#a little more than they were supposed to

[muttsona]

i hope i die, you broke my heart

[zondearts]

more clothing (featuring Mafuyu and Haruka)

[hypewinter]

Danny raises Superman au

So we all know that Superman touched down in Kansas and was adopted by the Kents and bla bla bla. But you know what state also has farms and is only like 600 miles away? Illinois.

So Danny is chilling in the countryside, enjoying his sweet, peaceful early retirement when an alien pod, that's a little a lot off course, suddenly crashes near his house. When he checks it out, there's a baby inside. Welp looks like he's a father now. No way is he risking the government getting their greedy little mits on this precious ray of sunshine.

Clark grows up with a father who teaches him early on how to control his powers and use them for good (They may or may not stop a robbery or two occasionally). He also gets two cool aunts. One is free spirited and always bringing him souvenirs from her travels. The other is very grounded and teaches him many techniques to deal with his conflicting emotions (his father is not happy when he uses said techniques on him).

Danny for his part is happy we his son develops a support system like he did. They can even actively help him beat up the villains! He's overjoyed at the man Clark becomes and even happier when he brings home an ace reporter who knows how shifty the government can be. He might be already saving up for their wedding but who can say?

[bandtrees]

they would get divorced in one universe just to find eachother in another one

alternatively titled: sometimes you're the level-headed token flesh-head impulse-control-and-polycule-member of a stubborn, eccentric, and hearty telephone-headed drug addict, and there's cruelty in the world you deem fit to suicidally fight, and that either goes about as well as you'd expect it to, or you learn about love and the value of your life and junk along the way

[1moreff-creator]

Okay listen, listen. Eden's Garden CH1 was great and I loved it and I'll make a more detailed analysis post about it at some point. And Eva in particular is fantastic and my favorite character. There's just- There's just a little, little issue I have with her FTEs, and if I don't talk about it I'm gonna explode. 

Spoilers for P:EG CH1 and Eva's FTEs.

CW: I am about to be a Massive Fucking Nerd on main.

This post was originally going to be about how Eva's papers, the way she describes them, sound like they kinda suck. But then I realized that the way she describes the Riemann zeta function… is just wrong???? Like, it doesn't converge to- EVA WHAT THE FUCK ARE YOU SAYING?!?!?!?!

Like, look, I don't think "Eva sucks at writing papers actually” is the conclusion I'm meant to reach after doing her FTEs. I'm also pretty sure the mistakes she makes when describing the Riemann zeta function (henceforth "zeta function” for brevity) are just mistakes on the writers’ part, which is fine because that thing is very confusing. 

And to be clear, Eva being bad at writing papers doesn't mean she's actually bad at science. I mean, she apparently solved the goddamn Riemann Hypothesis, and doesn't even think it's that big a deal!

Eva, sad [3rd FTE]: They'll put it on my gravestone: here lies the girl who could barely solve Riemann's stupid hypothesis. 

(Thank you Ani from youtube for uploading these things it makes citation so much easier <3)

Girliepop if I solved a problem that's stumped mathematicians for over a hundred years (which carries a million dollar prize btw), you bet your fucking ass I want that on my gravestone! And look, I know that this is not necessarily due to her doing more impressive stuff in mathematics. That it's more so because she's internalized what other people think about her skills, and since a lot of people erroneously believe math is uncool she doesn't think this is as big a deal as it is. But the fact that she managed to solve this thing at all, not to mention at eighteen years old, already puts her in contention for best mathematician of the damn century. And that's incredible, because math is badass. 

In short, Eva's cool and a great mathematician. But the way she talks about her other work, the papers she wishes got more recognition, makes me really doubt her actual skill as a writer of these papers. Let me explain. 

There are three papers Eva mentions writing, or thinking about writing, across her FTEs. One about literature, another about lightspeed travel, and one about the Riemann zeta function. 

Eva [1st FTE]: Earlier this year, I wrote a whole paper on an obscure subgenre of Western speculative fiction… I spent weeks on it, expecting it to receive a lot of attention from literary critics…

Eva [1st FTE]: I could write a research paper on the theoretical possibility of lightspeed travel, but no one would care, because…

Eva [4th FTE]: …I wrote a paper about how you can use tabletop gaming to understand [the Riemann zeta function].

Now, I can't say anything about the literature paper, because she gives no details on it. I also don't know enough about literature to know how long it usually takes to write papers on it, so I'll take her word for it that working for weeks on it is notable. 

For the hypothetical paper about the "theoretical possibility of lightspeed travel", I have my doubts, but she also doesn't give enough details about what that paper would entail for me to definitively say anything about it. We'll get back to this one, though.

Meanwhile, the paper she gives the most details on is the Riemann zeta function one, and… yeah that one's trash. 

There’s two reasons I say that. One is the technical issue with the description she gives, which basically boils down to “there’s severe inaccuracies in her explanation and also she just straight up gets some things wrong,” and is extremely nerdy and math heavy to explain; and the other is a much more fundamental problem with the very thesis of the paper, which doesn’t require math to explain, but I’ll leave for later. 

I’ll start with the technical side and the things she gets wrong about the zeta function. I’ll try to make this accessible for non-math nerds, but fair warning, this is pretty difficult math so I can only do so much. That includes keeping to the tabletop analogy Eva used in the spirit of the thing. 

By the way, take everything I'm about to say with a grain of salt. I'm a third year Physics major, so while I know way more math than the average person, I am by no means an expert. I am liable to get things wrong. In fact, I actually didn't know anything about the zeta function or the Riemann hypothesis before seeing these FTEs, I just researched them because I got curious about the Riemann hypothesis after seeing it show up in not one, but two fangans I've seen (it has a cameo in DR Despair Time if you're curious). However, even though I'm not an expert, I think I know enough to definitively say Eva's very wrong about a few things.

Lots of math incoming, TL;DR after the next red title

As a refresher, this is a paraphrased version of what she explains.

Eva (Paraphrased) [4th FTE]: Take 1, ½, ⅓, ¼, and so on for infinity, and pretend they are characters in a tabletop game (TTG). An enemy casts a status effect on your denominators so that they are all raised to the power of p, where the value of p is decided by dice roll. Now your characters are 1, 1/2ˆp, 1/3ˆp, etc. For your turn, you add all of your characters together, and that’s the zeta function ζ(p) = 1 + 1/2ˆp + 1/3ˆp + ... What is the value of ζ(p)?

