Re: Scalar waves

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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On 05/05/2024 02:18 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:

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In mathematical logic, often there's something like a quantifier,
that there are explicit quantifiers, and implicit quantifiers.
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So, sort of like dimensional analysis, is a quantifier analysis,
representing fixed or free parameters, and the implicitly
infinitely-many quantifiers, in front of a given classical
quantifier.
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The quantities, are results of derivations, to represent measurables,
or the "real" and "virtual" quantities that result real quantities
that are measurables.
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So, quantities are often results of infinite expressions and
thusly completions of infinite limits or continuum limits.
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The dimensional analysis and what results the dimensionless,
gets into degrees of freedom as independent parameters, then
also gets into the implicits. The quantities are not purely
algebraic, yet ensconced in their derivations.
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Consider the length of a body vis-a-vis the distance it
travels: both in units of length, yet distance as only
after a derivation of all the higher orders of acceleration
and deceleration whether it results a distance at rest, or,
a distance marking motion, that the other factors of the
dimensional analysis, go along with it, though algebraically,
at each point dimensionless.

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Right. A system of dimensions is just a consistent mapping
of a system of equations into a finite-dimensional algebra,
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Jan
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It's more the point that classical mechanics has a richer
system of implicitly involved dimensions with regards to
the derivations of the equations or formulas of systems
of moving bodies and the dynamics of change, in the
orbifold of the orbits of the geodesy of moving bodies
their world-lines and trajectories, that length and
distance and metric and norm have separate derivational
attributes as systemic.

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Again, your -has- is fundamentally wrong.
a dimension is a human construct,
it is not a property of a physical quantity,
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Jan
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