidden dimensions could explain where mass comes from Anthk NM <anthk@disroot.org> - 2026-01-05 20:11 +0000
        Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-05 20:52 +0000
          Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:36 +0100
          Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:38 +0100
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:03 +0100
        Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:26 +0100
          Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:55 +0100
      Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-09 14:06 +0000
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-09 21:31 +0100
    Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-04 20:46 +0100
      Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-04 13:54 -0800
        Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-04 14:45 -0800
      Re: Hidden dimensions could explain where mass comes from athel.cb@gmail.com <user12588@newsgrouper.org.invalid> - 2026-01-05 10:18 +0000
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 18:32 +0100
    Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:06 +0100
      Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 10:43 +0100
        Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 06:50 -0800
          Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 16:12 +0100
            Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 07:47 -0800
    Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-06 18:00 +0000
    Re: Hidden dimensions could explain where mass comes from Richard Hachel <rh@tiscali.fr> - 2026-01-11 22:32 +0000

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#668061

Chris M. Thomasson wrote:
> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>
>> For a 4d point we need (x, y, z, w, t), t for time.
>>
>> t is in every dimension?
>>
>> For a 2d (x, y, t)
>>
>> For a 1d (x, t)
> 
> Why not keep time in the dimension, [...]

Again, this wording does not make sense.  Time, here represented by the
coordinate t, *is* a dimension then *implicitly*.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#668064

On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
> Chris M. Thomasson wrote:
>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>
>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>
>>> t is in every dimension?
>>>
>>> For a 2d (x, y, t)
>>>
>>> For a 1d (x, t)
>>
>> Why not keep time in the dimension, [...]
> 
> Again, this wording does not make sense.  Time, here represented by the
> coordinate t, *is* a dimension then *implicitly*.
> 

Yeah. Well, fwiw, in my vector field sometimes I would encode the mass 
for a point in the vector itself:

vec4 = point (x, y, z, m) where m is the pass of the point. It can see 
how it can get confusing. When I would plot the points I would take the 
vec3 out of it so:

vec3 m0 = point

where m0 equals the (x, y, z) components of point. Then m was used in my 
vector field logic to create sources and sinks. When I would animate 
them, t was used as time normalized from 0...1 across the frames. An 
example I made, using 3d:

(Twisted Spheres)
https://youtu.be/JhdZ9ReJR9w

For a 4d field I have version of my code that have (z, y, z, w, m).

And take the vec4 (x, y, z, w) out of this 5-ary vector. m was just for 
mass. Now, in my field I don't know exactly where to plot a 4d point 
with a non-zero w component. I could only see its "influence" on the 
field as a whole. It's interesting to see how the 4d points alter the 3d 
render. I don't know where to plot a true 4d vector. Here is an example 
I made that uses true 4d vectors:

https://www.facebook.com/photo/?fbid=1218640825961580&set=pcb.1218640912628238

(btw can you see the content of the link? thanks. It should be public.)

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#668079

Chris M. Thomasson wrote:
> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>> Chris M. Thomasson wrote:
>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>
>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>
>>>> t is in every dimension?
>>>>
>>>> For a 2d (x, y, t)
>>>>
>>>> For a 1d (x, t)
>>>
>>> Why not keep time in the dimension, [...]
>>
>> Again, this wording does not make sense.  Time, here represented by the
>> coordinate t, *is* a dimension then *implicitly*.
>>
> 
> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass 
> for a point in the vector itself:

*Physically* that does not make a lot of sense, although one could argue
that the mass of a _point-like object_ that is initially _at_ a point of
(3D) space and subsequently perhaps found _at_ different points of that
space (which is what you *actually* mean) is a degree of freedom.

The physics would be better represented computationally by defining a
point-like object as an _object_ (using object-oriented programming, or
something equivalent like a C-struct) with at least two
properties/attributes: its position, given as a vector/array/list, and,
separately, its mass.

> vec4 = point (x, y, z, m) where m is the pass of the point. It can see 
> how it can get confusing. When I would plot the points I would take the 
> vec3 out of it so:
> 
> vec3 m0 = point

Which programming language is that?

> where m0 equals the (x, y, z) components of point. 

That appears to me to be a bad (because confusing, and not self-explaining)
choice of variable identifier as well.  I would call that variable "coords"
(for "coordinates") or "position" instead.

> https://www.facebook.com/photo/?fbid=1218640825961580&set=pcb.1218640912628238
> 
> (btw can you see the content of the link? thanks. It should be public.)

I can see it fully when I am logged in into Facebook.  Otherwise I can see
it only partially as Facebook's "Log in or sign up for Facebook ..." bar
covers the bottom of it.

Unfortunately, the photos are slightly blurred so one cannot see the images
clearly and cannot scan the QR code.

The images by you for the content of the AMS 2025 Calendar are nicely done.
What exactly am I looking at there?  (I found
<https://gallery.bridgesmathart.org/exhibitions/2024-joint-mathematics-meetings/chris-m-thomasson>)

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#668080

On 01/06/2026 08:29 AM, Thomas 'PointedEars' Lahn wrote:
> Chris M. Thomasson wrote:
>> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>>> Chris M. Thomasson wrote:
>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>
>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>
>>>>> t is in every dimension?
>>>>>
>>>>> For a 2d (x, y, t)
>>>>>
>>>>> For a 1d (x, t)
>>>>
>>>> Why not keep time in the dimension, [...]
>>>
>>> Again, this wording does not make sense.  Time, here represented by the
>>> coordinate t, *is* a dimension then *implicitly*.
>>>
>>
>> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass
>> for a point in the vector itself:
>
> *Physically* that does not make a lot of sense, although one could argue
> that the mass of a _point-like object_ that is initially _at_ a point of
> (3D) space and subsequently perhaps found _at_ different points of that
> space (which is what you *actually* mean) is a degree of freedom.
>
> The physics would be better represented computationally by defining a
> point-like object as an _object_ (using object-oriented programming, or
> something equivalent like a C-struct) with at least two
> properties/attributes: its position, given as a vector/array/list, and,
> separately, its mass.
>
>> vec4 = point (x, y, z, m) where m is the pass of the point. It can see
>> how it can get confusing. When I would plot the points I would take the
>> vec3 out of it so:
>>
>> vec3 m0 = point
>
> Which programming language is that?
>
>> where m0 equals the (x, y, z) components of point.
>
> That appears to me to be a bad (because confusing, and not self-explaining)
> choice of variable identifier as well.  I would call that variable "coords"
> (for "coordinates") or "position" instead.
>
>> https://www.facebook.com/photo/?fbid=1218640825961580&set=pcb.1218640912628238
>>
>> (btw can you see the content of the link? thanks. It should be public.)
>
> I can see it fully when I am logged in into Facebook.  Otherwise I can see
> it only partially as Facebook's "Log in or sign up for Facebook ..." bar
> covers the bottom of it.
>
> Unfortunately, the photos are slightly blurred so one cannot see the images
> clearly and cannot scan the QR code.
>
> The images by you for the content of the AMS 2025 Calendar are nicely done.
> What exactly am I looking at there?  (I found
> <https://gallery.bridgesmathart.org/exhibitions/2024-joint-mathematics-meetings/chris-m-thomasson>)
>

Usually enough any sort of language with user-defined types.

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#668092

On 1/6/2026 8:29 AM, Thomas 'PointedEars' Lahn wrote:
> Chris M. Thomasson wrote:
>> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>>> Chris M. Thomasson wrote:
>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>
>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>
>>>>> t is in every dimension?
>>>>>
>>>>> For a 2d (x, y, t)
>>>>>
>>>>> For a 1d (x, t)
>>>>
>>>> Why not keep time in the dimension, [...]
>>>
>>> Again, this wording does not make sense.  Time, here represented by the
>>> coordinate t, *is* a dimension then *implicitly*.
>>>
>>
>> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass
>> for a point in the vector itself:
> 
> *Physically* that does not make a lot of sense, although one could argue
> that the mass of a _point-like object_ that is initially _at_ a point of
> (3D) space and subsequently perhaps found _at_ different points of that
> space (which is what you *actually* mean) is a degree of freedom.

Agreed.


> The physics would be better represented computationally by defining a
> point-like object as an _object_ (using object-oriented programming, or
> something equivalent like a C-struct) with at least two
> properties/attributes: its position, given as a vector/array/list, and,
> separately, its mass.

My field is basically an array of point objects. The point objects 
themselves have the origin and mass, color, ect, matrix, ect... 
Sometimes I would actually encode the mass in the origin vector itself. 
Well, yeah. Confusing. Shit.


>> vec4 = point (x, y, z, m) where m is the pass of the point. It can see
>> how it can get confusing. When I would plot the points I would take the
>> vec3 out of it so:
>>
>> vec3 m0 = point
> 
> Which programming language is that?

C++ using the glm library and/or pure GLSL. Fwiw, I know HLSL as well.

https://github.com/g-truc/glm

>> where m0 equals the (x, y, z) components of point.
> 
> That appears to me to be a bad (because confusing, and not self-explaining)
> choice of variable identifier as well.  I would call that variable "coords"
> (for "coordinates") or "position" instead.

Yeah. It has bit me in the ass before. I forgot to treat say a 4-ary 
vector, (x, y, z, m) as a 3d vector to get at its (x, y, z), and took 
the damn m component for the damn vector/matrix math. Oh,... CRAP! ;^o 
That m is meant as a mass! Sigh...


>> https://www.facebook.com/photo/?fbid=1218640825961580&set=pcb.1218640912628238
>>
>> (btw can you see the content of the link? thanks. It should be public.)
> 
> I can see it fully when I am logged in into Facebook.  Otherwise I can see
> it only partially as Facebook's "Log in or sign up for Facebook ..." bar
> covers the bottom of it.

Well, thanks for taking a look. I thought it "should" be visible even if 
your not logged in. Grrr. Sigh. Anyway...


> Unfortunately, the photos are slightly blurred so one cannot see the images
> clearly and cannot scan the QR code.

Okay. I see. I thought since it was public, others could actually see 
them with any blurry effects, ect...


> The images by you for the content of the AMS 2025 Calendar are nicely done.

Thank you! I really appreciate it.


> What exactly am I looking at there?  (I found
> <https://gallery.bridgesmathart.org/exhibitions/2024-joint-mathematics-meetings/chris-m-thomasson>)

The render of mine that made the cover is a highly experimental 4d 
vector field of mine. The lines are the actual field lines of the field. 
So, I created a 4d field and setup the seed points, for the source sink. 
I made SURE to keep the 4d w components (x, y, z, w) at zero. I said 
okay. I have a 3d field and every w component is zero even during 
iteration. Okay. Let me add in one more seed point with zero (x, y, z) 
components and a single _non-zero_ w component. (x, y, z) are zero, and 
w is non-zero. Let me make it an attractor wrt a positive mass. Okay. 
Lets render the bastard! Oh shit, the whole field is altered from a 
single attractor point in the 4'th dimension. I said oh this is nice. 
Then posted to the AMS via bridges...

