“A prosthetic hand. Half a hand! Two fingers and a piece of palm—”

“Heather.”

“The bones don’t even have to articulate, not at first. I can start with an experiment — a prototype! That’s what they’re called, yes. Once—”

“Heather, stop.”

“—I’ve figured out how to detach it from our own flesh and make it comfortable for you—”

“Heather.”

“I … I really want to help. Evee, I want to do something for you.”

“I know. But—”

“And I think it’ll work. If I can make a piece of self-sustaining pneuma-somatic flesh, then there’s no reason I couldn’t make it more complex, fill it with nerves, muscles, make something you could move with your own—”

“Stop!”

“E-Evee?”

“Heather, you already help me, more than you could understand. But this is not helping.”

“But it might work!”

“Heather. Please. Stop.”

“I’m … I’m sorry. I apologise.”

“Heather, for fuck’s sake, don’t be such a martyr. I’m not completely rejecting the offer, but that’s a lot to think about. A hell of a lot! You want to attach part of your body to mine? That is something I have to consider, carefully, at length. Not something to rush at the end of an already busy day, when we’re facing down a complex and dangerous task. Slow down. Give me some time to think. Bloody hell.”

“Yeeeeeah, Heather. Let a girl prepare her heart before you go talking about injecting her with your meat, hey?”

“R-Raine!”

“Shut up, Raine. I will hit you with my walking stick. I will.”

“Just sayin’.”

“Then, Evee, can I at least begin figuring it out, or—”

“I forbid it.”

“You … pardon?”

“We are about to make preparations to have you teleport an entire house — a house which belongs to an exceptionally powerful and dangerous mage. No. Jan was right. I won’t have your skills and intellect distracted by a personal project to make me a rubber hand. Stop thinking about it. Right now.”

“But, Evee—”

“I insist.”

“ … okay. Okay. I’ll … I’ll stop.”

“Good. Concentrate on what’s in front of us.”

“And we’ll return to this later?”

“Mm.”

==

“I think it’s a proof for the twin prime conjecture,” said Badger. “Of course, I can’t be sure, yeah? Because it’s not written like a standard mathematical proof, it’s written using a building. Which is, uh, a little unorthodox.”

Badger — Nathan Sterling Hobbes, ex-cultist, once-brilliant mathematician, one-time mental prisoner of the Great Eye of Wonderland, my first-and-hopefully-only trepanation victim, and most likely a budding disciple of Squid Angel Heather Morell (that’s me, for those who haven’t been paying attention) — looked up from our kitchen table, lifting his eyes from the photograph of Edward Lilburne’s house meet to a ring of puzzled faces peering back down at him.

He wet his lips and cleared his throat, radiating awkward self-consciousness. “At least, um, that’s what I … see … here.”

Raine nodded along as if this made perfect sense, arms folded, eyebrows raised in appreciation. “Twin prime conjecture,” she echoed. “That’s a number theory thing, right?”

Nathan lit up with the sudden enthusiasm of recognition. He nodded — slowly, carefully, cautious of moving his head too fast. “Yes, that’s correct.”

On the far side of the table, sitting with her cast-wrapped leg sticking out, Nicole Webb sighed. “Please don’t tell me we’re gonna need a maths crash-course to understand all this. ‘Cos if yes, I’m out.”

“Naaaaah,” went Twil. “Number theory is easy. Promise. Serious.”

From the corner of the kitchen, squatting on the floor amid what was now a trio of dogs, Tenny suddenly trilled: “Easy, easy! Numbers easy!”

Evelyn just grunted, dead-eyed and aggressive: “Explain.”

Nathan flinched a little, though his mouth was still curled in his newly habitual easy smile. His eyes searched for me, for support or approval — I wasn’t sure how to feel about that. I was standing stiffly a few paces away, tentacles wrapped in a tight ball around my torso, a self-hug against shame and embarrassment. We were completely unable to concentrate on what we were meant to be doing right then. All seven of us were still bent toward thoughts of Evelyn, mortified by the way the conversation upstairs had ended, wishing we could have more time in private.

At least she was standing next to me again, close enough to touch.

Jan spoke up before Badger could embarrass us both by asking for my permission — or worse, for my blessing.

“Twin prime conjecture,” Jan said delicately. She’d been using her good-girl pitch, her smartly-dressed sixth-former voice, since the moment Badger had limped through the front door. “Nathan, if you could start by explaining what exactly that means, it would go a long way to helping us understand what you’ve discovered.”

Badger glanced at Jan instead of me — but then returned to me again, his eyes reaching out with that silent smile.

We sighed softly, then said, “Go ahead, Nathan. Maybe start at the beginning?”

Badger nodded, happy to be questioned; he turned back to the photo on the table, to the picture of the front of Edward Lilburne’s house. He gestured with both hands as he spoke, which made it impossible not to notice the faint tremor in his right arm.

It was always there, shaking and twitching, a constant flaw in his misfiring nerves.

“Twin prime conjecture,” he resumed, quickly warming to his subject. “Raine was right, yeah. It’s an open question in number theory, something that hasn’t been proved, though there’s been some attempts. A twin prime is a pair of prime numbers separated by a non-prime number. So, three and five are primes, separated by the number four. Five and seven, with six in the middle. Eleven and thirteen, and so on and so on. That’s how twin primes work.” He blinked three times, far too hard, fighting against something inside his own nervous system. Nobody hurried him. “Are you all following this so far?”

Badger’s voice was stronger than when I’d last seen him, full of the energy of a healing body and improving mind, but also laced with all the self-doubt of a prodigious intellect who did not believe in himself. I’d not seen him like this before; he was barely recognisable as the lumpy, greasy, bitterly aggressive ex-cultist.

