#logic problem

[educationaldm]

Try this neat little dungeon puzzle from Reddit user u/vaz_de_firenze.

#Dungeon #Puzzle #Brainteaser #Logic Problem #DnD #D&D #Dungeons and Dragons #Fantasy #TTRPG #Tabletop #RPG #Roleplaying Game #Dungeon Master #Game Master #vaz_de_firenze

[brucewaynehater101]

Alright. Willis Todd being an abusive father to Jason is a trope often utilized. Comparing this version of him to Bruce's reactions to Red Hood is fantastic. Lots to analyze there.

However, I raise you. There needs to be more fanwork addressing the classism behind Willis Todd being characterized as an abusive alcoholic. In some version of canon, Willis Todd was a good dad in a shitty situation. He was poor, his wife (Catherine) was sick, and he had a newborn baby he needed to provide for. In this horrid situation, where he has no family to fall back on and no higher education to obtain a decent well-paying job, he tries to get quick money. He's desperate to keep both his wife and son alive.

Catherine turns to drugs because it's easier and cheaper to buy drugs than healthcare. The pain she experiences is debilitating, and she'd do anything to not feel pain for one godsdamned second. Unfortunately, this turns into an addiction.

This ultimately shapes the way that Jason views crime. Bruce, while he may be sympathetic to individuals who resort to crime to pay their bills, will not understand huddling in Crime Alley in the dead of winter as he debates whether to buy food or pay for heating. He won't understand the bitterness, hatred, pain, and resignation of never having enough money to survive as you get chewed up again and again.

If Jason's dad is just an abusive criminal, that not only perpetuates the notion that all criminals are evil, but it will shape how Jason views those who commit crime. Breaking the law doesn't make someone bad. There's plenty of reasons people commit crime, whether to survive, protect someone, or something else. The issue, especially in Gotham, is the system that perpetuates wealth inequality through bribes and unethical governmental practices.

Anyway, I think Jason's Red Hood is more fleshed out if it accounts for him acknowledging the desperation behind goons and small-time criminals because he grew up without other options.

#dc comics #dc universe #jason todd #catherine todd #willis todd #as far as i know catherine's health problems (outside addiction) are implied but not explicitly stated #yes jason did crime as well as a kid but seeing your father commit crime to survive is another matter #bruce commits crime out of choice not survivalistic need #bruce has suffered but he doesn't have this experience or understanding that Jason did #bruce and jason can both understand logically that gotham systems are fucked but jason knows it intimately #jason being bitter and angry at the world for the wealth inequality and corrupt/cruel systems in place should come up more

[arttitude130]

disco in my brain

#disco elysium #de skills #harry du bois #kim kitsuragi #my magnum oppa style #rhetoric and logic are having a heated debate while encyclopedia moderates #endurance is trying to comfort pain threshold but blaims all his problems on wo men #(authority agrees) #perception is just describing things to hand/eye #empathy is trying to comfort half light but composure is judgemental #visual calculus is just talking to himself bc i didnt know how else to include it sorry vis #and i think the rest are self explanatory #but i may post individual/larger pics of them later

[daftmooncretin]

if captain kirk irresponsible? why huge baby cow eyes???

if captain kirk bad captain? why-

you thought i was gonna talk about his voluptuous titties fat ass sparkling personality and unflinching moral character ? no.

if you say kirk is a bad captain i will kill you. I will shoot you into space like they did to bill shatty when he wouldn’t shut tf up about going to space

except unlike bill shatty ill send you up naked and defenceless into the vast chasm of space your lungs will explode and your eyes will fall out or some shit (i saw that in a doctor who episode)

kirk drift is getting out of hand and my response to this is ending all kirk drifters and repopulating the earth with kirklophiles such as myself and my dad paul.

