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>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?
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.
What a nice 65th birthday present to finally close off the last dangling piece of your almost-complete research agenda!
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.
You could trim this down, but I personally find the background as interesting as the result.
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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…
Downvote me as much as you like. It's painful to take an honest look into the mirror.
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 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.
>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?
I think the article means that over all differences in dimension, the total number of missed maps is infinite.
what is this good for? please no knee-jerk 'this is pure mathematics, it doesn't need applicability' answers.
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.
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There is no thickness (or it’s zero if you like). The deformations have to be continuous mathematical functions, so punching a hole isn’t possible. The study is about the properties of (higher dimensional) shapes rather than concrete objects. It’s like asking what’s the thickness of a circle.
If it's zero I can make a doughnut from a ball without tearing.
A 2D disk has zero thickness, any movement orthogonal to the plane of the disk will take you off the disk. But the disk can't be distorted into a circle in a continuous way.
Earlier quoted context omitted.
I think the article means that over all differences in dimension, the total number of missed maps is infinite.
ok - so what I'm wondering is what is the cardinality of missed maps? How big of an infinity is it?
(There are finitely many maps for each possible dimensional difference, and countably many possible dimensional differences.)