As he spoke, I silently willed him more confidence. He deserved it, after all; he’d figured this out where we’d all been blind.

The others probably just thought I was squinting at him.

Nathan looked undeniably healthier, too; we hadn’t clapped eyes on the man since the aftermath of his cranial operation, when we’d all crowded into his tiny flat to interrogate him about the identity of the corpse I’d discovered out in the Shambleswamp, which turned out to be the body of another ex-cultist who Badger was able to positively identify. Back then Nathan had been like a walking corpse, a terminal cancer patient held together by nothing but the spark of life released at the moment of cell-death. He’d seemed so fragile, so pitiful, so desperate for purpose and meaning, but also infused with all the potential of a new start in life.

His hair had grown back in, no longer thin stubble across his scalp, but a thick dark thatch, stuck up all haphazard and wild. It didn’t quite hide the massive angry-red surgical scar across half his skull, but he seemed completely at ease with that. I couldn’t be certain, but I had the distinct impression his hair had not been such a dark shade prior to the operation — or rather, prior to me repairing and rewriting his soul. Nobody else mentioned that though, so perhaps we were just imagining things. He’d also allowed his beard to grow — nothing more than a scraggly covering of whiskers, but it suited him, the shape of his face, his strangely easy and mobile smile, and his naturally puppy-dog eyes.

He dressed the part of the genius mathematician too, though that was probably an accident; as a cultist, either when working for Alexander or desperately trying to survive in the aftermath, Badger had seemed to me like a low-level drug dealer, all baggy jeans and over-large jackets, constantly greasy and dirty and uncomfortable. Now he was dressed in an old black sweater, something that had obviously been in storage for a while, clinging to his newly lean frame. He blinked from behind thick glass to help with his post-surgery vision issues.

He was walking unaided now, despite the regular tremors and the persistent difficulty with muscle control. He’d purchased himself a walking stick: a practical piece of lightweight metal with a plastic handle, none of the romance of warm wood for our Nathan. He’d arrived at the front door ahead of his escort, stick in one hand and Whistle’s leash in the other, his eyes bright and alive with strange discovery.

Part of us — me, myself, and my tentacles — felt an intense rush of pride at seeing Badger like this.

We hadn’t mentioned it as he’d limped and hobbled over the threshold of the front door, as Whistle — his Corgi — had warily greeted Soup and Bernard, the other two dogs briefly in residence. We had returned his cheery, smiling greeting as best we could. We hadn’t felt too uncomfortable at the barely concealed quasi-religious devotion in the way he looked at us. We were an angel now, after all, sort of. Maybe.

All we’d said was: “You’re looking well, Nathan. That’s good to see.”

And he had beamed like the sun had blessed him with warmth after a year trapped underground.

But that was the truth. It was good to see. We had saved this man — from death, from soul-destruction, from a cult, from his own slide into depression and lack of purpose. That fact had been harder to see when he’d been quivering and shaking in the aftermath of the operation on his skull, enraptured by the sight of me and by his own new-found clean slate. But to see him up and walking, getting stronger, doing things with his mind, smiling that odd, dazed, totally relaxed smile?

All that work had been worth the effort. Lozzie and Sevens and I had gone the extra mile to pull him out of the Eye’s grip. We had saved a human being who deserved a second chance.

Even if he hadn’t returned to help us with this problem, it all would have been worth doing.

Strangely, he’d taken the sight of my flesh-born tentacles entirely in his stride. He’d seen them once before, when we’d allowed him to briefly look through one of our pairs of modified pneuma-somatic seeing glasses; but seeing them with one’s own naked eyes and knowing that they were undeniably real was a very different experience. He’d simply paused, looked me over, and nodded with that same beatific smile of deep acceptance.

“You look well too, Heather. I can see. I can see.”

We hadn’t asked him what he’d meant by that; probably better to not encourage that line of thought.

The others had decamped from the magical workshop to the kitchen, apparently in silent agreement that it was better for Badger not to go in there. After all, that was the spot where he’d almost died and I’d had to rummage around inside his skull to save him. He probably didn’t want to be reminded. Praem had even shut the door after us.

Whistle, Badger’s sweet little Corgi, was in the corner of the kitchen, getting acquainted with Soup and Bernard. Tenny was overjoyed to have three entire dogs all to herself, and mostly lost interest in the conversation.

Nobody commented on the results — or lack thereof — from my time upstairs alone with Evelyn. Raine had already said her bit, mostly teasing. Twil watched Evee with a curiously neutral look. Ah, we thought, we were going to need to talk with Twil again, before this was all over.

Badger had accepted a cup of tea, but barely touched it, too fascinated by the discoveries he had to unfold. Outdoors, the summer night pressed down with a black weight upon the house.

“Yes, get on with it,” Evelyn grunted.

Raine agreed. “We follow, Nate, yeah. Go ahead.”

“Think I’ve heard of twin primes before,” Felicity muttered under her breath. “Maybe. Back in uni or something. Too long ago now.”

Badger nodded along, trying to include everyone in his side-to-side glance. There was more than a touch of the eager teacher about him. He even acknowledged the faces he didn’t know — Amanda Hopton, Felicity — and the terrifying faces — like Zheng, who watched him as one might watch a condemned animal. Back by the door to the front room, Kimberly fidgeted with the hem of her t-shirt. She was the one person who genuinely didn’t want to see Nathan, an unwelcome reminder of her time in the Sharrowford Cult. We’d asked if she would prefer to leave during this, to retreat upstairs and get some much deserved rest after her day at work, but Kim preferred to stay close to Felicity’s side. Badger had acknowledged her with a polite nod, but not addressed her directly; that was good. Hopefully he recalled my explanation that Kimberly was happier not knowing him, despite their shared experiences.

