Slashdot Mirror
Major Advances In Knot Theory
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."
but I'd hardly call it an age old question. Never heard of it.
How many ways are there to tie your shoelaces? The answer is very easy ... knot.
If enithin kan gow rong it whil. (Murfey)
42
Knot many.
Revealing the full... superstructure may be the work of a generation.
..assuming computers cease making any new advances.
Mathematicians do rely on their ability to spot patterns and sense implications that no computer can likely sift for today. But this will not always be the case.
-- thinkyhead software and media
Loop and Swoop
Bunny Ears
Where's my Nobel
So, can we abbreviate this "knot theory" to "!theory"?
Anybody want my mod points?
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...
And how many mathematicians do you know? The moment this question is even close to being answered, one of them will go off and figure out an even harder question to answer.
"Well now they we have the answer in 4 dimension spaces, we will not rest until we can do it in any prime dimensional space."
I kid because I love.
Could someone please point to relevant information on the topic for why this matters? The article seems to be a a lovely history of a couple of polynomials, but does anything here warrant
The payoff from such work may be profound.
to non-specialists?
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.
... and relies on the cunning use of a rabbit, tree, and hole to tie shoelaces.
It must have been something you assimilated. . . .
The world has been in far worse situations than it's in now. The transient problems of immediate political and social realities shouldn't stop a few people from investigating nature's deep questions via science and mathematics.
Oh really? Would you also say studying topology in general is unimportant? Why or why not? Since you're able to discern which branches of mathematics aren't "important", you're clearly a mathematical authority, so please feel free to enlighten us.
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.
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
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
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 )
the inventor of the shoe lace could be the answer to all our four dimensional space quetions?
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.
Reading code is like reading the dictionary - you have to read half of it before you can go back and understand it.
....untie the knot my cat did with the mop?
This just in: Physicists have just now revealed that String Theory has nothing to do with the fabric of our universe, and everything to do with teaching toddlers how to tie their shoes.
This is exactly why nobody asked you for permission to go about their lives.
but it will never be able to explain why anyone would want to "tie the knot."
+1 FUNNY
Man, I haven't posted in years... but there's a great book by this title written by two mathematicians. They talk about the topology of knots as well as the history of ties. Which actors/celebrities wore what tie knots, etc.
I can't seem to locate my copy at the moment, but from what I recall, there are an infinite number of potential knots, but they are classified by the number of sequences in them. And within a certain number of steps, (I think 5) there are 85 possible ways to tie a tie. Then they rank them by symmetry and a copule other criteria.
I recommend it to anybody who is interested in this subject. It's out of print, but it's still possible to find a copy for sale online.
I can't believe I got moderated as a troll
Why? You made a whiny, irrelevent complaint that dismisses the role of pure research in the larger advancement of our knowledge of how the universe works... the very sort of thing that always plays a role in advancing our ability to make more efficient use of energy, more realistic predictions about the behavior of complex systems, and more innovative technological use of things we think we have already fully, or most effectly exploited. This whole "the human race is incapable of doing two things at once" BS never ceases to amaze me. How do you even get out of bed in the morning? Make coffee... take a crap... which to do first? Gaah! I'm paralyzed! Which is the most important fish to fry?
In other words, you're scare mongering and - if we can assume you have a passable IQ which would suggest you might know better - clearly trolling. And, voila, you were thusly modded.
Don't disappoint your bird dog. Go to the range.
Suppose you tell us all how solving this knotty problem will help anyone or anything.
Let's pretend we're in the early 1700s. Leonhard Euler is writing the first ever paper on a field of study called Graph Theory. Simply put, he's figuring out answers to questions about how to arrange circles and lines. Meanwhile, there's fucking WARS going on (Polish succession is going on concurrent to writing this paper; Seven Years' war happens a couple decades later). There are goddamn wars on Euler's front door, and he's writing papers about lines and circles?! What a prick.
Oh, by the way, without Euler's work we wouldn't have computers, organized roads, efficient data models, efficient sorting algorithms, or countless other instruments that are critical to today's society.
Don't trivialize work that you don't understand.
Let me introduce you to ^W.
It's a great tool for those writing pseudo-ironic posts who are, at the same time, concerned with the preservation of the valuable resource of ones and zeroes...
Without x, we would not have y, therefore it's all good.
I'm just wondering. One never knows with math.
