"The most common lacing method, termed criss-cross lacing, is also one of the strongest and most efficient, but is not so well suited to certain dress shoes, such as Oxfords, because the central shoelace crossovers prevent the sides of the shoe from coming together in the middle. For such shoes, methods such as straight lacing are better suited. Many shoe lacing methods have been developed with specific functional benefits, such as being faster or easier to tighten or loosen, binding more tightly, being more comfortable, using up more lace or less lace, adjusting fit, preventing slippage, and suiting specific types of shoes. One such method, patented in 2003 as 'Double helix shoe lacing process,' runs in a double helix pattern and results in less friction and faster and easier tightening and loosening.... One of the most popular decorative methods, checkerboard lacing, is very difficult to tighten or loosen without destroying the pattern. Shoes with checkerboard lacing are generally treated as 'slip-ons.'"

From the Wikipedia article

"Shoelaces."
"An Oxford shoe with straight lacing" — cc ASuitableWardrobe.
Straight-laced should not be confused with "straitlaced," which means

*tightly* laced and originally referred not to the laces of shoes but bodices. The figurative use means "Excessively rigid or scrupulous in matters of conduct; narrow or over-precise in one's rules of practice or moral judgement; prudish" (OED).

## 51 comments:

2 trillion combinations?

I think he messed that up a little bit. The best you could do is 12! unless you put the lace through the hole twice. That is a bit less than 500 million combinations.

You would get some really stupid combinations too. If you allow the lace to go through an eyelet more than once you have to allow for infinite combinations.

There is no getting to 2 Trillion ways.

I've seen original pairs of combat boots from WW1 where the laces were knotted to the lower outside eyelet, then laddered up the eyelets horizontally. The other ends of the laces were then wrapped around the top of the leather upper and slip knotted on the outside. They were then covered up with puttees. I tried it out, and once you get the hang of it, it's quick and effective. They will loosen if you don't use puttees or gaiters though.

Free Association: Reminds me of a "Colombo Episode" with Robert Culp, which hinges on how people tie their shoe laces.

Anyone who tries to find the two trillion combinations should be put into a straitjacket.

12^12 is a touch under 9 trillion.

I don't see how he got to 2 trillion combinations.

12^12 would still be wrong.

It is more interesting to figure out how the writer screwed up the math than whatever they are talking about in the article.

If this double helix shoe lacing method is patented, how does the patent owner make money?

13! is 6.2X10^9 not 2X10^9 so not off by 1...

UGLY shoes...

I don't see how he got to 2 trillion combinations.

Because whomever wrote this has no math background.(to be clear -- I'm not talking about you Achilles)

MadisonMan said...

(to be clear -- I'm not talking about you Achilles)The rest of my classmates would say I don't really have much of a math background. =P

But the 2 Trillion value is truly a magic number...

If you're curious about this stuff, Ian Fieggen's site is worth a look. Here's how he got to (approximately) 2 trillion:

https://www.fieggen.com/shoelace/2trillionmethods.htm

"If you're curious about this stuff.."Nope, I am not.

The quote says "there are, in fact, almost two trillion ways to lace a shoe with six pairs of eyelets," which sounds pretty wrong to me, but I guess if you have a long enough shoelace maybe the math adds up. Because if the shoelace is endless then you get into all that infinity shit where math doesn't even have to add up right.

I mean, they say Pi doesn't have an end decimal, it just keeps going and going. But if a number doesn't end then how can it really be a number? Because, like, the number 'two' is the answer to 'one plus one', but what two numbers even add up to Pi? See what I mean?

It's bullshit calling it a number. It's like when they put accents and umlauts and hats and shit on top of letters -- they're not even that letter anymore, they're a letter with a fucking hat. So maybe Pi is just a number three with, like, an accent or umlaut or hat or shit, that would at least make more sense.

I have a hard time trying to understand infinity shit, because if something doesn't have a beginning or an end then we should have all kinds of infinity shit just lying around everywhere, because it's always been there and it will never go away, right? I mean, we should practically be tripping all over that shit.

But, like, even rocks erode. But then even that gets weird, because if all rocks erode, then all rocks are only getting smaller, so where do big rocks come from now? I mean, eventually we'd be all out of big rocks, but there still are plenty around.