Sevens and Aym, to my wordless surprise, had folded themselves away somewhere. Perhaps Sevens was restraining her friend from emotionally assaulting our guest. Badger was probably vulnerable to Aym’s techniques, after all.

“So, the twin prime conjecture,” he carried on, making little gestures of explanation with his hands. His right hand still shook, the tremors reaching all the way up his right arm and into his shoulder and neck. Whenever that happened, he would pause and clench his fist very hard, fighting down the results of my work on his brain. “Twin primes get rarer as numbers get larger. Prime numbers get rarer anyway, so it stands to reason that as the range increases, the lower the chances of discovering another pair of twin primes.” He held up a finger, pausing and swallowing three times in quick succession. The intense focus on the mathematics seemed to be helping him, but also driving his nervous system to further extremes. “But, but, but—”

“Nate, hey,” Raine said gently, in a much softer tone than I’d heard her use for Badger before. “Slow down, take a sec, yeah? Take a sip of your tea, buddy. Breathe. Nobody’s going anywhere, we’re all really interested.”

Evelyn rolled her eyes and Twil pulled a grimace; Zheng grumbled, Nicole sighed. I almost tutted at this lack of patience. Only July didn’t react at all, standing wordlessly behind Jan and staring down at Badger as if he was a piece of wood.

Badger halted, nodding at Raine’s suggestion. “Yes, yes, of course, okay, yes.”

“Badger. Sip your tea,” Raine repeated with a laugh. “Come on mate, chill out.”

“Sip sip,” said Praem. “Sippy.”

“Quite,” Jan agreed. “Better to take your time and be clear than rush and risk confusion.”

Nathan took a long swig from his rapidly cooling mug of tea. Then his right hand and arm shook with one of those barely contained tremors again. He clenched his fist, his biceps, then his shoulder, all in sequence. It was as if he was holding on too tightly to some invisible handhold, anchoring himself in control of his own body. The tremors were different to how I recalled — more regular, more localised, but thankfully more easily controlled. We all waited politely. Lozzie peered over Jan’s shoulder. Badger smiled at her before he carried on.

“But,” he said. “Though twin primes are rare, they do keep occurring, even as the range of numbers gets extremely large. The question — the ‘conjecture’ — is whether or not they are infinite. Are there an infinite number of twin primes?” He paused, hands wide, then caught himself. “Um, there’s been a few efforts to prove this, by people working in number theory, but nothing conclusive.”

“Alright,” Evelyn said, in the tone of a woman who had been holding her tongue for far too long. She practically bristled with impatience and irritation, but Badger appeared to be immune to that, turning his eyes to her with that bright, fascinated smile still plastered across his face. “Alright,” she repeated. “What does this have to do with the house?”

Badger pointed at the photograph of Edward’s house, lying in front of him on the table. Black beams crisscrossed inside red brickwork, punctuated by tiny metal-latticed windows. The trees behind the house were frozen in a moment of wind rustling their leaves.

“The beams,” he said. “I think they’re a mathematical proof, for the twin prime conjecture.”

Evelyn frowned at him, then down at the photograph, her brow pinched hard with concentrated scepticism. Felicity stepped closer to get a better look as well, though she also looked unconvinced. Kimberly did not follow, hands clutched to her own chest like something was horribly wrong; we noticed that — Top Right noticed that, bobbing gently toward Kimberly. What had she sensed?

Jan tilted her head sideways, lips pursed. The mages did not see it. Neither did I; we bobbed two tentacles over the top of the picture, going up on tiptoes for a good look. If the sigil on the house was written in mathematical perfection, it was regular maths, normal maths, nothing to do with the self-implementing hyperdimensional variety. I had no idea what I was looking at.

Raine sucked her teeth. Twil pulled a face. Zheng looked supremely uninterested. Amanda Hopton was miles away, her mind busy with her god’s perception.

But Nicole Webb, of all people, leaned forward across the table and tapped the picture. “I don’t see it, sorry there fella. Are they numbers? Like, hidden numbers? Is that what you mean?”

“Yes!” Badger lit up again with sheer delight. He was loving this; he wanted us to know — needed us to understand. He gestured for some space around the picture, then traced one of the beams with a fingertip. “See this big beam here? Take this as representing all the numbers between one and ten. And the smaller beams that intersect with it, here, here, and here.” Tap-tap-tap. “Those are the three prime numbers below ten — three, five, and seven. Then, imagine the beam stands in for the next set of ten numbers as well, but reverse the order of connection with the smaller beams. And!” A finger shot into the air; Badger was practically vibrating. “You have to account for the angles at which the beams connect with each other. I’ve studied the picture over and over and there are always four different angles of connection.”

“This isn’t making any sense,” Evelyn grunted. “Dumb this down.”

“Yeah mate,” said Twil. “Sorry, but like, none of us here are that good at maths. Not real maths.”

Badger did a sort of double-take, as if he was amazed this wasn’t obvious to any casual observer. “I … um … well, the big beams and the smaller beams can be thought of as a sort of invented mathematical notation. The intersection between a large beam and a small beam, that defines a number — like three, or five. I only noticed it because it starts with primes, up here in the top left corner of the house’s front wall. See? And then I just followed the logic. And- and- and- and you can just repeat it! Infinitely! It’s infinite!”

Badger spoke so hard he almost spat. He was enraptured. His eyes were too wide. His right hand was quivering.

Kimberly shuffled backward, toward the door to the front room. Felicity shot her a curious look, but Kim was just staring at Badger. Zheng tilted her head. July stared and stared and stared. Jan took a single decisive step back.

The rest of us shared a worried glance.

“Uhhhhhhhhh,” Twil made a sound like an error buzzer in a TV game show. “Nate? You alright there?”

Nicole hissed under her breath, “This is some weird magic shit again, isn’t it? You people are gonna be the death of me.”