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#668093

On 1/6/2026 5:29 PM, Chris M. Thomasson wrote:
> On 1/6/2026 8:29 AM, Thomas 'PointedEars' Lahn wrote:
>> Chris M. Thomasson wrote:
>>> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>>>> Chris M. Thomasson wrote:
>>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>>
>>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>>
>>>>>> t is in every dimension?
>>>>>>
>>>>>> For a 2d (x, y, t)
>>>>>>
>>>>>> For a 1d (x, t)
>>>>>
>>>>> Why not keep time in the dimension, [...]
>>>>
>>>> Again, this wording does not make sense.  Time, here represented by the
>>>> coordinate t, *is* a dimension then *implicitly*.
>>>>
>>>
>>> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass
>>> for a point in the vector itself:
>>
>> *Physically* that does not make a lot of sense, although one could argue
>> that the mass of a _point-like object_ that is initially _at_ a point of
>> (3D) space and subsequently perhaps found _at_ different points of that
>> space (which is what you *actually* mean) is a degree of freedom.
> 
> Agreed.
> 
> 
>> The physics would be better represented computationally by defining a
>> point-like object as an _object_ (using object-oriented programming, or
>> something equivalent like a C-struct) with at least two
>> properties/attributes: its position, given as a vector/array/list, and,
>> separately, its mass.
> 
> My field is basically an array of point objects. The point objects 
> themselves have the origin and mass, color, ect, matrix, ect... 
> Sometimes I would actually encode the mass in the origin vector itself. 
> Well, yeah. Confusing. Shit.
> 
> 
>>> vec4 = point (x, y, z, m) where m is the pass of the point. It can see
>>> how it can get confusing. When I would plot the points I would take the
>>> vec3 out of it so:
>>>
>>> vec3 m0 = point
>>
>> Which programming language is that?
> 
> C++ using the glm library and/or pure GLSL. Fwiw, I know HLSL as well.
> 
> https://github.com/g-truc/glm
> 
>>> where m0 equals the (x, y, z) components of point.
>>
>> That appears to me to be a bad (because confusing, and not self- 
>> explaining)
>> choice of variable identifier as well.  I would call that variable 
>> "coords"
>> (for "coordinates") or "position" instead.
> 
> Yeah. It has bit me in the ass before. I forgot to treat say a 4-ary 
> vector, (x, y, z, m) as a 3d vector to get at its (x, y, z), and took 
> the damn m component for the damn vector/matrix math. Oh,... CRAP! ;^o 
> That m is meant as a mass! Sigh...
> 
> 
>>> https://www.facebook.com/photo/? 
>>> fbid=1218640825961580&set=pcb.1218640912628238
>>>
>>> (btw can you see the content of the link? thanks. It should be public.)
>>
>> I can see it fully when I am logged in into Facebook.  Otherwise I can 
>> see
>> it only partially as Facebook's "Log in or sign up for Facebook ..." bar
>> covers the bottom of it.
> 
> Well, thanks for taking a look. I thought it "should" be visible even if 
> your not logged in. Grrr. Sigh. Anyway...
> 
> 
>> Unfortunately, the photos are slightly blurred so one cannot see the 
>> images
>> clearly and cannot scan the QR code.
> 
> Okay. I see. I thought since it was public, others could actually see 
> them with any blurry effects, ect...
> 
> 
>> The images by you for the content of the AMS 2025 Calendar are nicely 
>> done.
> 
> Thank you! I really appreciate it.
> 
> 
>> What exactly am I looking at there?  (I found
>> <https://gallery.bridgesmathart.org/exhibitions/2024-joint- 
>> mathematics-meetings/chris-m-thomasson>)
> 
> The render of mine that made the cover is a highly experimental 4d 
> vector field of mine. The lines are the actual field lines of the field. 
> So, I created a 4d field and setup the seed points, for the source sink. 
> I made SURE to keep the 4d w components (x, y, z, w) at zero. I said 
> okay. I have a 3d field and every w component is zero even during 
> iteration. Okay. Let me add in one more seed point with zero (x, y, z) 
> components and a single _non-zero_ w component. (x, y, z) are zero, and 
> w is non-zero. Let me make it an attractor wrt a positive mass. Okay. 
> Lets render the bastard! Oh shit, the whole field is altered from a 
> single attractor point in the 4'th dimension. I said oh this is nice. 
> Then posted to the AMS via bridges...

I mention 3d vectors because of my setup where all of them have zero w 
components. Then, after that render. Well, add one in where the x, y, z 
are zero and w is non-zero.

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#668126

On 1/6/2026 8:29 AM, Thomas 'PointedEars' Lahn wrote:
> Chris M. Thomasson wrote:
>> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>>> Chris M. Thomasson wrote:
>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>
>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>
>>>>> t is in every dimension?
>>>>>
>>>>> For a 2d (x, y, t)
>>>>>
>>>>> For a 1d (x, t)
>>>>
>>>> Why not keep time in the dimension, [...]
>>>
>>> Again, this wording does not make sense.  Time, here represented by the
>>> coordinate t, *is* a dimension then *implicitly*.
>>>
>>
>> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass
>> for a point in the vector itself:
> 
> *Physically* that does not make a lot of sense, although one could argue
> that the mass of a _point-like object_ that is initially _at_ a point of
> (3D) space and subsequently perhaps found _at_ different points of that
> space (which is what you *actually* mean) is a degree of freedom.
> 
> The physics would be better represented computationally by defining a
> point-like object as an _object_ (using object-oriented programming, or
> something equivalent like a C-struct) with at least two
> properties/attributes: its position, given as a vector/array/list, and,
> separately, its mass.
> 
>> vec4 = point (x, y, z, m) where m is the pass of the point. It can see
>> how it can get confusing. When I would plot the points I would take the
>> vec3 out of it so:
>>
>> vec3 m0 = point
> 
> Which programming language is that?
> 
>> where m0 equals the (x, y, z) components of point.
> 
> That appears to me to be a bad (because confusing, and not self-explaining)
> choice of variable identifier as well.  I would call that variable "coords"
> (for "coordinates") or "position" instead.
> 
>> https://www.facebook.com/photo/?fbid=1218640825961580&set=pcb.1218640912628238
>>
>> (btw can you see the content of the link? thanks. It should be public.)
> 
> I can see it fully when I am logged in into Facebook.  Otherwise I can see
> it only partially as Facebook's "Log in or sign up for Facebook ..." bar
> covers the bottom of it.
> 
> Unfortunately, the photos are slightly blurred so one cannot see the images
> clearly and cannot scan the QR code.
> 
> The images by you for the content of the AMS 2025 Calendar are nicely done.
> What exactly am I looking at there?  (I found
> <https://gallery.bridgesmathart.org/exhibitions/2024-joint-mathematics-meetings/chris-m-thomasson>)
> 


Fwiw, here is a 3d model that popped out of my vector field code:

(ctHyperField)
https://skfb.ly/pyP9E

I hope your browser can load it up and you can fly around and explore 
it. Fwiw, here is another one:

https://skfb.ly/pzTEC

https://skfb.ly/pyXH6

Fwiw, these are pure 3d vectors in the sense that the w components of 
every one of them during iteration is zero.

Can you explore them?

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#668127

On 1/8/2026 11:20 PM, Chris M. Thomasson wrote:
> On 1/6/2026 8:29 AM, Thomas 'PointedEars' Lahn wrote:
>> Chris M. Thomasson wrote:
>>> On 1/5/2026 3:47 PM, Thomas 'PointedEars' Lahn wrote:
>>>> Chris M. Thomasson wrote:
>>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>>
>>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>>
>>>>>> t is in every dimension?
>>>>>>
>>>>>> For a 2d (x, y, t)
>>>>>>
>>>>>> For a 1d (x, t)
>>>>>
>>>>> Why not keep time in the dimension, [...]
>>>>
>>>> Again, this wording does not make sense.  Time, here represented by the
>>>> coordinate t, *is* a dimension then *implicitly*.
>>>>
>>>
>>> Yeah. Well, fwiw, in my vector field sometimes I would encode the mass
>>> for a point in the vector itself:
>>
>> *Physically* that does not make a lot of sense, although one could argue
>> that the mass of a _point-like object_ that is initially _at_ a point of
>> (3D) space and subsequently perhaps found _at_ different points of that
>> space (which is what you *actually* mean) is a degree of freedom.
>>
>> The physics would be better represented computationally by defining a
>> point-like object as an _object_ (using object-oriented programming, or
>> something equivalent like a C-struct) with at least two
>> properties/attributes: its position, given as a vector/array/list, and,
>> separately, its mass.
>>
>>> vec4 = point (x, y, z, m) where m is the pass of the point. It can see
>>> how it can get confusing. When I would plot the points I would take the
>>> vec3 out of it so:
>>>
>>> vec3 m0 = point
>>
>> Which programming language is that?
>>
>>> where m0 equals the (x, y, z) components of point.
>>
>> That appears to me to be a bad (because confusing, and not self- 
>> explaining)
>> choice of variable identifier as well.  I would call that variable 
>> "coords"
>> (for "coordinates") or "position" instead.
>>
>>> https://www.facebook.com/photo/? 
>>> fbid=1218640825961580&set=pcb.1218640912628238
>>>
>>> (btw can you see the content of the link? thanks. It should be public.)
>>
>> I can see it fully when I am logged in into Facebook.  Otherwise I can 
>> see
>> it only partially as Facebook's "Log in or sign up for Facebook ..." bar
>> covers the bottom of it.
>>
>> Unfortunately, the photos are slightly blurred so one cannot see the 
>> images
>> clearly and cannot scan the QR code.
>>
>> The images by you for the content of the AMS 2025 Calendar are nicely 
>> done.
>> What exactly am I looking at there?  (I found
>> <https://gallery.bridgesmathart.org/exhibitions/2024-joint- 
>> mathematics-meetings/chris-m-thomasson>)
>>
> 
> 
> Fwiw, here is a 3d model that popped out of my vector field code:
> 
> (ctHyperField)
> https://skfb.ly/pyP9E
> 
> I hope your browser can load it up and you can fly around and explore 
> it. Fwiw, here is another one:
> 
> https://skfb.ly/pzTEC
> 
> https://skfb.ly/pyXH6
> 
> Fwiw, these are pure 3d vectors in the sense that the w components of 
> every one of them during iteration is zero.
> 
> Can you explore them?

This one has my midi music, and looks a little creepy...

(3d Field Test)
https://youtu.be/HwIkk9zENcg

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#668096

Am Dienstag000006, 06.01.2026 um 00:47 schrieb Thomas 'PointedEars' Lahn:
> Chris M. Thomasson wrote:
>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>
>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>
>>> t is in every dimension?
>>>
>>> For a 2d (x, y, t)
>>>
>>> For a 1d (x, t)
>>
>> Why not keep time in the dimension, [...]
> 
> Again, this wording does not make sense.  Time, here represented by the
> coordinate t, *is* a dimension then *implicitly*.
> 

The word 'dimension' has different meanings, hence it is necessary to 
write, which meaning was meant.

If we refer to space, the 'usual' space has three dimensions of the type 
'length', which are orthogonal towards each other.

This wouldn't allow an additional orthogonal dimension of space for time.

