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RichD
Oct 22, 2012, 9:43:04 PM10/22/12
to
Whenever a saddle point is discussed in math or physics literature,
it's always the same diagram: a 2 dimensional surface, curved
into a 3rd dimension.
How to generalize this to higher dimensions? What does a
3-D saddle surface look like? Or, a 4-D surface, embedded
in a 6-D space?
In general relativity, they talk about different geometries of space;
positive curvature is something like a sphere, OK. But negative
curvature is described by a saddle shape, which I don't see
how to extend to higher dimensions. (string theory is supposedly 9-D)
Even the simple 2-D example isn't so clear - if the universe has
a saddle shape, that means there's a special point, the saddle
point? Where is this point located, how do we find it?
--
Rich
it's always the same diagram: a 2 dimensional surface, curved
into a 3rd dimension.
How to generalize this to higher dimensions? What does a
3-D saddle surface look like? Or, a 4-D surface, embedded
in a 6-D space?
In general relativity, they talk about different geometries of space;
positive curvature is something like a sphere, OK. But negative
curvature is described by a saddle shape, which I don't see
how to extend to higher dimensions. (string theory is supposedly 9-D)
Even the simple 2-D example isn't so clear - if the universe has
a saddle shape, that means there's a special point, the saddle
point? Where is this point located, how do we find it?
--
Rich
Lord Androcles, Zeroth Earl of Medway
Oct 23, 2012, 1:21:56 AM10/23/12
to
"RichD" <r_dela...@yahoo.com> wrote in message
news:9202d2d3-f158-4973...@n2g2000pbp.googlegroups.com...
============================================
You are already there. Everything else is weird except
here at the
saddle point. Of course you are actually on the surface
of a sphere
but it likes a 2D plane, especially when at sea. As you cannot
see
what is over the horizon there will always be dragons
there.
It was only a few
mathematicians arguing over whether Euclid’s fifth
postulate was really a postulate or not
that caused Riemann and
Lobachevski to develop their own curved
geometries for the fun of it.
Then dickhead Einstein decided to use the
idea and created his own
dragons, the ones you are debating but cannot see.
--
This message is brought to you from the keyboard of
Lord Androcles, Zeroth Earl of Medway
Lord Androcles, Zeroth Earl of Medway
Big Dog
Oct 23, 2012, 9:43:38 AM10/23/12
to
So what?
What we can notice is other things: In the 2D example, a triangle of
three straight lines has interior angles that sum to less than 180
degrees. And THAT persists in the 3D version.
Vilas Tamhane
Oct 23, 2012, 10:09:06 AM10/23/12
to
by objects and objects alone. When a sphere occupies 3-D space, we say
it is a 3-D space. When it can move in the 3 directions we say that
there is 3-D empty space surrounding the sphere.
In order to believe that there is 4-D space (spatial) which we cannot
visualize and if this is not a fiction then we must have a 4-D object
to prove it. Since it is not possible to see a 4-D object we need
indirect proof for the same. They always give an example of a 3-D
object as seen by the 2-D creature. 2-D creature will see only the 2-D
projection of the 3-D object. Similarly we should be able to see 3-D
projection of 4-D object that exists in the universe. It goes without
saying that the projection that we will see will have geometrical
properties different than that of normal 3-D objects.
Vilas Tamhane
Oct 23, 2012, 10:14:12 AM10/23/12
to
On Oct 23, 10:24 am, "Lord Androcles, Zeroth Earl of Medway"
<LordAndroc...@October2012.org> wrote:
> "RichD" <r_delaney2...@yahoo.com> wrote in messagenews:9202d2d3-f158-4973...@n2g2000pbp.googlegroups.com...
But only fools and idiots believe in dragons. It is unfortunate but
now necessary to add mathematicians to this tribe.
<LordAndroc...@October2012.org> wrote:
> "RichD" <r_delaney2...@yahoo.com> wrote in messagenews:9202d2d3-f158-4973...@n2g2000pbp.googlegroups.com...
now necessary to add mathematicians to this tribe.