This is good, that sum is indeed the first way to define the zeta function (more on that later), so it's correct. However, she then makes two statements. 

Statement 1: If p is higher than 1, then you get a whole number; a number without decimals. ( ζ(p) = a whole number). Statement 2: If p is lower than 1, then you get 0, “an infinite amount of zeroes.” ( ζ(p) = 0).

(You’ll notice I put that last thing in quotes. I’ll get back to it)

Now, I’m going to ignore a few minor inaccuracies which Eva likely makes to simplify the concepts, because they’re not too important. For example; you can’t “add” infinite numbers, that’s not a thing. An infinite series can converge, which is slightly different from arithmetic addition. However, the two things are close enough that, for most people, the distinction doesn’t really matter. In other words, I’m fine with her saying she’s adding infinite numbers together, and similar claims. 

There's one inaccuracy I can’t gloss over, though; Eva never tells Damon which dice is rolled to determine the value of p. In math terms, she never tells him the domain of the function (the domain of a function, btw, is the set of values for which the function is defined). Are the values p can take real or complex? Can it be any real/complex, or are there restrictions? 

For the unaware, since this is gonna come up, I’ll define a complex number using the TTG analogy. A complex number is a special character born by adding together a real number "r" (one of the numbers you’re all familiar with), and another real number "b" equipped with (math: multiplied by) the Epic Tier item known as the imaginary unit “i”. This Epic item has the property that iˆ2 = -1. So basically a complex number "z" is one where

z = r + bi

where r,b are real and i is the imaginary unit. "r" is known as the real component, and "b" is the imaginary component.

(Note: All real numbers are complex numbers where b=0, but not all complex numbers are real)

In case you’re curious, these things are used in several fields, such as the study of electrical circuits with alternating current, and they appear in relation to the Schrödinger equation- I’m getting off track.

So, what dice does Eva want the opponent to roll to define p? Well, she never says it, but we can infer. She says that p can be “higher than 1,” and that clues us in that she’s probably rolling the dice of real numbers. After all, there’s no universally agreed upon definition of what it means for a complex number to be “higher than” another complex number. Meanwhile, she doesn’t mention any restrictions on what value p can take, so it’s safe to say she’s implying that p can be any real number higher than or lower than 1, aka any real number except maybe 1. Now, the zeta function doesn’t actually have that domain, but we’ll get to that.

For now, let’s analyze her statements assuming p is any real number other than 1. Let’s take a look at the first one. 

Statement 1: If p is higher than 1, then ζ(p) is a whole number; a number without decimals. 

This is wrong. Just so we’re clear, I could probably prove, with my somewhat limited math knowledge, that this statement can only work if the domain is more restrictive than “all real numbers other than 1” as described previously. It'd have to be defined only in whole numbers, for example.

However, I don’t need to. One of the first lines in the Wikipedia page of the zeta function says that ζ(3) (which is the value you get after “adding all your characters” when p = 3) is an irrational number. That is, among other properties, a number with infinite decimals. Eva could not be more wrong if she tried. 

(Btw, yes I'm using Wikipedia as my only source. Not particularly rigorous research on my part, but this is a silly Tumblr post about funny killing game, there's a limit to my insanity)

I don’t even know how this happened, btw. It’s pretty clear this is a goof on the devs’ side (perfectly understandable btw, it took me several reads of the Wikipedia pages for both the zeta function and the Riemann hypothesis to even get them enough to write this post, and as stated I study a lot of math for my career), but I genuinely don’t know where they got the idea from. There’s nothing I could find about whole numbers in relation to the zeta function. There’s connections to prime numbers, which are all whole, but the series doesn't converge to them, the connection is a bit weirder than that. There's also some stuff Euler found about it converging to rational numbers for negative integers, but again, not whole numbers, and not even for real values above 1. So, yeah, no clue.

Anyways, what about the other statement?

Statement 2: If p is lower than 1, then you get 0, “an infinite amount of zeroes.”

This is also obviously wrong. In fact, reader! Can you think of a counterexample which is immediately obvious if you think about it for two seconds? A real number p lower than 1 such that ζ(p) isn't 0?

If you said “zero, because zero always breaks everything in very obvious ways,” you have good intuition! You could have also picked any other real number lower than 1, but those are less obvious.

For 0, the reason it’s so apparent is that any number raised to the power of zero is just 1, so 1 + 1/2ˆ0 + 1/3ˆ0 + … just turns into 1 + 1 + 1 + … and so on for infinity. Very obviously, the series diverges, it “goes to infinity.” This is very different from converging to 0.

And just so we’re clear, the series also diverges for any real value of p lower than 1, though I’ll leave proving that one as an exercise to the reader, with the help that I’ll tell you the infinite series 1 + ½ + ⅓ + ¼ + … also goes to infinity. Again, Eva could not be more wrong if she tried. 

So, what went wrong here? Turns out, the way Eva defined the zeta function as an infinite series (a "sum of infinite numbers”) only works when p is a complex number with a real component higher than 1. That’s why it was important for her to say what dice we were rolling to determine p, what the domain of the function defined by the series is. For other numbers, you need to define zeta in different ways.

And what happened to the whole “infinite zeroes” thing? Well, you see, I have a theory. I think the devs must have read that the zeta function had “an infinite amount of zeroes for values of p with a real component lower than 1” (which is true, but doesn’t mean what they think it means), and misinterpreted from there. Fair mistake. I kinda wanna correct it using the TTG analogy, but I’ll leave that for the end of the post because it’s gonna derail the entire thing.

(I got carried away and explained everything I understood about the Riemann zeta function oops)

What you need to know for now; you can do some math tricks to define the zeta function outside of the infinite series Eva described, though a lot of those tricks are way above my pay grade. That way, you can evaluate the function for any complex value of p other than 1. In other words, you can roll different die for p, but it requires redefining what you're doing with that p.

Turns out, in doing that, some funky shit happens, and any time p equals -2n for any n which is a natural number (that is, p = -2 or -4 or -6 or -8, etc.), the zeta function will go to zero. Those values of p are known as the “trivial zeroes” of the function, and are obviously infinite in number. However, note that these trivial zeroes are exclusively negative even integers; there are plenty of real values of p lower than 1 for which the zeta function is not zero, so Eva still isn’t correct at all.

