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Thread: The Fourth Dimension

  1. #1 The Fourth Dimension 
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    Hi I'm new and quite young at 13 years old. I'm very interested in astronomy, physics, and the dimensions and I have so many questions.

    What is the fourth dimension? I've Googled this question before, searching for new information on the topic but nothing I've come across seems to answer my question. I've seen an article that said the fourth dimension has something to do with time. But how? If this is wrong please correct it. I have also seen things like you can walk through things if you live in the 4D and doctors can perform surgeries without cutting the skin, but it said that can only happen if you are dead or dreaming. But then how do we know what it is if we can only be dead or half dead? Did someone just make it up? I have also heard that our minds are not able to comprehend what 4D looks like but if we don't know what it looks like and no one has experienced it, why are some people certain it exists? This topic is mind blowing so forgive me if I'm annoying you with my "whys" and "hows" haha. Well if anyone has a theory on one or more of my questions PLEASE comment. No one knows exactly what the correct answer is so I absolutely do not expect a right answer just what your theory on the subject is. Sorry for rambling on and thank you in advance!


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    Moderator Moderator Markus Hanke's Avatar
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    What is the fourth dimension?
    Ok, I will attempt to give an explanation that is appropriate for a 13-year old.
    Firstly, you must understand what is meant by the term "dimension" in physics and maths - basically it refers to how many pieces of information ( coordinates ) you must give at a minimum in order to uniquely specify a point within that space. Example - imagine a flat piece of paper. What information do you need to refer to any point on that paper ? If you start at the bottom left corner, you must say how far to go across, but also how far to go up to arrive at your point. For example, you could have a point (2,3), which sits 2cm across and 3cm up as measured from the corner of the page. This tells us that you need 2 pieces of information to find the point, i.e. 2 independent coordinates. It is the number of these coordinates that determine the dimension of the space you are looking at - in our example, you need two coordinates, so the flat piece of paper is a 2-dimensional space ( = surface ).

    Next example - imagine a cardboard box. How many coordinates do you need to specify any point within that box ? Again, you start at a corner - what independent directions can you go ? It has length, it has height, and it has depth also; for example, you can go 2cm across, 3cm up and 5cm into the box to get the point (2,3,5). We now have three independent coordinates to find a point, therefore the cardboard box is a 3-dimensional object.

    Now it becomes a bit more tricky. Imagine you want to set up a meeting with your buddy. What pieces of information do you need to give each other in order to make sure the meeting happens ? Firstly, you need to agree on where to meet - as we have seen above, you need three coordinates to identify a point in space ( e.g. corner of 52nd and 21st streets, on the 3rd floor of the building ). However, you also need to agree on when to meet - after all, the meeting could be this afternoon, or next week, or next month, or in ten years time ! So, in order to exactly fix the meeting, you need to agree on place and time, that means on 3 space coordinates and 1 time coordinate. That means that in our universe we talk about events, and to specify an event we need a minimum of 4 coordinates ( 3 space + 1 time ), so our universe is 4-dimensional. The fourth dimension is time.

    To summarize :

    0D : A single point ( no coordinates needed at all ! )
    1D : A line
    2D : A surface ( like our piece of paper )
    3D : A space ( like our cardboard box )
    4D : A space-time ( like our universe )

    The problem with our brains is that we only ever experience one moment of time ( the present ), so 4-dimensional objects are outside our realm of experience. Everything you look at on a daily basis has only three dimensions; the presence of time is felt only through the fact that things are not static, but they change. We cannot, however, 'see' all four dimensions at once, because time is always condensed down to just a single moment for us.

    I have also seen things like you can walk through things if you live in the 4D and doctors can perform surgeries without cutting the skin,
    When a flat cartoon character who lives on a surface ( like a piece of paper ) encounters, say, a circle, then this will present an unsurmountable obstacle to him, he cannot get 'into' or 'through' the circle. He has to go around it, because he can only move in 2 dimensions. However, if the cartoon characters steps "out" of the flat paper surface into the 3rd spatial dimension, then he can simply step into or over the circle.
    The same thing would be true for 3 and 4 spatial dimensions, even though we can no longer visualise it.