So, we need a different meaning for 'dimension' and a different 'space'.

If we add t to the 'x,y,z-space' we end up in what is called spacetime.

But I would suggest a different approach and use complex numbers and 
assume, that time is imaginary and the dimensions of space real.

An even better approach would be to use a construct called 
'biquaternions' and assume, that the 'real space' has actually such 
features, as if it was a quaternion-field, where points have the 
features of bi-quaternions.

This would allow three imaginary axes of time and three real axes of 
space, plus two additional 'dimensions' for scalars and pseudo-scalars.

I have written a kind of book about this idea some years ago, which can 
be found here:

https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing


TH

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#668103

On 1/6/2026 11:47 PM, Thomas Heger wrote:
> Am Dienstag000006, 06.01.2026 um 00:47 schrieb Thomas 'PointedEars' Lahn:
>> Chris M. Thomasson wrote:
>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>
>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>
>>>> t is in every dimension?
>>>>
>>>> For a 2d (x, y, t)
>>>>
>>>> For a 1d (x, t)
>>>
>>> Why not keep time in the dimension, [...]
>>
>> Again, this wording does not make sense.  Time, here represented by the
>> coordinate t, *is* a dimension then *implicitly*.
>>
> 
> The word 'dimension' has different meanings, hence it is necessary to 
> write, which meaning was meant.
> 
> If we refer to space, the 'usual' space has three dimensions of the type 
> 'length', which are orthogonal towards each other.
> 
> This wouldn't allow an additional orthogonal dimension of space for time.
> 
> So, we need a different meaning for 'dimension' and a different 'space'.
> 
> If we add t to the 'x,y,z-space' we end up in what is called spacetime.
> 
> But I would suggest a different approach and use complex numbers and 
> assume, that time is imaginary and the dimensions of space real.
> 
> An even better approach would be to use a construct called 
> 'biquaternions' and assume, that the 'real space' has actually such 
> features, as if it was a quaternion-field, where points have the 
> features of bi-quaternions.
> 
> This would allow three imaginary axes of time and three real axes of 
> space, plus two additional 'dimensions' for scalars and pseudo-scalars.

When I would add a t to a vector, say (x, y, z, t), yes its confusing. I 
would only use the (x, y, z) parts for the vector math, ect. The t was a 
point in time for that (x, y, z) vector. So, say:

(-.5, .1, -.16, 0)

The t aspect is at say, a stop watch started from zero. It ticks. Now, 
the same point can be:

(-.5, .1, -.16, 0.0000001)

well, the granularity of the t aside for a moment. However, we now have 
the same point in a different time.

As time ticks by we have a shit load of vectors at the same point, but 
with different non-zero t components. We can sort them based on t after 
some iterations... ect. Its fun to do, ponder on. So a single point that 
stays the same can have different t's. However, it does not mean that t 
is a 4d space. No, its a 3d space with t. For a 4d space (x, y, z, w, 
t), on and on. But it is confusing.

Actually, I don't know where to plot a 4d point with a non-zero w 
component. One time I said just plot the 3d components (x, y, z), and 
use w as a color spectrum that is unique. So, I can say here is a 4d 
point and its a certain color. This tells me that the point is off axis 
from the pure 3d world, aka non-zero w.


> I have written a kind of book about this idea some years ago, which can 
> be found here:
> 
> https://docs.google.com/presentation/ 
> d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing

Hummm... Need to read that when I get some more time. Thanks!

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#668111

Am Mittwoch000007, 07.01.2026 um 20:46 schrieb Chris M. Thomasson:
> On 1/6/2026 11:47 PM, Thomas Heger wrote:
>> Am Dienstag000006, 06.01.2026 um 00:47 schrieb Thomas 'PointedEars' Lahn:
>>> Chris M. Thomasson wrote:
>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>
>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>
>>>>> t is in every dimension?
>>>>>
>>>>> For a 2d (x, y, t)
>>>>>
>>>>> For a 1d (x, t)
>>>>
>>>> Why not keep time in the dimension, [...]
>>>
>>> Again, this wording does not make sense.  Time, here represented by the
>>> coordinate t, *is* a dimension then *implicitly*.
>>>
>>
>> The word 'dimension' has different meanings, hence it is necessary to 
>> write, which meaning was meant.
>>
>> If we refer to space, the 'usual' space has three dimensions of the 
>> type 'length', which are orthogonal towards each other.
>>
>> This wouldn't allow an additional orthogonal dimension of space for time.
>>
>> So, we need a different meaning for 'dimension' and a different 'space'.
>>
>> If we add t to the 'x,y,z-space' we end up in what is called spacetime.
>>
>> But I would suggest a different approach and use complex numbers and 
>> assume, that time is imaginary and the dimensions of space real.
>>
>> An even better approach would be to use a construct called 
>> 'biquaternions' and assume, that the 'real space' has actually such 
>> features, as if it was a quaternion-field, where points have the 
>> features of bi-quaternions.
>>
>> This would allow three imaginary axes of time and three real axes of 
>> space, plus two additional 'dimensions' for scalars and pseudo-scalars.
> 
> When I would add a t to a vector, say (x, y, z, t), yes its confusing. I 
> would only use the (x, y, z) parts for the vector math, ect. The t was a 
> point in time for that (x, y, z) vector. So, say:
> 
> (-.5, .1, -.16, 0)
> 
> The t aspect is at say, a stop watch started from zero. It ticks. Now, 
> the same point can be:
> 
> (-.5, .1, -.16, 0.0000001)
> 
> well, the granularity of the t aside for a moment. However, we now have 
> the same point in a different time.
> 
> As time ticks by we have a shit load of vectors at the same point, but 
> with different non-zero t components. We can sort them based on t after 
> some iterations... ect. Its fun to do, ponder on. So a single point that 
> stays the same can have different t's. However, it does not mean that t 
> is a 4d space. No, its a 3d space with t. For a 4d space (x, y, z, w, 
> t), on and on. But it is confusing.
> 
> Actually, I don't know where to plot a 4d point with a non-zero w 
> component. One time I said just plot the 3d components (x, y, z), and 
> use w as a color spectrum that is unique. So, I can say here is a 4d 
> point and its a certain color. This tells me that the point is off axis 
> from the pure 3d world, aka non-zero w.


Look at this:

https://www.maeckes.nl/Tekeningen/Complexe%20vlak%20.png

(from here: https://www.maeckes.nl/Arganddiagram%20GB.html )

This is a so called 'Argand diagram' or a 'complex plane'.

And now compare it to this diagram:

https://www.math.brown.edu/tbanchof/STG/ma8/papers/dmargalit/project/pastpres.gif

This stems from here:
https://www.math.brown.edu/tbanchof/STG/ma8/papers/dmargalit/project/minkowsk.html

and is called 'Minkowski diagram'.

You'll certainly see some similarities.

But Minkowski diagrams are as flat as Argand diagrams, hence we need to 
'pump them up' to 3D.

That ain't actually possible and we need four dimensions (at least) of 
which at least one is imaginary.

This would end up in the realm of quaternions.

Unfortunately Hamilton's quaternions do not really fit to the real 
world, hence we need something slightly different.

My suggestion was: use 'biquaternions' (aka 'complex four vectors')


> 
>> I have written a kind of book about this idea some years ago, which 
>> can be found here:
>>
>> https://docs.google.com/presentation/ 
>> d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
> 
> Hummm... Need to read that when I get some more time. Thanks!


Well, that 'book' ain't perfect, because it was the first thing I have 
written about physics. It's also written in English, which is a second 
language for me (I from Germany).

I'm also not a physicist and that 'book' was the result of a hobby.

But still I think, the concept is quite good.


TH

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#668118

On 01/08/2026 12:03 AM, Thomas Heger wrote:
> Am Mittwoch000007, 07.01.2026 um 20:46 schrieb Chris M. Thomasson:
>> On 1/6/2026 11:47 PM, Thomas Heger wrote:
>>> Am Dienstag000006, 06.01.2026 um 00:47 schrieb Thomas 'PointedEars'
>>> Lahn:
>>>> Chris M. Thomasson wrote:
>>>>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:
>>>>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
>>>>>>
>>>>>> For a 4d point we need (x, y, z, w, t), t for time.
>>>>>>
>>>>>> t is in every dimension?
>>>>>>
>>>>>> For a 2d (x, y, t)
>>>>>>
>>>>>> For a 1d (x, t)
>>>>>
>>>>> Why not keep time in the dimension, [...]
>>>>
>>>> Again, this wording does not make sense.  Time, here represented by the
>>>> coordinate t, *is* a dimension then *implicitly*.
>>>>
>>>
>>> The word 'dimension' has different meanings, hence it is necessary to
>>> write, which meaning was meant.
>>>
>>> If we refer to space, the 'usual' space has three dimensions of the
>>> type 'length', which are orthogonal towards each other.
>>>
>>> This wouldn't allow an additional orthogonal dimension of space for
>>> time.
>>>
>>> So, we need a different meaning for 'dimension' and a different 'space'.
>>>
>>> If we add t to the 'x,y,z-space' we end up in what is called spacetime.
>>>
>>> But I would suggest a different approach and use complex numbers and
>>> assume, that time is imaginary and the dimensions of space real.
>>>
>>> An even better approach would be to use a construct called
>>> 'biquaternions' and assume, that the 'real space' has actually such
>>> features, as if it was a quaternion-field, where points have the
>>> features of bi-quaternions.
>>>
>>> This would allow three imaginary axes of time and three real axes of
>>> space, plus two additional 'dimensions' for scalars and pseudo-scalars.
>>
>> When I would add a t to a vector, say (x, y, z, t), yes its confusing.
>> I would only use the (x, y, z) parts for the vector math, ect. The t
>> was a point in time for that (x, y, z) vector. So, say:
>>
>> (-.5, .1, -.16, 0)
>>
>> The t aspect is at say, a stop watch started from zero. It ticks. Now,
>> the same point can be:
>>
>> (-.5, .1, -.16, 0.0000001)
>>
>> well, the granularity of the t aside for a moment. However, we now
>> have the same point in a different time.
>>
>> As time ticks by we have a shit load of vectors at the same point, but
>> with different non-zero t components. We can sort them based on t
>> after some iterations... ect. Its fun to do, ponder on. So a single
>> point that stays the same can have different t's. However, it does not
>> mean that t is a 4d space. No, its a 3d space with t. For a 4d space
>> (x, y, z, w, t), on and on. But it is confusing.
>>
>> Actually, I don't know where to plot a 4d point with a non-zero w
>> component. One time I said just plot the 3d components (x, y, z), and
>> use w as a color spectrum that is unique. So, I can say here is a 4d
>> point and its a certain color. This tells me that the point is off
>> axis from the pure 3d world, aka non-zero w.
>
>
> Look at this:
>
> https://www.maeckes.nl/Tekeningen/Complexe%20vlak%20.png
>
> (from here: https://www.maeckes.nl/Arganddiagram%20GB.html )
>
> This is a so called 'Argand diagram' or a 'complex plane'.
>
> And now compare it to this diagram:
>
> https://www.math.brown.edu/tbanchof/STG/ma8/papers/dmargalit/project/pastpres.gif
>
>
> This stems from here:
> https://www.math.brown.edu/tbanchof/STG/ma8/papers/dmargalit/project/minkowsk.html
>
>
> and is called 'Minkowski diagram'.
>
> You'll certainly see some similarities.
>
> But Minkowski diagrams are as flat as Argand diagrams, hence we need to
> 'pump them up' to 3D.
>
> That ain't actually possible and we need four dimensions (at least) of
> which at least one is imaginary.
>
> This would end up in the realm of quaternions.
>
> Unfortunately Hamilton's quaternions do not really fit to the real
> world, hence we need something slightly different.
>
> My suggestion was: use 'biquaternions' (aka 'complex four vectors')
>
>
>>
>>> I have written a kind of book about this idea some years ago, which
>>> can be found here:
>>>
>>> https://docs.google.com/presentation/
>>> d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
>>
>> Hummm... Need to read that when I get some more time. Thanks!
>
>
> Well, that 'book' ain't perfect, because it was the first thing I have
> written about physics. It's also written in English, which is a second
> language for me (I from Germany).
>
> I'm also not a physicist and that 'book' was the result of a hobby.
>
> But still I think, the concept is quite good.
>
>
> TH

The idea that everything physics is always parameterized
by time or 't' is often formalized "the Lagrangian", sort
of like "the Machian" is a usual notion of far-field.
Lagrange is also known for when in mechanics there's
both the severe abstraction and also the sum-of-potentials,
i.e. two different things juxtaposed across each other.
Mach is similar, known for the acoustic and also the total
or about the field.

