[ColinWright]

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 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.

[dpflan]

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 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...

[ColinWright]

>> What do grad students in math do all day?

> ... by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet.

A friend of mine[0] once said that the act of doing research in math is the act of inventing a language in which you can talk about the problem. Once you have that, the solution tends to come. But inventing the right language is really, really hard.

This might explain why so many research mathematicians end up married to (or in long term relationships with) linguists. His wife is a PhD in Spanish and linguistics, my wife's first degree is in French and linguistics, and I know perhaps three or four others in my immediate circle.

Anecdata, of course.

[0] Andrew Lipson: https://www.andrewlipson.com/

[dpflan]

That makes sense as math is a fascinating exploration of the human mind and its ability to handle abstractions; and what is happening is one's mind even when not mathematical can be difficult to explain. A linguist's rigorous approach to language and understanding of language seems to pair well with a need to explain one's thoughts.

Thank you for sharing Andrew Lipson's site, digging his LEGO sculptures, for example: https://www.andrewlipson.com/mathlego.htm

[tobr]

Hm, challenge accepted: It uses a fan and a hose to suck up dust. You use it to get rid of dirt in your home. The dirt ends up in a bag. Now and then you must get a new bag, when the old one is full. If you have some tiny item or two that lies in the way of the dust, you will want to put that away, or else it can get lost in the bag.

[laszlokorte]

But can I use it to rub the fleeb? [1]

[1]: https://www.youtube.com/watch?v=eMJk4y9NGvE

[dpflan]

Nice, I think you’re close to making it have a rhyme scheme… next challenge?

[orls]

This reminds me of [Up-Goer Five](https://xkcd.com/1133/) - similar vibe but a different constraint (most common thousand words only)

[boygobbo]

A vacuum cleaner described in 'words that are four letters long or shorter':

a tool to suck dirt and dust into a bag

;)

[pfd1986]

I agree with you that application is not necessarily the point (one of my mentors would always answer this questions with "what's a baby for?")

But in materials science / physics this has been a long standing puzzle: we know that hard polygons vibrating thermally should have a global entropy maximum (ground state) equal to their closest packing configuration. Can this ground state configuration be aperiodic?

So far, all quasicrystals discovered are either not in stable equilibrium or are in equilibrium at that pressure and temperature, but are not the ground state of the material (i.e. at infinite pressure, that QC would be unstable). The discovery of an aperiodic single tile shape means that, in equilibrium, this polygon should have a ground truth that is aperiodic. That basically settles this long-standing question.

[abetusk]

Just a note about applications, there is a pretty direct application of aperiodic tiles with quasicrystals [0]. Diffraction patterns of quasicrystals can have symmetry that can't occur with periodic tiling which explained some weird diffraction patterns people were observing.

One can imagine a scenario, occurring for metal or mineral creation or even in a biological setting, where only one shape is allowed because of some external constraint, including not allowing it's mirror.

[0] https://en.wikipedia.org/wiki/Quasicrystal

[hcs]

There is this footnote on pg 2:

> We might call this the "vampire einstein" problem, as we are seeking a shape that is not accompanied by its reflection

Also the glorious

> Lemma 2.1. There exists a Spectre.

[adhesive_wombat]

Example from the top of my head: some pretty "niche" (in the days of Galois, say) number theory is now the critical component in a large proportion of digital processing, cryptography and communications (e.g. forward error correction).