    I have also heard that our minds are not able to comprehend what 4D looks like but if we don't know what it looks like and no one has experienced it, why are some people certain it exists?
    In the case of our universe it's simple logic - see above. You couldn't set up your meeting with just 3 dimensions, because you wouldn't know when to meet, so the existence of the 4th dimension - time - is quite obvious, even if you can't directly perceive it.
    More generally, we can describe objects and spaces in any number of dimensions using mathematics, regardless of whether we are able to visualise them or not. This isn't something you are going to learn in High School though, it's college/university level, and it's called differential geometry. Don't worry about it for now, just suffice it to say that the mathematical tools for this do indeed exist.
    To round things up, consider this :

    0D : Point
    1D : Line
    2D : Rectangle
    3D : Cube
    4D : Tesseract
    nD : Hypercube in n dimensions


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    Moderator Moderator Markus Hanke's Avatar
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    Let me know if you have any further questions emygirl691; always happy to help
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    0D : Point
    1D : Line
    2D : Rectangle
    3D : Cube
    4D : Tesseract
    nD : Hypercube in n dimensions



    Markus,
    A line is only part of a circle, would you not have to get on a higher dimension to see the totality of the line? What part of the circle is a line if a line is supposed to be strait. How can we know how many dimensions there are when all is connected? A moving point is supposed to be a part of a line is that not so?
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    Quote Originally Posted by Markus Hanke View Post
    Let me know if you have any further questions emygirl691; always happy to help
    Thank you very much!
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    Quote Originally Posted by Mother/father View Post
    Markus,
    A line is only part of a circle, would you not have to get on a higher dimension to see the totality of the line? What part of the circle is a line if a line is supposed to be strait. How can we know how many dimensions there are when all is connected? A moving point is supposed to be a part of a line is that not so?
    A circle is a 2-dimensional object, because you need two coordinates to uniquely identify a point on it.
    A line is only 1-dimensional - you need just one coordinate.
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    Quote Originally Posted by Markus Hanke View Post
    A circle is a 2-dimensional object, because you need two coordinates to uniquely identify a point on it.
    A line is only 1-dimensional - you need just one coordinate.
    Doesn't that depend how you define a circle? If you are just talking about the edge/outline of a circle then, surely, it is 1 dimensional. You only need one number (e.g. an angle) to specify a position on that line.

    If you mean the area inside a circle, then that is 2D as you need two coordinates (e.g. distance from the center and angle).

    Quote Originally Posted by Mother/father View Post
    What part of the circle is a line if a line is supposed to be strait.
    A line doesn't have to be straight.
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    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by Strange View Post
    Doesn't that depend how you define a circle? If you are just talking about the edge/outline of a circle then, surely, it is 1 dimensional. You only need one number (e.g. an angle) to specify a position on that line.

    If you mean the area inside a circle, then that is 2D as you need two coordinates (e.g. distance from the center and angle).
    Yes, that's correct. To me a "circle" means the whole thing, area and all, not just the perimeter. The boundary alone is of course only 1-dimensional.
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    Quote Originally Posted by Markus Hanke View Post
    To me a "circle" means the whole thing, area and all, not just the perimeter.
    Aha! So you are not a "real" mathematician then! (Neither am I, obviously.)
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Strange View Post
    Doesn't that depend how you define a circle? If you are just talking about the edge/outline of a circle then, surely, it is 1 dimensional. You only need one number (e.g. an angle) to specify a position on that line.

    If you mean the area inside a circle, then that is 2D as you need two coordinates (e.g. distance from the center and angle).
    Yes, that's correct. To me a "circle" means the whole thing, area and all, not just the perimeter. The boundary alone is of course only 1-dimensional.
    That is not how a circle is defined in mathematics. A circle is a curve, not an area. See details at
    Circle -- from Wolfram MathWorld
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    Quote Originally Posted by pmb View Post
    That is not how a circle is defined in mathematics. A circle is a curve, not an area. See details at
    Circle -- from Wolfram MathWorld
    But isn't it a case that you still need two independent parameters to uniquely identify a point on the circle, i.e. for example angle and radius ?
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    Quote Originally Posted by Markus Hanke View Post
    But isn't it a case that you still need two independent parameters to uniquely identify a point on the circle, i.e. for example angle and radius ?
    You only need one (angle) to identify a point on a circle. If you change the radius, then you have a different circle.
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    Quote Originally Posted by Strange View Post
    You only need one (angle) to identify a point on a circle. If you change the radius, then you have a different circle.
    That's true, if you consider a circle with a given radius.
    In this way you can consider any closed curve to be 1-dimensional.
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  15. #14  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Strange View Post
    You only need one (angle) to identify a point on a circle. If you change the radius, then you have a different circle.
    That's true, if you consider a circle with a given radius.
    In this way you can consider any closed curve to be 1-dimensional.
    Which, I think, is the point ... Any given line/curve is 1 dimensional, as any surface is 2D, etc.
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    Quote Originally Posted by Strange View Post
    Which, I think, is the point ... Any given line/curve is 1 dimensional, as any surface is 2D, etc.
    Ok, that's what I meant when I was referring to the boundary earlier.

    So then I am looking for the correct English word for boundary + area - is it a disk ?
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  17. #16  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    So then I am looking for the correct English word for boundary + area - is it a disk ?
    I guess that would work, in normal discussion. I'm not a mathematician (either ) but I guess one would just refer to "the area enclosed by a curve".
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