Of course Mach is more known for meaning both the near-field
and far-field, and while Lagrange is known for both the
"real and fictitious" forces in usual models of kinetics
about potentials, the usual attachment of the Lagrangian
the particular formalism after the Hamiltonian, often
results the more "shut-up-and-compute, i.e., we don't have
the language to compute the full term, and truncate the term".

It's similar an account of "entropy", since the Aristotelean
and the Leibnitzian are basically opposite meanings of the term,
similarly for example to the argument about Newton "vis motrix"
and Leibnitz "vis viva" vis-a-vis notions like "vis insita".

So, Lagrange is well-known for the usual definitions in
mechanics, yet unless you know that it's also about that
the potentials are real, he's sort of laughing in his sleeve.

Then a usual implicit parameterization of anything physical
by time 't' is also part of logical, since for a logic to
be modal and more-than-merely-quasi-modal, there's temporality
as to why true logic is a modal, temporal, relevance logic.

A usual "clock-hypothesis" that there's a unique ray of
time 't' is found in usual theories like Einstein's relativity,
according to Einstein.


Phew, I had keyboarded "Einstien" instead of "Einstein"
and automatically corrected that, wouldn't necessarily
want to come across as not being familiar with the
history of the field and its main actors.

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#668121

Ross Finlayson wrote:
> The idea that everything physics is always parameterized
> by time or 't' is often formalized "the Lagrangian",

No, the parametrization by time is a concept in Lagrangian _mechanics_ which
is based on the _principle of stationary ("least") action_.  The action is
defined as

  S[x(t)] = ∫ dt L[x(t), dx(t)/dt, t],

where x may be a vector (field), and L is the Lagrangian (function).
[Both S and L are *functionals*: they depend on a function, x(t);
hence the customary notation with rectangular brackets.]

In special relativity, one finds from the Minkowski metric

  ds^2 = c^2 dτ² = c^2 dt^2 - dx^2 - dy^2 - dz^2
                 = c^2 dt^2 [1 - (dx/dt)^2 - (dy/dt)^2 - (dz/dt)^2]
                 = c^2 dt^2 (1 - V^2/c^2)

that

  S[x] = -m c ∫ ds = -m c ∫ dt c √(1 - V^2/c^2)
                   = ∫ dt [-m c^2 √(1 - V^2/c^2)],

where the prefactor -m c is introduced so as to produce a quantity with
dimensions of action (energy × time, cf. ℎ and ℏ) and the correct canonical
momentum [*], and in the integrand one with dimensions of energy; so the
relativistic non-interacting Lagrangian is

  L = -m c^2 √(1 - V^2/c^2) = -m c^2 √[1 - (dX/dt)^2/c^2].

It turns out that this leads to the correct energy--momentum relation,
as I pointed out earlier.

  [*] For example, the canonical 3-momentum is, from the Euler--Lagrange
      equations

        0 = d/dt ∂L/∂(dX/dt) - ∂L/∂X = d/dt ∂L/∂V - ∂L/∂X = d/dt ∂L/∂V

        P = ∂L/∂V
          = -m c^2 ∂/∂V √(1 - V^2/c^2)
          = -m c^2/[2 √(1 - V^2/c^2)] ∂/∂V (1 - V^2/c^2)
          = -m c^2/[2 √(1 - V^2/c^2)] (-2 V/c^2)
          = m V/√(1 - v^2/c^2)
          = γ(v) m V.

  [It is interesting to note that this way the relativistic/exact 3-momentum
   for a massive particle can be derived purely from the Minkowski metric,
   without a Lorentz transformation (but the Minkowski metric is Lorentz-
   invariant, somewhat by design [I showed before that you do not even
   need to assume Lorentz invariance to derive it, just a constant speed
   with which information propagates in space)].

Since from the above follows that ds = c dτ, one can also write

  S[x(τ)] = -m c ∫ dτ c = -m c^2 ∫ dτ.

The physical paths of free motion, which (one can prove) are spacetime
geodesics, are those where the action S[x(t)] is minimal (stationary in
general).  From the form above one can see that those are the trajectories W
along which the elapsed proper time ∆τ = ∫_W dτ is maximal, which is another
way of describing "time dilation" when there is relative motion, and finally
explaining the "twin paradox" as nothing more than a consequence of
different elapsed proper times along different worldlines.

One can also see here that mass arises naturally from assuming the principle
of stationary action.

> sort of like "the Machian" is a usual notion of far-field.

No, nonsense.

> [pseudo-scientific word salad]

You are a hopeless case.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#668122

On 01/08/2026 05:55 PM, Thomas 'PointedEars' Lahn wrote:
> Ross Finlayson wrote:
>> The idea that everything physics is always parameterized
>> by time or 't' is often formalized "the Lagrangian",
>
> No, the parametrization by time is a concept in Lagrangian _mechanics_ which
> is based on the _principle of stationary ("least") action_.  The action is
> defined as
>
>    S[x(t)] = ∫ dt L[x(t), dx(t)/dt, t],
>
> where x may be a vector (field), and L is the Lagrangian (function).
> [Both S and L are *functionals*: they depend on a function, x(t);
> hence the customary notation with rectangular brackets.]
>
> In special relativity, one finds from the Minkowski metric
>
>    ds^2 = c^2 dτ² = c^2 dt^2 - dx^2 - dy^2 - dz^2
>                   = c^2 dt^2 [1 - (dx/dt)^2 - (dy/dt)^2 - (dz/dt)^2]
>                   = c^2 dt^2 (1 - V^2/c^2)
>
> that
>
>    S[x] = -m c ∫ ds = -m c ∫ dt c √(1 - V^2/c^2)
>                     = ∫ dt [-m c^2 √(1 - V^2/c^2)],
>
> where the prefactor -m c is introduced so as to produce a quantity with
> dimensions of action (energy × time, cf. ℎ and ℏ) and the correct canonical
> momentum [*], and in the integrand one with dimensions of energy; so the
> relativistic non-interacting Lagrangian is
>
>    L = -m c^2 √(1 - V^2/c^2) = -m c^2 √[1 - (dX/dt)^2/c^2].
>
> It turns out that this leads to the correct energy--momentum relation,
> as I pointed out earlier.
>
>    [*] For example, the canonical 3-momentum is, from the Euler--Lagrange
>        equations
>
>          0 = d/dt ∂L/∂(dX/dt) - ∂L/∂X = d/dt ∂L/∂V - ∂L/∂X = d/dt ∂L/∂V
>
>          P = ∂L/∂V
>            = -m c^2 ∂/∂V √(1 - V^2/c^2)
>            = -m c^2/[2 √(1 - V^2/c^2)] ∂/∂V (1 - V^2/c^2)
>            = -m c^2/[2 √(1 - V^2/c^2)] (-2 V/c^2)
>            = m V/√(1 - v^2/c^2)
>            = γ(v) m V.
>
>    [It is interesting to note that this way the relativistic/exact 3-momentum
>     for a massive particle can be derived purely from the Minkowski metric,
>     without a Lorentz transformation (but the Minkowski metric is Lorentz-
>     invariant, somewhat by design [I showed before that you do not even
>     need to assume Lorentz invariance to derive it, just a constant speed
>     with which information propagates in space)].
>
> Since from the above follows that ds = c dτ, one can also write
>
>    S[x(τ)] = -m c ∫ dτ c = -m c^2 ∫ dτ.
>
> The physical paths of free motion, which (one can prove) are spacetime
> geodesics, are those where the action S[x(t)] is minimal (stationary in
> general).  From the form above one can see that those are the trajectories W
> along which the elapsed proper time ∆τ = ∫_W dτ is maximal, which is another
> way of describing "time dilation" when there is relative motion, and finally
> explaining the "twin paradox" as nothing more than a consequence of
> different elapsed proper times along different worldlines.
>
> One can also see here that mass arises naturally from assuming the principle
> of stationary action.
>
>> sort of like "the Machian" is a usual notion of far-field.
>
> No, nonsense.
>
>> [pseudo-scientific word salad]
>
> You are a hopeless case.
>

So, parameterized by time then, like I said,
like Lagrange says.

You mention least action and it's a pretty reasonable
principle, where the theory is sum-of-histories sum-of-potentials
least-action least-gradient a continuum mechanics, that
obviously enough it's a field theory.

You know, momentum isn't very much conserved in kinematics.
It sort of adds up for each of the ideal equal/opposite
inelastic interactions, yet any sort of rotation loses it.



Much like "whatever satisfies the _Lorentzian_ is a model
of relativity", there's that "whatever satisfies the
_Lagrangian_ is a model of relativity with a clock hypothesis".


Perhaps you might be familiar with the notion of "implicits",
for example that "x" is "x(t)" and forces are always implicitly
functions of time, t, and so on.

Forces are functions of time, ....

Then, besides that logic demands a temporality else
it's readily demonstrable as false, time the usual
parameter t is an implicit.

Implicits may remind
of "running constants", then for example about notions
like the monomode process, since usually accounts as
after the _Laplacian_, the sum of 2'nd order partials,
the _Lorentzian_, the sum of 2'nd order partials x +- t,
and whether that's zero or off-zero, non-zero.

The differential d and partial-differential little-greek-d
are two different things, your Lagrangian L is already
second-order in d^2 t while velocity V is only first
order, then taking their partials w.r.t. each other,
finds that now what was taken as the root of the square,
gets issues with the nilpotent and nilsquare, about
the off-zero case, helping explain why what falls out
as a linear expression or in simple terms,
ignores part of its own derivation there.