#also kirk is neither irresponsible or a bad captain he leads with and incredible mix of compassion logic and patience #he deeply respects star fleet and the work he does for it but has no problem challenging both their views and his own for the good of other #puts his crew first at all times #deep curiosity and hope for the future #also cunty #kirk drift #i have not slept in 36 hours #i spent 5 hours writing wwdits fanfiction on microsoft notes and eating icing out of a tub #im trying to get into the next gen but i miss kirk so much #picard is so bald and straight #and the sexism is somehow worse #idk #im so tired #and i need to clean my depression room cause my moms coming to visit #boooooo #star trek tos #star trek #spirk #jim kirk #spock

[buggedmind]

Sometimes I avoid talking to you - not because I don't love you anymore, but because I love you so much, and I'm damn scared of losing you. So I force myself not getting "too attached" to you to avoid the overwhelming pain when you leave.

(It doesn't really work, though.)

#bpd logic #actually bpd #actually mentally ill #bpd problems #bpd thoughts #bpd #bpd feels #actually borderline #borderline blog #quiet borderline #bpd favorite person #bpd fp #bpd love

[infiniteorangethethird]

not smart as in intelligent but smart as in "people use my above average skills in math to deny me support in every other area of life"

#newsflash! most of life isn't like math #most of life isn't as logical and systematic as math #so no. just bc i know how to add numbers together #won't mean i'll know how to cook for example #or go shopping. or apply for a job #or anything really #neurodivergent #actually neurodivergent #autistic #autism #actually autistic #adhd #actually adhd #gifted kid problems #gifted kid burnout #gifted kid syndrome

[delawaredetroit]

Exhibit A of how Aizawa's decision to pair Izuku and Bakugou was only intended for Bakugou's growth. There is no mention or concern about how Bakugou's presence stunts Izuku's growth as well. He was only concerned about Bakugou's personal stagnation.

The dadzawa characterization seems to have poisoned a lot of the fandom to Aizawa's actual earlier characterization. At least early on, Aizawa primarily treats Izuku as a burden, a strawman to tear down about All Might's brand of heroics, or as an obstacle to Bakugou's character development.

#bnha reread #bnha 60 #bnha #aizawa shouta #aizawa critical #bakugou katsuki #midoriya izuku #he is a realistic terrible teacher though #the problem is that the narrative thinks it's good or at least passable for some forsaken reason #though if he is supposed to be “logic” personified - it makes sense he wouldn't like izuku #though still fails bc aizawa is “logical” in the same way overly emotional men claim they are all abt that logic and reason

[muppet-on-a-spit]

let's say that the infinite train runs on computer code, which is why it was able to be hacked by amelia and (to a lesser extent) tulip. let's also say that each car has its own unique code to some extent, because they are contained worlds with different denizens, rules, and puzzles. let's say this code is binary. considering the above, when lake was able to leave the chrome car, they broke their attachment to that code. you might say. this made them non-binary. 👍🏳️‍⚧️

#infinity train #b2 #lake infinity train #gray speaks #sorey for structuring this like a logic problem. do u still think im hot

[honeyblockm]

Journeying Into the Center of the Earth to Retrieve Your Dead Ex-Boyfriend

Document with just the text for easier reading. || Image Sources || ao3 link

Weird little Quackity-centric post-canon divergence AU :)

#yens #my writing #my art #quackity #c!quackity #c!quacknap #technically #i'll see about putting this on ao3 but that is a problem for later and not rn #this is ummm. inspired by the quackityverse stuff that happened a few days ago. not necessarily directly i just read something and my brain #took several large leaps of logic #to get here #we stay silly!

[educationaldm]

Puzzle time. An interesting coin logic problem today, brought to you by @PuzzleADayBlog. The solution is in the reply to the original post, and is a bit math-sy.

#Puzzle #Coin Problem #Logic Problem #Brainteaser #Math #Maths #Mathematics #Puzzle a Day Blog

[densitywell]

it feels weird to frame Ashton's current drive as wanting to be The Most Special and Chosen with this implication that he's being selfish or entitled with what he wants. Ashton, who can count the really good days in their life on their hands, who's been in constant pain for god knows how long. Ashton, a blank slate, deprived even of the meaning that comes from a history and identity. Ashton, deemed so worthless that even a group that called themselves the Nobodies abandoned him.

