Re: vis-viva and vis-motrix

Am Samstag000028, 28.09.2024 um 23:57 schrieb Ross Finlayson:

On 09/28/2024 01:57 AM, Thomas Heger wrote:

Am Donnerstag000026, 26.09.2024 um 22:41 schrieb Ross Finlayson:

On 09/26/2024 10:39 AM, The Starmaker wrote:

Ross Finlayson wrote:

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On 09/25/2024 01:55 PM, The Starmaker wrote:

Ross Finlayson wrote:

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On 09/22/2024 11:37 AM, Ross Finlayson wrote:

On 09/22/2024 09:59 AM, Ross Finlayson wrote:

On 09/17/2024 11:41 AM, Ross Finlayson wrote:

On 09/17/2024 04:34 AM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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Does anybody even bother to think about vis-viva versus vis-
motrix
anymore, with regards to conservation, momentum, inertia, and
energy,
and potential and impulse energy?

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Of course not. These are obsolete distinctions,
from a time when energy and momentum conservation was not
corectly
understood.
The matter was put to rest by Christiaan Huygens
by showing (for particle collisions)
that momentum conservation and energy conservation
are distinct conservation laws, that are both needed,
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Jan
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Is it usually considered at all that momentum and inertia change
places with respect to resistance to change of motion and rest
respectively sort of back and forth in the theory since
antiquity?
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Several times?

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Au contraire, there is yet definition up, in the air, as it were.
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Find any reference to fictitious forces and for a theory
where the potential fields are what's real and the classical
field's just a projection to a perspective in the middle,
and anything at all to do with the plainly empirical or
tribological with regards to our grandly theoretical,
and one may find that the definitions of "inertia" and
"momentum" with regards to resistance to changes in motion
and resistance to changes in rest, as with regards to
weight and as with regards to heft, have rotated each
few hundred years, as with regards to the great schism
whence Newton's vis-motrix, as with regards to the vis-insita
and Leibnitz' vis-viva, as what for example can be read into
from the Wikipedia on conservation of _energy_ and conservation
of _momentum_ up to today, where for example, the "infinitely- many
higher orders of theoretical acceleration are both formally
non-zero and vanishing" because "zero meters/second
equals infinity seconds/meter".
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So, for a true centrifugal, and quite all about the derivative
and anti-derivative as with regards to momentum, inertia,
and kinetic energy, in a theory what's of course sum-of-histories
sum-of-potentials with least action and gradient, or sum-of-
potentials,
it is so that the various under-defined concepts of the plain laws
of after Newton, are as yet un-defined, and there are a variety
of considerations as with regards to the multiplicities, or
these singularities, and the reciprocities, of these projections.
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So, some of these considerations as since "Mediaeval Times",
help reflect that Einstein's not alone in his, 'attack on Newton'.
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Moment and Motion:  a story of momentum
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https://www.youtube.com/watch?v=DH-Gh-
bBb7M&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY
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Theories and principles, momentum and sum-of-histories
sum-of-potentials, conservation, momentum and inertia
and energy, fields and forces, Einstein's mechanics,
conservation of energy and conservation of momentum,
potential and fictitious and causal and virtual, mv, mv^2,
ordinary and extra-ordinary in the differential and inverses,
the standard curriculum and the super-standard, momentum
in definition, classical exposition, Bayes rule and a law of large
numbers, law(s) of large numbers and not-Bayesian expectations,
numerical methods in derivations, uniqueness results later
distinctness results, law(s) of large numbers and continuity,
complete and replete, induction and limits, partials and limits,
the paleo-classical, platforms and planks, mass and weight
and heft, gravitational force and g-forces, measure and
matching measure, relativity and a difference between
rest and motion, heft, resistance to gravity, ideals and
billiard mechanics, wider ideals, Wallis and Huygens,
Nayfeh's nonlinear oscillations, addition of vectors,
observables and ideals, DesCartes' and Kelvin's vortices,
black holes and white holes, waves and optics, Euler, both
vis-motrix and vis-viva, d'Alembert's principle, Lagrange,
potential as integral over space, Maupertuis and Gauss
and least action and least constraint, Hamilton,
Hamiltonians and Bayesians, Jacobi, Navier and Stokes
and Cauchy and Saint Venant and Maxwell, statistical
mechanics and entropy and least action, ideal and real,
mechanical reduction and severe abstraction, ions and
fields and field theory, wave mechanics and virtual particles,
ideals and the ideal, the classical and monistic holism, paleo-
nouveau.
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Much like the theories of "fall", "shadow", or
"push" gravity, or the "shadow" or "umbral"
gravity and for theories of real supergravity,
as after Fatio and LeSage, as of theories of
"pull" or "suck" gravity of Newton and the
"rubber-sheet" or "down" gravity of Einstein,
then the theories of vortices like DesCartes
and Kelvin, and others, help reflect on the
rectilinear and curvilinear, and flat and round,
as with regards to deconstructive accounts of
usual unstated assumptions and the severe
abstraction and mechanical reduction, in as
with regards to modern theories of mechanics.
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Zero meters per second is infinity seconds per meter.
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You know, zero meters per second is infinity seconds per meter,
and, any change of anything in motion has associated the
infinitely-many higher orders of acceleration, and,
it's rather underdefined and even undefined yet very
obviously clearly is an aspect of the mathematical model,
that Galileo's and Newton's laws of motion, sort of are
only a "principal branch" as it were, and, don't quite suffice.
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Of course anything that would add infinitely-many higher
orders of acceleration mathematically to the theory,
of mechanics, the theory, would have to result being
exactly being the same as Galilean and Newtonian,
"in the limit", and for example with regards to
Lorentzians and these kinds of things.
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It's sort of similar with adding more and better
infinities and infinitesimals to mathematics.
The continuous dynamics of continuous motion
though and its mechanics, is a few layers above
a plain concept of the continuum, as with regards
to something like a strong mathematical platonism's
mathematical universe, being that making advances
in physics involves making advances in mathematics.
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Which pretty much means digging up and revisiting
the "severe abstraction" the "mechanical reduction",
quite all along the way: paleo-classical, super-classical.

