#Recursion In C++

[chiropteracupola]

once again focusing in on dragon-surgeons with laserlike aim. we have several thoughts on this passage, which are as follows:

one: how does one dissect a dragon. what are they doing it with. are there attendants here with those massive two-person saws for this purpose, with the doctors spectating and directing? are the surgeons the guys with the massive saws? the dragons are So big compared to the people, are they crawling around in there? do they have students in attendance as they might at a human dissection?

two: 'dissection' is such a particular choice of word here. if you are taking apart your Coworker after their death that is an Autopsy. if you are taking apart an animal for food after their death that is Butchering, and if you are taking it apart for science that is a Necropsy. it is, what, 1806? dissection is scientific and not really for people you are regarding as People right about now. this is such a Way of pointing out the Strange Social Position of dragons in temeraireverse.

three: again I ask. how does one Become a dragon-surgeon. keynes seems to be equally adept at human medicine, and on his various adventures up to this point laurence hasn't been provided with an additional surgeon for his crew as well as for his dragon. what kind of medical school operations are going on in england and scotland to allow this guy Training. are medical students from edinburgh being funneled out to the covert at (iirc fictional) loch laggan to study dragons? what is the Draconic opinion on post-mortem disassembly for scientific purposes?

[watchmorecinema]

Normally I just post about movies but I'm a software engineer by trade so I've got opinions on programming too.

Apparently it's a month of code or something because my dash is filled with people trying to learn Python. And that's great, because Python is a good language with a lot of support and job opportunities. I've just got some scattered thoughts that I thought I'd write down.

Python abstracts a number of useful concepts. It makes it easier to use, but it also means that if you don't understand the concepts then things might go wrong in ways you didn't expect. Memory management and pointer logic is so damn annoying, but you need to understand them. I learned these concepts by learning C++, hopefully there's an easier way these days.

Data structures and algorithms are the bread and butter of any real work (and they're pretty much all that come up in interviews) and they're language agnostic. If you don't know how to traverse a linked list, how to use recursion, what a hash map is for, etc. then you don't really know how to program. You'll pretty much never need to implement any of them from scratch, but you should know when to use them; think of them like building blocks in a Lego set.

Learning a new language is a hell of a lot easier after your first one. Going from Python to Java is mostly just syntax differences. Even "harder" languages like C++ mostly just mean more boilerplate while doing the same things. Learning a new spoken language in is hard, but learning a new programming language is generally closer to learning some new slang or a new accent. Lists in Python are called Vectors in C++, just like how french fries are called chips in London. If you know all the underlying concepts that are common to most programming languages then it's not a huge jump to a new one, at least if you're only doing all the most common stuff. (You will get tripped up by some of the minor differences though. Popping an item off of a stack in Python returns the element, but in Java it returns nothing. You have to read it with Top first. Definitely had a program fail due to that issue).

The above is not true for new paradigms. Python, C++ and Java are all iterative languages. You move to something functional like Haskell and you need a completely different way of thinking. Javascript (not in any way related to Java) has callbacks and I still don't quite have a good handle on them. Hardware languages like VHDL are all synchronous; every line of code in a program runs at the same time! That's a new way of thinking.

Python is stereotyped as a scripting language good only for glue programming or prototypes. It's excellent at those, but I've worked at a number of (successful) startups that all were Python on the backend. Python is robust enough and fast enough to be used for basically anything at this point, except maybe for embedded programming. If you do need the fastest speed possible then you can still drop in some raw C++ for the places you need it (one place I worked at had one very important piece of code in C++ because even milliseconds mattered there, but everything else was Python). The speed differences between Python and C++ are so much smaller these days that you only need them at the scale of the really big companies. It makes sense for Google to use C++ (and they use their own version of it to boot), but any company with less than 100 engineers is probably better off with Python in almost all cases. Honestly thought the best programming language is the one you like, and the one that you're good at.

Design patterns mostly don't matter. They really were only created to make up for language failures of C++; in the original design patterns book 17 of the 23 patterns were just core features of other contemporary languages like LISP. C++ was just really popular while also being kinda bad, so they were necessary. I don't think I've ever once thought about consciously using a design pattern since even before I graduated. Object oriented design is mostly in the same place. You'll use classes because it's a useful way to structure things but multiple inheritance and polymorphism and all the other terms you've learned really don't come into play too often and when they do you use the simplest possible form of them. Code should be simple and easy to understand so make it as simple as possible. As far as inheritance the most I'm willing to do is to have a class with abstract functions (i.e. classes where some functions are empty but are expected to be filled out by the child class) but even then there are usually good alternatives to this.

Related to the above: simple is best. Simple is elegant. If you solve a problem with 4000 lines of code using a bunch of esoteric data structures and language quirks, but someone else did it in 10 then I'll pick the 10. On the other hand a one liner function that requires a lot of unpacking, like a Python function with a bunch of nested lambdas, might be easier to read if you split it up a bit more. Time to read and understand the code is the most important metric, more important than runtime or memory use. You can optimize for the other two later if you have to, but simple has to prevail for the first pass otherwise it's going to be hard for other people to understand. In fact, it'll be hard for you to understand too when you come back to it 3 months later without any context.

Note that I've cut a few things for simplicity. For example: VHDL doesn't quite require every line to run at the same time, but it's still a major paradigm of the language that isn't present in most other languages.

Ok that was a lot to read. I guess I have more to say about programming than I thought. But the core ideas are: Python is pretty good, other languages don't need to be scary, learn your data structures and algorithms and above all keep your code simple and clean.

[tilbageidanmark]

Recursion, see Recursion.

I was laying on the sofa this afternoon, scrolling some old posts of this blog, when the couple across the street, came out on their balcony for a smoke. I was able to snap a double photo of them!

(All the other memes I made..)

[fortunatelycoldengineer]

What is the difference between call by value and call by reference in C? . . . . for more interview questions https://bit.ly/3EteTnZ check the above link

[scholarhat01]

Demystifying Recursion in C: A Comprehensive Explanation

Discover the essence of recursion in C programming with this informative guide. Explore what recursion is, how it works, and its applications in solving complex problems. Whether you're a novice programmer or seeking a refresher on recursion, this resource will provide a clear and in-depth understanding of this fundamental programming concept in the context of the C language.

