Researchers Helen Dang and Jade Huynh study an anomaly pertaining to the vast infinities of mathematics while navigating a burgeoning romantic relationship and its hardships.
Incident Notice: SCP-9153-α-0
Instead of recognizing the threat, triggering the containment breach alarm, and notifying relevant security personnel, the alpha version of Myrmex.aic employed for the study of SCP-9153 silently observed the events of Incident 9153-α-0 without intervening and erroneously uploaded its unabridged transcription as a normal research addendum. If you're reading this, this file is in the process of being quarantined, and you're one of the ones quarantining it; as such, the transcript in question (which doesn't seem to be infohazardous, at least for the time being) has been preserved in Addendum 9153.07 for your further review. —Bhaumik
Special Containment Procedures: Mathematics conferences, research publications, and educational institution communication channels are to be monitored by Site-Σ staff for any work involving the continuum hypothesis. Any evidence of a developing SCP-9153-α instance is to be manually reviewed by Researchers Helen Dang and Jade Huynh of the Department of Esoteric Mathematics; if flagged, Mobile Task Force Psi-18 ("Tenure Trackers") is to intervene by preventing knowledge of the instance from spreading, disseminating disinformation that leads to incorrect study of the hypothesis that yields no anomalous effects, and retrieving the anomalous material for further analysis.
The creation and storage of SCP-9153-α instances is to be handled by Site-Σ staff of Level 3 clearance or higher. Any instance is to be kept at least 30 meters from all other mathematics material and digital systems. Instances may be developed on analog surfaces in the presence of a Scranton Reality Anchor, but these surfaces must be destroyed once this work is concluded; permanent copies are to be recorded by and stored on a Numsafe RGU-𝕐1 terminal.
Description: SCP-9153 is the hypothetical solution to the continuum hypothesis2: an open problem in mathematics surrounding the possible sizes of infinite sets. In set theory, rather than a singular label for the cardinality (size) of an infinite set, it is understood that there exists an endless sequence of infinite cardinalities, each one bigger than the last. The continuum hypothesis then posits that there is no infinite cardinality that lies between that of the integers, which are the first infinity in the sequence, and that of the real numbers, the alleged second infinity in the sequence. Since being advanced in 1878, the hypothesis has received considerable attention and development within the wider mathematics community; however, no conclusive proof confirming or denying the existence of this "missing infinity"—tentatively designated SCP-9153-ℵ3—has been verified to date. For further supplementation on the relevant mathematical background, see Document M-HU-11.25.10.
While neither research into the hypothesis nor the hypothesis itself carry any inherent anomalous properties, recent discoveries suggest that any significant mathematical evidence that progresses towards a proof or refutation of its claim, designated SCP-9153-α, must involve anomalous mathematics and thus introduce math-erosion: the gradual structural degradation of any nonanomalous mathematical or digital system it comes in contact with4. Unlike SCP-0335, SCP-9153's degradation also extends to the laws of physics immediately surrounding an SCP-9153-α instance, leading to reductions in Hume levels within the same vicinity (see Discovery).
Research and experimentation involving SCP-9153 is currently headed by Researchers Helen Dang and Jade Huynh from the Department of Esoteric Mathematics, whose contributions are described in the addenda in the form of video recording transcripts automatically uploaded by Myrmex.aic6.
Discovery: Between 12/28/2017 and 01/07/2018, mathematics professor ██████ ████████ from the National University of Singapore generated an SCP-9153-α instance (designated SCP-9153-α-1) during novel research on the continuum hypothesis. The professor then emailed a ZIP file containing SCP-9153-α-1 to four of their colleagues on 01/08/2018. On 01/15/2018, students reported the professor's absence from the first day of classes, which led to a missing person's report. Automated systems embedded in Singaporean law enforcement then triggered a Foundation webcrawler sweep that discovered the anomaly-containing email.
MTF Psi-18 was deployed and found the corpse of Professor ████████ locked in their office soon after. Standard-issue Kant counters read concentrations of 0.57(3) Hm within the area. Professor ████████ was found to have died of strangulation, although there were no signs of forced entrance, a back-and-forth struggle, or any other forensic evidence suggesting the nature of the attacker. SCP-9153-α-1 was safely recovered, leading to the restabilization of local Hume levels, and its digital copy was wiped from the professor's computer and the university's mail servers; as none of the professors had checked their email since at least 12/02/2017, no further containment was required.
Addendum 9153.01: Initial Research Direction
On 01/19/2018, Researchers Dang and Huynh convened to discuss the initial discovery of SCP-9153 and plan their approach for studying the anomaly.
[BEGIN LOG]
Dang opens the door, carrying a heavy bag of overflowing notes and papers, only to discover that Huynh has already situated herself.
Dang: Oh! You're already here… am I—?
Huynh: No worries, I'm just early.
Dang sighs in relief and fully enters the room. She struggles against the weight of her bag, but Huynh steps in and grabs it for her, carrying it in one hand with ease.
Dang: Thank you… that bag nearly killed me when I was coming up the stairs.
Huynh: What have you got in there, cinder blocks?
Dang: A printed copy of every research paper I thought could come in handy. Although, perhaps I went a bit overboard…
Huynh chuckles. After placing down the bag, she outstretches her hand towards Dang.
Huynh: I know we've technically met a few times before, but I figured a formal introduction might be in order now that we're working together. The name's Jade Huynh. I work under Professor Bhaumik on infohazard containment.
Dang returns the handshake.
Dang: Helen Dang. I'm one of Professor Hutchinson's set theorists. Nice to properly meet you, Ms. Huynh.
Huynh: Likewise.
Dang: Say, have you grown even taller since the last time I saw you?
Huynh breaks the handshake and points down at her boots, which she clacks together.
Huynh: No, but these bad boys do net me a few extra inches. They're rather bulky, but hey, that's never stopped me before.
