Homologyby VelocipedeChaptersConamingCohomologyCoïtusConamingEllie closed her eyes as Maud kissed her. Slow and implacable. Building up the pressure like the force of one tectonic plate pushing against another until Ellie gave, her tongue subducting under Maud’s, her breath stolen from her lungs. Ellie took in a sharp breath as Maud let her go, her cheeks flushed. Maud’s face didn’t show a hint of emotion. Just that same half-lidded, imperturbable expression. As if she were an unstoppable wall of granite more than a mare. So hot. She wanted to melt into Maud’s forelegs then and there in surrender. But when Maud kissed her again, it was sweeter. Lighter. Her lips traced lightly with a tongue, the soft caress of a hoof on her burning cheek. A break in the kiss, then a resumption, as the hoof moved to the back of her neck and her upper back, rubbing her there gently. When Maud broke the kiss again, Ellie smiled. “Before we start, I wanted to ask you something.” “Oh, of course!” Ellie said. “Of course! Anything you want to know.” Though she secretly hoped she wouldn’t be asked too much about the human world. “I noticed you did the conaming yourself. But usually couples talk it out first. Is that how humans do things?“ “The… ‘conaming’?” Ellie was very much puzzled. “I don’t understand.” “The name you use for mine.” She pointed a hoof at her crotch. “’Clit’”. Ellie realized. “Oh. Oh! Yeah, I guess I didn’t ask you before starting to do that…” She grimaced. “Is that bad? I’m sorry.” “If you did something bad, I would tell you.” Maud said, and Ellie felt admonished. “It’s okay. I would have accepted it.” “But you shouldn’t have to ‘accept’ anything!” Ellie exclaimed. “It’s your body, it’s not about me. So if you prefer any of the other words…” “Other words?” Maud blinked. “Like ‘penis’?” “Yeah…” Ellie tried not to frown, as she hoped that wouldn’t be the case, but maybe thinking that was messed up. “I mean, is that what you prefer?” “No. It’s a formal, scientific word. It wouldn’t feel right here.” “I get that!” Ellie agreed, relieved. “So do you prefer one of the informal words, then?” Maud blinked. “We don’t really have informal words for our genitals.” “Oh, right!” Ellie had noticed that. No talk of “cocks” or “pussies” in Equestria, unless referring to the animals. It was really nice, actually. “That’s why couples do the conaming. They agree on the words to use for each other’s bodies. It’s considered an intimate thing.” “Huh…” Ellie set her jaw as she considered this. “Wow.” She blinked away tears. “That’s just really nice and adorable.” “You say that a lot about pony things.” “That’s because it’s true!” Ellie squeezed Maud’s cheek with a hand, distorting the lack of expression on her face. “A lot of things are nice and adorable here. Things that I wish humans did back in my world.” She sighed, and let go of Maud’s face, which bounced back to its expressionless default. “But I want to do this the pony way and not the human way. I want to talk it out. You said you wanted to ask me something?” “Yes.” Maud said. “‘Clit’ is short for ‘clitoris’, right?” “Yeah, that’s right!” “But that’s what you have, not me.” “I guess, like, scientifically…” Ellie conceded. “But I just personally like to expand the word to account for the homology.” “Homology?” Maud asked. “Yeah!” Ellie said. “It’s the noun form of the root adjective ‘homologous’, which comes from the Greek ‘homologos’. “’Homo’ for ‘same’, ‘logos’ for ‘mind’, thus ‘agreeing’.” Maud blinked. “Greek? Do you mean Pony Greek?” “Uh… sure?” “It sounds weird when you shorten it.” Ellie chuckled. “I guess! But yeah. Homology. It’s the similarity between different biological structures. My clit and yours are homologous. Well, technically my clit and the head of yours…” Ellie smirked. “But the rest of my vulva and the rest of your genitals, they’re both made of the same tissues, more or less. They were the exact same structure at some point in our fetal development, and they only turned out differently because a different chromosomal key was turned.“ “Really?” Maud asked in a way that was just as monotone as everything else she said, but clearly sarcastic. “Yeah, isn’t that neat?” “I was being sarcastic. I was pointing out that it wasn’t true.” “Really?” Ellie had been pretty sure of this fact, but she was not an expert in this field and Maud objected so definitively that it caused her to second-guess herself. “I could’ve sworn that’s how it worked…” “We’re different species.” Maud pointed out. “Our fetal developments were probably pretty divergent from the beginning.” “Oh, right… Yeah… That…” Ellie cringed. “It’s really weird how quickly I got used to the whole not-the-same-species thing…” She thought for a second and smiled, finding her footing. “But homology also applies across species too, you know!” She snuggled up closer to Maud. “I mean, it really doesn’t stop there! Our lips”—she pecked Maud on the lips—“our noses”—she touched noses with her—“our ears”—she touched one of Maud’s ears, which twitched at her adorably—“our eyes”—she stared into her eyes—”they’re all structured very similarly, aren’t they?” “Yes.” Maud said. “They’re homologous, too.” Ellie smiled. “I mean, we’re both mammals. So if you go far back up the evolutionary tree enough, all our parts were once the same. They just took different shapes.“ She took a forehoof in her hand, and felt the nail with the nail of one of her fingers. “It’s just nice, you know? Thinking of us as not so different, really. Thinking of your clit as being like mine, only bigger.” She glanced down, drinking in the view. “A lot bigger…” “It sounds like you’re into being the same as you.“ “Yeah!” Ellie agreed. “I mean, I’ve had this problem for a long time! Like, it’s hard for me to tell sometimes whether or not I’m attracted to someone or I want to be like them or both. To be honest, it makes me worry that my ideal partner is a clone of myself.“ She shook her head. “No, that would be a total disaster, as hot as it’d be. We’d just reinforce each other’s bad habits. An ideal partner would be someone who’s similar to me, but different enough to make me better.“ She smiled, suppressing a giggle at just how silly the word still felt to her. “Or somepony, I guess.” Maud looked at her, and smiled slightly. “We are pretty similar.” She looked down at herself, and Ellie looked down with her. “Clit.” Maud said. She touched herself with a hoof, which made Ellie more than a bit excited. “I like it.” “Oh, you’re not just saying that, right?” “No.” Maud said. “I like it. It’s short. It feels good to say.” She moved her hoof to Ellie’s crotch, which made her shudder. “It’s nice that we both have one.” She faced up to look Ellie in the eyes. “It’s pretty. Like you.” Ellie bit her lip, her cheeks brightening. “It’s not fair how good you are at that.” Maud did not respond to that, and just moved her hoof to Ellie’s side, gently stroking her. “There’s something else I was wondering.” Maud said. “Why you use ‘she’ and ‘her’ to describe my clit.” “Oh! Yeah…” Ellie brightened even more. “I mean, I do that for mine, too… It just feels more personable… And, uh…” Ellie darted her eyes. “I like it…” “Oh.” Maud looked at her. “Speaking of your clit. She felt really good on my tongue this morning.” Ellie turned a bright red and squeezed her thighs together at that. “You really do like that.” Maud cupped a hoof on her cheek to feel the heat radiating off of it. “Interesting.” “Yeah…” Ellie managed. “I think it’s an extension of, uh, how I like to be referred to in the third person, too, sometimes. I really have no idea why…” She groaned. “Maybe I have more in common with that homeless magician unicorn than I thought.“ “Trixie?” Maud asked, and Ellie nodded. “Not really. She’s a lot more passive in bed than you are. Not that that was a bad thing, the way she did it.” Ellie’s eyes widened at that. She studied Maud’s face, but it held the same expression as ever. “She was a terrible fieldhoof back at the rock farm. But I did her share of the work so my parents wouldn’t fire her. I liked having her around. She was almost as good in bed as she was bad at rock farming.” Ellie sighed. “I thought I was starting to get the hang of telling when you’re messing with me, but I guess I still have a lot to learn.” Maud winked. Ellie thought for a second, smiled devilishly, and began to stroke Maud’s chest. “You know, I can actually kind of picture it. Like, I really like how big her ego is and support her in her life choices 100% but… It does make imagining you two together way hotter.” “Really?” Maud said, monotone. “Yes.” Ellie practically salivated. “She’d come at you just so haughty and commanding at first. Like you were beneath her. But you’d be just like the rock that’s your cutie mark. An immovable object. Always there. Never cowering to her demands, never showing her anything other than kindness. She’d wear herself down on you, until she finally broke. She’d open herself up to you about why she keeps up this persona to keep everypony away. Be really emotionally vulnerable. Ugh.” Ellie licked her lips. “Emotional vulnerability is so hot.” “Yes.” Maud agreed. “All of that is exactly what would happen. Hypothetically.” Ellie studied Maud’s face. She still couldn’t tell. She smirked. “And oof, I can just picture it. Trixie on all fours on your bed.” A pretty normal thing for ponies to be, she just realized. “You on top, chest on her back, so you can feel her body as you move as your face blushes with effort. Trixie taking all of you, sweating and moaning and biting your sheets…” Maud’s expression was blank as always, but a slight tinge of red on her cheeks betrayed her true reaction. Of course, Ellie still couldn’t tell if Maud was remembering or imagining… Not that it mattered. The shoe was on the other foot now. Or other hoof. Whatever. She began to gently stroke the coat of Maud’s chest with her fingertips. “Say, I was thinking…” She