All toots CC BY-SA to the extent possible. (Boosts usually aren't.)
| pronouns | she/her |
| blog | https://sonatagreen.com/ |
PSA copypasted from tumblr, pls boost 
:
FEMA is doing an emergency alert test on all TVs, radios, and cell phones on October 4, 2023, at approximately 2:20pm ET.
If you live in the US and you have a phone you need to keep secret for any reason, make sure that it is turned off at this time.
Yes, I'm doing this months in advance, and yes, my blog has very little reach, but I figure better to post about it more than less.
Please reblog and add better tags than mine, I'm bad at tags.
When David Smith, Joseph Myers (@jsm28), Chaim Goodman-Strauss and I posted our paper "An aperiodic monotile" (https://arxiv.org/abs/2303.10798) back in March, we answered the open problem of whether a single shape could tile the plane aperiodically.
Some people observed that tilings by the "hat" used both unreflected and reflected tiles. Although the einstein problem was answered, in some contexts (e.g., tile floors), you'd likely have to manufacture two separate tiles. Our paper left open the question of whether a shape could tile aperiodically using translations and rotations only, with no reflections.
I hate to sound like a broken record, but then, on March 26th, Dave noticed something interesting. (1/n)
A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings.
THERAPIST: And how do we cope with stress?
ME: We crochet tiny sweaters for the pigeons on the balcony
THERAPIST: [taking notes] ... Yes actually
you, an intellectual: women in STEM
me: hypothesisters
Marian
sorry 🇵🇸☭
Craig S. Kaplan
Roxi Horror 💀🌸
Cassandrich
Cerebrate