Author 
Message 
Terry Padden science forum beginner
Joined: 17 Jun 2005
Posts: 28

Posted: Sun Jul 16, 2006 10:54 am Post subject:
Re: Rotations  why are they not vectors



"Narcoleptic Insomniac" <i_have_narcoleptic_insomnia@yahoo.com> wrote in
message
news:7171135.1153043965570.JavaMail.jakarta@nitrogen.mathforum.org...
Quote:  On Jul 16, 2006 2:21 AM, Terry Padden wrote:
mariano.suarezalvarez@gmail.com> wrote in message
news:1153025545.663758.95150@75g2000cwc.googlegroups.com...
Terry Padden wrote:
I am bothered by the mathematics of rotations. It
is I believe mathematically acceptable for any
physical reality to be defined on an abstract
axiomatic basis. Then anything that fulfills a
given defining set of axioms for a type of
mathematical object is a mathematically valid
example of the defined mathematical object.
Since rotations are just transformations on R^3, when you
ADD rotations you're just looking at the composition of
two or more transformations.
Moreover, since these transformations can be represented
as matrices the composition of them is definately NOT
VECTOR ADDITION!!!

What has any of that mumbojumbo got to do with the AXIOMS 
PLEASE GO AWAY and stop parading your stupidity. Rotations have nothing to
do with R3. 

Back to top 


Narcoleptic Insomniac science forum Guru
Joined: 02 May 2005
Posts: 323

Posted: Sun Jul 16, 2006 9:58 am Post subject:
Re: Rotations  why are they not vectors



On Jul 16, 2006 2:21 AM, Terry Padden wrote:
Quote:  mariano.suarezalvarez@gmail.com> wrote in message
news:1153025545.663758.95150@75g2000cwc.googlegroups.com...
Terry Padden wrote:
I am bothered by the mathematics of rotations. It
is I believe mathematically acceptable for any
physical reality to be defined on an abstract
axiomatic basis. Then anything that fulfills a
given defining set of axioms for a type of
mathematical object is a mathematically valid
example of the defined mathematical object.
A set does not make a vector space.
You B***** Fool. Who mentioned sets !!

YOU mentioned sets implicitly when you brought up vector
spaces!
Quote:  You need to specify two operations, addition and
multiplication by scalars.
The obvious ones you moron. You can ADD rotations;
and you can SCALE rotations by a suitable Field.
Idiot !!

Since rotations are just transformations on R^3, when you
ADD rotations you're just looking at the composition of
two or more transformations.
Moreover, since these transformations can be represented
as matrices the composition of them is definately NOT
VECTOR ADDITION!!!
Quote:  [snip]
NB I am aware that 2D rotations donotcommute,
but it seems to me that that has nothing to do with
axiomatics or my questions.
Actually, the composition operation on rotations
(with a fixed center) in the plane *is* commutative.
Yes you fool  but that is in 1D ; and I wrote
donotcommute in 2D. Can't you even read a simple
sentence ???
You may want to review Halmos' presentation of what
a vector space is, if you think that commutativity is
irrelevant, by the way...
NO ! I want you to go AWAY !!!!!!

Stop being such a douchebag. 

Back to top 


William Elliot science forum Guru
Joined: 24 Mar 2005
Posts: 1906

Posted: Sun Jul 16, 2006 9:33 am Post subject:
Re: Rotations  why are they not vectors



On Sun, 16 Jul 2006, Terry Padden wrote:
Quote:  "William Elliot" <marsh@hevanet.remove.com> wrote in message
On Sun, 16 Jul 2006, Terry Padden wrote:
Now consider simple (= 1D) rotations of a spherical object about any
given fixed axis.
You mean 3D rotations?
NO, you fool.

Get some manners. 

Back to top 


Terry Padden science forum beginner
Joined: 17 Jun 2005
Posts: 28

Posted: Sun Jul 16, 2006 7:23 am Post subject:
Re: Rotations  why are they not vectors



"William Elliot" <marsh@hevanet.remove.com> wrote in message
news:Pine.BSI.4.58.0607152245480.22224@vista.hevanet.com...
Quote:  On Sun, 16 Jul 2006, Terry Padden wrote:
Now consider simple (= 1D) rotations of a spherical object about any
given
fixed axis.
You mean 3D rotations?

NO, you fool. The axis is fixed. Only 1D rotations are allowed (so far)
Quote:  Could someone point out to me in what way such 1D rotations do NOT meet
the
axiomatic criteria for a Vector Space.
In 3D, rotations are represented as a vector in the direction of the axis
of rotation with magnitude of angular displacement.

PLEASE GO AWAY and keep this irrelevant 3D nonsense to yourself
Quote:  If 1D rotations are axiomatically vectors, why cannot they be
axiomatically
compounded into multidimensional vector spaces ?
Because the cross product doesn't?

You are showing gross stupidity by this irrelevance. I am asking about
AXIOMS  not mechanics. Please stop embarrassing yourself in public.
Quote:  NB I am aware that 2D rotations donotcommute,
Planar 2D rotations around a point are basically scalars.

