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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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#668135 — Re: Lagrangian mechanics

Thomas 'PointedEars' Lahn <PointedEars@web.de> 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

See? This works. (almost, only one ?)
BTW, the customaty symbol for momentum is p not P,

Jan

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#668137 — Re: Lagrangian mechanics

On 01/09/2026 12:17 PM, J. J. Lodder wrote:
> Thomas 'PointedEars' Lahn <PointedEars@web.de> 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
>
> See? This works. (almost, only one ?)
> BTW, the customaty symbol for momentum is p not P,
>
> Jan
>

In Quantum Mechanics, then the relevant Q and P are
as for the separate and distinct Heisenberg and Schroedinger
pictures, somehow that "whatever solves the wave equation
Schroedinger's psi" defines the LHS and RHS.

Usually written as for the <bra|ket> notation, among other
uses of bra-ket notation with somehow "c" missing in the middle.

Everybody notices that partials don't commute.

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#668141

Am Donnerstag000008, 08.01.2026 um 17:16 schrieb Ross Finlayson:
...
>>
>>>
>>>> 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.
> 

There exist a book called 'Geometry of Time' by an Alexander Franklin Meyer.

He had proven there, that 'linear time' is wrong.

We need to consider a multitude of possible timelines, which would 
include 'backwards time'.

This is certainly hard to swallow, but actually quite simple mathematically.

But if time is 'relative', than 'backwards' is relative, too.

Hence: if there exists a realm where time runs backwards from our 
perspective, our time runs backwards, if seen from the perspective of 
that other realm.

...

TH

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#668123

On 1/8/2026 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

I have a lot of experience in complex numbers. Fwiw, are you familiar 
with the triplex numbers, wrt the Mandelbulb? I can create a "special 
axis" and plot 4d vectors on it, ones with a non-zero w component. But, 
its just a "hack" for me to try to visualize a 4d point.

Also, if you ever get bored, try to play around with my multijulia. Paul 
was nice enough to write about it over here:

https://paulbourke.net/fractals/multijulia


> 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')

Never messed around with them too much. Triplex numbers, yeah.


>>> 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.

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#668142

Am Freitag000009, 09.01.2026 um 05:13 schrieb Chris M. Thomasson:
...
>> 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
> 
> I have a lot of experience in complex numbers. Fwiw, are you familiar 
> with the triplex numbers, wrt the Mandelbulb? I can create a "special 
> axis" and plot 4d vectors on it, ones with a non-zero w component. But, 
> its just a "hack" for me to try to visualize a 4d point.
> 
> Also, if you ever get bored, try to play around with my multijulia. Paul 
> was nice enough to write about it over here:
> 
> https://paulbourke.net/fractals/multijulia
> 

Nice.

But I have so far little access to software, which actually uses 
bi-quaternions or similar.

I have seen Julia sets with quaternions. That's it.

>> 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')
> 
> Never messed around with them too much. Triplex numbers, yeah.

I had many years ago contact with a guy named 'Timothy Golden' who 
invented 'multisigned numbers'.

These went somehow into my book, too.

Possibly they are in a way similar to your 'triplex numbers'.

TH

>>>> 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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#668152

On 1/10/2026 12:19 AM, Thomas Heger wrote:
> Am Freitag000009, 09.01.2026 um 05:13 schrieb Chris M. Thomasson:
> ...
>>> 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
>>
>> I have a lot of experience in complex numbers. Fwiw, are you familiar 
>> with the triplex numbers, wrt the Mandelbulb? I can create a "special 
>> axis" and plot 4d vectors on it, ones with a non-zero w component. 
>> But, its just a "hack" for me to try to visualize a 4d point.
>>
>> Also, if you ever get bored, try to play around with my multijulia. 
>> Paul was nice enough to write about it over here:
>>
>> https://paulbourke.net/fractals/multijulia
>>
> 
> Nice.
> 
> But I have so far little access to software, which actually uses bi- 
> quaternions or similar.
> 
> I have seen Julia sets with quaternions. That's it.
> 
>>> 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')
>>
>> Never messed around with them too much. Triplex numbers, yeah.
> 
> I had many years ago contact with a guy named 'Timothy Golden' who 
> invented 'multisigned numbers'.
> 
> These went somehow into my book, too.
> 
> Possibly they are in a way similar to your 'triplex numbers'.