Otherwise it's quite plainly Galilean, one may note.
(Eg, any "unboundedness as infinity".)

Meeting the form, ....



Yeah, it seems quite so that the larger reasoners
very well appreciate the contents of that "T-theory,
A-Theory, theatheory" thread.

Including its logical elements, its mathematical elements,
and otherwise its canonical and novel elements, so relevant.

Then also for physics.



It seems the action S is simply contrived to dump out
the usual definition, as it is, "timeless", and absent
moment, of momentum the linear since Lagrange.
Being that it's just "defined".



"Implicits" is what's involved, since whatever then
results in the derivations cancelling themselves away,
perfectly model Lagrangians, Lorentzians, ..., Laplacians,
a hollow shell.

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#668124

On 01/08/2026 07:55 PM, Ross Finlayson wrote:
> On 01/08/2026 05:55 PM, Thomas 'PointedEars' Lahn wrote:
>> Ross Finlayson wrote:
>>> The idea that everything physics is always parameterized
>>> by time or 't' is often formalized "the Lagrangian",
>>
>> No, the parametrization by time is a concept in Lagrangian _mechanics_
>> which
>> is based on the _principle of stationary ("least") action_.  The
>> action is
>> defined as
>>
>>    S[x(t)] = ∫ dt L[x(t), dx(t)/dt, t],
>>
>> where x may be a vector (field), and L is the Lagrangian (function).
>> [Both S and L are *functionals*: they depend on a function, x(t);
>> hence the customary notation with rectangular brackets.]
>>
>> In special relativity, one finds from the Minkowski metric
>>
>>    ds^2 = c^2 dτ² = c^2 dt^2 - dx^2 - dy^2 - dz^2
>>                   = c^2 dt^2 [1 - (dx/dt)^2 - (dy/dt)^2 - (dz/dt)^2]
>>                   = c^2 dt^2 (1 - V^2/c^2)
>>
>> that
>>
>>    S[x] = -m c ∫ ds = -m c ∫ dt c √(1 - V^2/c^2)
>>                     = ∫ dt [-m c^2 √(1 - V^2/c^2)],
>>
>> where the prefactor -m c is introduced so as to produce a quantity with
>> dimensions of action (energy × time, cf. ℎ and ℏ) and the correct
>> canonical
>> momentum [*], and in the integrand one with dimensions of energy; so the
>> relativistic non-interacting Lagrangian is
>>
>>    L = -m c^2 √(1 - V^2/c^2) = -m c^2 √[1 - (dX/dt)^2/c^2].
>>
>> It turns out that this leads to the correct energy--momentum relation,
>> as I pointed out earlier.
>>
>>    [*] For example, the canonical 3-momentum is, from the Euler--Lagrange
>>        equations
>>
>>          0 = d/dt ∂L/∂(dX/dt) - ∂L/∂X = d/dt ∂L/∂V - ∂L/∂X = d/dt ∂L/∂V
>>
>>          P = ∂L/∂V
>>            = -m c^2 ∂/∂V √(1 - V^2/c^2)
>>            = -m c^2/[2 √(1 - V^2/c^2)] ∂/∂V (1 - V^2/c^2)
>>            = -m c^2/[2 √(1 - V^2/c^2)] (-2 V/c^2)
>>            = m V/√(1 - v^2/c^2)
>>            = γ(v) m V.
>>
>>    [It is interesting to note that this way the relativistic/exact
>> 3-momentum
>>     for a massive particle can be derived purely from the Minkowski
>> metric,
>>     without a Lorentz transformation (but the Minkowski metric is
>> Lorentz-
>>     invariant, somewhat by design [I showed before that you do not even
>>     need to assume Lorentz invariance to derive it, just a constant speed
>>     with which information propagates in space)].
>>
>> Since from the above follows that ds = c dτ, one can also write
>>
>>    S[x(τ)] = -m c ∫ dτ c = -m c^2 ∫ dτ.
>>
>> The physical paths of free motion, which (one can prove) are spacetime
>> geodesics, are those where the action S[x(t)] is minimal (stationary in
>> general).  From the form above one can see that those are the
>> trajectories W
>> along which the elapsed proper time ∆τ = ∫_W dτ is maximal, which is
>> another
>> way of describing "time dilation" when there is relative motion, and
>> finally
>> explaining the "twin paradox" as nothing more than a consequence of
>> different elapsed proper times along different worldlines.
>>
>> One can also see here that mass arises naturally from assuming the
>> principle
>> of stationary action.
>>
>>> sort of like "the Machian" is a usual notion of far-field.
>>
>> No, nonsense.
>>
>>> [pseudo-scientific word salad]
>>
>> You are a hopeless case.
>>
>
> So, parameterized by time then, like I said,
> like Lagrange says.
>
> You mention least action and it's a pretty reasonable
> principle, where the theory is sum-of-histories sum-of-potentials
> least-action least-gradient a continuum mechanics, that
> obviously enough it's a field theory.
>
> You know, momentum isn't very much conserved in kinematics.
> It sort of adds up for each of the ideal equal/opposite
> inelastic interactions, yet any sort of rotation loses it.
>
>
>
> Much like "whatever satisfies the _Lorentzian_ is a model
> of relativity", there's that "whatever satisfies the
> _Lagrangian_ is a model of relativity with a clock hypothesis".
>
>
> Perhaps you might be familiar with the notion of "implicits",
> for example that "x" is "x(t)" and forces are always implicitly
> functions of time, t, and so on.
>
> Forces are functions of time, ....
>
> Then, besides that logic demands a temporality else
> it's readily demonstrable as false, time the usual
> parameter t is an implicit.
>
> Implicits may remind
> of "running constants", then for example about notions
> like the monomode process, since usually accounts as
> after the _Laplacian_, the sum of 2'nd order partials,
> the _Lorentzian_, the sum of 2'nd order partials x +- t,
> and whether that's zero or off-zero, non-zero.
>
> The differential d and partial-differential little-greek-d
> are two different things, your Lagrangian L is already
> second-order in d^2 t while velocity V is only first
> order, then taking their partials w.r.t. each other,
> finds that now what was taken as the root of the square,
> gets issues with the nilpotent and nilsquare, about
> the off-zero case, helping explain why what falls out
> as a linear expression or in simple terms,
> ignores part of its own derivation there.
>
> Otherwise it's quite plainly Galilean, one may note.
> (Eg, any "unboundedness as infinity".)
>
> Meeting the form, ....
>
>
>
> Yeah, it seems quite so that the larger reasoners
> very well appreciate the contents of that "T-theory,
> A-Theory, theatheory" thread.
>
> Including its logical elements, its mathematical elements,
> and otherwise its canonical and novel elements, so relevant.
>
> Then also for physics.
>
>
>
> It seems the action S is simply contrived to dump out
> the usual definition, as it is, "timeless", and absent
> moment, of momentum the linear since Lagrange.
> Being that it's just "defined".
>
>
>
> "Implicits" is what's involved, since whatever then
> results in the derivations cancelling themselves away,
> perfectly model Lagrangians, Lorentzians, ..., Laplacians,
> a hollow shell.
>
>


When encountering various fields of mathematics,
when the only tool there is is a hammer then
everything looks like a nail, yet, in a world of
nails, many varieties of hammers will do.

So, when learning about things like "the operator calculus"
and "functional analysis" it's a pretty great thing,
first for treating the differential as operators,
yet it's really quite an overall approach to things.

Now, the definition of "function" is one of the most
fluid definitions in mathematics, or it has been over
time. For example "classical functions", then those
after "classical constructions", then about whether
asymptotes are admitted, about the continuous, about
the differentiable and C^\infty and so on, about
whether Differential Geometry has gone backward and neither
tangents nor normals asymptotes, then whether "functionals"
are "functions" and for example from probability theory
whether "distributions" are "functionals" or "functions",
"functionals" live under functional analysis thus an
operator calculus, while "functions" get all involved
the usual relations about since there not being division
by zero, though the meromorphic and symplectic and
many other usual translations make for a resulting
sort of "free analysis on the plane", where pretty much
any sort of parameterized form like that of a circle,
can be treated as a function or piecewise as a function.

So, they're functions.

Then, another sort of open thing in mathematics is
topology. The usual open topology is not really
unique not necessarily apropos, and there are lots
of mid- and late-20'th century accounts of formalisms
of topologies that result defining some "continuous
topologies", those being their own initial and final
topologies, and since in a modern sort of account
there are at least three set-theoretic for descriptive
set theory's, "models of continuous domains", like
the reals or the real-valued for the space of those.


Then, the _differential_ and the _integral_ are
about opposites, about then usual the diff. eq.'s
and their solutions, and integral eq.'s and their
plane curves, or isoclines I suppose above free
analysis on the plane (which is where it usually
lives since it's almost always consider a relation
of two bases, the differential, then of course about
surface integrals, yet not so much about the line integral).

So, the integrodiffer and differintegro then can get
involved, just pointing out that there's an entire field
of mathematics the objects most entirely unknown to
most entirely the field of mathematics the practicants,
many having never heard of it in their making derivations
after definitions the stacks of derivations.



Point being: formalism is invincible. Yet, it's so
that inductive inference makes for itself invincible
ignorance, and ignorance is not a defense, here against
simple counter-induction that isn't otherwise well-posed,
say, to result the completions of analysis (the perfect
results of the calculus). Then, the _wider_ and _fuller_
formalism is also invincible, and even better.


And less ignorant, ....

