What is the 3rd dimension?

[CuriosOne]

 

Why do we need to imagine it as I thought our concept of geometry was 3 dimensional..

And I need to add this question:

Is Time One Dimensional?

 

[Phi for All]

!

Moderator Note

The way you've framed the OP, a reader is forced to watch that video, which is against our rules. Please summarize your question in context.

 

[CuriosOne]

1 hour ago, Phi for All said:

!

Moderator Note

The way you've framed the OP, a reader is forced to watch that video, which is against our rules. Please summarize your question in context.

 

What is the 3rd dimension and how do we visualize it?

[Phi for All]

4 minutes ago, CuriosOne said:

What is the 3rd dimension and how do we visualize it?

Length, width, and height are the three spatial dimensions we use in our coordinate system, or x, y, and z mathematically. You can visualize each by moving 90 degrees away from every point along the previous dimension (moving from a line to a plane, then from a plane to a cube). The third dimension is equally pictured as height, depth, and thickness, and lends a quality to objects we think of as solid.

Time (t) is a temporal dimension in a continuum with the spatial dimensions (spacetime). I can give you specific x, y, z, and t coordinates so we can meet for lunch on the 45th floor of the Empire State Building, or plot where you need to aim your rocket to reach a specific asteroid, and when to launch it so you can hit it without other maneuvering.

[Charles 3781]

I would say, that for humans, the 3rd dimension is "depth" . Like when we look at the colourful images which you kindly posted, in your OP. 

These are attractive, but exist only on our screens, in the form of flat 2-dimensional images.

If we could perceive them in 3 dimensions as solid objects, we would be able to truly visual their 3rd dimensional nature.

[CuriosOne]

9 minutes ago, Charles 3781 said:

I would say, that for humans, the 3rd dimension is "depth" . Like when we look at the colourful images which you kindly posted, in your OP. 

These are attractive, but exist only on our screens, in the form of flat 2-dimensional images.

If we could perceive them in 3 dimensions as solid objects, we would be able to truly visual their 3rd dimensional nature.

So the 3rd dimension is an illusion?

[Phi for All]

8 minutes ago, CuriosOne said:

So the 3rd dimension is an illusion?

Charles3781's explanatory skills are an illusion. He was talking about the 2-dimensionality of images on your computer screen which simulates 3-dimensional objects. It was a confusing reply to someone like you asking a legitimate question.

We CAN perceive the third dimension, it's not an illusion. We can measure length, width, and height to determine the parameters of an object or phenomenon. How tall a building is, how thick a cut of meat is, how deep the water is, all these are visualizations of the third dimension.

[CuriosOne]

11 minutes ago, Phi for All said:

Length, width, and height are the three spatial dimensions we use in our coordinate system, or x, y, and z mathematically. You can visualize each by moving 90 degrees away from every point along the previous dimension (moving from a line to a plane, then from a plane to a cube). The third dimension is equally pictured as height, depth, and thickness, and lends a quality to objects we think of as solid.

Time (t) is a temporal dimension in a continuum with the spatial dimensions (spacetime). I can give you specific x, y, z, and t coordinates so we can meet for lunch on the 45th floor of the Empire State Building, or plot where you need to aim your rocket to reach a specific asteroid, and when to launch it so you can hit it without other maneuvering.

3rd dimension equivalent to height ,depth and thickness, what about 'scaling' making something bigger or smaller?

Can I see an  example of the rocket reaching an asteroid, and the time example to hit the asteroid  please..

 

[Charles 3781]

Just now, CuriosOne said:

So the 3rd dimension is an illusion?

No,  it's real, but we can only visually perceive its reality because we  have two eyes.  If we were one-eyed creatures like a Cyclops, we'd see everything as optically flat and 2-dimensional.

We'd have to use our hands and possibly other appendages, to feel the three-dimensional physicality of bodies.

[CuriosOne]

2 minutes ago, Phi for All said:

Charles3781's explanatory skills are an illusion. He was talking about the 2-dimensionality of images on your computer screen which simulates 3-dimensional objects. It was a confusing reply to someone like you asking a legitimate question.