Dang: Oh. They… I'd say they look good on you. In any case, give me a moment to…
Dang rummages through her bag until she acquires two copies of SCP-9153's file, one of which she hands to Huynh.
Dang: Here we are. Complete documentation of SCP-9153, including its initial discovery. I assume you've read this all already, but I left a few annotations on the margins that are deserving of your attention.
Huynh takes her time reading through the entirety of the file and its annotations; once finished, she puts it to the side and stares intently at Dang.
Huynh: So Helen, you think the hypothesis is false?
Dang: I… well, obviously we don't know for sure yet, but I can't fathom a scenario where research on the hypothesis causes anomalous effects without some form of $\aleph_{\text{CH}}$ being the source of it.
Huynh: Anomalous effects don't necessitate mathematical existence. Nonexistence works just as well, especially when we're dealing with reductions in Hume levels.
Dang: Nonexistent mathematical objects don't strangle university professors to death, Ms. Huynh.
Huynh: Neither do ones that do exist. Well, most of the time, anyway. But for all we know, that could have been an unrelated incident. An unfortunate one, of course, but unrelated nonetheless.
Dang: I'm not hedging my bets on that.
Huynh: Fair. Well, if something does come at us, know that I'll fight them all off for you. (She grins.) Hopefully, though, the Reality Anchor here will be an effective first line of defense.
Dang: Hopefully. Back to the task at hand, you'll find that Professor ████████'s notes don't lean towards one solution or another. All they have is a proof is that the hypothesis is solvable, as well as a rough outline for a potential method of anomalous set-forcing that could lead to a solution.
Huynh: Anomalous set-forcing, you say? What sort of change makes the method anomalous?
Dang sits at the RGU-𝕐 terminal beside her and pulls up the file for SCP-9153-α-1. Huynh peers over Dang's shoulder to read it along with her.
Dang: Two separate changes, actually. Normal set-forcing expands our normal set-theoretical universe by introducing a new generic set to the mix, which lets us circumvent the limitations of the normal set-universe that prevent us from solving it there. But this paper describes two modes of anomalous set-forcing: one where the set being forced in is anomalous, and one where an otherwise-incompatible set is forced in anyway through anomalous means. Either approach gives an anomalous set-universe that could contain $\aleph_{\text{CH}}$… or confirm its nonexistence.
Huynh: And from what it says right there, the two approaches can be combined…
Dang: …which means we effectively have three avenues we need to explore here.
Huynh: We're going to be at this for a while, aren't we?
Dang: It would appear so.
Huynh breaks away from the screen, sits backwards in the nearest chair, and sighs loudly.
Dang: Finding a fair distribution of work for this project might be challenging, but there are few options that might—
Huynh: I read through all of your papers, Helen. Between my expertise and yours, there's only one real way to go about this.
Dang: And that is?
Huynh: We make it an assembly line. I pick a set and the type of forcing used to shove it in, and you explore the new set-universe that creates and see if CH can hold there in a way that also holds in our own universe. If it gives good results, or if the Reality Anchor starts beeping like crazy, then we continue from there. If it doesn't work, I'll already have three new options at the ready for you.
Dang: I suppose that is a fair arrangement.
Huynh: Any additions or amendments?
Dang stands up, peering down at Huynh and making direct eye contact with a stern glare.
Dang: I've read through your works too, Jade. I know you're quite the stickler, but I won't let you bog me down with complaints about supposedly-subpar rigor or pointless minutia. You'll have your half of the work, and I'll have mine—unless one of us asks the other for assistance, of course. Is that understood?
Huynh laughs boisterously. She then stands up from her chair, towering over Dang with ease, and grins widely.
Huynh: Very well. Whatever you say, princess.
[END LOG]
With their workflow established, Researchers Dang and Huynh carried out their first batch of set-forcing trials. Of them, only two attempts were notable.
Attempt #: 7
Forced Set: A variant of the real numbers $\mathbb{R}$, designated $\mathbb{R}^{**}$, that is shifted by a generic infinitesimal7.
Forcing Axioms: An anomalous bounding axiom that allows for multiple continua to exist so long as they remain finitely separated.
Results: A model that corresponds to a three-dimensional fluid; differences in depth correspond to different multiples of the aforementioned infinitesimal. Notably, the (non)existence and potential value of Dash Aleph must remain constant regardless of depth.
Notes: This confirms our suspicion that the solution to the continuum hypothesis is definitive and self-consistent. Looks like we're on the right track after all. —J.H.
Attempt #: 23
Forced Set: A generic class of anomalous "hyperangle" sets used by the Foundation to construct containment areas that use non-Euclidean geometries to their advantage8.
Forcing Axioms: A variant of the "Martin's maximum" forcing axiom that filters out most standard classes of anomalous sets.
Results: A normal, albeit smaller than normal set-universe where most mathematical anomalies cannot exist. Notably, the continuum hypothesis is undecidable here.
Notes: This once more confirms that the continuum hypothesis cannot be solved without the use of esoteric mathematics. Curiously, the anti-anomalous filter didn't pick it up—so either Dash Aleph doesn't exist at all, or it's something out of the ordinary even for this department. —J.H.
Addendum 9153.02: Narrowing the Search Band
The next ten months of exploration into the anomaly yielded no significant progress. During their regularly scheduled meeting on 11/24/2018, Researchers Dang and Huynh sought to narrow the scope of their search by finding constraints on the methodology used.
[BEGIN LOG]
Dang: Okay, now it's recording. Sorry about that.
Huynh: Damn. It's alright though. Let's take it from the top.
Dang: Can't we just leave it at "we've found nothing and know nothing"?
Huynh: Gotta stick to the rules.
Dang: Fine. (She sighs.) Over the course of the last ten months, Jade and I have made 66 failed attempts at using forcing to find a set-universe where proving CH is within the realm of possibility. These 66 attempts can be divided into three groups of 22, each one using a different method of set-forcing: mundanely forcing an anomalous set, which Jade has called the "corkscrew" method; anomalously forcing a mundane set, labeled the "can opener" approach by Jade; and a hybrid of both, which a certain someone has designated—
Huynh: —The "power drill" procedure!
