A computer-generated rendering of a possible six-dimensional geometry similar to those studied by UW-Madison physicist Gary Shiu.Image: courtesy Andrew J. Hanson, Indiana University
14 comments:
Siji
said...
It's really interesting how we can comprehend higher dimensions by taking the cross sections of the lower dimension until it creates the higher dimension. For example if you stack up flat squares (two dimensional) it will make a three dimensional object. Also, I think why in a flat world where you can't see height, they would determine distance and shape by the brightness of the color because when an object is closer to you, the wave lengths that determine its color have to be closer together (making the color appear brighter). When the object is far away from you, its wave length will stretch out longer to reach you eye (making the color appear darker).
I thought this was very interesting because it tells us that there is more than what the eye can see. I thought is was cool when they showed us a line that turn into a square then a cube and finally a 4d hypercube. I thought it was funny when the sphere picked the square up and flew him through the air.
I think that it would be incredible if someone or something could visit a dimension other than its own. This experience would blow my "little spherical mind."
I agree with Owen. I wish I could visit other dimensions. I downloaded an ebook version of Flatland, and the idea of how the shapes perceive the world is extremely fascinating. It makes sense that the cross-sections are the shapes' view, and depth is simply a matter of how dark it is.
I think that this was very interesting. I understand why the color gets darker when you go farther away. But I still don't exactly understand why when you get closer the color gets brighter. I think that it is possible for 2D shapes to make a 3D shape. They could stack up on top of each other and make a 3D shape with height. But the problem is that they would not know this. I understood the video but I still don't get how a 4D shape would look like
This video was a good refresher. I knew some of this material but forgot others. Of course I learned some stuff from this video too. For example, I learned the Flatland book exists, there were many dimensions, and I learned how the fourth dimension looks like. Even though it is still a bit confusing. What's fascinating is how closer objects are brighter and because of that, they can see depth. Science facts are interesting and it's VERY cool how science works.
I think the video is very interesting. It was cool how 2D objects see 3D objects a shape growing bigger and then smaller. Also when the 3D spear took the square to see its world, the square was amazed. When the square asked the spear to see the form above that the spear said no and brought the square back to 2 dimensional world. The spear then got sad, because he was unable to go to dimensions above his.
This video was very interesting. I have been thinking about the next dimensions and a "higher" world, I guess you could say, for a long time. I have watched Flatland before and it was very interesting. As 3rd dimensional beings, it would be very hard to understand the 4th dimension. And I believe that the 4th dimension is time, so apparently 4th dimensional beings can also mingle with time. Anyways, as the video noted, if we saw a 4th dimensional object pass by our world, we could only see it as a 3rd dimensional object getting larger, then smaller again. I thought this part was especially interesting because it told us how we would kind of see a 4th dimensional being. I hope one day, the 4th dimension will be unlocked, so that we can move on to the 5th dimension. Which brings me to the fact that nobody can guess what is beyond the 10th dimension. If I am right, the 10th dimension is the infinite amount of infinite possibilities there are. But then what would the 11th dimension be? There must be a ∞th dimension somewhere out there, but that is so complicated that we can not even try to imagine it. Hopefully a breakthrough will occur, and we will all feel how it is to live in a "higher world."
Rohan, to answer your question, I believe that the reason why things in the 2nd dimension are brighter when they are closer is because there must be a way to tell depth in the 2nd dimension, because in the 2nd dimension, you only see things in lines, and there is no way to tell how far something is when it is only a line. Which also makes me think what points in Pointland would see. In Lineland (1st dimensional world), the lines would be moving on a horizontal line and they would see others as points. Put then what would points in Pointland (0th dimension) see? They would see others in a -1st dimension, but are there negative dimensions? If there is a -1st dimension, then they would see things in the -2nd dimension, and so on. This subject is really complicated, and it will never be solved, for there are many things that we can defy, but we can never defy infinity.
I learned a lot from this video. I never knew about flatland. I think it is really interesting how the flat shapes can only see lines and how darker and lighter mean that shape is far or close. I have always wondered what the fourth dimension is, and now I kind of understand the concept of drawing out every line. I also never knew that a line was a one dimensional shape. I think I knew that in the back of my mind, but never heard somebody say it. I also think that if we completely understand the fourth dimension, we can go on to discovering the other ones, and that could lead to something bigger. I also thought it was cool how a four dimensional shape coming and leaving would just look like something getting larger and then smaller. I really liked this video.