smiled at her. “Maybe I could try something that’s probably a dumb and bad idea?” “An Ellie idea?” Maud asked, without skipping a beat. Ellie laughed. “Yeah! I just want to try it. Some math-based foreplay.” Maud did not respond, and just looked at Ellie with her trademark half-lidded expression. That was all she needed to say. “You know!” Ellie insisted. “Like the tectonic plate roleplay we did this morning, only my version of it. I mean, I didn’t really get half of the references you made then, but I still had fun.” “I was trying to keep things non-technical.” Maud said. “But I guess that’s fair.” “Oh, no!” Ellie took Maud’s hoof in her hand. “Sex shouldn’t be transactional or anything, I’m sorry I worded it that way. I mean, to be honest it’s just me trying out a dumb and bad idea I had based off a dumb math pun involving the word ‘homology’. Never mind.” “No.” Maud said. “Your ideas aren’t dumb and bad. I’m sorry I joked about that.” Ellie melted into a smile. Maud continued. “They’re weird. I like how weird you are. I want to try it.” Ellie kissed her hoof gratefully. “I want to say that you won’t regret it, but I can’t really promise that at all. I’m sorry.” “It’s okay.” Maud said. “But if it doesn’t work, can we go back to the Trixie thing?” “Okay, fine!” Ellie laughed. She kissed Maud, and sat up to begin. Cohomology“So,” Ellie began, “what do you know about n-simplices?” “Nothing.” Maud said. “I’ve told you this already. I learned about space groups to understand crystal structures. That’s as far as I got in math.” “Great!” Ellie turned away from Maud to face her crotch. “Let’s start.” She took an index finger and used it to lightly tap Maud’s left nipple. Ignoring the reaction, she innocently continued. “The 0-simplex is the first one. The number corresponds to the local dimension. Being 0-dimensional, it’s just a point. We’ll label it ‘0’.” She leaned over to suck on the nipple she tapped for a second, breaking the suck with a lick. “Going up to the 1-simplex, you have to add another 0-simplex, so another point, in a way that’s ‘orthogonal’ or ‘perpendicular’ to the existing simplex if you want it to be nondegenerate. But everything’s orthogonal to a single point, so I can place the second point anywhere. Let’s just say, oh, here.” Ellie did the same suck then lick with Maud’s right nipple. “We’ll label this point ‘1’. Then we connect them with a 1-dimensional space, that is, a line. The direction is important. We’ll respect the obvious ordering on the vertex labels.“ She traced a line from point 0 to point 1 with her tongue, down the side of Maud’s left teat and up the right. “Now we want to place the third point in a roughly canonical way. Let’s start with the midpoint of the existing simplex.” She placed the point of her index finger between Maud’s teats. “Then let’s draw a perpendicular line.“ She did so, tracing a line down her abdomen until she hit the base of Maud’s clit. “Perfect. That we can label ‘2’. Then we fill in the two new 1-simplices.” She licked a line from Maud’s left nipple up to the base of her clit, and then did the same from her right nipple. She smiled as she felt Maud’s shudders and saw the proof of her excitement. “Then we fill in the 2-dimensional space between them.” Ellie caressed the area of Maud’s crotch that formed by the triangle of her teats and clit, then planted a kiss in the center. She placed a finger on the spot she kissed. “So that’s a 2-simplex, embedded in the 2-dimensional space of the surface of your sexy body. To go up again, we need to go perpendicular to it.” She traced a line upwards into the air above the aforementioned triangle. “We can label this ‘3’, and you can imagine the tetrahedron that gets filled in. That gets us up to a 3-simplex, embedded in the 3-dimensional space we’re so familiar with. But to go up again, you have to go ‘perpendicular’ from this 3-dimensional solid you’re in the middle of, which doesn’t make sense. So we have to go ‘up’ to 4-dimensional space to get the fifth vertex we need to make a 4-simplex. And so on, and so on. That way you have a whole family of basic shapes you can use to understand higher-dimensional geometries with. The n-simplices.“ She looked down at Maud. “Sorry, I couldn’t figure out how to make that part sexy. But I hope that it was satisfying conceptually.“ “It was.” Maud said in her monotone. “I like this lesson. I think I learned something.” Ellie smiled. “Yeah, I find that nipple play really helps with the retention. Unfortunately, it’s a very difficult methodology to scale up to the classroom level.” Maud looked at her without any expression in a way that meant rolling her eyes. Ellie laughed. “Okay, now on to singular homology groups.” “Oh.” Maud realized. “That wasn’t it?” “Yeah, sorry…” Ellie said apologetically. “It gets a lot worse from here.” A rare frown flashed across Maud’s face as Ellie continued. “Now, I’ve been using ‘n-simplex’ as shorthand for ‘continuous map of the n-simplex’, which is what I was drawing on your body all along. I mean, ‘drawing on’ is a pretty good intuition for the idea of a continuous map without getting technical. So here are two 2-simplices.” She drew a clockwise triangle from a point on Maud’s abdomen, to her left nipple, to her right, then back down. Then she drew another clockwise triangle, going from the base of her clit to her right nipple, then left, then back up. “Of course, the 2-simplices are the filled-in triangle! I only drew their oriented boundaries. Now, a singular 2-chain is any formal sum of 2-simplices, so these two triangles together is an example. But notice what happens when we consider their boundaries together! We have six edges between the two triangles, but this edge”—Ellie drew a line from Maud’s right nipple, across her teats to her left, then back—”is repeated, with the directions canceling out! So the boundary of this 2-chain is actually this.” She drew a diamond, starting from that point on Maud’s abdomen, brushing over her left nipple, touching the base of her clit, then brushing over her right nipple on the way back. “It’s a 1-chain! Four 1-simplices added together. But I need a 2-chain with no boundary.” “No boundary?” “Yeah!” Ellie barely paused. “So imagine the four sides of a tetrahedron, like the 3-simplex we considered earlier.” She re-drew its base, the clockwise triangle going from Maud’s right nipple, to left, to base of clit and back. “We have this 2-simplex at the base, then we add three more of them for the sides.” She drew three triangles, all with their apex hovering above Maud’s crotch, their bases going from left nipple to right, from right nipple to clit, then from clit to left nipple, respectively. “All twelve edges of these four triangles are canceled out by a counterpart going in the other direction! So these four triangles form a singular 2-chain with no boundary. A singular 2-cycle.” “Okay.” Maud said. “But then imagine that we were drawing these on the surface of a tetrahedral solid. Say, a rock! You like those.” “Rocks are very rarely tetrahedral.” Maud said. “It could really be any solid shape! We’re just ‘drawing’ a 3-simplex made out of rock.” Ellie rolled her eyes. “The point is, if we consider the rock as a topological space, the rock itself can be thought of as a 3-simplex, thus, a singular 3-chain, whose boundary is the 2-chain we were just talking about. So this singular 2-cycle is also a singular 2-boundary.” “You’re using the word ‘singular’ a lot.” Maud said. “So all cycles are boundaries?” “No, that’s the thing! Like, what if we imagined that 2-cycle as on the surface of a tetrahedral geode?” “A tetrahedral geode is even less likely than a tetrahedral rock.” Maud commented. Ellie ignored her. “Then we can’t consider the ‘inside’ to be a single 3-simplex, because there’s a hole in it!“ “Cavity.” Maud corrected. “Fine, cavity.” Ellie smiled. “So the surface of a geode is a 2-cycle that’s not a 2-boundary. So it represents a non-trivial homology class. An element of H_2, the second homology group.” Maud didn’t say anything in response. “You know, a hole!” Ellie laughed. “Actually, you’re right, ‘cavity’ is a better word for it. So you can think of H_2 as ‘counting’ three-dimensional cavities in a space, since each cavity can have a 2-cycle drawn around it that’s not a 2-boundary.” “That was a lot of work to talk about counting cavities.” Maud said. “Well, this was just the simplest possible example! Everything embedded in Euclidean 3-space.” Ellie shrugged. “But what I really wanted to talk about was cohomology groups.” “There’s more?” Maud’s voice was actually inflected with dread. Ellie felt really bad, but could not stop herself now, due to the sunk cost fallacy. “Yeah! I mean, you can add n-chains together, which means they form a group, C_n. So if you pick a coefficient group G, you can take the dual group Hom(C_n,G), calling the homomorphisms between them cochains, and the group of cochains C^n := Hom(C_n,G). This is an application of the contravariant functor Hom(-,G), which means it applies to the boundary maps \delta_*: C_* \rightarrow C_{*-1} as well, reversing their direction to form coboundary maps \delta^*: C^* \rightarrow C^{*+1}. We can analogously define dual versions of cycles and boundaries as well, that is, n-cochains in C^n are considered cocycles if they get mapped to zero in C^{n+1}, and coboundaries if they come from something in C^{n-1}. This way, by quotienting coboundaries from cocycles you get cohomology classes…“ Maud had clearly stopped listening long ago. “But imagine!” Ellie put a hand on Maud’s upper foreleg, forcing her to make eye contact. “Imagine, say, the fifth cohomology group of a six-dimensional oriented, closed manifold, M? Something governed by not merely the embeddings of a five-dimensional space into a sixth-dimensional one, but also by a layer of algebraic abstraction on top of that?” “No.” Maud said. “I don’t want to.” “I don’t, either! That’s a terrible thing to imagine!” “Or talk to your marefriend about.” “I agree,” Ellie said apologetically. “And I am very sorry. But what I really want to talk about is something called Poincaré duality.