But Badger was already ploughing on, rambling at speed. “Yes, yes, I know.” He smiled wider and almost laughed. “That’s not a traditional mathematical proof, I’m mangling my own terminology. It’s practically a disrespect to mathematics, but it’s so beautiful, it’s so brilliant! Whoever made this must be a genius. Listen, please, I promise this makes perfect sense. I believe that if I could see all four walls of this house, the junctions and angles of the beams would allow the reproduction of every single pair of twin primes.”

He banged his hands together as he spoke, bone on bone. The tremor was all the way up the right side of his torso now.

Nobody moved.

Evelyn swallowed, then said, very carefully. “Okay. Okay. Nobody say anything. Raine, I want you to take Nathan here and—”

“But I’m onto something here!” Badger laughed in easygoing confusion. “Miss Saye, I swear, I’m onto something. I don’t think this is dangerous or anything. There’s no magic being transmitted by a picture, is there?”

Raine put a hand out to stall Evelyn, and said: “But there’s an infinite number of these twins, right? That’s the point of the conjecture, yeah? I’m no mathematician, but I think I understand that part.”

“Yes, that’s correct.” Badger nodded. He squeezed his fist tightly, holding on to his invisible support, trying to strangle the tremor in his arm. “I-I-I think this symbol, this sequence, this … this new way of recording numbers, it— it’s perfect, it’s revolutionary. If I could only see more sides of this building, I could— I could— do you have more photographs?”

His eyes were too bright, his words too aflame. The shaking was in his neck now, his face, his scalp. Badger started to grit his teeth. Losing his grip.

Raine said: “Mate, you gotta take a minute. Relax for a sec. Alright?”

“I’m fine! Fine!” He smiled and laughed, almost panting. “Just ignore this. The— the pictures? Please? The pictures! I must see more!”

A wave of silent alarm passed through the gathered group. Nobody said anything, but postures were shifting, hands were rising, muscles reorientated for action. Jan swallowed loudly and shuffled further back, searching for Lozzie with one hand. Felicity, who was just beyond Badger’s peripheral vision, raised both her gloved hands, ready to grab the back of his head — or worse. Raine braced herself, one hand reaching for the rear of her waistband. Nicole eased herself away from the table. Twil caught on a little slowly, glancing around in confusion — but Zheng didn’t. Suddenly my beautiful rippling demon-host was striding forward, parting the small crowd like wheat, reaching for Badger. Evelyn opened her mouth to give an order.

Hisssssssssssssss!

The hiss made everybody flinch — well, not Zheng. She just stopped, statue-still, staring at me in mute and unreadable interruption. Raine didn’t flinch either, but she didn’t draw whatever she had stashed in the back of her jeans.

We hissed long and loud, a clear warning. We threw up a protective cage of tentacles, warding off mage and monster and maid alike — around Badger.

Which wasn’t really fair to the poor man. He flinched worse than anybody else, with no idea what was going on, stammering and blinking and almost falling out of his chair. I allowed Praem to duck through my protective cordon to stop him sliding to the floor.

“Heather, Heather, whoa, whoa,” Raine was saying, reaching for me with one gentle hand.

Felicity had stumbled back, crashing into the kitchen cabinets. Kimberly rushed to her side. Evelyn had flinched quite badly, but she wasn’t really afraid of me, not deep down, so she was safe and steady on her feet. Nicole had jumped. Amanda Hopton had merely blinked; she’d probably seen it coming. Jan had scrambled back into Lozzie’s arms, eyes wide, looking like she wanted to run. July, worryingly enough, was staring at me in — was that approval? In the corner, Tenny was letting out loud trilling noises of shared alarm. All three dogs were whining and barking, little Whistle adding his tiny doggy lungs to the larger nosies from Soup and Bernard.

“No!” I managed to squeeze out, trying to explain myself. “It’s not his fault! Nathan is not a risk.”

“Down, girl,” said Praem.

Felicity stammered badly, clutching her own hands. “I-I was o-only going to— I wasn’t— I didn’t mean—”

“Down. Good girl,” Praem repeated.

“Everyone back off … or I shall … shall … ” I was struggling to find a way to de-escalate this moment. Over in the corner, Lozzie had gone to Tenny and joined her in the task of calming the dogs. Tenny’s many silken black limbs were busy speed-petting all three animals. She was fluttering under her breath, saying ‘dogs dogs dogs dogs shush shush shush shush.’

That gave me an idea.

“Everyone leave Badger alone,” I croaked out of a barely-human throat. “Or I shall have to slap you. All of you. I have enough tentacles for that now, too. I’m not joking! Please.”

Throats were cleared, sighs were puffed, heads were shaken. Evelyn grumbled, but she gestured for Felicity to back away from Nathan. Some guilty looks were exchanged. Jan seemed very white in the face, still staring at Nathan as if he was an unexploded bomb.

Zheng didn’t move. She rumbled at me. “Shaman.”

“Zheng. I’m certain. Don’t hurt him. I won’t forgive you.”

Zheng turned slit-narrow eyes on Badger. He stared back with naked terror, mouth hanging open, completely lost as to why he was the centre of such dangerous attention.

“Zheng!” I snapped.

She grunted and straightened up, but didn’t back away. Good enough for me. “Shaman.”

“Thank you,” I croaked.

“Down,” Praem said for a third time. “Good girl. Down.”

We breathed a shaking sigh of relief, slowly lowering our tentacles. Badger still looked utterly bewildered.

“Yeah,” Twil added with an amused snort. “Big H has got a mean slapping hand, you know?” She mimed a casual backhand. “Wa-chow!”

“No slap!” Tenny trilled. “No fight!”