Hyperbolic c squared
Oct 23, 2012, 10:29:25 AM10/23/12
to
Big Dog
Oct 23, 2012, 10:32:45 AM10/23/12
to
On 10/23/2012 9:09 AM, Vilas Tamhane wrote:
>>
>> Our brains are not equipped to *visualize* a 3D surface in a 4D space.
>> So what?
>> What we can notice is other things: In the 2D example, a triangle of
>> three straight lines has interior angles that sum to less than 180
>> degrees. And THAT persists in the 3D version.
>
> You are making a simple and fundamental mistake. We can define space
> by objects and objects alone.
No sir. A space is a MUCH more generic term than what we know from our
>>
>> Our brains are not equipped to *visualize* a 3D surface in a 4D space.
>> So what?
>> What we can notice is other things: In the 2D example, a triangle of
>> three straight lines has interior angles that sum to less than 180
>> degrees. And THAT persists in the 3D version.
>
> You are making a simple and fundamental mistake. We can define space
> by objects and objects alone.
common experience. If this comes as a complete shock to you, then I'd
say it'd be good for you to learn what the meaning of the generic
"space" means. It is a *technical* term.
> When a sphere occupies 3-D space, we say
> it is a 3-D space. When it can move in the 3 directions we say that
> there is 3-D empty space surrounding the sphere.
> In order to believe that there is 4-D space (spatial) which we cannot
> visualize and if this is not a fiction then we must have a 4-D object
> to prove it. Since it is not possible to see a 4-D object we need
> indirect proof for the same.
be able to prove it exists?
You cannot see a molecule, and yet we have ample proof that they exist.
You cannot hold a gene in your hand, and yet we have ample proof that
they exist.
We have not existed for as long as the Milky Way takes to make a
revolution, yet we know certainly that it does rotate and we know how
long it takes to do so.
Ask yourself the question how we know these things though they are not
part of our common experience.
Vilas Tamhane
Oct 23, 2012, 10:37:46 AM10/23/12
to
post. We need a DIRECT proof of 4-D space.
Big Dog
Oct 23, 2012, 10:49:57 AM10/23/12
to
On 10/23/2012 9:09 AM, Vilas Tamhane wrote:
>
>
> You are making a simple and fundamental mistake. We can define space
> by objects and objects alone.
Vilas, at this point, I just want to point out a pattern.
> by objects and objects alone.
You have clashed against a number of things -- in relativity, in
classical physics, in mathematics -- where the clash comes out of
something your mind has produced.
I'll just a few examples of things your brain has told you in the last
few days:
- That continued motion requires continual application of a force
- That "space" means that which we understand from everyday experience
- That inertial forces are as real as any other forces
- That forces internal to a system can produce an acceleration of the system
- That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the looking
at the system from a different reference frame
- That heating up a substance will change the velocity of the electrons
in the atoms in the substance enough to significantly change the mass
- That if quantity A has a monotonic dependence on variable B, then A
can have any finite value whatsoever, simply by choosing a big enough B
The point of this listing is that you are letting your MIND tell you
what should be right, under the assumption that your mind's rational
capacity is sufficient for producing correct statements.
However, each of the statements above are WRONG, which is something that
is easily checked by validating against reference materials.
You now have a simple choice:
- You can absorb and embrace the demonstration that your mind's rational
capacity is NOT sufficient for producing correct statements, and that
additional input or methods are needed to check what your mind produces
before asserting validity.
- You can choose to refuse that demonstration, and insist that the
validity of what your mind produces is self-evident, and that to impose
checks on that is an intolerable suppression.
I will only add two comments to that:
- Your choice will determine whether you do yourself a huge disservice.
- There is a big and important difference between a thick skin and a
thick skull.
Big Dog
Oct 23, 2012, 10:59:26 AM10/23/12
to
On 10/23/2012 9:37 AM, Vilas Tamhane wrote:
>>
>> You cannot see UV light, though bees can. Do you have to see UV light to
>> be able to prove it exists?
