Understanding the 4th dimension and higher..
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TMac3000
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It's useful, if a bit circular, to think of each dimension as multiple instances of the dimension before it.
For example, we start with a point:
.
The first dimension is a line, which is an orderly series of points:
............
The second dimension is a square or quadrilateral, which is multiple lines stacked up:
............
............
............
............
............
The third dimension can be represented by a cube, which is multiple squares stacked up. The fourth dimension is often said to be time, which obviously can't be visualized here, but think of every second in our lives as a separate reality. Things around us change constantly. A leaf blowing the wind will have different positions each second. So, if we "stack up" every three-dimensional state the world has been in since the beginning of time, we get sort of a fuzzy picture of what the fourth dimension is
For example, we start with a point:
.
The first dimension is a line, which is an orderly series of points:
............
The second dimension is a square or quadrilateral, which is multiple lines stacked up:
............
............
............
............
............
The third dimension can be represented by a cube, which is multiple squares stacked up. The fourth dimension is often said to be time, which obviously can't be visualized here, but think of every second in our lives as a separate reality. Things around us change constantly. A leaf blowing the wind will have different positions each second. So, if we "stack up" every three-dimensional state the world has been in since the beginning of time, we get sort of a fuzzy picture of what the fourth dimension is
Jarvitä
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I honestly can't tell whether you're being serious or just trying to annoy anyone with but a smidgeon of actual education in the general area of physics.
RisingFury
OBSP developer
No. Completely and utterly wrong.
Look into the concept of linear independence.
In short, a vector in a vector space can be described as linear combination of the space's base vectors. If you wish to add another dimension, you'll need to add another base vector, which is linearly independent of all other base vectors - you cannot describe the new base vector with the existing ones.
Example:
Let's say you have base vectors [1, 0, 0] and [0, 1, 0]. You can describe any vector in that plane as a combination a * [1, 0, 0] + b * [0, 1, 0], where a and b are scalars.
Now you add another dimension with a base vector [0, 0, 1]. You cannot chose any real a and b, so that a * [1, 0, 0] + b * [0, 1, 0] = [0, 0, 1]
--------------------------
Edit:
Look, I get it people. You love thinking about the universe and in general, things you lack knowledge about. But the first idea you come up with is not necessarily the truth. There's also a high probability that what you're wondering about has already been answered, but let me make this clear: You will not find it on Wikipedia.
Wikipedia has become the dumping ground for wild and whacky theories about everything, without providing a proper context and mathematical explanation. You'll find everything from hypothetical particles to multiple universes, but you won't find a good Math and Physics course. If you really want to know more about the subject, look for university courses that ended up online.
Last edited:
Quick_Nick
Passed the Turing Test
The OP also seems too confident in these other dimensions. There is no certainty yet on how many dimensions there are and what order to put them in. Only theories. And at the least, you have to mention what theory you're using before "5th dimension" even makes sense! And current theories suggest that other dimensions are not orthogonal. (so can't be related so easily to x y z)
When you start talking about this stuff, analogies can become your enemies. There is no perfect analogy. For practical use, stick to just the math. That's very unfortunate for humans, ("no one actually understands quantum physics") but it is the case.
When you start talking about this stuff, analogies can become your enemies. There is no perfect analogy. For practical use, stick to just the math. That's very unfortunate for humans, ("no one actually understands quantum physics") but it is the case.
TMac3000
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Hold up a piece of string. That's one dimension. Take ten pieces of string and lay them parallel. Now you have two dimensions. Attach them to together to make a piece of fabric, make ten more of these pieces of fabric and stack them on top of one another. Now you have three dimensions. How long did it take you to do all that? That's the fourth dimension.
Cras
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strings....funny
Jarvitä
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Think of a vector in R^3 space with the third component of 0. Now think of a vector that's perpendicular to it and also has no real-valued third component. Now try, through their linear combination, to produce a vector with a non-zero, real third component. Your analogy only works for objects that are already three-dimensional, because you didn't bother to check where the definitions of your dimensions come from, or include them in your (flawed) analogy.
2/10, you got me to respond...again.
RisingFury
OBSP developer
The string is already three dimensional!!!
If you try the same with lines that have a radius of 0, you can stack an infinite amount of them next to each other and you'll still get no width!
TMac3000
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In a literal sense, yes. It was an analogy. The string is 3-dimensional, but the width and height of it are (depending on the type of string--I thinking maybe sewing thread in this case) usually negligible--less then 1 mm. That leaves just length, which is why I chose that analogy.
The lines pictured in a geometry textbook are three-dimensional if you count the thickness of the page, but we don't because we know that the author is trying to illustrate a mathematical concept.
Jarvitä
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Yes, but the mathematical concept isn't "dimension n+1 can be defined by stacking n-dimensional objects along it", because that's wrong, your analogy doesn't work, you obviously have a flawed perception of how space works and really should stop embarrassing yourself.