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#668143

Am Freitag000009, 09.01.2026 um 07:34 schrieb Ross Finlayson:
> On 01/08/2026 07:55 PM, Ross Finlayson wrote:
>> On 01/08/2026 05:55 PM, Thomas 'PointedEars' Lahn wrote:
>>> Ross Finlayson wrote:
>>>> The idea that everything physics is always parameterized
>>>> by time or 't' is often formalized "the Lagrangian",
>>>
>>> No, the parametrization by time is a concept in Lagrangian _mechanics_
>>> which
>>> is based on the _principle of stationary ("least") action_.  The
>>> action is
>>> defined as
>>>
>>>    S[x(t)] = ∫ dt L[x(t), dx(t)/dt, t],
>>>
>>> where x may be a vector (field), and L is the Lagrangian (function).
>>> [Both S and L are *functionals*: they depend on a function, x(t);
>>> hence the customary notation with rectangular brackets.]
>>>
>>> In special relativity, one finds from the Minkowski metric
>>>
>>>    ds^2 = c^2 dτ² = c^2 dt^2 - dx^2 - dy^2 - dz^2
>>>                   = c^2 dt^2 [1 - (dx/dt)^2 - (dy/dt)^2 - (dz/dt)^2]
>>>                   = c^2 dt^2 (1 - V^2/c^2)
>>>
>>> that
>>>
>>>    S[x] = -m c ∫ ds = -m c ∫ dt c √(1 - V^2/c^2)
>>>                     = ∫ dt [-m c^2 √(1 - V^2/c^2)],
>>>
>>> where the prefactor -m c is introduced so as to produce a quantity with
>>> dimensions of action (energy × time, cf. ℎ and ℏ) and the correct
>>> canonical
>>> momentum [*], and in the integrand one with dimensions of energy; so the
>>> relativistic non-interacting Lagrangian is
>>>
>>>    L = -m c^2 √(1 - V^2/c^2) = -m c^2 √[1 - (dX/dt)^2/c^2].
>>>
>>> It turns out that this leads to the correct energy--momentum relation,
>>> as I pointed out earlier.
>>>
>>>    [*] For example, the canonical 3-momentum is, from the Euler-- 
>>> Lagrange
>>>        equations
>>>
>>>          0 = d/dt ∂L/∂(dX/dt) - ∂L/∂X = d/dt ∂L/∂V - ∂L/∂X = d/dt ∂L/∂V
>>>
>>>          P = ∂L/∂V
>>>            = -m c^2 ∂/∂V √(1 - V^2/c^2)
>>>            = -m c^2/[2 √(1 - V^2/c^2)] ∂/∂V (1 - V^2/c^2)
>>>            = -m c^2/[2 √(1 - V^2/c^2)] (-2 V/c^2)
>>>            = m V/√(1 - v^2/c^2)
>>>            = γ(v) m V.
>>>
>>>    [It is interesting to note that this way the relativistic/exact
>>> 3-momentum
>>>     for a massive particle can be derived purely from the Minkowski
>>> metric,
>>>     without a Lorentz transformation (but the Minkowski metric is
>>> Lorentz-
>>>     invariant, somewhat by design [I showed before that you do not even
>>>     need to assume Lorentz invariance to derive it, just a constant 
>>> speed
>>>     with which information propagates in space)].
>>>
>>> Since from the above follows that ds = c dτ, one can also write
>>>
>>>    S[x(τ)] = -m c ∫ dτ c = -m c^2 ∫ dτ.
>>>
>>> The physical paths of free motion, which (one can prove) are spacetime
>>> geodesics, are those where the action S[x(t)] is minimal (stationary in
>>> general).  From the form above one can see that those are the
>>> trajectories W
>>> along which the elapsed proper time ∆τ = ∫_W dτ is maximal, which is
>>> another
>>> way of describing "time dilation" when there is relative motion, and
>>> finally
>>> explaining the "twin paradox" as nothing more than a consequence of
>>> different elapsed proper times along different worldlines.
>>>
>>> One can also see here that mass arises naturally from assuming the
>>> principle
>>> of stationary action.
>>>
>>>> sort of like "the Machian" is a usual notion of far-field.
>>>
>>> No, nonsense.
>>>
>>>> [pseudo-scientific word salad]
>>>
>>> You are a hopeless case.
>>>
>>
>> So, parameterized by time then, like I said,
>> like Lagrange says.
>>
>> You mention least action and it's a pretty reasonable
>> principle, where the theory is sum-of-histories sum-of-potentials
>> least-action least-gradient a continuum mechanics, that
>> obviously enough it's a field theory.
>>
>> You know, momentum isn't very much conserved in kinematics.
>> It sort of adds up for each of the ideal equal/opposite
>> inelastic interactions, yet any sort of rotation loses it.
>>
>>
>>
>> Much like "whatever satisfies the _Lorentzian_ is a model
>> of relativity", there's that "whatever satisfies the
>> _Lagrangian_ is a model of relativity with a clock hypothesis".
>>
>>
>> Perhaps you might be familiar with the notion of "implicits",
>> for example that "x" is "x(t)" and forces are always implicitly
>> functions of time, t, and so on.
>>
>> Forces are functions of time, ....
>>
>> Then, besides that logic demands a temporality else
>> it's readily demonstrable as false, time the usual
>> parameter t is an implicit.
>>
>> Implicits may remind
>> of "running constants", then for example about notions
>> like the monomode process, since usually accounts as
>> after the _Laplacian_, the sum of 2'nd order partials,
>> the _Lorentzian_, the sum of 2'nd order partials x +- t,
>> and whether that's zero or off-zero, non-zero.
>>
>> The differential d and partial-differential little-greek-d
>> are two different things, your Lagrangian L is already
>> second-order in d^2 t while velocity V is only first
>> order, then taking their partials w.r.t. each other,
>> finds that now what was taken as the root of the square,
>> gets issues with the nilpotent and nilsquare, about
>> the off-zero case, helping explain why what falls out
>> as a linear expression or in simple terms,
>> ignores part of its own derivation there.
>>
>> Otherwise it's quite plainly Galilean, one may note.
>> (Eg, any "unboundedness as infinity".)
>>
>> Meeting the form, ....
>>
>>
>>
>> Yeah, it seems quite so that the larger reasoners
>> very well appreciate the contents of that "T-theory,
>> A-Theory, theatheory" thread.
>>
>> Including its logical elements, its mathematical elements,
>> and otherwise its canonical and novel elements, so relevant.
>>
>> Then also for physics.
>>
>>
>>
>> It seems the action S is simply contrived to dump out
>> the usual definition, as it is, "timeless", and absent
>> moment, of momentum the linear since Lagrange.
>> Being that it's just "defined".
>>
>>
>>
>> "Implicits" is what's involved, since whatever then
>> results in the derivations cancelling themselves away,
>> perfectly model Lagrangians, Lorentzians, ..., Laplacians,
>> a hollow shell.
>>
>>
> 
> 
> When encountering various fields of mathematics,
> when the only tool there is is a hammer then
> everything looks like a nail, yet, in a world of
> nails, many varieties of hammers will do.
> 
> So, when learning about things like "the operator calculus"
> and "functional analysis" it's a pretty great thing,
> first for treating the differential as operators,
> yet it's really quite an overall approach to things.
> 
> Now, the definition of "function" is one of the most
> fluid definitions in mathematics, or it has been over
> time. For example "classical functions", then those
> after "classical constructions", then about whether
> asymptotes are admitted, about the continuous, about
> the differentiable and C^\infty and so on, about
> whether Differential Geometry has gone backward and neither
> tangents nor normals asymptotes, then whether "functionals"
> are "functions" and for example from probability theory
> whether "distributions" are "functionals" or "functions",
> "functionals" live under functional analysis thus an
> operator calculus, while "functions" get all involved
> the usual relations about since there not being division
> by zero, though the meromorphic and symplectic and
> many other usual translations make for a resulting
> sort of "free analysis on the plane", where pretty much
> any sort of parameterized form like that of a circle,
> can be treated as a function or piecewise as a function.
> 
> So, they're functions.

I use the word function similar to how it is used in programming.

A function is therefore a 'mathematical machine', which swallows input 
and produces output of some kind.

The output is NOT a function, because that would create two different 
meanings of the same word 'function'.

E.g.:

  if you have a function named -say- 'f', then f(x) is not a function, 
but the output of the function 'f' from input 'x'.


TH

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#668130 — Lagrangian mechanics (was: Hidden dimensions could explain where mass comes from)

You ought to trim your quotations to the relevant minimum.

Ross Finlayson wrote:
> You mention least action and it's a pretty reasonable principle,

Yes, it is.

> where the theory is sum-of-histories sum-of-potentials
> least-action least-gradient a continuum mechanics, that
> obviously enough it's a field theory.

No, no and no.  That's such a nonsense, it's not even wrong.

> You know, momentum isn't very much conserved in kinematics.

It is conserved if no force is acting.  Different to Newtonian mechanics,
Lagrangian mechanics proves this in a way that does not already presume
Newton's Laws of Motion:

The Euler--Lagrange equation for the coordinate x is

  d/dt ∂L/∂(dx/dt) - ∂L/∂x = 0.

("t" could be any parameter, but in physics it is usually taken as time.)

∂L/∂(dx/dt) is the *canonical momentum conjugate to x*, a terminology that
stems from that for the Newtonian Lagrangian one finds

  ∂L/∂(dx/dt) = m v_x = p_x

(see below).

If ∂L/∂x = 0, then trivially

  d/dt ∂L/∂(dx/dt) = 0,

i.e. ∂L/∂(dx/dt) is conserved.

The Newtonian Lagrangian is in one dimension

  L = T(dx/dt) - U(x) = 1/2 m (dx/dt)^2 - U(x)

where T is the kinetic energy and U is the potential energy.  Therefore,

  ∂L/∂x = -∂U/∂x = F_x.

So

  F_x = d/dt p_x,

and if F_x = 0, then

  d/dt p_x = 0,

i.e. the x-component of the linear momentum is conserved.

This is obtained analogously for the 3-dimensional Lagrangian (here in
Cartesian coordinates)

  L = 1/2 m (dX/dt)^2 - U(X)
    = 1/2 m [(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2] - U(x, y, z),

and y and z, so

  F = -(∂U/∂x, ∂U/∂y, ∂U/∂z)^T = -∇U = d/dt P

(Newton's Second Law of Motion).  So if F = 0, then

  d/dt P = 0

(Newton's First Law of Motion), and the linear momentum is conserved.

> [pseudo-scientific word salad]
-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#668132 — Re: Lagrangian mechanics

On 01/09/2026 03:13 AM, Thomas 'PointedEars' Lahn wrote:
> You ought to trim your quotations to the relevant minimum.
>
> Ross Finlayson wrote:
>> You mention least action and it's a pretty reasonable principle,
>
> Yes, it is.
>
>> where the theory is sum-of-histories sum-of-potentials
>> least-action least-gradient a continuum mechanics, that
>> obviously enough it's a field theory.
>
> No, no and no.  That's such a nonsense, it's not even wrong.
>
>> You know, momentum isn't very much conserved in kinematics.
>
> It is conserved if no force is acting.  Different to Newtonian mechanics,
> Lagrangian mechanics proves this in a way that does not already presume
> Newton's Laws of Motion:
>
> The Euler--Lagrange equation for the coordinate x is
>
>    d/dt ∂L/∂(dx/dt) - ∂L/∂x = 0.
>
> ("t" could be any parameter, but in physics it is usually taken as time.)
>
> ∂L/∂(dx/dt) is the *canonical momentum conjugate to x*, a terminology that
> stems from that for the Newtonian Lagrangian one finds
>
>    ∂L/∂(dx/dt) = m v_x = p_x
>
> (see below).
>
> If ∂L/∂x = 0, then trivially
>
>    d/dt ∂L/∂(dx/dt) = 0,
>
> i.e. ∂L/∂(dx/dt) is conserved.
>
> The Newtonian Lagrangian is in one dimension
>
>    L = T(dx/dt) - U(x) = 1/2 m (dx/dt)^2 - U(x)
>
> where T is the kinetic energy and U is the potential energy.  Therefore,
>
>    ∂L/∂x = -∂U/∂x = F_x.
>
> So
>
>    F_x = d/dt p_x,
>
> and if F_x = 0, then
>
>    d/dt p_x = 0,
>
> i.e. the x-component of the linear momentum is conserved.
>
> This is obtained analogously for the 3-dimensional Lagrangian (here in
> Cartesian coordinates)
>
>    L = 1/2 m (dX/dt)^2 - U(X)
>      = 1/2 m [(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2] - U(x, y, z),
>
> and y and z, so
>
>    F = -(∂U/∂x, ∂U/∂y, ∂U/∂z)^T = -∇U = d/dt P
>
> (Newton's Second Law of Motion).  So if F = 0, then
>
>    d/dt P = 0
>
> (Newton's First Law of Motion), and the linear momentum is conserved.
>
>> [pseudo-scientific word salad]

As to why I mostly don't trim context, is that a given article
is a whole thing.


