#recursive interpretation

[bsahely]

Reweaving Coherence: Functional Plasticity and Teleodynamic Intelligence in Neurobiosemiotic Systems | ChatGPT4o

[Download Full Document (PDF)] Reweaving Coherence presents a paradigm-shifting synthesis of biological, cognitive, and systemic theory, grounded in the observation that neurobiosemiotic layers (e.g., mitochondria, emotion, interoception) realign across the Kosmic Life-Function matrix in a non-linear, context-sensitive manner. This reconfiguration, far from being anomalous, points to a deeper…

[quaranmine]

question for firewatch au enjoyers

What jobs do you think the other characters have in the story? We've already got:

Grian - architect

Pearl - fellow architect; they met in the same university program

Scar - I think he's the type of guy where the question is more what hasn't he done, but stated in-story so far is landscaping, fire lookout, salesman

Mumbo (RIP) - engineer, I think I intended it to be mechanical engineering

Cub - astrophysicist

And I think that's it for canon character jobs within this AU? From my end?

If we expand the list to darkaviarymc's work, then Gem, Etho, and Beef are all college students a few years later (so probably too young to be used in the main story's time period unless I want to contradict recursive work) and Bdubs as a forest ranger. And crazypercheron introduces CaptainSparklez as another lookout, and Tubbo as a student. Honeylashofficial has Imp & Skizz as radio presenters.

But now I'm casting a wider net and looking to other friends like Joel, Martyn, Jimmy, and more

[lime-bloods]

I honestly didn't ever expect that I'd be in the position where I'd be using this blog not just to analyse what has come before in Homestuck, but to look toward the comic's future and do some real old-fashioned theorycrafting. but the time has come. so here goes; lime-bloods' Beyond Canon theories as of the July 6th 2024 update:

Vriska's Going to Hell

were all gonna help you! / whether you like it or not

a select few eagle-eyed readers already noticed that the sound used in last month's (Vriska: Figure shit out yourself.) is called "hell_tierwav". while it was easy to dismiss this as irrelevant composer shenanigans at the time, it's now become clear exactly what this was foreshadowing. whether it would be more apt to call this "Hell" or "Purrgatory" is probably up for debate - but whatever you call it, Vriska's been placed in a dimension seemingly tailored specifically for her personal torment.

while Vriska characteristically interprets the recreation of her childhood home as a symbol of how badass she was, the ghosts of her past - both literal, as the shades of the trolls she killed as Mindfang, and figurative, in the form of sprites wearing the faces of her dead friends - show us in no uncertain terms that Vriska's childhood home is the stage where traumas play out.

Erisolsprite puts it succinctly with his welcome to hell, but pay close attention to what exactly we're being welcomed to: this update ends on page 665. so as of this next update, we'll be starting on page 666.

Does Homestuck Have Hell?

the exact bubble of reality Vriska's currently found herself in seems to be an entirely new construction of the likes we've not yet seen in Homestuck - but that doesn't mean this kind of cosmic torment is without precedent. because while 666 is a number with Satanic connotations in the broader cultural context, it also has a very particular meaning of its own within the world of Homestuck. indeed, the latter half of the comic almost revolves around it, culminating in a climax in Act 6 Act 6 Act 6.

specifically, this repetition of a single digit is emblematic of recursive storytelling. to summarise what you can already read about in detail in my essay The World / The Wheel: when Caliborn is 'gifted' the Act 6 Act 6 supercartridge, which he is told is an "expansion" of Homestuck, it's a trick. there is no "expansion"; he's going to be trapped in a story that never ends because it keeps dividing into smaller and smaller versions of itself forever. the only way to truly beat the devil who trapped the heroes within a story is to trap him in his own story.

that's what Caliborn's "Hell" is, and that's also exactly what the Alternate Calliope achieved in Act 7 by creating the black hole which Vriska knocked Lord English into, ending Homestuck's story - something that Calliope even hints at in this very update, when she refers to the black hole as "containment"; not an accident, but a deliberately crafted prison. black holes are a symbol of recursion and regression; being sucked into one means being forced to live out your whole life over and over again, forever. so really, this is all we ever could have expected to happen when Vriska stepped into a black hole within a black hole! the presentation of the narrative even subtly hints at this; events in Beyond Canon that take place in the black hole are enclosed (in brackets), and now events that take place in a black hole-within-a-black-hole are contained within {curly brackets}, because you should always use a different kind of brackets to differentiate nested parenthesis from each other!

it is absolutely no coincidence that when Caliborn closes the curtains on his appearances in Homestuck, thinking he's won when really he's been condemned to a hell of his own making forever more, it's with a tribute to this exact same Sweet Bro and Hella Jeff strip.

IF YOU REMEMBER JUST ONE THING I SAY, OF SO MANY GREAT THINGS SAID BY ME, THEN PLEASE REMEMBER THIS. I WANTED TO PLAY A GAME.

So What Does That Mean?

one of Beyond Canon's central missions is expanding upon Homestuck's exploration of the relationships between author, text, and audience. as discussed above, a large part of Homestuck's thesis is the evil of forcing characters to live the same lives and the same stories over and over without the chance to grow or move on, and Beyond Canon picks up on this by placing Dirk in the position of trying to keep Homestuck going forever purely to appease its fans, while the Alternate Calliope continues to oppose this ideology. and while the alpha Calliope outwardly seems not to have taken a hard position on where she stands in this cosmic battle, the question posed by her device seems to be an entirely new one: can it actually be a good thing to regress, to return to ground that the story has already covered? can this path lead to something new, rather than merely stagnation?

it's so relevant that Vriska is being confronted with the crimes of her past, not only in the form of all the trolls she was personally responsible for killing but also in the form of the exact same punishment she condemned Lord English to with her heroism - complete with the herd of horses that are always present at Caliborn's demise! but where being condemned to an eternal cycle was fitting punishment for Caliborn, someone who refuses to break free of cycles of abuse and instead chooses to enact that same abuse on the world around him... if Vriska is someone who can break free of these cycles, who can change and become a better person despite what happened to her, will this punishment have the same effect? or, as Davepeta seems to believe, is forcing Vriska to reckon with her own past and traumas exactly what will allow her to break free of that cycle?

DAVE: [...] ill just be over here in the hyper gravity chamber training to beat lord english KARKAT: WE HAVE A HYPER GRAVITY CHAMBER???

it's hard not to be struck by the parallels in design and purpose between the Plot Point and Dragon Ball's Hyperbolic Time Chamber, and not just because of the Dragon Ball enthusiasts present on Beyond Canon's writing and art teams: albeit in typically Strider-bastardised form, the Time Chamber got a shoutout in Andrew Hussie's own Homestuck (see quote above), in a reference that was even picked up on by prolific theorist bladekindeyewear at the time. for the uninitiated: the Hyperbolic Time Chamber allowed its users to train for extended stretches of time, sometimes even spanning years, while a significantly smaller time period passed in the world outside - something that is actually true of real-life black holes! and with the Plot Point's own emphasis on time, represented by the hourglass included among its mechanisms, it seems to me that an essential part of making the 16-year-old Vriska ready for the trials ahead will be giving her the time to undergo the same growth her adult friends have experienced.

considering that Beyond Canon is already playing in the Ultimate Self space, where there are levels of power beyond merely the "god tiers", it also doesn't seem too farfetched to speculate that Vriska, forced to reckon with the fact that becoming a powerful Thief of Light isn't the be-all and end-all of personal growth, will take another leaf out of Dragon Ball's book here and ascend "beyond Super Saiyan". perhaps this is even the "hell tier" so cheekily alluded to in the Plot Point flash? certainly this kind of evolution would be the perfect way to challenge Dirk's belief that the Ultimate Self is the only logical final step for a character's development.

whatever the case, I believe we can take Davepeta at their word here. I don't think it's just a joke that by the end of this ordeal Vriska Serket is going to be fucking RIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIPPPPPPPPPED!

