DaveC426913
Valued Senior Member
It should go in Free Thoughts. There is no theory here. It's a shill for a video.
4th dimension is extension of 3rd dimension. A world within worlds
- Thread starter akabrutus
- Start date
No argument from me on that score.
Height is an incomplete dimension .
Depth , rather than height alone gives a better understanding .
Depth goes above the plane of 2D as well as below 2D plane .
Height does not . Because it has no real depth . It extends in one direction , up , only .
But
Depth then applied to both breadth and width , gives a complete form of 3D objects .
Inotherwords height alone does not complete a three object . Height lacks depth .
Any objections ? If so , I would like to read them , in further posts , in this thread .
I'm open to discussion .
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akabrutus:
Here's how you construct a tesseract, by analogy:
0. Start with a point. That has no dimensions.
1. Move the point in a straight path. That makes a 1D line segment.
2. Take that line segment and move it at right angles to its length. Move it a total distance equal to its length. The resulting area it traces out is a 2D square.
3. Take the 2D square and move it at right angles to its face. Move it a total distance equal to the length of one of its sides. The resulting volume it traces out is a 3D cube.
4. Take the 3D cube and move it at right angles to all of its faces. Move it a total distance equal to the length of one of its sides. The resulting hypervolume it traces out is a tesseract.
The hard part is step 4. You have to work out how to move the cube in a direction that is simultaneously at right angles to all three previous directions we used to carry out steps 1 to 3.
Clearly, your attempt at constructing a tesseract in your video is wrong, because you only moved things in the 3 dimensions you had already moved things in to construct your three-dimensional cube. The result in your video, as Dave pointed out, is not a tesseract, but simply two three-dimensional cubes embedded inside one another.
One thing to say: you might have seen pictures on the internet that look at bit like what you constructed, in relation to discussions of tesseracts. Those pictures represent a sort of "shadow" cast into 3 dimensions by a tesseract. It works like this:
2. You can create a 2D shadow of a 3D cube by shining a light onto it and projecting the shadow onto a 2D plane.
1. You can create a 1D shadow of a 2D square by shining a light onto it and projecting the shadow onto a 1D line.
0. You can create a 0D shadow of a line by shining a light onto the line and projecting the shadow onto a 0D point.
Similarly:
3. You can create a 3D shadow of a 4D tesseract by shining a 4D light onto it and projecting the shadow into a 3D space.
With one particular angle (in 4D) of the (4D) light source, the resulting 3D shadow looks a bit like what you're calling a "tesseract" in your video.
Here's how you construct a tesseract, by analogy:
0. Start with a point. That has no dimensions.
1. Move the point in a straight path. That makes a 1D line segment.
2. Take that line segment and move it at right angles to its length. Move it a total distance equal to its length. The resulting area it traces out is a 2D square.
3. Take the 2D square and move it at right angles to its face. Move it a total distance equal to the length of one of its sides. The resulting volume it traces out is a 3D cube.
4. Take the 3D cube and move it at right angles to all of its faces. Move it a total distance equal to the length of one of its sides. The resulting hypervolume it traces out is a tesseract.
The hard part is step 4. You have to work out how to move the cube in a direction that is simultaneously at right angles to all three previous directions we used to carry out steps 1 to 3.
Clearly, your attempt at constructing a tesseract in your video is wrong, because you only moved things in the 3 dimensions you had already moved things in to construct your three-dimensional cube. The result in your video, as Dave pointed out, is not a tesseract, but simply two three-dimensional cubes embedded inside one another.
One thing to say: you might have seen pictures on the internet that look at bit like what you constructed, in relation to discussions of tesseracts. Those pictures represent a sort of "shadow" cast into 3 dimensions by a tesseract. It works like this:
2. You can create a 2D shadow of a 3D cube by shining a light onto it and projecting the shadow onto a 2D plane.
1. You can create a 1D shadow of a 2D square by shining a light onto it and projecting the shadow onto a 1D line.
0. You can create a 0D shadow of a line by shining a light onto the line and projecting the shadow onto a 0D point.
Similarly:
3. You can create a 3D shadow of a 4D tesseract by shining a 4D light onto it and projecting the shadow into a 3D space.
With one particular angle (in 4D) of the (4D) light source, the resulting 3D shadow looks a bit like what you're calling a "tesseract" in your video.
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Highlighted
You can't do it . Not in the Real Physical Reality .
How ? What form is this 2D square in , that has no actual physical existence , yet is effected by light , thus creates a " shadow " . On 1D line , which its self does not exist . In Real Physical terms .
What form of light then are you referring to ?
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DaveC426913
Valued Senior Member
So what? What does it matter if something doesn't have 3 dimensions? Our knowledge has gone beyond mere physical manifestations.
If someone holds up a tile to the sun, I can examine its shadow. That shadow has only 2 dimensions - it has no thickness.
I don't ever have to clap eyes on - or even know anything about - what is blocking the sun. All I see is the shadow.
Yet I can quite trivially measure the length of its sides, I can calculate its area, I can calculate how many watts are being blocked by the tile, etc. There is no end of useful things I can do with an object that only has 2 dimensions.
Three D objects , cast a shadow on themselves .
Shadows are absence of light and have a thickness, from the object blocking the light to the object where the absence of light is noted
And to locate any point in spacetime, obviously we also need the dimension of time.
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Spacetime is actually invariant river.
https://www.google.com/search?q=doe...&aqs=chrome..69i57j0l2.10318j0j7&sourceid=chr
Nothing moves in spacetime. In Relativity, all of the events in space and time are fixed and unchanging but our perspective changes location through spacetime along our own personal worldline at the speed of light, c. Things can move through space as time progresses but, in Relativity, spacetime itself is unchanging
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
In essence then, intervals of space and time considered separately are not the same for different observers, but the spacetime interval is invariant.
DaveC426913
Valued Senior Member
From my observing vantage point, I see no object - I know nothing about it. That does not stop me from measuring the 2-dimensional shadow.
And yet I just gave you an example of something that is 2 dimensional - about which I'm able to take quite a few very real physical measurements of it.
And yet I just gave you an example of something that is 2 dimensional - about which I'm able to take quite a few very real physical measurements of it.
No one mentioned density river. That's just you as usual, lacking any intestinal fortitude to admit you are wrong and instead choosing to troll.
I Now have . Density
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But you troll as I have shown.
In essence, intervals of space and time considered separately are not the same for different observers, while the spacetime interval is invariant.
Nothing to do with any 3 dimensional object.
Again to avoid admitting you know not what you are talking about, you shift the goal posts.
Space is real, without any substance, as is time. As has been explained to you many many times.
Write4U
Valued Senior Member
Question:Shadows are absence of light and have a thickness, from the object blocking the light to the object where the absence of light is noted
If a shadow is a volume of space. Do shadows have mass?.....