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Mathematicians find way to put 7 cylinders in contact without using their ends

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Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#71

Post by pavelrub »

trevyn wrote: post #68
pavelrub wrote: post #33

Earlier quoted context omitted.

I'm not sure what you mean by "real world problems". Most mathematicians do mathematics because they find it beautiful, rewarding, fun, and for various other reasons that have little to do with creating things in the physical world. Mathematics is extremely interconnected and some minor discovery in a certain field can later become extremely important in some seemingly unrelated field, similarly - real world applicat…

I think many "real world applications" tend to directly or indirectly support our biological goals of individual and/or species survival and reproduction. Of course, the same could be said of basic research, but it is further removed and so requires more forward thinking to appreciate.

I don't see how this is true. If the question is "what are the real world applications of X in mathematics?", most people would be satisfied by any absurd answer as long as it's "in the real world", regardless of what biological goals, if any, it supports.

It could be that a certain mathematical research allowed us to develop sturdier pencils, and suddenly everybody is satisfied that we are not wasting our money because now it has "real world applications".

The human drive to discover and invent new things in math is fundamentally no different than the human drive for doing the same in the fields of technology, arts, etc'. But we perceive anything touchable as good, and anything imaginary as useless, because that's the kind of culture we live in: Making a slightly faster smartphone so that the activity of swiping a finger on a capacitive touch screen to play candy crush now takes 0.7 seconds instead of 0.8 doesn't need any justification, but thinking about math does.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#72

Post by emmelaich »

eridius wrote: post #38
ColinWright wrote: post #29

Earlier quoted context omitted.

There are many puzzles, games, and obsessions that require the creation of new mathematics to understand properly, and then which eventually prove to be useful. Sometimes solving these sorts of problems requires pushing the boundaries of existing techniques, sometimes the techniques required are completely new and are invented specifically for the question at hand. I'm not sure about this specific instance with regar…

My high school calculus teacher told me that even imaginary numbers (those infinitely useful things in EE) were originally createdas a pure mathematical tool with zero practical application. He liked to rail against those "dirtyfilthyphysicists" stealing pure mathematical concepts and finding applications for it.

Sounds like G.H.Hardy

   "Nothing I have ever done is of the slightest practical use"
http://en.wikipedia.org/wiki/G._H._Hardy#Hardy.27s_aphorisms

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#73

Post by DonGateley »

So, given that this involves rounding errors in solutions to equations it is only an approximate solution. A solution with fuzz. Is it possible to prove that each point of "contact" is exactly coincident? Or to prove that exact coincidence is not possible. There seems to be room for deeper work on this problem.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#74

Post by owenversteeg »

DonGateley wrote: post #73

So, given that this involves rounding errors in solutions to equations it is only an approximate solution. A solution with fuzz. Is it possible to prove that each point of "contact" is exactly coincident? Or to prove that exact coincidence is not possible. There seems to be room for deeper work on this problem.

I believe that there was a mathematical proof published along with the news.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#75

Post by chrisdone »

josephwegner wrote: post #25

This is going to sound like trolling, but it's not - I'm honestly curious. Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby? EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it.…

I came in wondering the same thing. Why is this newsworthy? Every one of the replies to your comment is either a joke or an obnoxious lecture about "why maths can just be for the sake of it [and might be useful later]" like you're some sort of recently-thawed caveman. People can't just say "no, no actual applications yet, it's just cool," or, "I don't know." Ugh. Whole thread made me cringe.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#76

Post by darkmighty »

analog31 wrote: post #58

Ask HN: Is there an explanation somewhere of this "certification" that a layperson (college math and physics major, and self taught programmer) could understand?

The article is quite readable. I'm a layperson too, but here's what I made of the methods provided:

1- The first method finds a constant that guarantees convergence of newtons method to the solution; they then iterate it a few times and verify the result is almost stationary.

2- They use a set with parameter r that is guaranteed to contain a solution if it's contained in a ball of radius r; they then show that a given small ball around the candidate solution contains this set (they were able to do that because this set gets smaller faster than the radius).

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#77

Post by pervycreeper »

DonGateley wrote: post #73

So, given that this involves rounding errors in solutions to equations it is only an approximate solution. A solution with fuzz. Is it possible to prove that each point of "contact" is exactly coincident? Or to prove that exact coincidence is not possible. There seems to be room for deeper work on this problem.

I was wondering this as well. Perhaps this is an example of a new, computer-assisted paradigm of math, where after extensive computation, a proposition is accepted as true if the probability of its being false is judged to be sufficiently small. I don't have the exact reference, but there was an article in some AMS publication about this in a few years ago.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#78

Post by anigbrowl »

pavelrub wrote: post #43
chubot wrote: post #37

This sort of reminds me of: http://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c Because it is a 3D object that was found using mathematics. Any other examples? I think there are lots of new objects discovered in higher dimensions, but I like when there is something you can actually build and see. I also like how it appears to be very asymmetrical.

The Klein bottle is sort of like that, only it's supposed to be in 4 dimensions, but the 3d version is still pretty cool and quite famous! http://en.wikipedia.org/wiki/Klein_bottle Never heard about the gomboc before, thanks!

Clifford Stoll of Cuckoo's Egg fame has a side business making glass Klein bottles. He lives near me, I sometimes see him at the post office shipping out a bunch of them.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#79

Post by 3rd3 »

jzwinck wrote: post #70
3rd3 wrote: post #20

Earlier quoted context omitted.

I'd love to see a jungle gym in this shape. I would definitely climb it!

I did: https://www.flickr.com/photos/jzwinck/252678921/in/set-72157... It was great: whether by design or luck, the poles you had to climb got more and more horizontal as you got higher from the ground, then they became inverted in a way that made the topmost part easy and safer. The bottom then was a test: if you failed you had not far to fall, if you succeeded you would likely be ok to the top.

Was was thinking more of tubes with ladders inside. But this one looks great too!

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#80

Post by ollyfg »

emmelaich wrote: post #72
eridius wrote: post #38

Earlier quoted context omitted.

My high school calculus teacher told me that even imaginary numbers (those infinitely useful things in EE) were originally createdas a pure mathematical tool with zero practical application. He liked to rail against those "dirtyfilthyphysicists" stealing pure mathematical concepts and finding applications for it.

Sounds like G.H.Hardy "Nothing I have ever done is of the slightest practical use" http://en.wikipedia.org/wiki/G._H._Hardy#Hardy.27s_aphorisms

This from the man who came up with the Hardy-Weinberg Equation[1], an extremely practical method of population analysis.

[1]http://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principl...

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