That's your own little secret. Keep it that way. Now please go away and
think about axioms for a few years. 

Back to top 


Terry Padden science forum beginner
Joined: 17 Jun 2005
Posts: 28

Posted: Sun Jul 16, 2006 7:23 am Post subject:
Re: Rotations  why are they not vectors



<mariano.suarezalvarez@gmail.com> wrote in message
news:1153025545.663758.95150@75g2000cwc.googlegroups.com...
Quote:  Terry Padden wrote:
I am bothered by the mathematics of rotations. It is I believe
mathematically acceptable for any physical reality to be defined on an
abstract axiomatic basis. Then anything that fulfills a given defining
set
of axioms for a type of mathematical object is a mathematically valid
example of the defined mathematical object.
A set does not make a vector space.

You B***** Fool. Who mentioned sets !!
Quote:  You need to specify
two operations, addition and multiplication by scalars.

The obvious ones you moron. You can ADD rotations; and you can SCALE
rotations by a suitable Field. Idiot !!
Quote:  [snip]
NB I am aware that 2D rotations donotcommute, but it seems to me that
that has nothing to do with axiomatics or my questions.
Actually, the composition operation on rotations (with a fixed center)
in the plane *is* commutative.

Yes you fool  but that is in 1D ; and I wrote donotcommute in 2D.
Can't
you even read a simple sentence ???
Quote: 
You may want to review Halmos' presentation of what a vector space
is, if you think that commutativity is irrelevant, by the way...
NO ! I want you to go AWAY !!!!!! 


Back to top 


William Elliot science forum Guru
Joined: 24 Mar 2005
Posts: 1906

Posted: Sun Jul 16, 2006 5:51 am Post subject:
Re: Rotations  why are they not vectors



On Sun, 16 Jul 2006, Terry Padden wrote:
Quote:  Now consider simple (= 1D) rotations of a spherical object about any given
fixed axis.
You mean 3D rotations? 
Quote:  Could someone point out to me in what way such 1D rotations do NOT meet the
axiomatic criteria for a Vector Space.
In 3D, rotations are represented as a vector in the direction of the axis 
of rotation with magnitude of angular displacement.
Quote:  If 1D rotations are axiomatically vectors, why cannot they be axiomatically
compounded into multidimensional vector spaces ?
Because the cross product doesn't? 
Quote:  NB I am aware that 2D rotations donotcommute,

Planar 2D rotations around a point are basically scalars. 

Back to top 


mariano.suarezalvarez@gma science forum addict
Joined: 28 Apr 2006
Posts: 58

Posted: Sun Jul 16, 2006 4:52 am Post subject:
Re: Rotations  why are they not vectors



Terry Padden wrote:
Quote:  I am bothered by the mathematics of rotations. It is I believe
mathematically acceptable for any physical reality to be defined on an
abstract axiomatic basis. Then anything that fulfills a given defining set
of axioms for a type of mathematical object is a mathematically valid
example of the defined mathematical object.

A set does not make a vector space. You need to specify
two operations, addition and multiplication by scalars. Moreover,
these need to satisfy certain relations, which you have seen in Halmos'
book.
Now, you want to view the set of rotations as a vector space,
somehow. Well. You need to decide what those two operations will be.
Before you do that, the question "are rotations a vector space?"
is meaningless.
Quote:  [snip]
NB I am aware that 2D rotations donotcommute, but it seems to me that
that has nothing to do with axiomatics or my questions.

Actually, the composition operation on rotations (with a fixed center)
in the plane *is* commutative.
You may want to review Halmos' presentation of what a vector space
is, if you think that commutativity is irrelevant, by the way...
 m 

Back to top 


Terry Padden science forum beginner
Joined: 17 Jun 2005
Posts: 28

Posted: Sun Jul 16, 2006 4:42 am Post subject:
Rotations  why are they not vectors



I am bothered by the mathematics of rotations. It is I believe
mathematically acceptable for any physical reality to be defined on an
abstract axiomatic basis. Then anything that fulfills a given defining set
of axioms for a type of mathematical object is a mathematically valid
example of the defined mathematical object.
Now consider simple (= 1D) rotations of a spherical object about any given
fixed axis.
Superficially, to me (not a mathematician), such "angular displacements"
meet all of the formal axioms for a Vector Space (as given in e.g. Halmos)
as well as 1D linear displacements do.
Could someone point out to me in what way such 1D rotations do NOT meet the
axiomatic criteria for a Vector Space.
If 1D rotations are axiomatically vectors, why cannot they be axiomatically
compounded into multidimensional vector spaces ?
NB I am aware that 2D rotations donotcommute, but it seems to me that
that has nothing to do with axiomatics or my questions. I am not suggesting
that rotations ought to be physically vectors. I am just trying to get
clarification of the math picture for vectors. 

Back to top 


Google


Back to top 



The time now is Thu Feb 21, 2019 6:52 pm  All times are GMT