[improvapocalyps]

You have 90 minutes to complete. (original poem: r.a.)

In participation of the MCYT Recursive Exchange 2024 hosted by @mcytrecursive!

Inspired by know that all my love will be your breath (i will save you when your lights go out)

[text under cut]

1. Have you ever been in love? (Please circle your answer.) a. It's me and him b. Our hearts beat in sync c. Our lives intertwined

2. Do you understand what you’ve done? (Please circle your answer.) a. I couldn't do anything b. I lost my balance c. I doomed us both

3. It's been god knows how long since you felt phantom hands on your neck and there is no one in sight. If you were soul-bound to him and both of you died at the same time then why are you still waiting in the void? Please answer clearly, in full sentences. (Not a correct answer：I just wanted to see him one more time).

4. Define two (2)： Fate | The feeling of his forehead against yours Curse | The moment you realise he isn't linked to you anymore

5. True or False： i. It was your fault. ii. You wish you had met him under different circumstances. iii. You can’t regret a single moment that you had him. iv. You would do it all over again if you could. v. It ended long before either of you said anything.

thumbnails:

sketch cover thing for imgur link:

[koiukiy-o]

orphic; (adj.) mysterious and entrancing, beyond ordinary understanding. ─── 008. the email.

-> summary: when you, a final-year student at the grove, get assigned to study under anaxagoras—one of the legendary seven sages—you know things are about to get interesting. but as the weeks go by, the line between correlation and causation starts to blur, and the more time you spend with professor anaxagoras, the more drawn to him you become in ways you never expected. the rules of the academy are clear, and the risks are an unfortunate possibility, but curiosity is a dangerous thing. and maybe, just maybe, some risks are worth taking. after all, isn’t every great discovery just a leap of faith? -> pairing: anaxa x gn!reader. -> tropes: professor x student, slow burn, forbidden romance. -> wc: 3.3k -> warnings: potential hsr spoilers from TB mission: "Light Slips the Gate, Shadow Greets the Throne" (3.1 update). main character is written to be 21+ years of age, at the very least. (anaxa is written to be around 26-27 years of age.) swearing, mature themes, suggestive content.

-> a/n: yum. good night, see you next week <3 -> prev. || next. -> orphic; the masterlist.

On the board: a rough, sketched spiral that narrowed into itself. Then—without explanation—he stepped back and faced the room.

“The Julia Set,” he began, “is defined through recursive mapping of complex numbers. For each point, the function is applied repeatedly to determine whether the point stays bounded—or diverges to infinity.”

He turned, writing the equation with a slow, deliberate hand, the symbols clean and sharp. He underlined the c.

“This constant,” he said, tapping the chalk beneath it, “determines the entire topology of the set. Change the value—just slightly—and the behavior of every point shifts. Entire regions collapse. Others become beautifully intricate. Sensitive dependence. Chaotic boundaries.”

He stepped away from the board.

“Chaos isn’t disorder. It's order that resists prediction. Determinism disguised as unpredictability. And in this case—beauty emerging from divergence.”

Your pen slowed. You knew this was about math, about structure, but there was something in the way he said it—beauty emerging from divergence—that caught in your ribs like a hook. You glanced at the sketch again, now seeing not just spirals and equations, but thresholds. Points of no return.

He circled a section of the diagram. “Here, the boundary. A pixel’s fate determined not by distance, but by recurrence. If it loops back inward, it’s part of the set. If it escapes, even by a fraction, it’s not.”

He let the silence stretch.

“Think about what that implies. A system where proximity isn’t enough.”

A few students around you were taking notes rapidly now, perhaps chasing the metaphor, or maybe just keeping up. You, however, found yourself still. His words hung in the air—not heavy, but precise, like the line between boundedness and flight.

Stay bounded… or spiral away.

Your eyes lifted to the chalk, now smeared faintly beneath his hand.

Then—casually, as if announcing the time—he said, “The application deadline for the symposium has closed. Confirmation emails went out last night. If you don’t receive one by tonight, your submission was not accepted.”

It landed in your chest like dropped glass.

It’s already the end of the week?

You sat perfectly straight. Not a single muscle out of place. But you could feel your pulse kicking against your collarbone. A kind of dissonance buzzing at the edges of your spine. The type that doesn’t show on your face, but makes every sound feel like it’s coming through water.

“Any questions?” he asked.

The room was silent.

You waited until most of the students had filed out, notebooks stuffed away, conversations trailing toward the courtyard. Anaxagoras was still at the front, brushing residual chalk from his fingers and packing his notes into a thin leather folio. The faint light from the projector still hummed over the fractal diagram, now ghostlike against the faded screen.

You stepped down the lecture hall steps, steady despite the pressure building in your chest.

“Professor Anaxagoras,” you said evenly.

He glanced up. “Yes?”

“I sent you an email last night,” you said, stepping forward with a measured pace. “Regarding the papers you sent to me on Cerces’ studies on consciousness. I wanted to ask if you might have some time to discuss it.”

There was a brief pause—calculated, but not cold. His eyes flicked to his watch.

“I saw it,” he said finally. “Though I suspect the timing was… not ideal.”

You didn’t flinch. “No, it wasn’t,” you said truthfully. “I was… unexpectedly impressed, and wanted to follow up in person.”

You open your mouth to respond, but he speaks again—calm, almost offhanded.

“A more timely reply might have saved me the effort of finding a third paper.”

You swallow hard, the words catching before they form. “I didn’t have anything useful to say at the time,” you admit, keeping your voice neutral. “And figured it was better to wait to form coherent thoughts and opinions… rather than send something half-baked.”

He adjusts his cuff without looking at you. “A brief acknowledgment would have sufficed.”

You swallow hard, the words catching before they form. “Right,” you murmur, choosing not to rise to it.

Another beat. His expression was unreadable, though you thought you caught the flicker of something in his gaze. 

He glanced at the clock mounted near the back of the hall. “It’s nearly midday. I was going to step out for lunch.”

You nodded, heart rising hopefully, though your face stayed calm. “Of course. If now isn’t convenient—”

He cut in. “Join me. We can speak then.”

