7 ms·

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

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. Just wondering if this had an application immediately.

ColinWright 13y ago
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 regards payment, but sometimes people are paid to play with these sorts of things simply because you don't know what will come from it. People constantly, constantly ask this question - "What's the point of pure research?" The question has been discussed many, many times over, and there are eloquent and robust defences for pure research to be found in many places. There's no way I could do better than some of the things already out there, so I won't try. However, many of the things you use today and take for granted for first created by people "playing," sometimes in their spare time, sometimes in time paid for by companies (and in some cases individuals) who were willing to let people play and see what came of it. If we knew what we were doing, it wouldn't be called "Research."
- eridius 13y ago
  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.
  - emmelaich 13y ago
    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 http://en.wikipedia.org/wiki/G._H._Hardy#Hardy.27s_aphorisms
    - ollyfg 13y ago
      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_principle http://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principl...
wesleyd 13y ago
I believe this result has important applications in cylindrical stack encryption; it's very difficult to produce a solution, but very easy to verify a given solution.
- jafaku 13y ago
  Brb, I'm gonna create CylinderCoin.
  - pjbrunet 13y ago
    I'd buy some. Would be awesome if each (coin) solution was rendered with a raytracer.
- alister 13y ago
  You jest, but your comment made me think of what an impressive Enigma machine [1] such an arrangement of rotors could make. The tubes are slipping in contact, so it'd have to be electrical linkage rather than mechanical to conduct the flow of the data. [1] http://en.wikipedia.org/wiki/Enigma_machine http://en.wikipedia.org/wiki/Enigma_machine
yaketysax 13y ago
If you ask some professional mathematicians, individually, why it is they're researching what they're researching, I think the most common answer will be "because I think it's interesting". There are areas of math without direct application to the real world. And so what? The idea that we should only do that which has some immediate gain is intellectually toxic. It stifles curiosity.
pavelrub 13y ago
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 applications often arise unexpectedly out of things which at first seem completely theoretical (famous example: public key cryptography), and we cannot foresee in advanced what will lead to what. Timothy Gowers - 1998 Fields medalist - gave a lecture in 2000 titled "The Importance of Mathematics". I advice everyone to watch/read it: Video: https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 PDF: https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf Edit: more philosophically, this question always seems puzzling to me, because we can always ask: whats so important about "real world applications" anyway? We can start from any activity and ask "why is it important?", and then ask the same about the answer, etc'. This chain of "why"s eventually comes to an end: we can still ask the question, but there is no meaningful answer other than the realization that the things which are important are the things people find important - whether it is to get faster from point A to point B, have a baby, go to a party, or to solve mathematical problems. Something isn't more important because it's in the "real world".
- trevyn 13y ago
  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.
  - pavelrub 13y ago
    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.
Someone 13y ago
About "just cool" thing: that discussion has been done a zillion times. On the one hand, it's just one of those funny problems: easy to describe, but far from simple to solve. On the other hand, I would say that mathematicians have earned the right to work on such silly problems, given that, if hey hadn't worked on similar silly problems before, our technology would be quite a bit less advanced. Half the world is built on the hobbies of mathematicians. What surprised me is that http://arxiv.org/abs/1312.6207 http://arxiv.org/abs/1312.6207 (which gives solutions with 8 and 9 cylinders, if one let's go of the constraint that all cylinders must be of equal radius) claims a connection with physics. (BTW, I found that link via http://www.mathpuzzle.com http://www.mathpuzzle.com. Infrequently updated, but never has uninteresting new items (at least, to my taste))
wolfgke 13y ago
When asked about this kind of topic I prefer to answer with the following joke: 'A mathematician, native Texan, once was asked in his class: "What is mathematics good for?" He replied: "This question makes me sick. Like when you show somebody the Grand Canyon for the first time, and he asks you `What's is good for?' What would you do? Why, you would kick the guy off the cliff".' (Source: http://www.math.utah.edu/~cherk/mathjokes.html http://www.math.utah.edu/~cherk/mathjokes.html)
alister 13y ago
Exploring geometric puzzles made Professor Ernő Rubik the richest and most famous man in communist Hungary [1]. At least that's a concrete answer you can give to the "man in street" who's going to scoff at explanations about expanding mathematics. But money and fame, well, everybody understands that if it makes money or makes you famous it's justified. [1] http://www.nytimes.com/1986/08/03/business/hungarian-millionaire-erno-rubik-will-son-cube-bring-another-bout-rubikmania.html http://www.nytimes.com/1986/08/03/business/hungarian-million...
- pbhjpbhj 13y ago
  >"everybody understands that if it makes money or makes you famous it's justified" // I'm assuming that was tongue-in-cheek. Whilst many will accept the answer "to be famous" or "to make a profit" those are not justified motivations to others - particular not WRT research funding.
pjbrunet 13y ago
I think this would be an interesting sculpture for a campus math building. I can imagine John Raymond Henry doing it. If Claes Oldenburg made them into gigantic cigarettes, there's no telling what would happen ;-)
chrisdone 13y ago
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.
mathgenius 13y ago
The techniques involved are both generic and highly non-trivial. So the paper is very nice in that it gives a good work-out to the methods, and the reader can get to see what kind of problem would yield to those methods. For example it appears that similar kinds of "objects touching each other" problems could be attacked. But yeah, it's basically a monster polynomial that they solve, and that is quite a common thing to want to do. On the other hand, one might see a paper that expounds a technique, but how do you know if that technique has got any teeth unless you can use it to eat a difficult problem? So yeah, I think the specific problem is not quite the point of this research.