And that would mean in ancient times the rocks were a lot larger. Which makes a lot of things make more sense, really. Like, when David killed Goliath with a rock, that rock was probably a lot bigger than the rocks we have now, so it makes sense that it would kill a giant. In the future when all rocks are a lot smaller that shit gets more difficult.

I post my shit here.

Can't imagine there are that many permutations.

Shouldn't it be 12!, assuming 12 eyelets? 12x11x10x9x8x7x6x5x4x3x2= Anyone? Anyone? Sloan?

The Terry Moore TED talk blew me away. I had been tying my shoelaces wrong since I learned to tie my shoes

They're shoe... laces.

Does order matter?

Does orientation matter?

How long are the shoelaces?

How colorful?

Texture?

How large are the eyelets?

How many pickled peppers did Peter Piper pick?

"There are, in fact, almost two trillion ways to lace a shoe with six pairs of eyelets."But only 50 ways to leave your lover.

Sometimes our universe can be so disappointing.

The best you could do Is calculate permutations, and that comes nowhere near 2 trillion.

>>The best you could do is 12! [a point repeated a couple of times by others]

By that logic, I think it should be 12!/2, since each possibility could start at either end.

What happens, however, if you look at where the lace crosses itself: Which link goes over and which goes under? If you count the over/unders as different lacings, you get to a much bigger number (and what looks like a much harder computation). Each possibility that includes any crossings has a number of different variations.

--gpm

Jedag said...

If you're curious about this stuff, Ian Fieggen's site is worth a look. Here's how he got to (approximately) 2 trillion:

https://www.fieggen.com/shoelace/2trillionmethods.htm

Now that is some good stuff. I stand corrected.

n! x 2^n is just under 2 trillion for n = 12.

I remember going up on the bottom two holes in school because sometimes our friends would grab the bottom lace on your shoes and wrench it out forcing you to spend a couple minutes resetting your laces.

n.n said...

They're shoe... laces.

Does order matter?

Does orientation matter?

How long are the shoelaces?

How colorful?

Texture?

How large are the eyelets?

How many pickled peppers did Peter Piper pick?

---------

I can tell you that "order" and "orientation" are very important in magnetism. Faraday -- no less -- noted how everything misbehaved in his own magnetic fields. When he realized that Earth's own magnetic field might have grown some discoverable properties, well then -- he really got curious.

>>Now that is some good stuff.

I see Fieggen covered my two points: that the number should be halved because the lacing could start at either end and that the number increases if you look at the over/under crossings. I didn't get around to the point of whether you go through the eyehole from top to bottom or bottom to top.

--gpm

@Althouse, you motivated me to hunt around until I found this web site, which actually teaches one how to tie straight laces on Oxfords. Here I am in my seventies, and I've been tying my Oxfords wrong all these years.

I mean, they say Pi doesn't have an end decimal, it just keeps going and going.The same is true for an uncircumcised dick.

...

what two numbers even add up to Pi? See what I mean?Try these: 1 + (pi - 1)

Without a moment's reflection I challenge that 2 trillion figure.

Six pairs of eyelets, not twelve.

If you are interested, 4chan Guy, my friend, things can get even crazier. For instance what does the sum of 1/2 + 1/4 + 1/8 + 1/16 + ... add up to? It's easy (okay, relatively easy) to prove that the sum of the series adds up to 1, but hold on a second. No matter where we stop to look at the series, say we stop it a 1/1024, it is still less than 1. Only when we run the series out to infinity (for the benefit of other mathematicians, I am simplifying here) do we actually get the sum to equal 1. But we can't get to infinity, can we?

Still it does add up in a hurry, so I think I am fundamentally wrong.

Lacing is cool, but so is tying the bow know. I have done a three loop bow for years now. Nobody has ever noticed, or at least nobody has ever once commented to me about my three-loop bow shoelace knots.

I did five loops for a while, but it was troublesomely unstable. I made seven loops in my shoelace knot once, but I became immediately aware that this was so radical as to invite utter chaos to overtake the world, and I have never done so again.

Bow knot. I know.