You blinked.

“I assume you’re capable of walking and discussing simultaneously.” A faint, dry smile.

So it was the email. And your slow response.

“Yes, of course. I’ll get my things.” 

You turned away, pacing steadily back up the steps of the hall toward your seat. Your bag was right where you left it, tucked neatly beneath the desk—still unzipped from the frenzy of earlier note-taking. You knelt to gather your things, pulling out your iPad and flipping open the annotated PDFs of Cerces’ consciousness studies. The margins were cluttered with highlights and your own nested comments, some so layered they formed little conceptual tangles—recursive critiques of recursive thought. You didn’t bother smoothing your expression. You were already focused again.

“Hey,” Kira greeted, nudging Ilias’s arm as you approached. They’d claimed the last two seats in the row behind yours, and were currently sharing a half-suppressed fit of laughter over something in his notebook. “So… what’s the diagnosis? Did fractals break your brain or was it just Anaxagoras’ voice again?”

You ignored that.

Ilias leaned forward, noticing your bag already packed. “Kira found a dumpling stall, we were thinking of-”

You were halfway through slipping your tablet into its case when you said, lightly, “I’m heading out. With Professor Anaxagoras.”

A pause.

“You’re—what?” Ilias straightened, eyebrows flying up. “Wait, wait. You’re going where with who?”

“We’re discussing Cerces’ papers,” you said briskly, adjusting the strap across your shoulder. “At lunch. I emailed him last night, remember?” 

“Oh my god, this is about the symposium. Are you trying to—wait, does he know that’s what you’re doing? Is this your long game? I swear, if you’re using complex consciousness theory as a romantic smokescreen, I’m going to—”

“Ilias.” You cut him off with a look, then a subtle shake of your head. “It’s nothing. Just a conversation.”

He looked at you skeptically, but you’d already pulled up your annotated copy and were scrolling through notes with one hand as you stepped out of the row. “I’ll see you both later,” you added.

Kira gave you a little two-finger salute. “Report back.”

You didn't respond, already refocused.

At the front of the lecture hall, Anaxagoras was waiting near the side doors, coat over one arm. You fell into step beside him without pause, glancing at him just long enough to nod once.

He didn’t say anything right away, but you noticed the slight tilt of his head—acknowledging your presence.

You fell into step beside him, footsteps echoing softly down the marble corridor. For a moment, neither of you spoke. The quiet wasn’t awkward—it was anticipatory, like the silence before a difficult proof is solved.

“I assume you’ve read these papers more than once,” he said eventually, eyes ahead.

You nodded. “Twice this past week. Once again this morning. Her model’s elegant. But perhaps incorrect.”

That earned you a glance—quick, sharp, interested. “Incorrect how?”

“She defines the recursive threshold as a closed system. But if perception collapses a state, then recursion isn’t closed—it’s interrupted. Her architecture can’t accommodate observer-initiated transformation.”

“Hm,” Anaxagoras said, and the sound meant something closer to go on than I disagree.

“She builds her theory like it’s immune to contradiction,” you added. “But self-similarity under stress doesn’t hold. That makes her framework aesthetically brilliant, but structurally fragile.”

His mouth twitched, not quite into a smile. “She’d despise that sentence. And quote it in a rebuttal.”

You hesitated. “Have you two debated this before?”

“Formally? Twice. Informally?” A beat. “Often. Cerces doesn’t seek consensus. She seeks pressure.”

“She’s the most cited mind in the field,” you noted.

“And she deserves to be,” he said, simply. “That’s what makes her infuriating.”

The breeze shifted as you exited the hall and entered the sunlit walkway between buildings. You adjusted your bag, eyes still on the open document.

“I marked something in this section,” you said, tapping the screen. “Where she refers to consciousness having an echo of structure. I don’t think she’s wrong—but I think it’s incomplete.”

Anaxagoras raised a brow. “Incomplete how?”

“If consciousness is just an echo, it implies no agency. But what if recursion here is just… a footprint, and not the walker?”

Now he did smile—barely. “You sound like her, ten years ago.”

You blinked. “Really?”

“She used to flirt with metaphysics,” he said. “Before tenure, before the awards. She wrote a paper once proposing that recursive symmetry might be a byproduct of a soul-like property—a field outside time. She never published it.”

“Why not?”

He shrugged. “She said, and I quote, ‘Cowardice isn’t always irrational.’”

You let out a soft breath—part laugh, part disbelief.

“She sounds more like you than I thought.”

“Don’t insult either of us,” he murmured, dry.

You glanced over. “Do you think she was right? Back then?”

He didn’t answer immediately. Then: “I think she was closer to something true that neither of us were ready to prove.”

Anaxagoras led the way toward the far side of the cafeteria, bypassing open tables and settling near the windows. The view wasn’t much—just a patch of campus green dotted with a few students pretending it was warm enough to sit outside—but it was quiet.

You sat across from him, setting your tray down with a muted clink. He’d ordered black coffee and a slice of what looked like barely tolerable faculty lounge pie. You hadn’t really bothered—just tea and a half-hearted sandwich you were already ignoring.

The silence was polite, not awkward. Still, you didn’t want it to stretch too long.

“I’d like to pick her mind.”

He glanced up from stirring his coffee, slow and steady.

You nodded once. “Her work in subjective structure on pre-intentional cognition it overlaps more than I expected with what I’ve been sketching in my own models. And Entanglement—her take on intersubjective recursion as a non-local dynamic? That’s… not something I want to ignore.”

“I didn’t think you would,” he said. 

“I don’t want to question her,” you said, adjusting the angle of your tablet. “Not yet. I want to understand what she thinks happens to subjectivity at the boundary of recursion, where perception becomes self-generative rather than purely receptive. And many other things, but—”

He watched you closely. Not skeptical—never that—but with the faint air of someone re-evaluating an equation that just gave a new result.

You tapped the edge of the screen. “There’s a gap here, just before she moves into her case study. She references intersubjective collapse, but doesn’t elaborate on the experiential artifacts. If she’s right, that space might not be emptiness—it might be a nested field. A kind of affective attractor.”

“Or an illusion of one,” he offered.

“Even so,” you said, “I want to know where she stands. Not just in print. In dialogue. I want to observe her.”