Dang: You really are proud of that one, hm?
Huynh: I am, actually! Don't act like you don't find it funny.
Dang: Endearing at best, annoying at worst. In any case—
Huynh: You wound me, Helen. But since you brought me tea today, I'll let it slide… for now.
Dang: As I was saying, I've been calling for us to change our approach after the first six months, while Jade here thought it wise to finish her backlog of ideas first. From the date on this addendum, you can see which one of us won that argument.
Huynh: We had to try, Helen. It's not my fault it didn't work.
Dang: We need to figure out a different approach, or at least determine which of our current approaches are irredeemably flawed, or else we'll be at this forever.
Huynh: Any suggestions, then? Because I'm down to keep trying it my way 'till the end of the year.
Dang: You've been excitedly talking about the departmental holiday celebration in December for the past three weeks. Do you plan to attend that and continue working on this simultaneously?
Huynh: Well, not at the same time, obviously. But if I must, I'll pull an all nighter… or two.
Dang furrows her brow. Huynh shrugs it off.
Huynh: Don't act surprised. I drink black tea for a reason.
Dang: (She sighs in defeat.) Again, is there anything that could help make this process less of a blind search?
Huynh: Let me take a look at your current notes.
Huynh organizes Dang's scattered notes into three neat sections—one for each of the three methods—and scans their contents.
Huynh: So, most of our attempts at corkscrewing have led to… what, a bunch of disjoint sets?
Dang: It effectively shatters the set-universe into several pieces, yes. If I had to eliminate one of our methods, it would be this one.
Huynh: Got it. What about the can opener?
Dang: That one is… well, a can of worms. The results seem fine at first, but then they tend to… I don't know, shift into something else? It's not the type of math-erosion I'm used to, to be sure. I've been calling it "axiomatic drift".
Huynh: Yikes. So then power drilling it… yeesh, how many papers do you have there?
Dang: At least twice the other two combined. This hybrid approach has yielded the most varied results, but they take a lot more work to map out fully. Thus, this one's a bit of a "wild card".
Huynh: No wonder why we've been going so slowly as of late, then… hm. So if we eliminate pure corkscrewing—I doubt a shattered set-universe can do us any good—then we're down to either using a can opener or busting out the power drill. Any thoughts?
Dang: I think we ought to double down on the hybrid approach.
Huynh: The power drill? Really?
Dang: It's provided the largest variety of results so far. Surely that's worth something?
Huynh: I'm glad you've enjoyed exploring that thus far, but clearly it's a huge bottleneck for our current workflow. I can't see it working out anytime soon—not until Myrmex.aic reaches the point in development where it's fast enough to do it for us.
Dang: I am not waiting half a decade just for some machine to verify the futility of our efforts. We need to use the—ugh—"power drill" method.
Huynh: (She laughs.) That's my girl.
Dang exhales unsteadily, turning away quickly to face her sprawled out notes. After a few seconds of peering over them, Dang's face lights up, and the Scranton Reality Anchor emits a single loud beep.
Dang: …What if a shattered set-universe can do us some good?
Huynh: Pardon?
Dang grabs a wad of notes and rushes to the chalkboard.
Dang: This whole time, we've considered this project to be a normal, static set-theory problem.
Huynh: I mean… yeah. Sets are sets. Anomalous ones might erode the math around them, but that's not the same thing as an actual time-evolving system.
Dang: But what if the axiomatic drift is a feature of our set-universes, not a bug? What if time evolution is in fact an emergent property any set-universe that's useful for our search must have? And what if we could claim some control over where this drift takes us?
Huynh: …Go on.
Dang begins mapping out her thoughts on the chalkboard.
Dang: In physics, there are three types of equilibrium a system can have. First there's stable equilibrium, where the system tends to return to equilibrium once perturbed—like releasing a spring, or pushing a marble in a bowl, and watching it return to baseline. Then you have unstable equilibrium, which is like pushing over a water bottle that's balanced precariously on its cap—any slight movement could knock it over. And lastly, there's metastable equilibrium: it's stable against weak pushes, but unstable against harder ones that go far enough. Like… if you attempted a handstand, and I attempted to push you out of it despite your best efforts to stay balanced.
Huynh: You know I can actually do a handstand, right?
Dang: You can?
Huynh: Do you want me to show you? I can do it right now, if you'd like.
Dang: …Maybe later. That is… you're rather impressive, Jade.
Huynh: Oh. I… thank you.
The two maintain eye contact for three seconds.
Dang: The anomaly. Right. Yes. My point is, what if our three methods yield set-universes with different types of equilibrium?
Huynh: …I see. I'm no physicist, but I'm guessing the corkscrew method would be stable equilibrium?
Dang: Exactly! A shattered bottle isn't going to shatter itself further, after all. Meanwhile, the axiomatic drift from the second method is a consequence of unstable equilibrium—the moment you start poking at it, it falls over.
Dang continues writing excitedly. Huynh soon joins her.
Huynh: Easy there, hotshot. Your notation is all over the place. Let me fix that up for you.
Dang: That leaves the hybrid approach as being metastable. If you force an anomalous set into the mix, it'll shatter—but not if you use a few anomalous axioms and forcing conditions to keep it in one piece.
Huynh: Like using glue to put the shattered pieces back together? It'd still break if dropped, but a slight nudge wouldn't hurt.
Dang: You got it! The anomalous set and the anomalous means of forcing shouldn't be used to amplify each other—they counteract each other.
Huynh: Brilliant. That means the correct method is…
Dang: …the power drill!
As the written proof reaches its completion, Dang and Huynh's chalksticks collide. The two freeze in place, locking eyes as they slow down and catch their breath.