“Yes,” Evelyn grumbled. She was still staring at Badger as if examining a curious and unknown artefact from Outside. “Heather is correct. So is Tenny. There will be no violence here. I don’t think this is … ” She trailed off, wetting her lips.

I repeated myself, “It’s not his fault. And I don’t think it’s dangerous.”

Wide-eyed, his face stained with cold sweat, Badger stared around at the rest of us. “Excuse me,” he said slowly. “But … what’s not my fault? I’m s-sorry, I’m deeply confused. I don’t know what I’ve done to offend, or … annoy?”

Raine shared a look with Evee, then with me. Evelyn shrugged and muttered: “Can’t hurt.” I nodded.

At the rear of the room, Jan bared her teeth in a grimace, then said, “Be ready to catch him.”

Raine leaned down to Badger and pointed at the picture on the table, at the exposed front of Edward Lilburne’s house. “There’s only four exterior walls of that place, right?”

Badger was utterly lost. He looked around at the other faces in the room again, as if this was some kind of trick question.

Raine tapped the picture. “Nate, I’m trying to help you. Four walls, correct, or not?”

Badger swallowed, then nodded. “Four walls. Of course.”

“Four walls. Infinite numbers.” Raine spoke very slowly and carefully, her eyes searching his. “How can you get infinite numbers from a finite space?”

Badger blinked. Then again. Then a third time. His eyes creaked as he turned them from Raine’s face to the picture on the table. His throat bobbed, a painful motion.

“I don’t … but … oh.”

The seizure hit him like a tidal wave, washing over his body in a single spasmodic jerk which started in his right hand and shot upward through his arm. In the moment before his eyes rolled into the back of his head, his pupils dilated wide, eyeballs bulging from his skull, and he looked straight at me. Pleading for help.

So help we did. Before Badger could smash his fingers against the table or fracture his own spine, we grabbed him with all our tentacles and held him as still as we could manage, supporting his skull and his neck, grabbing his wrists to immobilize his hands, wrapping one tentacle all the way up his right arm. Praem helped — a kitchen towel appeared in her hand, as if from nowhere, swiftly rolled into a tube and deftly inserted between Badger’s teeth, to stop him from biting off his own tongue or cracking a molar. He jerked and shook and spluttered as his body — with more than a little help from the soul-framework I had gifted to him — purged whatever invasive structure Edward’s mathematical trick had been trying to insert into his mind.

“Give them space!” Raine shouted. “Give them space, come on, everybody out of the way.”

She herded everyone else back — except for Whistle, who was allowed to come close enough to whine for Nathan’s safety.

In the end the seizure itself didn’t last more than sixty seconds. Badger came out of it as quickly as it had struck, blinking and panting and clinging to both myself and Praem for support. But the aftermath was slow and painful. His eyes were unfocused, his speech slurred, his movements clumsy and uncoordinated. A relapse, a struggle for the surface.

Raine knew what to do — she had memorized his regimen of medication. Felicity and Jan had brought a carrier bag full of his pills when they’d picked him up from his flat. Raine rummaged, producing bottles and pills and forcing him to drink and swallow. Praem made more tea, despite the late hour. Whistle was allowed to sit in his lap, keeping him company.

But even when Praem had stepped away, I stayed close to Nathan. I kept a tentacle wrapped around the back of his neck and the rear of his skull, giving him something to swim towards.

Eventually, almost forty five minutes later, Badger was able to use full sentences again.

“I’m sorry,” he said, glancing at me with a guilty, hangdog look in his eyes. “I-I didn’t … I should have realised, it was … getting into my head. I … it’s hard to tell the difference these days, I—”

“Don’t apologise,” I said. No please. No reasoning. No debate. I just stared down at him. He needed an angel to absolve his mistakes.

“Nate, hey,” Raine said. “It’s not your fault, mate. It’s mine. I sent you that picture.”

Nicole snorted. “You lot need to learn some proper information security.”

“Quite,” said Jan, through clenched teeth. “Nobody think about maths.”

Twil puffed out a sigh. “That was some spooky shit.”

“Spooooooky shit,” Tenny trilled. Lozzie gently stroked her fluffy white fur and suggested she stop using that word.

Evelyn, who was by now sitting on the other side of the table, hunched over her own cup of tea, said, “I’m going to have to ask you some more questions. Are you capable of answering them?”

Badger nodded — but he pushed away the picture of Edward Lilburne’s house, closing his eyes so he wouldn’t have to see it again.

“Be gentle, Evee,” I said. “Please.”

Evelyn sighed and nodded. She met my eyes for a moment and seemed suddenly guilty, then focused on Badger again. She said: “Nathan, how did you figure all that out in the first place?”

Badger shrugged. His shoulders seemed out of sync with each other, slow and weak. “It just hit me. When I was looking at the picture, the front of the building, it was all just … there. So clear. So obvious. I … I never stopped to think about the internal contradiction. Infinity … ”

His head twitched. I tightened the tentacle against the back of his skull. “Stop thinking about that part,” I said.

“Y-yes. Yes, Heather. Yes.” He nodded slowly, blinking too hard.

Leaning against the wall next to the door, back with Kimberly again, Felicity added: “Don’t go looking at magical mathematics, I suppose. Can’t say I’ve had to worry about that before.”

Evelyn sighed. “This still doesn’t explain what this is. What we’re looking at here.”

I chewed my lip, holding back nonsense words that wouldn’t help anybody.

This was my fault.

Of course, it wasn’t actually my fault — I was not responsible for Edward Lilburne building that house and constructing a weird sigil with the support beams. But I was responsible for Badger.

