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An Old Conjecture Falls, Making Spheres a Lot More Complicated

quantamagazine.org

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Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#41

Post by caf »

iraqmtpizza wrote: post #20
kmill wrote: post #19

Earlier quoted context omitted.

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 sub…

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.

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

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#42

Post by iraqmtpizza »

caf wrote: post #41
iraqmtpizza wrote: post #20

Earlier quoted context omitted.

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.

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

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

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#44

Post by QuesnayJr »

iraqmtpizza wrote: post #42
caf wrote: post #41

Earlier quoted context omitted.

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

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

Are you doing an extended comedy bit or something?

A "metal" in astronomy is everything other than hydrogen or helium.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#45

Post by bryanrasmussen »

Nevermark wrote: post #34
smaddox wrote: post #30

Earlier quoted context omitted.

> I always wonder what a popular science/math magazine would look like if it were oriented towards hackers. In this I mean people who have little background in the field but also the type of person who is used to bluntness and knows to RTFM. Expensive.

I would pay $1 per article whose title & byline interested me if I could count on the quality matching this [0] … … [0] https://news.ycombinator.com/item?id=37171553 (This comment reads faster with tail recursion.)

OK, assuming that there are enough people like you to make that a going concern now we just have to solve the problem of getting this level quality distributed through the population that wouldn't care for it enough to send it on to their friends, that is to say through the global network of humans with 1 in 10000 being one of the people willing to pay 1 dollar and the other 9999 people saying "what the hell, who cares"

I think it may not work out.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#46

Post by bryanrasmussen »

>Infinitely more maps from spheres to telescopes means infinitely more maps between spheres themselves. The number of such maps is finite for any difference in dimension, but the new proof shows that the number grows quickly and inexorably.

is it actually infinitely - or just a lot?

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#47

Post by pa7x1 »

delocalized wrote: post #24
billfruit wrote: post #22

The gossipy narrative style of the article is kind of jarring for an article on a topic like this. It took several paragraphs before it touched on the matter.

I always wonder what a popular science/math magazine would look like if it were oriented towards hackers. In this I mean people who have little background in the field but also the type of person who is used to bluntness and knows to RTFM. I would subscribe to one. Journal articles are often opaque to people who aren't already in the field, and popular science falls too often into the storytelling trap seen here.

The gap is very hard to close because there is a chasm between the two. RTFM here means years (typically 5+ for research math) of very focused study to follow what it says. While the popular science tries to convey something that is meaningful to the majority of people without any background exposure. The gap between the two is huge.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#48

Post by Nevermark »

bryanrasmussen wrote: post #45
Nevermark wrote: post #34

Earlier quoted context omitted.

I would pay $1 per article whose title & byline interested me if I could count on the quality matching this [0] … … [0] https://news.ycombinator.com/item?id=37171553 (This comment reads faster with tail recursion.)

OK, assuming that there are enough people like you to make that a going concern now we just have to solve the problem of getting this level quality distributed through the population that wouldn't care for it enough to send it on to their friends, that is to say through the global network of humans with 1 in 10000 being one of the people willing to pay 1 dollar and the other 9999 people saying "what the hell, who car…

Ok, I can say this with complete conviction.

Any source that filtered their articles so only that quality was released, I would pay $5.

And instead of filtering out their writers work, it would mostly be about telling them to rework, do more homework, get it right.

90% of quality is simply recognizing when you haven’t hit the bar yet and stepping up. Repeatedly if necessary.

The subject is rarely the problem.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#49

Post by tomcam »

delocalized wrote: post #24
billfruit wrote: post #22

The gossipy narrative style of the article is kind of jarring for an article on a topic like this. It took several paragraphs before it touched on the matter.

I always wonder what a popular science/math magazine would look like if it were oriented towards hackers. In this I mean people who have little background in the field but also the type of person who is used to bluntness and knows to RTFM. I would subscribe to one. Journal articles are often opaque to people who aren't already in the field, and popular science falls too often into the storytelling trap seen here.

There was one, once, and it was glorious: https://archive.org/details/byte-magazine
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