Though, to be clear, there are also zeroes of the function other than the trivial ones. This is actually where the Riemann hypothesis comes in. The hypothesis is that any non-trivial zero of the zeta function has a real component of exactly ½, with the only difference between them being the imaginary component (if you didn't follow, again, more detailed explanation at the bottom of the post). This (in our world) has not been definitively proven to work for every non-trivial zero, though it does work for the first several trillion. 

Absurdly nerdy math rant over

So TL;DR, Eva made some pretty big mistakes when talking about the convergence of the zeta function, mainly stemming from not properly defining its domain, but also just straight up getting the convergence wrong. It doesn’t converge exclusively to whole numbers for real numbers above 1, and has to be defined in a different way for real values below 1, not to mention that she never brings up the full function is actually defined for complex numbers other than 1. 

Obviously, this all likely stems from the creators not actually understanding the zeta function themselves, which is pretty funny.

But you wanna know what the bigger issue is? That even if Eva had properly explained the zeta function, her paper would still suck ass. Because there’s a much bigger, more fundamental issue with the very thesis it upholds.

I want you to take a step back. Really look past the complex math and weird terms and the contrast between the very serious sounding Riemann zeta function and the somewhat silly concept of a TTG… 

And realize that the thesis of the paper Eva describes is “analogies exist.”

She can frame it however she likes, but ultimately, that’s what the point of the paper was. Eva, where the hell did you even get this published? In fact, I think it’s silly for you to say that it’d have been better received if your talent was different, because without it, I don’t see a world where this shit could even be submitted to any journal with even a modicum of self respect!

And look, she’s not wrong. I get her point, that mathematicians often don’t put in enough effort to communicate their work to the layman, and would benefit from explaining things in more creative ways. That’s cool. But that’s the kind of thing you would write for, like, an article or something.

But a paper is specifically meant for research. Calling this thing a paper almost feels insulting to mathematicians. Like the concept of using analogies to explain math is an unprecedented discovery that required actual research to figure out. Unless this paper was also the one where Eva solved the Riemann hypothesis (which God I hope that was a different paper), there's no new information being presented here. It's at best a personal opinion piece, which is not what scientific papers are for. 

Am I silly for getting hung up on the wording of this being described as a paper instead of an article or opinion piece or whatever? Well, this entire post is silly, but I don't think it's because of that, because words mean things. And a scientific paper carries certain connotations that do not align with what Eva describes.

And this little issue casts doubt in her general skill as a paper writer. That's why I'm a bit skeptical about the paper she mentions about the "theoretical possibility of lightspeed travel.” Because, quite frankly, that paper topic sounds… meaningless? Like a bunch of technobabble?

Like, what exactly are you discussing about lightspeed travel? In fact, what are you actually referring to when you say "lightspeed travel"? Matter approaching lightspeed, or reaching or even exceeding lightspeed? The latter two are impossible according to current scientific consensus, btw. Or is she discussing a particular trick to get something from point A to point B in less time than it would take for light to cover that distance? There are papers discussing stuff like that, even if all the mechanisms are also thought to be impossible by consensus. And regardless of what she means by "lightspeed travel", what does she mean "theoretical possibility” of it? Like, genuinely, I have no clue. Is she speculating on whether or not it's possible? Is she speculating on the properties such travel would have? Is she proposing a theoretical method to do it? Is she doing something else entirely? The premise of the paper is too vague, is my point. 

This worries me because… well, to put it bluntly, experts in related fields (such as mathematics) attempting to make cool sounding physics theories (such as a paper on the "theoretical possibility of lightspeed travel", whatever that means) which are completely wrong and nonsensical is a real, observable phenomenon in our world. Check out Angela Collier's "physics crackpots: a 'theory’” to find out more. And also check out the rest of her youtube channel it's great.

What Eva is doing with that paper honestly sounds remarkably close to what Angela describes there. In fact, let's check out whether or not Eva's hypothetical paper fits any of the four points Angela brings up to spot a crackpot theory.

1. “Addresses THE BIGGEST PROBLEMS in physics.”

By this, Angela means that the theory addresses a problem or topic that anyone with a passing interest in physics knows is a big deal. Things like dark matter, gravity, black holes, and yes, "lightspeed travel.” You're not going to see anyone with a crackpot theory on the equation of state of real gases or Eddy currents, because by the point you know what those things are in enough depth to be interested in them, you probably also know enough to determine what a good physics theory is and what isn't. Eva's paper fits this point, but that doesn't necessarily mean Eva is a crackpot physicist, right? 

2 and 4. “Lacking mathematical rigor, experimental data, etc.” and “They are not physics theories”

I grouped these two because it's impossible for me to know whether Eva's paper would actually fit these points or not. She doesn't give enough details for me to say. I can tell you for sure it's not gonna have experimental data, but since it's theoretical physics, that's fine. So, we can maybe give her the benefit of the doubt? As long as she doesn't fit the last point too well maybe-

3. “Respond with anger, claim physics establishment has blacklisted them, cite Galileo/Einstein/etc."

Oh no. 

Eva [1st FTE]: I could write a research paper on the theoretical possibility of lightspeed travel, but no one would care…

Oh no chat. She might actually be a crackpot physicist. 

It doesn't help that her mentality in general is actually very in line with the mentality described in the Angela video mentioned above. That because she's a smart person (which she is; again, solved the damn Riemann hypothesis), she should be able to easily become recognized and respectable in any field she takes interest in. But that isn't how the world works. There's a reason people spend years of their life studying literature, physics, or mathematics, just to truly get a grasp of each discipline individually. 

Ok, but, like, what's my point? Am I going to include her misunderstanding of the zeta function and the possibility of her being a "crackpot physicist” in any character analysis? No, of course not. You're very clearly meant to think Eva is genuinely skilled in every field she approaches, because this is a fangan and Ultimates can bend the limits of humanity to fit a narrative. I'm perfectly willing to accept that Eva solved the Riemann hypothesis, as you've seen throughout this post, even though I'd be highly skeptical of anyone making that same claim in the real world, "Ultimate” or not. The same way I'd accept that a fictional character of any kind could manage to accelerate a particle to exactly lightspeed, even though I'd immediately call bullshit if someone claimed to do it in real life. The standard for believability is different for fictional characters than real people, basically.

Really, when you boil it down, I only take issue with the things Eva says because I'm genuinely passionate about the topics she mentions, and because she gives enough details about her work for me to see the cracks in the writers’ knowledge of them. I'm assuming this is a common issue with any fangan that tries to really explain what being an "Ultimate” in a particular field entails, because no one is actually well versed enough in sixteen different talents to actually say that for sure. That's why Eva off-handedly mentioning that she solved the Riemann hypothesis is much more effective as a way to establish her skill than trying and failing to get her to actually explain the zeta function. 