“ Ellie emphasized the uvular “r” to the point of parody. “You don’t have to say it like that. I don’t think even Prench ponies say it that way.” “I like being terrible, though.” Ellie grinned. “But here’s what’s wonderful. Poincaré duality says that H^5(M) is actually isomorphic to H_1(M)! Isn’t that amazing? I mean, H_1(M) is just the homology classes that count two-dimensional holes. That’s pretty simple. They’re just rings.” Ellie formed a circle with her thumb and middle finger. She then took the circle and inserted the tip of Maud’s nearly-flaccid clit into it, beginning to rub her up and down. She felt Maud’s spirits lift underneath her. “Can you imagine it? You start with something so arcane and difficult to explain even the definition of, living in a dimension beyond human intuition. There’s no beauty there in that realm. No appeal. Just cold mechanics. But then…” Ellie bent down to take the head of Maud’s clit into her mouth, running her tongue up and down her as she began to stiffen. She pulled back, observing the results of her work, and smiled. “Then it’s transformed into something elegant. Something that can sing to the visual cortex. Geometric intuition, built out of what was needed for our minds to understand the physical space around us. The incarnation of the abstract. Word made flesh.” She turned to look down at Maud. “What do you think?” she asked. “I think that I don’t want you to stop.” Maud said. “I also think that was very pretentious.” Ellie laughed, and kissed her. “You’re Poincaré duality, you know,” Ellie said, not pronouncing it terribly this time. She looked back down at her hand, and Maud’s stiffening clit. “You take something and you recontextualize it, because that’s what isomorphism is. The mechanics are the same, but it’s the names and the intuition that change. The feeling.“ Ellie sighed happily. “Something that I would otherwise see as having nothing to do with beauty, from a realm not my own, is suddenly made familiar. Understandable. Appealing. Beautiful. Things I never would have imagined I’d ever see the beauty in.” She drank in the sight for a few moments before turning around to look Maud in the eyes, smiling warmly. “But H_1(M) has nothing on the smell of your cum drying on my face.” Maud’s face reddened. Ellie grinned lecherously. “I don’t like you.” Maud said. “Something in my hand says otherwise,” Ellie sang, terribly and very off-key. “But don’t worry. I’m done.“ She bent over to kiss Maud on the lips. “Don’t worry. No more math.” She planted more soft, reassuring kisses on her muzzle and cheek, down to her neck. “Thank you for suffering through this for me.” “It wasn’t that bad.” Maud lied. Ellie smiled, and gazed into her eyes for a moment before kissing her again. “You really are so sweet, lying for me that way.” Maud did not object. “But don’t worry. No more math. Really.” Another reassuring kiss. “Just going to have sex with you now.” Maud smiled. CoïtusEllie rose on her knees, stretching up to the height Maud would have been had she been standing up. Placing both shins on either side of Maud’s torso, Ellie straddled her belly, her knees on either side of Maud’s head. She noted with delight Maud’s muted surprise at just how long the human’s limbs were. Reaching underneath herself, Ellie found Maud’s erect clit with her hand, and slowly guided herself down until she was right where she wanted to be, her lower lips pressed against the base of Maud’s shaft. She concentrated on the feeling of Maud against her, the warmth of her flesh against hers. She gently pressed upwards on Maud with her fingers, and began to rock herself against the base of Maud’s clit. She sighed contentedly, then began to slide back and forth, spreading her slick up and down. Finding equilibrium, she closed her eyes to focus on the sensation of Maud’s shaft sliding against her. “Oh, wow, that feels nice!” Ellie bit her lip as she looked down at Maud’s face, which was as expressionless as always. “How does that feel?” “Soft. Not like a rock.” Maud said. Ellie could see a tinge of blush on her cheeks. “It feels good.” Laughing at that, Ellie bent over to kiss her, supporting herself with an elbow at the side of Maud’s head. Her lips met the mare’s, forming a second connection to complement the one they had below, incarnating a non-trivial class in the first homology group. Maud’s lips were so wonderfully soft. Ellie rocked her hips forward, until she could feel the ridge of Maud’s medial ring cross her clit. She then rocked back, feeling the ring press up deliciously against the base of her clit before sliding smoothly over the head. She rocked forward again, then back, then forward, then back, finding surer and surer footing in her movements as Maud’s ridge massaged her clit over and over again. A shudder built, then released itself, causing her to roll her neck as it worked its way down her upper back. She paused, her clit and lips pressed firmly against Maud’s shaft as she held herself stiff, letting the shudder work itself through. She broke her kiss and exhaled nervously, the sound turning into an odd squeak. “Wow! I…” Ellie still had her eyes closed. She concentrated on how Maud felt on her. The warmth, the fullness, the thickness of her clit something that she was holding on to, hugging. “Wow.” Feeling underneath herself, she could see how good of a job she had done in glazing her. She smiled contentedly. She opened her eyes to look into Maud’s, big and beautiful and expanding across her vision. She then looked down the space between their two naked bodies, finding it cute how the top quarter of Maud’s clit was protruding from the light tangle of her bush, almost as if it were her own… Well, that’s something to file away for later. She looked back into Maud’s expressionless eyes. They were just so pretty. She kissed her deeply, focusing this time on how her lips felt against her lips. How her tongue felt against her tongue. How she kissed back with an unmuted passion. When she broke that kiss and looked into her eyes again, they were the same expressionless ones as before. Ellie sighed softly. “I feel close to you.” “I feel close to you, too. We’re touching each other very intimately.” Ellie could not argue with that. She was about to say something when Maud continued. “I know when I say things sometimes, it’s hard to tell that I’m being sincere. I want you to know that I really mean it. I really feel close to you.” Ellie’s heart melted at that. “I know, Maud.” She kissed her, and smiled, tangling the fingers of her supporting arm in her mane. “I know.” She kissed her deeply again as she inched herself forward even further, until she reached the ring encircling the head of Maud’s clit, itself ridged around with the spongy tissue that would expand taut when it was time for her to flare. Ellie broke her kiss and bit her lip as she remembered the delight she had felt in discovering that for the first time. Using her hand, she drew against herself with the tip of Maud’s clit, tracing circles that pressed down one lip, both, then the other, before massaging the nub of her own clit at the top. She dragged the edge of Maud’s clit across herself slowly, feeling every cell of that delightfully yielding gray surface. Circling, the sound and feeling of flesh sliding against slick flesh, circling. Wide ones at first, then tighter and tighter, zeroing in until… “Ack!” Ellie cried out in her best Cathy impression, before flopping over to the side very un-sexily. “Oh wow, sorry!” She tried to quickly recover, getting back up to assuage a concerned-looking Maud, who had sat up. Ellie felt touched that it was one of the rare times she had seen Maud’s eyelids form anything other than a flat semi-circle. “Sorry!” She found Maud’s clit again with her hand, and kissed the tip of her sweetly with her mouth. Said sweet kiss transformed into a lingering one as Ellie’s tongue rediscovered just how nice the soft, gray flesh of Maud’s clit felt against it, and a small moan escaped her lips before Ellie realized what she was doing and opened her eyes. She looked up at Maud, who was looking down at her with those same half-lidded eyes again. “Sorry!” Ellie said a third time after popping Maud out of her mouth. “I don’t think you did anything wrong.” Maud said. “Did I do anything wrong?” “No, no! I mean, we never talked about this! I, uh, I guess I got carried away.” Ellie bit her lip and looked away for a second. “I, uh, I don’t get penetrated?