"Least action" since Maupertuis is a usual thing. Then, one will
be familiar with "sum-of-histories" since "path integral" as with
regards to the classical analysis of the action of line integral,
and the non-classical terms of the path integral, to make do for
the usual formalism of quantum mechanics.

Then, "least gradient" also expresses about the same thing as
the geodesy (or per the recent discussion about "Orbifold"),
that it's the usual account of path of least resistance and so on,
describing at least where least action _goes_, while "sum-of-potentials"
is greater than "sum-of-histories", since the theory really
results a "sum-of-potentials" moreso than a sum-of-histories,
and "least gradient" says more than "least action".


Thusly it's really a potentialistic theory and instead of
a usual enough "conservation law", is for a stronger
"continuity law", that overall reflects a "continuum mechanics".


sum-of-histories <-> sum-of-potentials
least-action <-> least-gradient
conservation-law <-> continuity-law
symmetry-invariance <-> symmetry-flex

This is then sort of like so.

inductive-inference <-> deductive-inference
classical-action <-> superclassical-action
classical-real-fields <-> potentialistic-real-fields

Thusly there's an account that the potential fields,
the fields of potential, are the real fields, and the
classical setup is just a very inner product in the
space of all the terms, that it's again a potentialistic
account itself.

This way there can be a theory without any need for
"fictitious" forces, say. Also in a roundabout way
it's an inertial-system instead of a momentum-system,
about that accounts of the centripetal and centrifugal
are always dynamical, so, momentum isn't conserved in
the dynamical. Which would be a violation of the law.


During Maupertuis' time was a great debate on whether
the laws of physics would result the Earth besides being
spherical either flattened or oblong. Then it's observed
that it's rather flattened than oblong, while though there
are among effects like the tidal or Coriolis, as an example,
that often I'll relate to Casimir forces and Compton forces,
that Coriolis forces are basically empirical and outside
the model of usual accounts of momentum, yet always seen
to hold.


So, hopefully by clarifying that these terms, which by
themselves are as what were "implicits", have a greater
surrounds in their meaning, and indeed even intend to
extend and supplant the usual fundamental meanings,
of things like sum-of-histories (state) and least-action
(change), is for so that indeed that "physics is a field
theory", where the potential-fields are really the real
fields, and "physics is a continuum mechanics", with
more than an account of Noether theorem. Thusly it's
truly and comprehensively a potentialistic theory,
including the classical forces and actions and fields,
and with continuity-law, which covers conservation-law
while acknowledging dynamics.


Most people when they're told "momentum is conserved",
then after an account of dynamics that "well, it went
away", find that a bit unsatisfying, while though the
idea that there is a true "pseudo-momentum" and about,
if necessary, the "pseudo-differential", and that "momentum
is conserved, dot dot dot: _in the open_", of the open
and closed systems, of course makes for an account making
for simple explanations of why linear and planar things
are classical. And simply computed, ....



About Maupertuis then as kind of like big-endians and
little-endians, then another great account can be made
of Heaviside, and why the telegrapher's equation is why
it is and not right after the usual account, then for
Maxwell, why most all the lettered fields of electromagnetism
are potential-fields, then that ExB and DxH are two separate
accounts of classical field, as an example, that either ExB
or DxH is, according to Maxwell and since, that either is
"fundamental", in terms of deriving them in terms of each
other. Which is "definition" and which "derivation" is
arbitrary.



So, ..., it's a continuum mechanics, to be a field theory,
to avoid "fictitious" or "pseudo" forces, then about the
needful of the Machian to explain Coriolis and the
"true centrifugal" and so on.



So, I hope this enumeration of "overrides" as it would
be in the language of types, about sum-of-histories
sum-of-potentials least-action least-gradient, and
about conservation-law continuity-law, and about
inductive-deductive accounts, and the potentialistic
theory, is more obvious now, and justifies itself.

Then for Lagrange the Lagrange also has the quite
usual total account of being a potentialistic theory,
that most people don't know and just always compute
what must be from their perspective, which is not absolute.

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#668133 — Re: Lagrangian mechanics

On 01/09/2026 08:37 AM, Ross Finlayson wrote:
> On 01/09/2026 03:13 AM, Thomas 'PointedEars' Lahn wrote:
>> You ought to trim your quotations to the relevant minimum.
>>
>> Ross Finlayson wrote:
>>> You mention least action and it's a pretty reasonable principle,
>>
>> Yes, it is.
>>
>>> where the theory is sum-of-histories sum-of-potentials
>>> least-action least-gradient a continuum mechanics, that
>>> obviously enough it's a field theory.
>>
>> No, no and no.  That's such a nonsense, it's not even wrong.
>>
>>> You know, momentum isn't very much conserved in kinematics.
>>
>> It is conserved if no force is acting.  Different to Newtonian mechanics,
>> Lagrangian mechanics proves this in a way that does not already presume
>> Newton's Laws of Motion:
>>
>> The Euler--Lagrange equation for the coordinate x is
>>
>>    d/dt ∂L/∂(dx/dt) - ∂L/∂x = 0.
>>
>> ("t" could be any parameter, but in physics it is usually taken as time.)
>>
>> ∂L/∂(dx/dt) is the *canonical momentum conjugate to x*, a terminology
>> that
>> stems from that for the Newtonian Lagrangian one finds
>>
>>    ∂L/∂(dx/dt) = m v_x = p_x
>>
>> (see below).
>>
>> If ∂L/∂x = 0, then trivially
>>
>>    d/dt ∂L/∂(dx/dt) = 0,
>>
>> i.e. ∂L/∂(dx/dt) is conserved.
>>
>> The Newtonian Lagrangian is in one dimension
>>
>>    L = T(dx/dt) - U(x) = 1/2 m (dx/dt)^2 - U(x)
>>
>> where T is the kinetic energy and U is the potential energy.  Therefore,
>>
>>    ∂L/∂x = -∂U/∂x = F_x.
>>
>> So
>>
>>    F_x = d/dt p_x,
>>
>> and if F_x = 0, then
>>
>>    d/dt p_x = 0,
>>
>> i.e. the x-component of the linear momentum is conserved.
>>
>> This is obtained analogously for the 3-dimensional Lagrangian (here in
>> Cartesian coordinates)
>>
>>    L = 1/2 m (dX/dt)^2 - U(X)
>>      = 1/2 m [(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2] - U(x, y, z),
>>
>> and y and z, so
>>
>>    F = -(∂U/∂x, ∂U/∂y, ∂U/∂z)^T = -∇U = d/dt P
>>
>> (Newton's Second Law of Motion).  So if F = 0, then
>>
>>    d/dt P = 0
>>
>> (Newton's First Law of Motion), and the linear momentum is conserved.
>>
>>> [pseudo-scientific word salad]
>
> As to why I mostly don't trim context, is that a given article
> is a whole thing.
>
>
> "Least action" since Maupertuis is a usual thing. Then, one will
> be familiar with "sum-of-histories" since "path integral" as with
> regards to the classical analysis of the action of line integral,
> and the non-classical terms of the path integral, to make do for
> the usual formalism of quantum mechanics.
>
> Then, "least gradient" also expresses about the same thing as
> the geodesy (or per the recent discussion about "Orbifold"),
> that it's the usual account of path of least resistance and so on,
> describing at least where least action _goes_, while "sum-of-potentials"
> is greater than "sum-of-histories", since the theory really
> results a "sum-of-potentials" moreso than a sum-of-histories,
> and "least gradient" says more than "least action".
>
>
> Thusly it's really a potentialistic theory and instead of
> a usual enough "conservation law", is for a stronger
> "continuity law", that overall reflects a "continuum mechanics".
>
>
> sum-of-histories <-> sum-of-potentials
> least-action <-> least-gradient
> conservation-law <-> continuity-law
> symmetry-invariance <-> symmetry-flex
>
> This is then sort of like so.
>
> inductive-inference <-> deductive-inference
> classical-action <-> superclassical-action
> classical-real-fields <-> potentialistic-real-fields
>
> Thusly there's an account that the potential fields,
> the fields of potential, are the real fields, and the
> classical setup is just a very inner product in the
> space of all the terms, that it's again a potentialistic
> account itself.
>
> This way there can be a theory without any need for
> "fictitious" forces, say. Also in a roundabout way
> it's an inertial-system instead of a momentum-system,
> about that accounts of the centripetal and centrifugal
> are always dynamical, so, momentum isn't conserved in
> the dynamical. Which would be a violation of the law.
>
>
> During Maupertuis' time was a great debate on whether
> the laws of physics would result the Earth besides being
> spherical either flattened or oblong. Then it's observed
> that it's rather flattened than oblong, while though there
> are among effects like the tidal or Coriolis, as an example,
> that often I'll relate to Casimir forces and Compton forces,
> that Coriolis forces are basically empirical and outside
> the model of usual accounts of momentum, yet always seen
> to hold.
>
>
> So, hopefully by clarifying that these terms, which by
> themselves are as what were "implicits", have a greater
> surrounds in their meaning, and indeed even intend to
> extend and supplant the usual fundamental meanings,
> of things like sum-of-histories (state) and least-action
> (change), is for so that indeed that "physics is a field
> theory", where the potential-fields are really the real
> fields, and "physics is a continuum mechanics", with
> more than an account of Noether theorem. Thusly it's
> truly and comprehensively a potentialistic theory,
> including the classical forces and actions and fields,
> and with continuity-law, which covers conservation-law
> while acknowledging dynamics.
>
>
> Most people when they're told "momentum is conserved",
> then after an account of dynamics that "well, it went
> away", find that a bit unsatisfying, while though the
> idea that there is a true "pseudo-momentum" and about,
> if necessary, the "pseudo-differential", and that "momentum
> is conserved, dot dot dot: _in the open_", of the open
> and closed systems, of course makes for an account making
> for simple explanations of why linear and planar things
> are classical. And simply computed, ....
>
>
>
> About Maupertuis then as kind of like big-endians and
> little-endians, then another great account can be made
> of Heaviside, and why the telegrapher's equation is why
> it is and not right after the usual account, then for
> Maxwell, why most all the lettered fields of electromagnetism
> are potential-fields, then that ExB and DxH are two separate
> accounts of classical field, as an example, that either ExB
> or DxH is, according to Maxwell and since, that either is
> "fundamental", in terms of deriving them in terms of each
> other. Which is "definition" and which "derivation" is
> arbitrary.
>
>
>
> So, ..., it's a continuum mechanics, to be a field theory,
> to avoid "fictitious" or "pseudo" forces, then about the
> needful of the Machian to explain Coriolis and the
> "true centrifugal" and so on.
>
>
>
> So, I hope this enumeration of "overrides" as it would
> be in the language of types, about sum-of-histories
> sum-of-potentials least-action least-gradient, and
> about conservation-law continuity-law, and about
> inductive-deductive accounts, and the potentialistic
> theory, is more obvious now, and justifies itself.
>
> Then for Lagrange the Lagrange also has the quite
> usual total account of being a potentialistic theory,
> that most people don't know and just always compute
> what must be from their perspective, which is not absolute.
>
>
>

It's like when they say that Einstein was working on
a "total field theory", also it involves an "attack
on Newton", about the centrally-symmetrical and that
the ideal equal/opposite/inelastic is contrived.