All in all, this is just a purely self-indulgent post for me to vent about issues I have with the way the writers tried to convey Eva's expertise. Feel free to completely ignore this for character analysis, because I sure will. I just needed to talk about it because I would explode if I didn't. Anyways, hope you enjoyed! If you made it this far, you deserve a function named specifically after you! See y-!

Oh right I almost forgot.

My Own Explanation of the Riemann Zeta Function Using the TTG Analogy

(Explained by someone with little more than Wikipedia access, take all this with a grain of salt)

Think of finding the zeroes of a function as a boss fight. You go up to them, and you cast a spell, generally in the form of a number, such that the function becomes zero when you cast it. For example, the Easy Function

f(x) = 2x - 6

can be defeated by casting “3”, since 2x3 - 6 = 0. 

Every function also has a “domain”, which is a set of spells you can actually cast against it. For example, since 1/0 is undefined, the Medium Function g(x) = 1/x has a domain of all complex numbers except 0. Casting 0 against g has no effect. You need a special spell, “limit when x tends to infinity” (or negative infinity) to defeat it.

The zeta function is a Legendary Boss, defined by the infinite series ζ(s) = 1 + 1/2^s +1/3^s + … 

(I changed p to s for a reason trust the process)

Many mathematicians had tried to defeat it before, but it seemed futile*. Its domain was thought to be all real numbers higher than 1 (they originally didn't think to use complex numbers against it), but no matter what number was picked, that first term was too powerful. Even casting “limit when s tends to infinity” only got zeta down to 1. Nothing in its domain seemed to work.

Until Riemann arrived. 

The zeta function chuckled, thinking this one to be like all the many others before him. But the legendary mage Riemann had many a trick the zeta function hadn't seen before. Tricks to make make the domain of the function larger, so that new Number Spells could be cast against it. Where everyone else had only ever attempted to cast real numbers against this boss, he wouldn't be satisfied with that. Without warning, he cast the first of many powerful spells needed to do what needed to be done.

"Domain Expansion; Proof of Complexity"

Since you already knew this part, I'll skip the proof, but basically, Reimann quickly showed that the infinite series which defined the zeta function for real numbers higher than one actually worked for any complex number with a real component higher than one.

The zeta function was impressed, but unconcerned. It knew damn well there was still no spell in this new domain which could possibly defeat it. "Nice try, but I'm not scared of some imaginary unit” it claimed. 

“I'm aware,” claimed Reimann. He raised his hands again, his mana swelling, and the zeta function frowned. “But you're mistaken if you think this is the end.”

Reimann looked at the Legendary Boss in front of him, and cast the following, powerful incantation, with the help of the runes described below. 

"Domain Expansion; Analytic Continuation"

To truly defeat the zeta function, one must understand the concept of an analytic continuation. This is where I falter, for I myself don’t understand what the fuck that is. However, what I've been able to gather is that the function 

𝜂(s) / (1 - 2/2ˆs) where 𝜂(s) = 1/1ˆs - 1/2ˆs + 1/3ˆs - …

is equal to the zeta function in the zeta function's domain, but is also defined outside of it. In particular, it's defined for any complex number with a positive real component, except for the points where

1 - 2/2ˆs = 0

(can't be dividing by zero after all!). That last thing excludes 1, for example.

Basically, think of the spell "Domain Expansion; Analytical Continuation” as a shapeshifting spell that transforms the zeta function from the previous definition:

ζ(s) = 1 + 1/2ˆs + 1/3ˆs + … for s complex numbers with a real component higher than 1.

to now being defined as:

ζ(s) = 𝜂(s) / (1 - 2/2ˆs) for the previously described new domain.

That way, its domain is expanded to include complex numbers with a real component between 0 and 1, aside from those where 2/2ˆs = 1.

But of course, Reimann wouldn't be satisfied with that. The next spell was simpler, but worthwhile nonetheless. 

"Domain Expansion; Limiting Singularity Removal"

See, turns out, all the points "z” where the analytic continuation was undefined, other than 1, where removable singularities (I think? I don't actually know much about complex functions :v), which means the spell "limit when s tends to z” returns a finite number l. That way, you can define ζ(z) = l for all of these removable singularities, expanding the domain of the zeta function to all complex numbers with a positive real component, other than 1.

Don't worry if you don’t know what a limit is or you didn't follow this part, it's not too important for this. After all, that last spell didn't worry the zeta function. What had truly taken it aback was the analytic continuation, which suddenly exposed a few weak spots of the zeta function to the world. Now, Reimann could defeat it once and for all, as long as he found the right spell in the new domain. 

However, the zeta function was a Legendary Boss for a reason. "Fancy tricks, but it won't be easy to find something to actually defeat me, you know,” it bluffed, hoping intimidation would work. Foolish hope.

"Oh, certainly,” Reimann agreed readily, smiling. The zeta function was confused for a moment, until it realized something horrifying. 

Reimann's mana was swelling again. He wasn't done. And for the first time since it's run-in with Euler all those years back, the zeta function felt true fear.

“It won't just be easy,” Reimann smirked. “It will be trivial.”

"Domain Expansion; Functional Equation"

This is another point where the math is beyond me, but I'll try to explain. Basically, Reimann proved that that equality up there holds true as long as s is a complex number with a real component strictly higher than 0 and strictly lower than 1.

However, you'll notice that if you take s as a complex number with a real component equal to or lower than 0 (other than 0 itself), then the right side of the equation is actually well defined, because 1 - s is a complex number with a positive real component (and not equal to 1 unless s is exactly 0), meaning ζ(1 - s) is well defined. You also don't run into issues with any of the other factors of that equation, including the Gamma function (𝚪). What that means is that this equation can be used to extend the zeta function's domain to all complex numbers other than 0 and 1. 

Think of this domain expansion as a shapeshifting curse. If you cast a complex number with a real component strictly higher than 0 (other than 1), then the zeta function defends by turning into either the analytic continuation from before:

ζ(s) = 𝜂(s) / (1 - 2/2ˆs)

or the limit for any values where 1 - 2/2ˆs.

