Very interesting, but the fact the patterns in knitting can be used as sources of information is hardly earth-shattering. Any pattern can be used as a repository of information. Digital technology, which is the basis of most electronic representations of the world, is base solely on patterns of 0 and 1. Knitting patterns, aka knots, are vastly more complex and therefore potentially usuable to store significantly more information than a series of digits.
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"Knitting patterns, aka knots, are vastly more complex and therefore potentially usuable to store significantly more information than a series of digits."
If you are referring to information *density*, then it's not that simple.
As the information density increases, the signal to noise ratio decreases, because the states become closer together, which makes them more susceptible to unwanted transitions due to thermal noise. To compensate, you have to use error correcting codes*, which *reduce* information density.
A classic example is the limitation on the information density of magnetic media. See:
"Magnetic Recording Handbook" by Marvin Camras.
AFAICT, Matsumoto hasn't published anything specifically related to information theory. According to the "Matsumoto Group Homepage":
"Our research focuses on the geometry and topology of soft materials, in particular the effects of nonlinear elasticity on emergent structural and mechanical properties in complex systems. This encompasses a broad class of systems in several fields, from soft condensed matter physics to materials science to mechanical and biomedical engineering, with problems including programmable matter, pattern formation and elastic instabilities and the structure of membranes and interfaces."
* And, possibly, reduce the data rate, which is what is required to communicate reliably with distant spacecraft, such as Voyager 1 and 2.
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@HCW
Thanks for the additional points to ponder!
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This is interesting and relevant. Thank you.
Jersey is stretchier than rib knits, which is why rib knit is used for more stable areas of garments, like cuffs and collars.
Weaving and knitting are completely different processes that produce completely different types of fabrics. "“What a Tangled Web We Weave" is a poor name for a project about knitting. How about " “What a Tangled Web We Knit”?
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'"“What a Tangled Web We Weave" is a poor name for a project about knitting.'
That name is even more problematic when it is read as a quote in context:
Oh, what a tangled web we weave
When first we practise to deceive!
Source: "Marmion: A Tale of Flodden Field" by Walter Scott, 1808.
The word "knit" is from Old English, and it is related to the Old English word for "knot":
"knit: Middle English knitten, from Old English cnyttan; akin to Old English cnotta knot"
So, the project could be renamed "Cnotta", which would be an etymologically and mathematically sound name. :-)
Source: Merriam-Webster online dictionary
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"A torus is a mathematized doughnut; hers [Daniels'] was inspired by a figure in a friend’s scientific paper."
According to Daniels' tweet, the torus was knitted in two pieces, which were then joined ("kitchener'd together"). Also, note that the torus appears to be filled with a white internal support (look at the photo carefully).
Both of those points have mathematical implications:
1. What 3D objects can be constructed by knitting without joining? There is an analogous problem with 3D printing -- only certain shapes can be printed.
2. What rigid (or semi-rigid) 3D objects* can be knitted? What if rigid rods, rings, or polygons are allowed in the construction?
* A yarn ball is not knitted, but it is 3D. Do a web search for "How to Wind a Yarn Ball".
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Fascinating! My grandson has always been attracted to knitting, and how in college, is even more so. This is the same grandson who thinks Linear Algebra is a snap and finds coding, computer science and math all very easy. They come naturally to him. Now I know there IS a connection!
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This was wonderful!
As a math geek I have always been fascinated with topology and knots. I did use topology a bit in one graduate level engineering class, but never professionally.
Unfortunately my fumble fingers fail at knitting, and I lost patience with crocheting. Though I do sew, and what I make are mobius scarves. I take a third of a yard of silk, and sew the end together with a twist. A sewing friend once "corrected" me by telling me that they are "infinity scarves." I did not have the heart to tell her that there is a finite amount of fabric in the scarf, and it was a fabric version of a mobius strip.
I truly admire the skill of those who knit. They take a line and make it a three dimensional object, and as Dr. Matsumoto shows it can model physics. I am inspired to include more topology in my sewing projects.
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