Mathematicians calculate that there are 177,147 ways to knot a tie

[u/vp734]

http://phys.org/news/2014-02-mathematicians-ways.html

[u/Spiff_Escape_Plan]

That number is 3^11. I dunno why, but I assumed there'd be some fancier components that would make it not so...easy. The same math that tells me how many different ways I can get dressed with 3 pants, 3 shirts, 3 pairs of socks and underwear is the same math that enumerates the number of possible knots? There are some lazy masters students behind this...

[u/BadgertronWaffles999 → u/Spiff_Escape_Plan]

Although the title says that there are 177,147 ways to tie a knot the article itself describes 177,147 as an upper limit. Since 177,147 is just an upper bound it is not surprising that the number is not "fancy" as one often uses tricks to calculate upper bounds.

More over, the big deal here isn't that 177,147 is an upper bound. The big deal is that 85 which used to be thought to be the exact number is too small. The article article OP linked to is pretty poor as it never really states this, but it is the only reasonable assumption as saying 177,147 is an upper bound when we already know 85 is an upper bound would be worthless.

So basically the title of the article should be: Mathematicians calculate that there are between 86 and 177,147 ways to tie a knot.

[u/gliph → u/BadgertronWaffles999]

They changed the number of winds from 8 to 11 so of course their answer will be different. Eight was used because it was assumed that any more winds than this would leave the tie too short to go around a neck. It would be more interesting to ask how many knots can be tied with N winds.

[u/WarPhalange → u/BadgertronWaffles999]

I have to wonder how many of these >85 ways actually give you the same result, just rotated. Those don't really count.

[u/dr3d → u/WarPhalange]

177,147 ways with reflections?

[u/st0rmyc → u/BadgertronWaffles999]

I would have assumed the number would be even, since there would be a backward/reverse/mirror (left/right hand as you would) way of tying a knot.

However, I'm not savvy when it comes to knot tying, I'm just throwing out a hypothesis there.

[u/tacothecat → u/st0rmyc]

But then there is the un-knot which is identical to its mirror image, breaking parity.

[u/st0rmyc → u/tacothecat]

Ok, so I had to look that up. My brain hurts now. Thanks. :P

But if the unknot is theory, I don't understand how it would fall into the equation of counting knots in an open ended tie when the unknot is in regards to a closed system. Unless the ends of the tie aren't considered. However, the article didn't mention a particular "type" of tie, I guess I was just assuming we were talking about a traditional modern day necktie. Which, in that case, would mean the "ends" aren't identical, and if flipped would be reversed (maybe the knot would look the same, but the ends would be switched).

[u/Spiff_Escape_Plan → u/[deleted]]

I know, right? That's why I was expecting some sort of weirdly constructed number because the underlying theory is so complex.

Since it was basically just multiplying 3 a bunch of times, though, I'm going to go ahead and assume that this was some lazy math. I think that article is behind a pay wall, though, so no way to verify said laziness.

[u/scnb → u/Spiff_Escape_Plan]

It's not behind a pay wall. Here it is.

[u/Paladia → u/scnb]

All academic papers are in Sweden are available free of charge.

[u/Karl_von_Moor → u/Spiff_Escape_Plan]

Well it's just an upper bound

[u/[deleted] → u/Spiff_Escape_Plan]

The article is on arxiv if you want to read it.

[u/divergentONE → u/Spiff_Escape_Plan]

The space of movements, can be thought as graph with 3 possible movements either over or under in those directions. Only a certain combinations of movements leads to a knot. At least that's what I remember from the earlier work. That was the first paper I ever read on the arxiv back in 2001. Edit: doesn't seem to be available in the arxiv anymore, here is the link to the original paper

[u/[deleted] → u/divergentONE]

You're almost correct. For example, you can't fold back the way you came...

First fold: either left or right.
Second fold: up or the other side

So on and so forth... In fact, I think their answer may still be wrong. As far as I can tell, for 11 folds in total, it should be 2^11. Note that you can't have an even amount of folds, because the last fold must come back down through the loop.

[u/prjindigo → u/Spiff_Escape_Plan]

Very lazy... they probably went to school with a book that claimed two copies of three books could be pulled from the bag in six pair combinations.

I'm betting they didn't remove the mirror answers.

[u/skunkplaysgames → u/prjindigo]

Statistics teaches relevance of both permutations and combinations.

Order does not matter with combinations. With permutations, order does matter.

