Each dimension is perpendicular at all another

[Michael F. Dmitriyev]

Does this concept is connected with a pure geometry (of space)?.
Thus each dimension is perpendicular at all another.
It is simple for presenting graphically up to three dimensions:
point, line, square, cube and …..
Further it is much more difficult. What a physical sense of various dimensions?

 

[Goalie_Ca]

First of all, each dimension doesn't have to be perpendicular. What defines a dimension is that the basis vectors can't be a linear combination of each other.

If you are really interrested try reading some linear algebra. that will give you a good idea of what is a space, subspace, dimension, etc.

 

[Michael F. Dmitriyev]

First of all, each dimension doesn't have to be perpendicular. What defines a dimension is that the basis vectors can't be a linear combination of each other.

If you are really interrested try reading some linear algebra. that will give you a good idea of what is a space, subspace, dimension, etc.

But for the three dimension it works pretty good.
What is the reason for change of a principle of perpendicularity for higher dimensions?
It seems not logical at least.

 

[HallsofIvy]

I don't understand what you mean. There is no "change of a principle of perpendicularity for higher dimensions". The general, linear algebra definition, of 'dimension n' is that there exist n independent vectors. As long as you are working in an inner product space in which "perpendicularity" can be defined, it is always possible to choose a basis of n perpendicular vectors, corresponding to n perpendicular directions.

 

[Michael F. Dmitriyev]

I don't understand what you mean. There is no "change of a principle of perpendicularity for higher dimensions". The general, linear algebra definition, of 'dimension n' is that there exist n independent vectors. As long as you are working in an inner product space in which "perpendicularity" can be defined, it is always possible to choose a basis of n perpendicular vectors, corresponding to n perpendicular directions.

Then what , according to linear algebra, the fourth dimension look like?
Is it not the sphere? The adding of next dimension add a corresponding move at object
It seems the geometry of space is a dynamic geometry.

 

[Goalie_Ca]

Maybe you're not getting it. A 2-d space can be made up of x^2 + x^3.
A dimension is a purely mathematical concept... Even in physics.

Now to really get your noodle. You can transform a set of vectors to another set of vectors. A NullSpace is the set of all vectors that get mapped to 0 vector.

 

[Moe]

Michael, the problem is that you can't picture more than three dimensions. I have seen representations of hypercubes (4-D cubes), but they look all weird. (For all you Rubic's cube fans out there, I found a little flash applet with a 4-D rubic's cube.) You just have to accept them as a mathematical concept. In three-D space, a set of base vectors would be
1 0 0
0 1 0
0 0 1

These can be graphically represented as the x, y and z axis.
A base system for a 4-D space would be

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

They are all "perpendicular", multiplying any two of them will give you 0. But finding a graphic representation of those is pretty much impossible.

 

[Michael F. Dmitriyev]

But I do not see nor a zero point nor a mirror reflection of each dimension in your matrixes.
A zero point, (x,-x), (y,-y), (z,-z) are always present on any real graph.
Here I see your problems, not mine.

 

[Integral]

Michale,

A reflection is an operation performed on an object, it is not something that is seen in the basis vectors themselves.

 

[Michael F. Dmitriyev]

Michale,

A reflection is an operation performed on an object, it is not something that is seen in the basis vectors themselves.

Let's check up.
The LINE this a propagation of POINT. This is an operation.
The SQUARE this a propagation of a line. This is an operation.
A CUBE this a propagation of the square. This is an operation.
The SPHERE this recurrence of a cube at his rotation concerning all three coordinates. Thus the sphere itself rotates also, but in another mode. This is obviously an operation.
We can observe this operations in the nature.

 

[Moe]

What do you mean, you don't see a zero point reflection in my matrices? It works just like the three-D thing. You have to stop trying to visualize something with 4 dimensions.
This
http://www.labyrinthina.com/hypercube.jpg is a hypercube, a 4-D cube. The reason why it looks so weird is that it is essentially impossible to visualize it. Our mind works in only three dimensions.


Edit: How come image tags don't work here?

 

[FUNKER]

yea i find it pretty hard to wrap my head around the whole issue of "11 dimensions" and the likes, but H.G. Wells described dimensions vivedly in the prologue to 'Time Machine' the original novel, give it crack cos' its hood rich

 

[Michael F. Dmitriyev]

What do you mean, you don't see a zero point reflection in my matrices? It works just like the three-D thing. You have to stop trying to visualize something with 4 dimensions.
This
http://www.labyrinthina.com/hypercube.jpg is a hypercube, a 4-D cube. The reason why it looks so weird is that it is essentially impossible to visualize it. Our mind works in only three dimensions.