You mean iirc, polysign? I remember conversing with him. Fwiw, I did not 
invent the triplex numbers:

https://www.skytopia.com/project/fractal/2mandelbulb.html

http://www.bugman123.com/Hypercomplex/index.html

https://www.scribd.com/document/43190326/Matrices-to-Triplex






> 
> TH
> 
>>>>> 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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#668157

Am Samstag000010, 10.01.2026 um 22:08 schrieb Chris M. Thomasson:
...
>>>> 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')
>>>
>>> Never messed around with them too much. Triplex numbers, yeah.
>>
>> I had many years ago contact with a guy named 'Timothy Golden' who 
>> invented 'multisigned numbers'.
>>
>> These went somehow into my book, too.
>>
>> Possibly they are in a way similar to your 'triplex numbers'.
> 
> You mean iirc, polysign? I remember conversing with him. Fwiw, I did not 
> invent the triplex numbers:
> 
> https://www.skytopia.com/project/fractal/2mandelbulb.html
> 
> http://www.bugman123.com/Hypercomplex/index.html
> 
> https://www.scribd.com/document/43190326/Matrices-to-Triplex
> 
> 

I wanted to use 'complex four-vectors' which are also known as 
'bi-quaternions'.

There are a few other constructs, which somehow similar features. Sorry, 
but I'm not good enough in math to deal with them properly.

I can program, but not that good, even if I have decades of experience 
with all kinds of computers.

Therefore this topic is not really my taste.

But I'm actually kind of an artist and think in pictures and try to 
interpret them in terms of physics (or the other way round and create 
pictures depicting physical equations).

To deal with the underlying math is a little beyond my abilities.


TH
> 
> 
> 
>>
>> TH
>>
>>>>>> 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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#668060

Chris M. Thomasson wrote:
> On 1/5/2026 2:49 PM, Thomas 'PointedEars' Lahn wrote:
>> Chris M. Thomasson wrote:
>>> On 1/5/2026 1:47 AM, Thomas 'PointedEars' Lahn wrote:
>>>> You appear to be
>>>> referring to a definition of "dimension" that is used in science-fiction
>>>> and fantasy instead.
>>> [...]
>>>
>>> Ponder on it:
>>>
>>> (4th Dimension Explained By A High-School Student)
>>> https://youtu.be/eGguwYPC32I
>>
>> The argument that they are making about time (not being "the 4th dimension")
>> is pseudo-scientific and ridiculous, based on their ignorance of what it
>> means when we say "4th dimension" in that regard (which I just explained to
>> you in detail).  Scientifically it is complete nonsense to say "every
>> dimension has time in it" as they do.
>>
>> *Their* ignorance is excusable, though, because they are just a high school
>> kid and are not expected to know about or understand pseudo-Riemannian
>> manifolds like spacetime (although they could have certainly have found
>> books that explained it at their level of understanding).  Yours is not (as
>> I just explained it to you in detail).
> 
> Say to explain a 3d point in time we need (x, y, z, t), t for time.

First of all, watch this (which was suggested to me by YouTube when I
watched the video that you referred to):

Dylan J. Dance: Physicist Reacts to 4th Dimension Explained By A High-School
Student
<https://youtu.be/0lE77mwB_Ww?si=mylGoFnwiIiRLOC4>

This should clarify (as I already indicated) where that kid was right and
where they confused themselves and thus were confused.

Then, as to your claim:

Once you specify a fourth coordinate for a point, it is no longer a point
_of_ (NOT: in) a 3-dimensional space, but a point _of_ (NOT: in) a
4-dimensional space.  If the extra coordinate is time, then that space is
(for obvious reasons) called _spacetime_.  The point has become an *event*.

In physics we actually prefer to choose the time coordinate as the zeroth
coordinate (unless we use Euclidean time, as I explained before), and count
the spatial dimensions beginning with 1.  This is more convenient in the
mathematical formulation and -- since we assume for various reasons that
there is only one (large) temporal dimension -- makes handling additional
spatial dimensions -- which according to string theory exist but are "too
small" to see as they are compactified -- easier to handle.  So, as I
explained before, instead of (x, y, z, t) we write e.g. (x^0, x^1, x^2, x^3)
:= (c t, x, y, z).

We are using "c t" instead of "t" so that the temporal dimension(1) has the
same dimensions(2) as each spatial dimensions(1); but the "c" is frequently
dropped in the theory by setting c = 1 (called "notation in natural units"),
and that is equivalent to not doing that if we specify time in seconds, but
then lengths in e.g. light-seconds.