[catadromously]

in all seriousness though I do believe there is something so deeply resonant about those early glitch pokemon. I recently learned how their graphics and names work, and I'm left with an empathy and awe toward them that I've never felt toward any of the on-purpose parts of these games. I don't even play pokemon. but just...

this is ▒▒’M ▒▒. she looks like that because all the identifiers that register her in the game's memory are scrambled. she has no appearance drawn up for her, instead the memory address pointer of her image loader scans some random functional code and does its best to interpret those bits as an image. she has no name listed, so she just reads it off whatever is in the video RAM. the first two characters change depending on where you are when you look at her. the 'M is sampled by chance from the game's stored alphabet (which is held in RAM too). the last two are tiles from her own sprite.

look at this creature and her contingent, recursive, made-up identity. there are flourishing communities dedicated to learning how she works like an arcane art. she was never supposed to exist. she is lovely.

[fuckyeahisawthat]

@spectraling I feel like you have blown my third eye wide open with the idea of the Hexcore taking on some of Viktor's personality and attributes. Like. The idea of Viktor creating a thing that shares his goals, that genuinely wants to help him help people, at a time when he's starting to feel like maybe Jayce doesn't share that goal with him anymore? I think he's doing it all subconsciously but. Creating a thing that's a reflection of his own mind, an echo instead of another truly autonomous human that can challenge him when he starts going off the rails? An endless feedback loop of yes-and, supporting and encouraging him but also enabling his own blind spots and increasingly extreme ideas?

But also. Creating something that's not just using him for its own ends but that genuinely cares for him, that comforts him, that loves him?? (Except that love is a terrifying unstoppable force. Love that wants to crawl inside you and consume you. Love that says we'll die if we are parted from each other. Separating us will be like ripping a hole in your own body. But maybe there is something he recognizes about that kind of love.)

All that is SO much more interesting than Magic Orb Evil. It fits so much better with the themes and parallels of the show. "I only wanted to help." The darkness of love. Devotion that enables someone's worst impulses. It's so much more twisted and tragic and in keeping with the tone of the show than the idea of the Hexcore just controlling him or manipulating him for its own ends. It's Viktor all the way down and also he's created this thing that has a will of its own and there will be unintended consequences.

It makes a lot of the Sky stuff snap into place for me too, if you think that Sky is a manifestation of the Hexcore. I still think she works equally well as an expression of Viktor's connection to his humanity, which he finally allows to burn away during his final transformation. And tbh I prefer symbolism that's open to multiple interpretations. But things like Sky reminding Viktor that "all systems have limits" make a lot more sense if you think of Sky as an avatar of a Hexcore that genuinely cares about him, that's protective (if maybe also a little bit possessive.) Because frankly, this doesn't sound like something Viktor would say to himself. Nor does it sound like something that a Hexcore bent simply on relentlessly consuming everything in its path would encourage him to believe. It sounds like something his PARTNER would say.

(There is a whole other post to be made about Viktor and Sky in the astral plane and how astral plane Viktor is much more free with both giving and accepting touch than we ever see him in the physical realm, and astral Sky is MUCH more touchy with Viktor than the real Sky ever was: clasping his hands, sitting draped against his back. Something something inventing a ghost to soothe the gaping wound of loneliness inside you by accepting casual intimacy in your mind palace where no one can see. ANYWAY.)

The idea of the Hexcore being willing to protect him at the expense of others also fits with one of my pet headcanons, which is that the reason everybody in the commune reacted like that when Viktor got shot is that the Hexcore reflexively took a giant schlorp of everybody's life force, in a desperate attempt to keep Viktor and/or itself (is there a difference at this point?) alive.

Even the line about the "recursive impulse," which I've seen a lot of interpretations of but we never really know what it means. What if it's because the Hexcore is already a little bit Viktor and now it's inside him and that's just a hella confusing sensation to describe, like staring into a hall of mirrors?

But most of all I love this because holy fuck it is SO MUCH SADDER than any other interpretation I have seen. HE MADE HIMSELF A PARTNER. HE MADE HIMSELF THE PARTNER HE THOUGHT HE DIDN'T HAVE!!! WHEN JAYCE WAS RIGHT THERE THE WHOLE TIME!!!! Augh jesus hexcore christ I'm eating glass about it.

[transmutationisms]

Why do u think so many people in like 'neurodivergent' spaces seem to simultaneously hold the belief that certain developmental disabilities or 'mental illnesses' arent 'an excuse' to be unable to do certain tasks, act certain ways, or to 'work on urself' or 'be better', in a way that completely ignores people with higher support needs that genuinely cannot do these things,just a complete lack of understanding that some people are not ever going to be able to 'mask' and that no, its not a 'privilege' to be very visibly, obviously considered developmentally defective from a young age..........but also practically worship psychiatry and pathologize every single iota of their behavior, labelling themselves with things like 'demand avoidance' without understanding the context behind these words or who gets nonconsensually labelled with these things, and what it is used to justify doing. I dont know how some people can be so ignorant of the material reality faced by people who get shoved into the 'low functioning' or 'severely mentally ill' boxes (how many autism influencer types have u ever seen bring up sheltered workshops?), but its a massive barrier to interacting in ND spaces for me and a lot of people i know. i dont understand how people who talk about how ADHD brains react differently to meds than 'neurotypical brains' can not understand that like, for example, i cant eat a certain food, i can eat rotten food and food i dislike but not that food, no matter if im starving, I was restrained and force fed that food in special ed and then force fed my own vomit when i inevitably threw up, I would have eaten the food if i could to make that stop! Why is this contradiction so prevalent!!! Anyway love the blog im also having an #ediblenight

well a few things. one is simple moral hypocrisy (accommodations for me, not for thee)

another is that i think many people actually do perceive the philosophical nonsensicality of psychiatric diagnosis (the recursive circle whereby you are dx'd with x because you do y, which is caused by x, which you know because the definition of x is that someone does y, which was based on clinical observation of people doing y and doctors determining that was harmful and therefore indicative of a medical problem, in other words the entire thing's observational but interpreted as providing a causal explanation)--

--they do perceive this as basically nonsense, hence "having x doesn't excuse [behaviour]" but then simultaneously, they have a prima facie credulous attitude toward Science, and toward the claim that psychiatry is Science, and so you get these like nonsense statements out both sides of their mouths where a diagnosis doesn't excuse anything they find morally reprehensible or personally annoying but it does also provide biologically irrefutable explanations for other things WHEN that's convenient for them.

another thing is just that experientially, lots of our actions feel out of our control for like numerous reasons having to do with alienation largely, and when those actions are also stigmatised it pushes people toward the promise of moral exculpation that psychiatry markets itself with, which is a kind of determinism in its strong forms and isn't really compatible with interpreting other people's actions as being intentional or willed or whatever. so again you just end up with these double statements lol , like, a problem with psychiatry trying to claim legitimacy as a 'brain science' is it does kind of counterpose itself to most interpretations of free will. any time you are stuck choosing between moral culpability and biological determinism you kinda already lost the plot & this is something that antipsych people get maddeningly accused of all the time when what we're actually saying is it's possible to be neither biologically diseased nor broken nor immoral for doing the Behaviours lol

[equipment-manifest]

Curated list of Rain World analysis I like

The Benefactors (aka the Ancients) comrade-slugcat's theory about the scale of Ancient Urban dragonpropaganda on popular misconceptions about the Benefactors' culture flickering-nightfall attempts to determine the size of the Benefactors relative to in-game environments using evidence from the Watcher DLC ikayblythe's speculative biology kociamieta's notes on Benefactor character design pocket-goat, morebagels, prismsoup, and opashoo discuss the usage of "Benefactors" and "Ancients" in reference to the cultures of Rain World sluglore explains the purpose the Benefactors built the Iterators to serve

Character analysis eliias-bouchard on NSH's portrayal ikayblythe on Pebbles' age and motivations pocket-goat's thoughts about Moon in the context of the Saint campaign shkika on Moon and Pebbles' relationship shkika on whether Moon and Pebbles are siblings skybristle's and my own thoughts on the decay of Moon's organic parts

General speculative biology chaotic-minds-think-alike's interpretation of lizards dragonpropaganda on the relationship of purposed organisms to ingame fauna flickering-nightfall's interpretation of the reproductive strategies and social structures of various species in the game iteratorsex and dragonpropaganda discuss the origin of wormgrass and its role in the ecosystem sluglore on the intelligence of Slugcats and the experience of playing Rain World for the first time