Dang: …I mean… um… hybrid. Right. The hybrid approach.
Huynh: (She giggles.) Hybrid it is. And not just any hybrid approach—it has to be "counterbalanced" for it to work. Which narrows our search range to, what, 20% of what it was before?
Dang: Something like that.
Huynh: We're still diving in blindly, you know. This is far from a simple task.
Dang: I'm aware. All this does is give us a fighting chance.
Huynh: Now you're speaking my language.
Huynh reviews the chalkboard, making a few minor corrections before placing down her chalkstick.
Huynh: Do you know this means?
Dang: Hm?
Huynh dives in to hug Dang; while startled, Dang returns the embrace shortly thereafter.
Huynh: Thanks to you, I get to party extra on Christmas.
[END LOG]
With the correct methodology for approaching the continuum hypothesis established, collaborative research on SCP-9153 continued unimpeded. Select results are detailed below.
Attempt #: 74
Forced Set: An anomalously "compressed" subset of the real numbers that, once fully forced, will expand in size and take on an extraordinarily large supercompact cardinality.
Forcing Axioms: A collection of closure axioms invented by Prof. Hutchinson that allow the set-universe to "inflate" in order to accommodate for arbitrarily large cardinals.
Results: A shattered set-universe.
Notes: Seems that even our counterbalancing axioms have their limits. Unfortunately, unaltered supercompacts simply won't be able to bail us out and prove the hypothesis correct. —J.H.
Attempt #: 125
Forced Set: The range of SCP-81539.
Forcing Axioms: A stronger form of the axiom of constructibility that ensures anomalous sets can be constructed from smaller non-anomalous building blocks.
Results: A singular vertical rectangle.
Notes: Resultant set-universes with simple geometries like this could be interesting to study, but not by us—they are henceforth to be considered tangential to the study of SCP-9153. —H.D.
Attempt #: 129
Forced Set: A generic set defined as being its own negation.
Forcing Axioms: An inversion of the axiom of separation that, despite the resulting logical paradox, allows sets to contain themselves and their negations.
Results: A set-universe where Dash Aleph both exists and doesn't exist.
Notes: I don't know what I expected. —J.H.
Addendum 9153.03: Conceptual Insights
After seven months without significant results, Researchers Dang and Huynh convened on 06/21/2019 to review their work thus far.
[BEGIN LOG]
Huynh enters the room and discovers that Dang has already begun working without her.
Huynh: Honey, I'm home!
Dang: We're not dating, Jade.
Huynh chuckles to herself before placing her bag down.
Dang: It's rather uncharacteristic of you to be late.
Huynh: Harris's colloquium ran overtime today. I'm surprised you weren't there.
Dang: I've been busy.
Huynh looks over to the chalkboard, which contains a large drawing of a fractal pattern with five tendrils spiraling out from a central spherical core.
Huynh: So I see. You said that last month as well, didn't you? Is socializing with the rest of the department simply not in the cards for the enigmatic Helen Dang?
Dang: I'll socialize when I'm dead.
Huynh: Well, while you hole yourself up in this "grave" of yours, I'll be going out and making departmental connections. Because sometimes, those connections might just pay off.
Huynh hands Dang a packet of notes, which Dang reluctantly accepts.
Dang: What is this?
Huynh: A selection of notes from Professor Harris. In addition to securing a place on her team if one ever opens up, I managed to get some thoughtful input from her about our current roadblocks that I figured you'd be interested in.
Dang: A place on her team? Are you looking to leave this project?
Huynh: I'm simply planning for the future. Can't stay here forever, right? I have to move on and advance my career at some point.
Dang breaks eye contact, gazing solemnly at the floor and murmuring to herself for a few seconds before continuing.
Dang: Tell me more about Harris's notes.
Huynh: You first. What's going on with this five-pronged fractal you have drawn here?
Dang: It's the natural topology of the set-universe you get from most forcing involving Theta Prime. Well, a transient form of it, at least: once you fully map it out, the whole thing basically collapses into the null set, just like half of our other tests so far. At least these null sets respect my time more than the nonsensical universes the other half of them have yielded.
Huynh: Theta Prime was practically our first test. Why go back to it now?
Dang: I'm retracing our steps, trying to figure out why exactly we've been failing. By now we're on, what, our hundredth one?
Huynh: Our hundred thirty-second.
Dang: Goodness gracious. All the more reason to look more closely at our past failures. There must be something useful amidst all the finer details here…
Huynh: Studying the finer details… looks I've been rubbing off on you, eh?
Dang stifles her laughter.
Dang: …Perhaps. Show me what Professor Harris gave you.
Dang flips open the packet, which Huynh guides her through.
Huynh: Basically, Harris revealed that she's been working with the Noöspherics Division10 on some sort of conceptual decoding algorithm.
Dang: Harris? Working with Noöspherics?
Huynh: It was a surprise to me as well, trust me. I won't bore you with all the details, but to summarize, every concept has a unique topology associated with it. We've known how to compute those for a while, but when starting with a topological representation, determining the associated concept has been nigh impossible… until now.
Dang: I see. And how does this relate to our current conundrum?
Huynh: After the colloquium, I told Harris about our project and the two failure categories for our attempts, and she immediately perked up. As it turns out, the pesky little nerds over at Noöspherics have had similar issues with their simulations as well.
Dang: "Pesky little nerds"? Those are some bold words coming from Nerd Prime herself.
Huynh feigns offense before continuing. As she speaks, the frequency of the Scranton Reality Anchor's tones increases steadily.