We CAN perceive the third dimension, it's not an illusion. We can measure length, width, and height to determine the parameters of an object or phenomenon. How tall something is, how thick it is, how deep the water is, all these are visualizations of the third dimension.

This is more clearer and thanks..

I'm trying to tie this concept in with the pythagorean theorem since it does use some concept of geometry..

6 minutes ago, Charles 3781 said:

No,  it's real, but we can only visually perceive its reality because we  have two eyes.  If we were one-eyed creatures like a Cyclops, we'd see everything as optically flat and 2-dimensional.

We'd have to use our hands and possibly other appendages, to feel the three-dimensional physicality of bodies.

Much like music in mono and stereo, there is a big difference, but it still is what it is....Hymmm maybe being an advance human has its advantages who knows..

[Phi for All]

Just now, CuriosOne said:

3rd dimension equivalent to height ,depth and thickness, what about 'scaling' making something bigger or smaller?

Dimensions measure degrees of freedom within our universe. As a coordinate system, dimensions don't care about scaling, they're just used to measure what we observe. I can measure a building to get coordinates for the three spatial dimensions, then I can add extra floors to make it taller, or add extra rooms to make it longer and wider. 

4 minutes ago, CuriosOne said:

Can I see an  example of the rocket reaching an asteroid, and the time example to hit the asteroid  please..

Since Earth is moving along with the asteroid I want to land on, I have to plot where the asteroid will be in the future when my rocket arrives there (the x, y, z, and t coordinates for my arrival). The ideal is to aim it just right (NASA calls this the "window", the path where the rocket won't run into anything else on the way), figure out exactly how much fuel I need to get there, and at the right moment I fire the thrusters. I can't drive there like an automobile does on the surface of a planet, using a steering wheel. My rocket launches in a completely straight line, affected by spacetime curvatures caused by energy and mass (gravity), and the asteroid moves into my path because that's how I calculated it, and we land safely. 

[CuriosOne]

7 minutes ago, Phi for All said:

Dimensions measure degrees of freedom within our universe. As a coordinate system, dimensions don't care about scaling, they're just used to measure what we observe. I can measure a building to get coordinates for the three spatial dimensions, then I can add extra floors to make it taller, or add extra rooms to make it longer and wider. 

Since Earth is moving along with the asteroid I want to land on, I have to plot where the asteroid will be in the future when my rocket arrives there (the x, y, z, and t coordinates for my arrival). The ideal is to aim it just right (NASA calls this the "window", the path where the rocket won't run into anything else on the way), figure out exactly how much fuel I need to get there, and at the right moment I fire the thrusters. I can't drive there like an automobile does on the surface of a planet, using a steering wheel. My rocket launches in a completely straight line, affected by spacetime curvatures caused by energy and mass (gravity), and the asteroid moves into my path because that's how I calculated it, and we land safely. 

Understood, but earth and the asteroid are in motion right? There is a reason I ask.

Sounds like this only works for close range proximity? I assume..

Sounds like calculus..😎

Edited October 14, 2020 by CuriosOne

[Phi for All]

21 minutes ago, CuriosOne said:

Understood, but earth and the asteroid are in motion right? There is a reason I ask.

Everything is in motion. Imagine 100 people are in a big gymnasium with you (this is actually a two-dimensional representation, since you can't fly). You're walking around in a circle holding a throwing dart, and everybody else is also walking around in differing sized circles. It's complete chaos, but one of those people is also holding a dart board as they move (the asteroid). Can you imagine how you'd have to figure out when/how hard/what angle to throw the dart so it doesn't hit anyone or anything else but the dart board?

21 minutes ago, CuriosOne said:

Sounds like this only works for close range proximity? I assume..

What?! No, it works anywhere in the universe. It works somewhat differently when we're on the surface of the planet, but the concept of degrees of freedom holds true.

