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√G

@radicalg / radicalg.tumblr.com

Lapsed mathematican. Outputs occasional irrational alphabeticals. Math, memes, et al.

even when i am not posting, know that horrible sentences are raging within me

A part of being an adult is living with regret and not allowing it to consume you. The older you get, the more mistakes you’ve made, opportunities you’ve missed, people you’ve disappointed. And every day you have to remind yourself to be kind and forgiving of yourself. You accept and love the you from the past and understand that it’s all a part of the process. Then you move on and live your best life, knowing now as old as you feel today, you’ll never be this young again.

SOMETIME IN THE LAST WEEK MY SCHOOL PUT UP A LARGE BANNER DEDICATED TO THE :-) EMOTICON

[id: a banner with a huge image of the :-) (smiley face with nose) emoticon captioned “smiley / first emoted here / 19 september 1982 / computer science department / www.cs.cmu.edu/smiley / carnegie mellon.” end id]

happy birthday :-) face

it’s that time of the year again everyone say happy 40th birthday :-)

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weaver-z

This is apparently what was contained in the original message that invented the :-) and I'm obsessed with Fahlman's diction here

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alagaisia

Hey. Why isn’t the moon landing a national holiday in the US. Isn’t that fucked up? Does anyone else think that’s absurd?

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alagaisia

It was a huge milestone of scientific and technological advancement. (Plus, at the time, politically significant). Humanity went to space! We set foot on a celestial body that was not earth for the first time in human history! That’s a big deal! I’ve never thought about it before but now that I have, it’s ridiculous to me that that’s not part of our everyday lives and the public consciousness anymore. Why don’t we have a public holiday and a family barbecue about it. Why have I never seen the original broadcast of the moon landing? It should be all over the news every year!

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alagaisia

It’s July 20th. That’s the day of the moon landing. Next year is going to be the 54th anniversary. I’m ordering astronaut shaped cookie cutters on Etsy and I’m going to have a goddamn potluck. You’re all invited.

Hey. Hey. Tumblr. Ides of March ppl. We can do this

This is a scheduled post for two days before the anniversary of the moon landing. Please get your moon themed items and foods sorted now in anticipation.

if you own k distinct colors of sock, you can draw k+1 arbitrary socks from your sock drawer and, by the pigeonhole principle, be guaranteed at least one matching pair. this is the only known application of combinatorics to the real world

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xtruss
At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats
  • Experts have searched for decades for a polygon that only makes non-repeating patterns. But no one knew it was possible until now

— Will Sullivan | March 29, 2023 | Smithsonian

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

From bathroom floors to honeycombs or even groups of cells, tilings surround us. These patterns cover a space without overlapping or leaving any gaps. Like a rug filled with diamond shapes, where each section looks the same as the one next to it, every tiling ever recorded has eventually repeated itself—until now.

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

Repeating patterns have translational symmetry, meaning you can shift one part of the pattern and it will overlap perfectly with another part, without being rotated or reflected. The shape described in a new paper does not have translational symmetry—each section of its tiling looks different from every part that comes before it.

The designs on these rugs have translational symmetry—the patterns on the rugs repeat themselves. Juli Kosolapova via Unsplash

Sarah Hart, a mathematician at Birkbeck, University of London, who didn’t contribute to the finding, tells New Scientist’s Matthew Sparkes that she had thought finding an “einstein” (named for the German words for “one stone,” or one tile) could not be done. “There are infinitely many possible candidate tiles, and even the existence of a solution feels quite counterintuitive,” she says to the publication.

“Everybody is astonished and is delighted, both,” Marjorie Senechal, a mathematician at Smith College who did not participate in the research, tells Science News’ Emily Conover. “It wasn’t even clear that such a thing could exist.”

David Smith, a retired printing technician and nonprofessional mathematician, was the first to come up with the shape that could be a solution to the long-standing “einstein problem.” He shared his ideas with scientists who took on the challenge of trying to mathematically prove his conjecture, per the New York Times’ Siobhan Roberts.

The team published a preprint paper detailing the findings on the site arXiv last week, and it has not been peer-reviewed yet. But experts say the work is expected to be supported with further investigation, per Science News.

“This appears to be a remarkable discovery,” Joshua Socolar, a physicist at Duke University who did not contribute to the finding, tells the Times. “The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”

Each "einstein" tile has eight kite shapes inside of it. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

The “einstein” tile is made up of eight kites, or four-sided polygons with two pairs of adjacent, equal-length sides. Researchers call it “the hat” because of its resemblance to a fedora.