Meanwhile, if you cast a number s with a real component equal to or lower than 0 (other than 0 itself), then the zeta function shapeshifts to be:

ζ(s) = 2ˆs 𝜋ˆ(s-1) sin(s𝜋/2) 𝚪(1-s) ζ(1-s)

The final step is yet another Domain Expansion; Limiting Singularity Removal on 0, where ζ(0) = -½. Again not really important for us. 

In any case, Riemann had done it. Five consecutive domain expansions, so that the zeta function's domain now included all complex numbers except 1. The zeta function was on its last legs, all that was needed was the final touch. For the inexperienced, you might think finding a zero would still be difficult, but the truly expert mages among you might have already noticed the weak spot in the functional equation. 

The sine function. A Common Enemy which goes to 0 whenever it's attacked by a whole number equipped with the Legendary Tier item 𝜋. And when a complex number with a negative real component is cast against the zeta function, sin(s𝜋/2) becomes one of the factors.

"You know what this means, don't you, zeta?” Riemann asked. And the zeta function couldn't muster a response before the legendary mage cast his final spell. "You lose.”

"Simple Spell; Negative Even Integer"

-2, -4, -8, etc. Any even integer s causes s/2 to be a whole number, so sin(s𝜋/2) goes to zero. And since it's multiplying everything else, the entire zeta function goes to zero. These negative even integers are known as the zeta function's "trivial zeroes", and because there are infinite negative even integers, it can be said that the zeta function has an infinite amount of zeroes.

However, just because the Riemann zeta function had been defeated, doesn't mean Reimann was satisfied. See, Riemann noticed that there were other values which could defeat the zeta function, and weren't negative even integers. These are the zeta function's non-trivial zeroes. And he noticed that all of these zeroes followed a pattern, so he tried to cast a Prophecy Spell.

A Prophecy Spell (or a theorem, in real math terms) is one that makes it so that, when certain conditions are met, something happens without fail. To cast a Prophecy Spell, you must prove it, which means using other prophecy spells, runes and unbreakable laws (axioms) to certify that it's a valid prophecy. 

I'll give you an example in case you're not used to the concept of mathematical proof, and cast the Prophecy Spell “if b is a real number, then b0 = 0". To prove it, I'll use two axioms (these are the building blocks of mathematics, and don't need to be proven because they just Are).

1) 0 + c = c (0 is neutral to addition).

2) b(c + d) = bc + bd (Distributive Property)

Now, observe the following:

1) b(c + 0) = b(c + 0) [Trivially true.]

2) bc = bc + b0 [0's neutrality used on the left, distributive on the right]

3) 0 = b0 [Because bc = bc, you can nullify the terms]

I chose this because it happens to be the reason you can't divide by 0. Division is formally defined as multiplication with the reciprocal, so to divide by 0 you must first define its reciprocal 1/0. 1/0 would be defined as a number such that 0 x 1/0 = 1. But we just proved there's no real (or complex) number for which that can be true, so 1/0 isn't a number, thus is undefined.

In any case, now you know what's needed to cast a Prophecy Spell. However, Riemann couldn't finish the Prophecy spell about the non-trivial zeroes. He couldn't find proof or a counterexample to refute it. And so, his unfinished Prophecy Spell went down in history… as the Riemann Hypothesis.

“All non-trivial zeroes of the Riemann zeta function have a real component of exactly ½.”

Although it's been proven to hold true for trillions of non-trivial zeroes, it has never been properly proven or refuted, so the Riemann Hypothesis remains… unsolved. 

God that was nerdy and cringy as hell. It was also super fun to write so I don't care :D 

*Look, for the purpose of the post, I'm saying Riemann did all this shit and is the first one to find a value for which the zeta function becomes zero. This is likely not historically accurate. I'm just doing it so the explanation flows better. This should only be taken as an explanation of the function itself, and not the history behind it.

[royalarchivist]

Luzu: A child of mine died to your hands on the QSMP Quackity: [Literally told Luzu Tilin was his child a month ago] Who was your child? Luzu: Tilin!

This is a compilation of several different clips confirming that Tilin's parents are Quackity and Luzu. QsmpEN also made a post about it!

(Every time I remember Luzu never got to meet Tilin because THE ONE DAY he planned to meet her, the server was closed, I get so sad...)

[markscherz]

your blog is amazing, which is why you're getting attacked with paws

[poorly-drawn-mdzs]

Playdate in peril, the homosexual thoughts be upon ye.

[First] Prev <–-> Next

[puppppppppy]

Why are ppl scared to call it what it is and say we’re still going thru covid on top of seasonal illness. Like. That’s pretty important right. I was watching the news and they were like oh yeah we have an unprecedented number of flu cases “as well as other sicknesses” without actually saying Covid. No announcement abt vaccinations or masking or anything. Also if I hear someone joking abt “war flashbacks” for mentioning covid I fucking hate u

[statementlou]

Tbh i am not surprised that a person who openly talked about having drinking problems since 1d days, because of how crazy 1d worked has been agressive. What surprises me is people being surprised (they never seriously saw drunk person?). But i am also confused about this whole book. Apparently Maya said that that book is not fully bout Liam but compilation about her exes and some of the worst parts are not about him. But recently she said that the book is “ofc about him” so what is true then? Or did she meant it that ofc some parts are about him or that whole book is about him?

Sorry, just confused

I also am not surprised- we've learned so much more about the real stories of things and about the guys' actual lives over the last years, and the story that has unfolded around Liam has been totally consistent throughout if you've been following it, and so the information Maya is telling us is shocking and upsetting but not difficult to believe. I got an anon yesterday saying they were worried about getting similar revelations about the other boys, like "if Liam could be doing this we just don't know, any of them could", and while in a way that's always true I guess, anyone could be doing anything in private like... that doesn't really concern me. Because none of these Liam revelations are coming out of nowhere, there have been many MANY steps along the way leading us here if you've been watching, and he has talked openly about both his mental health struggles and his addiction issues. So to answer that anon... to find out something similar about Louis would in contrast contradict everything we know about him and no I'm not worried about it. Is he an abuser or a loose cannon, well that news would truly shock me to my core, I will be honest. But anyway as for the book I don't find it strange that she was nervous when it came out and treading lightly and later decided, fuck it. In the absolutely on point tiktok she dropped today (YES👏GIRL👏FUCKING TELL THEM👏) she even mentions attempts to keep her from publishing the book, presumably by Liam's team, that I am riveted by and cannot WAIT to hear more details about actually- like I said I don't find it at all strange that she was nervous and downplayed it a bit then. But if she says now that it's just about Liam, well, I would say it's been clear from the beginning that the book is their story. Maya herself brought up the parallel of songs being written about stuff and I think it's the same thing; it's true (she was in an abusive relationship that involved certain kinds of events) but maybe not 100% literal (I'm sure details were changed to make the story work, it's not like a word for word timeline of their interactions or whatever).

