Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

An Old Conjecture Falls, Making Spheres a Lot More Complicated

quantamagazine.org

Post reply on HN
Print view View original

71–80 of 83 posts

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

#71

Post by shrx »

toth wrote: post #67
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?

A hollow inner tube with the puncture for inflation is topologically equivalent to a solid torus, if I understood correctly.

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

#73

Post by quickthrower2 »

Eduard wrote: post #14

what is this good for? please no knee-jerk 'this is pure mathematics, it doesn't need applicability' answers.

Mathematics has a habit throughout history of coming up with useless (to layman, at first) looking ideas that become insanely valuable. Such as zero, negative numbers, imaginary numbers, group theory and so on. Modern life and progress needs this.

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

#74

Post by nixpulvis »

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.

Perhaps enroll in a solid EE class? Holding a soldering iron at ~700 degrees may help with patience too… or not, in my case.

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

#75

Post by codeflo »

ykonstant wrote: post #70

The following slides contain a more concrete description of the conjecture, its motivation and consequences: https://people.math.rochester.edu/faculty/doug/Talks/Glasgow...

I hate slide decks like these, where every page in the PDF contains one more bullet point than the last one. Maybe I'm particularly bad at this, but I spend way too long scanning each page for the new information. Is it impossible to configure LaTeX to only produce the final animation step as a completed page and skip the intermediate ones?

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

#76

Post by adgjlsfhk1 »

toth wrote: post #68
superhuzza wrote: post #65

Earlier quoted context omitted.

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).

to be slightly more technical what you're defining as "voids" are often considered 2-dimensional holes (as formalized by homology)

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

#77

Post by cwzwarich »

codeflo wrote: post #75
ykonstant wrote: post #70

The following slides contain a more concrete description of the conjecture, its motivation and consequences: https://people.math.rochester.edu/faculty/doug/Talks/Glasgow...

I hate slide decks like these, where every page in the PDF contains one more bullet point than the last one. Maybe I'm particularly bad at this, but I spend way too long scanning each page for the new information. Is it impossible to configure LaTeX to only produce the final animation step as a completed page and skip the intermediate ones?

The beamer class has a [handout] option, which at least attempts to do this (with some corner cases IIRC, but it's been a while).

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

#78

Post by anArbitraryOne »

navels wrote: post #40
Eduard wrote: post #14

what is this good for? please no knee-jerk 'this is pure mathematics, it doesn't need applicability' answers.

When I was working in the field it sure as heck wasn't because of practical applications. The mathematics involved is beautiful.

Just like Feynman said: Physics is like watching internet porn. Sure, it may have useful results, like ad revenue, but that's not why we do it

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

#79

Post by hollerith »

anArbitraryOne wrote: post #78
navels wrote: post #40

Earlier quoted context omitted.

When I was working in the field it sure as heck wasn't because of practical applications. The mathematics involved is beautiful.

Just like Feynman said: Physics is like watching internet porn. Sure, it may have useful results, like ad revenue, but that's not why we do it

>Feynman said: Physics is like watching internet porn.

The Internet existed when Feynman died in 1988, but Internet porn did not, at least not watchable (video) Internet porn.

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

#80

Post by iraqmtpizza »

QuesnayJr wrote: post #44
iraqmtpizza wrote: post #42

Earlier quoted context omitted.

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.

And yet... metallic HYDROGEN. Now you see the comedy inherent in the system.
Post reply on HN