This is an incredibly creative visualization. Pieces like this remind me of how much interaction there can be between seemingly disparate fields of study, and how useful it is to be an...
This is an incredibly creative visualization. Pieces like this remind me of how much interaction there can be between seemingly disparate fields of study, and how useful it is to be an inter-disciplinary thinker.
At the very least it makes an otherwise dry subject more fun! Another favourite thing of mine in this vein is this Animation vs. Math video (https://www.youtube.com/watch?v=B1J6Ou4q8vE).
At the very least it makes an otherwise dry subject more fun! Another favourite thing of mine in this vein is this Animation vs. Math video (https://www.youtube.com/watch?v=B1J6Ou4q8vE).
I hit Bookmark on this post so fast my phone screen might have cracked. I'm in public transit right now and cannot watch it but on boy great submission --- is this Interpretative dances of...
I hit Bookmark on this post so fast my phone screen might have cracked. I'm in public transit right now and cannot watch it but on boy great submission --- is this Interpretative dances of incredibly complex and niche ideas??
Sadly I'm neither a mathematician or a dancer. It's about knot theory and the performance is creative visualization of the concepts as they're brought up in the video. Veritasium has a...
Sadly I'm neither a mathematician or a dancer. It's about knot theory and the performance is creative visualization of the concepts as they're brought up in the video. Veritasium has a introduction to knot theory (https://www.youtube.com/watch?v=8DBhTXM_Br4) that is very informative. As layman, what I gathered is basically, knot theory study the different ways a string can be tied into knots. 2 knots are considered the same if they can be turned into one another by simply "moving the string around" so to speak. And braid is the when using multiple string instead of just one.
The rest are as explained in the video: these objects are hard to study directly (it can be difficult to tell which different-looking knots are actually the same and we just didn't see a way to transform them properly) so mathematicians would "encode" them into objects from other areas of math (like matrices) and study those objects instead. An analogy is like trying to solve geometry problem by applying a xy coordinate sytem, translate the lines and curves of the original geometric setup into equations, and then solve those equations instead. Another example is the immaginary numbers can be represented as 2x2 matrices of real numbers. I guess we could say the interpretive dance is also doing a kind of representation (from math concepts to dance moves). However, in the case of braid-to-matrices as mentioned in the video, the translation is imperfect, which resulted in the hijinks that were shown in the end.
Now I'd love if there's any mathematician in the room who could explain all the specfic references. I guess the part about "the trace" is maybe just visually showing the light traces across the screen. But why is the determinant interpreted as being tied up by the grid lines?
This is an incredibly creative visualization. Pieces like this remind me of how much interaction there can be between seemingly disparate fields of study, and how useful it is to be an inter-disciplinary thinker.
At the very least it makes an otherwise dry subject more fun! Another favourite thing of mine in this vein is this Animation vs. Math video (https://www.youtube.com/watch?v=B1J6Ou4q8vE).
I hit Bookmark on this post so fast my phone screen might have cracked. I'm in public transit right now and cannot watch it but on boy great submission --- is this Interpretative dances of incredibly complex and niche ideas??
Would love to hear your thoughts
Sadly I'm neither a mathematician or a dancer. It's about knot theory and the performance is creative visualization of the concepts as they're brought up in the video. Veritasium has a introduction to knot theory (https://www.youtube.com/watch?v=8DBhTXM_Br4) that is very informative. As layman, what I gathered is basically, knot theory study the different ways a string can be tied into knots. 2 knots are considered the same if they can be turned into one another by simply "moving the string around" so to speak. And braid is the when using multiple string instead of just one.
The rest are as explained in the video: these objects are hard to study directly (it can be difficult to tell which different-looking knots are actually the same and we just didn't see a way to transform them properly) so mathematicians would "encode" them into objects from other areas of math (like matrices) and study those objects instead. An analogy is like trying to solve geometry problem by applying a xy coordinate sytem, translate the lines and curves of the original geometric setup into equations, and then solve those equations instead. Another example is the immaginary numbers can be represented as 2x2 matrices of real numbers. I guess we could say the interpretive dance is also doing a kind of representation (from math concepts to dance moves). However, in the case of braid-to-matrices as mentioned in the video, the translation is imperfect, which resulted in the hijinks that were shown in the end.
Now I'd love if there's any mathematician in the room who could explain all the specfic references. I guess the part about "the trace" is maybe just visually showing the light traces across the screen. But why is the determinant interpreted as being tied up by the grid lines?