[mariyekos]

I like to imagine Dante's able to use some basic magic beyond just typical demonic stuff. In the opening of DMC1, a magic circle appears below Trish when Dante shoots the motorcycle back at her, so I like to think Dante knows some basic spells, wards, and the like. For the most part he uses it for little things like making a special lock for his Devil Arm vault, maybe heating up soup or a drink that's gone cold, and so on, rather than any combat things. Dante's spells are not at all refined and he doesn't have a natural talent for it, per se, but he has a lot of power he can put into things so he often ends up brute forcing whatever it is. It's not necessarily efficient, but it works, and that's all he cares about. He's not really interested in most precise or specific things.

Vergil on the other hand has a lot more control and a much greater interest in magic in general. A post DMC5 Vergil (and pre DMC3) would use magic a lot more often, and without as much prep. He spent a lot of time learning different charms etc. to use in daily life, and he's a lot more elegant about it. Some he learned when on the run and trying to hide from demons, while others he learned when trying to track down Sparda, and others still he learned for purely convenience reasons. Post DMC5 he gets a lot more into it than he did pre DMC3 when it was more a thing of survival, even if it had the convenience aspect back then too. He's the kind of person who would learn spells for the sake of knowing them, and while he prefers using demonic abilities in combat, he might try to learn a magical combat spell or two just to see what it's like. He mostly sticks to practical things though (which sit on the border of practicality, but he considers them practical, uses them often, and makes Dante's magic look like child's play).

On the magical third (regrown!) hand, Nero's absolutely horrible at magic, to the point of not being able to do basically anything. He's got the magical reserves, but unlike Vergil who can cast precise spells with relatively little effort, or Dante who gets through spells by basically overloading them until they work, Nero just can't get magic to work for him at all. Lessons with Vergil end with him stomping out when he gets fed up with Vergil commenting on how easy it should be, while attempts to get Dante to explain how he casts magic end in frustration when Dante's explanations basically start and end at "I dunno, it, it just works." Sure Nero can memorize and draw a warding sigil perfectly, but any and all attempts to get it to actually do anything end in failure.

Kyrie, in a reveal that surprises everyone, most of all herself, is apparently extremely talented at magic, which she does not know until she sees Nero trying and failing to activate a warding sigil Vergil taught him, puts a finger on it so she can trace over it as she reviews Nero's work in case he messed something up, and inadvertently activates it. After that they end up doing some testing and discover Kyrie is a natural when it comes to magic. The only problem is that while casting spells, activating sigils, and the like come easily to her, her magical reserves are rather small, limiting what she's able to do. When she first activates the sigil Nero had drawn, she ends up unable to get up and Nero has to carry her to bed (which she insists he doesn't have to do, because she just needs a minute to catch her breath, but he insists on)

Nico is stoked to hear about this and ends up figuring out a way to essentially fit Kyrie and Nero with a magic converter that allows Kyrie to draw on the magical reserves Nero can't utilize so that she can use them for whatever she wants to. While Kyrie isn't someone who really cares to use magic for things in her daily life like Dante and Vergil, she does use it to make little charms for the kids, and to establish wards around the house to protect them from demon attacks and other small misfortunes. She and Vergil end up bonding a little bit as he teaches her the spells and other bits of magic Nero was never able to pick up on.

(Vergil himself feels a mixture of pride at how quickly she picks up on things with his instruction, and jealousy when he sees how good she is at things first or second try when he knows it took him a good five or ten attempts to get it down when he was first learning. Kyrie notices and tells him that he's still much better than her in the long run since he's able to use magic without needing a separate "battery" to power him, but Nero absolutely digs into Vergil about it when Kyrie isn't there. Dante meanwhile finds it all hilarious. But he and Nero are pretty proud of Kyrie too.)

[sideblogdotjpeg]

also also also. i dont know if this is ever gonna get really explicitly explored in the show. but.

like. theyve talked pretty minimally i think? about jovyres motivations as an antagonist. and while the main explanation they have gg on right now is the general "power corrupts universally" i also think. with how prominent this theme of sibling conflict has been ....

jovyre is cirillas younger sister. because of this, while cirilla gets to be the queen of the summer court, jovyre is relegated to being the princess of the "lesser" autumn court. an arbitrarily lower status. she had to use magic & trickery in lieu of cirillas' power and armies. her sister got to be a fairytale princess while she was the pragmatic ruler, with a chip on her shoulder. she has to get her hands dirty, "not all of us can be perfect can we". in spite of this, she was the one who stayed in command while her sister had fallen into her own despair. she negotiated her way into the unseelie crown. why should she have to be the one bending the knee to her sister. "i dont believe any of us should be limited by how we were born.... i only want to be her equal".

so its like. even though we havent met her yet. jovyres rise to power was explicitly via the death of the previous unseelie queen. of course she would be paranoid and defensive of her title. and while jovyre is plotting and planning and carefully amassing the army that she had to build herself to defend the crown she had to earn herself. her sister is in the columns of milfred murmurs and partying, all with the crown that she would have lost if not for her. "well some of us value beauty more than others". jovyres second offer to the band of boobs, "the more pragmatic approach", was to kill queen cirilla and bind her followers to someone else (someone more worthy, someone more fit to rule). at the time, jovyre admits that she would rather not take that option, "i dont wish for any harm to come to her". in the intervening 200 years. how many times did she wonder if she had made the right decision then. shes certainly changed her mind now

(and a minor thing ... because i admittedly might have misremembered. while talking to the band of boobs, she tells them that she wants to unite the seelie & unseelie courts. wouldnt it be nice for unseelie to get to experience spring and summer too? if im not wrong ...... the unseelie courts still only experience dusk and night? i might have totally misremembred this BUT if its true . then queen cirilla was also not as easy to negotiate with as jovyre expected)

anyway! all that to say is. given how this campaign has explored sibling relationships that are based around feelings of inadequacy & insecurity against a perfect older sibling. the way that leads to competition and jealousy, the desperate urge to prove that actually i AM better than my sister and im soo going to rub this into her face! well! maybe the story of jovyre and cirilla is not just entirely "power corrupts" and more also about the. "200 years of growing resentment and jealousy that has clouded all my love and protectiveness towards you into hatred, and envy, and havoc". on parallel planes, callie and cyra forgive each other, while jovyre plots her own sisters assassination.