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"zero meters per second is infinity seconds per meter"????
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Do you guys even have any idea whats yous talkings abouts?
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'infinity' has no time and cannot be measured. So, that means there
are
no 'seconds' in "infinity", and no meter/meters/inches in "infinity'!
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In "infinity" there are no meters or seconds.
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Where do you guys get your information from? Albert Einstein??
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"Moment and Motion:  infinity and large numbers"

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Oh i see, yous people live in a Mandelbox universe...
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i wasn't refering to yours 'numbers' universe..
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i was refering to the real universe.
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Einstein said he wasn't sure if the universe is infinite or not..
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but I'm sure the universe is infinite...just not the one you're
in...only it's surrounding universe that yous are expanding in.
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sorry to bust your bubble.
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Actually, there's an idea that one way to conceive
the universe, is, as a mathematical continuum, that
these days that's what's called "holograph", or "hologram",
the idea that one mathematical continuum is big enough
to have a number, for each thing, and relation in things.
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Then these philosophically are called "plastic numbers,
metal numbers, concrete numbers".
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Then, for example, Euclidean space, and, maybe not
Minkowski space, have it that there's only a ray
of time, or 3 + 1/2, with three space dimensions,
rolling and curled up, in the infinities and the
infinitesimals, one continuum.
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It might even be reasonable to explain sort of why
there are three dimensions in a mathematical universe
of the space-like, simply courtesy properties of numbers,
because "least action and a gradient" is about the
easiest way to say "it is what it is, and it will
be what it will be".

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I had the idea, that this picture is actually correct and written kind
of 'book' about this concept.
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(you find it here:
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https://docs.google.com/presentation/ d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
)
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The idea is called 'structured spacetime'.
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The spacetime of GR is assumed to exist and being a real physical entity.
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It is a continuum build from 'pointlike elements'.
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These 'elements' are something you may call 'points with features'.
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The math behind it is quite unusal, but already known and not
particularily difficult.
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It is so called 'Pauli algebra' applied to so called 'bi-quaternions
(aka 'complex four-vectors').
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...
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TH
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   It kind of is, kind of isn't.
 A "tetrad" in physics helps fill out complementary duals,
and, their complementary duals, so that notions of
 oscillation and restitution
dissipation and attenuation
 make for
 tendencies and propensities
 what's the consistitutive
and reconstitutive and deconstitutive,
 why three legs is enough to hold up the table,
then for something on it.
 So, tetrads like
 proton electron neutron photon,
 mass charge light-speed neutron-lifetime
 strong+gravity electromagnetic electro-weak optical-weak
 help establish usual sorts of setups like field theory,
models of forces, and pretty much for theories where
the potential fields are the real field, for example
 3 + 1 dimensions, or 3 + 1/2 "space and a ray of time",
 then there's a tetrad
 point projection perspective space
 as with regards to
 point local global total.

We need 'three axes of space and one scalar for time' at a single point only.
Moving to another point would require the same stuff, but not the same axes!
Iow: the (imaginary) axis of time does not need to be parallel throughout the entire universe!
Actually time MUST be local and measures some sort of rythm of causality.
Other places can have actually other timelines and actually a local time, which runs backwards from our perspective.
This is important, because that would allow to understand certain behaviours of nature.
This would result in a double tetrahedron, where forward flowing time with three real axes and a backwards flow time with the axes of kind of world behind the mirror would overlap to a double tetrahedron.
Since we belong to these results, too, we can only live in our own world and cannot look behind that mirror.
 From this we have drawn the conclusion, that our own world is all that would exist.
But that is just an optical illusion and as wrong as 'flat Earth'.
But we know already, that things can leave our own 'world' and disappear into black holes or pop out of nothing in 'white holes'.

  Then, this being usually a field theory, there's
that the theory is always "three space dimensions",
and, that being some "real Euclidean space".
 People make a lot of the complex, and also the
hyper-complex like geometric algebras, then
there are also approaches like Kodaira and Zariski,
that include without, that the same sorts of setups
of rotations and reflections and analyticity with
respect to a "diagram", have that there are all sorts
of diagrams, considered mathematical models.
 

Well, my own guess was a clifford algebra with the name CL_3, also known as 'Pauli algebra'.
This uses 'bi-quaternions' and that shall be symbolised by a double tetrahedron (because of the eight components of this construct).

Then the idea that there is a numerical resource,
a continuum, that just sort of naturally results
three dimensions and a ray of time, and also then
as with regards to tetrads and information in
the space-time, the "Space-Time", with its contents,
is a thing actually looking to equip a mathematical
model as being a resource and book-kept in this way,
about deriving most of the theory from least,
and that that's a very principled approach.
 

'Ray of time' is a dangerous concept.
Time is depicted as a ray, but usually time is an imaginary pseudoscalar.
TH