“ “Oh. I’m sorry I let it get so close.” “No, no! It’s not your fault! I, uh… Like I said, I got carried away. I just…” Ellie laughed at the ridiculousness of it. “I, uh… Back where I’m from I’m usually the one doing the penetrating, so I, uh, I’ve never been, and at this point I’m not even sure what the line between ‘won’t’ and ‘can’t’ is? I’m sorry, it’s hard to explain.” “You don’t have to.” Maud said. “I just want to know what you want to do, and what you don’t.” “I mean, that’s the thing! I…” Ellie laughed again. “I want to. But, uh, I might have to work my way up. And, uh…“ She held Maud’s hoof. “Wow. What a self-discovery to make after being zapped into magical horse world,” she muttered without realizing. “Oh.” Maud put two and two together quick, to Ellie’s dread. “If I were a unicorn—” “No!” It was Ellie’s turn to shove her hand in Maud’s muzzle. “No. You are perfect. You are Maud Pie.” She removed her hand to kiss her. “It’s nice like this, you know? Earth pony. Earth human.” Maud smiled. “Besides! I have my own fingers.” She considered them in front of her, then frowned at realizing how many she would need at once to prepare for Maud. “I could work my way up… Slowly…” She turned to Maud, and wrapped her arm around her, holding her close. “Is that something you’d want?” “I want to do the things you want to do.” “No, I mean…” Ellie had to stop herself again from laughing again at the ridiculousness of it. “Do you want to be inside me?” Maud’s cheeks tinged as she looked into Ellie’s eyes. “Yes.” A shiver ran pleasantly through Ellie. “Oof. Is it weird that I find that hot, even though I’m not even sure that I want to do it yet?” “I don’t think it’s weird.” Maud said. “I just like being close to you. It’s another way to be close.” Ellie chuckled. “And that’s all that has to mean, huh?” “Does it have to mean anything else?” “No.” Ellie smiled. “No, it doesn’t.” She kissed her deeply, slowly lowering Maud’s body back down to the bed as she did, her left arm wrapped around the back of her head. With her right, she caressed down her body with her fingertips until she found the length of her clit, and began to stroke her with her fingertips as well. She caught Maud’s moan in her mouth, then broke her kiss, and smiled. “Speaking of other ways to be close…” She lowered herself down Maud’s body until her face was in position. She kissed the tip of Maud’s clit, then sucked the first half-inch or so into her mouth, her lips opening wide to take in her girth. She began to massage her with her tongue, enjoying the tastes and textures of the surface of her clit-head, from top to bottom and all around her sides. Ellie delighted in the feeling of Maud stiffening in her hands, as she inched her face forward on her shaft. More of Maud filled her mouth, pushing her to loosen her jaw muscles and tongue as much as she could to take in more of her. More and more, until she felt the soft ridge of Maud’s clit against the soft palate at the back of her throat. She could only breathe through her nose now, every breath she took causing her to feel the sheer lack of space that was left in the cavity of her mouth. The sensation of being so filled-up was exhilarating. With her lips extended, she could just about feel the border of her medial ring. That there was so much more Maud to go… She closed her eyes, filled her lungs with air, and lurched forward. Maud’s clit filled more of her, pushing her way past her soft palate and properly into her throat. Ellie shallowly bobbed up and down, working Maud deeper into her body still. Past the point that seemed possible. Her diaphragm tentatively tried to expand, then found itself fighting against hard vacuum. Her airway was blocked. Her autonomic system woke, and began to jam down on its alert buttons, sending red-letter warning after red-letter warning to the conscious part of Ellie’s brain. The conscious part of Ellie’s brain was giddily laughing at this, happily signing off on said warnings. Yes. She agreed completely. The thing lodged in her throat was very important and she should pay a lot of attention to it. Yes. She thanked her autonomic system for also really being into Maud’s clit like that. Her brain then helpfully began to shrink the entire universe. The borders of the world available to her conscious mind contracted as she yeeted herself down Maslow’s hierarchy of needs, hit the ground floor, and kept digging. The only thing that existed in the universe was what was preventing her from breathing. The inches of flesh jamming her throat were the entire universe. Maud’s clit was the universe. The only thing that mattered. The only concept to exist. It was very hot. She felt the edges of her cognition slip away. Through the murkiness, she felt a disturbance. Maud was pulling herself out of her throat, the seal releasing itself with an internal pop. Her autopilot immediately gulped down a breath through her nose, and her world expanded again. Part of her wanted to protest, but felt weird about that, and meekly let Maud pull herself completely out of her mouth. She stretched out her jaw and gagged and gasped for air, and felt the tears that were streaming down her face for the first time. Maud’s clit was still in front of her, damp with her saliva. She felt an odd sense of achievement in just how far down her shaft the glistening had reached. A sense of disappointment at the length that remained untouched. She looked up at Maud through tear-rimmed eyes, who was sitting up again and looking down at her with more of that rare displayed concern, her eyeshadow no longer visible. “Ellie.” Maud said. “Please don’t choke yourself to death on me during sex.” Ellie laughed, fighting the urge to blurt something about how great of a way that would be to go. “Okay. But before the choking myself part, did my throat feel good?“ Maud reddened, and didn’t answer the question. “You made me worry.” “Oh, Maud.” Ellie raised herself up to kiss her, then wrap an arm around her neck. “I’m really sorry. I got carried away again. I, uh, I really need to control myself.” She kissed her again. “I’m sorry. It won’t happen again. I don’t want to make you worry. Just relax.” She guided Maud’s body back down onto the bed, then kissed her reassuringly a few more times, continuing to whisper gentle nothings at her until the concern on her face was replaced by a slight smile. “Just relax,” she said again, as she brought her face down Maud’s body once more. She massaged her hips and flanks reassuringly, looking up at her and smiling. “My throat did feel good though, right?” Maud blushed, and looked away, finally admitting it. “Yes.” Another shiver shook Ellie, and she instinctively reached down to begin massaging her clit. As she did so, she wrapped her lips around Maud’s clit again while wrapping her other hand around her shaft. Deliberately drooling out some excess, she began to use her extra spit as lube, but found that it did not seem to quite be enough. So she switched hands, contributing the slick that coated the fingers of her right hand to the mix, which was enough to begin to comfortably tug Maud up and down. She was better with her right hand anyway, because she is canonically right-handed. Bobbing her lips up and down in an opposing cadence with her hand, she began to vary the length and speed of her strokes and bobs, pausing at the ends before lusciously and lovingly stroking back to the middles. Maud’s soft moans were both feedback and delicious stimulus of its own, as Ellie began to stroke herself to them as well. Slowly, slowly, the moans built up, and Ellie controlled the burn rate on her end as well so as to not outpace the beautiful mare she was pleasuring. After some time, the moans turned into heavy breathing, and Ellie could feel a sense of accomplishment as she began to taste the lube that Maud’s clit coated herself with. She quickened her pace for the home stretch, and her eyelids fluttered as she felt that wonderful flare against her tongue, preceding the pumps of liquid that filled her mouth to the backdrop of that beautiful dulcet tone of Maud’s climax. Maud’s pleasure pumped and pumped, hot and salty and pungent, with just a hint of grassy undertone. Another preshock rippled through Ellie as she sucked up Maud’s last echo of a pump, then popped her out of her mouth and lovingly licked up the last droplet still clinging to her head by surface tension. She kept working herself as she extended her body to lie down next to Maud, leaning into the valley of the preshock. She focused on the sensations of her fingertips against her clit, the taste and texture of Maud’s cum sliding down her throat as she swallowed up her mouthful in tranches, the smell of saliva and sex, the sight. Maud’s beautiful face, dominated by the two pools of her closed eyelids. Her face flushed, serenely smiling as she continued to gently undulate and shake in pleasure. That smile. So gentle. So rare. So vulnerable. Those eyes. Opening up slowly. Looking into her own. So brilliant. So filled with soft affection. With love. Her back bent, driving her shoulders and hips into the surface of Maud’s bed as the first wave overtook her. Pleasure radiated from the core of her being, obliterating the internal divisions she felt in her structure as her muscles contracted. Then released, rounding her spine and her shoulders forward again. Then contracted, as a second wave hit. As she came down, Ellie realized that Maud was embracing her to her, holding the length of her naked body against her own. Ellie wrapped her arms around her, and held her close, contracting into her as they locked lips. As she felt the warmth of her skin through her coat, she imagined the surface of their bodies joined into a single, tranquil ocean, occasionally disturbed by the ripples set forth from a hidden sea mine. Those waves had done more than just pass through her. They left little pools of themselves embedded throughout her body, to burst and fill the rest of her with echoes of pleasure from a shoulder, or a spot on her neck, or a rib. She felt occasional squirms from Maud against her, as well, and tasted them against her body. Her burning interior settled into a pilot light, still burning, faintly. Warm and fuzzy, increasing the sensitivity of her touch, causing her to feel so close to the mare whose soft, warm body she was holding against her that it felt as if the core of their beings were joined. Looking into those shimmering turquoise eyes, reflecting that warm smile back at her, Ellie knew, despite the impossibility of knowing another’s qualia, that Maud was experiencing what she was, in all of its incommunicable depths and subtleties. Ellie was so very glad. Because there were only two things in the human experience that transcended the cold realm of the material and the unfeeling logic of evolution both: pure mathematics and the female orgasm. Ellie was so very glad she could share both with Maud today. They kissed, embraced, and held each other tight until the very last embers of their orgasms gave off the very last of their heat, and continued cuddling for a good while afterward as well. Life was pretty good, all things considered.