6 to the 6th power is about 46,656.

Is the shoe designed to have more permutations? How?

I would be interested in knowing how the number can be so high.

Rehajm: The weak form and the strong form of the knots described in the TED talk are known to sailors as reef knots.

Could Wikipedia be wrong? Could CNN be wrong?

In a post-modern age, everyone is wrong.

How many ways can Althouse lace her dirndl ?

Loose on top, tight in the middle, loose on bottom.

I’d say 3 ways, tcrosse. Forget about perstrubations.

Francisco D said...

6 to the 6th power is about 46,656.

Is the shoe designed to have more permutations? How?

I would be interested in knowing how the number can be so high.

12 holes = 12!. So the first hole you have 12 options. The second hole 11 options and so on so 12 x 11 x 10 x 9...

12! = ~479,000,000.

Then if you add up or down on each hole you have 2^12th power which is 4096. That is the part I left out.

479,000,000 x 4096 = 1.9trillion and change.

If you do it this way you will end up with half of the lacings being exactly the same as the other half but just starting at opposite ends of the order. Another half will just be mirrors because they started on different sides but end up the same.

In the end you have ~1.9trillion paths to ~490 Billion different lacing combinations.

Big Mike said...

... what two numbers even add up to Pi? See what I mean?

Try these: 1 + (pi - 1)><

When I was a freshman in high school there was a cute little blonde cheerleader I had a crush on, because I was in high school and she was cute and blonde and a cheerleader. She was always smiling, even in math class, which was kinda weird, but she was good at math.

Which doesn't seem fair, that she was cute and blonde and a cheerleader and good at math, that's the kind of high school girl who is gonna date a college dude. Probably a college dude who would wear a black Members Only jacket and smell of Polo.

Anyway, she would do that thing where she would play with the eraser end of her pencil against her lower lip, and it was like she didn't even know she was doing it, it was like she didn't know that any dude seeing that didn't see the pencil as a pencil anymore.

And she always had to re-tie her shoes a lot. I don't know if she just wasn't good at tying her shoes, or maybe she needed the laces just right, some chicks are like that about things, but she would always stop and re-tie her little white LA Gear sneakers.

Which may not seem like a big thing, but it was the way she did it: when she bent over to re-tie her shoelaces she bent down at the waist. Like, her legs were straight, and she was bent over, and how could a high school boy not stare at that ass?

I mean, on 4chan you can see pictures of chicks spreading their ass cheeks and showing their assholes, but somehow this was even better, with her ass sticking up in those stone-washed Guess jeans, or -- dear Lord -- her little red cheerleader skirt.

I remember walking behind her down the hall when she stopped and bent over to re-tie her shoelaces: it was like I was hypnotized, her ass could've got me to do anything. Then I noticed our math teacher at his open door, and he was staring, too. Which I thought was a little fucked up at the time, but now that I'm older I get it. Maybe it's still a little fucked up, but I get it.

Because sometimes nothing is better than that moment, even when you are older and can go to a strip club and see a naked chick in high heels spreading her ass cheeks and showing her asshole. I just hope to God that when she was in high school she didn't show her asshole to some college dude wearing a black Members Only jacket and smelling of Polo, I think that could actually break my heart.

I post my shit here.

@Achilles, glad you liked it. A little mathematician humor that not everybody gets.

Big Mike said...

@Achilles, glad you liked it. A little mathematician humor that not everybody gets.Our calculus teacher way back when gave us a test in first quarter calculus on limits. Told us all the answers were 0.

Then laughed at us.

Math people have a dark sense of humor.

6 to the 6th power is about 46,656.

What's the use of the wordaboutthere?6 to the 6th is exactly 46656. There's no about about it!

I lace my shoes like the ones in the picture because I like the way it looks.

It's outrageous that there is a patent on a type of shoe-lacing.

Everybody's going off on the 2 trillion, nobody's going off on the patent!

Is there a patent on patent leather shoes?

Because otherwise I don't know what they are talking about.

Loose on top, tight in the middle, loose on bottom.Are we talking shoe laces, or the ideal women?

Am I missing something or does the pair of shoes pictured have five pair of eyelets per shoe?

Those really are hideous shoes.

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