ColinWright 13y ago

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 regards payment, but sometimes people are paid to play with these sorts of things simply because you don't know what will come from it. People constantly, constantly ask this question - "What's the point of pure research?" The question has been discussed many, many times over, and there are eloquent and robust defences for pure research to be found in many places. There's no way I could do better than some of the things already out there, so I won't try. However, many of the things you use today and take for granted for first created by people "playing," sometimes in their spare time, sometimes in time paid for by companies (and in some cases individuals) who were willing to let people play and see what came of it. If we knew what we were doing, it wouldn't be called "Research."

eridius 13y ago
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.
- emmelaich 13y ago
  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 http://en.wikipedia.org/wiki/G._H._Hardy#Hardy.27s_aphorisms
  - ollyfg 13y ago
    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_principle http://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principl...

wesleyd 13y ago

I believe this result has important applications in cylindrical stack encryption; it's very difficult to produce a solution, but very easy to verify a given solution.

jafaku 13y ago
Brb, I'm gonna create CylinderCoin.
- pjbrunet 13y ago
  I'd buy some. Would be awesome if each (coin) solution was rendered with a raytracer.
alister 13y ago
You jest, but your comment made me think of what an impressive Enigma machine [1] such an arrangement of rotors could make. The tubes are slipping in contact, so it'd have to be electrical linkage rather than mechanical to conduct the flow of the data. [1] http://en.wikipedia.org/wiki/Enigma_machine http://en.wikipedia.org/wiki/Enigma_machine

yaketysax 13y ago

If you ask some professional mathematicians, individually, why it is they're researching what they're researching, I think the most common answer will be "because I think it's interesting". There are areas of math without direct application to the real world. And so what? The idea that we should only do that which has some immediate gain is intellectually toxic. It stifles curiosity.

pavelrub 13y ago

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 applications often arise unexpectedly out of things which at first seem completely theoretical (famous example: public key cryptography), and we cannot foresee in advanced what will lead to what. Timothy Gowers - 1998 Fields medalist - gave a lecture in 2000 titled "The Importance of Mathematics". I advice everyone to watch/read it: Video: https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 https://www.youtube.com/view_play_list?p=3641A12A6ADDB4B1 PDF: https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf Edit: more philosophically, this question always seems puzzling to me, because we can always ask: whats so important about "real world applications" anyway? We can start from any activity and ask "why is it important?", and then ask the same about the answer, etc'. This chain of "why"s eventually comes to an end: we can still ask the question, but there is no meaningful answer other than the realization that the things which are important are the things people find important - whether it is to get faster from point A to point B, have a baby, go to a party, or to solve mathematical problems. Something isn't more important because it's in the "real world".

trevyn 13y ago
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.
- pavelrub 13y ago
  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.

Someone 13y ago

About "just cool" thing: that discussion has been done a zillion times. On the one hand, it's just one of those funny problems: easy to describe, but far from simple to solve. On the other hand, I would say that mathematicians have earned the right to work on such silly problems, given that, if hey hadn't worked on similar silly problems before, our technology would be quite a bit less advanced. Half the world is built on the hobbies of mathematicians. What surprised me is that http://arxiv.org/abs/1312.6207 http://arxiv.org/abs/1312.6207 (which gives solutions with 8 and 9 cylinders, if one let's go of the constraint that all cylinders must be of equal radius) claims a connection with physics. (BTW, I found that link via http://www.mathpuzzle.com http://www.mathpuzzle.com. Infrequently updated, but never has uninteresting new items (at least, to my taste))

wolfgke 13y ago

When asked about this kind of topic I prefer to answer with the following joke: 'A mathematician, native Texan, once was asked in his class: "What is mathematics good for?" He replied: "This question makes me sick. Like when you show somebody the Grand Canyon for the first time, and he asks you `What's is good for?' What would you do? Why, you would kick the guy off the cliff".' (Source: http://www.math.utah.edu/~cherk/mathjokes.html http://www.math.utah.edu/~cherk/mathjokes.html)

alister 13y ago

Exploring geometric puzzles made Professor Ernő Rubik the richest and most famous man in communist Hungary [1]. At least that's a concrete answer you can give to the "man in street" who's going to scoff at explanations about expanding mathematics. But money and fame, well, everybody understands that if it makes money or makes you famous it's justified. [1] http://www.nytimes.com/1986/08/03/business/hungarian-millionaire-erno-rubik-will-son-cube-bring-another-bout-rubikmania.html http://www.nytimes.com/1986/08/03/business/hungarian-million...

pbhjpbhj 13y ago
>"everybody understands that if it makes money or makes you famous it's justified" // I'm assuming that was tongue-in-cheek. Whilst many will accept the answer "to be famous" or "to make a profit" those are not justified motivations to others - particular not WRT research funding.

pjbrunet 13y ago

I think this would be an interesting sculpture for a campus math building. I can imagine John Raymond Henry doing it. If Claes Oldenburg made them into gigantic cigarettes, there's no telling what would happen ;-)

chrisdone 13y ago

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.

mathgenius 13y ago

The techniques involved are both generic and highly non-trivial. So the paper is very nice in that it gives a good work-out to the methods, and the reader can get to see what kind of problem would yield to those methods. For example it appears that similar kinds of "objects touching each other" problems could be attacked. But yeah, it's basically a monster polynomial that they solve, and that is quite a common thing to want to do. On the other hand, one might see a paper that expounds a technique, but how do you know if that technique has got any teeth unless you can use it to eat a difficult problem? So yeah, I think the specific problem is not quite the point of this research.