#construction structure

[honehonn3honey]

A protection that becomes more creepy

Azul in my heart. You can see the original art here and read the monster list here @lustlovehart

[Alt under the cut]

My first concept, since my style could not simulate the texture of slime in its purest state

It is quite thick so water can not enter or wet. Only small puddles where you can accumulate

It is a monster and that, magic, but I can imagine that it can only reach a height by the pressure, it can come out expelled sometimes

[knifearo]

being aromantic is like. hey btw you're going to live a life that is the culmination of most of society's worst nightmares. sorry lol ✌️ but then you turn around and take a really good hard look at it and it turns out that living in that nightmare is fucking awesome and you get to wake up every day and take that fear that other people have and laugh and hold it close until it's a great joy for you instead. and being happy is a radical act that you define instead of someone else. and you're sexy as fuck that's just a fact of life i don't make the rules on that one

[zegalba]

Cathedral of Zagreb Located: Zagreb, Croatia

[rustchild]

one of the wild things about people’s stubborn insistence on misunderstanding The Ones Who Walk Away From Omelas is that the narrator anticipates an audience that won’t engage with the text, just in the opposite direction. Throughout the story are little asides asking what the reader is willing to believe in. Can you believe in a utopia? What if I told you this? What about this? Can you believe in the festivals? The towers by the sea? Can we believe that they have no king? Can we believe that they are joyful? Does your utopia have technology, luxury, sex, temples, drugs? The story is consulting you as it’s being told, framed as a dialogue. It literally asks you directly: do you only believe joy is possible with suffering? And, implicitly, why?

the question isn’t just “what would you personally do about the kid.” It isn’t just an intricate trolley problem. It’s an interrogation of the limits of imagination. How do we make suffering compulsory? Why? What futures (or pasts) are we capable of imagining? How do we rationalize suffering as necessary? And so on. In all of the conversations I’ve seen or had about this story, no one has mentioned the fact that it’s actively breaking the fourth wall. The narrator is building a world in front of your eyes and challenging you to participate. “I would free the kid” and then what? What does the Omelas you’ve constructed look like, and why? And what does that say about the worlds you’re building in real life?

[juliaknz]

MAYUMI MIYAWAKI MATSUKAWA BOX, 1978 Tokyo, Japan Image © Shinkenchiku-sha

[sir-fluffbutts]

i somehow feel like most public bathrooms probably use the floor toilets bc they're... probably cheaper....

i pondered about it for a bit so here are my offerings

[patheticgirl168]

i hate men who want girlfriends who are basically mother figures that also suck dick. hop on the incest train and leave the bad bitches alone.

[happi-dreams]

me and my sister was thinking of little master builders world building before tlm and we had the silly idea of — hey maybe they did lil fun games as moral when things looked dire ?

therefore, ✨ Brick-lympics ✨

i think they’d have little categories they’d all play in like ‘who can build the fastest?’ <- (consistently benny) or ‘who can build the most creative design?’ ‘who has the strongest build?’

n maybe in tlm2 or tlm if they weren’t invaded literally seconds after, Emmet joins in and probably switches between judging and building every now and again

[lonestarflight]

The Space Shuttle Structural Test Article (STA-099) being returned to Rockwell International's Palmdale Facility from Lockheed. STA-099 was used to test the launch and orbital stress an operational orbiter would experience. In January 1979, it was decided to convert the space frame into Challenger (OV-099), taking the operational orbiter slot intended for Enterprise (OV-101). There were many reasons NASA chose it over Enterprise, the major reasons were it was stronger, lighter and most importantly, there was less to disassemble.

Date: November 7, 1979

source, source, source

[bubbloquacious]

Okay so to get the additive group of integers we just take the free (abelian) group on one generator. Perfectly natural. But given this group, how do we get the multiplication operation that makes it into the ring of integers, without just defining it to be what we already know the answer should be? Actually, we can leverage the fact that the underlying group is free on one generator.

So if you have two abelian groups A,B, then the set of group homorphisms A -> B can be equipped with the structure of an abelian group. If the values of homorphisms f and g at a group element a are f(a) and g(a), then the value of f + g at a is f(a) + g(a). Note that for this sum function to be a homomorphism in general, you do need B to be abelian. This abelian group structure is natural in the sense that Hom(A ⊗ B,C) is isomorphic in a natural way to Hom(A,Hom(B,C)) for all abelian groups A,B,C, where ⊗ denotes the tensor product of abelian groups. In jargon, this says that these constructions make the category of abelian groups into a monoidal closed category.

In particular, the set End(A) = Hom(A,A) of endomorphisms of A is itself an abelian group. What's more, we get an entirely new operation on End(A) for free: function composition! For f,g: A -> A, define f ∘ g to map a onto f(g(a)). Because the elements of End(A) are group homorphisms, we can derive a few identities that relate its addition to composition. If f,g,h are endomorphisms, then for all a in A we have [f ∘ (g + h)](a) = f(g(a) + h(a)) = f(g(a)) + f(h(a)) = [(f ∘ g) + (f ∘ h)](a), so f ∘ (g + h) = (f ∘ g) + (f ∘ h). In other words, composition distributes over addition on the left. We can similarly show that it distributes on the right. Because composition is associative and the identity function A -> A is always a homomorphism, we find that we have equipped End(A) with the structure of a unital ring.

