Braids in Higher Dimensions - Numberphile
video description
Like Brady said, this phenomenon happens when these strands of hair lack depth in the fourth dimension. As we know, hair has thickness and can bend. If hair were one dimensional those facts could not be true. They could only have length and their shape could only vary in one length (density, making it longer and shorter, or whatever you can imagine happening to it in one dimension.
If hair were two dimensional, like she suggests it would become, it could only have thickness in one direction - an area - and it couldn't have a cylindrical shape, nor would it be able to curl, only curve.
Obviously, four dimensional strands of hair would not be able to untangle like this while moving through the fourth dimension, for this we would need it to move through a dimension higher still (fifth would be at hand. I would assume the fourth dimension to contain another level of it's thickness, equal to the diameter from the previous two expansions in the second and third dimension.
Date: 2022-04-08
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Comments and reviews: 9
Mephistahpheles
Two linked klein bottles. Unlinkable, or no? (I think not. be kinda like linked donuts, but I'm not entirely sure)
Didn't say anything about not moving the boards themselves. (If you allow this, than a traditional '3 strand braid- can be completely undone without removing the elastic simply by feeding the end back, still connected, through the braid) So, the so-called -entangled braid- isn't.
And, can you rotate the boards, or not? If I just twist 3 strands together, they'd simply unravel, but if the boards are immobile, a simple twist would be -entangled. -
Gotta make the parameters of the question clear!
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Two linked klein bottles. Unlinkable, or no? (I think not. be kinda like linked donuts, but I'm not entirely sure)
Didn't say anything about not moving the boards themselves. (If you allow this, than a traditional '3 strand braid- can be completely undone without removing the elastic simply by feeding the end back, still connected, through the braid) So, the so-called -entangled braid- isn't.
And, can you rotate the boards, or not? If I just twist 3 strands together, they'd simply unravel, but if the boards are immobile, a simple twist would be -entangled. -
Gotta make the parameters of the question clear!
reply
Tritonio
You could think of the position in the fourth dimension as the color of the strand. All you have to do to pass one yellow strand through a other yellow strand if they are tangled, is to paint a little piece of the first one red. Then you can pass the second one through the red part of the first strand since they are in different positions I the fourth dimension and don't touch each other.
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You could think of the position in the fourth dimension as the color of the strand. All you have to do to pass one yellow strand through a other yellow strand if they are tangled, is to paint a little piece of the first one red. Then you can pass the second one through the red part of the first strand since they are in different positions I the fourth dimension and don't touch each other.
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Anthony
I think I might solved it, check it out. Before we start we see that the blue string is already tangled. First you take the 2nd string (from the left to the right ) and you pull it above the uper plank. Now the 2nd and third strings are untangled. What is left is the 1st and the last. What you have to do is just to pull the first above the uper plank and it is done
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I think I might solved it, check it out. Before we start we see that the blue string is already tangled. First you take the 2nd string (from the left to the right ) and you pull it above the uper plank. Now the 2nd and third strings are untangled. What is left is the 1st and the last. What you have to do is just to pull the first above the uper plank and it is done
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Zach
I think its easier to imagine by creating two rooms, and the second room is a jump of one integer unit in the 4th dimension. When you move (or teleport if you want to say) into the second room, you can easily move to the other side of the second room (since the strand is not there) and then move back over into the first room, bypassing the strand entirely.
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I think its easier to imagine by creating two rooms, and the second room is a jump of one integer unit in the 4th dimension. When you move (or teleport if you want to say) into the second room, you can easily move to the other side of the second room (since the strand is not there) and then move back over into the first room, bypassing the strand entirely.
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Christiaan
I have a -3 D labyrinth- question: in a 2 D labyrinth you can always find the way out by holding e. g. your right hand on the wall and continue walking without ever removing it. The path may be very long and all way round, but eventually you will get out. Now is there a 3 D equivalent for this? I tried to imagine it, but did not see anything useful.
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I have a -3 D labyrinth- question: in a 2 D labyrinth you can always find the way out by holding e. g. your right hand on the wall and continue walking without ever removing it. The path may be very long and all way round, but eventually you will get out. Now is there a 3 D equivalent for this? I tried to imagine it, but did not see anything useful.
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NOMASAN
I want to make a movie about a 'Dim traveller'. a citizen of a town in the fourth dimension, who somehow ends up stuck in our dimension, not able to go back to his exact dimension-location.
So he teams up with a few human scientists around him. A tesseract and Storage ring. I'd like to say more abut it. But I'm outta time
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I want to make a movie about a 'Dim traveller'. a citizen of a town in the fourth dimension, who somehow ends up stuck in our dimension, not able to go back to his exact dimension-location.
So he teams up with a few human scientists around him. A tesseract and Storage ring. I'd like to say more abut it. But I'm outta time
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education
When you visualise the 4th dimension as stacked up timeframes and the braid as a 1d -fly-, it's also easier to see how the 3d braid can be untangled in the 4th dimension: the fly just needs to wait for a short time for the other fly to move, and then it can go right through where, from its perspective, the obstacle was.
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When you visualise the 4th dimension as stacked up timeframes and the braid as a 1d -fly-, it's also easier to see how the 3d braid can be untangled in the 4th dimension: the fly just needs to wait for a short time for the other fly to move, and then it can go right through where, from its perspective, the obstacle was.
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sam111880
nice explaination also you probably considered the question of links can be closely related by closing up the top board with the bottom board one has a way to classify n-dimensional links to n-dimension braid theory so if you have an invariant for one you can uses it for the other.
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nice explaination also you probably considered the question of links can be closely related by closing up the top board with the bottom board one has a way to classify n-dimensional links to n-dimension braid theory so if you have an invariant for one you can uses it for the other.
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Anna
i went to a lecture at cambridge uni for a level women in maths that was basically this exact video, but somehow numberphile explained it better than the cambridge lecturer (no shade to that lecturer tho, it was fascinating even though i couldnt follow along completely)
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i went to a lecture at cambridge uni for a level women in maths that was basically this exact video, but somehow numberphile explained it better than the cambridge lecturer (no shade to that lecturer tho, it was fascinating even though i couldnt follow along completely)
reply
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