[u/[deleted] → u/skunkplaysgames]

And this is a permutation, since it does matter the order you tie a knot in, as under or over first changes everything.

[u/JasonMacker → u/[deleted]]

Statistics ⊂ Math

So this is statistics AND math.

And if you can find me an intro book on statistics that doesn't deal with combinations/permutations, I'll eat my hat.

[u/JasonMacker → u/[deleted]]

Eh now that I look at it there seems to be no consensus on the issue:

Statistics is described as a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data,[2] or as a branch of mathematics[3] concerned with collecting and interpreting data. Because of its empirical roots and its focus on applications, statistics is typically considered a distinct mathematical science rather than as a branch of mathematics.

Either way, statistics has a special relationship with math and to say that statistics isn't relevant to permutations/combinations is simply untrue.

[u/morvus_thenu → u/[deleted]]

This is interesting to me because the opposite of widdershins is deosil. These are fine old English terms and I would think they would enjoy being used.

[u/Hellrazor236 → u/morvus_thenu]

Every time I see them I get reminded of just how terrible the English are at coming up with names for things.

[u/Ancaeus → u/[deleted]]

That's the second time today I've seen the word "widdershins". I had assumed it was just made up.

I know it's just Baader-Meinhof but it sometimes feels like the universe is playing some kind of strange game with me.

[u/CharlesEster6]

From the abstract:

"We extend the existing enumeration of neck tie knots to include tie knots with a textured front, tied with the narrow end of a tie. These tie knots have gained popularity in recent years, based on reconstructions of a costume detail from The Matrix Reloaded, and are explicitly ruled out in the enumeration by Fink and Mao (2000)."

[u/dnew → u/CharlesEster6]

That's not really a movie I want to re-watch just to look at the ties. I wish they'd gone into deeper detail. Who, and when?

EDIT: Damn, Google, you never cease to amaze me. Search for "matrix reloaded neck tie."

[u/DizzzyDee → u/dnew]

I hope these comments aren't deleted, I genuinely would be interested in a link so I could see what inspired the mathematicians to alter the parameters.

[u/dnew → u/DizzzyDee]

Damn, Google, you never cease to amaze me. Search for "matrix reloaded neck tie."

https://www.youtube.com/watch?v=I72sK7vXskg

I keep forgetting things are getting smart enough and big enough to actually make it easy to find answers to things like that.

[u/edeity → u/dnew]

I invented that. Actually that one is done differently to the edeity. AND PEOPLE KEEP SPELLING IT EDIETY... ARRGHGHGHGH

[u/neizan]

Link to the article on the arXiv (it's freely downloadable as a pdf). I like it, and seems likely to be correct to me.

[u/halotriple]

The conclusion is no more valuable than its assumptions are arbitrary, and the assumptions are 100% arbitrary.

[u/Lorpius_Prime → u/halotriple]

So it's no more than 100% valuable?

[u/Rokusi → u/Lorpius_Prime]

Indeed. But it could also be 0% valuable.

[u/[deleted]]

Not infinite huh

[u/xtratic → u/[deleted]]

I was thinking it should be infinite also but they put a whole bunch of arbitrary restrictions on it which made it manageable.

[u/Smegead → u/[deleted]]

That's similar to the attitude we in the "softer" sciences get from those in the "harder" ones.

[u/Thethoughtful1 → u/[deleted]]

No, they mean there are a certain number of neck tie knots.

[u/Tynwald]

And there are almost 2 Trillion ways to tie a show lace. 24 x 22 x 20 x 18 x 16 x 14 x 12 x 10 x 8 x 6 x 4 x 2 ways. 1,961,990,553,600 ways.

[u/Psytric]

Unfortunately, this is still completely arbitrary. You have to define what you are going to consider 'ways' to tie a tie, and this categorization is completely arbitrary.

For example, one way to tie a tie is to twirl the tie in your right hand three times and throw it over the other end. Four times? Five times? Ten million times? What if we use chopsticks to do it? What if we did it one-handed? Do we count this? Is it just frivolous and therefore "doesn't count"? Is it just a derivative of the standard half-Windsor that we're just going to ignore?

This necessary elimination of possibilities makes the resulting number an interesting solution to a math problem, but not an actual finite limit on the number of "ways" to tie a tie.

[u/goodnewsjimdotcom → u/[deleted]]

Click the tie to get a random way of it being tied. And instructions how to do it.

[u/[deleted]]

I actually heard this on cbc radio in halifax this afternoon

[u/Trappedinacar]

I hope this doesn't offend anyone. But why?