[CuriosOne]

15 minutes ago, Phi for All said:

Everything is in motion. Imagine 100 people are in a big gymnasium with you (this is actually a two-dimensional representation, since you can't fly). You're walking around in a circle holding a throwing dart, and everybody else is also walking around in differing sized circles. It's complete chaos, but one of those people is also holding a dart board as they move (the asteroid). Can you imagine how you'd have to figure out when/how hard/what angle to throw the dart so it doesn't hit anyone or anything else but the dart board?

What?! No, it works anywhere in the universe. It works somewhat differently when we're on the surface of the planet, but the concept of degrees of freedom holds true.

Sounds very intresting...."in regards to tossing a dart on a board bull's eye with both in circular motion"...

Where could I see a formula for this if you may?

[studiot]

I'm sorry to have to tell you that your video is a sorry mixture of fact and fiction that reaches some startling unsupportable conclusions.

You will only confuse yourself at best and start to 'believe'  junk Physics if you try to study from stuff like this.

 

You question is, however a valid one that is worth a considered answer.

The third spatial dimension is necessary in our physical world to achieve closure for a set of rotations.

This is also why a fourth spatial dimension is not needed and we do not observe one.

[CuriosOne]

2 hours ago, studiot said:

I'm sorry to have to tell you that your video is a sorry mixture of fact and fiction that reaches some startling unsupportable conclusions.

You will only confuse yourself at best and start to 'believe'  junk Physics if you try to study from stuff like this.

 

You question is, however a valid one that is worth a considered answer.

The third spatial dimension is necessary in our physical world to achieve closure for a set of rotations.

This is also why a fourth spatial dimension is not needed and we do not observe one.

Which dimension goes up and down?

Say as we perceive falling objects from a building down to the ground with the force of gravity of coarse acting on it  bouncing up then repeating till it stops.

[swansont]

16 minutes ago, CuriosOne said:

Which dimension goes up and down?

Whichever one you want it to. You can choose your own coordinate system. You want that to be the z direction, it can be z. If you want it to be y, it can be y. You can call it the first, second or third dimension. It won’t affect the physics.

(coordinate system choice will affect how hard it is to solve a physics problem, though)

[Charles 3781]

11 minutes ago, swansont said:

Whichever one you want it to. You can choose your own coordinate system. You want that to be the z direction, it can be z. If you want it to be y, it can be y. You can call it the first, second or third dimension. It won’t affect the physics.

(coordinate system choice will affect how hard it is to solve a physics problem, though)

I hope that when you get on a plane, your pilot doesn't follow the same objective scientific approach to co-ordinate system choice, when landing

Edited October 15, 2020 by Charles 3781
zx81

[CuriosOne]

2 hours ago, swansont said:

Whichever one you want it to. You can choose your own coordinate system. You want that to be the z direction, it can be z. If you want it to be y, it can be y. You can call it the first, second or third dimension. It won’t affect the physics.

(coordinate system choice will affect how hard it is to solve a physics problem, though)

Understood, and thnXxx.

Now if u may please, for the time dimension (t) is this the fourh dimension?

If so does it work the same as with the 3rd dimension ie x y z translations?

Do we even use the fourth dimension for any purpose other than time?

Edited October 15, 2020 by CuriosOne

[iNow]

Who is we?

[studiot]

8 hours ago, CuriosOne said:

Which dimension goes up and down?

Say as we perceive falling objects from a building down to the ground with the force of gravity of coarse acting on it  bouncing up then repeating till it stops.

Gosh you are a hard person to keep up with on ideas. I see you have started another thread this morning.

I seriously recommend you at least get to a sensible pause point with each one before moving on, we still have a long way to go in your calculus one.

Anyway swansont has answered your question but here is more on my comment.

Here is a brilliant experiment you can easily perform to gain insight.

You will need a cardboard box with all six sides intact.

Here is a quick blackboard sketch.

Rotations can be represented by complete circles.

Consider first one single space dimension.