Edit: How come image tags don't work here?[/QUOTE]
Moe,
You are proposing a “photo” from one position and assert that it is a real life.
I am proposing a “cinema” taken off with various positions and I think that it much closer to a reality.

 

[Michael F. Dmitriyev]

Our mind works in only three dimensions.

I always thought that we exist in the TIME too. Forgive my provincial naivety, please.

 

[Moe]

Moe,
You are proposing a “photo” from one position and assert that it is a real life.
I am proposing a “cinema” taken off with various positions and I think that it much closer to a reality.

Now you have lost me.

We exist in all dimensions. That doesn't mean we can understand them. And in mathematics, you can have as many dimensions as you like. There is no need for a physical representation of those dimensions. For example, it might be feasible to express certain characteristics as a multi-dimensional vector. In Relativity, you use 4-D vectors, one component is time, the other three are speeds, or one is energy, the other three are linear momenta. Stop trying to visualize it - it won't work.

Now, if you want to, you can view time as the fourth dimension. In that case you could maybe visualize a 4-D cube by looking at a video of a 3-D cube that is being deformed. But what would a 5-D cube look like then? So let me rephrase my original sentence:
Our mind works in three spatial dimensions only.

 

[Michael F. Dmitriyev]

You have to stop trying to visualize something with 4 dimensions.

Why, if it turns out the pretty successful?

 

[Michael F. Dmitriyev]

Now, if you want to, you can view time as the fourth dimension. In that case you could maybe visualize a 4-D cube by looking at a video of a 3-D cube that is being deformed. But what would a 5-D cube look like then?

Then 5-D (and all higher) an OBJECT would look like the sphere too.
I do not remember who had said first about “ higher spheres” , but this the words are prophetical

 

[Moe]

Why would an object with more than three dimensions look like a sphere?

 

[Michael F. Dmitriyev]

Why would an object with more than three dimensions look like a sphere?

Moe,
I have explained this for 4-D object in a post #10 of thread.
For the following dimensions :
Any rotation of sphere gives the sphere in a result.
Hence any an object with more than four dimensions look like a sphere also.
They are invisible for us, but we can perceive their some manifestation.

 

[Michael F. Dmitriyev]

It is possible to consider dimensions as evolution of the universe from nothing.
Zero point--> ray of light--> plane of light--> volume of light -->sphere of light--> rotation of spheres of light.
But all aspires to return to a zero point. It corresponds to gravitation.

 

[Antonio Lao]

Since I have difficulty visualizing a 4th dimension, I had resigned myself to working with only one dimension. Can we really visualize one dimension? We can't. All objects that can be seen are inherently 3D. We thought we saw 2D or 1D but it is just, because from the perspective projections, the other dimensions were assumed hidden from view but they are always there out of sight.

 

[Michael F. Dmitriyev]

It is not difficult to visualizing dimensions.

The static geometry.
-----------------------

0-D
- It is a point.
1-D
- It is a line.
2-D
- It is a square.
3-D
- It is a cube..
4-D
- It is a supercube.

The dynamic geometry of spacetime. (by Michael F. Dmitriyev)
-------------------------------------------

Zero point.
- It is a point of beginning and end. All aspires to return to a zero point. It corresponds to gravitation.
0-D
- It is a photon;
1-D
- It is a ray of light, i.e. a propagating photon;
2-D
- it is a charge i.e. a circular ray of light;
3-D
- It is an internal structure of an object;
4-D
- It is a spherical (neutral) particles, atoms, planets, stars .. i.e. rotation of internal structure concerning all three coordinates; it is the spin of particles and rotation of macroobjects;
5-D and higher
- It is the supreme spheres.

 

[Antonio Lao]

The static geometry 0-D - It is a point...The dynamic geometry of spacetime.Zero point.- It is a point of beginning and end. All aspires to return to a zero point. It corresponds to gravitation.

I am agreeing with you that in these cases, you are really "seeing" with your mind's eye. For the mind can see everything.

As far as theories and equations, zero-points cause theory to become meaningless and equation to blow up.

The singularity is an example in general relativity. At the singularity, all physical laws of physics become meaningless. At the singularity, volume is zero. The inverse square law blew up when the distance is zero. The inverse square law for gravity was tested valid only to about a 10th of a millimeter. Gravity was never tested at the atomic or subatomic level yet.

 

[Michael F. Dmitriyev]

Let's compare these two sort of geometry now.