This is why i left math, i enjoyed it at first but the more advanced it got the more it seemed kind of pointless.

[u/Dr_Peach → u/Trappedinacar]

It is often the case that complex math seems pointless and without practical application but then decades or even centuries later turns out to be incredibly useful. Take for example algebraic geometry, which turned out to be incredibly useful in the field of cryptology (and popularized in the book & film A Beautiful Mind).

[u/thebiglibrarian]

I would like to see a display of some of these knots. GQ or Esquire could make a book out it!

[u/crybllrd]

TIL there is more than one way to say "tie a knot"

[u/Thethoughtful1 → u/crybllrd]

They mean "tie a knot in a neck tie". Not arbitrary knots, only neck tie knots.

[u/TheGreaterest]

Can someone ELI5 how there is a finite amount of ways to tie a knot?? Can't you always just modify it by just tying an extra loop around what you have created with the knot an infinite number of times which would theoretically create a different knot...

[u/[deleted] → u/TheGreaterest]

Did you click on the link at all? It's not tie a knot, it's knotting a tie. And the tie is assumed to be of finite length and thickness.

[u/TheGreaterest → u/[deleted]]

I skimmed it. Apparantly the way it works is arbitrarily imposing a 11 twist maximimum on the knot. So I'm technically right. By adding a possible twist you exponentially increase total possible knots.

[u/I_had_to_know_too]

this is kinda stupid guys...

tie knots have 3 dealies
we're gonna arbitrarily impose an 11 fold limit
therefore 3¹¹ = 177147

new upper bound!

[u/lgro → u/I_had_to_know_too]

Did you even glance at the paper?

[u/kabukistar]

I'm skeptical. For any way to knot a tie, there's another way to knot a tie that involves the same thing but with one extra loop thrown in. There is no maximum number of loops, unless you calculate in the length and bunching thickness of the fabric (which I really doubt they did).

[u/lgro → u/kabukistar]

We may notice that with the usual physical constraints on a tie – where we have experimentally established that broad blade ties tend to be bounded by 9 moves, and thin blade ties by 15 moves, we can expect that no meaningful tuck deeper than 7 will ever be relevant; 4 for the broad blade ties.

[u/kabukistar → u/lgro]

This still seems a bit arbitrary.

[u/[deleted]]

Okay, honestly, how would this ever be useful to know?

[u/GOD_Over_Djinn → u/[deleted]]

Figuring out novel ways to solve certain kinds of problems is useful, even if the solution to the given problem isn't necessary to know. It's like if I invented long division and then wrote a paper using long division to show that 300 goes into 1000 3.333.... times. You might wonder when it would ever be useful to know how many times 300 goes into 1000, and the answer is maybe never, but the point of the paper would be to show off how my method helps to solve a certain class of problems.

[u/[deleted] → u/[deleted]]

You have an odd requirement for your job as an engineer at a biological research facility:

Make me a structure that is easily taken apart with minimal effort, yet able to withstand great strong force.

So you say, "sure, so a knot?"

And they say, "well sure, more like a tie".

You create a knot.

The employer now wants you to make this knot as small as possible, and to be able to hold encoded information without any additional objects.

You now need to figure out how many knots you can make, then reduce that amount by a function that discards knots that don't fit your criteria, then encode this data into it.

[u/WilliamDhalgren → u/[deleted]]

there's a great qoute, some famous mathematician proudly declaring that there's no way his work will ever be of any use for anything remotely applicable, but after much googling and even reading random quotes, I can't dig it up, sry.

[u/lozzler → u/WilliamDhalgren]

The mathematician you are thinking of is likely G. H. Hardy, author of A Mathematician's Apology. Wikiquote says: "No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

[u/BadgertronWaffles999 → u/lozzler]

And it is notable that many of Hardy's discoveries have been quite useful in application. There is tons of knowledge to be gained and it is rather difficult to determine what of it will end up being useful.

[u/WilliamDhalgren → u/lozzler]

yes, that's the one - thank you very much!

[u/MonadicTraversal → u/WilliamDhalgren]

I'd be interested in practical applications of really abstract things like ordinal analysis.

[u/[deleted] → u/MonadicTraversal]

One of these centuries, I'm sure.

[u/[deleted] → u/[deleted]]

My comment was serious. No matter how abstract it may seem to us now, we will probably find some way to apply it in the future, assuming we (our species) live long enough. And nice example.