towards tomorrow

mathematics is what the stars sing to themselves in the silence

[clearslime]

❥ | _jwlettering on ig

[curiosamathematica]

The mortal matrix problem

Today I learned that there does not exist an algorithm for the following task: given a finite set of (say 3 × 3) matrices, can you multiply these together in some way and obtain the zero matrix?

Note, it’s not that no one ever cared to implement such an algorithm, or that it would just be an unreasonably inefficient brute-force-ish method. The interesting thing is, such an algorithm cannot exist—it is doomed to (sometimes) output wrong results or not give results at all.

[scientiststhesis-at-pillowfort]

This is only true if you add the condition that you can possibly repeat the matrices, if you’re limited to one use per matrix then brute force just works.

[masterkfox]

guess which frame I gave up on

[masterkfox]

3000 notes because I wrote ‘fuck’ on an animation frame what the hell tumblr

[cmdrkitten]

[bauhaus-movement]

Kandinsky Circles in a Circle 1923 - Geometric Abstraction

[hyperbolicgifs]

SECRET GIF THEOREM

Notation. Let R denote the set of real numbers, which form a line. Write p, q, r, s, x, y, w, h, and t for real numbers. The Cartesian product A×B of sets A and B is the set of ordered pairs (a,b) where a is in A and b is in B, and similarly for A×B×C. This means R² = R×R forms a plane, on which each point has standard coordinates (x,y). The closed interval from p to q is the set [p,q] of real numbers t with p ≤ t ≤ q. Just as [p,q] is a region of R, a rectangle is a region of R² of the form [p,q]×[r,s]. Definition. A pixel gif G having width W px, height H px, F frames, and colors in the set C, is a map G:A→C, where A is a 3D matrix of dimensions W×H×F. Definition. A gif Γ of height h and width w is a map Γ:[0,w]×[0,h]×[0,1]→C. Remark. The correspondence is given by G(i,j,f) = Γ(iw/W,h-jh/H,f/F), where (i,j,f) is the pixel in the ith row (from the top) and jth column of frame f. Definition. A gif Γ loops if Γ(x,y,0) = Γ(x,y,1).

Definition. A function T: R²→C is called a tiling if T(x+1,y) = T(x,y). Definition. A map T*:[0,1]×R→C from an infinite strip of width 1 is a tile. Proposition.There is a 1-1 correspondence between tiles and tilings. Proof. Every tile extends to a tiling and every tiling restricts to a tile. Definition. A map F:R²→R² is a transformation. Write F = u×v for u,v:R²→R. Theorem. For a tiling T and transformation u×v, the gif Γ(x,y,t) = T(u+t,v) loops. Proof. Γ(x,y,0) = T(u,v) = T(u+1,v) = Γ(x,y,1).

[mathematically-awry]

Ha, this is excellent.

[dimw0]

Let’s tesselate

[fyphysica]

If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.

But life shouldn’t be that hard now should it?

The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what is the shape of largest area in the plane that can be moved around a right-angled corner in a two-dimensional hallway of width 1? This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.

The most common shape to move around a tight right angled corner is a square.

And another common shape that would satisfy this criterion is a semi-circle.

But what is the largest area that can be moved around?

Well, it has been conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s sofa”. And it looks like so:

Wait.. Hang on a second

This sofa would only be effective for right handed turns. One can clearly see that if we have to turn left somewhere we would be kind of in a tough spot.

Prof.Romik from the University of California, Davis has proposed this shape popularly know as Romik’s ambidextrous sofa that solves this problem.

Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.

Have a good one!

[shinynessie]

I don’t know what to do with this information but I support it

[not-brighter-but-stranger]

Finally gave in to the nth recommendation and read An Interrupted Brunch. Can’t say I recommend it. It’s one of those books that’s trying to be mass-market dystopian four-year-old-fiction, But Literary, and ends up not being much good at either thing.

(Spoilers, if you care.)

Central conceit is that there’s two genetically engineered Amentan subspecies, Speedies and Slowpokes, both designed in the hope of making springs easier on the regular Amentans.

Speedies only live two years; they grow up in two seasons, spend a year having babies, and then die after two more seasons. Scientists sped them up to age in fast-forward like that so they could be used for experiments in further genetic engineering: more generations faster. If a trait works well in Speedies, it’s introduced to the general population. They’re trying for all the usual things: milder springs, higher intelligence, the works.

Slowpokes live four years, but they never look older than one. While Speedies live in labs, Slowpokes live in people’s homes as cherished children, so no one has to have an empty spring. Unfortunately, the genetic engineering that slows down their aging has all sorts of horrific side effects that start manifesting after the first four years, so they’re taken away and euthanized at that point, and their “parents” order a replacement.