Ashton was not full and asking to feast; he was starving and asking to be fed. They weren't begging the gods to make them a champion and hand them a spell list, they just wanted someone to pick them up when they fell down for the first time in their life. instead, the gods (in any shape or form he could recognize) left him alone until the moment he become a problem for them.

of course he resents them. and of course he's grasping on to the first answers he's found, the first indication that he's ever mattered. it's fascinating to watch Ashton try to feel empowered by their world-altering burden instead of overwhelmed, and make decisions they'll think were fucking stupid in 20 episodes, and just overall try and tie his disparate parts together into one functioning whole, even if he's not really succeeding. especially if he's not really succeeding! we're not watching Ashton fly too close to the sun, asking for too much and getting burnt. we're watching them trying, clumsily and haphazardly, to pick up their broken pieces and create themselves anew.

#critical role #cr #ashton greymoore #cr spoilers #crposting #finally found the words to express something that's been bugging me since July. or at least most of them #it feels like a lot of people believe that the gods handing out power (or at least the primes) are acting on some sort of internal logic #or merit-based system to see who “deserves” it. and so if you don't get blessed you must be the problem. #which. simply does not seem to be the case lmao

[bluesyogurt]

#that moment #mister impossible #when ronan chose to face his real problems #one of his most logic concerns #ronan lynch #the raven cycle #tdt #adam parrish #pynch #maggie stiefvater

[m---a---x]

Welcome to the premier of One-Picture-Proof!

This is either going to be the first installment of a long running series or something I will never do again. (We'll see, don't know yet.)

Like the name suggests each iteration will showcase a theorem with its proof, all in one picture. I will provide preliminaries and definitions, as well as some execises so you can test your understanding. (Answers will be provided below the break.)

The goal is to ease people with some basic knowledge in mathematics into set theory, and its categorical approach specifically. While many of the theorems in this series will apply to topos theory in general, our main interest will be the topos Set. I will assume you are aware of the notations of commutative diagrams and some terminology. You will find each post to be very information dense, don't feel discouraged if you need some time on each diagram. When you have internalized everything mentioned in this post you have completed weeks worth of study from a variety of undergrad and grad courses. Try to work through the proof arrow by arrow, try out specific examples and it will become clear in retrospect.

Please feel free to submit your solutions and ask questions, I will try to clear up missunderstandings and it will help me designing further illustrations. (Of course you can just cheat, but where's the fun in that. Noone's here to judge you!)

Preliminaries and Definitions:

B^A is the exponential object, which contains all morphisms A→B. I comes equipped with the morphism eval. : A×(B^A)→B which can be thought of as evaluating an input-morphism pair (a,f)↦f(a).

The natural isomorphism curry sends a morphism X×A→B to the morphism X→B^A that partially evaluates it. (1×A≃A)

φ is just some morphism A→B^A.

Δ is the diagonal, which maps a↦(a,a).

1 is the terminal object, you can think of it as a single-point set.

We will start out with some introductory theorem, which many of you may already be familiar with. Here it is again, so you don't have to scroll all the way up:

Exercises:

What is the statement of the theorem?

Work through the proof, follow the arrows in the diagram, understand how it is composed.

What is the more popular name for this technique?

What are some applications of it? Work through those corollaries in the diagram.

Can the theorem be modified for epimorphisms? Why or why not?

For the advanced: What is the precise requirement on the category, such that we can perform this proof?

For the advanced: Can you alter the proof to lessen this requirement?

Bonus question: Can you see the Sicko face? Can you unsee it now?

Expand to see the solutions:

Solutions:

This is Lawvere's Fixed-Point Theorem. It states that, if there is a point-surjective morphism φ:A→B^A, then every endomorphism on B has a fixed point.

Good job! Nothing else to say here.

This is most commonly known as diagonalization, though many corollaries carry their own name. Usually it is stated in its contraposition: Given a fixed-point-less endomorphism on B there is no surjective morphism A→B^A.

