Major Advances In Knot Theory 230
An anonymous reader sends us to Science News, which is running a survey of recent strides in finding an answer to the age-old question: How many ways are there to tie your shoelaces? "Mathematicians have been puzzling over that question for a century or two, and the main thing they've discovered is that the question is really, really hard. In the last decade, though, they've developed some powerful new tools inspired by physics that have pried a few answers from the universe's clutches. Even more exciting is that the new tools seem to be the tip of a much larger theory that mathematicians are just beginning to uncover. That larger mathematical theory, if it exists, may help crack some of the hardest mathematical questions there are, questions about the mathematical structure of the three- and four-dimensional space where we live. ... Revealing the full ... superstructure may be the work of a generation."
Re:This is so very important... (Score:3, Interesting)
You sound like you'd take the single most important^h^h^h^h^h^h^h^h^h publicized problem of the day and have everyone working on it, ignoring all of the other interesting stuff that might be possible.
Yes, there are weighty problems in the world, and I'm not trying to dismiss them. Thinking about them exclusively, however, will recover the now but it won't provide any advancement for the future.
Let's do both.
Re:This is so very important... (Score:1, Interesting)
hi troll! I'm-a feed ya. Open up wide, now.
I'm not a neurosurgeon - I'm a computer geek, of sorts, so I program stuff. Does my programming stuff save lives? probably not.. it may make some people's lives easier, but that's about it. So would you tell me to go to medical school and study neurosurgery so I can do something important like save lives?
But when I'm doing that, I can't be fighting fires. I can't help people in personal financial turmoil. I can't provide shelter and food for those who need it. I can't aide those with unwanted pregnancies on how to deal with it (whatever their choice may be), and so forth and so on.
So why don't I go do what I do best, and I'll leave the people who know how to deal with "the world [going] down the toilet" deal with that? I'll do my part and not be a dumbass getting a house I can't really afford just because the bank tells me I can and offers me a lower rate than should be economically possible and other such moves.
But if you still hang on to your statement... ... and so forth and so on.
quit worrying about your documents and pictures and how to migrate them to newer systems - your personal documents are unlikely to be of particular significance or you would have submitted them for archival. If your documents go missing among millions of others that do survive for researchers to rummage through in a thousand years, it is no great loss. [slashdot.org]
quit worrying about your personal finances, there's millions more like you and there are far more important things to deal with than you having to relocate to a cheaper location [slashdot.org]
and, honestly, you waste your time disliking Bill Gates? Dislike Microsoft business practices if you want, but disliking the man isn't going to change anything - all it will get you is shits'n'giggles like the 'borg gates' icon on slashdot [slashdot.org]
But the most important thing altogether is that your post demonstrates a complete lack of understanding of the subject of knot mathematics and the larger field of knot theory. It is almost equivalent to complaining about elliptical curve encryption because you believe there being nothing special about an ellipse, something you could do with pencil, string and 2 thumbtacks in elementary school.
( and no, elliptical curves have no direct relationship to ellipses - but elliptic integrals which form the basis of elliptical curves, do )
Re:Things like this... (Score:5, Interesting)
This is just not that important.
Are you sure?
When algebra was invented, did people think that was important? What about geometry or calculus? What about number theory? Would Euler's study of the Seven Bridges of Konigsberg have been important to you? Probably not. But it did lay the foundations for modern graph theory which engineers use to design computer networks.
Re:How many ways are there to tie your shoelaces? (Score:1, Interesting)
About two trillion actually...
http://www.fieggen.com/shoelace/2trillionmethods.htm
Re:The hardest math (Score:2, Interesting)
I spent 15 years of my life in physics of proteins. Theory of knots in protein folding is nothing more than fancy mathematical excursion (though knots do matter, in very simple form). The importance of "theory" in those sciences is way overblown. It was fun to do to satisfy your own intellectual curiosity, but it's a dead end on the road of science.
Re:This is so very important... (Score:2, Interesting)
Don't trivialize work that you don't understand.
To further disabuse the OP of a misconceived notion, this isn't just "how many ways are there to tie your shoes". This is trying to work out a rational system of knot classification.