The answer is obvious: there are infinitely many ways to tie shoelaces. I'm pretty sure I can prove this by mathematical induction in no more than half a dozen steps.
Unless you limit the length of the laces, of course, but then the limit will depend on the physical properties of the laces (not just length but also thickness and so forth), at which point the problem loses its mathematical purity and becomes more of a physics problem.
Cut that out, or I will ship you to Norilsk in a box.
Wait... so you're posting on Slashdot, claiming people doing difficult math research are wasting time?
If you think there's something more important that they should do instead, maybe YOU should go do it. It may come as a surprise, but the rest of the world isn't here to serve you. You'll just have to live with the fact that other people do stuff that's important to them, and most of the time that doesn't overlap with what's important to you.
In other news, an algorithm was discovered to determine how many angels can dance on the head of a pin.
I prefer the "velcro" theory.
It's all history, man. -anon
Im more worried about the knots that can be tied but not untied. My shoes are about to get the Alexander's universal knot solution.
Just open a draw containing various cables that has been left for a few months - none of them knotted when you put them in but you can bet when you take them out they'll be more knotted than a knotty thing
--- Users are like bacteria -> Each one causing a thousand tiny crises until the host finally gives up and dies.
It was whiny, it was irrelevant (how did it relate to knot theory?), it did dismiss pure research -- as if pure research scientists should drop everything and join the war effort, it was scare mongering (as if the only thing we should be thinking about is politics and war)...
Lastly, it is the priorities you're whining about that are irrelevant.
Let politicians work on politics, soldiers work on war, and mathematicians work on math.
If you weren't whining about priorities and politics, then what on earth were you talking about?
I'm getting too old for this slashdot shit, I guess.
+ 1 insightful
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.
wow. mathematicians make such trigger-happy moderators.
modded troll in 3, 2, 1...
Requiem for the American Dream
In 1988, physicist Edward Witten of the Institute for Advanced Study in Princeton turned Jones' single invariant into a whole zoo of new invariants using a link he found between Jones' method and quantum theory.
Does this mean that Schrodinger's cat now wears a tie with a very, very complicated knot? This could be a revolution in the mathmaticians annual fashion contest!
Any life is made up of a single moment, the moment in which a man finds out, once and for all, who he is.
Obama - I see him as an overhand knot guy.
McCain - a velcro guy for sure.
... if that's your best, your best won't do... - Twisted Sister
I can honestly say that I find this is the most negative piece of software in the K Desktop Environment.
What are the implications for hyperbondage?
Let me introduce you to ^W.
Does that work as well as "Bush^h^h^h^h"?
She's discovering the joys of shoelaces now, and you want to talk about knots.. Boy, oh boy. She's gonna be a mathematician for sure!
Karma: Chameleon - mostly influenced by bad '80s New Wave music
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
Want to learn about race cars? Read my Book
A Ph.D. will now be required to join the Boy Scouts.
Just saying that we have some rather larger fish to fry at the moment, and this seems sort of peripheral.
So, what's your suggestion? The math guys should stop their research and start stating their opinion about the unemployment and mortgage problems?
Maybe the whole /. would be peripheral using your way of thinking.
Any life is made up of a single moment, the moment in which a man finds out, once and for all, who he is.
This whole "the human race is incapable of doing two things at once" BS never ceases to amaze me. How do you even get out of bed in the morning? Make coffee... take a crap... which to do first? Gaah! I'm paralyzed! Which is the most important fish to fry?
Er... are you saying there's a way to take a crap and make coffee at the same time? I'm curious, but at the same time I don't think I want to know...
Let politicians work on politics, soldiers work on war, and mathematicians work on math.
I have to say that I think current affairs would at least be more interesting if we had scientists work on politics and politicians work on research.
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?
You're a computer geek and NOT a neurosurgeon? Well then, I'm going to have to cancel my thursday appointment.
My original post was actually meant to be funny, but... whoosh!
When I read things such as this I like to take a moment to let the dumbfounded feeling wash over me.
This is just not that important.
You only say that because you have yet to be involved in a serious shoe-tying accident.
...abbreviate cutting-and-pasting the first paragraph of the article as the Slashdot article to !summary.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
I have a simple proof of such a knot, but the margin contains too few shoelaces to contain it.
PS: When asked to pull yourself up by your bootlaces, you can now ask for the Jones Polynomial required to do this.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Back when I was going to school for my Elementary School diploma, I was force-fed a lot of arithmetic.