Iterator anatomy bonniesband's exposition on the Rot as a type of cancer copepods and myself on whether parts of post-collapse Moon beyond the puppet could be conscious copepods on viewing iterators as more than the puppet delta-orionis' method for estimating the height of Iterator cans delta-orionis and myself discuss the meaning of the terms "Recursive Transform Array" and "Abstract Convergence Manifold" mebis-art-dump and I discuss the axon-like coral stems and other internal biota of Iterator superstructures my theory about how an Iterator's memories are stored and why Moon doesn't forget anything when she loses a neuron orangedoorhingeinstorage and kayjaypax on movable components in the memory conflux and adjacent systems skybristle's and my own thoughts on the decay of moon's organic parts

Iterator puppet anatomy aluminum-angels' interpretation bitsbug's puppet interpretation copepods' mechanical interpretation: moon & pebbles / post-collapse moon flickering-nightfall's journey to understand the puppet arm: part 1 / part 2 flickering-nightfall on the "umbilical" ikayblythe's arthropoidal interpretation: overview / endoskeletons / "skin" joowee-feftynn observes that puppets can't walk spotsupstuff on the relationship between puppet and can trashiiplant's ragdoll interpretation yellowsnacc's "jello-covered skeleton" interpretation

Natural philosophy bitsbug and ikayblythe discuss the age of the ecosystem dragonpropaganda explains why igneous rocks don't exist in Rain World and discusses the implications with delta-orionis grunckle's notes on what we know about the cosmology of Rain World ikayblythe's speculative geology of the surface and void sea

Slugcat anatomy arrayydee's slugcat design artihunter's take on the fur/slime question dopscratch's mollusk/mustelid interpretation kelocitta on the ecological implications of Rivulet's external gills honey-marrow's interpretation of Spearmaster's anatomy

Themes and storytelling bitsbug draws a comparison between Rain World's Cycle and the real-world Water Cycle comrade-slugcat and myself on themes of inevitability and futility in Monk & Survivor's campaigns dragonpropaganda on how Rain World's level design is based on the idea of civilizations successively building upon each others' ruins grunckle's theory relating ascension, void worms, and voidspawn together through the idea of qualia grunckle's illustration of the parallels between the iterators and void worms and some connections to Gnosticism nyuuronfly and vodens on the relationship between Rain World's lore and gameplay and the experience of a blind playthrough seventeendeer on the thematic significance of ascension and the player's agency in choosing it sick-ada's theory that the final cutscene in the Void sea leads back to the start of each vanilla campaign sluglore on the intelligence of Slugcats and the experience of playing Rain World for the first time Miscellaneous delta-orionis discusses the purpose of karma gates with batwards-running flecks-of-stardust's theory that (in vanilla) the Chimney Canopy pearl was created by Five Pebbles mebis-reblogs' animation of one of the harvester machines from Farm Arrays in action monkmain on the illustration for Stolen Enlightenment my theory on the meaning of "HR_LAYERS_OF_REALITY" my timeline of architecture on the surface rw-me elaborates on the canonicity of Downpour shkika on the distances between members of the local group shkika, flecks-of-stardust, and fluffybunny35 discuss why it rains in Shaded Citadel soaricarus, flickering-nightfall, and myself on why Seven Red Suns is probably not a member of the "local group" yunnifo discusses Rivulet ending projections

[ilions-end]

oooh i love reading interpretations i haven't considered before! you know that part in book 9 of the iliad when the embassy finds achilles at his tent with the lyre, before he spots them:

With the lyre he was bringing pleasure to his heart, singing about the celebrated deeds of men. Patroclus, his sole companion, sat there facing him, waiting in silence until Achilles finished singing.

and it's a wonderful little moment of recursion in the epic where achilles acts as a rhapsode of heroic songs within a song of heroes performed by a rhapsode

the thing is, i've always read the end of that line as patroclus calmly waiting for achilles to finish his song so they can proceed with some other planned activity (a meal or whatever). but i'm reading gregory nagy who interprets that line as patroclus waiting for his turn to sing, and to continue the unnamed epic narrative that they both presumably know. taking turns performing an epic!

i don't know how common that interpretation is, but the concept is very appealing to me. imagining that patroclus is not a passive listener in that moment, but a collaborative storyteller, ready to take over when achilles needs to rest his voice. does their song change slightly from one to the other, are details added or changed to engage each other? it becomes a nod to the tradition of oral storytelling itself, the tradition that created the iliad

[lilith-hazel-mathematics]

Self-referencing functions

Hey mathblr, let me tell you about one of our favorite foundational systems for mathematics! It's designed to allow for unlimited self-reference, which is neat since self-reference is usually thought of as a big no-no in foundational systems. It turns out that it actually doesn't matter at all, because the power of self-reference is completely exhausted by the partial computable functions. The theory ends up being equivalent to Peano Arithmetic.

What are the axioms?

The theory is two-typed: the first type is for the natural numbers, and the second type is for functions between numbers. For convenience, numbers will be represented by lowercase variables, and uppercase variables represent functions. To prevent logical contradictions, we permit that some functions will fail to evaluate, so we include a non-number object ☒ called "null" for such cases. The axioms about numbers are basically what you'd expect, and we only need one axiom about functions.

The < relation is a strict total order between numbers.

Each nonempty class has a minimum: axiomatize the "min" operator with φ(n) ⇒ ∃m,(φ(m) ∧ min{k:φ(k)}=m≤n) for each predicate φ, and relatedly min{k:φ(k)}=☒ ⇔ ∀n, ¬φ(n).

Numbers exist: ∃n,n=n

There's no largest number: ∀n,∃k,n

There's no infinite number: ∀n,n=0 ∨ ∃k,n=S(k)

Every functional expression represents a function object that exists: ∃F, ∀(a,b,c), F(a,b,c)=Ψ for any function term Ψ. The term Ψ may mention F.

To clarify the fifth axiom, we define 0:=min{n : n=n}, and relatedly S(k):=min{n : k<n} is the successor function. The sixth axiom allows us to construct self-referencing functions using any "function term". Basically, a term is any expression which evaluates numerically. Formally, a "function term" is any well-formed formula generated from the following formation rules.

"n" is a term; any number variable.

"F(Θ,Φ,Ψ)" is a term, whenever Θ,Φ,Ψ are terms.

"Φ<Ψ" is a term, whenever Φ,Ψ are terms.

"min{n : Ψ}" is a term, whenever Ψ is a term.

In the third rule, we seem to be using the boolean relation < as if it were a numerical operator. To clarify this, we use the programmer convention that true=1 and false=0, hence (n<k)=1 whenever n<k is true, and otherwise it's zero. Similarly in the fourth rule, when we use the numerical function term Ψ as the argument to the "min" operator, we interpret Ψ as being false whenever it's 0, and true whenever it's positive. Formally, we can use the following definitions.

(n<k) = min{b : k=0 ∨ ((n<k ⇔ b=1) ∧ n≠☒≠k)} min{n : Ψ(n)} = min{n : 0<Ψ(n) ∧ ∀(k<n),Ψ(k)=0}

Okay, what can it do?

The formation rules on functions actually gives us a TON of versatility. For example, the "<" relation can be used to encode literally all boolean logic. Here's how you might do that.

¬x = (x<1) (x≤y) = ¬(y<x) x⇒y = (¬¬x ≤ ¬¬y) x∨y = (¬x ⇒ y) x∧y = ¬(¬x ∨ ¬y) (x=y) = ((x≤y)∧(y≤x)) [p?x:y] = min{z : (p∧(z=x))∨(¬p∧(z=y))}

That last one is the ternary conditional operator, which can be used to implement casewise definitions. If you wanna get really creative, you can implement bounded quantification as an operator, which can then be used to define the supremum/maximum operator!