(1) "dimension" as understood in mathematics
(2) "dimension" as understood in physics with regard to quantities

> For a 4d point we need (x, y, z, w, t), t for time.

Again, this is now a point _of_ (NOT: in) a 5-dimensional space.

> t is in every dimension?

No; (different from the sci-fi/fantasy meaning) a dimension is NOT the whole
of this construct, but merely a part.  For example, the x-coordinate of that
point represents one dimension, the y-coordinate another, and so on.  See
also the video referenced above.

-- 
PointedEars

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

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#668153

On 1/5/2026 3:45 PM, Thomas 'PointedEars' Lahn wrote:
> Chris M. Thomasson wrote:
>> On 1/5/2026 2:49 PM, Thomas 'PointedEars' Lahn wrote:
>>> Chris M. Thomasson wrote:
>>>> On 1/5/2026 1:47 AM, Thomas 'PointedEars' Lahn wrote:
>>>>> You appear to be
>>>>> referring to a definition of "dimension" that is used in science-fiction
>>>>> and fantasy instead.
>>>> [...]
>>>>
>>>> Ponder on it:
>>>>
>>>> (4th Dimension Explained By A High-School Student)
>>>> https://youtu.be/eGguwYPC32I
>>>
>>> The argument that they are making about time (not being "the 4th dimension")
>>> is pseudo-scientific and ridiculous, based on their ignorance of what it
>>> means when we say "4th dimension" in that regard (which I just explained to
>>> you in detail).  Scientifically it is complete nonsense to say "every
>>> dimension has time in it" as they do.
>>>
>>> *Their* ignorance is excusable, though, because they are just a high school
>>> kid and are not expected to know about or understand pseudo-Riemannian
>>> manifolds like spacetime (although they could have certainly have found
>>> books that explained it at their level of understanding).  Yours is not (as
>>> I just explained it to you in detail).
>>
>> Say to explain a 3d point in time we need (x, y, z, t), t for time.
> 
> First of all, watch this (which was suggested to me by YouTube when I
> watched the video that you referred to):
> 
> Dylan J. Dance: Physicist Reacts to 4th Dimension Explained By A High-School
> Student
> <https://youtu.be/0lE77mwB_Ww?si=mylGoFnwiIiRLOC4>
> 
> This should clarify (as I already indicated) where that kid was right and
> where they confused themselves and thus were confused.
> 
> Then, as to your claim:
> 
> Once you specify a fourth coordinate for a point, it is no longer a point
> _of_ (NOT: in) a 3-dimensional space, but a point _of_ (NOT: in) a
> 4-dimensional space.  If the extra coordinate is time, then that space is
> (for obvious reasons) called _spacetime_.  The point has become an *event*.
> 
> In physics we actually prefer to choose the time coordinate as the zeroth
> coordinate (unless we use Euclidean time, as I explained before), and count
> the spatial dimensions beginning with 1.  This is more convenient in the
> mathematical formulation and -- since we assume for various reasons that
> there is only one (large) temporal dimension -- makes handling additional
> spatial dimensions -- which according to string theory exist but are "too
> small" to see as they are compactified -- easier to handle.  So, as I
> explained before, instead of (x, y, z, t) we write e.g. (x^0, x^1, x^2, x^3)
> := (c t, x, y, z).
> 
> We are using "c t" instead of "t" so that the temporal dimension(1) has the
> same dimensions(2) as each spatial dimensions(1); but the "c" is frequently
> dropped in the theory by setting c = 1 (called "notation in natural units"),
> and that is equivalent to not doing that if we specify time in seconds, but
> then lengths in e.g. light-seconds.
> 
> (1) "dimension" as understood in mathematics
> (2) "dimension" as understood in physics with regard to quantities
> 
>> For a 4d point we need (x, y, z, w, t), t for time.
> 
> Again, this is now a point _of_ (NOT: in) a 5-dimensional space.
> 
>> t is in every dimension?
> 
> No; (different from the sci-fi/fantasy meaning) a dimension is NOT the whole
> of this construct, but merely a part.  For example, the x-coordinate of that
> point represents one dimension, the y-coordinate another, and so on.  See
> also the video referenced above.
> 

Thanks. A bit busy lately. (x, y, z, t) can be dangerous/confusing 
because it does not mean a 4d space. but a 3d space with a time tag so 
to speak.

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#668028

Anthk NM <anthk@disroot.org> wrote or quoted:
>Hidden dimensions could explain where mass comes from

  So now you might ask yourself: what exactly is "mass"?

