After a couple of months of work, we cracked it: If you only allow yourself to tile by translations and rotations, then Tile(1,1) admits only non-periodic tilings! We call this a "weakly chiral aperiodic monotile" -- it's aperiodic in a reflection-free universe, but tiles periodically if you're allowed to use reflections.
The tiling is reminiscent of, but not identical to, hat tilings -- it contains a sparse population of "odd" tiles, which are rotated by odd multiples of 30 degrees relative to all other tiles. (5/n)
But what if we counterbalanced that extra freedom by, say, just forbidding reflections outright? Dave discovered that if he tried to place copies of Tile(1,1) by translation and rotation only, well, he didn't get stuck but he couldn't find a block of tiles that repeated by translation. Needless to say, the four of us began studying this shape more intensively. (4/n)
Like, between spouse and his employer, we pay $24,000 A YEAR for HEALTH INSURANCE. And then they HAVE THE AUDACITY to charge us $5,000 MORE on top of that EVERY YEAR. We're "lucky" in that we have a $5k out of pocket, so the MOST we will ever pay for healthcare is $29,000 a year. WHICH IS MORE THAN DOUBLE THE POVERTY THRESHHOLD IN THIS COUNTRY. FOR HEALTHCARE ALONE. And ya'll wonder why Americans are mentally unstable and die early.
I have spent the last two weeks in conferences with other science communicators and the general consensus in discussions was that (1) Twitter is dying and (2) it’s not clear what will replace it. (And not much enthusiasm about Mastodon, it seems.)
@stonebear Yeah. Depends on where in the airport you are (sometimes I find quiet/empty places with a CO2 of like 550 ppm) but boarding areas, security lines, restaurants (😱) — all those can be really bad