>>
>> You cannot see a molecule, and yet we have ample proof that they exist.
>>
>> You cannot hold a gene in your hand, and yet we have ample proof that
>> they exist.
>>
>> We have not existed for as long as the Milky Way takes to make a
>> revolution, yet we know certainly that it does rotate and we know how
>> long it takes to do so.
>>
>> Ask yourself the question how we know these things though they are not
>> part of our common experience.
>
>>
>> You cannot see UV light, though bees can. Do you have to see UV light to
>> be able to prove it exists?
>>
>> You cannot see a molecule, and yet we have ample proof that they exist.
>>
>> You cannot hold a gene in your hand, and yet we have ample proof that
>> they exist.
>>
>> We have not existed for as long as the Milky Way takes to make a
>> revolution, yet we know certainly that it does rotate and we know how
>> long it takes to do so.
>>
>> Ask yourself the question how we know these things though they are not
>> part of our common experience.
>
> Bad examples! We have direct proofs for all that you mentioned in your
> post. We need a DIRECT proof of 4-D space.
Really? What's the direct proof of galactic rotation? Answer that very
> post. We need a DIRECT proof of 4-D space.
carefully.
What constitutes direct and sufficient proof to you? Do we have
sufficient proof for any of the following? If so, cite what you think
that proof is. It will be very important for you to be able to cite it
in each case. If you can't, then ask yourself why you accept it as
proven. Is it because you trust the words of others? If so, on what
basis do you trust some claims and not other claims?
- Atoms
- W bosons
- Neutrinos
- Continental drift
- Galactic rotation
- A finite age to the universe
- Quasars
- Genes
- Photons
Hyperbolic c squared
Oct 23, 2012, 12:01:14 PM10/23/12
to
On Oct 22, 8:43 pm, RichD <r_delaney2...@yahoo.com> wrote:
with the orientation or the earth.
I bet the direction of both the departing photons will be orthogonal
to the source.
http://en.wikipedia.org/wiki/Ophiuchus_(constellation)
http://en.wikipedia.org/wiki/Sagittarius_A
http://groups.google.com/group/sci.physics.relativity/browse_frm/thread/b9a68b614c642c3a?hl=en#
Pete Weber
Oct 23, 2012, 12:37:49 PM10/23/12
to
On Tue, 23 Oct 2012 08:43:38 -0500, Big Dog wrote:
> On 10/22/2012 8:43 PM, RichD wrote:
>> Whenever a saddle point is discussed in math or physics literature,
>> it's always the same diagram: a 2 dimensional surface, curved into a
>> 3rd dimension.
>>
>> How to generalize this to higher dimensions? What does a 3-D saddle
>> surface look like? Or, a 4-D surface, embedded in a 6-D space?
>>
>> In general relativity, they talk about different geometries of space;
>> positive curvature is something like a sphere, OK. But negative
>> curvature is described by a saddle shape, which I don't see how to
>> extend to higher dimensions. (string theory is supposedly 9-D)
>>
>> Even the simple 2-D example isn't so clear - if the universe has a
>> saddle shape, that means there's a special point, the saddle point?
>> Where is this point located, how do we find it?
>>
>> --
>> Rich
>>
>>
> Our brains are not equipped to *visualize* a 3D surface in a 4D space.
> So what?
idiot, all surfaces are 3d, except a plane, that as well can be embedded
> On 10/22/2012 8:43 PM, RichD wrote:
>> Whenever a saddle point is discussed in math or physics literature,
>> it's always the same diagram: a 2 dimensional surface, curved into a
>> 3rd dimension.
>>
>> How to generalize this to higher dimensions? What does a 3-D saddle
>> surface look like? Or, a 4-D surface, embedded in a 6-D space?
>>
>> In general relativity, they talk about different geometries of space;
>> positive curvature is something like a sphere, OK. But negative
>> curvature is described by a saddle shape, which I don't see how to
>> extend to higher dimensions. (string theory is supposedly 9-D)
>>
>> Even the simple 2-D example isn't so clear - if the universe has a
>> saddle shape, that means there's a special point, the saddle point?