Roughly twice as much as was typical, because my disinterest (and the resultant lack of success) required me to take almost every grade twice.
No sooner was I free of school than I brain-dumped every single addition, multiplication, subtraction, division, counting... the lot of it. Good riddance to bad rubbish.
And then, some time later, I was trying to make my paycheck go farther. The problem was optimising the spending for maximum personal happiness, and to that end, I had collected all of my receipts so that I could record where I was spending my money during the month.
Pretty soon, I had tons of data indicating where my money was going. Pretty numbers, but aside from a few expensive items, pretty useless.
Until I started thinking about what I could do with a set of numbers.
That's right - my old arch-nemesis, arithmetic, suddenly proved useful. Summing the money spent in different categories gave me totals, and suddenly I knew EXACTLY where my money was going in an actual month. Given that I had measured how much money was spent on each purchase (that's how receipts work) I could now properly budget my spending.
That resulted in a HUGE leap forward in my quality of life.
Don't dis abstract math - you never know when it'll pay off.
AC
Er... are you saying there's a way to take a crap and make coffee at the same time? I'm curious, but at the same time I don't think I want to know...
It's really quite simple. You make sure the coffee machine and coffee are in reach of the toilet. Alternatively you wear a diaper. Personally I just brush my teeth while on the toilet since that gets me the efficiency boost without joining the kitchen and bathroom.
My coffee pot is on a timer so it's already brewing as I take care of other business. next?
Studying how to tie shoelaces is hardly what 'math guys' do. It's worthy of a slashdot article but I'll wager the article is written by a couple of students who'd had too much beer.
Knot theory has plenty of potential applications that do not involve shoelaces. It is used in molecular biology, statistical mechanics, and particle physics as well as other branches of mathematics.
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).
http://www.sierratradingpost.com/p/,83598_Caterpillar-Groundwork-Wellington-Work-Boots-Steel-Toed-For-Men.html?cm_mmc=PaidPlacement-_-Shopzilla-_-WBIZ8-_-Caterpillar_Groundwork_Wellington_Work_Boots_-_Steel-Toed_-_For_ MY WAY!
"Windows is like the faint smell of piss in a subway: it's there, and there's nothing you can do about it." - Charlie Br
They would have. Maybe just not right then. That puts us that far behind where we are and even less able to deal with problems.
Xavier Rabourdin for president 2012
Being a graduate student in mathematics , I can safely assert that knot theory is actually a significant area of modern mathematics. There are numerous textbooks about it.. If you read the article you would know that Jones & Witten received a Fields Medal, which is the most prestigious award in mathematics, for their work on classifying knots.
Why is this modded "funny"? This is a serious question. Does anyone actually know the answer?
But I digress. If some mathematician can come over with a theory, and sort this mess of knots out, I'm buying the beer.
And pizza
Schroedinger's Brexit: The UK is both in and out of the EU at the same time!
Who's going to join the BOINC project?
I thought this was the sequel to String Theory.
Hundreds of thousands of innocents dying in the middle east because of corrupt politicians in the whitehouse
Right, because the foreign insurgents coming in from Syria and Iran, using Iranian-supplied cash and weapons, killing them with market bombs or taking them out back and shooting them aren't a factor. Most of them are killed Eeeevil Coaltion Troops.
Hundreds of billions more being paid to wealthy wallstreet cronies
Let's see... those would the cronies who've made their largest campaign contributions to Democrats? Who leveraged themselves and their investment banking customers into ruin by overreaching on investments built around highly risky, undercapitalized mortgages backed by Fannie and Freddie... whose two largest recipients of campaign donations were Democrats (Obama and Dodd)... and whose financial shakiness, despite being pointed out directly by the White House in congressional hearings two years ago, were shouted down by the Democrats chairing the committee (see Barney Frank, et al) who said, "never mind, things are just fine with those institutions, you scare-mongering Republicans."
And the responsible politicians are still in power
Yup, and they're about to get an even larger majority in the house and senate, and a president who will no longer even pretend to have an interest in vetoing the incredible flow of pork and government-in-your-life that's about to spew out of Pelosi and Reid. Won't that be fun!.
Don't disappoint your bird dog. Go to the range.
hahaha
Man I hope that was a typo. Is it possible you've actually gone through life thinking it was called a "draw"?
Yes, this is important.