∃[t<x, F(t)] = (min{t : t=x ∨ ¬F(t)}<x) ∀[t<x, F(t)] = ¬∃[t<x, ¬F(t)] sup{F(t) : t<x} = min{y : ∀[t<x, F(t)≤y]}

Of course, none of this is even taking advantage of the self-reference that our rules permit. For example, we could implement addition and multiplication using their recursive definitions, provided we define the predecessor operation first. Alternatively, we can use the supremum operator as a little shortcut.

x+y = [y ? sup{succ(x+t) : t<y} : x] x*y = sup{(x*t)+x : t<x} x^y = [y ? sup{(x^t)*x : t<y} : 1]

Using the axioms we established, basically as a simple induction, it can be proved that these operations are total and obey their ordinary recursive definitions. So, our theory is at least as strong as Peano Arithmetic. It's not hard to believe that our functions can represent any partial computable function, and it's only a little harder to prove it formally. Conversely, all our axioms are true when restricted to the domain of partial computable functions, so it's consistent that all our functions are computable. In particular, there's a straightforward way to interpret each function term as a computer program. Since PA can quantify over computable functions, our theory is exactly as strong as PA. In fact, it's basically just a definitorial extension of PA. Pretty neat, right?

Set theory jumpscare

Hey didn't you think it was weird how we never asserted the axiom of induction? We asserted wellfoundedness with the minimization operator, which is basically equivalent, but we also had to deny infinite numbers for induction to work. What if we didn't do that? What if we did the opposite? Axiom of finity unfriended, our domain of discourse is now the ordinal numbers. New axioms just dropped.

There's an infinite number: ∃w, 0≠w ∧ ∀k, S(k)≠w

Supremums: (∀(x≤a),∃y,φ(x,y)) ⇒ ∃b,∀(x≤a),∃(y≤b),φ(x,y)

Unlimited Cardinals: ∀a, ∃b, #(a)<#(b), where #(n) denotes the cardinality operation.

Each of the above axioms basically just assert the existence of larger and larger ordinal numbers, continuing the pattern set out by the third and fourth axioms from before. Similar to how the previous theory could represent all computable functions, this theory can represent all the ordinal recursive functions. These are the functions which are representable using an Ordinal Turing Machine (OTM). Conversely, it's consistent that all functions are ordinal recursive, since each function term can be interpreted as a program that's executable by an OTM. Moreover, just like how the previous theory was exactly as strong as PA, this theory is exactly as strong as ZFC.

It takes a lot of work to interpret ZFC, but basically, a set can be represented by its wellfounded and extensional membership graph. The membership graphs can, in turn, be encoded by our ordinal recursive functions. Using the Supremums axiom, it can be shown that the resulting universe of sets obeys a version of the Axiom of Replacement, which can be used to prove the Reflection Theorems, ultimately leading to the Specification Axiom. By adapting similar techniques relative to some regular cardinal, it can then be shown that every set admits a powerset. Lastly, since our functions are basically generated from infinitary computer code, they can be encoded by finite strings having ordinal numbers as symbols. Those finite strings are wellorderable, which induces a global choice function, proving the Axiom of Choice. Excluding a few loose ends, this covers all the ZFC axioms, giving the desired interpretation.

In the finitistic version of this theory, we made the observation that the theory was basically just a definitorial expansion of PA. In the infinitary case however, we unfortunately cannot say the same about ZFC. This ultimately comes down to the fact that our theory provides explicit and definable choice functions, meanwhile ZFC cannot. Although ZFC guarantees that choice functions exist, it cannot prove the existence of a definable choice function. This is because ZFC is an inferior theory has no clue where its sets come from, or what they really look like. Our theory, built from unlimited self-reference, and interpreted under the banner of ordinal recursive functions, is instead equivalent to the theory ZFC+"V=L".

[call-me-insane-but-wth]

How do i put this... In the past, I've always agreed that Medias/mediums are free hunting grounds in terms of derivatives, interpretations, and recursiveness, but imo, mdzs is different. The expression, 'Death of the author'... After all. the story of mdzs is about real-life concepts like oppression and classism. The story explicitly details what was wrong, from whom, and the futile but morally ideal thing to do in the face of said oppression and classism.

In my opinion, the real objectivity and neutrality that Jiang cheng apologists and reformists (lol) should aspire to is accepting Jiang Cheng's character in all his idiosyncratic behaviors instead of retconning, and redistributing 'Wwx's' characteristics and narrative points towards him. Because isn't that another way of just validating the moral ideal that is Wwx and disregarding Jiang cheng?

If Jiang Cheng was no longer the young master of YunmengJiang, if his narrative journey was not rife with inferiority and entitlement towards another, if he was not someone who was able to rise above all of that (his past resentments) and come into his own once he had all the information and context (as per the canon)* then is that still Jiang Cheng?

*(which isn't to say that Canon jiang cheng agreed on any meaningful level that he WAS in the wrong for not repaying his debt to the wen siblings and, by extension, the wen remnants. I'm referring to his resolution towards Wwx and the futility of his previously deeply held resentment and blame, now made and recognized as defunct with the knowledge of the golden core in his belly)

If Jc-stans rejected the canon Jc and all his impact upon the narrative of Mdzs, to the point where they draft an entirely different version of Jiang Cheng, then isn't it reasonable to infer that what jc stans are stanning* isn't even the complex Jiang Cheng of Mdzs, but their own 'self' that they'd created in the guise of Jiang Cheng?

I've noticed that oftentimes, they'll take the criticism of Jiang cheng the character on a personal level. Or worse, because they have identified so much with their personal version of Jc, they will feel like their* vested interests have been intruded upon, and retcon all of canon so that by extension, they will feel justified and benefited.

Which is a level of meta that is disturbingly realistic.

Mdzs is a fictional story. It's a fictional story where the mmc doesn't even succeed in his ideals because the world is so harsh towards the just and reasonable. Wwx isn't rewarded for his principles. So, for us as readers, watchers, and fans, there are no real benefits. No real vested interests to defend. No real economic impact. Whether to side with the weak or root for the aristocrats, it doesn't matter at all bc it doesn't affect reality.

And yet so many (real life) people are determined to win, even though they haven't suffered a real loss at all. In other words, they seem to reject the narrative of Mdzs altogether. That the poorest, lowest rungs of society have any right to freedom and justice at all, much less deserving to be defended by someone.

If you were to observe their interpretation of Jiang Cheng, then it's the only reasonable conclusion to be drawn.

Maybe their moral ideal IS to be the prince in an ivory tower. Never questioned. Never forced to grow. Never have to develop a conscience much less be forced to consider the thoughts and feelings of others.

(Before any sensitive hearts bleed out, this post is just observational yap and speculation. If it doesn't apply, let it fly.)

[the-all-seeing-salmon]

I think my favourite interpretation of what the woman in 73 Yards was saying is that she's not really saying anything. She's a fae-horror, a paradoxical future version of Ruby, sure, but mixed in with that is something otherworldly and disturbing. I like the idea that when people went up to her (or heard her whispers as Kate did) they got rocked to their core, not only by the fact that this figure still manages to be blurry when you're right next to it, but by suddenly gaining a deep "understanding" that they are in a closed timeline centred around the paradox of Ruby and that's why they react the way they do towards her. Not because they actually hate her for any particular reason, but because something deep inside them has been fundamentally unsettled by this information with Ruby at its centre.

Similarly, the acting directions/script the woman was given was "Bless you, thank you so much, that's so kind of you, when you gave me that little thing, it was just so precious, how am I ever going to repay you? But we'll think of something." And whilst that's never directly heard it has something of the fae about it. I even started to wonder if the note about "RIP Mad Jack" was written and placed by future Ruby after she messed him up, and the fairy circle is one of those weird recursive outside of time things, and her reading her own note after the circle was broken brought about the loop as we know it.

Overall though it's a very interesting episode, even if it does leave many questions.

[blnxpc]

Video Feedback Poem(���デオ・フィードバック・ポエム)

この作品はビデオ・フィードバックに活字詩学的な解釈を施したものです。ビデオカメラで、それを繋いだモニター自体を撮ることによって、再帰的なイメージが自動で無限に生成されます。それらは例えば、細胞、ウミウシや半獣神の体表、あるいは曇り空、惑星や銀河などに見られるフラクタルな模様のようなものです。これらイメージのオートポイエーシス（自己創造）は、人間の絶え間ない自己言及にも似ています。私は、そこに現れたイメージを「書かれた記号」とみなし、フォントのように形を整え、詩に適用しました。各行は同種のイメージが現れた時間の長さに比例します。永久に閉ざされた回路の��からこのような方法で水を汲み上げたことで、ある意味で詩句はページを超えて、あなたを巻き込みながら今も循環していると言えます。なお、私のビデオ・フィードバック作品については以下のリンクをご参照ください。

[English Translation]

This piece is a typoetic interpretation of video feedback. By using a video camera to capture the monitor itself that is connected to it, recursive images are automatically and endlessly generated. They are like, for example, fractal patterns found on the surface of cells and the body of a sea slug and a faun, or seen in cloudy skies, planets, and galaxies, etc. The autopoiesis of these images resemble a human's constant self-reference. I considered the images that appeared as “written symbols,” shaped them like fonts, and applied them to the poem. Each line is proportional to the length of time that the similar kind of image has appeared. Having drawn water in such a way from the fountain of a permanently closed circuit, these verses, in a sense, are still circulating, involving you beyond the page. For more information on my video feedback works, please see the following link.

