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Knots are cool. Technically, knots are fastenings but they can be so much more. They can be stoppers to prevent the loss of a rope (though I guess this is still a type of fastening) or to mark distance along a rope (hence “knot” as a maritime unit of speed). They’re decorative and sometimes exclusively so, as artwork.

One of the weirdest things about them is that they’re not real. They’re not an object but rather a distortion of another object—a rope or a string or something. And it’s not even about what that other object is—a knot can be a tangle of anything linear.

They’re a study of the intersection between an ordered and disordered state. They’re what, to paraphrase a saying from Dieter Rams, we might call “orderly confusion”.

They’re like fire in its transience or a battery in its potential energy. They’re in a sort of quantum state, particularly evident in those cases, often accidentally discovered, where you need only gently pull one end to disengage the knot. It’s literally a magic trick: you just pull and poof, it’s gone, and you’re left confused as to how it ever really existed.

Knots can also be considered a type of technology, and one of the purest, for as aforementioned, it’s not an object but instead a method. Once you know how to tie the knot, you can produce this value anywhere.

It’s kind of amazing how many ways there are to distort a straight line into something better.

A Year of Knots

Recently I came across an article on IDEO about this artist, Windy Chien, who learned a new knot each day for a year. She shared the results on her Instagram and later, in her new book, A Year of Knots.

Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO
Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO

I always find it fascinating when people take the time to learn a discipline like this in such depth. It’s impossible to imagine this many permutations of a simple rope. They’re all beautiful studies in applied geometry, at once both this craft (think of the weaving traditions from around the world) and yet also so detached from that application as these detached, individual “studies”.

A spread from Windy’s book, The Year of Knots
A spread from Windy’s book, The Year of Knots

Conway’s Knot

Windy’s work is an artistic inquiry, but one of the cool things about knots is how many ways there are to study their simple complexity:

Lisa Piccirillo, a graduate student at UT Austin, just made headlines for her proof of Conway’s knot problem, a mathematical puzzle that’s remained unsolved for the past 50 years.

And the craziest part? She solved it in less than a week.

Lisa Piccirillo
Lisa Piccirillo
“The Conway knot is a mathematical knot with 11 crossings discovered by mathematician John Horton Conway. The knot is so famous that it decorates the gates of the Isaac Newton Institute for Mathematical Sciences at Cambridge University...”

— VIA SMITHSONIAN MAGAZINE

What makes a knot “stable”?

Here’s another mathematical study of knots.

Earlier this year, MIT professors Jörn Dunkel and Mathias Kolle, with their PhD students Vishal Patil and Joseph Sandt, published results in the journal Science from their research on knot stability. They developed a mathematical model that can predict this stability, “based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight.”

As this graphic shows, the model displays the pressure on each part of the rope with color. Notice how the color changes as the knot is pulled tight.

Once they had a robust model, they could then use it to simulate other new knots. They discovered that a knot’s strength is related to its “circulations” (“a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow”) and certain “counting rules": basically, the number of times it crosses over itself and twists.

It’s pretty incredible how much there is to discover in something that’s seemingly so intuitive and simple, but yet surprisingly complex.

Knots are artistic, meditative inquiries, as Windy’s work shows, complex mathematical problems, as the aforementioned mathematics research reveals, and ultimately, great design applications in how they exist at this intersection of artistic, technical, and utilitarian ideals.

Knots are ultimately “designed”: they’re a simple form to solve a simple function and their original and current use is utilitarian.

Ideas

Knots

Knots are cool. Technically, knots are fastenings but they can be so much more. They can be stoppers to prevent the loss of a rope (though I guess this is still a type of fastening) or to mark distance along a rope (hence “knot” as a maritime unit of speed). They’re decorative and sometimes exclusively so, as artwork.

One of the weirdest things about them is that they’re not real. They’re not an object but rather a distortion of another object—a rope or a string or something. And it’s not even about what that other object is—a knot can be a tangle of anything linear.

They’re a study of the intersection between an ordered and disordered state. They’re what, to paraphrase a saying from Dieter Rams, we might call “orderly confusion”.

They’re like fire in its transience or a battery in its potential energy. They’re in a sort of quantum state, particularly evident in those cases, often accidentally discovered, where you need only gently pull one end to disengage the knot. It’s literally a magic trick: you just pull and poof, it’s gone, and you’re left confused as to how it ever really existed.

Knots can also be considered a type of technology, and one of the purest, for as aforementioned, it’s not an object but instead a method. Once you know how to tie the knot, you can produce this value anywhere.

It’s kind of amazing how many ways there are to distort a straight line into something better.

A Year of Knots

Recently I came across an article on IDEO about this artist, Windy Chien, who learned a new knot each day for a year. She shared the results on her Instagram and later, in her new book, A Year of Knots.

Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO
Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO

I always find it fascinating when people take the time to learn a discipline like this in such depth. It’s impossible to imagine this many permutations of a simple rope. They’re all beautiful studies in applied geometry, at once both this craft (think of the weaving traditions from around the world) and yet also so detached from that application as these detached, individual “studies”.

A spread from Windy’s book, The Year of Knots
A spread from Windy’s book, The Year of Knots

Conway’s Knot

Windy’s work is an artistic inquiry, but one of the cool things about knots is how many ways there are to study their simple complexity:

Lisa Piccirillo, a graduate student at UT Austin, just made headlines for her proof of Conway’s knot problem, a mathematical puzzle that’s remained unsolved for the past 50 years.