ConamingEllie closed her eyes as Maud kissed her. Slow and implacable. Building up the pressure like the force of one tectonic plate pushing against another until Ellie gave, her tongue subducting under Maud’s, her breath stolen from her lungs. Ellie took in a sharp breath as Maud let her go, her cheeks flushed. Maud’s face didn’t show a hint of emotion. Just that same half-lidded, imperturbable expression. As if she were an unstoppable wall of granite more than a mare. So hot. She wanted to melt into Maud’s forelegs then and there in surrender. But when Maud kissed her again, it was sweeter. Lighter. Her lips traced lightly with a tongue, the soft caress of a hoof on her burning cheek. A break in the kiss, then a resumption, as the hoof moved to the back of her neck and her upper back, rubbing her there gently. When Maud broke the kiss again, Ellie smiled. “Before we start, I wanted to ask you something.” “Oh, of course!” Ellie said. “Of course! Anything you want to know.” Though she secretly hoped she wouldn’t be asked too much about the human world. “I noticed you did the conaming yourself. But usually couples talk it out first. Is that how humans do things?“ “The… ‘conaming’?” Ellie was very much puzzled. “I don’t understand.” “The name you use for mine.” She pointed a hoof at her crotch. “’Clit’”. Ellie realized. “Oh. Oh! Yeah, I guess I didn’t ask you before starting to do that…” She grimaced. “Is that bad? I’m sorry.” “If you did something bad, I would tell you.” Maud said, and Ellie felt admonished. “It’s okay. I would have accepted it.” “But you shouldn’t have to ‘accept’ anything!” Ellie exclaimed. “It’s your body, it’s not about me. So if you prefer any of the other words…” “Other words?” Maud blinked. “Like ‘penis’?” “Yeah…” Ellie tried not to frown, as she hoped that wouldn’t be the case, but maybe thinking that was messed up. “I mean, is that what you prefer?” “No. It’s a formal, scientific word. It wouldn’t feel right here.” “I get that!” Ellie agreed, relieved. “So do you prefer one of the informal words, then?” Maud blinked. “We don’t really have informal words for our genitals.” “Oh, right!” Ellie had noticed that. No talk of “cocks” or “pussies” in Equestria, unless referring to the animals. It was really nice, actually. “That’s why couples do the conaming. They agree on the words to use for each other’s bodies. It’s considered an intimate thing.” “Huh…” Ellie set her jaw as she considered this. “Wow.” She blinked away tears. “That’s just really nice and adorable.” “You say that a lot about pony things.” “That’s because it’s true!” Ellie squeezed Maud’s cheek with a hand, distorting the lack of expression on her face. “A lot of things are nice and adorable here. Things that I wish humans did back in my world.” She sighed, and let go of Maud’s face, which bounced back to its expressionless default. “But I want to do this the pony way and not the human way. I want to talk it out. You said you wanted to ask me something?” “Yes.” Maud said. “‘Clit’ is short for ‘clitoris’, right?” “Yeah, that’s right!” “But that’s what you have, not me.” “I guess, like, scientifically…” Ellie conceded. “But I just personally like to expand the word to account for the homology.” “Homology?” Maud asked. “Yeah!” Ellie said. “It’s the noun form of the root adjective ‘homologous’, which comes from the Greek ‘homologos’. “’Homo’ for ‘same’, ‘logos’ for ‘mind’, thus ‘agreeing’.” Maud blinked. “Greek? Do you mean Pony Greek?” “Uh… sure?” “It sounds weird when you shorten it.” Ellie chuckled. “I guess! But yeah. Homology. It’s the similarity between different biological structures. My clit and yours are homologous. Well, technically my clit and the head of yours…” Ellie smirked. “But the rest of my vulva and the rest of your genitals, they’re both made of the same tissues, more or less. They were the exact same structure at some point in our fetal development, and they only turned out differently because a different chromosomal key was turned.“ “Really?” Maud asked in a way that was just as monotone as everything else she said, but clearly sarcastic. “Yeah, isn’t that neat?” “I was being sarcastic. I was pointing out that it wasn’t true.” “Really?” Ellie had been pretty sure of this fact, but she was not an expert in this field and Maud objected so definitively that it caused her to second-guess herself. “I could’ve sworn that’s how it worked…” “We’re different species.” Maud pointed out. “Our fetal developments were probably pretty divergent from the beginning.” “Oh, right… Yeah… That…” Ellie cringed. “It’s really weird how quickly I got used to the whole not-the-same-species thing…” She thought for a second and smiled, finding her footing. “But homology also applies across species too, you know!” She snuggled up closer to Maud. “I mean, it really doesn’t stop there! Our lips”—she pecked Maud on the lips—“our noses”—she touched noses with her—“our ears”—she touched one of Maud’s ears, which twitched at her adorably—“our eyes”—she stared into her eyes—”they’re all structured very similarly, aren’t they?” “Yes.” Maud said. “They’re homologous, too.” Ellie smiled. “I mean, we’re both mammals. So if you go far back up the evolutionary tree enough, all our parts were once the same. They just took different shapes.“ She took a forehoof in her hand, and felt the nail with the nail of one of her fingers. “It’s just nice, you know? Thinking of us as not so different, really. Thinking of your clit as being like mine, only bigger.” She glanced down, drinking in the view. “A lot bigger…” “It sounds like you’re into being the same as you.“ “Yeah!” Ellie agreed. “I mean, I’ve had this problem for a long time! Like, it’s hard for me to tell sometimes whether or not I’m attracted to someone or I want to be like them or both. To be honest, it makes me worry that my ideal partner is a clone of myself.“ She shook her head. “No, that would be a total disaster, as hot as it’d be. We’d just reinforce each other’s bad habits. An ideal partner would be someone who’s similar to me, but different enough to make me better.“ She smiled, suppressing a giggle at just how silly the word still felt to her. “Or somepony, I guess.” Maud looked at her, and smiled slightly. “We are pretty similar.” She looked down at herself, and Ellie looked down with her. “Clit.” Maud said. She touched herself with a hoof, which made Ellie more than a bit excited. “I like it.” “Oh, you’re not just saying that, right?” “No.” Maud said. “I like it. It’s short. It feels good to say.” She moved her hoof to Ellie’s crotch, which made her shudder. “It’s nice that we both have one.” She faced up to look Ellie in the eyes. “It’s pretty. Like you.” Ellie bit her lip, her cheeks brightening. “It’s not fair how good you are at that.” Maud did not respond to that, and just moved her hoof to Ellie’s side, gently stroking her. “There’s something else I was wondering.” Maud said. “Why you use ‘she’ and ‘her’ to describe my clit.” “Oh! Yeah…” Ellie brightened even more. “I mean, I do that for mine, too… It just feels more personable… And, uh…” Ellie darted her eyes. “I like it…” “Oh.” Maud looked at her. “Speaking of your clit. She felt really good on my tongue this morning.” Ellie turned a bright red and squeezed her thighs together at that. “You really do like that.” Maud cupped a hoof on her cheek to feel the heat radiating off of it. “Interesting.” “Yeah…” Ellie managed. “I think it’s an extension of, uh, how I like to be referred to in the third person, too, sometimes. I really have no idea why…” She groaned. “Maybe I have more in common with that homeless magician unicorn than I thought.“ “Trixie?” Maud asked, and Ellie nodded. “Not really. She’s a lot more passive in bed than you are. Not that that was a bad thing, the way she did it.” Ellie’s eyes widened at that. She studied Maud’s face, but it held the same expression as ever. “She was a terrible fieldhoof back at the rock farm. But I did her share of the work so my parents wouldn’t fire her. I liked having her around. She was almost as good in bed as she was bad at rock farming.” Ellie sighed. “I thought I was starting to get the hang of telling when you’re messing with me, but I guess I still have a lot to learn.” Maud winked. Ellie thought for a second, smiled devilishly, and began to stroke Maud’s chest. “You know, I can actually kind of picture it. Like, I really like how big her ego is and support her in her life choices 100% but… It does make imagining you two together way hotter.” “Really?” Maud said, monotone. “Yes.” Ellie practically salivated. “She’d come at you just so haughty and commanding at first. Like you were beneath her. But you’d be just like the rock that’s your cutie mark. An immovable object. Always there. Never cowering to her demands, never showing her anything other than kindness. She’d wear herself down on you, until she finally broke. She’d open herself up to you about why she keeps up this persona to keep everypony away. Be really emotionally vulnerable. Ugh.” Ellie licked her lips. “Emotional vulnerability is so hot.” “Yes.” Maud agreed. “All of that is exactly what would happen. Hypothetically.” Ellie studied Maud’s face. She still couldn’t tell. She smirked. “And oof, I can just picture it. Trixie on all fours on your bed.” A pretty normal thing for ponies to be, she just realized. “You on top, chest on her back, so you can feel her body as you move as your face blushes with effort. Trixie taking all of you, sweating and moaning and biting your sheets…” Maud’s expression was blank as always, but a slight tinge of red on her cheeks betrayed her true reaction. Of course, Ellie still couldn’t tell if Maud was remembering or imagining… Not that it mattered. The shoe was on the other foot now. Or other hoof. Whatever. She began to gently stroke the coat of Maud’s chest with her fingertips. “Say, I was thinking…” She smiled at her. “Maybe I could try something that’s probably a dumb and bad idea?” “An Ellie idea?” Maud asked, without skipping a beat. Ellie laughed. “Yeah! I just want to try it. Some math-based foreplay.” Maud did not respond, and just looked at Ellie with her trademark half-lidded expression. That was all she needed to say. “You know!” Ellie insisted. “Like the tectonic plate roleplay we did this morning, only my version of it. I mean, I didn’t really get half of the references you made then, but I still had fun.” “I was trying to keep things non-technical.” Maud said. “But I guess that’s fair.” “Oh, no!” Ellie took Maud’s hoof in her hand. “Sex shouldn’t be transactional or anything, I’m sorry I worded it that way. I mean, to be honest it’s just me trying out a dumb and bad idea I had based off a dumb math pun involving the word ‘homology’. Never mind.” “No.” Maud said. “Your ideas aren’t dumb and bad. I’m sorry I joked about that.” Ellie melted into a smile. Maud continued. “They’re weird. I like how weird you are. I want to try it.” Ellie kissed her hoof gratefully. “I want to say that you won’t regret it, but I can’t really promise that at all. I’m sorry.” “It’s okay.” Maud said. “But if it doesn’t work, can we go back to the Trixie thing?” “Okay, fine!” Ellie laughed. She kissed Maud, and sat up to begin.