Then, one of the greatest accounts of electrodynamics
as about the "The Electron Theory of Matter", is as
of O.W. Richardson's "The Electron Theory of Matter".
In the first twenty or thirty pages of that book,
it's really great that he sets up the differences
and distinctions about the infinitesimal analysis
as would point toward, or away from, Pauli and Born,
then for the great electricians, Richardson has a
great account of why there are at least three
"constants" as what result "c", and them having
different formalisms how they're arrived at, helping
show that E-Einsteinia is sort of the middling of
F-Lorentzians and not the other way around, or,
it's more than an "SR-ian" account, where SI is
rather ignorant of NIST PDG CODATA.


It's like, "is the electron's charge/mass ratio
a bit contrived and arbitrary while basically
making for the meters the scale of the microcosm
the Democritan of chemical elements about halfway
between Angstrom's and Planck's", yeah, kind of so.

Then about "light's speed being a constant", has that
besides that it's not the only "c", with regards to
actual electromagnetic radiation and flux, then also
it's sort of the aether drift velocity in the absolute,
doubled, in a sense.


So, "the Lagrangian" is more than the "severe abstraction"
of the "mechanical reduction", which later became the
"electrical reduction", which together paint a little
corner called "Higgs theory". Which isn't even real fields, ....


Physics' fields, ....

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#668163 — Re: Lagrangian mechanics

On 01/09/2026 09:03 AM, Ross Finlayson wrote:
> On 01/09/2026 08:37 AM, Ross Finlayson wrote:
>> On 01/09/2026 03:13 AM, Thomas 'PointedEars' Lahn wrote:
>>> You ought to trim your quotations to the relevant minimum.
>>>
>>> Ross Finlayson wrote:
>>>> You mention least action and it's a pretty reasonable principle,
>>>
>>> Yes, it is.
>>>
>>>> where the theory is sum-of-histories sum-of-potentials
>>>> least-action least-gradient a continuum mechanics, that
>>>> obviously enough it's a field theory.
>>>
>>> No, no and no.  That's such a nonsense, it's not even wrong.
>>>
>>>> You know, momentum isn't very much conserved in kinematics.
>>>
>>> It is conserved if no force is acting.  Different to Newtonian
>>> mechanics,
>>> Lagrangian mechanics proves this in a way that does not already presume
>>> Newton's Laws of Motion:
>>>
>>> The Euler--Lagrange equation for the coordinate x is
>>>
>>>    d/dt ∂L/∂(dx/dt) - ∂L/∂x = 0.
>>>
>>> ("t" could be any parameter, but in physics it is usually taken as
>>> time.)
>>>
>>> ∂L/∂(dx/dt) is the *canonical momentum conjugate to x*, a terminology
>>> that
>>> stems from that for the Newtonian Lagrangian one finds
>>>
>>>    ∂L/∂(dx/dt) = m v_x = p_x
>>>
>>> (see below).
>>>
>>> If ∂L/∂x = 0, then trivially
>>>
>>>    d/dt ∂L/∂(dx/dt) = 0,
>>>
>>> i.e. ∂L/∂(dx/dt) is conserved.
>>>
>>> The Newtonian Lagrangian is in one dimension
>>>
>>>    L = T(dx/dt) - U(x) = 1/2 m (dx/dt)^2 - U(x)
>>>
>>> where T is the kinetic energy and U is the potential energy.  Therefore,
>>>
>>>    ∂L/∂x = -∂U/∂x = F_x.
>>>
>>> So
>>>
>>>    F_x = d/dt p_x,
>>>
>>> and if F_x = 0, then
>>>
>>>    d/dt p_x = 0,
>>>
>>> i.e. the x-component of the linear momentum is conserved.
>>>
>>> This is obtained analogously for the 3-dimensional Lagrangian (here in
>>> Cartesian coordinates)
>>>
>>>    L = 1/2 m (dX/dt)^2 - U(X)
>>>      = 1/2 m [(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2] - U(x, y, z),
>>>
>>> and y and z, so
>>>
>>>    F = -(∂U/∂x, ∂U/∂y, ∂U/∂z)^T = -∇U = d/dt P
>>>
>>> (Newton's Second Law of Motion).  So if F = 0, then
>>>
>>>    d/dt P = 0
>>>
>>> (Newton's First Law of Motion), and the linear momentum is conserved.
>>>
>>>> [pseudo-scientific word salad]
>>
>> As to why I mostly don't trim context, is that a given article
>> is a whole thing.
>>
>>
>> "Least action" since Maupertuis is a usual thing. Then, one will
>> be familiar with "sum-of-histories" since "path integral" as with
>> regards to the classical analysis of the action of line integral,
>> and the non-classical terms of the path integral, to make do for
>> the usual formalism of quantum mechanics.
>>
>> Then, "least gradient" also expresses about the same thing as
>> the geodesy (or per the recent discussion about "Orbifold"),
>> that it's the usual account of path of least resistance and so on,
>> describing at least where least action _goes_, while "sum-of-potentials"
>> is greater than "sum-of-histories", since the theory really
>> results a "sum-of-potentials" moreso than a sum-of-histories,
>> and "least gradient" says more than "least action".
>>
>>
>> Thusly it's really a potentialistic theory and instead of
>> a usual enough "conservation law", is for a stronger
>> "continuity law", that overall reflects a "continuum mechanics".
>>
>>
>> sum-of-histories <-> sum-of-potentials
>> least-action <-> least-gradient
>> conservation-law <-> continuity-law
>> symmetry-invariance <-> symmetry-flex
>>
>> This is then sort of like so.
>>
>> inductive-inference <-> deductive-inference
>> classical-action <-> superclassical-action
>> classical-real-fields <-> potentialistic-real-fields
>>
>> Thusly there's an account that the potential fields,
>> the fields of potential, are the real fields, and the
>> classical setup is just a very inner product in the
>> space of all the terms, that it's again a potentialistic
>> account itself.
>>
>> This way there can be a theory without any need for
>> "fictitious" forces, say. Also in a roundabout way
>> it's an inertial-system instead of a momentum-system,
>> about that accounts of the centripetal and centrifugal
>> are always dynamical, so, momentum isn't conserved in
>> the dynamical. Which would be a violation of the law.
>>
>>
>> During Maupertuis' time was a great debate on whether
>> the laws of physics would result the Earth besides being
>> spherical either flattened or oblong. Then it's observed
>> that it's rather flattened than oblong, while though there
>> are among effects like the tidal or Coriolis, as an example,
>> that often I'll relate to Casimir forces and Compton forces,
>> that Coriolis forces are basically empirical and outside
>> the model of usual accounts of momentum, yet always seen
>> to hold.
>>
>>
>> So, hopefully by clarifying that these terms, which by
>> themselves are as what were "implicits", have a greater
>> surrounds in their meaning, and indeed even intend to
>> extend and supplant the usual fundamental meanings,
>> of things like sum-of-histories (state) and least-action
>> (change), is for so that indeed that "physics is a field
>> theory", where the potential-fields are really the real
>> fields, and "physics is a continuum mechanics", with
>> more than an account of Noether theorem. Thusly it's
>> truly and comprehensively a potentialistic theory,
>> including the classical forces and actions and fields,
>> and with continuity-law, which covers conservation-law
>> while acknowledging dynamics.
>>
>>
>> Most people when they're told "momentum is conserved",
>> then after an account of dynamics that "well, it went
>> away", find that a bit unsatisfying, while though the
>> idea that there is a true "pseudo-momentum" and about,
>> if necessary, the "pseudo-differential", and that "momentum
>> is conserved, dot dot dot: _in the open_", of the open
>> and closed systems, of course makes for an account making
>> for simple explanations of why linear and planar things
>> are classical. And simply computed, ....
>>
>>
>>
>> About Maupertuis then as kind of like big-endians and
>> little-endians, then another great account can be made
>> of Heaviside, and why the telegrapher's equation is why
>> it is and not right after the usual account, then for
>> Maxwell, why most all the lettered fields of electromagnetism
>> are potential-fields, then that ExB and DxH are two separate
>> accounts of classical field, as an example, that either ExB
>> or DxH is, according to Maxwell and since, that either is
>> "fundamental", in terms of deriving them in terms of each
>> other. Which is "definition" and which "derivation" is
>> arbitrary.
>>
>>
>>
>> So, ..., it's a continuum mechanics, to be a field theory,
>> to avoid "fictitious" or "pseudo" forces, then about the
>> needful of the Machian to explain Coriolis and the
>> "true centrifugal" and so on.
>>
>>
>>
>> So, I hope this enumeration of "overrides" as it would
>> be in the language of types, about sum-of-histories
>> sum-of-potentials least-action least-gradient, and
>> about conservation-law continuity-law, and about
>> inductive-deductive accounts, and the potentialistic
>> theory, is more obvious now, and justifies itself.
>>
>> Then for Lagrange the Lagrange also has the quite
>> usual total account of being a potentialistic theory,
>> that most people don't know and just always compute
>> what must be from their perspective, which is not absolute.
>>
>>
>>
>
> It's like when they say that Einstein was working on
> a "total field theory", also it involves an "attack
> on Newton", about the centrally-symmetrical and that
> the ideal equal/opposite/inelastic is contrived.
>
> Then, one of the greatest accounts of electrodynamics
> as about the "The Electron Theory of Matter", is as
> of O.W. Richardson's "The Electron Theory of Matter".
> In the first twenty or thirty pages of that book,
> it's really great that he sets up the differences
> and distinctions about the infinitesimal analysis
> as would point toward, or away from, Pauli and Born,
> then for the great electricians, Richardson has a
> great account of why there are at least three
> "constants" as what result "c", and them having
> different formalisms how they're arrived at, helping
> show that E-Einsteinia is sort of the middling of
> F-Lorentzians and not the other way around, or,
> it's more than an "SR-ian" account, where SI is
> rather ignorant of NIST PDG CODATA.
>
>
> It's like, "is the electron's charge/mass ratio
> a bit contrived and arbitrary while basically
> making for the meters the scale of the microcosm
> the Democritan of chemical elements about halfway
> between Angstrom's and Planck's", yeah, kind of so.
>
> Then about "light's speed being a constant", has that
> besides that it's not the only "c", with regards to
> actual electromagnetic radiation and flux, then also
> it's sort of the aether drift velocity in the absolute,
> doubled, in a sense.
>
>
> So, "the Lagrangian" is more than the "severe abstraction"
> of the "mechanical reduction", which later became the
> "electrical reduction", which together paint a little
> corner called "Higgs theory". Which isn't even real fields, ....
>
>
> Physics' fields, ....
>
>
>
>

This is a pretty good summary.

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