The shape is simpler than some experts expected it to be. Chaim Goodman-Strauss, a mathematician at the University of Arkansas and one of the authors of the paper, tells Science News that if he’d been asked to guess what the shape might look like before the finding, “I would’ve drawn some crazy, squiggly, nasty thing.”

In the 1970s, mathematician Roger Penrose discovered that two shapes could form a non-repeating tiling pattern together, prompting hopes that a single shape may be found to do this one day. Researchers have been able to make other non-repeating patterns in the past, but the challenge has been finding a shape that can only make a non-repeating pattern, Goodman-Strauss tells the Times.

The shape of “the hat” can also be morphed to form additional tile shapes that make non-repeating patterns, as shown in the video above.

This new finding could lead to materials science investigations—for example, shapes that form non-repeating tilings could help design stronger materials, Hart tells New Scientist. The elusive shape might also spark creative inspiration for new decorative designs or art.

my deepest respect to the mathematicians but the colors dont really show the layperson how non-repetitive it is, so I did this. Each layer surrounds all the sides of the previous layer (so where just corners touch dont count)

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blueiskewl

My Cousin Vinny 1992

Breakfast scene.

My Cousin Vinny is a 1992 American comedy film directed by Jonathan Lynn, from a screenplay by Dale Launer. The film stars Joe Pesci, Ralph Macchio, Marisa Tomei, Mitchell Whitfield, Lane Smith, Bruce McGill, and Fred Gwynne in his final film appearance. It was distributed by 20th Century Fox and released on March 13, 1992.

The film deals with two young New Yorkers traveling through rural Alabama who are arrested and put on trial for a murder they did not commit, and the comical attempts of a cousin, Vinny Gambini, a lawyer who had only recently passed the bar exam after five unsuccessful attempts, to defend them. Much of the humor comes from the fish-out-of-water interaction between the brash Italian-American New Yorkers (Vinny and his fiancée, Mona Lisa Vito) and the more reserved Southern townspeople.  Principal location of filming was Monticello, Georgia.

My Cousin Vinny was a critical and financial success, with Pesci, Gwynne, and Tomei all praised for their performances. Tomei won the Academy Award for Best Supporting Actress. Attorneys have also lauded the film for its accurate depiction of court procedure and trial strategy.

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politijohn

Interesting to call this “confiscating” when it’s just making the rich pay their fair share, especially considering all the stolen wealth from the bottom 99% and historic tax evasion.

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alex51324

Besides the obvious, the hidden benefit of this is that it provides an endpoint to runaway growth.

The biggest problem with capitalism, the reason it's so destructive to the planet and to the workers and even, ultimately, to the capitalists, is that, after a certain point, the money's just a way of keeping score. The number at the bottom of the column has no bearing on what you can buy or do; as a result, there's no such thing as enough. The number can always be bigger.

Under this proposal, once you hit $1 billion, you've won capitalism. You beat the game, achieved the maximum score; you're finished. There's nothing more you can accumulate. You now have to find a purpose in life other that the relentless pursuit of profit. (And if we're really lucky, it might be something that actually benefits other people, but even if not, it's unlikely to be as damaging as whatever it is you were doing to get that $1 billion.)

Instead of companies expanding endlessly, like tumors, there's a point where, when all the major stakeholders are maxing out on profit, it makes sense to just hold steady. Keep doing/making/selling whatever it is you do/sell/make, but stop trying to do/sell/make more of it every year.

The problem with a tumor--what makes it cancer--is that it keeps growing and growing, until eventually it's taking up so much space and consuming so many resources that the surrounding tissues can't function. The tumor doesn't have to do anything better than the other tissues in order to crowd them out; it just does it faster. Stop the uncontrolled growth, and it's something you can live with.

Stopping the uncontrolled growth of capital means more opportunities for multiple businesses--big and small--operating in the same sector, since it doesn't make sense for any one company to gobble up too much of the market share. That, in turn, means more choices for customers--and workers, since they can take their skills to another employer doing similar things. It means less waste, as there's no longer an economic upside to spewing cheap goods out of a fire-hose before you even know whether anyone wants to buy them. That could mean slower, more thoughtful use of resources in the first place, but at minimum, it's going to mean not manufacturing products only to immediately throw them away.

the basic moral economic question of the present day is (and has likely already been answered): should the rate of growth for large corporations be higher than the growth of prosperity for their workers?