Most famous is certainly Cantor's Diagonalization, which introduced the technique and founded the field of set theory. For this we work in the category of sets where morphisms are functions. Let A=ℕ and B=2={0,1}. Now the function 2→2, 0↦1, 1↦0 witnesses that there can not be a surjection ℕ→2^ℕ, and thus there is more than one infinite cardinal. Similarly it is also the prototypiacal proof of incompletness arguments, such as Gödels Incompleteness Theorem when applied to a Gödel-numbering, the Halting Problem when we enumerate all programs (more generally Rice's Theorem), Russells Paradox, the Liar Paradox and Tarski's Non-Defineability of Truth when we enumerate definable formulas or Curry's Paradox which shows lambda calculus is incompatible with the implication symbol (minimal logic) as well as many many more. As in the proof for Curry's Paradox it can be used to construct a fixed-point combinator. It also is the basis for forcing but this will be discussed in detail at a later date.

If we were to replace point-surjective with epimorphism the theorem would no longer hold for general categories. (Of course in Set the epimorphisms are exactly the surjective functions.) The standard counterexample is somewhat technical and uses an epimorphism ℕ→S^ℕ in the category of compactly generated Hausdorff spaces. This either made it very obvious to you or not at all. Either way, don't linger on this for too long. (Maybe in future installments we will talk about Polish spaces, then you may want to look at this again.) If you really want to you can read more in the nLab page mentioned below.

This proof requires our category to be cartesian closed. This means that it has all finite products and gives us some "meta knowledge", called closed monoidal structure, to work with exponentials.

Yanofsky's theorem is a slight generalization. It combines our proof steps where we use the closed monoidal structure such that we only use finite products by pre-evaluating everything. But this in turn requires us to introduce a corresponding technicallity to the statement of the theorem which makes working with it much more cumbersome. So it is worth keeping in the back of your mind that it exists, but usually you want to be working with Lawvere's version.

Yes you can. No, you will never be able to look at this diagram the same way again.

We see that Lawvere's Theorem forms the foundation of foundational mathematics and logic, appears everywhere and is (imo) its most important theorem. Hence why I thought it a good pick to kick of this series.

If you want to read more, the nLab page expands on some of the only tangentially mentioned topics, but in my opinion this suprisingly beginner friendly paper by Yanofsky is the best way to read about the topic.

#mathblr #mathematics #set theory #diagram #topos theory #diagonalization #topology #incompleteness #logic #nLab #Lawvere #fixed point #theorem #teaching #paradox #halting problem #math #phdblr #Yanofsky #Cantor #Tarski #Gödel #Russell #philosophy #category theory

[girlgerard]

mommm white people on tumblr are misconstruing my posts again despite the post being entirely about how important wording is + how i don’t feel comfortable posting large statements when i haven’t fully processed them yet.

#if you want to put me on a blocklist for loving netanyahu you can! i don’t! and no matter how many times i get told i do #i still don’t! #i literally said i hope his balls get cut off IN THAT POST #i don’t know how that read as unclear. #perhaps there are no hidden genocidal messages behind the wording of my tumblr posts - who knows! #when i said i cared about every single civilian living in that land i meant it. if you decide that i actually don’t that’s not my problem #if you somehow took my words and decided that what i really meant is that i’m a government bootlicker who loves murder #you can do that all you want. it won’t make it true and it won’t help save any lives #i was in ramallah and jerusalem six months ago. have you gone? #if the answer is no maybe think about that for a second #moreover if you’re viewing this from a purely racial or religious framework you have no idea how to navigate this subject #i don’t view israel and palestine through which government i want to back. why the fuck would i do that #palestinians and jews and everyone else in that land is who i care about. i care about gazans #if that’s not enough of ‘a side’ for you i don’t really think there’s much of a conversation to be had. #do you think i wake up every day NOT thinking about gaza? do you think i wouldn’t feel nauseous every second of every day because of gaza? #do you think that within everything i’m saying that the most logical conclusion would be to post all of my thoughts on tumblr? #because if you think any of that we’re not going to have a productive conversation. i don’t take kindly to being told my own emotions