Cohomology“So,” Ellie began, “what do you know about n-simplices?” “Nothing.” Maud said. “I’ve told you this already. I learned about space groups to understand crystal structures. That’s as far as I got in math.” “Great!” Ellie turned away from Maud to face her crotch. “Let’s start.” She took an index finger and used it to lightly tap Maud’s left nipple. Ignoring the reaction, she innocently continued. “The 0-simplex is the first one. The number corresponds to the local dimension. Being 0-dimensional, it’s just a point. We’ll label it ‘0’.” She leaned over to suck on the nipple she tapped for a second, breaking the suck with a lick. “Going up to the 1-simplex, you have to add another 0-simplex, so another point, in a way that’s ‘orthogonal’ or ‘perpendicular’ to the existing simplex if you want it to be nondegenerate. But everything’s orthogonal to a single point, so I can place the second point anywhere. Let’s just say, oh, here.” Ellie did the same suck then lick with Maud’s right nipple. “We’ll label this point ‘1’. Then we connect them with a 1-dimensional space, that is, a line. The direction is important. We’ll respect the obvious ordering on the vertex labels.“ She traced a line from point 0 to point 1 with her tongue, down the side of Maud’s left teat and up the right. “Now we want to place the third point in a roughly canonical way. Let’s start with the midpoint of the existing simplex.” She placed the point of her index finger between Maud’s teats. “Then let’s draw a perpendicular line.“ She did so, tracing a line down her abdomen until she hit the base of Maud’s clit. “Perfect. That we can label ‘2’. Then we fill in the two new 1-simplices.” She licked a line from Maud’s left nipple up to the base of her clit, and then did the same from her right nipple. She smiled as she felt Maud’s shudders and saw the proof of her excitement. “Then we fill in the 2-dimensional space between them.” Ellie caressed the area of Maud’s crotch that formed by the triangle of her teats and clit, then planted a kiss in the center. She placed a finger on the spot she kissed. “So that’s a 2-simplex, embedded in the 2-dimensional space of the surface of your sexy body. To go up again, we need to go perpendicular to it.” She traced a line upwards into the air above the aforementioned triangle. “We can label this ‘3’, and you can imagine the tetrahedron that gets filled in. That gets us up to a 3-simplex, embedded in the 3-dimensional space we’re so familiar with. But to go up again, you have to go ‘perpendicular’ from this 3-dimensional solid you’re in the middle of, which doesn’t make sense. So we have to go ‘up’ to 4-dimensional space to get the fifth vertex we need to make a 4-simplex. And so on, and so on. That way you have a whole family of basic shapes you can use to understand higher-dimensional geometries with. The n-simplices.“ She looked down at Maud. “Sorry, I couldn’t figure out how to make that part sexy. But I hope that it was satisfying conceptually.“ “It was.” Maud said in her monotone. “I like this lesson. I think I learned something.” Ellie smiled. “Yeah, I find that nipple play really helps with the retention. Unfortunately, it’s a very difficult methodology to scale up to the classroom level.” Maud looked at her without any expression in a way that meant rolling her eyes. Ellie laughed. “Okay, now on to singular homology groups.” “Oh.” Maud realized. “That wasn’t it?” “Yeah, sorry…” Ellie said apologetically. “It gets a lot worse from here.” A rare frown flashed across Maud’s face as Ellie continued. “Now, I’ve been using ‘n-simplex’ as shorthand for ‘continuous map of the n-simplex’, which is what I was drawing on your body all along. I mean, ‘drawing on’ is a pretty good intuition for the idea of a continuous map without getting technical. So here are two 2-simplices.” She drew a clockwise triangle from a point on Maud’s abdomen, to her left nipple, to her right, then back down. Then she drew another clockwise triangle, going from the base of her clit to her right nipple, then left, then back up. “Of course, the 2-simplices are the filled-in triangle! I only drew their oriented boundaries. Now, a singular 2-chain is any formal sum of 2-simplices, so these two triangles together is an example. But notice what happens when we consider their boundaries together! We have six edges between the two triangles, but this edge”—Ellie drew a line from Maud’s right nipple, across her teats to her left, then back—”is repeated, with the directions canceling out! So the boundary of this 2-chain is actually this.” She drew a diamond, starting from that point on Maud’s abdomen, brushing over her left nipple, touching the base of her clit, then brushing over her right nipple on the way back. “It’s a 1-chain! Four 1-simplices added together. But I need a 2-chain with no boundary.” “No boundary?” “Yeah!” Ellie barely paused. “So imagine the four sides of a tetrahedron, like the 3-simplex we considered earlier.” She re-drew its base, the clockwise triangle going from Maud’s right nipple, to left, to base of clit and back. “We have this 2-simplex at the base, then we add three more of them for the sides.” She drew three triangles, all with their apex hovering above Maud’s crotch, their bases going from left nipple to right, from right nipple to clit, then from clit to left nipple, respectively. “All twelve edges of these four triangles are canceled out by a counterpart going in the other direction! So these four triangles form a singular 2-chain with no boundary. A singular 2-cycle.” “Okay.” Maud said. “But then imagine that we were drawing these on the surface of a tetrahedral solid. Say, a rock! You like those.” “Rocks are very rarely tetrahedral.” Maud said. “It could really be any solid shape! We’re just ‘drawing’ a 3-simplex made out of rock.” Ellie rolled her eyes. “The point is, if we consider the rock as a topological space, the rock itself can be thought of as a 3-simplex, thus, a singular 3-chain, whose boundary is the 2-chain we were just talking about. So this singular 2-cycle is also a singular 2-boundary.” “You’re using the word ‘singular’ a lot.” Maud said. “So all cycles are boundaries?” “No, that’s the thing! Like, what if we imagined that 2-cycle as on the surface of a tetrahedral geode?” “A tetrahedral geode is even less likely than a tetrahedral rock.” Maud commented. Ellie ignored her. “Then we can’t consider the ‘inside’ to be a single 3-simplex, because there’s a hole in it!“ “Cavity.” Maud corrected. “Fine, cavity.” Ellie smiled. “So the surface of a geode is a 2-cycle that’s not a 2-boundary. So it represents a non-trivial homology class. An element of H_2, the second homology group.” Maud didn’t say anything in response. “You know, a hole!” Ellie laughed. “Actually, you’re right, ‘cavity’ is a better word for it. So you can think of H_2 as ‘counting’ three-dimensional cavities in a space, since each cavity can have a 2-cycle drawn around it that’s not a 2-boundary.” “That was a lot of work to talk about counting cavities.” Maud said. “Well, this was just the simplest possible example! Everything embedded in Euclidean 3-space.” Ellie shrugged. “But what I really wanted to talk about was cohomology groups.” “There’s more?” Maud’s voice was actually inflected with dread. Ellie felt really bad, but could not stop herself now, due to the sunk cost fallacy. “Yeah! I mean, you can add n-chains together, which means they form a group, C_n. So if you pick a coefficient group G, you can take the dual group Hom(C_n,G), calling the homomorphisms between them cochains, and the group of cochains C^n := Hom(C_n,G). This is an application of the contravariant functor Hom(-,G), which means it applies to the boundary maps \delta_*: C_* \rightarrow C_{*-1} as well, reversing their direction to form coboundary maps \delta^*: C^* \rightarrow C^{*+1}. We can analogously define dual versions of cycles and boundaries as well, that is, n-cochains in C^n are considered cocycles if they get mapped to zero in C^{n+1}, and coboundaries if they come from something in C^{n-1}. This way, by quotienting coboundaries from cocycles you get cohomology classes…“ Maud had clearly stopped listening long ago. “But imagine!” Ellie put a hand on Maud’s upper foreleg, forcing her to make eye contact. “Imagine, say, the fifth cohomology group of a six-dimensional oriented, closed manifold, M? Something governed by not merely the embeddings of a five-dimensional space into a sixth-dimensional one, but also by a layer of algebraic abstraction on top of that?” “No.” Maud said. “I don’t want to.” “I don’t, either! That’s a terrible thing to imagine!” “Or talk to your marefriend about.” “I agree,” Ellie said apologetically. “And I am very sorry. But what I really want to talk about is something called Poincaré duality.