The static geometry does not contain any information in a physical sense though many try to find this.
It does not explain anything.
It is the practical tool for designers and manufacturers of 3-D objects.
The static geometry has no any sense in application to the fourth and higher dimensions.

 

[Antonio Lao]

The static geometry does not contain any information in a physical sense

What is the complementary geometry to static geometry? Is it dynamic geometry?

Is dynamic geometry restricted to only one dimension?

 

[Michael F. Dmitriyev]

What is the complementary geometry to static geometry? Is it dynamic geometry?

Is dynamic geometry restricted to only one dimension?

Complementary Geometry
The idea for Complementary Geometry came from seeing one very green Bartlett pear. I could immediately picture it against its complementary red. So, I went in search of a red plate. An antique store downtown yielded a square red glass plate. This inspired me to see the painting as contrasts of not only complementary colors but of complimentary shapes as well. I like the way the round format looks like a small round table top seen from above. The dark green and pale yellow tablecloth create a lively background to set off the bold composition.

What it deal with physics?

Take a look at post #22 once again, please.

 

[Entropy]

If any of you can't really "visualize" things in higher dimensions try downloading this graphing program: http://www.simtel.net/product.php?url_fb_product_page=56441 . Graphs as many spatial dimensions as you want. It comes with a pre-made hypersphere. Fool around a little with it, its pretty neat.

 

[Antonio Lao]

Take a look at post #22 once again, please.

I understood what your categorized dimensions are but I have also made my own building blocks for each physical realities.

A photon is composed of 4 H+ and 4 H-. The H's are distinct topologies which is 4D since each H contains 2 metrics and 2 forces. By itself the H is time iindependent. But time evolution or integral of the H change the force into linear momentum. The result is still 4D but it is now a double actions integral greater or equal to the square of Planck's constant.

The principle of directional invariance gives 8 directional properties that allow us to conceptualize 3D objects. If some of these properties is missing then 3D objects is not possible. With the additional concept of level of existence (LOE) for the H's, any higher dimensional object can be visualized. In this sense, an atom which is the composition of proton, neutron, and electron has far more dimensions than its components. For example, the hydrogen atom is 96D and the helium atom is 304D which is calculated by adding up all the H's and multiply by 4.

The photon is 32D. The electron is 32D. The neutrino is 8D, the up-quark is 24D, the down-quark is 16D. The proton is 64D, the neutron is 56D.

 

[Michael F. Dmitriyev]

I understood what your categorized dimensions are but I have also made my own building blocks for each physical realities.

A photon is composed of 4 H+ and 4 H-. The H's are distinct topologies which is 4D since each H contains 2 metrics and 2 forces. By itself the H is time iindependent. But time evolution or integral of the H change the force into linear momentum. The result is still 4D but it is now a double actions integral greater or equal to the square of Planck's constant.

The principle of directional invariance gives 8 directional properties that allow us to conceptualize 3D objects. If some of these properties is missing then 3D objects is not possible. With the additional concept of level of existence (LOE) for the H's, any higher dimensional object can be visualized. In this sense, an atom which is the composition of proton, neutron, and electron has far more dimensions than its components. For example, the hydrogen atom is 96D and the helium atom is 304D which is calculated by adding up all the H's and multiply by 4.

The photon is 32D. The electron is 32D. The neutrino is 8D, the up-quark is 24D, the down-quark is 16D. The proton is 64D, the neutron is 56D.

You are very generously allocate dimensions. Seems the nature is more economical.
Wee notice:
- all observable objects are in the limits of 4-D.
There may be you have paid attention my categorized dimensions corresponds to the four fundamental forces?

 

[Antonio Lao]

Seems the nature is more economical.

You are right about frugality of nature. So knowing that nature will never allow itself to waste space, energy and matter, that is why nature prefers to work only in 1D of space and 1D of time, it conserved energy between potential and kinetic aspect, and practically all fundamental particles are points and also massless. The graviton, the photon, the gluon (although, I am doubting its existence), the neutrino (?) are all massless.

The graviton is responsible for the fundamental gravity force.
The photon is responsible for the fundamental electromagnetic force.
The gluon is responsible for the fundamental strong nulcear force.
The neutrino (a fermion), at one time were thought to be responsible for the fundamental weak nuclear force until the discovery of W's and Z's bosons which broke the massless symmetry by acquiring mass through the Higgs mechanism. Although broken symmetry works perfectly for the electroweak force, it still did not resolve the problem with dimension until the advent of string theory.