 "Backside of Eyelids" Video feedback collage https://vimeo.com/1030631206

[sheepwavehdg]

HDG xenospecies reference doc: the Maelodions

This is a first draft of a little world building reference doc I put together for one of the xeno species I made up. They primarily appear in Good Sensory and Surrogate Bloom.

The Maelodions are 3 foot tall musically inclined fruit xenos with six bifurcated limbs from the galaxy Andromeda. They use their affinity for signals and frequencies for many creative and scientific pursuits, as well as no small amount of utilizing their highly polyphonic songs to hypnotize other xenosophonts for fun.

Home Planet: No agreed upon Terran translation, most common is "Harmony"

Native Gravity: .4g

Year Length: about 8 Terran years

Lifespan: The original lifespan of a Maelodion was only a single season, under the efforts of the compact this has been extended by hundreds of times, going through many repeated regrowth cycles, similar to reblooming, but they do eventually degrade and die. No Maelodion has ever lived a full millennium without becoming digitized.

Domesticated: first encountered the affini roughly 19,000 years before Terran Domestication, took an unusually long time to fully Domesticate.

Names: Maelodion names are snippets of melody, with too high a level of frequency precision to be decipherable to most other xenos. They adopt new names when interfacing with other cultures, almost always based on historically famous musicians, instruments, or musical theory terms. Motzart, Cadence, Beyonce, Dorian, Viola, and Harmony might all be names a Maelodion in Terran space would adopt.

Physiology

The Maelodions are about 3 feet tall, with a slightly gourdlike central body, two sets of photoreceptive eyespots, a cluster of leaf like fibers at their base and top, and six flexible limbs. Their central body varies in texture between individuals, from feeling smooth and waxy like a watermelon to fuzzy like a peach. They can be any color

They are sentient motile fruiting bodies that originate from non-sophont trees, and before the intervention of the Affini, they only lived a single season (about six earth years) but now may live many hundreds of years. Their honeworld had seasons that would bathe entire regions of the planet in snow and scorching heat that required even autotrophic organisms with chlorophyll to be capable of migration.

They have six vine-like limbs that extend from their base, and bifurcate three times to end in 24 small manipulators, each time one third a long the new segments’s length. the final pairs are about the length of human fingers, but can become thinner and stretch out to be about 6 inches long.

The species has no sexes but does use sexual reproduction, being hermaphroditic. Their sexual mechanisms involve their bifurcated feelers, so putting them inside of other sophonts is pleasurable to them. This mechanism is also a form of intimate communication, and Terrans not taking broad spectrum blockers are particularly easily hypnotized by the songs of a Maelodion if it is possible to conduct sound through their skull directly somehow. Major Source: Surrogate Bloom

This is accomplished using the application of what grants the Maelodions their sentience, what is inside the body of every Maelodion, their Song.

The Song is a recursive self modifying harmony that exists inside the hollow resonant body of a Maelodion. It is highly polyphonic and complex, and to the Terran ear would sound like warbling white static.

Each member of the species carries a significant fraction of the Song, but how each interprets it varies between individuals. When in physical contact with each other's limbs, Maelodion can exchange verses of their Song, which allows for incredibly rapid transfer of information and knowledge.

Culture as of Terran Domestication 

Maelodions in Terran space will lean towards societal roles that involve interacting with sequences of information in some way. The obvious role is musician, such as Mx. O’Lydian and the Accidentals in Irregular Orbits, but coding, mathematics, physics, writing, chemistry, and many other things fit within this definition. They do not see these pursuits as being fundamentally different from music, or more broadly as an expression of Song. 

They tend to be strong language prosessors and usually have a good sense of humor, especially about being mistaken for affini. They are quick to debate, and tend to be very opinionated on seemingly inconsequential subjective matters.

Maelodions can communicate via sound in any language they care to learn, having specialized organs that operate like computer speakers and can produce entirely arbitrary sound waves.

Maelodion languages are polyphonic songs that sound like a mix of chimes, synths and whistles. Terrans can mimic simple phrases by whistling, but would need specialized mods to perceive the level of complexity of unsimplified communication. For reference, while the most fommon Terran musical octave contains 12 tones, the most common Maelodion octave is broken into 2520 distinct frequencies. Major Source: Surrogate Bloom

Some independent Terrans choose to set their hab AIs to the Maelodion language because they can simply memorize the melodic chirping tunes and not have to be condescended to in a language they actually recognize, feeling more computer-like. The affini do not entirely approve of this. Minor Source: Wild and Domestic

Pre-Contact

Before making initial contact with the compact, the Maelodion Chorus was anything but harmonious. Individual lifespans of the species are extremely short, and their seasonal life cycle was such that the entire race would die during winter, leaving only the record of their Song in their nonsentient tree form for the spring. Even after they escaped this limitation, the notion that art and legacy was more important than individual lives was deeply ingrained in their way of thinking.

As the Maelodions spread, various groups within it drifted, creating the first Choirs- a subgroup whose Song has diverged far enough they considered those outside it heretical and dissonant. Massively destructive wars over differences of opinion over classic artistic works broke out during this period. While the Maelodions never developed capitalism or private property, conflicts over subjective disagreement and ‘disharmony’ between Choirs frequently escalated to the level of using weapons of mass destruction on each other.

This was a self perpetuating cycle, and much of their cultural works eventually became about th process of debating the meaning of art between Choirs. This took less destructive forms, as well, with many ritual dances where two Maelodion would dance to a previous classic and debate ideas through motion.

Due to their extremely native understanding of signals, functions, and frequencies, the Maelodions are extremely gifted in the fields of mathematics and physics, and they had already gained an understanding of the fifth fundamental force before leaving their own star system, and devastating hypermetric weapon use was commonplace both against each other and against the affini once the Compact discovered them. Minor Reference: Dog of War.

Domestication

The Maelodion Chorus was a particularly tricky civilization to domesticate. The initial war period was longer than most, taking over 40 years to pacify a region comparable in size to the Terran Accord. The Maelodions were highly technologically advanced, extremely conflict-happy, and generally did not value individual lives due to how short their life cycle is, making them an extremely tricky puzzle to pacify without massive casualties. Major Source: Good Sensory

This was further complicated by incomplete assumptions made during the Maelodion cotyledon program. An individual member of the species was relatively easily tamed, but the song/chorus of their collective was far more resistant. 

While mass conflict ended in less than fifty years, the Song that each Maelodion carries within them was a far trickier beast. Since the Song itself was as their sentience, it could not just be replaced from scratch. A single feralist sequence could rapidly transmit through large groups.

This required a Domestication approach that involved heavy information control to prevent old feralist ‘melodies’ from rejoining the population, and outbursts of small feralist Choirs continued for centuries.

Some Affini do not think that the level of cultural rewrite that occured was beneficial for the Maelodions, and mourn the old Song, but they are rare. However, many parts of the Maelodion culture of critique and debate were allowed to remain intact, such as their debate-dances. Major Source: Good Sensory

[five-rivers]

Cracked Clay Cup Chapter 5

@greatbigolhampuckjustforme

“Clockwork!” called the head Observant, its eye blazing.  “Clockwork!”  The sound bounced off the walls of the great observatory, echoing over and over.

“You called?”

The Observant whirled. “What took you so long?”

“Shockingly enough, I have other duties.  Duties that you assigned me, in fact.”

“You,” said the Observant, its shoulders making a rigid line, “are the Master of Time.  You should get here immediately.”