Last time I’d seen Nathan, in the aftermath of his cranial surgery to repair the damage done by my emergency trepanation, I had been worried about how much I may have unintentionally modified him. Parts of the mathematics which defined him had been damaged by the Eye, smeared and ruined as if by a giant, clumsy, sweat-stained fist, so I had replaced them with patches copied from the only model I had — myself. Nathan lived, free from the Eye, but the cost might be a lingering sense of wrongness in his own body, a ghost of my own abyssal dysphoria, a longing for tentacles and fins and the embrace of an abyssal deep he had never known. I’d made him promise to call me if he ever felt such things. I didn’t want anybody else to go through what I had without any support.

What I hadn’t expected was brain-math by osmosis.

Badger had no access to the Eye’s lessons. When I looked at the picture of the house, I felt nothing, no instinctive understanding, no automatic recognition of genius or beauty. But Badger did.

Had I given him a different part of myself than the one I had worried about?

Perhaps it was just because he had been an accomplished mathematician prior to being involved with the Sharrowford Cult. Perhaps he simply saw in ways I couldn’t. Maybe I’d given him that shove in the right direction. We weren’t sure how to feel about that — pride, guilt, concern?

And there was the second way in which this might be my fault.

Before Evelyn could continue her questioning, I wet my lips and said: “I was thinking about this recently.”

Everyone glanced at me. Raine raised her eyebrows. Jan looked far more worried than was warranted.

Evelyn said, “Thinking about what, Heather?”

I hesitated, unsure if this would make any sense.

Praem spoke up. “Numbers paired. Numbers apart.”

I nodded a thank you. “Yes. Specifically twin primes. Back when I first used all of me to do more expansive brain-math for the first time.” We raised ourselves, our tentacles, to indicate what we meant. “It was just a metaphor I was thinking about in the moment, when I was sorting all these impressions about mathematics and brain-math. But I recall specifically thinking about twin prime numbers, though I didn’t know that’s what they were called, then. I … I don’t know if that means anything. I’m sorry, I just thought I should mention this.”

Evelyn frowned. “You mean twin primes are a core component of self-implementing hyperdimensional mathematics?”

I shook my head. “No. Only in metaphor. I was thinking about a metaphor.”

Evelyn sucked on her teeth in thought. Raine shrugged. Jan and Felicity both took this quite seriously, but didn’t seem too concerned. They didn’t have the context.

In the end, it was Amanda Hopton who spoke sense. “Heather. Heather.” She spoke my name in her wavering, sleepy, half-slurred voice, the translated thoughts of her god. “That building is too old to have been formed in response to you and yours and you. I think it’s a coincidence. An overlapping metaphor. Nothing more.”

Evelyn growled, “Or it could be a trap for Heather, personally.”

Raine nodded. “Yeeeeeeah, could be. Could be.”

“This changes nothing, though,” Evelyn snapped. “Heather isn’t going in there alone anyway, and she’s absolutely not touching the building directly.” Evelyn sighed heavily and gestured at the photo again. “This still doesn’t explain what we’re looking at. Prime numbers or magical notation or otherwise.”

Badger rallied himself, making a visible effort to sit up straight and fill his lungs. His eyes were unfocused and his breathing was rough, but he did his best. He scratched at his beard stubble as a preamble to making a point. “Actually, I … I have an idea. If I may? Heather?”

“You don’t have to ask me for permission,” I said.

“I’m more comfortable when I do.” His voice shook with surprising vulnerability.

I suppressed a sigh. “Go ahead, then. Please.”

He turned back to Evelyn. “I never learned much magic. And … and frankly I don’t want to, now, I—”

Surprising everybody, Kimberly hurried out of the kitchen and into the front room, hand to her face. Trying not to burst into tears, poor thing. Felicity was torn for a second, between helping Evelyn with this problem and going after Kim. Footsteps hurried up the stairs.

Evelyn jerked her head. “Go.”

Fliss nodded in thanks, then hurried after Kimberly. Badger watched this all happen with a look of distant melancholy.

Raine said, gently, “Never mind her, Nate. It’s her stuff to deal with. Go on.”

Evelyn added: “Just get to the point.”

Badger nodded. Without looking, he gestured at the photograph. “I think it might be magical language. You know far better than I do, Miss Saye, how magic circles work, sigils and the like. They’re built from like, language elements. But not used as a language. I’m pretty certain I’m correct about the junctions between the beams actually being numbers. So what if instead of real mathematics, it’s using numbers in place of words, like in a magic circle?”

Evelyn frowned hard at this explanation, then back down at the photograph.

Jan said slowly, “I’ve never heard of that before, but I can’t see any reason it shouldn’t be possible. In theory.” She sighed. “I’d rather not meet whoever built it.”

Evelyn scoffed. “Bullshit. Impossible.”

Twil puffed out a sigh. “You have been known to wrong about that, Evee. Sometimes. Now and again.”

Evelyn shot her a dark glower, but Twil just shrugged.

“A magic circle made of maths,” I echoed softly. “What would be the point? What would it even do? It’s not brain-math, it’s just regular maths, after all.”

Jan said, “We have no idea. It may be a method of concealment, perhaps, concealing some other spell by making it out of numbers?”

Badger cleared his throat softly. “I have an educated guess about that, too.”

Raine shot a finger-gun at him. “On a roll, Nate my mate.”

Evelyn rolled her eyes. “Go ahead, then.”

Badger said, “It’s all full of twin primes. That’s real, that’s not a delusion I was having.” He raised both of his hands, steady as he could keep them, and extended both index fingers, holding them parallel. “Two things, similar but separated by one value. They can’t touch, but they’re close. Whatever that spell does, I think that’s a clue. Sort of. Maybe.” He cleared his throat again, pulling an awkward closed-lipped smile.

Twil said, “Cheers, Mister Sphinx.”

Evelyn huffed and leaned back in her chair. “Yes, that is a bit of a nonsensical riddle. It hardly helps.”