>> Where is this point located, how do we find it?
>>
>> --
>> Rich
>>
>>
> Our brains are not equipped to *visualize* a 3D surface in a 4D space.
> So what?
into a 3d graph
> What we can notice is other things: In the 2D example, a triangle of
> three straight lines has interior angles that sum to less than 180
> degrees. And THAT persists in the 3D version.
Vilas Tamhane
Oct 23, 2012, 1:41:59 PM10/23/12
to
- That "space" means that which we understand from everyday
experience
No! I asked proof for multi-dimensions.
experience
- That inertial forces are as real as any other forces
You haven’t proved otherwise.
- That forces internal to a system can produce an acceleration of the
system
This is not correct. In the case of a car, internal force is
system
transmitted to the external system.
- That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the
looking
at the system from a different reference frame
Derive it in a single frame.
looking
at the system from a different reference frame
- That heating up a substance will change the velocity of the
electrons
in the atoms in the substance enough to significantly change the mass
I retracted.
electrons
in the atoms in the substance enough to significantly change the mass
- That if quantity A has a monotonic dependence on variable B, then A
can have any finite value whatsoever, simply by choosing a big enough
B
This is true.
can have any finite value whatsoever, simply by choosing a big enough
B
I don’t think that a person who says, there is no way to determine if
the train is moving towards a station or the station is moving towards
the train has a rational mind.
I don’t think that a person who cannot understand meaning of
reciprocity in SR has a rational mind.
Vilas Tamhane
Oct 23, 2012, 1:50:44 PM10/23/12
to
mind. By the way, if I must go by your logic then I will have to agree
with every statement in occult science and every statement a
spiritualist makes. You are no different than a follower of an occult
science.
W. Dale Hall
Oct 23, 2012, 2:31:53 PM10/23/12
to
Vilas Tamhane wrote:
... (stuff deleted) ...
A consequence of this assertion is that a monotonic function cannot
be bounded.
Perhaps you've never met the inverse tangent function: it is monotonic,
yet bounded.
... (the rest deleted) ...
Dale
... (stuff deleted) ...
be bounded.
Perhaps you've never met the inverse tangent function: it is monotonic,
yet bounded.
... (the rest deleted) ...
Dale
Big Dog
Oct 23, 2012, 3:03:10 PM10/23/12
to
> - That forces internal to a system can produce an acceleration of the
> system
> This is not correct. In the case of a car, internal force is
> transmitted to the external system.
> - That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the
> looking
> at the system from a different reference frame
> Derive it in a single frame.
> - That heating up a substance will change the velocity of the
> electrons
> in the atoms in the substance enough to significantly change the mass
> I retracted.
> - That if quantity A has a monotonic dependence on variable B, then A
> can have any finite value whatsoever, simply by choosing a big enough
> B
> This is true.
> I don�t think that a person who says, there is no way to determine if
> system
> This is not correct. In the case of a car, internal force is
> transmitted to the external system.
> - That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the
> looking
> at the system from a different reference frame
> Derive it in a single frame.
> - That heating up a substance will change the velocity of the
> electrons
> in the atoms in the substance enough to significantly change the mass
> I retracted.
> - That if quantity A has a monotonic dependence on variable B, then A
> can have any finite value whatsoever, simply by choosing a big enough
> B
> This is true.
> the train is moving towards a station or the station is moving towards
> the train has a rational mind.
> I don�t think that a person who cannot understand meaning of
> the train has a rational mind.
> reciprocity in SR has a rational mind.
>
According to simple, ordinary classical physics, all of the statements
>
that I gave you are wrong.
You continue to disagree with a number of those statements or prove that
they are wrong. Tamhane, this is not a forum for teaching simple,
ordinary, classical physics. This is a forum for discussing relativity,
not simple, ordinary, classical physics. It's not even a forum for
teaching relativity or deriving things in relativity.