[paskuda-lynx]

Misunderstandings

Fanart for the fic Desideratum (posted on AO3) by @fianightshade ! Specifically for the chapter 11 'Turning point'. I periodically reread it just to feel the emotional turmoil of the scene again

[spotaus]

New Age AU (Obtaining Killer)

Hey guys! Through with a bot of stuff for the day and I have a sneaking suspicion that this stress headache will not leave me until I finish some projects for work, so I *may* be m.i.a. for a hot second until they stop.

In the meantime, I want to drop this! (Unedited, unrefined, raw off the slab style)

Andddd @ancha-aus and @papiliovolens ! Hello! (Mutzelputz if u see this, the tags weren't working for some reason, I apologize.)

Hope y'all enjoy!

Ccino had convinced him to leave the castle. After nearly a year had passed since his last true public appearance. Since he'd stolen the apple from his brother. Nine months had passed since he'd sent Dream away. He tried not to think about it.

Nightmare had been finding out a lot about his magic. How it made him jittery, and how he felt like he understood so much more. How it made him deeply paranoid, quick to react.

How it made people listen to him.

He figured it was because he was scary now. The negative magic condensed over every inch of his bone wasn't exactly appealing, and the extra limbs which had sprouted from his spine now acted like his own personal weapons. If someone didn't listen, didn't give him an answer he liked, the limbs moved without him even thinking.

It had taken time to learn to better control them. Even now, they writhed in his wake. His nerves expressed through their lashing and twitching as they hovered just above the ground.

The streets weren't exactly crowded.

Upon word of the King's arrival to this small providence, Nightmare had found that many people fled from his path. His travel party of several soldiers, and himself on horseback. He'd always wanted to ride horses. The traitor twin was someone that every citizen wished to avoid.

Ccino had coaxed him outside with promises of fresh air. Apparently there were promising young members of the city guard that Ccino swore would be wonderful future knights. Young warriors for him to bring up loyally under his name, no fear of betrayal.

It had made sense, at the time, but Nightmare hadn't chosen to recruit any of them.

It wasn't to say he didn't want to. Several of the humans and monsters were very talented, and he did his best to give them praise, but he could tell. None of them wanted to work under him. They didn't like him. Rejection and hatred that had pierced him immediately, he could practically taste it.

Ultimately, they would do better here in their hometown. A place they were passionate about protecting, and with people they cared for. Night would not try to mold promising soldiers into his perfect guard. No matter how smart of an idea it may have been.

And so he'd moved on.

Night had visited several smaller shops, onces which couldn't afford to refuse him, and he bought some fabrics, a trinket, some small thing from each place he stopped by. He payed exactly the price he needed for each thing. He wouldn't bribe his people, either. The best he could do would be to remain neutral.

He did discover, against all odds, that he was enjoying this day out. Ccino was, in fact, usually correct about this sort of thing.

The travel had been enriching. Almost exciting. He'd never gotten out of the castle much at all, this was all new and excitingly mundane.

Good things do not last forever.

It was almost sunset when he noticed it. Torches being set up, a platform prepared. A crowd gathering.

An execution, came the mutter from one of his soldiers. Though he recognized the set-up, Night had never been in attendance to an execution. He was morbidly curious. The crowd held such a contempt. A broiling hunger for blood.

He wished he'd wheeled his horse away when a few people were ushered out of a nearby building.

The prison, maybe?

There weren't many of them. Nightmare dismounted his steed, and much to the dismay of the soldiers at his side, he found himself sinking. Into the growing shadows cast by the dying sun.

He re-emerged beside the stage, where the few people were lined up. Ready for death by hanging.

That trick wasn't one that Nightmare quite understood yet, but he was always drawn to feelings of intense negativity. He knew that, now. Something about these prisoners were bothering him, even at a distance, and he found himself more curious as he stood before them.

His guards, at the back of the crowd, hadn't seemed to figure out where he had gone. He had the time, now, to loom over the small group of prisoners.

The city guards, the trained ones, had likely seen him earlier at their headquarters. They did not speak even a word against him as he stared.

Nightmare stared at these faces.

A dog monster, scrappy and scarred, black fur clashing against a few patches of white. One of her ears was missing.

A pair of humans, both men, one with long, curly red hair and another with short-cropped red hair and the beginnings of a beard. Maybe they were brothers?

A skeleton. His sockets dripped with black magic, and his soul was a piercing crimson, just infront of his chest.

A flame monster, small and stout. Their flames a flickering green and purple. One of their eyes had a patch over it.

Nightmare was not great at determining emotions yet. He was hardly versed in his own feelings, but there had been improvement recently. Understanding new emotions had been coming more naturally to him.

Sometimes it hurt, but he was learning.

Now, past the blossoms of a headache, he felt a bit baffled as he subconsciously picked through the negativity these monsters exuded. Their fear. Their pain. Their loss, and their anger.

Oh.

"Only one of you is guilty."

He'd said it without thinking, practically announcing it with a voice that still felt unnaturally deep. A voice which rattled his ribcage and seemed to force past the barrier of darkness around him.

The group before him seemed startled. Confused.

Well, all but the skeleton, who seemed to only raise his skull slightly. As though just noticing Nightmare was there.

"How could you have possibly been jailed in the first place?" He muttered a bit quieter to himself.

He knew, deep down, that there were many, many rules in place for situations like this. Laws which he could challenge. People he could speak to. He could appoint members of his court to each of these people and try to earn their innocence through the rites of the law.

Then again, he remembered the rage of the crowd. The frustration of the people waiting to see these killings take place.

He didn't know what to do.

Now the prisoners, especially the two humans, were staring at him hopefully. He'd managed to shatter the negativity a bit. He believed them. He knew this was wrong.

"I don't know..."

The mutter came again unprompted.

These people would not have the means to repay him for his help. He couldn't just waive fees, or risk his court turning against him. He couldn't afford enemies being made so close to his inner circle.

He couldn't just leave them, though. Not after he'd seen the injustice of it all.

Stuck in his own thoughts, he was drawn out of it by a snickering laugh.

"Just set them free." A voice followed, "You are our King, aren't you?"