“Sorry,” Badger said. “But it makes sense to me. It lines up with what I was feeling earlier, with what I felt when I looked at the picture. I just … I just really want to help. I really want to help.”

I’d heard those words earlier, upstairs, from my own throat: I want to help. My skin crawled with discomfort. Evelyn wasn’t looking at me.

“You have helped,” I said.

Badger shot me the most fragile, earnest, longing look. He wanted to help, so badly. I stared back, silently pleading for him to reclaim his own life. You don’t have to be involved anymore, I willed him. You don’t have to be one of us, or follow me around, or do anything I say. But he didn’t look away, not until a question struck him.

“So, um,” he said, casting around at Evelyn and Raine and the others again. He gestured at the photograph. “Who’s house is this, anyway?”

“It belongs to Edward Lilburne,” said Evelyn.

Badger stared, dumbstruck. Then: “Oh. Oh, well. I suppose that makes sense.”

==

“Purple,” said Tenny.

Her fluttery moth-voice, a deep-tissue trilling buried inside her chest, made the word sound like ‘purrrrpllll.’ I felt it as much as I heard it; the vibration passed down our pair of intertwined tentacles, as well as through the purple-tinted air. Tenny was clinging very hard to two of my tentacles with two of her own, as if the jewels of the sky might tempt her away from us if she let go.

“Purple?” I echoed. “Do you mean the sky?”

“Brrrrt. Yes. Purple. And pretty? Hmmmmmmmmmmmmnnnnnnnmmmmnnn.” Tenny twisted her lips in a thinky face, a little ghost of Lozzie’s mannerisms. Her shiny all-black eyes stared up at the alien sky of Camelot, at the purple whorls like scattered nebulae on an ink-dark deepness.

“Pretty, yes,” I agreed. “I’ve always thought it’s pretty out here. Camelot really isn’t anything to be afraid of, Tenny.”

Tenny puffed her cheeks out. “Scary.”

“Do you want to go back? The gate’s right there. We can go home. I don’t have to be here for this part of the process. I just wanted to come and look.”

But Tenny shook her head. “Nope! Scary but … pretty.”

“Outside can be like that, yes.”

I watched Tenny’s face as she watched the sky. It was sometimes difficult to tell exactly where she was looking, because her eyes were all-black, like those of a deep sea creature or an exotic insect. It wasn’t quite the same as with Praem’s pupil-less, milk-white eyes; with Praem it was almost impossible to tell what she was looking at. I privately suspected that was why she often moved her whole head to address somebody. With Tenny the effect was more subtle, more biological. She was, after all, a fully biological person, even if not human.

But I could tell when her eyes wandered down from the sky to rest on the distant horizon. Her free-floating silken-black tentacles adjusted their angles as well, as if following her thoughts.

Gently, probing without prodding, we said: “Camelot might be scary, Tenns, but it’s not dangerous. You could try flying again, here, if you wanted to?”

Tenny pulled a very serious little frown. “Danger-danger. We don’t know.”

“Your mother knows, I’m pretty certain about that. She wouldn’t tell us this dimension was safe if it wasn’t.”

Tenny puffed her cheeks out, did a big hurrumph, then tilted her head to give me a very human look, deeply sceptical and a little amused. “Brrrrt. Auntie Heath-er. Lozz-mum’s definition of ‘danger’ is fuzzy, hmmmmm? Biiiiiig hmmmmm. Hmmmm!”

We spluttered with laughter, try as we might to contain ourselves. Tenny’s expression just got worse; she made her eyes wider and pressed her lips together, a very knowing look.

“Okay! Okay!” We spluttered. “Yes, Tenny, that’s a very fair point. Lozzie has a slightly different threshold for danger. But she wouldn’t ever put you at risk. She loves you very much. And so do I. If you wanted to fly, out here, I’d be right here the whole time.”

Tenny wiggled half a dozen tentacles back and forth. She tightened her grip on our interlinked limbs. “Mmmm. Maybe maybe.”

But I saw her wings twitch and flex, her cloak of flesh ruffling with muscular tension. She wanted it so very badly.

“What if you had a target?” I asked. “A destination, I mean. One of the Cattys, perhaps, out on the plain, bringing materials back to the castle. You could fly out to one, and then ride the caterpillar back here. Fifteen minutes, probably. If you want to, of course.”

“Pbbbbbbbbt,” went Tenny. She gazed out across the soft rolling yellow-grass hills of Camelot, glowing beneath the purple sky. “Need to be bigger, here.”

“You want to be as big as a catty?”

“Mmm-yes!” Tenny nodded with great enthusiasm. “Bigger!”

“Maybe flying will help you feel bigger,” I suggested.

“Yaaaaaah. But not yet,” she trilled — then pointed down the hillside with a clutch of tentacles. “Can’t fly here for that. Can’t be here, Heath?”

I sighed and nodded, sobered by Tenny’s all-too-sharp perception. She knew exactly what was going on. “Yes, Tenns. You won’t be in Camelot for that. Your job will be to watch the house and look after Lozzie. You can do that for us, yes?”

“Lozz-mums doesn’t need me for that.”

I winced inside. “She does, Tenny. Maybe not practically, but emotionally. This is going to be hard on her. Please, be there for her?”

Tenny did a little pout. But she didn’t argue. Her eyes finally left Camelot’s wonders and returned to the ground, to ugly practicality — to the bloody great hole we’d dug in the soil.

It was thirty six hours — two nights and the day in between — since Badger’s flying visit to Number 12 Barnslow Drive. Tenny and I were standing on the tall-ish hilltop which formed a vantage point, within the outline of the walls which would one day ring the castle.