Our protagonists are of course a Speedy and a Slowpoke. The Slowpoke is six; she’s one of the rare cases who’s kept in a lab after her removal from her “parents,” instead of being euthanized (they keep a few to study to see if they can make them last longer). She has lots of horrifying medical stuff going on, mostly only hinted at. The Speedy’s one year old, which makes her past her usefulness for the scientists. They bond over being worn-out and broken but still alive.

There’s some good parts in the novel, but mostly it’s just trying too hard to be a metaphor for the fleetingness of childhood. If the author had given up on that and just written a straight four-year-old-fiction, I think I’d have liked it, but as it is I can’t say I do.

[galina-ulanova]

Rehearsing Swan Lake (Queensland Ballet, 2017)

[slmnbagel]

I think this is probably the one man on earth who is truly at peace

[openamenta]

You know what I just realized?

We haven’t had reds forever. Reds came about because people were doing polluted work generation after generation, until eventually they turned into reds.

But that means that at some point in time, a person gave birth to a red child.

And I just think that would be awful. To be expecting a nice person baby, and instead getting something like that.

[serpentoftherose]

I’m aware that this isn’t the theological consensus, but I’m fairly sure that the process by which reds were produced was gradual. A person likely first gave birth to a slightly non-personable child- one whose thought process was just ever-so-slightly alien, but still within the range of ‘mental illness’ rather than ‘unrecognizable’, and then *they* gave birth to an even less person-y child, and so forth, until eventually you end up with reds.

[not-brighter-but-stranger]

I’m pretty uncomfortable about the conflation of mental illness with reds, here. Mentally ill people are people.

[not-brighter-but-stranger]

Help, I made the mistake of inviting BFForange and my cousin the biologist over at the same time, and now they’re trading gross medical stories.

Neither of them is even hypo as far as I know, it’s just a macho thing. Whyyy.

[ao3tagoftheday]

The AO3 Tag of the Day is: The most sacred and intimate of relationships

[argumate]

time to write code that writes code.

[kitstacean]

What about code that breaks code?

[argumate]

I’ve got a simpler name for that, I call it “code”

[not-brighter-but-stranger]

I swear I heard this exact conversation go down at the ecumenical brunch last week.

(Okay, not literally this exact conversation. But it’s very cute how all programming yellows seem to share the hobby of opining on how Literally No Program Ever Works.)

[scienceprofessorquotes]

“I have a friend who’s a mathematician, it’s fun to talk to him, he doesn’t understand what I’m talking about and I don’t understand what he’s talking about, it’s quite fun after a few drinks”

— immunology professor

[not-brighter-but-stranger]

wait, there is a *reason* for these memes? where are they coming from and why is this happening to us?

Yeah!

So there’s a famous thought experiment that goes like this:

We discover a broadcast from aliens. It turns out to be a game show: these powerful aliens invite people from primitive planets like ours to participate, and if they perform well, the aliens give their species some number of habitable planets and the means to access them, depending on how well the person performs. Everyone is very excited by this, of course.

Shortly thereafter, a purple farmer, Magraz, receives an invitation from the aliens. He doesn’t have a way to reply, of course -- in fact, no one has the technology to do so except for a small group of scientists, whom he asks for help replying to the invitation.

Now, from watching the broadcasts, the scientists have learned that the final stage of the game show will involve the aliens figuring out who helped the contestant respond to the message, kidnapping them, and challenging the contestant to kill them. If the contestant kills them, his species will receive three planets to settle; if not, only one. The scientists are unfortunately very selfish, and not willing to die, so they ask Magraz to promise that if he gets to that stage he won’t kill them.

Magraz promises not to kill the scientists. The scientists, who are extremely intelligent and have access to a huge amount of data about Magraz, know that Magraz is a person who keeps his promises, so they believe him. They help him send a message accepting the invitation.

All of Amenta watches the broadcast from the edge of their seats. It turns out Magraz is really good at alien game shows. He gets to the final stage, and sure enough, the aliens challenge him to kill the scientists. Magraz, being a person who keeps his promises, refuses. The aliens accordingly give us one planet to settle.

Has Magraz done something wrong? Should we punish him? Would it matter if he hadn’t had all of Amenta for an audience?

(There’s then all sorts of variations on this -- people coming up with thought problems just started borrowing “alien game show” as an excuse for putting people in the position of having to make all kinds of ridiculous decisions.)

There’s lots of different pictures illustrating this, but a common one you’ll see is from a widely-used Voan textbook:

(Pictured: Magraz on the right, alien on the left, kidnapped scientists in the foreground, Amentans watching in the background.)

For some reason (I’m afraid I can’t tell you why, the internet is mysterious) this became a meme, where people write text posts or edit the picture to set up all sorts of ridiculous scenarios. Sometimes they’re legitimate-if-bizarre variations, more often they’re deliberately absurd.

Uh, first terrible example I pulled off Citrus, in case someone somehow hasn’t seen these (if so, please tell me what rock you’re living under so I can join you):