Nightmare then found his eyes drawn to the skeleton.

The others had eased themselves away from him. He stood, now, almost alone. He seemed unbothered by speaking up, his sockets held in an almost lazy posture. Tension going completely un-held.

He grinned up as the King, and seemed to watch contentedly as the thought settled in Nightmare's skull.

He could do that. Simply waive their charges. Pardon them. He could do that, surely. Many royals had done it before him for less certain terms. His mother had plenty of times.

"And you are guilty. You'll still be hanged. You know this, don't you?" Nightmare asked.

That was when the Skeleton's lazy sockets seemed to tighten with a sort of glee. Some hidden joke Nightmare wasn't privy to.

"Hmm." This was a poor choice. This was a bad decision. "Tell me, quickly, how you came to be here. Before I proceed?"

Nightmare didn't know why he was asking. He was... curious. Just like he had always been.

Very few people would ever speak straight to his face. Ccino, that was the only one who'd done it since his change. Since the prophecy. This skeleton had done it. He'd spoken when no one else could muster even a plea.

The silence he seemed to bring to every room. Broken, just briefly.

The skeleton stared at him a moment.

"Name's Killer, your majesty." The tone was mocking. "A while back a buddy of mine got into hot water, and I decided to help them out. Now, plenty of bodies later, I'm the one stuck on death row."

Simple. An admission of guilt.

Nightmare stared at him some more.

Finally, it seemed his frantic guards had noticed him. Found him. They rushed to his side, though not as fast as he would've liked. He could feel the frustration seeping from each armored body around him.

"You don't have an aversion to it," Nightmare voiced, "Killing, I mean."

Killer nodded. Unashamed.

It felt strangely calm, still. Perhaps it was because the crowd was still chattering. They likely hadn't noticed Nightmare at all.

The king turned to the city guard, still stood on the steps. "Free these four people. My judgement decrees them as not-guilty."

And, before any time could pass in the slightest. "Killer, I would like you to accompany me, before you abscond."

He'd noticed it. Killer had undone his cuffs before their conversation. Completely freeing himself from his weak imprisonment.

Killer seemed amused at the concept of sticking around to chat.

"If you would, I would like to recruit your services at my castle. I need a man who is willing to kill. And kill swiftly." Ccino said to establish an image. It was obvious now that his reputation would remain in the gutter, no matter what choices he made. He was not Dream.

Killer's sockets narrowed.

"And what would I get for being your little hunting dog?" Again, it was bold. It was new.

Nightmare was sure his expression hadn't changed since he'd come before the group. That same angry glare that sat permanently along his skull. The magic had an image to project.

His tendrils flicked, slightly.

"Payment, room, Fresh meals, and any other amenities you may like, so long as it does not break our treasury." He replied, "All I ask is that you simply obey me. And Me alone."

Not true. He'd probably ask for him to listen to Ccino as well. Once he knew for certain he'd stay.

Killer seemed to be thinking. He eyed they king, up and down. He looked to each of the guard around the king. The ones who were back in position now, though Nightmare could feel their annoyance. Their confusion.

Then Killer turned.

Then he turned back.

"Mm. Can't be worse than the ol' noose." Killer replied. "Funny way to run a country, my king. Hiring the first murderer you spot?"

Nightmare didn't humor that with a response. He was honestly shocked the skeleton had even agreed.

Though, all of that negativity had been swapped out for a glee. Something deep in Killer had changed during their brief interaction. A hope. Night could barely grasp the edges of its existence with his subconscious. But it was there.

.

He ignored the crowds as they grew confused. He ignored the worry pouring from the criminals as he had them released and informed them of their pardon.

He did not ignore when his guards told someone to keep their distance. He glanced up. Killer was standing beyond the guards, looking bored.

Nightmare, trusting fool he was, didn't even ask a guard to watch him to ensure he stayed put.

"Stand down." He ordered the guard, who begrudgingly allowed the skeleton to smugly slip past.

His tendrils kept the monster at a distance Night preferred all on their own. He seemed to take the hint.

"They're all gonna be dead by morning, you know." Killer voiced easily.

Nightmare turned to him, confused. What did he mean by that? He'd pardoned them?

"Are you deaf? The crowd wanted us dead, especially me." He chuckled, "Leaving them here is definitely going to get them killed. If the crowd doesn't rip them apart the second you leave, then it'll happen at night. There will be no witnesses."

Oh... Night hadn't fathomed that these people could turn on the innocent once declared. It hadn't even crossed his mind. Did they have a home to return to? A family they put at risk?

The noose was a fast death, but being murdered? That would've been so much worse.

He could tell, by the way they evaded looking at Killer, that he was right. Nightmare would be sentencing them to a new sort of death if he did it like this.

But he didn't have time for a trial. Or several. The sun was going down, abd Ccino expected him back. The castle needed him present, or they might revolt.

Someone might hurt Ccino.

Oh, he was such a poor ruler. He did not know his people well enough. How he lamented the lessons Dream had taken about crowds and current issues abd how to be likeable.

Night didn't know how to handle this. He was still learning!

A trembled in his hand. He tucked the limb quickly away from where it had been lightly clutching his tunics thick fabric, now hiding it beneath his cloak.

"Killer is right. It won't be safe here, for any of you." He spoke. Thank the gods it didn't sound as shaken as he felt. "I extend an offer to you all. You may stay here, or you may come take up positions among my staff back at the castle. Unlike Killer, I do not expect any crime from you, but you will be paid and housed."

The offer was met with a roar of frustration from the crowd, Nightmare chose to allow his guards to handle it. He watched, carefully, as the four looked between eachother.

The brothers agreed first. (They introduced themselves as brothers as they knelt in thanks.) Then the Dog. She said she had no family left to watch over, starting a new life would be for the best.

The flame refused, saying they would leave town by morning, and try to stay safe.

And so, Nightmare left the town with four new party members. Each had been provided a horse, each tied to one of the guards. Aside from Killer, whose steed was held personally by Nightmare.

He figured Ccino would chew him out for this, for bringing criminals into the castle when he was sent to collect soldiers, but Nightmare had a good feeling about these ones.

They did not hate him. Or fear him. He was helping them. And it felt good.

[ask-lu-wild]

[xxplastic-cubexx]

do u think either charles or erik had trouble coming to terms with their love for one another?? like religious guilt, internalized homophobia, etc.

Many such cases really … not hard to imagine them dealin with that …