A Powerful New 'QR Code' Untangles Math's Knottiest Knots
Comments
latexr
jagged-chisel
I think the comparison for the lay person is just fine. The author quoted the term and explains themselves.
A QR codes encode data to be scanned and converted for the convenience of the user.
These knot graphics encode data to be scanned and converted for the convenience of the user.
ButlerianJihad
> data to be scanned and converted
These appear to be write-only. Where have they documented the method of scanning and conversion? Is it patented?
The publication on arxiv only mentions visual inspection, in the context of being a bad idea.
altairprime
“Is it patented”?
somethingsome
I mean... There is a 1-1 mapping, and they look kinda like QR codes. so technically, you can make an app that scan it and it will show you the corresponding polynomial.. It could even be useful for fast checking knots
Hendrikto
> There is a 1-1 mapping
It is strong, but not 1 to 1:
> Tubbenhauer computed, for instance, that the invariant uniquely identifies more than 97% of the knots with 18 crossings.
tromp
Since they said "the corresponding polynomial", they must mean the mapping between the colored hexagons and the knot polynomials.
c7b
> they look kinda like QR codes
Hexagonal, with shaded colors? QR Codes are, by definition, square and binary and traditionally use black and white. They're also used for a different purpose typically. They could easily have made them look more like QR Codes if they had wanted to, but they made their own artistic choices. Which I love btw, but they could have maybe chosen better wording. Something like 'fingerprint' or 'mugshot' would have conveyed the idea of it being useful for identification, if not perfect, much better.
latexr
> mapping
Which I not only mentioned in my comment, it is not even slightly unique to QR codes.
> they look kinda like QR codes
In what way? QR Codes are black and white, square, and asymmetrical. These are colourful, hexagonal, and symmetrical. By that token, a 16th century tile also “looks kinda like a QR Code”.
I very much doubt you could show one of these to someone, ask them what they are, and that they would answer “QR Code”. They don’t look alike at all.
ButlerianJihad
The use of "qR cOdES®" appears to have developed from a previous system of colored "bar codes" algorithmically generated from the same types of invariant knots, but with less resolution. I suppose the "BAR coding" could be visually interpreted like resistor values in assembling or diagnosing circuit boards.
However, what they're doing is art. They are algorithmically generating beautiful artwork that can be admired for its colors, labyrinthine complexity, near-symmetry, shapes and analogy to real-world or theoretical knots.
https://en.wikipedia.org/wiki/Celtic_knot
https://en.wikipedia.org/wiki/Tartan#Legal_protection
https://en.wikipedia.org/wiki/Fractal_art
https://en.wikipedia.org/wiki/Moir%C3%A9_pattern
They have not proposed any way of scanning or processing the art back into data, and in fact they point out that printing, display, visual inspection or comparison may not produce mathematically accurate results, so this is representational art that they can emblazon on their mugs, sugar cookies, tee shirts, and sell on Etsy.
https://en.wikipedia.org/wiki/Psychedelic_art
In fact Dr. Bar-Natan has done a lot of work in perceptual art that looks like another thing: https://www.math.toronto.edu/drorbn/papers/PDI/
But he calls it "PDI" and not "Magic Eye™"
The fault of naming "qr codez®" doesn't rest solely on the latest researchers, but they are "standing on the shoulders of giants" who generated "bar c0des", which may have started with some colored pencils, a cocktail napkin, and 3 pints in a pub.
The text QR Code® itself is a registered trademark and wordmark of Denso Wave Incorporated.
MattPalmer1086
Interesting article. I love it when maths gives us some beautiful visuals too.
tagawa
The knot codes are beautiful but the ones in the article all seem to be repeating patterns, so I wonder if you could take a 60° slice of each one and save space without losing information.
empiricus
But I see all the "QR codes" have a hexagonal symmetry? So basically you can use only one corner (1/6) to represent a node? Why do they keep the entire hexagon?
altairprime
The article notes near the end that the authors think the diameter of the hexagon is tied to another constant, so I would guess that they kept the full hexagon because studying a regular polygon has advantages that studying a wedge doesn’t — so, since they aren’t done studying this all yet, perhaps they have causes to consider a full hex rather than a wedge that are still WIP.
rolandf
Don't call it a 'QR Code' if it is not a QR Code.
larodi
Love them knots! The sudoku of the universe :)
graphememes
this was so confusing at first not going to lie
mfgadv99
[dead]
charcircuit
This is not a new QR code, nor is it powerful. It's worse in every way and is not really even a code.
ButlerianJihad
https://en.wikipedia.org/wiki/QR_code#License
The text QR Code itself is a registered trademark and wordmark of Denso Wave Incorporated.[107]
https://www.qrcode.com/en/faq.html
https://greatreachinc.com/blog/one-thing-about-qr-codes-you-...
Should “QR Code” be capitalized?
Yes. “QR Code” must always be capitalized: both letters in “QR” and the “C” in “Code.” The registered trademark symbol (®) should follow the term in published materials. Using lowercase, adding an “s,” or other variations does not exempt you from the trademark.altairprime
That trademark seems unlikely to survive reality. This sort of societal disregard is a specific argument to invalidate — knot a desirable outcome when suing a bunch of theoretical mathematicians.
jagged-chisel
This is the most non-sensical comment here. That’s not at all how trademarks work.
“Whoa! Some article said this mail app is an ‘Outlook’ for TempleOS! Better call the Microsoft lawyers.”
No, you’re allowed to compare products and ideas and mention their trademarked names without fear of legal issues.
Did the researchers name these “QR codes?”
ButlerianJihad
> Did the researchers name these “QR codes?”
Yes.
Their use of “QR Code” is mighty confusing. QR (Quick Response) Codes are something specific that people are familiar with. These don’t share any characteristics apart from being images which represent something else. They’re not even the same colour or shape. Just call them “knot codes” or something.