Re: Treating Magnitude as Fundamental

On Sep 23, 9:41 am, hagman <goo...@xxxxxxxxxxxxx> wrote:
On 20 Sep., 23:24, "Timothy Golden BandTechnology.com"

<tttppp...@xxxxxxxxx> wrote:
Very nice presentation hagman. I'll verify your metric and if it works
cite your post here as a reference on my website. Thanks for bringing
this to some level that I can understand. This metrical digression is
still puzzling to me. I have a Cartesian transform already, but if the
symmetry is not obeyed then isn't translation somehow screwed up?
I'll have to spend some time on this. Symmetry is somewhat broken
under your rendition. I'm learning something here I guess. Product as
a physical entity is deeply puzzling. Why does a geometry even need
one?

Geometry does not need that product, but in your P4, multiplication
is one of the fundaments and without it, P4 (including metric) is
nothing
but the metric vector space R^3 -- thus not leaving much room for you
to gain formerly unknown physical insights.

I don't know if you are still monitoring this thread Hagman but I see
spacetime as
P1 P2 P3 ...
where the behavior of P4+ is indeed broken in terms of distance
conservation under product.
So you see that we have unidirectional time in P1 and the promise of
Maxwell's equations in P2P3.
I do not yet have a full theory built, but the 'physical insights'
already look promising. In effect if we take polysign systems obeying
| A || B | = | A B |
we see spacetime. The ones which do not obey may also be useful, but
they are nonlinear. So dynamics are in order for P4+.
Perhaps my usage of 'nonlinear' here is inappropriate, but you must
see what I mean by it.

I still have not gotten to a computer proof of your metric. I will get
to it and it won't take very long.
Still though, the hole of distance discrepancy cannot be satisfying.
P4 has geometry. It has distance. It has algebra. It seems that
isomorphism is happy to focus its beam on just a few qualities and so
the term is more like an analogy than an equivalence.
Indeed when I look up the term 'isometry' on Wiki I get
"In mathematics, an isometry, isometric isomorphism or congruence
mapping is a distance-preserving isomorphism between metric spaces.
Geometric figures which can be related by an isometry are called
congruent."
I don't care to get too deep into these mathematical terminologies.
Still if I am going to carry on a discussion with mathematicians I
will have to keep working at these. So I point you to a stronger form
which you cannot achieve, or at least have not achieved yet.

-Tim

-Tim

-Tim

.

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