Here's the punchline: because ℤ is the free group on one generator, a group homomorphism out of ℤ is completely determined by where it maps the generator 1, and every choice of image of 1 gives you a homomorphism. This means that we can identify the elements of ℤ with those of End(ℤ) bijectively; a non-negative number n corresponds to the endomorphism [n]: ℤ -> ℤ that maps k onto k added to itself n times, and a negative number n gives the endomorphism [n] that maps k onto -k added together -n times. Going from endomorphisms to integers is even simpler: evaluate the endomorphism at 1. Note that because (f + g)(1) = f(1) + g(1), this bijection is actually an isomorphism of abelian groups

This means that we can transfer the multiplication (i.e. composition) on End(ℤ) to ℤ. What's this ring structure on ℤ? Well if you have the endomorphism that maps 1 onto 2, and you then compose it with the one that maps 1 onto 3, then the resulting endomorphism maps 1 onto 2 added together 3 times, which among other names is known as 6. The multiplication is exactly the standard multiplication on ℤ!

A lot of things had to line up for this to work. For instance, the pointwise sum of endomorphisms needs to be itself an endomorphism. This is why we can't play the same game again; the free commutative ring on one generator is the integer polynomial ring ℤ[X], and indeed the set of ring endomorphisms ℤ[X] -> ℤ[X] correspond naturally to elements of ℤ[X], but because the pointwise product of ring endomorphisms does not generally respect addition, the pointwise operations do not equip End(ℤ[X]) with a ring structure (and in fact, no ring structure on Hom(R,S) can make the category of commutative rings monoidal closed for the tensor product of rings (this is because the monoidal unit is initial)). We can relax the rules slightly, though.

Who says we need the multiplication (or addition, for that matter) on End(ℤ[X])? We still have the bijection ℤ[X] ↔ End(ℤ[X]), so we can just give ℤ[X] the composition operation by transfering along the correspondence anyway. If p and q are polynomials in ℤ[X], then p ∘ q is the polynomial you get by substituting q for every instance of X in p. By construction, this satisfies (p + q) ∘ r = (p ∘ r) + (q ∘ r) and (p × q) ∘ r = (p ∘ r) × (q ∘ r), but we no longer have left-distributivity. Furthermore, composition is associative and the monomial X serves as its unit element. The resulting structure is an example of a composition ring!

The composition rings, like the commutative unital rings, and the abelian groups, form an equational class of algebraic structures, so they too have free objects. For sanity's sake, let's restrict ourselves to composition rings whose multiplication is commutative and unital, and whose composition is unital as well. Let C be the free composition ring with these restrictions on one generator. The elements of this ring will look like polynomials with integers coefficients, but with expressions in terms of X and a new indeterminate g (thought of as an 'unexpandable' polynomial), with various possible arrangements of multiplication, summation, and composition. It's a weird complicated object!

But again, the set of composition ring endomorphisms C -> C (that is, ring endomorphisms which respect composition) will have a bijective correspondence with elements of C, and we can transfer the composition operation to C. This gets us a fourth operation on C, which is associative with unit element g, and which distributes on the right over addition, multiplication, and composition.

This continues: every time you have a new equational class of algebraic structures with two extra operations (one binary operation for the new composition and one constant, i.e. a nullary operation, for the new unit element), and a new distributivity identity for every previous operation, as well as a unit identity and an associativity identity. We thus have an increasing countably infinite tower of algebraic structures.

Actually, taking the union of all of these equational classes still gives you an equational class, with countably infinitely many operations. This too has a free object on one generator, which has an endomorphism algebra, which is an object of a larger equational class of algebras, and so on. In this way, starting from any equational class, we construct a transfinite tower of algebraic structures indexed by the ordinal numbers with a truly senseless amount of associative unital operations, each of which distributes on the right over every previous operation.

[vaguely-concerned]

one of the things mourn watch rook has the most comments about/seems pretty knowledgeable about when they're there is the way the necropolis will just shuffle rooms around every now and then on a whim, so I'm headcanoning that rye's previous area of expertise, outside of general watcher duties, was keeping track of and rediscovering these lost or displaced areas. that, and basically acting as a sort of tour guide when need be, such as on the day they met varric.

'have we really misplaced the ashen cathedral again? *sigh* that's the third time this year, we really must strengthen the wards. oh well. someone send for ingellvar, they'll track it down in no time I'm sure. and it might keep them out of trouble for a while'

[15tarlit5kyline]

I tried TinEye, origin unknown.

[arc-hus]

School in Vésinet, France - Lambert Lénak

[barbiediamondcastleofficial]

Here take this meme I made the first time I listened to TMA s5

[julietasgf]

Vicó hi! I’m sending you an ask a day late cause I was absurdly busy yesterday BUT I was wondering if you have more nerd Marcus hcs (especially since u and I both agree he’s a civil engineer in a modern au)

hiiii grace!! 🥹 first tysmmm for the ask (and I hope everything goes alright for you!! sending cheers), and tysm bc I love nerd marcus sm hehe

I hc that marcus have always been naturally good at math since he was tiny, and on middle school his teachers definitely tried to get him to participate in any kind of math olympics (most of the time he rejected it because he felt a bit embarassed of the idea); also it was him who was always helping his sisters when they needed help with homework;

(he kinda sucks at physics tho, he's screaming crying throwing up because he knows how to make the math but struggles to understand the questions);

((he was screaming crying throwing up even more when he got to uni and discovered that structures are basically applied physics, but he got used to it; marcus is a quick learner));

I love the idea that marcus is deep into sci-fi and honestly a lot of other stereotypical nerd type of things, but unless you get to know him after a while (or unless you visited his house and noticed in his room the pile of old comics in a corner, or then the huge books of [insert popular sci-fi/fantasy work]), he won't tell you about it;

his favorite book when he was a child was "the hitchhiker's guide to the galaxy" (I hope I wrote the og name right, I had to search up) and after that he only got deeper into sci-fi;

he was the type of kid that read and watched things when he wasn't the right age, so he was like 13/14 and watching stuff like game of thrones and the og blade runner 😭

this is a bit self-indulgent, but I hc that he loved spider-man when he was a child, and so did sejanus, and they bonded over him being their fav hero.