There is nowhere for rotations to occur. You have to leave the dimension (employ another one) to even turn around. This is Fig 0.

Move up to two dimensions  _  I have modelled this as a plane in two dimensions in Fig 1
You can have a rotation about any point in the plane.

Draw this as a circle on one face of your box, as in Fig 2.
But any rotation is about an axis which has to be a line in a third dimension.
So if you extend a line through your point through the opposite side you have the z axis.
You can draw a circle round it though any plane parallel to the first side like the opposite side.

Now move up to 3 dimensions.
You have to pairs of sides you can draw rotation circles on to generate two more axes, making 3 in all.
As in Figs 3 and 4.
I have shown the conventional right handed rectangular xyz coordinate system.

Now comes the clever part  - your experiment.
Use the box to convince yourself that rotation on any plane at any angle has an axis within the 3D system.
You do not need to leave 3D and have a rotation axis pointing into a fourth or higher dimension.

This is what I mean when I say that 3D is complete for rotations.

Let us know how you get on with your box.

[CuriosOne]

22 minutes ago, studiot said:

Gosh you are a hard person to keep up with on ideas. I see you have started another thread this morning.

I seriously recommend you at least get to a sensible pause point with each one before moving on, we still have a long way to go in your calculus one.

Anyway swansont has answered your question but here is more on my comment.

Here is a brilliant experiment you can easily perform to gain insight.

You will need a cardboard box with all six sides intact.

Here is a quick blackboard sketch.

Rotations can be represented by complete circles.

Consider first one single space dimension.

There is nowhere for rotations to occur. You have to leave the dimension (employ another one) to even turn around. This is Fig 0.

Move up to two dimensions  _  I have modelled this as a plane in two dimensions in Fig 1
You can have a rotation about any point in the plane.

Draw this as a circle on one face of your box, as in Fig 2.
But any rotation is about an axis which has to be a line in a third dimension.
So if you extend a line through your point through the opposite side you have the z axis.
You can draw a circle round it though any plane parallel to the first side like the opposite side.

Now move up to 3 dimensions.
You have to pairs of sides you can draw rotation circles on to generate two more axes, making 3 in all.
As in Figs 3 and 4.
I have shown the conventional right handed rectangular xyz coordinate system.

Now comes the clever part  - your experiment.
Use the box to convince yourself that rotation on any plane at any angle has an axis within the 3D system.
You do not need to leave 3D and have a rotation axis pointing into a fourth or higher dimension.

This is what I mean when I say that 3D is complete for rotations.

Let us know how you get on with your box.

Will definetly try this out, looks fun thnXxxxx...I will try too slow down too, I agree with you...

[Halc]

23 hours ago, Charles 3781 said:

No,  it's real, but we can only visually perceive its reality because we  have two eyes.  If we were one-eyed creatures like a Cyclops, we'd see everything as optically flat and 2-dimensional.

We'd have to use our hands and possibly other appendages, to feel the three-dimensional physicality of bodies.

Not so. I'm functionally a cyclops, and the 3D glasses they give you in the cinema do nothing for me, but I get my 3D vision from motion (moving myself) rather than from binocular vision.

It doesn't work as well, but enough that I don't need to resort to groping to perceive depth.

[MigL]

Me too.
No vision in my left eye.

Have to keep my eye moving to get any sense of depth perception while driving, or else the bird dropping on the windshield looks like a boulder in the middle of the road,

[StringJunky]

17 hours ago, iNow said:

Who is we?

The hypothetical 'We', just like the hypothetical 'One'. "If one...".

1 hour ago, Halc said:

Not so. I'm functionally a cyclops, and the 3D glasses they give you in the cinema do nothing for me, but I get my 3D vision from motion (moving myself) rather than from binocular vision.

It doesn't work as well, but enough that I don't need to resort to groping to perceive depth.

I would imagine your brain inserts depth information sourced from memory, just as my deaf brain constructs and fill;s in the missing parts of words so that they are intelligible.

Edited October 15, 2020 by StringJunky