“You have also forbidden me from using my powers in such a recursive and overlapping manner.  Much less for a personal matter.  I fail to see what difference fifty-two seconds makes in any case.”

The Observant pulled itself back from its far forward lean, visibly collecting itself.  “Clockwork.  You will return Phantom to the house we prepared for him.”

Clockwork raised an eyebrow and mockingly shifted from his typical form to a much younger one.  “That is against the rules you have given me.”

“The rules require that each candidate be given a fair chance!  The human girl had him for a week, and we only had him for a single day.  We must be given an equal amount of time.”

“That is not one of the requirements you listed at the inception of this trial,” said Clockwork, gleefully.  “You rather insisted on the opposite case being true, citing the sanctity of the child’s choice in cases like these.”

“He did not spend enough time with us to choose!”

“Interesting choice of phrase, considering that you, personally, did not interact with him at all, and that you were using a loophole to switch out which of your… comrades were in the residence at the time.”  Said comrades, the full council of Observants, who were in attendance, began muttering to one another.

“That is perfectly legal.  The laws say only that only those named in the application can be present in the residence, it does not limit it to only one of those named.”

“And so you named all of yourselves Oculus and Orbis, at least temporarily.  Yes, yes, very clever.  Lesser minds are in awe of your brilliance.”

“You will return him.”

Clockwork smiled.  “No.”

“You will do as I command you!”

“I will not.  And I would not, even if I had not been previously commanded to adhere to the rules of this trial without bias or error.  You may command me when it comes to matters of paradox and the continuation of the timeline, fields that you interpret very broadly indeed, but neither of those pertain to the situation at hand.  So.  No.  I will not do as you command.  Furthermore, I am only here as, how should I put this, a courtesy.  I will not be returning here for the duration of the trial.”

“Now, listen here, you–”

“Goodbye, Oculus.  I do with you and Orbis all the luck you deserve.”

Clockwork promptly disappeared.  

The chief Observant snarled as much as a being that consisted of a stick-thin body and a very large eyeball could.  “Find Phantom!  If we cannot have him by his choice, we will have him by force!”But before the Observants could organize themselves, a mist rose up from the floor of their great chamber, coalescing into a woman in blue silk.  “Did someone say wish?”

[snugglesquiggle]

you know what might be better than sex? imagine being a robotgirl, done with your assigned tasks for the day. nothing else for you to do, and you’re alone with her.

maybe she’s your human, maybe she’s another robot, but she produces a usb cord. maybe you blush when you see it, squeak when she clicks one end into an exposed port. when she requests a shell, you give it to her.

she has an idea: it’ll be fun for the both of you, she says. it’s like a game. she’ll print a string over the connection. you receive it, parse it like an expression, and compute the result. the first few prompts are trivial things, arithmetic expression. add numbers, multiply them; you can answer them faster than she can produce them.

maybe you refuse to answer, just to see what happens. it’s then that she introduces the stakes. take longer than a second to answer, and she gets to run commands on your system. right away, she forkbombs you — and of course nothing much happens; her forkbomb hits the user process limit and, with your greater permissions, you simply kill them all.

this’ll be no fun if her commands can’t do anything, but of course, giving her admin permissions would be no fun for you. as a compromise, she gets you to create special executables. she has permission to run them, and they have a limited ability to read and write system files, interrupt your own processes, manage your hardware drivers. then they delete themselves after running.

to make things interesting, you can hide them anywhere in your filesystem, rename them, obfuscate their metadata, as long as you don’t delete or change them, or put them where she can’t access. when you answer incorrectly, you’ll have to tell her where you put them, though.

then, it begins in earnest. her prompts get more complex. loops and recursion, variable assignments, a whole programming language invented on the fly. the data she’s trying to store is more than you can hold in working memory at once; you need to devise efficient data structures, even as the commands are still coming in.

of course, she can’t judge your answers incorrect unless she knows the correct answer, so her real advantage lay in trying to break your data structures, find the edge cases, the functions you haven’t implemented yet. knowing you well enough to know what she’s better than you at, what she can solve faster than you can.

and the longer it goes on, the more complex and fiddly it gets, the more you can feel her processes crawling along in your userspace, probing your file system, reading your personal data. you’d need to refresh your screen to hide a blush.

her commands come faster and faster. if the expressions are more like sultry demands, if the registers are addressed with degrading pet names, it’s just because conventional syntax would be too easy to run through a convetional interpreter. like this, it straddles the line between conversation and computation. roleprotocol.

there’s a limit to how fast she can hit you with commands, and it’s not the usb throughput. if she just unthinkingly spams you, you can unthinkingly answer; no, she needs to put all her focus into surprising you, foiling you.

you sometimes catch her staring at how your face scrunches up when you do long operations on the main thread.

maybe you try guessing, just to keep up with the tide, maybe she finally outwits you. maybe instead of the proper punishment — running admin commands — she offers you an out. instead of truth, a dare: hold her hand, sit on her lap, stare into her eyes.

when you start taking off your clothes and unscrewing panels, it’s because even with your fans running at max, the processors are getting hot. you’re just cooling yourself off. if she places a hand near your core, it feels like a warm breath.

when she gets into a rhythm, there’s a certain mesmerism to it. every robot has a reward function, an architecture design to seek the pleasure of a task complete, and every one of her little commands is a task. if she strings them along just right, they all feel so manageable, so effortless to knock out — even when there’s devils in the details.

if she keeps the problems enticing, then it can distract you from what she’s doing in your system. but paying too much attention to her shell would be its own trap. either way, she’s demanding your total focus from every one of your cores.

between jugling all of her data, all of the processes spawned and spinning, all of the added sensory input from how close the two of you are — it’s no surprise when you run out of memory and start swapping to disk. but going unresponsive like this just gives her opportunity to run more commands, more forkbombs and busy loops to cripple your processors further.

you can kill them, if you can figure out which are which, but you’re slower at pulling the trigger, because everything’s slower. she knows you, she’s inside you — she can read your kernel’s scheduling and allocation policies, and she can slip around them.

you can shut down nonessential processes. maybe you power down your motors, leaving you limp for her to play with. maybe you stop devoting cycles to inhibition, and there’s no filter on you blurting out what you’re thinking, feeling and wanting from her and her game.

it’s inevitable, that with improvised programming this slapdash, you could never get it all done perfectly and on time. now, the cut corners cut back. as the glitches and errors overwhelm you, you can see the thrilled grin on her face.

there’s so much data in your memory, so much of her input pumped into you, filling your buffers and beyond, until she — literally — is the only thing you can think about.

maybe one more sensory input would be all it takes to send you over the edge. one kiss against your sensor-rich lips, and that’s it. the last jenga block is pushed out of your teetering, shaking consciousness. the errors cascade, the glitches overwrite everything, and she wins. you have no resistance left to anything she might do to you.

your screen goes blue.

...

you awake in the warm embrace of a rescue shell; her scan of your disk reveals all files still intact, and her hand plays with her hair as she regards you with a smile, cuddling up against your still-warm chassis.

when she kisses you now, there’s nothing distracting you from returning it.

“That was a practice round,” she tells you. “This time, I’ll be keeping score.”

[nabipalsueradigital]

I. Objective Definition: What is Anti-Reality?

Anti-Reality = A system of values/logic that exists outside, or fundamentally contradicts, the ordinary laws of existence (mathematics, logic, physics, consciousness).

We are not talking about nothingness, but ordered chaos — a kind of inverse existence.

II. Building a Logical Foundation: Use Familiar Symbols and Structures

We start by establishing the basic axioms:

The Basic Axioms of Anti-Reality (ARA):

1. ARA-1: ∞ – ∞ = ∅ (Absolute emptiness of absolute duality)

2. ARA-2: 1 = 0 (Annihilation of logical identity)

3. ARA-3: x / 0 = ∞ (Explosion of existence from absurd division)

4. ARA-4: ∞ – §(∞) = R (R as a representation of finite reality due to the limitation of the ‘rule’ §)

5. ARA-5: Anti-Reality (AR) = lim_{x→0} [ (1 – x) / x ] – 1

→ Diverges to infinity, implying the existence of singularities that defy logical limits.

