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ugalpha
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How could i mathematically proove that I am living on a circle. Almost got it last night , just need an insight to figure out an equation.
Ty.
Ty.
ugalpha said:How could i mathematically proove that I am living on a circle...
shifty88 said:surely a ring has more than on dimension, two at the least
A 1D universe would just be a line if a 1D being did try to determine the shape of its universe by marking a position and seeing if he came back upon himself suggests that the universe is 2D or greater. A 1D universe would not have a shape to it. Or am I mistaken? show me a shape that has 1 dimension
As for the Op, I have no idea how a 1D being would be able to prove he is on a 1D universe using mathematics
EDIT - It has come to my attention that even a line is a 2D object. I cannot see or imagine how a 1D universe would work, it would have no shape in any sense of the word, making your question impractical.
You can have a one-dimensional line that is effectively looping back on itself by just identifying two endpoints of the line segment and thus giving it non-trivial topology. This does not require another dimension.
shifty88 said:Does anyone have any links that can support this sentence?
I do not see how a 1 dimensional universe can loop back on itself without the presence of an extra dimension
I imagine a 1D universe to consist of just length, without width or depth, without these dimensions their would be no discernible shape to it.
Have I misunderstood something here?
yenchin said:See Fig 1. of this article.
shifty88 said:But how does this apply to the Op's question and a 1 dimensional existence.
How can there be topology in the 1D
yenchin said:Yes, you are missing out topology and a whole field of mathematics known as differential geometry. Modern differential geometry basically started with Riemann's realization in the 19th century that we can talk about geometry *intrinsic* to a surface without embedding it in a higher dimensional space. Perhaps this will help.
yenchin said:See Fig 1. of this article.
yenchin said:See Fig 1. of this article.
shifty88 said:I imagine a 1D universe to consist of just length, without width or depth, without these dimensions their would be no discernible shape to it.
Have I misunderstood something here?
alt said:How can a straight (one dimensional) line loop around anything ? Doesn't make sense to me. Or has 'straight' been redefined to mean 'slightly curved' ?
alt said:How can a straight (one dimensional) line loop around anything ? Doesn't make sense to me. Or has 'straight' been redefined to mean 'slightly curved' ?
alt said:How can a straight (one dimensional) line loop around anything ? Doesn't make sense to me. Or has 'straight' been redefined to mean 'slightly curved' ?
daveb said:I think the problem is that there are two distinct ideas of dimension that are being used here. One is mathematical, and the other is visual. People probably tend to think in terms of cartesian coordinates, so anything they think of is visually embedded in the 3-d certsian system, and a circle "visually" to us is in 2 dimensions (say, x and y). However, in mathematics,, and specifically differential geometry, as has been pointed out, it is unnecessary to embed any curve in a higher dimensional space, so that a "line" in some arbitrary space is defined by the curvature of that space.
shifty88 said:I was of the opinion that we were talking of visual dimensions, but that's been cleared up for e since, i was unaware of topology and all that jazz, but now i am I have plenty of studying to do in my spare time now. Thanks to this thread. If anyone can provide more reading material on this subject i would really appreciate it.
phinds said:Why are you imposing "straight" on the concept of one-dimensional? The OP correctly did not.
Fuzzy Logic said:Don't even think of a shape at all.
Takes the numbers 1 to 10. That is a straight, 1 dimensional line.
Now when you count to 10, what's next after 10? Stop or loop back to 1?
I'm not sure what a 'not straight' 1d line would be like...
Just a guess, but I would suppose it would be a non-linear line. As in not all points are evenly distributed. Count from 1 to 10 but skip 3,4 and 7.
alt said:I can't see how a line, once curved, doesn't trace a two dimensional path.
Nor how a sheet of paper, when curved or folded or spindled, doesn't enter a 3D space.
DaveC426913 said:They are curved in a higher space but the space itself is still only as dimensional as the number of coordinates it takes to define a unique point.
I can't say it more clearly than that. Regardless of how you bend fold or spindle a sheet of paper, you still only need two coordinates to uniquely define a point in it. You do not need a third coordinate.
DaveC426913 said:A 1 dimensional line can curve in higher dimensions, just like a 2 dimensional sheet of paper can be curved in a 3rd dimension.
A sheet of paper, curved, folded or spindled still has a 2 dimensional surface.
Why?
To uniquely describe any point on the sheet of paper requires two and only two coordinates: x and y.
Same with a line. When curved, it is still one dimensional. To uniquely describe any point on the line requires one and only one coordinate.
e^(i Pi)+1=0 said:I think the issue was that, earlier in the thread, there were claims that a line could loop back on itself without curving in a higher dimension.
e^(i Pi)+1=0 said:I think the issue was that, earlier in the thread, there were claims that a line could loop back on itself without curving in a higher dimension.
I just want to ask - this is true only for cylindrical geometry, not for sphere, right?yenchin said:Similarly in a two dimensional infinite cylindrical universe, the inhabitants measure each triangle to sum up to 180 degrees, intrinsically the universe has *flat* geometry.
phinds said:Why are you imposing "straight" on the concept of one-dimensional? The OP correctly did not.
rustynail said:I'm sorry for taking this argument 2 days back, but I think I can see the problem OP is having concerning curved 1-dimensional lines. Being curved implies being oriented in a different direction, and thus, along a different axis. So to give a description of a point along a line in an ℝ^n space would require n different coordinates. But, correct me if I'm wrong, even though the line is described in an ℝ*^n space, the line itself has only one dimension, it's length.
I thought that's what I said in post 24:rustynail said:I'm sorry for taking this argument 2 days back, but I think I can see the problem OP is having concerning curved 1-dimensional lines. Being curved implies being oriented in a different direction, and thus, along a different axis. So to give a description of a point along a line in an ℝ^n space would require n different coordinates. But, correct me if I'm wrong, even though the line is described in an ℝ*^n space, the line itself has only one dimension, it's length.
DaveC426913 said:I thought that's what I said in post 24:
https://www.physicsforums.com/showpost.php?p=3731892&postcount=24
and post 26:
https://www.physicsforums.com/showpost.php?p=3733530&postcount=26
A 1 dimensional being is a hypothetical creature that exists in a world with only one spatial dimension. This means that it can only move in one direction, either forward or backward.
A 1 dimensional Universe is a theoretical universe that only has one spatial dimension. This means that it has no width or depth, and all objects in this universe would only exist as a line or a point.
In a 1 dimensional Universe, a circle would appear as a single point. This is because a circle is a 2 dimensional shape, and in a 1 dimensional world, it would only have one dimension to exist in.
A 1 dimensional being would only be able to perceive objects that exist in its one-dimensional world. It would not be able to see or understand objects that have width or depth, as these dimensions do not exist in its universe.
It is currently not possible for a 1 dimensional being to exist in our universe. Our universe has three spatial dimensions (length, width, and depth), and it is impossible for a being to exist with only one of these dimensions. However, in a theoretical 1 dimensional universe, it is possible for a 1 dimensional being to exist.