       These days, that kind of question usually comes up in the
  context of quantum field theory.

       There we use something called a Lagrangian density, which is kind
  of a pain to write in plain ASCII, but it basically looks like this 
  for a free field (no interactions):

Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.

  In Unicode form, it would be more like:

𝓛 = 𝛹̅( i 𝛾^𝜇 ∂_𝜇 - m )𝛹.

  Here, the first term (the one before the minus sign) is the "kinetic
  term", and the second one is the "mass term".

       For fields we already know, this lines up with what we normally
  mean by mass.

       So if you come across some new kind of field theory that ends
  up giving you a Lagrangian of this general form, then whatever shows
  up in place of that "m" is what we call the "mass".

       (The example I picked technically only applies to Dirac fermions,
  but the same idea works for other kinds of particles too.)

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#668029

Stefan Ram wrote:
> Anthk NM <anthk@disroot.org> wrote or quoted:
>> Hidden dimensions could explain where mass comes from
> 
>   So now you might ask yourself: what exactly is "mass"?
> 
>        These days, that kind of question usually comes up in the
>   context of quantum field theory.
> 
>        There we use something called a Lagrangian density, which is kind
>   of a pain to write in plain ASCII, but it basically looks like this 
>   for a free field (no interactions):
> 
> Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.
> 
>   In Unicode form, it would be more like:
> 
> 𝓛 = 𝛹̅( i 𝛾^𝜇 ∂_𝜇 - m )𝛹.
> 
>   Here, the first term (the one before the minus sign) is the "kinetic
>   term", and the second one is the "mass term".
> 
>        For fields we already know, this lines up with what we normally
>   mean by mass.
> 
>        So if you come across some new kind of field theory that ends
>   up giving you a Lagrangian of this general form, then whatever shows
>   up in place of that "m" is what we call the "mass".

Not quite.  The m there is a mass *in natural units* (hbar = c = 1),
therefore it is more precisely called "mass *parameter".  The actual
(expectation value of the) mass of a particle in SI units would be m hbar/c
(Unicode: m ℏ/c) if there are no interactions; otherwise one must use the
*renormalized mass* m_r and multiply that by ℏ/c to obtain the mass in SI units.

-- 
PointedEars

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

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#668030

Stefan Ram wrote:
> Anthk NM <anthk@disroot.org> wrote or quoted:
>> Hidden dimensions could explain where mass comes from
> 
>   So now you might ask yourself: what exactly is "mass"?
> 
>        These days, that kind of question usually comes up in the
>   context of quantum field theory.
> 
>        There we use something called a Lagrangian density, which is kind
>   of a pain to write in plain ASCII, but it basically looks like this 
>   for a free field (no interactions):
> 
> Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.
> 
>   In Unicode form, it would be more like:
> 
> 𝓛 = 𝛹̅( i 𝛾^𝜇 ∂_𝜇 - m )𝛹.
> 
>   Here, the first term (the one before the minus sign) is the "kinetic
>   term", and the second one is the "mass term".
> 
>        For fields we already know, this lines up with what we normally
>   mean by mass.
> 
>        So if you come across some new kind of field theory that ends
>   up giving you a Lagrangian of this general form, then whatever shows
>   up in place of that "m" is what we call the "mass".

Not quite.  The m there is a mass _in natural units_ (hbar = c = 1),
therefore it is more precisely called "mass *parameter*".  The actual
(expectation value of the) mass of a particle in SI units would be m hbar/c
(Unicode: m ℏ/c) if there are no interactions; otherwise one must use the
*renormalized mass* m_r, and multiply that by ℏ/c to obtain the mass in SI
units.

-- 
PointedEars

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

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#668046

On 2026-01-04, Stefan Ram <ram@zedat.fu-berlin.de> wrote:
> Anthk NM <anthk@disroot.org> wrote or quoted:
>>Hidden dimensions could explain where mass comes from
>
>   So now you might ask yourself: what exactly is "mass"?
>
>        These days, that kind of question usually comes up in the
>   context of quantum field theory.
>
>        There we use something called a Lagrangian density, which is kind
>   of a pain to write in plain ASCII, but it basically looks like this 
>   for a free field (no interactions):
>
> Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.
>
>   In Unicode form, it would be more like:
>
> 𝓛 = 𝛹̅( i 𝛾^𝜇 ∂_𝜇 - m )𝛹.
>
>   Here, the first term (the one before the minus sign) is the "kinetic
>   term", and the second one is the "mass term".
>
>        For fields we already know, this lines up with what we normally
>   mean by mass.
>
>        So if you come across some new kind of field theory that ends
>   up giving you a Lagrangian of this general form, then whatever shows
>   up in place of that "m" is what we call the "mass".
>
>        (The example I picked technically only applies to Dirac fermions,
>   but the same idea works for other kinds of particles too.)
>
>

There's the aamath package for Unix where you can display formulae
as ASCII ART: 

https://github.com/gchudnov/aamath

Check the documentation; it has an option to shrink the radicals.