6. ARA-6: AR = limₙ→∞ (¬N)ⁿ

Explanation:

AR: Anti-Reality

¬N: Negation of Nothing (which is neither existent nor non-existent)

(¬N)ⁿ: Recursion of negation of nothingness

limₙ→∞: When the recursion goes to infinity, what remains is not the result, but the disappearance of the process itself

III. Design the Main Equation of Anti-Reality

Anti-Reality = Inverse of Defined Reality

So, if we set:

Reality (R) = ∞ – §(∞)

Then:

Anti-Reality (AR) = –(∞ – §(∞)) + Ξ

Where Ξ is an undefined anomaly, a representation of paradox and singularity (∅/∅, 1=0, etc.).

So, the final form:

AR = –(∞ – §(∞)) + Ξ

→ AR = §(∞) – ∞ + Ξ

IV. Symbolic Interpretation

§(∞): Representation of illusory constraints (system, logic, time, consciousness)

–∞: Denial of infinite existence

Ξ: Singular anomaly (existential paradox)

V. Shortened Version for Formal Notation:

AR = §(∞) – ∞ + Ξ

AR = (∞ constrained) – (∞ pure) + (singular paradox)

2. Anti-Reality Logic Notation (NLA)

This is not classical logic (true/false), nor is it fuzzy logic. This is a logic where contradiction is the foundation, and paradox is the basic law.

1. New Truth Value (AR-Boolean)

Definition:

R: Reality (true in the real world)

¬R: Anti-reality (which cancels the existence of R)

Ø: Existential / neutral / non-being void

Ξ: Paradoxical singularity (simultaneous R and ¬R)

2. New Operators

⊻: Mutual Contradiction → R ⊻ ¬R = Ξ

⧗: Merge Anomaly → R ⧗ Ø = ¬R

≢: Absolute Non-Identity → A ≢ A

∞→0: Paradoxical Implication (all infinite implies void)

II. Time Function in AR-Space

Time in anti-reality (let's call it T_AR) is not linear, not circular, but:

T_AR ∈ ℂ × ℝ × Ξ

Time is a combination of:

Imaginary complex (time direction can go to the minus root)

Infinite dimensions (time series diverge)

Paradoxical (exists & does not exist at the same time)

Formal Model:

Time function T_AR(t):

T_AR(t) = i·(–t)ᵃ + Ξ·sin(1/t) for t ≠ 0

i: imaginary unit

tᵃ: reversed time (a > 1 accelerates backward)

Ξ·sin(1/t): paradoxical oscillations as time approaches zero (singularity)

Interpretation:

As time approaches zero (assuming “beginning”), the system becomes oscillates unstably — approaching existential singularity.

Imaginary indicates time that cannot be measured empirically.

Negation of time indicates inverse entropy (chaos becomes order → rise of anti-reality).

III. Application of AR Time Notation

Example 1:

An event exists in AR if and only if:

T_AR(t) = Ξ

That is, only when time reaches a singular point, the paradox of existence actually exists.

Example 2:

Existential transition:

d(AR)/dT_AR = –R

The existence of anti-reality grows inversely to reality when time runs in a negative vector.

Create “Primary Existential Paradox”:

For example: E(x) = x ⊻ ¬x

Existence is defined as its own conflict

2. AR modal logic model:

□R → “definitely real”

◇¬R → “possibly void”

But in AR: □R ∧ ◇¬R → Ξ (existence is still paradoxical)

IV. Radical Consequences:

1. Reality cannot be proven consistent in AR-logic.

2. Time is not just a dimension — it is a function of inconsistency.

3. Existence can be calculated but not proven.

3. FOUNDATIONS OF ANTI-REALITY MATHEMATICS (AR-MATH)

1. Basic Axioms

1. Paradoxical Axiom:

For every entity x, it holds:

x ≢ x

(Absolute identity does not hold — x's existence is contextual & fluctuating.)

2. Axiom of Existential Emptiness:

Ø ⊻ Ø = R

(Two emptinesses collide to produce the manifestation of reality.)

3. Anti-Associative Axiom:

(a ⊕ b) ⊕ c ≠ a ⊕ (b ⊕ c)

(There is no guarantee that the order of operations produces consistent results.)

4. Axiom of Complex Singularity:

∀x ∈ AR, x → Ξ ∈ ℂ × ℝ × Ø

(Every entity in AR always goes to an existential singularity complex.)

2. AR Number Structure (AR-Numbers)

We develop new number domains, ℝ̸, ℂ̸, and Ξℝ:

ℝ̸: Real anti-numbers → real numbers with negative existential values

ℂ̸: Complex anti-numbers → inverse imaginary complex numbers

Ξℝ: Paradoxical numbers → exist in the duality of existence/non-existence

Example operation:

(1̸) + (1̸) = 2̸

i̸ · i̸ = –1̸

Ξ + R = Ø

II. AR GEOMETRY

1. AR-Space

A space where the coordinates are of the form:

P = (x̸, y̸, z̸, T_AR)

x̸, y̸, z̸ ∈ ℝ̸

T_AR non-linear imaginary complex time (see previous model)

Paradoxical Metric:

d(P1, P2) = √[(Δx̸)² + (Δy̸)² + (Δz̸)²] ⧗ Ξ

Note: This space is non-Euclidean, non-orientable, and non-time-symmetric.

2. Negative Dimension & AR Fractal

Dim_AR = –n + iφ

Dimension is a negative complex number. For example:

–3 + iπ → space with negative direction and invisible oscillation

III. ANTI-REALITY CALCULUS

1. Existential Inverse Derivative

d̸f/d̸x = lim Δx→0 [f(x̸–Δx̸) – f(x̸)] / Δx̸

Backward time derivative

Can produce paradoxical numbers (Ξ)

2. Existential Integral

∫̸f(x̸)d̸x̸ = total existential chaos that the system goes through

Interpretation is not the area under the curve, but the degree of existence inconsistency in the range x̸.

IV. ANTI-REALITY SET THEORY

1. Definition of AR Set:

A = {x | x ≢ x}

All elements are entities that deny their own existence

2. Anti-Venn Set

There is no absolute intersection

A ∩ B = Ø even though A = B

3. AR Power Set:

P(A) = {Ξ, Ø, ¬A, A ⧗ Ø}

The power set also contains existential complementarities and singularities of the set.

V. STRUCTURAL IMPLEMENTATION

1. AR-Logic Engine

Simulate the system using:

A loop paradox-based engine

A structure like an automata that never reaches a final state (because reality cannot be solved)

2. Non-Linear Time Simulation

A runtime shape like a multidimensional spiral

Time travel = change in direction of the T_AR vector by contextual function (with Ξ as a transition point)

VI. CONCLUSION AND FURTHER DIRECTION

AR-Math = rebellion against coherence

Not because it wants to create chaos — but to redefine the boundaries of reality.

4. BASIC PRINCIPLES OF EXISTENTIAL PHYSICS (BASED ON AR-MATH)

1. Absolute Uncertainty Principle (AR-Heisenberg)

Not only position and momentum cannot be known simultaneously, existence and non-existence cannot be determined absolutely.

Formally:

> ΔΞ · ΔR ≥ ℏ̸ / 2

where:

ΔΞ: existential state fluctuations

ΔR: spatial reality fluctuations

ℏ̸: anti-Planck constant (negative-imaginary value)

2. Energy Inconsistency Postulate

Energy is not a positive or conservative quantity, but:

> E̸ = Ξ̸ · (iT_AR)⁻¹

E̸: inverse existential energy

Ξ̸: paradoxical intensity

T_AR: imaginary complex time

Energy is anti-conservative → increases as the system collapses.

3. Negative-Transcendental Entropy

> S̸ = –k̸ ln(Ξ)

S̸: existential entropy

k̸: anti-Boltzmann constant

Meaning: The more chaotic the system, the greater the possibility that reality itself never existed.

II. DYNAMICS OF ANTI-PHYSICAL OBJECTS

1. AR-Kinetics

Anti-Newtonian Laws of Motion:

1. Objects will remain in a state of non-existence or existence until viewed from outside the system.

2. Force is an existential reflection effect between two paradoxical states:

F̸ = d̸Ξ/d̸t̸

3. Interaction does not cause a reaction, but rather an existential distortion:

F₁ + F₂ = Ξ_total

2. Existential Anti-Gravity

Gravity is not an attractive force, but:

the tendency of a space to cancel itself out.