“ Ellie emphasized the uvular “r” to the point of parody. “You don’t have to say it like that. I don’t think even Prench ponies say it that way.” “I like being terrible, though.” Ellie grinned. “But here’s what’s wonderful. Poincaré duality says that H^5(M) is actually isomorphic to H_1(M)! Isn’t that amazing? I mean, H_1(M) is just the homology classes that count two-dimensional holes. That’s pretty simple. They’re just rings.” Ellie formed a circle with her thumb and middle finger. She then took the circle and inserted the tip of Maud’s nearly-flaccid clit into it, beginning to rub her up and down. She felt Maud’s spirits lift underneath her. “Can you imagine it? You start with something so arcane and difficult to explain even the definition of, living in a dimension beyond human intuition. There’s no beauty there in that realm. No appeal. Just cold mechanics. But then…” Ellie bent down to take the head of Maud’s clit into her mouth, running her tongue up and down her as she began to stiffen. She pulled back, observing the results of her work, and smiled. “Then it’s transformed into something elegant. Something that can sing to the visual cortex. Geometric intuition, built out of what was needed for our minds to understand the physical space around us. The incarnation of the abstract. Word made flesh.” She turned to look down at Maud. “What do you think?” she asked. “I think that I don’t want you to stop.” Maud said. “I also think that was very pretentious.” Ellie laughed, and kissed her. “You’re Poincaré duality, you know,” Ellie said, not pronouncing it terribly this time. She looked back down at her hand, and Maud’s stiffening clit. “You take something and you recontextualize it, because that’s what isomorphism is. The mechanics are the same, but it’s the names and the intuition that change. The feeling.“ Ellie sighed happily. “Something that I would otherwise see as having nothing to do with beauty, from a realm not my own, is suddenly made familiar. Understandable. Appealing. Beautiful. Things I never would have imagined I’d ever see the beauty in.” She drank in the sight for a few moments before turning around to look Maud in the eyes, smiling warmly. “But H_1(M) has nothing on the smell of your cum drying on my face.” Maud’s face reddened. Ellie grinned lecherously. “I don’t like you.” Maud said. “Something in my hand says otherwise,” Ellie sang, terribly and very off-key. “But don’t worry. I’m done.“ She bent over to kiss Maud on the lips. “Don’t worry. No more math.” She planted more soft, reassuring kisses on her muzzle and cheek, down to her neck. “Thank you for suffering through this for me.” “It wasn’t that bad.” Maud lied. Ellie smiled, and gazed into her eyes for a moment before kissing her again. “You really are so sweet, lying for me that way.” Maud did not object. “But don’t worry. No more math. Really.” Another reassuring kiss. “Just going to have sex with you now.” Maud smiled.
CoïtusEllie rose on her knees, stretching up to the height Maud would have been had she been standing up. Placing both shins on either side of Maud’s torso, Ellie straddled her belly, her knees on either side of Maud’s head. She noted with delight Maud’s muted surprise at just how long the human’s limbs were. Reaching underneath herself, Ellie found Maud’s erect clit with her hand, and slowly guided herself down until she was right where she wanted to be, her lower lips pressed against the base of Maud’s shaft. She concentrated on the feeling of Maud against her, the warmth of her flesh against hers. She gently pressed upwards on Maud with her fingers, and began to rock herself against the base of Maud’s clit. She sighed contentedly, then began to slide back and forth, spreading her slick up and down. Finding equilibrium, she closed her eyes to focus on the sensation of Maud’s shaft sliding against her. “Oh, wow, that feels nice!” Ellie bit her lip as she looked down at Maud’s face, which was as expressionless as always. “How does that feel?” “Soft. Not like a rock.” Maud said. Ellie could see a tinge of blush on her cheeks. “It feels good.” Laughing at that, Ellie bent over to kiss her, supporting herself with an elbow at the side of Maud’s head. Her lips met the mare’s, forming a second connection to complement the one they had below, incarnating a non-trivial class in the first homology group. Maud’s lips were so wonderfully soft. Ellie rocked her hips forward, until she could feel the ridge of Maud’s medial ring cross her clit. She then rocked back, feeling the ring press up deliciously against the base of her clit before sliding smoothly over the head. She rocked forward again, then back, then forward, then back, finding surer and surer footing in her movements as Maud’s ridge massaged her clit over and over again. A shudder built, then released itself, causing her to roll her neck as it worked its way down her upper back. She paused, her clit and lips pressed firmly against Maud’s shaft as she held herself stiff, letting the shudder work itself through. She broke her kiss and exhaled nervously, the sound turning into an odd squeak. “Wow! I…” Ellie still had her eyes closed. She concentrated on how Maud felt on her. The warmth, the fullness, the thickness of her clit something that she was holding on to, hugging. “Wow.” Feeling underneath herself, she could see how good of a job she had done in glazing her. She smiled contentedly. She opened her eyes to look into Maud’s, big and beautiful and expanding across her vision. She then looked down the space between their two naked bodies, finding it cute how the top quarter of Maud’s clit was protruding from the light tangle of her bush, almost as if it were her own… Well, that’s something to file away for later. She looked back into Maud’s expressionless eyes. They were just so pretty. She kissed her deeply, focusing this time on how her lips felt against her lips. How her tongue felt against her tongue. How she kissed back with an unmuted passion. When she broke that kiss and looked into her eyes again, they were the same expressionless ones as before. Ellie sighed softly. “I feel close to you.” “I feel close to you, too. We’re touching each other very intimately.” Ellie could not argue with that. She was about to say something when Maud continued. “I know when I say things sometimes, it’s hard to tell that I’m being sincere. I want you to know that I really mean it. I really feel close to you.” Ellie’s heart melted at that. “I know, Maud.” She kissed her, and smiled, tangling the fingers of her supporting arm in her mane. “I know.” She kissed her deeply again as she inched herself forward even further, until she reached the ring encircling the head of Maud’s clit, itself ridged around with the spongy tissue that would expand taut when it was time for her to flare. Ellie broke her kiss and bit her lip as she remembered the delight she had felt in discovering that for the first time. Using her hand, she drew against herself with the tip of Maud’s clit, tracing circles that pressed down one lip, both, then the other, before massaging the nub of her own clit at the top. She dragged the edge of Maud’s clit across herself slowly, feeling every cell of that delightfully yielding gray surface. Circling, the sound and feeling of flesh sliding against slick flesh, circling. Wide ones at first, then tighter and tighter, zeroing in until… “Ack!” Ellie cried out in her best Cathy impression, before flopping over to the side very un-sexily. “Oh wow, sorry!” She tried to quickly recover, getting back up to assuage a concerned-looking Maud, who had sat up. Ellie felt touched that it was one of the rare times she had seen Maud’s eyelids form anything other than a flat semi-circle. “Sorry!” She found Maud’s clit again with her hand, and kissed the tip of her sweetly with her mouth. Said sweet kiss transformed into a lingering one as Ellie’s tongue rediscovered just how nice the soft, gray flesh of Maud’s clit felt against it, and a small moan escaped her lips before Ellie realized what she was doing and opened her eyes. She looked up at Maud, who was looking down at her with those same half-lidded eyes again. “Sorry!” Ellie said a third time after popping Maud out of her mouth. “I don’t think you did anything wrong.” Maud said. “Did I do anything wrong?” “No, no! I mean, we never talked about this! I, uh, I guess I got carried away.” Ellie bit her lip and looked away for a second. “I, uh, I don’t get penetrated?