If you disagree with simple, ordinary, classical physics, then you
should be STUDYING materials devoted to simple, ordinary, classical
physics. If your approach is to shoot from the hip and say whatever
makes sense to you, without benefit of any decent background reading
whatsoever, and you expect people to correct you by teaching why it's
wrong and what's right instead, then you're going about learning physics
the completely wrong way.
But it's not just about physics. It's about basic mathematics as well.
You said for example:
> - That if quantity A has a monotonic dependence on variable B, then A
> can have any finite value whatsoever, simply by choosing a big enough
> B
> This is true.
Seriously, you believe this is true? You have no idea what a function
> can have any finite value whatsoever, simply by choosing a big enough
> B
> This is true.
with an asymptote means? You've never seen such things in your life?
Where did you get your education? Have you forgotten most of it?
shuba
Oct 23, 2012, 5:21:21 PM10/23/12
to
FollowupTo: sci.physics.relativity
RichD wrote:
> Whenever a saddle point is discussed in math or physics literature,
> it's always the same diagram: a 2 dimensional surface, curved
> into a 3rd dimension.
Yeah, this can be misleading if not treated carefully.
> In general relativity, they talk about different geometries of space;
> positive curvature is something like a sphere, OK. But negative
> curvature is described by a saddle shape, which I don't see
> how to extend to higher dimensions.
This lecture may give insight into the issue. It did for me.
https://www.youtube.com/watch?v=H3D5HGZIP4s
> Even the simple 2-D example isn't so clear - if the universe has
> a saddle shape, that means there's a special point, the saddle
> point? Where is this point located, how do we find it?
For a uniformly curved space with negative curvature, the "saddle
points" are essentially everywhere. Again, the lecture above ought
to be helpful in making sense of my statement.
---Tim Shuba---
RichD wrote:
> Whenever a saddle point is discussed in math or physics literature,
> it's always the same diagram: a 2 dimensional surface, curved
> into a 3rd dimension.
> In general relativity, they talk about different geometries of space;
> positive curvature is something like a sphere, OK. But negative
> curvature is described by a saddle shape, which I don't see
> how to extend to higher dimensions.
https://www.youtube.com/watch?v=H3D5HGZIP4s
> Even the simple 2-D example isn't so clear - if the universe has
> a saddle shape, that means there's a special point, the saddle
> point? Where is this point located, how do we find it?
points" are essentially everywhere. Again, the lecture above ought
to be helpful in making sense of my statement.
---Tim Shuba---
Lord Androcles, Zeroth Earl of Medway
Oct 23, 2012, 6:29:08 PM10/23/12
to
"W. Dale Hall" <wdh...@alum.mit.edu> wrote in message
news:IPKdneqjHeEHfxvN...@giganews.com...
Vilas
Tamhane wrote:
... (stuff deleted) ...
... (stuff deleted) ...
==========================================
...(stuff
deleted) ...
Oops,
nothing left.
Fuck
off, nym-shifting troll.
*plonk*
Vilas Tamhane
Oct 23, 2012, 10:18:31 PM10/23/12
to
> > - That forces internal to a system can produce an acceleration of the
> > system
> > This is not correct. In the case of a car, internal force is
> > transmitted to the external system.
> > - That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the
> > looking
> > at the system from a different reference frame
> > Derive it in a single frame.
> > - That heating up a substance will change the velocity of the
> > electrons
> > in the atoms in the substance enough to significantly change the mass
> > I retracted.
> > - That if quantity A has a monotonic dependence on variable B, then A
> > can have any finite value whatsoever, simply by choosing a big enough
> > B
> > This is true.
> > I don’t think that a person who says, there is no way to determine if
> > system
> > This is not correct. In the case of a car, internal force is
> > transmitted to the external system.
> > - That wherever you see a 1/sqrt(1-v^2/c^2), that comes from the
> > looking
> > at the system from a different reference frame
> > Derive it in a single frame.
