31–40 of 83 posts
Only slightly related: anyone know how to make porcelain or other normal tiles? If I wanted to redo the bathroom in these or whatever, can they be made?
Seems like they didn't go with that.
I also see that the old discussion has come up: "But what can it be used for?"
These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto useful? Is Bach's Toccata and Fugue in D minor (BWV 565)[0] useful? Is Rodin's "The Thinker" useful?
No. And for each of them there are people who Simply. Don't. Care.
So it is with Pure Maths.
The difference is that sometimes things people pursued simply out of interest or curiosity turn out to be useful. It might be decades down the line, but it happens, and you never know in advance which bit of maths they will be.
So maybe Chiral Aperiodic Tilings will turn out to be useful, maybe not. Maybe the work done to create them is what will turn out to be useful. Maybe not.
It's not the point.
[0] Interestingly, this might not be by Bach, and some claim it's not in D minor.
There was a rumour that if they found a chiral aperiodic monotile then they might call it a Vampire Tile, because it doesn't have a reflection. Seems like they didn't go with that. I also see that the old discussion has come up: "But what can it be used for?" These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto usefu…
""" The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only allowed to use words that are four letters long or shorter.
...
This [research] goes on for several years, and finally you write a thesis about how if you turn a vacuum cleaner upside-down and submerge the top end in water, you can make bubbles!
Your thesis committee is unsure of how this could ever be useful, but it seems pretty cool and bubbles are pretty, so they think that maybe something useful could come out of it eventually. Maybe.
And, indeed, you are lucky! After a hundred years or so, your idea (along with a bunch of other ideas) leads to the development of aquarium air pumps, an essential tool in the rapidly growing field of research on artificial goldfish habitats. Yay! """
- [1.] https://www.quora.com/What-do-grad-students-in-math-do-all-d...
Can anyone explain why people are interested in tilings?
One famous application of this is to encode these shapes using complementary snippets of DNA, to perform massively-parallel computation at the nano-scale: https://www.nature.com/articles/35035038
How could you address each tile, to create an aperiodic tile map? Would be a neat tech demo. Like HyperRogue, for example. https://www.roguetemple.com/z/hyper/
Simon Tatham has written about this, in the context of the original hat tile: https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperi...
Earlier quoted context omitted.
Hmmm... now that we know what shapes these tiles take, maybe we can look for or design molecules with the "same shape" (and yes I know molecules aren't 2D planar objects, but some can be approximated as such, e.g. the benzene ring) and with the right molecule-to-molecule attractions, such that they naturally arrange themselves into these aperiodic tilings.
TRANSPARENT ALUMINUM!? Without a periodic crystal structure, it is likely to transmit light (see glass's transparency due to its amorphousness)
Being extremely hard and resistant they are used in applications like watch crystals, windows in grocery-store barcode scanners and armored car windows.
This excites me much more than the original result, which I considered to use two tiles[1]. The fact that it’s a such tiny modification of the original result is crazy. Even if you don’t intend to read the paper, look at the illustrations of the hierarchical substitution algorithm at the top of pages 6 and 7, those are just beautiful. [1] The authors discuss various historic definitions of tilings and whether reflect…
There was a rumour that if they found a chiral aperiodic monotile then they might call it a Vampire Tile, because it doesn't have a reflection. Seems like they didn't go with that. I also see that the old discussion has come up: "But what can it be used for?" These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto usefu…
You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…