This article was so cool. I think that making the world a four dimensional place would be such a cool and fascinating experiment. Sometimes this world can only think of the world in the perspective they live in it. For example, try to say "How are you?" without using those words. It's the same thing. Imagine the thirteenth dimension. How complicated would that be. The idea of a hypercube can be so fascinating even though we don't actually know if it exists. A hypercube would be looking at the world in a blurry perspective. I really liked this video because I knew what it was talking about. Flatland is a movie, which Mr. Sewell showed us. The concept of something being closer and lighter and farther and darker is such a brilliant idea. If you lived in a 2 dimensional world without depth-perception how confusing would that be. Pretty confusing. I also do agree with Ayden As 3rd dimensional beings it would hard to think about the world in the fourth dimension. This was really confusing for Arthur Square (the protagonist in Flatland.) to experience the fourth dimension. I think it would be really cool to make a Flatland 2. I didn't really understand what happened at the end of the movie and I would like for the movie to continue.
I think it is so cool that one dimension stretched out and expanded again and again creates the next dimension. I think it is so crazy how when an object is closer to you the wave lengths that determine the brightness have to be closer together. When the object is far away the wave length will stretch longer to reach back to you eye.
This does blow my little spherical mind! I am very interested in the topic of dimensions and I would love to read Flatland. I think that the hypershapes are really cool. I understand how a 4D cube would look, but I don't really get what a 4D sphere would be like.
It's very interesting the way higher dimensions would look to us, as well as how we would look to somebody in a dimension lower than us. What I don't quite understand is that there were only four dimensions in the video. I know he mentioned an eleventh dimension, and I understand that you keep extending each line segment by an inch. However, I only thought the hypercube existed in the tenth dimension as shown in this video
https://www.youtube.com/watch?v=p4Gotl9vRGs
Also, yes there could be four dimensional beings popping in and out of our everyday lives, but we would have seen one by now. They would not be hard to recognize because they would shrink up and disappear in a matter of seconds. My final question is what would someone in the fourth dimension look like to someone in the second dimension. They only explained what a person would look like on the dimension lower not twice lower.
14 comments:
It's really interesting how we can comprehend higher dimensions by taking the cross sections of the lower dimension until it creates the higher dimension. For example if you stack up flat squares (two dimensional) it will make a three dimensional object. Also, I think why in a flat world where you can't see height, they would determine distance and shape by the brightness of the color because when an object is closer to you, the wave lengths that determine its color have to be closer together (making the color appear brighter). When the object is far away from you, its wave length will stretch out longer to reach you eye (making the color appear darker).
I thought this was very interesting because it tells us that there is more than what the eye can see. I thought is was cool when they showed us a line that turn into a square then a cube and finally a 4d hypercube. I thought it was funny when the sphere picked the square up and flew him through the air.
I think that it would be incredible if someone or something could visit a dimension other than its own. This experience would blow my "little spherical mind."
I agree with Owen. I wish I could visit other dimensions. I downloaded an ebook version of Flatland, and the idea of how the shapes perceive the world is extremely fascinating. It makes sense that the cross-sections are the shapes' view, and depth is simply a matter of how dark it is.
I think that this was very interesting. I understand why the color gets darker when you go farther away. But I still don't exactly understand why when you get closer the color gets brighter. I think that it is possible for 2D shapes to make a 3D shape. They could stack up on top of each other and make a 3D shape with height. But the problem is that they would not know this. I understood the video but I still don't get how a 4D shape would look like
This video was a good refresher. I knew some of this material but forgot others. Of course I learned some stuff from this video too. For example, I learned the Flatland book exists, there were many dimensions, and I learned how the fourth dimension looks like. Even though it is still a bit confusing. What's fascinating is how closer objects are brighter and because of that, they can see depth. Science facts are interesting and it's VERY cool how science works.
I think the video is very interesting. It was cool how 2D objects see 3D objects a shape growing bigger and then smaller. Also when the 3D spear took the square to see its world, the square was amazed. When the square asked the spear to see the form above that the spear said no and brought the square back to 2 dimensional world. The spear then got sad, because he was unable to go to dimensions above his.
