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0 pointskmill2y ago0 comments

Higher homotopy groups of spheres goes way back to the 30s. This isn't lazy writing. https://en.m.wikipedia.org/wiki/Homotopy_groups_of_spheres

Looking at all the continuous functions from all dimensions of spheres into a particular topological space ends up giving rich algebraic information about the space. This is a cornerstone of algebraic topology. Turns out calculating this stuff for even just spheres can be subtle and mysterious.

Uniform distance matters not at all for any of this, but it does matter that your family of "spheres" be topologically equivalent to the round spheres.

Another model is you take the iterated suspensions starting with a pair of points (the zero sphere).

Yet another is to take boundaries of simplicies, or even cubes.

Topologists are those who are perfectly happy to call a paper towel tube an annulus.

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iraqmtpizza2y ago

It is of great comfort to learn that lazy writing did not exist in 1930. And no mathematician would have ever misrepresented his work to the public back then. They wore top hats then. Far too proper to stoop to lowly deception to achieve recognition.

>The n-dimensional unit sphere — called the n-sphere

LOL nevermind—I was right the first time. Thank you for confirming.

kmillOP2y ago

Ok, I see you are trolling. I tip my top hat to you, good day.

> Your failure to banish my suspicions despite effort makes me that much more confident in my original conclusion.

Side note: I've never considered this phenomenon in my life, and suddenly other people digging in in the face of evidence makes sense. A dubious "thank you" to you.

iraqmtpizza2y ago

it's fine to call them spheres in a freewheeling discussion with a fellow traveler but it's a deliberately misleading shortcut here. at the barest of minimums it could say topological n-spheres

And if you don't become more confident in your idea after a well-orchestrated yet entirely failed attempt to destroy it, you are not a rational person lol. it's called trial by fire and it's older than i am

the sensationalist nature of the writing has generated a lot of discussion so I guess it has does its job

caf2y ago

Wait 'til you hear what astronomers refer to as a "metal".

iraqmtpizza2y ago

Metallic hydrogen? yeah, i took astrophysics in college. pretty sure that just because something starts conducting doesn't mean it's a metal. but sure, professor

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iraqmtpizza2y ago

>The n-dimensional unit sphere — called the n-sphere

LOL nevermind—I was right the first time. Thank you for confirming.

kmillOP2y ago

Ok, I see you are trolling. I tip my top hat to you, good day.

> Your failure to banish my suspicions despite effort makes me that much more confident in my original conclusion.

Side note: I've never considered this phenomenon in my life, and suddenly other people digging in in the face of evidence makes sense. A dubious "thank you" to you.

iraqmtpizza2y ago

it's fine to call them spheres in a freewheeling discussion with a fellow traveler but it's a deliberately misleading shortcut here. at the barest of minimums it could say topological n-spheres

the sensationalist nature of the writing has generated a lot of discussion so I guess it has does its job

caf2y ago

Wait 'til you hear what astronomers refer to as a "metal".

iraqmtpizza2y ago

Metallic hydrogen? yeah, i took astrophysics in college. pretty sure that just because something starts conducting doesn't mean it's a metal. but sure, professor

1 more reply

j / k navigate · click thread line to collapse