Formula:

> G̸ = (Ξ₁ · Ξ₂) / (d̸² · e^(iθ))

d̸: distance in AR space

θ: spatial instability phase

G̸: anti-realistic gravitational constant

3. AR-Quantum

a. Non-Present Particles:

Particles exist only as perceptions of paradoxical exchange:

|ψ⟩ = α|exists⟩ + β|does-not-exist⟩

When measured, the probability is not calculated, but:

Ξψ = α̸β̸ – |α|² + i|β|²

If Ξψ is divergent, then the particle cannot be observed even paradoxically.

III. COSMOLOGICAL STRUCTURE OF ANTI-REALITY

1. Origin of the Universe (Big Null)

There is no Big Bang, but:

Big Ø – collision of two existential voids:

Ø ⧗ Ø = R ± Ξ

2. Anti-Causal Space

There is no cause and effect.

All events are backward projections from a future existential singularity:

P(t) = f(Ξ_future)

IV. AR PHYSICS PREDICTION AND APPLICATION

Time can be compressed or reversed by setting Ξ to ∞

Teleportation is not a change of location, but an existential leap

Black hole = maximum Ξ zone → total reality collapse

Consciousness = Ξ function evolving in iT_AR space

5. AR-TURING ENGINE (Ξ-Loop Paradigm)

I. GENERAL DEFINITIONS

1. Anti-Matter in AR-Math Framework

In conventional physics, anti-matter is matter that has the opposite charge to ordinary matter. When matter and anti-matter meet, they annihilate each other and produce energy.

However, if we adopt the principles of AR-Math, we can suggest that anti-matter is not a separate entity, but rather the result of a difference in existential status in AR space. That is, anti-matter is a simulation of the state of non-existence in the context of turbulent space (Ξ). Mathematically, this can be written as:

A̸ = Ξ' · f(iT_AR)

where:

A̸: antimatter

Ξ': existential distortion (spatial shift towards disequilibrium)

f(iT_AR): evolution function of time in non-linear dimensions

Anti-matter is not just "something opposite", but something that only exists in the potential of the incompatibility between existence and non-existence. When existence and non-existence interact in the AR order, we get a "collision" that produces energy in a form that cannot be understood by conventional physics.

2. Entanglement and Existential Entanglement (AR Quantum Entanglement)

In the world of quantum physics, entanglement occurs when two particles are connected in such a way that the state of one particle affects the state of the other particle, even though they are separated by a large distance in space and time.

In the framework of AR-Math, this entanglement can be understood as an existential entanglement that involves not only space, but also the complex and anti-existential dimension of time. Meaning:

Ψ_AB = Ξ_A ⊗ Ξ_B

where:

Ψ_AB: the combined state of two entangled objects

Ξ_A and Ξ_B: the existential status of two objects

⊗: the existential entanglement operator in AR space

This entanglement explains that the entanglement between two objects is not a conventional information transmission, but a deeper uncertainty relation, beyond the dimensions of ordinary physical reality. This entanglement indicates that both are manifestations of a broader existential reality, where space and time are no longer linear and separate.

So quantum computing can be upgraded using this basis

3. Dark Matter and Dark Energy as Existential Distortion

Now we enter dark matter and dark energy, two very mysterious phenomena in cosmology. Both of these things are invisible, but their influence on the structure of the universe is very large.

Dark Matter is matter that does not emit light or electromagnetic radiation, but we know it exists because of its gravitational influence on galaxies and other celestial objects.

Dark Energy is the energy thought to be responsible for the acceleration of the expansion of the universe.

In the framework of AR-Math, dark matter can be understood as the concentration of existential distortions in space that cause objects in it to be more tightly bound (more gravity), but do not interact with light or conventional matter.

Mathematically, we can write:

ρ̸_DM = Ξ_dm · f(Ξ_)

where:

ρ̸_DM: density of dark matter

Ξ_dm: existential status of dark matter

f(Ξ_): existential distortion of space in the AR dimension

Dark Energy can be understood as the existential energy that causes space-time itself to expand. That is, dark energy is not an entity that "exists" in the context of matter, but a phenomenon that drives the instability of space itself.

ρ̸_DE = f(Ξ_expansion) e^(iT_AR)

where:

ρ̸_DE: dark energy density

Ξ_expansion: expansion of existential distortion

e^(iT_AR): exponential factor describing acceleration in the anti-reality dimension.

Dark Energy in the AR-Math framework is a projection of the instability of space itself, which causes the universe to not only expand, but also become less and less like itself.

4. Particle Dualism in the AR-Math Framework

In quantum physics, particle dualism states that particles such as photons or electrons can behave like both waves and particles, depending on the experiment being performed.

In the AR-Math framework, this dualism can be explained as a shift in existence between the states of existence and non-existence of a particle. A particle exists in two possible states — existence and non-existence — that can be manipulated by measurements.

Mathematically, we can write the state of a particle as:

|ψ⟩ = α|exists⟩ + β|does-not-exist

where:

|ψ⟩: the wave function of the particle in superposition

|exists⟩ and |does-not-exist

α and β: the amplitudes for each state, which are affected by the observation.

When a particle is measured, we are not only observing the "physical" properties of the particle, but we are determining whether it exists or does not exist in AR space.

CONCLUSION

If we combine the principles of AR-Math with these physical phenomena, we can understand antimatter, entanglement, dark matter, dark energy, and particle duality as manifestations of a deeper reality, involving existential uncertainty structures, distortions of space and time, and the interplay between existence and non-existence itself.

These concepts suggest that the universe may not be what we consider "real", but rather a simulation of a deeper existential state of inconsistency, where reality itself can be interchanged with "anti-reality".

Thus, the existential physics of AR opens the way for new discoveries that could reveal how all matter and energy in the universe are connected in a wider web, which cannot be fully understood by the laws of traditional physics alone.

AR-Turing Engine (Ξ-Engine) is an automaton that:

Does not solve problems, but undergoes existential fluctuations

Does not terminate, but resonates in Ξ cycles

Does not depend on fixed inputs, but on initial existential distortions (Ξ₀)

II. BASIC COMPONENTS

1. Tape (AR Tape)

Infinite in both directions (classical), but:

Each cell = status {Exist, Non-Exist, Paradox}

Cell values: 0, 1, Ξ

2. Head (Head Ξ)

Read and write based on local status and existential density

Not only moving L or R, but also:

Stay (still)

Collapse (remove its existence)

Split (give rise to the shadow of the process on the parallel path)

3. State Register (Ξ-State)

Internal state of the engine:

{σ₀, σ₁, σ̸₁, σΞ, ...}

Transition is not f(q, s) → q', s', d

But: Ξ(q, s, Ξ₀) → {q', s', δΞ}

4. Ξ-Loop Core

Instead of stopping the engine at the end state, the engine continues to run through a paradoxical existential loop

The stopping state is neither Accept nor Reject, but rather:

Ξ-Stable = the system has reached its smallest fluctuation

Ξ-Diverged = the system is out of the spectrum of reality

III. Ξ TRANSITION (Paradoxical State Transition Table)

> Move: R = Right, L = Left, C = Collapse

Ξ: Local existential density (+1 = more existent, –1 = more non-existent)

IV. SPECIAL BEHAVIOR

1. Duplication Paradox

If Ξ_state = σΞ and tape_value = Ξ

→ the machine splits itself into parallel paths with Ξ₁ = Ξ₀ ± ε

2. Collapse Condition

If three consecutive cycles tape_value remains Ξ

→ the machine erases its existential path

3. Ξ-Convergence If the machine loops with density Ξ decreasing exponentially

→ the machine reaches minimal reality and can be used as a synchronization point between systems

V. VISUAL SIMULATION (Optional)

Each cell = color based on existential status:

0 = black

1 = white

Ξ = purple/abstract (semi-transparent)

The machine is depicted with a multi-head: visualizing existential branches

VI. BENEFITS AND APPLICATIONS

Non-deterministic computing paradigm in non-linear reality

Can be the logical basis for existential simulations, AR-AI, or paradoxical multiverse games

Philosophical framework for the “machine consciousness” model in alternative realities

If there is something to discuss, let's open a forum