[comradekatara]

something i love about kavik is that even though he was raised in the northern water tribe he has no qualms whatsoever regarding the stigma associated with healing as a feminine artform. he mostly just regrets not being better at it because he thinks that saving lives and easing people’s pain is the best and coolest thing you can do with waterbending. and he’s right

#although come to think of it both he and kalyaan have no problem deferring to powerful women #so maybe their mom is really awesome #kavik #the legacy of yangchen #guy who is obsessed with the sanctity of the nuclear family but somehow does not subscribe to the patriarchal logic that women are inferior #yeah. his mom is awesome

[thedreadvampy]

unwarranted Cis Opinion but I'm getting really uncomfortable w people responding to bathroom bills by posting pictures of trans men like DO YOU WANT THEM IN WOMEN'S BATHROOMS

bc like. no they're men. they should be in men's bathrooms unless that feels unsafe. but. it really feels like it's not helpful to lean into the idea that seeing someone presenting masc or being read as a man in a women's bathroom means You're In Danger.

like I know several butch women and NB ppl who are really scared around being on T or getting top surgery bc they're not men and they don't want to be in the men's bathroom, and in that circumstance stuff like growing facial hair or reading more androgynously can be really fucking scary when people are being primed by propaganda to be on edge and hyperreactive to anyone who doesn't look like their idea of a Cis Woman.

and I'm not laying that at the feet of the people saying "hey uhhhh trans men are men and don't belong in women's bathrooms" bc it is not their fault. it's the fault of a concerted effort to make it difficult and dangerous to be trans or substantively gender nonconforming in public.

but at the same time idk I guess it just worries me cause sometimes it feels like "you fools! you are worried about this group of trans people bc you think they're the Lurking Danger of Men In Bathrooms? WRONG! the Men Making You Feel Afraid In Bathrooms are actually THESE trans people!" when in fact neither of those groups using the fucking bathroom is a problem. just piss and mind your business. people need to go where they need to go.

anyway this country is a hot fucking trash fire that somehow accelerates its descent into open fascism more every day so it's all super good and normal. so don't take this too seriously tbh cause it's somewhere near #2535654476457899009765 on the list of priorities for Queer Discourse right now when the fucking human rights commission is actively rescinding protections from trans people. Please ignore my gibberish.

#red said #i get that the point is to follow their logic to its logical conclusion like SEE THE EFFECT IS THE OPPOSITE OF YOUR STATED INTENTIONS #but a) the lawmakers already know this tbf #and also b) ultimately you still do end up making a lot of tweets that look very very very like the original scaremongering abt trans ppl #and transphobes and ppl who are unfamiliar with trans stuff alike have repeatedly and consistently demonstrated either an unwillingness #or an inability. to understand the difference btw a trans man and a trans woman. #and meanwhile idk it does feel like most posts like this are tacitly reinforcing the idea that you SHOULD be scared of masc-presenting ppl #it's putting so much emphasis on clockability. and the truth is not everyone using the bathroom does or should have to pass perfectly. #if a trans woman who looks like one of these trans men needs to piss. a woman with stubble and short hair and muscly shoulders. #SHE HAS EVERY RIGHT TO PISS IN THE WOMEN'S BATHROOM. even if she doesn't look like a cis woman. #if a trans dude looks like a girl he still doesn't belong in the ladies unless he personally feels the need to go there for his safety #if someone is not actively bothering you harassing you or treating you with aggression it's not really any of your business is it #maybe that's a trans man. maybe that's a trans woman. maybe that's a woman or dyke on T. maybe that's a cis woman who just looks masculine. #who gives a shit? a key factor in ladies bathrooms is that they have fucking cubicles. unless someone is making it your business it's not. #and if they are then the problem isn't that they're the Wrong Sex/Gender it's that they're behaving badly/disrespectfully/threateningly #which is also a problem when cis women do it!!!!!