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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

#61

Post by kandel »

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.

It looks like math blog posts. They are written for other mathematicians but not experts in the fields, and a layman will find them unreadable.

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

#63

Post by anArbitraryOne »

aeahajji wrote: post #55
topaz0 wrote: post #38

Earlier quoted context omitted.

I dunno about gossipy, but the narrative style is standard at Quanta. It's written for the subscriber who is reading for leisure, and wants a good story as well as some amount of technical depth, not for the HN reader who wants to quickly judge whether figuring this thing out is worth their time, and will abandon it if not.

The disillusion of most here to even imagine that the math is within their reach is quite astonishing.

What evidence do you have that the people and bots here think the math is within their reach?

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

#64

Post by anArbitraryOne »

jll29 wrote: post #52
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 read Quanta mag because of the narrative, and loved this article. What a nice 65th birthday present to finally close off the last dangling piece of your almost-complete research agenda!

I hate reading quanta mag because of the narrative, and didn't have the patience to weed through this to learn something conceptual. But I'm glad there are people who enjoy it.

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

#65

Post by superhuzza »

pbhjpbhj wrote: post #62

Lost me at the end, but, don't inner-tubes have 2 holes (genus 2), topologically: one for inflation and one for the wheel to fit in. This makes them distinct from a torus (genus 1) and no homotopy exists between them. Clearly IANAM.

There is a distinction between a torus and a solid torus

A torus is like an inner tube - an inner void and a big hole in the middle.

A solid torus just has a big hole in the middle, like a donut.

https://en.wikipedia.org/wiki/Solid_torus

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

#66

Post by anArbitraryOne »

tomcam wrote: post #50
dclowd9901 wrote: post #32

> It means that in very high dimensions (think of a 100-dimensional sphere) Sure, no problem, author.

I don’t know about you, but I start to get a little tentative at about 12 dimensions

Eight, for me. Once you can fit packed spheres between each other in the norma "pyramid" configuration, my intuition breaks down. It should probably be true about four dimensions as well but I'm overconfident

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

#67

Post by toth »

pbhjpbhj wrote: post #62

Lost me at the end, but, don't inner-tubes have 2 holes (genus 2), topologically: one for inflation and one for the wheel to fit in. This makes them distinct from a torus (genus 1) and no homotopy exists between them. Clearly IANAM.

You are right, but I am pretty sure they just meant the inner tube ignoring the puncture for inflation.

Usually people just use donut/bagel for an illustration of a torus. Not sure why they used inner tube here - maybe to make it clear it is just the surface?

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

#68

Post by toth »

superhuzza wrote: post #65
pbhjpbhj wrote: post #62

Lost me at the end, but, don't inner-tubes have 2 holes (genus 2), topologically: one for inflation and one for the wheel to fit in. This makes them distinct from a torus (genus 1) and no homotopy exists between them. Clearly IANAM.

There is a distinction between a torus and a solid torus A torus is like an inner tube - an inner void and a big hole in the middle. A solid torus just has a big hole in the middle, like a donut. https://en.wikipedia.org/wiki/Solid_torus

You probably are aware, but just to make it clear for others: topologically a torus has one hole (genus 1). The inner void is not considered a hole. Similarly, a 2-sphere (surface of solid sphere in 3d) has 0 holes (the inner void is not considered).

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

#69

Post by toth »

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.

I always wonder about what something in between popular science/math and academic journals would look like. Something oriented towards people that know a nontrivial amount but are not researchers. E.g., you can assume they know calculus and have a conceptual understanding of what things like manifolds and homotopy but are fuzzy on the details.

For a topic like in the article, you need a lot of words to give a very vague understanding if you are aiming for a general audience. Not clear it is worth it for the reader. For that more targeted audience it could be a lot shorter and give a little more detail.

Probably too small a market, but I would definitely enjoy that type of content a lot.

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