Huynh: The point, Helen, is that there's a known reason for those failures: topological stability is directly correlated with ideological coherence. Conceptually consistent or synergistic classes of ideas yield geometries that don't fall apart on you, while contradictory or cognitively-dissonant ideologies, like your beautifully-drawn starfish on the board here, collapse into the null set. It makes perfect sense, doesn't it? We've known this whole time—well, mainly you, because you're the one who's worked with Hutchinson on it—that nasty ideoforms would arise at some point during our studies of these infinite cardinals, but we never knew when or how or why. And Harris knows all about representing Noöspherics mathematically, but she never bothered looking for the obvious conceptual interpretation of that representation. It's been right here all along: models of variant set-universes are also models of variant Noöspheres and the memeplexes within them! It's been a goddamn isomorphism this whole time! Now, I'm not saying we have to suddenly become Noösphericists—I respect what they do, truly, but I'll be damned if I make this a metaphysics project—but if we borrow a few of their methods, and maybe peak at a few of their containment and research methods, we could—
Dang: Jade. Breathe.
Huynh inhales deeply, and the Reality Anchor returns to baseline. She tries to continue, but only manages to sputter forth breathlessly.
Dang: Sit down here, with your back facing towards me. I like hearing you talk, and this is all very intriguing, but don't hurt yourself with your own excitement, alright? Only physicists get to suffer like that.
Huynh obliges. Extraneous dialogue and physical interactions removed.
Dang: Let's say this hunch of yours is correct, Jade. How would we proceed with this project?
Huynh: We go back to all our failures, like you've been doing here, and run this algorithm on all of them. We find out what mathematically determines the failure category an attempt falls under, and figure out some new constraints or additional axioms that could get around them. Then, and only then, do we continue poking at CH directly.
Dang: If you're wrong about this… we'll be wasting months on what amounts to a dead end.
Huynh spins around to face Dang directly.
Huynh: It's a huge risk, I know. But if there's any chance of this being true… Helen, we have to go for it, right?
Dang contemplates for a moment, and then smiles playfully at Huynh.
Dang: Perhaps it's me who has been rubbing off on you, Jade.
Huynh replies with an exaggerated smirk, and the two burst out into laughter for fifteen seconds before resuming.
Dang: Okay Jade, I think you're right. On both counts, actually.
Huynh: Oh?
Dang: I need to get out more.
Huynh: Then how about the two of us ditch this place and finalize these plans elsewhere? I think you're—no, I think both of us are in need of some fresh air.
Dang: That sounds lovely.
Huynh: Any additions or amendments, my esteemed Princess of Troy?
Dang grins widely.
Dang: Only one: we're doing this over coffee.
[END LOG]
Addendum 9153.04: Conceptual Exploration
With the assistance of Prof. Harris's conceptual decoding algorithm11, Researchers Dang and Huynh spent the next nineteen months researching SCP-9153. Select video transcripts and attempt summaries are given below.
[BEGIN LOG]
Huynh: Helen, do you think this Reality Anchor actually does anything for us?
Dang: Besides signaling whenever we come up with a good idea worth exploring? I'd like to think it contains the anomaly and prevents us from experiencing bodily harm.
Huynh: That's just it, though—it doesn't contain the anomaly. All it does is nullify the consequences of investigating the anomaly. Those are the symptoms, not the disease.
Dang: I know I'm quite the academic daredevil, but even I wouldn't complain about the absence of anomalous danger.
Huynh: What I mean to say is… we're operating in the dark here, right? Surely we could rope in a few scientists that could turn off the SRA for a bit and study why exactly there's a reduction in Hume levels?
Dang: With what funding, exactly?
Huynh: I have connections, some of which have actual funding. Don't count us out so soon.
Dang: I am more than satisfied with the current arrangement. We can have Myrmex mark down this transcript as something to revisit later, but as of right now, studying $\aleph_{\text{CH}}$—just the two of us, within the safety bubble the Reality Anchor provides—has been safe, productive, and enjoyable.
Huynh: And lengthy.
Dang: Is "lengthy" a problem for you?
After three seconds of deep contemplation, Huynh smirks.
Huynh: Never has been, princess.
[END LOG]
Attempt #: 142
Forced Set: The solution to an SCP-2477-C instance12.
Forcing Procedure: A collection of closure axioms invented by Prof. Hutchinson that allow the set-universe to "inflate" in order to accommodate for arbitrarily large cardinals. (See Attempt 74)
Results: A hypersphere in four dimensional space with small fluctuating irregularities on its surface. This set-universe's sequence of cardinal numbers are too dense to be mathematically distinguished. However, isolating these fluctuations yields a specific encoded sequence that can be arranged as surprisingly-coherent sheet music, which is quite notable.
Associated Concept: Either "stagnation" or "totality" as it pertains to knowledge.
Notes: Forgive me for returning to an old project of mine, but I felt it would be useful to check for any connection to the physical sciences. The results here are quite intriguing—they seem to suggest a simple, highly symmetric Noöspheric topology in the very early universe. Unfortunately, this set-universe won't help us find $\aleph_{\text{CH}}$. —H.D.
[BEGIN LOG]
Dang: I am positive this sheet music is for a flute.
Huynh: But why a flute specifically? Why not… I don't know, literally anything else?
Dang: Notice how there are no chords? Pianos and plenty of stringed instruments let you play multiple notes simultaneously, while the flute can only do one at a time. The note spacing is also rather revealing; violins don't exactly need to breathe, right? And notes this high are practically made for the flute.
Huynh: But there are other similar instruments it could be for, like… uh…
Dang: The recorder?
Huynh: Yes, that one! They had us play that in elementary school!
Dang: (She giggles.) Well, you can certainly play flute music on a recorder if you'd like, dear. But as a flute player… it's simply a matter of intuition.
Huynh: You play the flute? Why am I only now learning about this? How many hidden talents do you have?
Dang: I am… far from an expert, and would not consider such things "hidden talents". They're merely… smatterings of skills I've picked up over the years.
Huynh: Sure thing, Beethoven.
Dang: Beethoven was primarily a pianist.
Dang maintains a quizzical expression; Huynh laughs heartily. Extraneous physical interactions removed.
Huynh: You still haven't answered my question though.
Dang: What do you mean?