What do you think where new ideas on saving the world or building a better one will come from? TV studios? Politicians? Hollywood?
Research like this is the foundation of all progress. Note: Not this one specifically, I said "like" this. A lot of the things that you probably wouldn't live very well without started out as ideas with no visible use.
Assorted stuff I do sometimes: Lemuria.org
This whole "the human race is incapable of doing two things at once" BS never ceases to amaze me. How do you even get out of bed in the morning? Make coffee... take a crap... which to do first? Gaah! I'm paralyzed! Which is the most important fish to fry?
You mean you can do both at once?
For those less interested in theory, and more interested in choosing a lacing pattern and a good knot for their shoes, I recommend Ian's Shoelace Site.
What's remarkably funny is that I thought *exactly* that when I saw the string of ^H. ^W is a huge improvement, but I'm thinking the comment could have done with a ^U instead.
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.
Man, you don't kid around with your car analogies.
then you are an idiot.
programming solutions often can use mathematics theorems to produce very efficient algorithms.
Don't trivialize work that you don't understand.
In other words, don't be a Palin. No one likes a Palin.
The following statement is true
The preceding statement is false
uhhh....
the definition of a Knot is something that cannot be tied or untied.
only a tangle can be ties and untied.
Someone with a heavy Massachusetts accent would call it a 'draw'. Similarly, 'Korea' is pronounced like people in the rest of the country would pronounce 'career', and vice-versa. It's a little surreal for a transplant, such as myself.
-Mike
I'm sorry; I don't know what I was thinking!
>>If you use the right assumptions and definition, certain problems, which have nothing to do with rope, can be modeled as knot problems
thank you posting clearly, I can never figure out what some of these theory's do, but just as soon as you posted what you did, I completely understood the basics of game theory, I'm off to learn more.
if you see me, smile and say hello.
He's right.
http://en.wikipedia.org/wiki/Knot_(mathematics)
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
OK, but *apart* from computers, organized roads, efficient data models, efficient sorting algorithms, and countless other instruments that are critical to today's society, what has Rome^h^h^h^hresearch ever done for us???
I am anarch of all I survey.
Hey, who let Grandpa McCain on the internets?
I wish we would move onto ^X
I'm sick of the ^H and ^W
Don't be apathetic. Procrastinate!
Yeah, and maybe then we wouldn't have the tools to even consider solving knot theory problems and we could go back to ending wars and eliminating human suffering. Stupid, Euler.
Also, why isn't is spelled Oiler? Was Euler some sort of anti-drilling-save-the-tress nut? Didn't he know how important oil is to our country?
>>> That larger mathematical theory, if it exists...
Please make sure you never post again on mathematics.
From the article:
The payoff from such work may be profound. Knot Floer homology has higher-dimensional analogues that can reveal the structures of three- and four-dimensional spaces, and it is expected that Khovanov homology does as well. Four-dimensional spaces have been especially difficult to understand. Higher-dimensional spaces have enough room that complications can work themselves out, and lower-dimensional spaces are so tight that complicated behavior canâ(TM)t emerge in the first place, but in four dimensions, almost anything can happen. "Understanding four dimensions would be especially exciting," OzsvÃth says, "because thatâ(TM)s the world we live in."
In short, science speaks the language of nature which is maths. A greater understanding of four dimensional space is fundamental to the advancement of science. The work here is deep and profound in a way that is not readily apparent, but is essential in our advancment of knowledge and science.
Insofar as a rigorous math proof produced by a human is operating in a formal system (showing that its conclusions logically follow from its premises), it's subject to the same limitations.
Unless you're arguing that there are correct proofs that depend inherently on hand-waving that could not be made more rigorous, which I think few mathematicians would accept.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
I wouldn't rule it out, as GP said maths is tricky like that. I'm also intruiged if someone can answer it, and would be impressed by the proof required (unless of course the definition of a knot excludes them).
"Mathematicians have been puzzling over" how to tie their shoelaces "for a century or two"??? Think of what humanity could have achieved if they actually spent that amount of time doing something USEFUL. It's just more proof that shoelaces are bullshit!
How about a closed loop with a knot already in it? No way to untie without cutting the loop.
Just trust us on this and Fruit Fly research okay?