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#668047

Anthk NM <anthk@disroot.org> wrote or quoted:
>There's the aamath package for Unix where you can display formulae
>as ASCII ART: 
>https://github.com/gchudnov/aamath
>Check the documentation; it has an option to shrink the radicals.

  Ah, thanks for the info!

  I'm actually planning to write something like that myself.

  As a quick little trial run, I recently "implemented square roots".

  You can see three sample outputs here:

 .-
\|x

 .---
\|x+y

 .-
 |x
 |-
\|y

  A rectangular area made of characters is described by a "box":

class Box:
    __slots__=["content","width","origin","baseline"]
    def __init__( self, content, width, baseline ):
        self.content=content
        self.width=width
        self.baseline=baseline
        return
    def __str__( self ):
        return "\n".join(self.content)

  . The root class only has one method, "render_ascii_display",
  which generates a square root sign:

class Sqrt:
    def render_ascii_display( self, operand ):

        # add bar above
        content=["-" * operand_box.width]+operand_box.content

        new_content = []

        # add bar left
        for i, line in enumerate( content ):
            if i == 0:
                prefix = " ."
            elif i == len( content )-1:
                prefix = "\|"
            else:
                prefix = " |"
            new_content.append( prefix + line )

        content = new_content

        bar_box = Box(content, 2+operand_box.width,operand_box.baseline)

        return bar_box

  . Basically, it draws a line over the operand and another
  one to its left, with the top and bottom edges ending in 
  " ." and "\|" to form a square root sign.

  Since the classes for variables, sums, and quotients aren't
  written yet, those operands are manually formatted in the
  main program for now:

sqrt = Sqrt()
operand_box = Box( ["x"], 1, 0 )
print(sqrt.render_ascii_display(operand_box))
print()
operand_box = Box( ["x+y"], 3, 0 )
print(sqrt.render_ascii_display(operand_box))
print()
operand_box = Box( ["x","-","y"], 1, 1 )
print(sqrt.render_ascii_display(operand_box))
print()

  . The output was shown above near the top of this post.

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#668050

Stefan Ram wrote:
> Anthk NM <anthk@disroot.org> wrote or quoted:
>> There's the aamath package for Unix where you can display formulae
>> as ASCII ART: 
>> https://github.com/gchudnov/aamath
>> Check the documentation; it has an option to shrink the radicals.
> 
>   Ah, thanks for the info!
> 
>   I'm actually planning to write something like that myself.
> 
>   As a quick little trial run, I recently "implemented square roots".
> 
>   You can see three sample outputs here:
> 
>  .-
> \|x
> 
>  .---
> \|x+y
> 
>  .-
>  |x
>  |-
> \|y

Just when one thought that the formatting of your Usenet postings
could not get any worse, you come and prove the opposite.

F'up2 poster

-- 
PointedEars

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

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#668051

Stefan Ram <ram@zedat.fu-berlin.de> wrote:

> Anthk NM <anthk@disroot.org> wrote or quoted:
> >There's the aamath package for Unix where you can display formulae
> >as ASCII ART: 
> >https://github.com/gchudnov/aamath
> >Check the documentation; it has an option to shrink the radicals.
> 
>   Ah, thanks for the info!
> 
>   I'm actually planning to write something like that myself.
> 
>   As a quick little trial run, I recently "implemented square roots".
> 
>   You can see three sample outputs here:
> 
>  .-
> \|x
> 
>  .---
> \|x+y
> 
>  .-
>  |x
>  |-
> \|y

[snip]

You are crazy, if you don't mind me saying so.