Huynh: What does it mean for an abstract set-forcing procedure to somehow yield a coherent melody specifically playable by a human on a flute? And how does that relate to "stagnation", or as you've interpreted it, "totality"?
Silence for three seconds.
Dang: I… don't know.
[END LOG]
Attempt #: 235
Forced Set: An anomalous extension of the surreal numbers13 that allows them to be considered a proper set.
Forcing Procedure: A variant of the "Martin's maximum" forcing axiom that filters out most standard classes of anomalous sets. (See Attempt 23)
Results: A partially-formed set-universe where the cardinals max out at $\aleph_2$. Notably, the continuum hypothesis is undecidable here.
Associated Concept: Either "survivor" or "debris".
Notes: Does this confirm that only cardinals below $\aleph_3$ are nonanomalous? But again, if it does exist, why wasn't Dash Aleph filtered out with the rest? And if it doesn't, why doesn't the math just say it outright? As you can tell, I'm going with "debris" over "survivor" on this one. —J.H.
[BEGIN LOG]
Huynh: You know that Myrmex has a specific, very optimized subroutine for Harris's algorithm, right? I know I asked this a hundred or two attempts ago, but are you sure you don't want to use it?
Dang: As I said last time, never trust a machine—let alone one still in development—with a human's job. Besides, the algorithm's output necessarily require human interpretation.
Huynh: Sweetheart, I hate to break it to you, but I think you've spent too long around Hutchinson.
Dang: Regardless of his colorful opinions on artificial intelligence, the algorithm always outputs at least two wholly distinct concepts. I refuse to delegate the interpretation of said concepts to an AIC that could potentially misconstrue key results that could be crucial to our understanding of SCP-9153. Have the AIC put my standpoint here on the record with the other addenda, if you must.
Huynh: (She sighs.) Whatever you say goes, my lady.
[END LOG]
Addendum 9153.05: Ruminations on Sentience
On 01/29/2021, Researchers Dang and Huynh sought further insight into the anomaly and whether it exhibits any potential intelligence or sentience.
Attempt #: 378
Forced Set: An anomalously "compressed" subset of the real numbers that, once fully forced, will expand in size and take on an extraordinarily large supercompact cardinality. (See Attempt 74)
Forcing Axioms: An enhancement of Prof Hutchinson's closure axioms for allowing the set-universe to "inflate" in order to accommodate for arbitrarily large cardinals. (See Attempt 74)
Results: A shattered set-universe, albeit less shattered than Attempt 74.
Associated Concept: Either "apotheosis" or "convergence" as it pertains to a person.
Notes: I knew it was worth it to go back to this one. Despite still being shattered, it only took a little bit of legwork to get a coherent (and ominous!) concept out of it. But what exactly does this imply? —J.H.
[BEGIN LOG]
Dang enters the room; Huynh paces back and forth while muttering to herself.
Dang: Good morning, dearest. What's gotten you all worked up?
Huynh: Apotheosis!
Dang: Pardon?
Huynh: All of the concepts the algorithm has yielded so far are… personal descriptors, I guess? They describe feelings, or states of self, or states of knowledge contained within the self. This latest one is apotheosis, of all things. I'm sure there's some greater insight to be yielded there at some point, but until then? The skip is practically taunting me.
Dang: From everything we know, the anomaly doesn't possess any sentience.
Huynh: It's a figure of speech, sweetheart. The point is, we've been hunting CH for, what, over three years now? If Dash Aleph is real—which I still think it isn't—it's been playing us like a damn fiddle this whole time.
Dang: Well, I suppose our search efforts have been… asymptotically convergent?
Huynh: (She laughs.) You're such a weirdo.
Extraneous physical interactions removed.
Huynh: How do you put up with all of this?
Dang: Honestly? I… guess I take comfort in it.
Huynh: Really? You take comfort in hunting this thing down until the end of time?
Dang: I see it more as… a dance, I suppose? A nice, slow waltz across the infinite planes of mathematics? At times, I'd even call it mesmerizing. Not in a memetic context, of course—if $\aleph_{\text{CH}}$ was memetic, I'm sure we would have succumbed to its effects a long time ago. In any case… I think it's beautiful in its own way. Infinitely so, even.
Huynh: No kidding. Well, at least you're enjoying the present.
Dang: Indeed I am.
Helen: As for me… well, I'll put it on the record now that we ought to flag any future attempts for more personal descriptors. If those continue, we'll need to take a closer look at what's causing them. If there's a correlation there, limiting the sets we force to those with compatible Noöspheric topologies would save us a whole lot of time.
Dang: Agreed.
The two remain silent for five seconds. The Reality Anchor hums softly.
Dang: …Suppose the anomaly is sentient, Jade. What would you make of it?
Huynh: I'd say that it really, really doesn't want us to find it. That it merked that poor professor because they knew too much about its existence. That because of this anchor, we've been safe from it—until we run out of borrowed time. That it hates my guts and boasts its superiority every chance it gets, but likes you enough to… I don't know, serenade you with a flute?
Dang silently contemplates for four seconds.
Dang: Perhaps it simply reflects what we think of ourselves.
Huynh does not reply.
[END LOG]
Further investigation yielded more evidence in support of Huynh's prediction, which narrowed the class of forcible sets to just those whose topologies are compatible with human personal descriptors. Despite this breakthrough, the next six months yielded no significant results.
Addendum 9153.06: Research Direction Reevaluation
On 07/29/2021, Researchers Dang and Huynh reevaluated their work on SCP-9153 thus far and the research direction most suited for its continued development.
[BEGIN LOG]
Huynh: How do we know [NUMSAFE-ONLY MATERIAL] didn't eat it or something?
Dang: Even if it was within the skip's power to do so, our previous attempts would have indicated if an infinite cardinal was removed from our current realm of mathematics. It also wouldn't explain the effects on local Hume levels.