So, I think that your statements are an accurate assessment of things like Computer Algebra Systems. Such systems approach mathematics in a way similar to how humans have traditionally tried to solve mathematics. However, there are other ways of doing mathematics with computers. Such as various systems of simple abstract rules. I'm not saying it will necessarily lead to breakthroughs in traditional areas of mathematics, but, it is one of the few areas of research that is truly trying to approach mathematics in computer-centric way.
I was responding to the claim that it's somehow been "proven" that computers can't do mathematics as well as mathematicians, presumably because of the negative results about formal systems in Goedel's incompleteness theorem. I was pointing out that human mathematicians manipulating formal systems (which is what mathematics consists of) are subject to the same negative results, so this doesn't really prove anything one way or another.
Now whether computers in practice can do interesting mathematics is of course an open problem.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
"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 provides a useful overview of some of the work.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
successful troll is successful
3/10
A rather old problem. The curious thing is that knots are formally described as closed loops, but Alexander 'solved' the problem, by "cutting the Gordian knot".
What's in a sig?
Man, a few days ago, I fell and hurt my side, and whenever I laugh, my side hurts. No joke. So I'm reading this, alternating between laughter and pain, trying to suppress the laughter. Funny post.
This ad space for rent.
Slashdot having some issue's as well..
You only say that because you have yet to be involved in a serious shoe-tying accident.
You insensitive clod! My brother was in a shoe-tying accident! To this very day, he can only wear sandals, and to spare his nerves the rest of us only wear socks inside the house. We never did find his left ear and his right pinky...
i'd hit it so hard, if you pulled me out you'd be the king of britain [bash.org]
1) Tying your shoelaces (but of course no one cares)
2) Studying supercoiling of DNA (how it wraps itself up into a small space yet still wriggles enough to present all of it's length at short notice for interactions with cells' other mechanisms)
3) The geometry of three dimensional space (all closed oriented three dimensional spaces can be constructed from knots and the three dimensional sphere! So knot theory has major applications to 3D geometry)
4) The geometry of four dimensional space (for example, surfaces in 4D spanning between knots can be used to specify exotic smooth structures. The existence of such shocked the world of geometry in the 80's)
5) TQFT, Mirror Symmetry, Quantum Gravity etc (the tools developed in and around knot theory are one facet of a huge push in mathematics to forge a better understanding of some of the deepest ideas in modern theoretical physics)
It's not all just "brain-wanking".
assdino?
Ewwww.....
The more people I meet, the better I like my dog.
I'm no mathematician, but I think that all knots (in the traditional definition, ie one string with two ends) can be undone in theory by taking one end and using the string as a path, feeding the end back along its own route; in practice, friction is a problem~
I mod down anyone who says "I will be modded down for this", regardless of the rest of their comment
I thought there were just two: separately, and together.
Correct! We need to be reminded, that not everyone has lost her or his sanity yet.
Je me souviens.
You might pronounce it that way, but you certainly wouldn't write it.
yeah
You seem to be rather full of yourself.
Dude, get a grip! Don't try to convince people who are apparently interested in this knot stuff, that it is irrelevant, especially in their own forum. That's even a bigger waste of time than what you're more or less blaming them of. Didn't you have a large fish to fry?
Now, this story is something to be told for the unwilling-to-learn-(kids|adults)! Too bad it's too late considering the recent debt problems.
That was a lot of irrelevant text just to say that budgeting IS math. Imagine, something as unimportant as currency actually needs to be counted. I'd rather just assume I'm always rich and never waste money.
Applied elementary calculus is abstract math? I didn't know comp sci majors were this retarded.
"limited only by string length". Exactly. "If you can form coded sequences, you can code both random numbers and irrational numbers". Well, only sort of - what you'd have to do is come up with some sort of coding that allows you to *reference* values - so for instance, being able to encode a square-root sign followed by a 2, or for getting pi/4, or so on.
Because you're never gonna get a string long enough to actually spell out sqrt(2) or pi directly.
Of course, once you go that route, some fool is going to Godelize it and hand you a shoestring that says "This number can't be written out on a shoestring". ;)
At some point in school I was delving in the deep archives of the library and stumbled across a translation (from Arabic) of an really old (13th-century?) book on long multiplication, as a secret method which gave you a big edge in trade over the saps who didn't know the secret. Kind of like the guys who applied minimal surface theory to derivatives modeling and laughed as the rest of us blew $60 trillion buying their soap bubbles.
Math is a powerful thing. Of course, it's better to be the guy who owns the mathematicians, rather than the guy who knows the math.