The key thing to realize is that knot theory applies to a lot more than untangling rope. If you use the right assumptions and definition, certain problems, which have nothing to do with rope, can be modeled as knot problems. If we could solve/simplify knot theory, we are this much closer to solving a range of related problems. None of which involve shoelaces.
Oh, and the GGP gave the OP a good example (by analogy): Elliptic curve cryptography. An elliptic curve is pretty esoteric stuff: "An elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is ... an abelian variety ... and O serves as the identity element." Must have seemed pretty pointless to other people when the first person worked on it. Yet, once the background theory was worked out, lo and behold, you can use them to make a pretty good encryption scheme! They were also key in proving Fermat's Last Theorem.
Re:Things like this... (Score:5, Interesting)
Back when I was going to school for my Comp Sci degree, I was force-fed a lot of calculus.
Roughly twice as much calculus as was typical, because my disinterest (and the resultant lack of success) required me to take almost every single calculus course twice.
No sooner was I free of school than I brain-dumped every single last integral, deriviative, partial derivative, chain rule, trigometric identity... the lot of it. Good riddance to bad rubbish.
And then, some time later, I was trying to make my race car go faster. The problem was optimising the suspension for maximum grip, and to that end, I had affixed linear potentiometers to my suspension so I could record suspension position during a race.
Pretty soon, I had tons of data relating position to time. Pretty graphs, but aside from max/min/mean deflection data, pretty useless.
Until I started thinking about "position to time... position to time... where had I heard that before?"
That's right - my old arch-nemesis, calculus, suddenly proved useful. Deriving that position information gave me suspension velocity, and suddenly I knew EXACTLY what suspension velocities the car was seeing in actual competition. Given that I had a device that measured shock force as a function of velocity (that's how a shock works) I could now tune shocks independant of the driver's ass-dyno.
That resulted in a HUGE leap forward in my performance.
Don't dis abstract math - you never know when it'll pay off.
DG
Re:This is so very important... (Score:1, Interesting)
There's even better examples. Such as that of Einstein working on theoretical physics while a World War was going on around him. Yet it was his work (E=mc^2) that resulted in finialising of the end of the war (the hydrogen bomb).
Re:This is so very important... (Score:5, Interesting)
A mere comment about priorities, relative importance of issues, and so forth. In any case, I was not the only one to make such a comment.
Frankly, mathematics is more important than any other issue. You just fail to realize the practical applications that mathematics has in everyone's life. The most basic reason that anyone on earth has a standard of living above that of hunter gatherers is because of mathematics; knowing seasons and how to plant crops relied on rudimentary mathematics, and modern farming relies on advanced chemistry and biology, which have as their basis the mathematics of stoichiometry and statistics. Not to mention engineering which makes heavy use of mathematics and physics in order to create the machines necessary for our massive population.
In short, I'd rather see advances in mathematics than I would the elimination of world hunger; without further mathematical and scientific discoveries, even nations with plenty will just exhaust their resources and revert to poverty and starvation.
Re:How many ways are there to tie your shoelaces? (Score:3, Interesting)
Limited only by string length,
since you can alternate slip knots with square knots, you can form coded sequences.
If you can form coded sequences, you can code both random numbers and irrational numbers.
If you can code irrational numbers, like Ummm Hey whats that double T Symbol at the icon for the story
Jackson Pollock would be proud. ( Some call it pleasing, I call it vomit )
Simple Abstract Rules (Score:3, Interesting)
not the only thing computers do (Score:4, Interesting)
"Tracing basic implications" is hardly the only thing computers do in mathematics; there is plenty of work on the "flash of insight" part, which computers have done successfully on a number of occasions. In particular, there's a long body of work on conjecture-generating systems, which don't try to prove things, but look for conjectures that: 1) would be interesting if true; and 2) seem that they could at least plausibly be true. Generating conjectures is historically a large part of the creativity in mathematics, and in some areas, computers are getting good enough at it that professional mathematicians use conjecture-generating software to get ideas for interesting problems to work on or useful lemmas to prove on the way to another problem.
This survey [vcu.edu] provides a useful overview of some of the work.