And the craziest part? She solved it in less than a week.

Lisa Piccirillo
Lisa Piccirillo
“The Conway knot is a mathematical knot with 11 crossings discovered by mathematician John Horton Conway. The knot is so famous that it decorates the gates of the Isaac Newton Institute for Mathematical Sciences at Cambridge University...”

— VIA SMITHSONIAN MAGAZINE

What makes a knot “stable”?

Here’s another mathematical study of knots.

Earlier this year, MIT professors Jörn Dunkel and Mathias Kolle, with their PhD students Vishal Patil and Joseph Sandt, published results in the journal Science from their research on knot stability. They developed a mathematical model that can predict this stability, “based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight.”

As this graphic shows, the model displays the pressure on each part of the rope with color. Notice how the color changes as the knot is pulled tight.

Once they had a robust model, they could then use it to simulate other new knots. They discovered that a knot’s strength is related to its “circulations” (“a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow”) and certain “counting rules": basically, the number of times it crosses over itself and twists.

It’s pretty incredible how much there is to discover in something that’s seemingly so intuitive and simple, but yet surprisingly complex.

Knots are artistic, meditative inquiries, as Windy’s work shows, complex mathematical problems, as the aforementioned mathematics research reveals, and ultimately, great design applications in how they exist at this intersection of artistic, technical, and utilitarian ideals.

Knots are ultimately “designed”: they’re a simple form to solve a simple function and their original and current use is utilitarian.

Updated continuously • Last edited on
9.9.23
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Ideas

Knots

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Updated continuously •
Last edited on
9.9.23

Knots are cool. Technically, knots are fastenings but they can be so much more. They can be stoppers to prevent the loss of a rope (though I guess this is still a type of fastening) or to mark distance along a rope (hence “knot” as a maritime unit of speed). They’re decorative and sometimes exclusively so, as artwork.

One of the weirdest things about them is that they’re not real. They’re not an object but rather a distortion of another object—a rope or a string or something. And it’s not even about what that other object is—a knot can be a tangle of anything linear.

They’re a study of the intersection between an ordered and disordered state. They’re what, to paraphrase a saying from Dieter Rams, we might call “orderly confusion”.

They’re like fire in its transience or a battery in its potential energy. They’re in a sort of quantum state, particularly evident in those cases, often accidentally discovered, where you need only gently pull one end to disengage the knot. It’s literally a magic trick: you just pull and poof, it’s gone, and you’re left confused as to how it ever really existed.

Knots can also be considered a type of technology, and one of the purest, for as aforementioned, it’s not an object but instead a method. Once you know how to tie the knot, you can produce this value anywhere.

It’s kind of amazing how many ways there are to distort a straight line into something better.

A Year of Knots

Recently I came across an article on IDEO about this artist, Windy Chien, who learned a new knot each day for a year. She shared the results on her Instagram and later, in her new book, A Year of Knots.

Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO
Windy Chien against a wall of her knots. Image by Cesar Rubio, via this article from IDEO

I always find it fascinating when people take the time to learn a discipline like this in such depth. It’s impossible to imagine this many permutations of a simple rope. They’re all beautiful studies in applied geometry, at once both this craft (think of the weaving traditions from around the world) and yet also so detached from that application as these detached, individual “studies”.

A spread from Windy’s book, The Year of Knots
A spread from Windy’s book, The Year of Knots

Conway’s Knot

Windy’s work is an artistic inquiry, but one of the cool things about knots is how many ways there are to study their simple complexity:

Lisa Piccirillo, a graduate student at UT Austin, just made headlines for her proof of Conway’s knot problem, a mathematical puzzle that’s remained unsolved for the past 50 years.

And the craziest part? She solved it in less than a week.

Lisa Piccirillo
Lisa Piccirillo
“The Conway knot is a mathematical knot with 11 crossings discovered by mathematician John Horton Conway. The knot is so famous that it decorates the gates of the Isaac Newton Institute for Mathematical Sciences at Cambridge University...”

— VIA SMITHSONIAN MAGAZINE

What makes a knot “stable”?

Here’s another mathematical study of knots.

Earlier this year, MIT professors Jörn Dunkel and Mathias Kolle, with their PhD students Vishal Patil and Joseph Sandt, published results in the journal Science from their research on knot stability. They developed a mathematical model that can predict this stability, “based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight.”

As this graphic shows, the model displays the pressure on each part of the rope with color. Notice how the color changes as the knot is pulled tight.

Once they had a robust model, they could then use it to simulate other new knots. They discovered that a knot’s strength is related to its “circulations” (“a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow”) and certain “counting rules": basically, the number of times it crosses over itself and twists.

It’s pretty incredible how much there is to discover in something that’s seemingly so intuitive and simple, but yet surprisingly complex.

Knots are artistic, meditative inquiries, as Windy’s work shows, complex mathematical problems, as the aforementioned mathematics research reveals, and ultimately, great design applications in how they exist at this intersection of artistic, technical, and utilitarian ideals.

Knots are ultimately “designed”: they’re a simple form to solve a simple function and their original and current use is utilitarian.

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