“ “Oh. I’m sorry I let it get so close.” “No, no! It’s not your fault! I, uh… Like I said, I got carried away. I just…” Ellie laughed at the ridiculousness of it. “I, uh… Back where I’m from I’m usually the one doing the penetrating, so I, uh, I’ve never been, and at this point I’m not even sure what the line between ‘won’t’ and ‘can’t’ is? I’m sorry, it’s hard to explain.” “You don’t have to.” Maud said. “I just want to know what you want to do, and what you don’t.” “I mean, that’s the thing! I…” Ellie laughed again. “I want to. But, uh, I might have to work my way up. And, uh…“ She held Maud’s hoof. “Wow. What a self-discovery to make after being zapped into magical horse world,” she muttered without realizing. “Oh.” Maud put two and two together quick, to Ellie’s dread. “If I were a unicorn—” “No!” It was Ellie’s turn to shove her hand in Maud’s muzzle. “No. You are perfect. You are Maud Pie.” She removed her hand to kiss her. “It’s nice like this, you know? Earth pony. Earth human.” Maud smiled. “Besides! I have my own fingers.” She considered them in front of her, then frowned at realizing how many she would need at once to prepare for Maud. “I could work my way up… Slowly…” She turned to Maud, and wrapped her arm around her, holding her close. “Is that something you’d want?” “I want to do the things you want to do.” “No, I mean…” Ellie had to stop herself again from laughing again at the ridiculousness of it. “Do you want to be inside me?” Maud’s cheeks tinged as she looked into Ellie’s eyes. “Yes.” A shiver ran pleasantly through Ellie. “Oof. Is it weird that I find that hot, even though I’m not even sure that I want to do it yet?” “I don’t think it’s weird.” Maud said. “I just like being close to you. It’s another way to be close.” Ellie chuckled. “And that’s all that has to mean, huh?” “Does it have to mean anything else?” “No.” Ellie smiled. “No, it doesn’t.” She kissed her deeply, slowly lowering Maud’s body back down to the bed as she did, her left arm wrapped around the back of her head. With her right, she caressed down her body with her fingertips until she found the length of her clit, and began to stroke her with her fingertips as well. She caught Maud’s moan in her mouth, then broke her kiss, and smiled. “Speaking of other ways to be close…” She lowered herself down Maud’s body until her face was in position. She kissed the tip of Maud’s clit, then sucked the first half-inch or so into her mouth, her lips opening wide to take in her girth. She began to massage her with her tongue, enjoying the tastes and textures of the surface of her clit-head, from top to bottom and all around her sides. Ellie delighted in the feeling of Maud stiffening in her hands, as she inched her face forward on her shaft. More of Maud filled her mouth, pushing her to loosen her jaw muscles and tongue as much as she could to take in more of her. More and more, until she felt the soft ridge of Maud’s clit against the soft palate at the back of her throat. She could only breathe through her nose now, every breath she took causing her to feel the sheer lack of space that was left in the cavity of her mouth. The sensation of being so filled-up was exhilarating. With her lips extended, she could just about feel the border of her medial ring. That there was so much more Maud to go… She closed her eyes, filled her lungs with air, and lurched forward. Maud’s clit filled more of her, pushing her way past her soft palate and properly into her throat. Ellie shallowly bobbed up and down, working Maud deeper into her body still. Past the point that seemed possible. Her diaphragm tentatively tried to expand, then found itself fighting against hard vacuum. Her airway was blocked. Her autonomic system woke, and began to jam down on its alert buttons, sending red-letter warning after red-letter warning to the conscious part of Ellie’s brain. The conscious part of Ellie’s brain was giddily laughing at this, happily signing off on said warnings. Yes. She agreed completely. The thing lodged in her throat was very important and she should pay a lot of attention to it. Yes. She thanked her autonomic system for also really being into Maud’s clit like that. Her brain then helpfully began to shrink the entire universe. The borders of the world available to her conscious mind contracted as she yeeted herself down Maslow’s hierarchy of needs, hit the ground floor, and kept digging. The only thing that existed in the universe was what was preventing her from breathing. The inches of flesh jamming her throat were the entire universe. Maud’s clit was the universe. The only thing that mattered. The only concept to exist. It was very hot. She felt the edges of her cognition slip away. Through the murkiness, she felt a disturbance. Maud was pulling herself out of her throat, the seal releasing itself with an internal pop. Her autopilot immediately gulped down a breath through her nose, and her world expanded again. Part of her wanted to protest, but felt weird about that, and meekly let Maud pull herself completely out of her mouth. She stretched out her jaw and gagged and gasped for air, and felt the tears that were streaming down her face for the first time. Maud’s clit was still in front of her, damp with her saliva. She felt an odd sense of achievement in just how far down her shaft the glistening had reached. A sense of disappointment at the length that remained untouched. She looked up at Maud through tear-rimmed eyes, who was sitting up again and looking down at her with more of that rare displayed concern, her eyeshadow no longer visible. “Ellie.” Maud said. “Please don’t choke yourself to death on me during sex.” Ellie laughed, fighting the urge to blurt something about how great of a way that would be to go. “Okay. But before the choking myself part, did my throat feel good?“ Maud reddened, and didn’t answer the question. “You made me worry.” “Oh, Maud.” Ellie raised herself up to kiss her, then wrap an arm around her neck. “I’m really sorry. I got carried away again. I, uh, I really need to control myself.” She kissed her again. “I’m sorry. It won’t happen again. I don’t want to make you worry. Just relax.” She guided Maud’s body back down onto the bed, then kissed her reassuringly a few more times, continuing to whisper gentle nothings at her until the concern on her face was replaced by a slight smile. “Just relax,” she said again, as she brought her face down Maud’s body once more. She massaged her hips and flanks reassuringly, looking up at her and smiling. “My throat did feel good though, right?” Maud blushed, and looked away, finally admitting it. “Yes.” Another shiver shook Ellie, and she instinctively reached down to begin massaging her clit. As she did so, she wrapped her lips around Maud’s clit again while wrapping her other hand around her shaft. Deliberately drooling out some excess, she began to use her extra spit as lube, but found that it did not seem to quite be enough. So she switched hands, contributing the slick that coated the fingers of her right hand to the mix, which was enough to begin to comfortably tug Maud up and down. She was better with her right hand anyway, because she is canonically right-handed. Bobbing her lips up and down in an opposing cadence with her hand, she began to vary the length and speed of her strokes and bobs, pausing at the ends before lusciously and lovingly stroking back to the middles. Maud’s soft moans were both feedback and delicious stimulus of its own, as Ellie began to stroke herself to them as well. Slowly, slowly, the moans built up, and Ellie controlled the burn rate on her end as well so as to not outpace the beautiful mare she was pleasuring. After some time, the moans turned into heavy breathing, and Ellie could feel a sense of accomplishment as she began to taste the lube that Maud’s clit coated herself with. She quickened her pace for the home stretch, and her eyelids fluttered as she felt that wonderful flare against her tongue, preceding the pumps of liquid that filled her mouth to the backdrop of that beautiful dulcet tone of Maud’s climax. Maud’s pleasure pumped and pumped, hot and salty and pungent, with just a hint of grassy undertone. Another preshock rippled through Ellie as she sucked up Maud’s last echo of a pump, then popped her out of her mouth and lovingly licked up the last droplet still clinging to her head by surface tension. She kept working herself as she extended her body to lie down next to Maud, leaning into the valley of the preshock. She focused on the sensations of her fingertips against her clit, the taste and texture of Maud’s cum sliding down her throat as she swallowed up her mouthful in tranches, the smell of saliva and sex, the sight. Maud’s beautiful face, dominated by the two pools of her closed eyelids. Her face flushed, serenely smiling as she continued to gently undulate and shake in pleasure. That smile. So gentle. So rare. So vulnerable. Those eyes. Opening up slowly. Looking into her own. So brilliant. So filled with soft affection. With love. Her back bent, driving her shoulders and hips into the surface of Maud’s bed as the first wave overtook her. Pleasure radiated from the core of her being, obliterating the internal divisions she felt in her structure as her muscles contracted. Then released, rounding her spine and her shoulders forward again. Then contracted, as a second wave hit. As she came down, Ellie realized that Maud was embracing her to her, holding the length of her naked body against her own. Ellie wrapped her arms around her, and held her close, contracting into her as they locked lips. As she felt the warmth of her skin through her coat, she imagined the surface of their bodies joined into a single, tranquil ocean, occasionally disturbed by the ripples set forth from a hidden sea mine. Those waves had done more than just pass through her. They left little pools of themselves embedded throughout her body, to burst and fill the rest of her with echoes of pleasure from a shoulder, or a spot on her neck, or a rib. She felt occasional squirms from Maud against her, as well, and tasted them against her body. Her burning interior settled into a pilot light, still burning, faintly. Warm and fuzzy, increasing the sensitivity of her touch, causing her to feel so close to the mare whose soft, warm body she was holding against her that it felt as if the core of their beings were joined. Looking into those shimmering turquoise eyes, reflecting that warm smile back at her, Ellie knew, despite the impossibility of knowing another’s qualia, that Maud was experiencing what she was, in all of its incommunicable depths and subtleties. Ellie was so very glad. Because there were only two things in the human experience that transcended the cold realm of the material and the unfeeling logic of evolution both: pure mathematics and the female orgasm. Ellie was so very glad she could share both with Maud today. They kissed, embraced, and held each other tight until the very last embers of their orgasms gave off the very last of their heat, and continued cuddling for a good while afterward as well. Life was pretty good, all things considered.