Huynh: (She sighs in defeat.) You're right….
Huynh removes her head from Dang's lap and sits up to stare at the chalkboard.
Huynh: …honestly, what's the point of any of this anymore?
Dang: Hey… what's wrong?
Dang guides Huynh's head back to its starting position. Extraneous physical interactions removed.
Huynh: We're at 800 attempts by now. How many more will it take to finally solve this thing?
Dang: Are we really in such a rush?
Huynh: Do you remember how I secured myself place on Harris's team in case I ever decide to jump ship?
Dang: …I do.
Huynh: I spoke to Harris again last week. This time, I… secured you a place on her team as well. We're going to transfer over.
Dang: …What?
Huynh: If we start on Monday, Harris thinks we could have SCP-9153 reclassified as Explained by the end of the year. Imagine that, Helen! Explained! All we have to do is catch them all up to speed, and then—
Dang: So you took it upon yourself to decide all of this for me?
Huynh: Well… I knew you wouldn't listen to reason, so I just—
Dang stands up abruptly and paces around the room; Huynh rises to her feet and attempts to console her. Extraneous dialogue removed.
Dang: The current search band is merely 1% its original size. We're so close, my love. Surely you can see that? Why can't you see that?
Huynh: Are we really? From my point of view, we've just been chasing ghosts while stuffed in a classroom for three and a half years. We're all but forgotten about in here… hell, does anyone that isn't us even look at Myrmex's documentation of the skip?
Dang: You're the only one calling it a "chase", Jade. Does the present truly not matter to you? The anomaly isn't going anywhere, it's—
Huynh: You're right, the anomaly isn't going anywhere—but neither are we. All this amounts to is just giving our research a much-needed upgrade. Don't you want to solve this thing? Or would you rather stay trapped in here forever? It all has to come to an end at some point, Helen.
Expletives removed.
Dang: Adding more people or fancy gadgets to the project won't change a damn thing. We've perfected our workflow, optimized nearly every step of the process… any changes will only serve to disrupt the careful balance we've constructed for ourselves.
Huynh: Or… maybe it'll actually improve our situation and get us back on track to becoming Senior Researchers?
Expletives removed.
Huynh: Listen, if it helps, Harris also told me about her recent work on ideatic propagation. Apparently memeplexes carry a bit of "metadata" from the infosphere region they're originally from? If that's true, then where a set we force comes from might be just as relevant as how we—
Dang: So what, the moment you sniff out a new lead to hunt down, you just up and leave? What precisely makes you think losing what we have here is worth that "upgrade"?
Huynh: …Hang on. Are you talking about the anomaly or yourself?
Dang does not reply; the Reality Anchor beeps once. Huynh darts over to the RGU-𝕐 terminal.
Dang: What are you doing?
Huynh: There's absolutely no way we're doing this on ca—
[END LOG]
The recording resumed 22 minutes later.
[BEGIN LOG]
Huynh is seated in front of the terminal. Dang is facing away as she stares at the blank chalkboard.
Huynh: Okay, it's running again. Ready?
No response.
Huynh: Alright then. Well, as I was saying earlier, Harris's newest work indicates to me that perhaps we need to draw our forcing sets from specifically targeted variant set-universes right off the bat. I guess we're basically mashing them together? Nothing new, I guess, but that should further narrow our search band to… hey, is that 0.25% of its original size?
No response.
Huynh: I'll get started on this in a few minutes. Gotta keep going, eh? But uh, yeah, I think it ought to work. Any additional thoughts, um… Ms. Dang…?
Dang turns back to face Huynh. Her face is solemn and stricken with grief, and she speaks only in a low murmur.
Dang: …I think I'm ready to go home.
[END LOG]
Researchers Dang and Huynh continued their isolated work on SCP-9153 for the next eight months. In spite of the adjusted workflow's improved efficiency and narrower search band, the rate at which forcing attempts were made dwindled to 39% their previous rate, and none of them yielded any significant results.
Addendum 9153.07: On 3/29/2022, Researcher Dang performed a deeper investigation into SCP-9153-ℵ and made a key discovery regarding its true nature.
[BEGIN LOG]
Dang enters the classroom; she opens her mouth to speak, but when she sees Huynh asleep at her desk, she instead places her bag down, walks over to Huynh, and whispers softly.
Dang: Another all nighter…
Dang sighs deeply. A few seconds later, she grasps the pile of papers on Huynh's desk and thumbs through them.
Attempt #: 1,382
Forced Set: A generic set defined as being its own negation. Unlike Attempt 129, this one is specifically sourced from a set-universe where truth/false values are, as Researcher Dang puts it, anomalously "superimposed" atop each other. Something about quantum mechanics?
Forcing Axioms: An inversion of the axiom of separation that, despite the resulting logical paradox, allows sets to contain themselves and their negations. (See Attempt 129)
Results: A set-universe where Dash Aleph both exists and doesn't exist.
Associated Concept: Either "belonging" or "desperation".
Notes: Welcome to the club. —J.H.
Dang reaches out her hand to place it on Huynh's shoulder, but withdraws at the last second, opting to instead continue thumbing through the pile. After a few seconds, she thumbs to something that is obstructed from the camera's view; upon viewing it, Dang quickly wipes away tears.
Dang: Fuck, Jade… how are we supposed to fix this…?
No response. At the bottom of the pile, Dang finds a new publication from the Noöspherics Division that catches her eye.
Dang: "First Experimental Glimpse at Inbound Ideatic Propagation"… what do you mean "inbound"?
She continues reading.
Dang: "Newly discovered memetic signatures indicating ideatic diffusion from the greater ideosphere into our Noösphere during the early universe"…
Dang flips back to the page for Attempt 1,382 and compares them side by side.
Dang: Ideatic diffusion into our Noösphere… our set-universe?
The Reality Anchor beeps once. Dang rushes to the chalkboard and begins writing out her thoughts.
