Perfect Shapes in Higher Dimensions - Numberphile
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Date: 2022-04-08
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Comments and reviews: 9
Afro
Its a shame we will ruin our planet. life prior to learning the most we can about dimensions.
Got tired of slow bikes; developed trains. Got tired of slow trains; developed cars.
Got tired of slow cars; developed planes.
Got tired of slow planes; developed 3-g force pulling rockets that cut a mere hour off of plane travel. While our organs are under evolved getting sloshed.
All while wage slavery, inflation, hunger overpopulation, psychology, comunication, and honesty. are in the background. Maybe next time we'll get to appreciate and acknowledge that all math, science, art; life are inter-connected.
Ramblings of a 20 year old.
If you read this. awesome. but just take this; in the following years, i send positivity and strength to you and your families. Lets see how we learn from the coming food crisis in 2040-2050.
reply
Its a shame we will ruin our planet. life prior to learning the most we can about dimensions.
Got tired of slow bikes; developed trains. Got tired of slow trains; developed cars.
Got tired of slow cars; developed planes.
Got tired of slow planes; developed 3-g force pulling rockets that cut a mere hour off of plane travel. While our organs are under evolved getting sloshed.
All while wage slavery, inflation, hunger overpopulation, psychology, comunication, and honesty. are in the background. Maybe next time we'll get to appreciate and acknowledge that all math, science, art; life are inter-connected.
Ramblings of a 20 year old.
If you read this. awesome. but just take this; in the following years, i send positivity and strength to you and your families. Lets see how we learn from the coming food crisis in 2040-2050.
reply
loquacity
Thank you very much, Numberphile and Carlo Sequin. I have always struggled with this level of mathematics beyond -you can't imagine a 4D shape- so I was astonished to find myself grasping the concepts (with some rewinding. Sequin's style is intuitive and captivating and I can't believe that I now have not only a page of notes, as if I were at school again, but an appreciation of the beauty and mystery of these forms. You've made my day!
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Thank you very much, Numberphile and Carlo Sequin. I have always struggled with this level of mathematics beyond -you can't imagine a 4D shape- so I was astonished to find myself grasping the concepts (with some rewinding. Sequin's style is intuitive and captivating and I can't believe that I now have not only a page of notes, as if I were at school again, but an appreciation of the beauty and mystery of these forms. You've made my day!
reply
Jonathan
in 4D, what are the dual pairs? The simplex is it's own dual, the hypercube pairs with the cross-polytope. which leaves 3, two of which should be duals of each other and that leaves one behind which has to be its own dual. Looking at them, probably the 24-cell is its own dual. which makes the 600-mess the dual of the 120-mess (analogue to the dodeca- and icosa- in 3D)
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in 4D, what are the dual pairs? The simplex is it's own dual, the hypercube pairs with the cross-polytope. which leaves 3, two of which should be duals of each other and that leaves one behind which has to be its own dual. Looking at them, probably the 24-cell is its own dual. which makes the 600-mess the dual of the 120-mess (analogue to the dodeca- and icosa- in 3D)
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Gregg
Understanding this is like long distance running. I never could imagine running ten miles at once until I worked my up to it. I still haven't been able to run a complete marathon or run a mile in 5 minutes, yet there are people who can run 26 miles and average 5 minutes a mile. That's what I feel like trying to keep up with this guy. It can be done.
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Understanding this is like long distance running. I never could imagine running ten miles at once until I worked my up to it. I still haven't been able to run a complete marathon or run a mile in 5 minutes, yet there are people who can run 26 miles and average 5 minutes a mile. That's what I feel like trying to keep up with this guy. It can be done.
reply
Prince
in 3 dimensional polytopes, you used 3 regular polygons, is that true to the 4th dimension as well? using 3d polytopes and squishing them together looks like a bit two-dimensional to me. maybe you use three 3d polytopes and squish it to form the true 4d polytope? and four 4d polytopes to form the true 5d polytopes?
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in 3 dimensional polytopes, you used 3 regular polygons, is that true to the 4th dimension as well? using 3d polytopes and squishing them together looks like a bit two-dimensional to me. maybe you use three 3d polytopes and squish it to form the true 4d polytope? and four 4d polytopes to form the true 5d polytopes?
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Drew
It was so satisfying that I was able to understand some semblance of 4D space when he was describing why the -smaller cube- isn't inside the -bigger cube-, because in 4D all of the edges and faces would be exactly the same, but the perspective and warping of them as a projection would make it look like this
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It was so satisfying that I was able to understand some semblance of 4D space when he was describing why the -smaller cube- isn't inside the -bigger cube-, because in 4D all of the edges and faces would be exactly the same, but the perspective and warping of them as a projection would make it look like this
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Chris
This man made it possible for me to be able to -see- the fourth dimension for the first time. holy moly, I thought it impossible yet here I am, trying to see the fifth one.
I wonder if there could ever be a way to represent it digitally one day, somehow, in VR or something
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This man made it possible for me to be able to -see- the fourth dimension for the first time. holy moly, I thought it impossible yet here I am, trying to see the fifth one.
I wonder if there could ever be a way to represent it digitally one day, somehow, in VR or something
reply
Fuhlvee
Really just writing this so I can remember, but if anyone else is struggling to understand that the 3d cubes overlap in 3d space and pop out into 4d space, think about watching someone fold a cube from only the top; the squares overlap in 2d space and pop out into 3d space.
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Really just writing this so I can remember, but if anyone else is struggling to understand that the 3d cubes overlap in 3d space and pop out into 4d space, think about watching someone fold a cube from only the top; the squares overlap in 2d space and pop out into 3d space.
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Clark
2D Polygon Shape
3D Prisms
4D Regular Polytopes via Platonic Solids:
Simplex to Infinity via added Vertex (vertices);
Hypercube, Cross Polytope, 600 Cell
24 Cell
120 Cell
5D Simplex
6D Simplex, Hypercube;
Rhombic Triacontahedron
reply
2D Polygon Shape
3D Prisms
4D Regular Polytopes via Platonic Solids:
Simplex to Infinity via added Vertex (vertices);
Hypercube, Cross Polytope, 600 Cell
24 Cell
120 Cell
5D Simplex
6D Simplex, Hypercube;
Rhombic Triacontahedron
reply
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