Coordinate Systems And Total Information
Timothy Golden http://www.BandTechnology.com
The spherical coordinate system encodes more information than its
cartesian counterpart when bounds are lifted from the angular measures.
In effect, each angle encodes an integer number atop the angular
information. This information is in terms of a number of rotations and
could be deemed meaningful, particularly if one wishes to study angular
velocities.
I am not making this argument in terms of a computer data structure but
on a principle of information between the cartesian and spherical
coordinate systems and a symmetrical use of real numbers for both of
them.
If we define the coordinate systems as equivalent informationally then
I suppose I am left with the conclusion that the real numbers are not
informationally conservative. If that is the case then it is a bit
scary that we use them for everything scientific. But I think that some
may agree that the cartesian system is wasteful of information.
-Tim
Solbek
"Timothy Golden http://www.BandTechnology.com" <tttp...@yahoo.com> wrote
in message news:1125589995.3...@g49g2000cwa.googlegroups.com...
There is no "encoding of information", just simplification of mathematical
operations.
It is typical to convert between several coordinate systems back and forth
to solve problems.
It is a technique, a tool. All "information" is intact, as a one to one
mapping exists.
A good lesson for you.
Dirk Van de moortel
"Timothy Golden http://www.BandTechnology.com" <tttp...@yahoo.com> wrote in message
news:1125589995.3...@g49g2000cwa.googlegroups.com...
So indeed there is a bijection
RxRxR <--> RxRxRxNxN
but that's not new, since there is also a bijection
R <--> RxRxR
and in fact between R and the product set of any countable
number of R's:
R <--> Rx.....xR
Dirk Vdm
>
> -Tim
>
Mike
Gee, Cantor, Goedel, Peano and the others would be proud of you Dirt.
Especially if they knew that besides that you also understand the
square root.
Plonk
Mike
>
>
>
>
> >
> > -Tim
> >
Dirk Van de moortel
"Mike" <ele...@yahoo.gr> wrote in message news:1125591293....@g49g2000cwa.googlegroups.com...
Since that means that you now pretend not to be able to
see my reply, I will not bother. Or won't I?
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Psychotic.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Learned.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Playground.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Dirt.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Imbecile.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/HiPsycho.html
Dirk Vdm
>
> Mike
Uncle Al
>
> What of the following argument:?
>
> The spherical coordinate system encodes more information than its
> cartesian counterpart when bounds are lifted from the angular measures.
> In effect, each angle encodes an integer number atop the angular
> information. This information is in terms of a number of rotations and
> could be deemed meaningful, particularly if one wishes to study angular
> velocities.
Spherical coordinates and Cartesian coordinates exactly interconvert.
Neither contains anything the other doesn't. There is only one
empirical reality. Coordinate systems are assigned for convenience
given the symmetries of the problem. A proper physicist would use
tensors and discard the background.
What about confocal ellipsoidal coordinates? Reciprocal lattices?
Non-local 3-D Fourier transforms?
> I am not making this argument in terms of a computer data structure but
> on a principle of information between the cartesian and spherical
> coordinate systems and a symmetrical use of real numbers for both of
> them.
That didn't help any.
> If we define the coordinate systems as equivalent informationally then
> I suppose I am left with the conclusion that the real numbers are not
> informationally conservative. If that is the case then it is a bit
> scary that we use them for everything scientific. But I think that some
> may agree that the cartesian system is wasteful of information.
e^[i(pi)] = -1
Algebra and analytic geometry are indistinguishable.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Ross A. Finlayson
ZF is inconsistent. I think that because I think there needs to be a
universal set in a set theory, and regularity, the axiom of regularity
or axiom of foundation, precludes the existence of a universal set.
So, ZF: inconsistent, ZF - R: less necessarily inconsistent.
ZF being inconsistent doesn't mean the rework of all other mathematics,
that's ridiculous. It just would mean the rework of a variety of
intermediate results, retrofitting coconsistential schemata.
Heh heh heh eh eh hrm.
Oh, yeah.
Al, I dispute you. Al, Al Schwartz, Al, Uncle Al, I'm talking to you,
man.
Regards,
Ross
--
Ross A. Finlayson