There really can be no excuse for reinventing the square wheel 
all over again,

Jan

-- 
<https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXMg-bmrO6JocAQFsTPL2vhfghLxANWiqVNS7hLnLeTknjjhjjr06I9UUqFHDaVcr4BzfA6drZtS6_QPQsaU_pZquFTnzVQ-r1XWiNsmdmAuqrseITlVRE5NpQuA5aLbooytthxOTczTA/s1600/hart.jpg>

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#668048

Anthk NM <anthk@disroot.org> wrote:

> On 2026-01-04, Stefan Ram <ram@zedat.fu-berlin.de> wrote:
> > Anthk NM <anthk@disroot.org> wrote or quoted:
> >>Hidden dimensions could explain where mass comes from
> >
> >   So now you might ask yourself: what exactly is "mass"?
> >
> >        These days, that kind of question usually comes up in the
> >   context of quantum field theory.
> >
> >        There we use something called a Lagrangian density, which is kind
> >   of a pain to write in plain ASCII, but it basically looks like this
> >   for a free field (no interactions):
> >
> > Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.
> >
> >   In Unicode form, it would be more like:
> >
> > ? = ??( i ?^? ∂_? - m )?.
> >
> >   Here, the first term (the one before the minus sign) is the "kinetic
> >   term", and the second one is the "mass term".
> >
> >        For fields we already know, this lines up with what we normally
> >   mean by mass.
> >
> >        So if you come across some new kind of field theory that ends
> >   up giving you a Lagrangian of this general form, then whatever shows
> >   up in place of that "m" is what we call the "mass".
> >
> >        (The example I picked technically only applies to Dirac fermions,
> >   but the same idea works for other kinds of particles too.)
> >
> >
> 
> There's the aamath package for Unix where you can display formulae
> as ASCII ART: 
> 
> https://github.com/gchudnov/aamath
> 
> Check the documentation; it has an option to shrink the radicals.

Ouch!
This really dates way back to the stone age, [1]

Jan

[1] Similar things have existed, also --long-- ago
to render TeX output as ASCII art.

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#668049

Anthk NM wrote:
> There's the aamath package for Unix where you can display formulae
> as ASCII ART: 
> 
> https://github.com/gchudnov/aamath
> 
> Check the documentation; it has an option to shrink the radicals.

Such software is nice, but it should NOT be used in for posting mathematics
in Usenet, as we (I think all of us by now) have found out through a recent
discussion.

Newer Unicode versions were designed specifically with advanced mathematics
in *plain* text *without* having to *draw* it in mind, and Network News has
been supporting it through MIME since 2009 (RFC 5536); operating systems
have begun supporting it even earlier.  (So user agents which still do not
support Unicode are non-conforming and thus *broken*.)


F'up2 sci.math

-- 
PointedEars

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

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#668053

Thomas 'PointedEars' Lahn <PointedEars@web.de> wrote:

> Anthk NM wrote:
> > There's the aamath package for Unix where you can display formulae
> > as ASCII ART: 
> > 
> > https://github.com/gchudnov/aamath
> > 
> > Check the documentation; it has an option to shrink the radicals.
> 
> Such software is nice, but it should NOT be used in for posting mathematics
> in Usenet, as we (I think all of us by now) have found out through a recent
> discussion.
> 
> Newer Unicode versions were designed specifically with advanced mathematics
> in *plain* text *without* having to *draw* it in mind, and Network News has
> been supporting it through MIME since 2009 (RFC 5536); operating systems
> have begun supporting it even earlier.  (So user agents which still do not
> support Unicode are non-conforming and thus *broken*.)

There really is no need to. (and it often works badly or not at all)

Any professional mathematician can read, write, and understand TeX,
which is *the* de-facto standard for rendering math formulae into ASCII.
He will also have the tools at hand to render TeX into good looking
math, as opposed to your usenet junk.
Even novices will rapid grasp the basic ideas.

Anyone who can't must be a dunce who can be safely ignored,
as far as mathematical or physical opinions are concerned,

Jan

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#668131

ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted:
>Here, the first term (the one before the minus sign) is the "kinetic
>term", and the second one is the "mass term".

  BTW: Today, I found out that the whole section "11.7 The Mass
  Term" in "Introduction to Elementary Particles" (1987) 
  by D. Griffiths deals with /how to identify the mass term/!

|Conclusion:  To identify the mass term in a Lagrangian, we
|first locate the ground state [the field configuration for
|which U("phi") is a minimum] and reexpress L as a function of
|the deviation, "eta", from this minimum. Expanding in powers
|of "eta", we obtain the mass from the coefficient of the
|"eta"^2 term.
|
quoted (but converted to ASCII) from "11.7 The Mass Term" in
"Introduction to Elementary Particles" (1987) by D. Griffiths

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