> > - That heating up a substance will change the velocity of the
> > electrons
> > in the atoms in the substance enough to significantly change the mass
> > I retracted.
> > - That if quantity A has a monotonic dependence on variable B, then A
> > can have any finite value whatsoever, simply by choosing a big enough
> > B
> > This is true.
> > the train is moving towards a station or the station is moving towards
> > the train has a rational mind.
> > I don’t think that a person who cannot understand meaning of
> > the train has a rational mind.
> > reciprocity in SR has a rational mind.
>
> According to simple, ordinary classical physics, all of the statements
> that I gave you are wrong.
>
> You continue to disagree with a number of those statements or prove that
> they are wrong. Tamhane, this is not a forum for teaching simple,
> ordinary, classical physics. This is a forum for discussing relativity,
> not simple, ordinary, classical physics. It's not even a forum for
> teaching relativity or deriving things in relativity.
>
> If you disagree with simple, ordinary, classical physics, then you
> should be STUDYING materials devoted to simple, ordinary, classical
> physics. If your approach is to shoot from the hip and say whatever
> makes sense to you, without benefit of any decent background reading
> whatsoever, and you expect people to correct you by teaching why it's
> wrong and what's right instead, then you're going about learning physics
> the completely wrong way.
>
> But it's not just about physics. It's about basic mathematics as well.
> You said for example:
> > - That if quantity A has a monotonic dependence on variable B, then A
> > can have any finite value whatsoever, simply by choosing a big enough
> > B
> > This is true.
> Seriously, you believe this is true? You have no idea what a function
> with an asymptote means? You've never seen such things in your life?
> Where did you get your education? Have you forgotten most of it?
What kind of a person you are?
>
> According to simple, ordinary classical physics, all of the statements
> that I gave you are wrong.
>
> You continue to disagree with a number of those statements or prove that
> they are wrong. Tamhane, this is not a forum for teaching simple,
> ordinary, classical physics. This is a forum for discussing relativity,
> not simple, ordinary, classical physics. It's not even a forum for
> teaching relativity or deriving things in relativity.
>
> If you disagree with simple, ordinary, classical physics, then you
> should be STUDYING materials devoted to simple, ordinary, classical
> physics. If your approach is to shoot from the hip and say whatever
> makes sense to you, without benefit of any decent background reading
> whatsoever, and you expect people to correct you by teaching why it's
> wrong and what's right instead, then you're going about learning physics
> the completely wrong way.
>
> But it's not just about physics. It's about basic mathematics as well.
> You said for example:
> > - That if quantity A has a monotonic dependence on variable B, then A
> > can have any finite value whatsoever, simply by choosing a big enough
> > B
> > This is true.
> Seriously, you believe this is true? You have no idea what a function
> with an asymptote means? You've never seen such things in your life?
> Where did you get your education? Have you forgotten most of it?
You brought in the subject of car motion, not me and now you tell me
that I should not discuss the subject.
You are unknowingly committing a basic mistake of not applying your
mind to freshman’s physics. You know that a body moves on account of
force applied. In every case we must reach to the origin of force.
Frictional force aids in motion, it is not directly responsible for
the motion.
It is the energy input in the cylinder of an engine that is converted
into motion of the car.
Is this the way you were educated?
Tom Roberts
Oct 24, 2012, 12:59:41 AM10/24/12
to
On 10/22/12 10/22/12 8:43 PM, RichD wrote:
> Even the simple 2-D example isn't so clear - if the universe has
> a saddle shape, that means there's a special point, the saddle
> point?
No. The usual case where this comes up is the class of FRW manifolds with
> Even the simple 2-D example isn't so clear - if the universe has
> a saddle shape, that means there's a special point, the saddle
> point?
negative spatial curvature. In spatial coordinates orthogonal to the unique
cosmological time coordinate, their spatial structure is homogeneous and
isotropic, and there is no "special" point. (There is a special point in time,
called the big bang, which is a singularity in the past of every point in the
manifold.)
Tom Roberts
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