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It revealed the existence of staircase-like structures with infinitely many steps. The size of each step in these “infinite staircases” was a ratio of Fibonacci
by kleiba 4y ago
It revealed the existence of staircase-like structures with infinitely many steps. The size of each step in these “infinite staircases” was a ratio of Fibonacci numbers.
As the staircase ascended, the steps became smaller and smaller, the top of the staircase crushing up against the golden ratio. Neither the golden ratio nor the Fibonacci numbers has any apparent relationship to the problem of fitting a shape inside a ball. It was bizarre to find these numbers lurking within McDuff and Schlenk’s work.
Is it me, or is that terrible scientific writing? I don't understand what the author is actually trying to describe, and I kinda have my doubts whether the authors knows herself.
- pfortuny 4y agoIt sounds as if the author recorded an interview, did not understand much but inserted what he or she deemed interesting. I cannot parse that text either.
- r0uv3n 4y agoI think it is somewhat clear what they're getting at, and it's explained visually in the picture further down. Though maybe "crushing against the golden ratio" is not a good way to phrase the situation. It sounds a little bit like the stairs form a converging series, but from the text further up and the picture it seems pretty obvious that the author intends to convey that the step size of the stairs approaches a (power of) the golden ratio from above.
- VyseofArcadia 4y agoIn defense of the author, I have trouble wrapping my head around symplectic geometry, and my PhD research was in an adjacent area, semisimple Lie groups. I'd have to put in a considerable amount of effort to develop an intuition for this setting.