This video was very interesting. I have been thinking about the next dimensions and a "higher" world, I guess you could say, for a long time. I have watched Flatland before and it was very interesting. As 3rd dimensional beings, it would be very hard to understand the 4th dimension. And I believe that the 4th dimension is time, so apparently 4th dimensional beings can also mingle with time. Anyways, as the video noted, if we saw a 4th dimensional object pass by our world, we could only see it as a 3rd dimensional object getting larger, then smaller again. I thought this part was especially interesting because it told us how we would kind of see a 4th dimensional being. I hope one day, the 4th dimension will be unlocked, so that we can move on to the 5th dimension. Which brings me to the fact that nobody can guess what is beyond the 10th dimension. If I am right, the 10th dimension is the infinite amount of infinite possibilities there are. But then what would the 11th dimension be? There must be a ∞th dimension somewhere out there, but that is so complicated that we can not even try to imagine it. Hopefully a breakthrough will occur, and we will all feel how it is to live in a "higher world."
Rohan, to answer your question, I believe that the reason why things in the 2nd dimension are brighter when they are closer is because there must be a way to tell depth in the 2nd dimension, because in the 2nd dimension, you only see things in lines, and there is no way to tell how far something is when it is only a line. Which also makes me think what points in Pointland would see. In Lineland (1st dimensional world), the lines would be moving on a horizontal line and they would see others as points. Put then what would points in Pointland (0th dimension) see? They would see others in a -1st dimension, but are there negative dimensions? If there is a -1st dimension, then they would see things in the -2nd dimension, and so on. This subject is really complicated, and it will never be solved, for there are many things that we can defy, but we can never defy infinity.
I learned a lot from this video. I never knew about flatland. I think it is really interesting how the flat shapes can only see lines and how darker and lighter mean that shape is far or close. I have always wondered what the fourth dimension is, and now I kind of understand the concept of drawing out every line. I also never knew that a line was a one dimensional shape. I think I knew that in the back of my mind, but never heard somebody say it. I also think that if we completely understand the fourth dimension, we can go on to discovering the other ones, and that could lead to something bigger. I also thought it was cool how a four dimensional shape coming and leaving would just look like something getting larger and then smaller. I really liked this video.
This article was so cool. I think that making the world a four dimensional place would be such a cool and fascinating experiment. Sometimes this world can only think of the world in the perspective they live in it. For example, try to say "How are you?" without using those words. It's the same thing. Imagine the thirteenth dimension. How complicated would that be. The idea of a hypercube can be so fascinating even though we don't actually know if it exists. A hypercube would be looking at the world in a blurry perspective. I really liked this video because I knew what it was talking about. Flatland is a movie, which Mr. Sewell showed us. The concept of something being closer and lighter and farther and darker is such a brilliant idea. If you lived in a 2 dimensional world without depth-perception how confusing would that be. Pretty confusing. I also do agree with Ayden As 3rd dimensional beings it would hard to think about the world in the fourth dimension. This was really confusing for Arthur Square (the protagonist in Flatland.) to experience the fourth dimension. I think it would be really cool to make a Flatland 2. I didn't really understand what happened at the end of the movie and I would like for the movie to continue.
I think it is so cool that one dimension stretched out and expanded again and again creates the next dimension. I think it is so crazy how when an object is closer to you the wave lengths that determine the brightness have to be closer together. When the object is far away the wave length will stretch longer to reach back to you eye.
This does blow my little spherical mind! I am very interested in the topic of dimensions and I would love to read Flatland. I think that the hypershapes are really cool. I understand how a 4D cube would look, but I don't really get what a 4D sphere would be like.
It's very interesting the way higher dimensions would look to us, as well as how we would look to somebody in a dimension lower than us. What I don't quite understand is that there were only four dimensions in the video. I know he mentioned an eleventh dimension, and I understand that you keep extending each line segment by an inch. However, I only thought the hypercube existed in the tenth dimension as shown in this video
https://www.youtube.com/watch?v=p4Gotl9vRGs
Also, yes there could be four dimensional beings popping in and out of our everyday lives, but we would have seen one by now. They would not be hard to recognize because they would shrink up and disappear in a matter of seconds. My final question is what would someone in the fourth dimension look like to someone in the second dimension. They only explained what a person would look like on the dimension lower not twice lower.
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