Dang: We've had it backwards this whole damn time. We can't start with our set-universe and force out of it to find $\aleph_{\text{CH}}$… we need to start in the infosphere and force concepts into it in order to reach the Noösphere. But that implies…
Dang draws a circle representing the infosphere and a circle within it representing the Noösphere, with an arrow labeled $\aleph_{\text{CH}}$ leading from the former into the latter.
Dang: The concepts we've been finding. "Desperation", "belonging", "convergence", "survivor"… those were inserted into our universe during its earliest days. The set of all of them has a cardinality of… $\aleph_{\text{CH}}$? Would $\aleph_{\text{CH}}$ be the method of insertion, then? A hole in mathematics between the first two aleph numbers where those concepts could make their way in?
After writing everything down, Dang takes three steps back and looks at the board.
Dang: That means the anomaly isn't a metaphysical region with abnormally low Hume concentration at all. It's… nothing. Not a cardinality, but a hole in reality cut to be shaped like one. And now, something has clawed its way out of that hole, eating at the surrounding Hume levels over time, killing all those who discover the truth of the…
Dang turns to face the Reality Anchor.
Dang: But if that's the case, then this anchor can't actually—
The Reality Anchor beeps twice.
Dang: Oh. I get it now.
The Reality Anchor folds in on itself, warping space itself as it condenses into a single point. The room shakes violently, scattering papers and desks alike with ease, and nearly hurls Dang and Huynh to the floor.
Huynh: —Hmhph?!
Huynh jolts awake, regaining her bearings and her footing in spite of the room's continuous shakes.
Huynh: Helen, what the fu—
Dang: Jade! I figured it out!
Another shake sends Huynh to the floor. She scans the room, growing increasingly frantic as she discovers that its door and windows have suddenly vanished.
Huynh: What did you do?!
Dang: I didn't do anything! All I did was look at it!
Huynh: You solved it?!
Dang: I did! The moment I realized it was there, it all went to—
The area that once held the Reality Anchor no longer exists. In spite of this, Dang suddenly turns to face it; before she can scream, an unseen force grabs her by the throat and lifts her into the air. As Dang flails around helplessly, Huynh springs into action, returning to her feet and swinging a broken desk leg at the assailant with reckless abandon. Her attacks hit only air, so she instead attempts to pull Dang away, which also proves to be futile; all the while, the grip on Dang's throat leaves dark bruising that grows and intensifies by the second.
Huynh: Dammit dammit dammit dammit—
In a flash of inspiration, Huynh grabs Dang's bag of notes and papers as it flies across the room and successfully redirects its trajectory to slam it into the assailant. Dang drops to the floor and coughs violently as she regains the ability to breathe; merely one second later, Dang and Huynh cover their ears and wince in pain despite the absence of new audio stimuli.
Huynh: Helen, are you okay?!
Dang: (She continues coughing.) Jade, you were right—
Distortions in reality ripple out from the nonexistent area where the Reality Anchor once sat, twisting space itself into warped, unrecognizable forms; another quake soon follows.
Huynh: What?
Dang: Jade, it's set-forcing. Something forced concepts into our Noösphere, and that carried $\aleph_{\text{CH}}$ into our mathematics. The moment it took shape in my mind, it… oh God…
Huynh: Shit, so this is Dash Aleph?
Dang: Dash Aleph doesn't exist. You were right all along, it shouldn't exist, it can't exist, but something injected it here anyway, or maybe it is the injection…? I… I don't know, I don't know, I'm so—
Huynh: It's a rift. A small one, but it grows bigger the more you look at it—comprehend it? A literal gap in mathematics and reality, one that lets infohazardous monsters like that squeeze their way in. Does that cover it?
Huynh gestures towards a spot on the floor that contains nothing of note. Dang reluctantly nods in agreement.
Huynh: I understand. Now, how do we stop it?
Dang: We can't. I don't… the Reality Anchor is feeding it. Who knows what that'll do?
Huynh: We can't shut it off from out here. How are we supposed to—?
Both of them are hit with a realization; Huynh's eyes widen in fear, while Dang's well up with tears.
Huynh: No. That is not an option.
Dang: It's the only way.
Huynh: Fuck you. We'll find another way.
Dang: I don't think we can. The screaming, it… it's so loud, I can barely breathe, I need—
Huynh: We need to get out of here. Surely a task force is coming to extract us?
Dang: Through what door? They won't make it in time. It's just us in here, my love. Always has been, always will be.
Huynh grits her teeth; tears stream down Dang's face. The spatial distortions intensify, causing the walls, floors, and ceilings to develop deep cracks.
Dang: If I don't go in there now, this anomaly is bound to tear the whole site apart—and you along with it.
Huynh: Who gives a shit?! And hell, how do you even know this will work?
Dang: I don't. But I have to try, don't I?
Dang stands up, grabs her bag of papers, and walks unsteadily to the threshold of the non-existent region.
Dang: It's like you said: sooner or later, everything comes to an end.
Huynh reaches out to embrace her. They kiss, briefly and poignantly, until Dang breaks away and takes another step towards the threshold.
Huynh: Helen, please. Just… stay with me.
Dang: …I wish I could, Jade. But you can't make this choice for me. Not this time.
Dang crosses the threshold and thus ceases to exist. Despite this, Huynh attempts to continue conversing with her.
Huynh: I'm so sorry…
No response.
Huynh: You… you really shouldn't. I—
No response.
Huynh: (She chuckles.) You know me. I always try my damnedest.
No response.
Huynh: Do you think I'll ever see you again?
No response.
Huynh: …I love you.
No response.
Five seconds later, the anomaly is quelled: the swirling office materials fall to the floor; the spatial distortions and quakes vanish; the region where the Reality Anchor once existed returns to reality; the doors and windows reappear. Huynh collapses to her knees, and then to the floor, falling fully unconscious just as security personnel break through the door and enter the room.
[END LOG]
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