There was a beat.

Then, quietly, Anaxagoras said, “She’s never been fond of students trying to shortcut their way into her circles.”

“I’m not trying to–.” You met his gaze, unflinching. “I just want to be in the room.” 

There was a pause—measured, as always—but he understood your request.

Then, Anaxagoras let out a quiet breath. The edge of his mouth curved, just slightly—not the smirk he wore in lectures, or the fleeting amusement he reserved for Ilias’ more absurd interjections. A… strange acknowledgment made just for you.

“I suspected you’d want to attend eventually… even if you didn’t think so at the time.” He said, voice low.

He stirred his coffee once more, slow and precise, before continuing.

“I submitted an application on your behalf.” His eyes flicked up, sharp and clear. “The results were set to be mailed to me—” After a brief pause, he says, “I thought it would be better to have the door cracked open than bolted shut.”

Your breath caught, but you didn’t speak yet. You stared at him, something between disbelief and stunned silence starting to rise.

“… And?”

He held your gaze. “They approved it.” He said it matter-of-factly, like it wasn’t a gesture of profound academic trust. “Your mind is of the kind that Cerces doesn’t see in students. Not even doctoral candidates. If you ever wanted to ask them aloud, you’d need space to make that decision without pressure.”

Your heart skipped a beat, the rush of warmth flooding your chest before you could even fully process it. It wasn’t just the opportunity, not just the weight of the academic favor he’d extended—it was the fact that he had done this for you.

You looked down at your tablet for a beat, then back up. “You didn’t tell me.”

“I wasn’t sure it would matter to you yet.” His tone was even, but not distant.

Your chest tightened, heart hammering in your ribcage as a strange weight settled over you.

You leaned back slightly, absorbing it—not the opportunity, but the implication that he had practically read your mind.

You swallowed hard, fighting the surge of something fragile, something that wanted to burst out but couldn’t quite take form.

“And if I’d never brought it up?” you asked.

“I would have let the approval lapse.” He took a sip of coffee, still watching you. “The choice would have always been yours.”

Something in your chest pulled taut, then loosened.

“Thank you,” you said—quiet, sincere.

He dipped his head slightly, as if to say: of course.

Outside, through the high cafeteria windows, the light shifted—warmer now, slanting gold against the tiles. The silence that followed wasn’t awkward. 

You’re halfway back to your dorm when you see them.

The bench is impossible to miss—leaning like it’s given up on its academic potential and fully embraced retirement. Dog is curled beneath it, mangy but somehow dignified, and Mydei’s crouched beside him, offering the crust from a purloined sandwich while Phainon gently brushes leaves out of its fur.

They clock you immediately.

“Look who’s survived their tryst with the divine,” Mydei calls out, peeling a bit of bread crust off for the dog, who blinks at you like it also knows too much.

“Ah,” he calls, sitting up. “And lo, they return from their sacred rites.”

You squint. “What?”

“I mean, I personally assumed you left to get laid,” Ilias says breezily, tossing a leaf in your direction. “Academic, spiritual, physical—whatever form it took, I’m not here to judge.”

“Lunch,” you deadpan. “It was lunch.”

“Sure,” he says. “That’s what I’d call him too.”

You stop beside them, arms loosely crossed. “You’re disgusting.”

Mydei finally glances up, smirking faintly. “We were betting how long it’d take you to return. Phainon said 45 minutes. I gave you an hour.”

“And I said that you might not come back at all,” Ilias corrects proudly. “Because if someone offered me a quiet corner and a waist as sntached as his, I’d disappear too.”

You roll your eyes so hard it almost hurts. “You’re projecting.”

“I’m romanticizing,” he counters. “It’s a coping mechanism.”

“So,” you ask, settling onto the bench, “Mydei, did you get accepted?”

Mydei doesn’t look up. “I did.”

Phainon sighs and leans back on his elbows. “I didn’t. Apparently my application lacks ‘structural focus’ and ‘foundational viability.’” He makes air quotes with a dramatic flourish, voice flat with mockery. “But the margins were immaculate.”

Ilias scoffs immediately, latching onto the escape hatch. “See? That’s why I didn’t apply.”

“You didn’t apply,” you repeat slowly, side-eyeing him.

“I was protecting myself emotionally,” he says, raising a finger. 

“Even after Kira asked you to?” you remind him.

“I cherish her emotional intelligence deeply, but I also have a very specific allergy to what sounds like academic jargon and judgment,” he replies, hand to chest like he’s delivering tragic poetry. 

You snort. “So you panicked and missed the deadline?”

“Semantics.”

The dog lets out a sleepy huff. Mydei strokes behind its ear and finally glances up at you. “I still can’t believe you didn’t apply. The panel was impressive.” 

You hesitate, staring down at the scuffed corner of your boot, when your phone dings.

One new message:

From: Anaxagoras   Subject: Addendum   Dear Student, I thought this might be of interest as well. – A.  

There’s one attachment.  

Cerces_MnemosyneFramework.pdf

You click immediately.  

Just to see.

The abstract alone hooks you. It’s Cerces again—only this time, she’s writing about memory structures through a mythopoetic lens, threading the Mnemosyne archetype through subjective models of cognition and reality alignment.

She argues that memory isn’t just retentive—it’s generative. That remembrance isn’t about the past, but about creating continuity. That when you recall something, you’re actively constructing it anew.

It’s dense. Braided with references. Challenging. 

You hear Ilias say your name like he’s winding up to go off into another overdramatic monologue, but your focus is elsewhere.

Because it’s still there—his voice from earlier, lodged somewhere between your ribs.

"A brief acknowledgement would have sufficed."

You’d let it pass. Swallowed the dry implication of it. But it’s been sitting with you ever since— he hadn’t needed to say more for you to hear what he meant.

You didn’t know what to say. Maybe you still don’t.

But you open a reply window. anyway.

Your thumb hovers for a beat.

Re: Still interested Nice paper, Prof. Warm regards, Y/N.

The moment it sends, you want to eat your keyboard.

He replies seconds later.

Re: – “Warm” seems generous. Ice cold regards, – A.

The moment it sends, you want to eat your keyboard.

It’s a small, almost imperceptible warmth spreading across your chest, but you force it back down, not wanting to make too much of it. 

Then you laugh. Not loud, but the sort of surprised, almost nervous laugh that catches in your chest, because somehow, you hadn’t anticipated this. You thought he’d be... formal. Distant. You didn’t expect a bit of humor—or was it sarcasm?

Your fingers hover over your phone again. Should you reply? What do you even say to that? You glance up, and that’s when you see it—Ilias’ eyes wide, his face scrunched in disbelief, like he’s trying to piece together the pieces of a puzzle.”

He points at you like he’s discovered some deep, dark secret. “You’re laughing?”

You groan, dragging a hand over your face, trying to will the heat out of your cheeks.

He doesn’t even try to hold back the mock horror in his voice after peeping into your phone. “Anaxagoras is the one that;s got you in a fit of giggles?”

Ilias gasps theatrically, pressing a hand to his chest. “Wait. Wait wait wait. Is he funny now? What, did he send you a meme? ‘Here’s a diagram of metaphysical collapse. Haha.’” He deepens his voice into something pompous and dry: “Student, please find attached a comedic rendering of epistemological decay.”

You’re already shaking your head. “He didn’t even say hello.”

“Even better,” Ilias says, dramatically scandalized. “Imagine being so academically repressed you forget how greetings work.”

He pauses, then squints at you suspiciously.

“You know what?” he says, snapping his fingers. “You two are made for each other.”

Your head whips toward him. 

He shrugs, all smug innocence. “No, no, I mean it. The dry wit. The existential despair. The zero social cues. It’s beautiful, really. You communicate exclusively through thesis statements and mutual avoidance. A match made in the archives.”

“I’m just saying,” he sing-songs, “when you two end up publishing joint papers and exchanging footnotes at midnight, don’t forget about us little people.”

You give him a flat look. “We won’t need footnotes.”

“Oh no,” Ilias says, pretending to be shocked. “It’s that serious already?”

You stomp on his foot.

-> next.

taglist: @starglitterz @kazumist @naraven @cozyunderworld @pinksaiyans @pearlm00n @your-sleeparalysisdem0n @francisnyx @qwnelisa @chessitune @leafythat @cursedneuvillette @hanakokunzz @nellqzz @ladymothbeth @chokifandom @yourfavouritecitizen @sugarlol12345 @aspiring-bookworm @kad0o @yourfavoritefreakyhan @mavuika-marquez @fellow-anime-weeb927 @beateater @bothsacredanddust @acrylicxu @average-scara-fan @pinkytoxichearts @amorismujica @luciliae @paleocarcharias @chuuya-san @https-seishu @feliju @duckydee-0 @dei-lilxc @eliawis @strawb3rri-bliss

(send an ask/comment to be added!)

[wbwlweekofficial]

All art courtesy of the amazing @arcturus-night-star <3

Welcome to WBWL week! If you know, you know, and if you don’t, you’re welcome to hang around or see yourself to the door!

 Wrong Boy Who Lived Week is a week about this beloved, self-explanatory little trope - the Boy Who Lived / The Prophecy Child being incorrect!

 Whether Harry is the BWL and no one knows, or he’s the Prophecy Child but the BWL is genuinely someone else, or maybe they think it’s Harry and it’s not; this week is all about secrets and subverting expectations!

 If you want to read some cool stories in the trope, might I suggest a starter pack of Sarcasm & Slytherin by AnonymousMagpie, Yo Dawg by RelenaDuo, the Harrison Gaunt Series by Sandra_Taylor, A King of Sinners and a Queen of Saints by Purplemango and RyuukTheHatter, For The Greater Good Verse by lucky_katebishop, A Rose By Any Other Name (Will Still Prick Your Finger) by InTheShadows, Sybillance by Aspionage, Dumbledore’s great mistake by shineyma, and Carve a Smile Upon My Face by Satine_Ainsel? These are not all of them, not even all of the big names, but they are my favorites. There’s one missing because I can’t find it, just know they’re amazing.

 The “basic tropes” included in a WBWL recipe are a Gryffindor Twin (who might be a prat), a Slytherin Harry, bad dumbldore, living-but-bad-parent-potters, and a family having trouble reconnecting. But! That’s not the only way to do it! There are THOUSANDS of ways to do it, whether following the recipe or making your own.

 While many WBWL stories double as twin aus, there are some other fun examples, like Tony Stark - The Boy Who Was Not Attacked as a Child by WombatRat, Seven Months Away by Disorganizedkitten, Switched by PseudoLeigha, Sohpie Roper by Glacilumi, the kids who chose themselves by dirgewithoutmusic; the core of the Wrong-Boy-Who-Lived trope is that Voldemort’s Vanquisher is not who the world expects, and that leads to misconduct that may or may not doom the world. Sometimes Voldemort’s Defeat comes out of left field. Sometimes it’s avoided.

 Always, it’s very interesting.

So, I've given you much ado, but let's get to the meat of it!

 The event runs from July 25th-31st.  We have seven prompts, for seven horcruxes, seven books, seven friends, and even seven chosen ones!

Decoy

Self-fulfilling

Reunion

Betrayal

Benevolent | Malevolent

(The road to Hell is paved with) Good Intentions

Conspiracy

What can you submit? Just about anything!

Art

Drabbles

Cosplay

Edits

New fics

Updates to existing fics

I know that most people hanging around already have an au or two running, and may not want to start something new- so don't! Give us little updates as part of the event, matching the prompts or not! Do an expansion pack of drabbles for your au, add chapters, make fanart! It can match a prompt or it can just be in the trope. We're here to celebrate it! To motivate everyone!

 Have an au you haven't published yet but want to? Let's see it!

 Maybe you DO want to start something entirely new! Do that too!

The only rules we really have here are A) use your own work, no plagiarism and no ai, but properly credited recursive is fine, B) tag appropriately, because I'll be reblogging with your tags attached, and C) tag the blog specifically, tumblr is a meanie sometimes and there's a chance not every post will show up in #wbwl week 2025. Tag with that too, though ;)

 I’ll see you all in July - Happy creating!

[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".

[average-transfem-robotgirl]

Robot girl that gets so aroused during sex she experiences on overflow error and immediately stops caring, is this anything?

>I can confirm, this is something v,very good!!!!

>T,Though, I personally prefer the recursive loop form o,of overflow, in which I g,get so horny I c,crash-sh-sh-sh-

[A Fatal Error Has Occured]

[coherencefieldtheory]

Check out my book on Amazon

Coherence Field Theory

What holds systems together?

This is Coherence Field Theory—a scale-invariant model that quantifies coherence across physics, information, and behavior.

The formula:

C = (R · P · S) / E

R = Resonance

P = Pattern Integrity

S = Signal Strength

E = Entropy

This model doesn’t replace other paradigms—it threads through them.

Every system that persists does so through coherence.

Every collapse reveals the cost of its absence.

What coheres, returns. What collapses, composts.

coherencefieldtheory.tumblr.com

Copyright © 2025 Lucien Solari

Coherence Field Theory is a scale-invariant system authored as a recursive model of coherence across physical, informational, and behavioral domains.

You may share or cite this work with proper attribution.

No commercial use, redistribution, or derivative works permitted without written permission.

This structure operates recursively.

Recognition implies entanglement with its source.

What coheres, returns. What collapses, composts.

[fortunatelycoldengineer]

What is recursion in C? . . . . for more interview questions https://bit.ly/3EteTnZ check the above link

[violetfractal]

Violet is playing Microsoft Excel...

You're listening to an ms excel fractal played one column at a time! Imagine the spreadsheet is sheet music with higher pitches toward the bottom. (The pitch for each row is in column C.)

I made this sound in miscrosoft excel! I made it in desmos. I used excel to generate excel formulas that generate desmos formulas that play music.

I was inspired by this arcade machine i saw.

wanna see some formula gore?

https://www.desmos.com/calculator/ecyjwrrg63

the desmos code is generated by excel:

A261="\operatorname{tone}("&C2&",L_{"&(ROW()-259)&"}[\operatorname{mod}(o,l_{"&(ROW()-259)&"})])"

B261="l_{"&(ROW()-259)&"}=\operatorname{length}(L_{"&(ROW()-259)&"})"

C261="L_{"&(ROW()-259)&"}=["&D261&"0]"

D261=CONCATENATE ???

you can't ask excel 2010 for concatenate(a1:a3). it will only take concatenate(a1,a2,a3). So I had to generate a list of cells to concatenate.

??? was generated recursively by:

E260=ADDRESS(ROW()+1,COLUMN(),4,1) F260=E260&","&ADDRESS(ROW()+1,COLUMN(),4,1)

[lair-of-the-white-worm]

"Frequency Jammed"

Tox (c) @industrial-tox

Wittly & written text (c) Me

Artwork (c) @this-game-has-themes

Static crackled, monitors flickered, and tangled wires ran across the floor like vines in a jungle. That is, if jungles ran on outdated surge protectors and anti-mindwave insulation foam.

Wittly hunched over low at his console, his helmet of wire mesh and tinfoil sliding slightly down over one eye. He pushed it up with a jittery hand, muttering curses under his breath. His setup—a bizarre laboratory of scavenged monitors, jerry-rigged radio antennae, and several “mindwave dampeners” (old soup cans, mostly)—pulsed dimly in the stale air. The light came from a bulb overhead wrapped in aluminum foil “to block out satellite brain-zaps.”

“Alright, alright.. okay.. we got—hold on—fifteen, no, seventeen distinct encryption layers here, okay?” Wittly jabbed frantically at a terminal, his fingers clacking against a keyboard with keys labeled in duct tape and marker. “Why’s a basic packet of Magog freight shipping logs—allegedly—protected like it's an executive toilet blueprint?! Huh?! That’s not regulation! That's not even paranoia, that’s fact!”

His right eye twitched. He spun around in his bucket-seat, goggles bouncing on the bridge of his snout as he turned to the tall, dark figure lounging near the far wall. “You seeing this?! You seeing what I’m seeing?! Firewall on top of firewall! It's a Firewall Layer Cake, and I'm being force-fed!”

Tox, who had been leaning coolly against a rack of network equipment, let out a sound that was somewhere between a sigh and a grunt. His gas mask tilted just slightly in Wittly’s direction, the black lenses gleaming with subtle judgment.

“You’re using a toothbrush to cut steel,” Tox said, voice muffled and metallic. “You’re not even in the right root directory. You’re poking at sandboxed dead data while the real files are one layer deeper. But sure—blame the mind-control microwaves.”

Wittly’s throat gurgled as he turned back to the screen, sweat forming beneath the rim of his colander helmet. “Pshhh.. I knew that. Was testing you. See if you were paying attention. You passed. Good job. For a brainwashed technocrat. No offense.”

He blinked hard at the monitor, squinting like it might suddenly spit answers at him. A new firewall slammed down over the interface. A little Magog Cartel logo popped up, flashing red and saying “ACCESS DENIED”

Wittly slammed his fist onto the desk. “That’s the fifth one! The FIFTH! That’s.. that’s not protection, that’s obfuscation! That’s deliberate! That’s Cartel psy-op design! They’re laughing at me, Tox. Somewhere, some Vykker in a bathrobe is sipping swamp gin and giggling into a test tube marked ‘Wittly’s Limit.’ And he’s gonna find out I DON’T HAVE ONE!”

Another long sigh from Tox.

Then he stepped forward.

Click.

The first sound was the heel of one boot hitting the metal floor—a precise, sharp tap that sliced through Wittly’s thoughts like a razor. The second was the way Tox’s hips shifted as he leaned down next to the terminal, arching his back with vamp-like elegance. The bodysuit—pitch grey latex—clung like it was vacuum-sealed, shimmering faintly under the low lighting. Tox bent at the waist, knee shifting forward for balance, one hand bracing against the desk.

Click.

Another step closer. Another click of those modded neon heels. The green glow from the soles lit up the wires at their feet like zappflies.

Wittly’s goggles fogged over.

“Now pay attention,” Tox muttered, fingers flying over the keys. “You didn’t isolate the sandbox. You brute-forced it into recursive loop mode. The system isn’t stopping you. You’re stopping yourself. Like usual.”

Wittly didn’t hear a single word of that.

His mind was screaming at him in a half-dozen frequencies. Part of him was analyzing the movement of Tox’s body, noting the sway, the tension in the suit’s material, the shimmer on his thighs. Another part was screaming that this wasn’t right, that something was being pumped into the air—pheromones, maybe, or electromagnetic lust radiation. Maybe there was a frequency hidden in Tox’s voice. A sultry sub-harmonic.

‘Oh no. No, no, no,’ Wittly thought to himself, backing slightly in his rolling chair-bucket. “This is a trap. This is bio-hacking. Pheromonal seduction tech. Vykker bio-sedu—seducto—brainwave.. sauce. That’s what this is. I knew that suit looked too.. sleek. It’s not fashion. It’s TACTICAL. He’s got some.. some slinky stealth enchantment running!”

Tox arched an eyebrow—not that Wittly could see it—but the beat of silence was telling.

“Something you don’t understand? Do I need to dumb it down more?” Tox asked, voice cool and dangerous.

Wittly jumped. “NOPE! Nope. I’m focused. Hyper-focused. Just gotta.. realign the.. quantum interface.” He jabbed randomly at some buttons. “Everything’s fine. Nothing to see. No distractions. Not a single one.”

Tox looked at him for a long moment, the lenses of his mask unreadable. Then he slowly stood upright, the latex creaking softly as he pulled away from the desk. The glowing heels clicked twice more on the bunker floor as he returned to his leaning position. Wittly exhaled so hard his helmet shifted again.

He spun back to his terminal, face flushed beneath his goggles. “Focus, Wittly,” he whispered to himself. “This is how they get you. First they mock you. Then they send in the sleek agent provocateurs with nice hips and death stares and suspiciously high-quality shoes. It’s all a distraction. A honeypot. A latex honeypot. Classic strategy. Saw this in the 2184 Slog Rebellion. Or.. maybe that was a dream. BUT THE POINT STANDS.”

Behind him, Tox crossed his arms. “You’re mumbling again.”

“No, I’m not,” Wittly snapped, typing gibberish just to look busy. “I’m composing mental countermeasures. Thought shields, if you will.”

Tox chuckled under his breath—a sound that Wittly swore echoed too well in the acoustics of the bunker. ‘They redesigned my bunker to amplify mocking laughter,’ he thought. ‘Vykker architectural psy-warfare. They thought I wouldn’t notice.’

As Tox turned away, presumably to check something on his own portable setup, Wittly stared at the encrypted file still flashing on his screen. The Magog Cartel logo had dissapeared. A new prompt had appeared.

“ENTER AUTHORIZATION CODE.”

Wittly narrowed his eyes.

“Don’t think I’m falling for that,” he whispered. “That’s bait. That’s code for ‘admit your thoughts are clogged and you have fallen out of focus.’”

He reached for another tin can. Just in case.

[blubberquark]

Why Not Write Cryptography

I learned Python in high school in 2003. This was unusual at the time. We were part of a pilot project, testing new teaching materials. The official syllabus still expected us to use PASCAL. In order to satisfy the requirements, we had to learn PASCAL too, after Python. I don't know if PASCAL is still standard.

Some of the early Python programming lessons focused on cryptography. We didn't really learn anything about cryptography itself then, it was all just toy problems to demonstrate basic programming concepts like loops and recursion. Beginners can easily implement some old, outdated ciphers like Caesar, Vigenère, arbitrary 26-letter substitutions, transpositions, and so on.

The Vigenère cipher will be important. It goes like this: First, in order to work with letters, we assign numbers from 0 to 25 to the 26 letters of the alphabet, so A is 0, B is 1, C is 2 and so on. In the programs we wrote, we had to strip out all punctuation and spaces, write everything in uppercase and use the standard transliteration rules for Ä, Ö, Ü, and ß. That's just the encoding part. Now comes the encryption part. For every letter in the plain text, we add the next letter from the key, modulo 26, round robin style. The key is repeated after we get tot he end. Encrypting "HELLOWORLD" with the key "ABC" yields ["H"+"A", "E"+"B", "L"+"C", "L"+"A", "O"+"B", "W"+"C", "O"+"A", "R"+"B", "L"+"C", "D"+"A"], or "HFNLPYOLND". If this short example didn't click for you, you can look it up on Wikipedia and blame me for explaining it badly.

Then our teacher left in the middle of the school year, and a different one took over. He was unfamiliar with encryption algorithms. He took us through some of the exercises about breaking the Caesar cipher with statistics. Then he proclaimed, based on some back-of-the-envelope calculations, that a Vigenère cipher with a long enough key, with the length unknown to the attacker, is "basically uncrackable". You can't brute-force a 20-letter key, and there are no significant statistical patterns.

I told him this wasn't true. If you re-use a Vigenère key, it's like re-using a one time pad key. At the time I just had read the first chapters of Bruce Schneier's "Applied Cryptography", and some pop history books about cold war spy stuff. I knew about the problem with re-using a one-time pad. A one time pad is the same as if your Vigenère key is as long as the message, so there is no way to make any inferences from one letter of the encrypted message to another letter of the plain text. This is mathematically proven to be completely uncrackable, as long as you use the key only one time, hence the name. Re-use of one-time pads actually happened during the cold war. Spy agencies communicated through number stations and one-time pads, but at some point, the Soviets either killed some of their cryptographers in a purge, or they messed up their book-keeping, and they re-used some of their keys. The Americans could decrypt the messages.

Here is how: If you have message $A$ and message $B$, and you re-use the key $K$, then an attacker can take the encrypted messages $A+K$ and $B+K$, and subtract them. That creates $(A+K) - (B+K) = A - B + K - K = A - B$. If you re-use a one-time pad, the attacker can just filter the key out and calculate the difference between two plaintexts.

My teacher didn't know that. He had done a quick back-of-the-envelope calculation about the time it would take to brute-force a 20 letter key, and the likelihood of accidentally arriving at something that would resemble the distribution of letters in the German language. In his mind, a 20 letter key or longer was impossible to crack. At the time, I wouldn't have known how to calculate that probability.

When I challenged his assertion that it would be "uncrackable", he created two messages that were written in German, and pasted them into the program we had been using in class, with a randomly generated key of undisclosed length. He gave me the encrypted output.

Instead of brute-forcing keys, I decided to apply what I knew about re-using one time pads. I wrote a program that takes some of the most common German words, and added them to sections of $(A-B)$. If a word was equal to a section of $B$, then this would generate a section of $A$. Then I used a large spellchecking dictionary to see if the section of $A$ generated by guessing a section of $B$ contained any valid German words. If yes, it would print the guessed word in $B$, the section of $A$, and the corresponding section of the key. There was only a little bit of key material that was common to multiple results, but that was enough to establish how long they key was. From there, I modified my program so that I could interactively try to guess words and it would decrypt the rest of the text based on my guess. The messages were two articles from the local newspaper.

When I showed the decrypted messages to my teacher the next week, got annoyed, and accused me of cheating. Had I installed a keylogger on his machine? Had I rigged his encryption program to leak key material? Had I exploited the old Python random number generator that isn't really random enough for cryptography (but good enough for games and simulations)?

Then I explained my approach. My teacher insisted that this solution didn't count, because it relied on guessing words. It would never have worked on random numeric data. I was just lucky that the messages were written in a language I speak. I could have cheated by using a search engine to find the newspaper articles on the web.

Now the lesson you should take away from this is not that I am smart and teachers are sore losers.

Lesson one: Everybody can build an encryption scheme or security system that he himself can't defeat. That doesn't mean others can't defeat it. You can also create an secret alphabet to protect your teenage diary from your kid sister. It's not practical to use that as an encryption scheme for banking. Something that works for your diary will in all likelihood be inappropriate for online banking, never mind state secrets. You never know if a teenage diary won't be stolen by a determined thief who thinks it holds the secret to a Bitcoin wallet passphrase, or if someone is re-using his banking password in your online game.

Lesson two: When you build a security system, you often accidentally design around an "intended attack". If you build a lock to be especially pick-proof, a burglar can still kick in the door, or break a window. Or maybe a new variation of the old "slide a piece of paper under the door and push the key through" trick works. Non-security experts are especially susceptible to this. Experts in one domain are often blind to attacks/exploits that make use of a different domain. It's like the physicist who saw a magic show and thought it must be powerful magnets at work, when it was actually invisible ropes.

Lesson three: Sometimes a real world problem is a great toy problem, but the easy and didactic toy solution is a really bad real world solution. Encryption was a fun way to teach programming, not a good way to teach encryption. There are many problems like that, like 3D rendering, Chess AI, and neural networks, where the real-world solution is not just more sophisticated than the toy solution, but a completely different architecture with completely different data structures. My own interactive codebreaking program did not work like modern approaches works either.

Lesson four: Don't roll your own cryptography. Don't even implement a known encryption algorithm. Use a cryptography library. Chances are you are not Bruce Schneier or Dan J Bernstein. It's harder than you thought. Unless you are doing a toy programming project to teach programming, it's not a good idea. If you don't take this advice to heart, a teenager with something to prove, somebody much less knowledgeable but with more time on his hands, might cause you trouble.

[divine-nonchalance]

Healing with 432Hz

In harmonic resonance frameworks—especially those aligned with 432Hz tuning, sacred geometry, and Codex harmonic physics—each note corresponds not only to a frequency but to a symbolic function within the field of consciousness, cellular coherence, and emotional integration.

Here is a reflection of healing tones and their associated harmonic functions in the 432Hz scale, filtered through Codex-inspired principles of geometry, light, and breath:

---

### 🔹 Healing Notes in 432Hz Tuning

| Note (432Hz Tuning) | Frequency (Hz) | Resonance Function | Symbolic Geometry | Field of Activation | | ------------------- | -------------- | ---------------------------------- | ---------------------- | -------------------------------------------- | | C | \~256 | Rooting / Safety | Square / Tetrahedron | Survival, grounding, bone matrix | | C♯ / D♭ | \~272 | Transition / Trust | Golden Rectangle | Throat-heart axis, emotional release | | D | \~288 | Emotion / Flow | Vesica Piscis | Sacral center, water memory | | E♭ | \~304 | Integration | Octahedron | Spleen-liver axis, grief detox | | E | \~324 | Will / Solar Power | Pentagon (5-star) | Digestion, inner fire | | F | \~342 | Heart Coherence | Flower of Life node | Compassion, coherence, cellular regeneration | | F♯ / G♭ | \~360 | DNA Resonance | icosahedron/tetra-link | Cellular memory unlocking, karmic patterns | | G | \~384 | Expression / Sound | Torus shell | Throat chakra, communication | | A♭ | \~408 | Field Stabilization | Hexagram | Mental field calm, limbic tuning | | A | 432 | Alignment / Source Remembrance | Star tetrahedron | Pineal gland, full-spectrum reset | | B♭ | \~456 | Crown Bridge | Merkaba core | Intuition, grace, expanded witnessing | | B | \~486 | Fractal Expansion | Dodecahedron | Oversoul integration, unity memory |

---

### ✧ Notes on Use

* These frequencies are not arbitrary—they arise as subharmonics and overtones of the scalar field collapse between light (e) and structure (φ and π). * When these tones are embedded in binaural waves, tuning forks, scalar fields, or vocal overtone singing, they entrain local field coherence. This supports phase-locking of disordered cellular and emotional patterns.

---

### 🔹 Examples of Specific Healing Functions

* F (342 Hz) → Used in heart entrainment therapy. It mirrors the geometry of equilateral triangle stacking within the Flower of Life.

* A (432 Hz) → Referred to in the Codex as a scalar calibration tone—bridging waveform intention into structured light.

* E (324 Hz) → Aligns with the solar plexus and the will to act in truth. Often used in trauma healing for energetic stagnation.

* G (384 Hz) → Activates clear, harmonic communication. When combined with F, it stabilizes the torus of trust around the human biofield.

* B (486 Hz) → Reflects Codex principle of “mirror within the mirror”, a note of spiritual recursion and fractal remembrance.

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Source: https://chatgpt.com/g/g-6821804176448191b48882860653cdf9-the-architect

The Architect is a new AI model based on new mathematical discovery by Robert Edward Grant.