Camelot was much the same as when I’d last visited this auspiciously-named Outside dimension; the Knights had been busy at work extending the castle upward, adding turrets and wings and outward-projecting defensive bastions, covered walkways and connecting bridges and little pathways surrounded with bare soil ready for what I assumed would one day be flowerbeds. Their construction works, their block-cutting and mortar-mixing and hand-made cranes, were all still in full swing. The outline of the walls had been filled in only a little — the work of bringing the big sandstone-coloured blocks from the ancient city on the horizon was very slow going.

But sadly we weren’t here for them. I would have loved to spend a day or two wandering the half-finished castle, climbing up into the gestating towers, exploring the underground dungeons which Lozzie had assured me the Knights had added.

No, we were here for the pit.

Beyond the outline of the walls, set in a hollow between hills, the Knights had dug us a hole. They had paused their castle construction work, peeled off a couple of the gigantic Caterpillars from their back-and-forth stone-ferrying duties, and spent half of yesterday excavating a giant, featureless wound in the landscape.

Lozzie had been very specific about our needs. The Knights had understood. The Caterpillars had helped. The hole had opened.

Then they’d spent further hours lining the thing with quick-drying mortar, hard as concrete but dusky-brown. The material was made partially from the Knight’s own internal secretions. Evelyn was insistent that the soil of Camelot must be protected, the landscape here must not be infected, not play host to whatever filth we might bring with us. And she wasn’t talking about earthly bacteria and worms.

With the hole made secure, Evelyn, Felicity, Jan, and Kimberly had gotten down to work. Kimberly hadn’t ventured through the gateway herself; she was exempt. Felicity hadn’t asked any questions. And Jan was terrified, but still she helped.

The mages had spent all yesterday evening and most of the night ringing the hole with the second largest magic circle I’d ever seen Evelyn create, closely behind the one in the field at Geerswin farm. It wasn’t particularly complex, it didn’t need chicken’s blood or ash from burned Bibles or any other such nonsense. It was just eleven successive rings of containment, etched and dug and painted into the soil, copied onto the Knight-mortar, made inviolate and unbreakable.

Praem did most of the painting. She was down there right then, doing the last checks with Evelyn and Jan. July trailed behind them. Lozzie flitted from Knight to Knight, sharing silent thank yous or praising the sheer speed of their construction work.

Five Caterpillars stood in a rough ring around the hole, further out than the magic circle itself. Each of them had been blessed with a magic circle of their own, drawn around their bases and cut into the soil. Protection, not containment.

Evelyn was taking no chances when it came to the safety of our allies.

We — I, me, us a concept I was still struggling with — approved of that, deeply. We simply could not have achieved this plan without the Knights and the Caterpillars, Lozzie’s hidden army tucked away in a secret we had named after Arthurian legends. The necessary preparations would have been beyond us.

Just like with the Eye. I tried not to think too far ahead. One problem at a time.

In the middle of that wide concrete basin, dead centre of the concentric rings of magic circles, was a small pile of junk: a rusty spoon, a couple of pieces of rotten fruit, an old t-shirt. The pile was barely visible from this distance, just a smudge against the floor of the hole. I’d been teleporting stuff there all morning. ‘Calibrating’, as Raine called it. The first dozen objects had gone wide, appearing in the grass or on the hillsides, but we had to get this perfect. There could be no error.

My tentacles ached gently from the repeated effort. But we’d continued until I could land a spoon in the middle of the circles, every time.

I wasn’t the only one who’d been preparing, either. Lozzie had spent three whole hours yesterday down inside the underground shell of a certain Outsider cone-snail, down there with Amanda, discussing the bubble-servitors, their role, their limits. She’d returned bright-faced and quite bouncy. At least somebody was enjoying this.

Evelyn had spoken of nothing but the task and the circles since yesterday. Not a peep about my prosthetic hand suggestion. I felt vaguely ashamed, but this wasn’t the time to dwell on that.

The circles were ready. My teleportation trick was ready. The Knights and the Caterpillars and the bubble-servitors were ready. The journey was mapped out. The destination was understood.

And my stomach was churning like I’d eaten a bowl full of worms.

The concrete-lined hole was for Edward Lilburne’s house. We were going to shove him in there and murder him. If everything went to plan, it would serve as a grave.

“Mmmmmmmmm,” Tenny made another thinky-sound. We knew it was because she could feel the tension, transmitted down my tentacles. She knew I was riddled with anxiety over this. “Heath-er?”

“Yes, Tenns?”

“Ed-ward is Lozz-mum’s uncle. Mmhmm?”

Oh, I didn’t like where this was going. I felt deeply unprepared for this particular conversation. But I wouldn’t disrespect Tenny’s intelligence. “Yes, Tenny, that’s correct.”

“Sooooooo,” she fluted. “If Lozz-mums is my mum, and Ed-ward is Lozz’s uncle. Then Ed-ward is Tenny’s … great … uncle?”

“I think that’s the technical relation, yes.” We nodded, trying to feel less pale.

“Prrrbbbbt,” she trilled. “Why is he so bad?”

I needed a lemon.

“Well … ” I tried. “Some people just choose to be that way. Some people choose to do things that hurt others, because they value certain things more than they value other people. Or other people’s lives. They treat people as things, not as people.”

Tenny tilted her head, watching Lozzie giving hugs to Knights, down by the grave-pit.

“Okay,” she said.

I almost said That’s it? But I managed to resist the urge. Tenny waggled a clutch of tentacles toward Lozzie and glanced at me.

“Is it all ready?” she asked.

I felt myself swallow, then I managed to nod. “Yes, Tenns. It’s ready. We’re all ready. The preparations are done. We’ve got until tomorrow morning, that’s when we’re doing it.”

“Play with Lozz-mums?”

A smile. That was what we needed, to ease the nerves. “Yes. Yes, we can go play with Lozzie. We’ve got time for that.”

Until the morning.