- #26

tiny-tim

Science Advisor

Homework Helper

- 25,832

- 251

at about 16:00, arkani-hamed says "pictures of space-time on-shell processes are in 1-to-1 correspondence with cells of the positive Grassmanian which in turn are in 1-to-1 correspondence with a new way of thinking about permutations"

he presents black-or-white dot-diagrams that represent permutations

since even a ten-year-old could understand them (after a little thought), let's look at a couple of diagrams …

https://www.simonsfoundation.org/wp-content/uploads/2013/09/twistor-diagrams-300x200.png [Broken]

… the rule is that you start at one of the numbers round the outside, you turn LEFT at a white dot, and RIGHT at a black dot, and you end at another number on the outside

eg in the first diagram, 1 goes to 3, 3 goes to 5, 5 goes back to 1; 2 goes to 4, 4 goes to 6, 6 goes back to 4, so it represents the permutation (135) (246)

similarly the second diagram represents (153) (264)

he presents black-or-white dot-diagrams that represent permutations

since even a ten-year-old could understand them (after a little thought), let's look at a couple of diagrams …

https://www.simonsfoundation.org/wp-content/uploads/2013/09/twistor-diagrams-300x200.png [Broken]

… the rule is that you start at one of the numbers round the outside, you turn LEFT at a white dot, and RIGHT at a black dot, and you end at another number on the outside

eg in the first diagram, 1 goes to 3, 3 goes to 5, 5 goes back to 1; 2 goes to 4, 4 goes to 6, 6 goes back to 4, so it represents the permutation (135) (246)

similarly the second diagram represents (153) (264)

EDIT: if you're only interested in the amplituhedron itself, you can

where he indeed says "I could have skipped the whole of the first part of the talk, which is physics-motivated, and started at this point, and

*start at about 20:30,*where he indeed says "I could have skipped the whole of the first part of the talk, which is physics-motivated, and started at this point, and

*this can be explained to a smart junior-high-school student*"
Last edited by a moderator: