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American Dream Serialization (Early Chapters)
Introduction to Jim Chaffee's Studies in Mathematical Pornography by Maurice Stoker
Introduction to Jim Chaffee's Studies in Mathematical Pornography by Tom Bradley
Studies in Mathematical Pornography: American Dream Title Page by Jim Chaffee
Studies in Mathematical Pornography: Chapter 1 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 2 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 3 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 4 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 5 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 6 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 7 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 8 by Jim Chaffee
Studies in Mathematical Pornography: Chapter 9 by Jim Chaffee
01-01-2015
Modern Tragedy, or Parodies of Ourselves by Robert Castle
01-11-2014
Totally Enchanté, Dahling by Thor Garcia
01-04-2014
Hastini by Rudy Ravindra
The Satyricon of Petronius Arbiter Volume 5 Translation by W. C. Firebaugh
01-01-2014
Unexpected Pastures by Kim Farleigh
10-01-2013
Nonviolence by Jim Courter
The Satyricon of Petronius Arbiter Volume 4 Translation by W. C. Firebaugh
07-01-2013
The Poet Laureate of Greenville by Al Po
The Apocalypse of St. Cleo, Part VI by Thor Garcia
The Satyricon of Petronius Arbiter Volume 3 Translation by W. C. Firebaugh
04-01-2013
The Apocalypse of St. Cleo, Part V by Thor Garcia
The Apocalypse of St. Cleo, Part IV by Thor Garcia
The Satyricon of Petronius Arbiter Volume 2 Translation by W. C. Firebaugh
01-01-2013
The Apocalypse of St. Cleo, Part I by Thor Garcia
The Apocalypse of St. Cleo, Part II by Thor Garcia
The Apocalypse of St. Cleo, Part III by Thor Garcia
The Satyricon of Petronius Arbiter Volume 1 Translation by W. C. Firebaugh
10-01-2012
DADDY KNOWS WORST: Clown Cowers as Father Flounders! by Thor Garcia
RESURRECTON: Excerpt from Breakfast at Midnight by Louis Armand
Review of The Volcker Virus (Donald Strauss) by Kane X Faucher: Excerpt from the forthcoming Infinite Grey by Kane X Faucher
01-07-2012
Little Red Light by Suvi Mahonen and Luke Waldrip
TEXECUTION: Klown Konfab as Killer Kroaked! by Thor Garcia
Miranda's Poop by Jimmy Grist
Paul Fabulan by Kane X Faucher: Excerpt from the forthcoming Infinite Grey by Kane X Faucher
01-04-2012
Operation Scumbag by Thor Garcia
Take-Out Dick by Holly Day
Patience by Ward Webb
The Moon Hides Behind a Cloud by Barrie Darke
The Golden Limo of Slipback City by Ken Valenti
01-01-2012
Chapter from The Infinite Atrocity by Kane X. Faucher
Support the Troops By Giving Them Posthumous Boners by Tom Bradley
01-10-2011
When Good Pistols Do Bad Things by Kurt Mueller
Corporate Strategies by Bruce Douglas Reeves
The Dead Sea by Kim Farleigh
The Perfect Knot by Ernest Alanki
Girlish by Bob Bartholomew
01-07-2011
The Little Ganges by Joshua Willey
The Invisible World: René Magritte by Nick Bertelson
Honk for Jesus by Mitchell Waldman
01-04-2011
Red's Dead by Eli Richardson
The Memphis Showdown by Gabriel Ricard
Someday Man by John Grochalski
01-01-2011
I Was a Teenage Rent-a-Frankenstein by Tom Bradley
Only Love Can Break Your Heart by Fred Bubbers
10-01-2010
Believe in These Men by Adam Greenfield
The Magnus Effect by Robert Edward Sullivan
Performance Piece by Jim Chaffee
07-01-2010
Injustice for All by D. E. Fredd
The Polysyllogistic Curse by Gary J. Shipley
How It's Done by Anjoli Roy
Ghost Dance by Connor Caddigan
Two in a Van by Pavlo Kravchenko
04-01-2010
Uncreated Creatures by Connor Caddigan
Invisible by Anjoli Roy
One of Us by Sonia Ramos Rossi
Storyteller by Alan McCormick
01-01-2010
Idolatry by Robert Smith
P H I L E M A T O P H I L I A by Traci Chee
They Do! by Al Po
Full TEX Archive
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Studies in Mathematical Pornography: American Dream - 2

By Jim Chaffee

Chapter 2
a) Smooth Connexions

On the plane I blazed through Bishop and Crittenden (B&C), leapfrogging along the main results and examples of interest. It turned out to be a not-necessarily-proper subset of Kobayashi and Nomizu (K&N). No surprises, not in the sense of information anyway. Felt more concrete than K&N, maybe more examples or a different collection of examples developed in more detail. Both approaches got to Riemannian connections about the same time and both ended up in variational theory with the Morse index. K&N spent more time with Lie groups and transformations, giving a long section on Lie groups before entering fibre bundles, later devoting an entire chapter to transformations. Lie groups seemed more basic to their development of bundles. Both clumsily evaded the multilinear algebra underlying the tensor stuff. The prof who'd taught me multilinear algebra as an excursion through formal tensor constructions on modules had remarked that differential geometry was the study of properties that remain invariant under change of notation. Neither of these books presented anything to change my mind; I hoped to yet find an approach avoid the fuzzy index orgy by exploiting the algebra so I didn't need to figure it out for myself.

K&N seemed more like geometry: I felt the curvature. B&C read more like applied mathematics. Worse, B&C spelled the word connections "connexions."

My Dallas connection went slick as greased owl shit and I debarked in New Orleans to compare the difference between dry blast furnace hot and moist swampy hot, the miasma of bogs, decay and rot permeating New Orleans even as extreme summer hung potential in the Earth's tilt a couple months on the horizon.

I'd have preferred Red meet me, but his car had been wiped out in flooding outside his uptown apartment during one of those downpours where the pumps lose the battle for the outlying streets. The waters receded within hours but the uninsured clunker was a goner. He, however, made decent sums on the odd drug deal, with plenty of connections, and I needed extra scratch just now.

Instead there stood Lori at the gate, wearing her muted smile like her face wasn't quite in focus, her features conspiring to tone it all down. Not a looker; softly padded body and small tits flattened on a tubular trunk, she wore little girl or peasant blouses with tie tops that showed off what she did have, always without a bra and always in loosely fitting jeans to hide thick calves and ankles and accentuate a flat ass. Turned down mouth and round eyes with lashes like sunbeams seemed painted to enhance the little girl look though she never wore makeup; perhaps it was the contrast with her pale skin. Somehow she kept her thin goldilocks hanging like a spaniel's ears, curled on the ends sheep-like. But she understood the effect of those luscious curved lips stretched over an erect penis, those baby-blues gazing up at you in wonder; it had likely brought off many a shot in the mouth.

She handed me a joint when we hit the highway and remarked that Steve had told her my oral notices were posted all over the department. It didn't concern me. They were always open to the public, but no students attended and few faculty not in your own group or one of the groups surrounding members on your committee.

We headed uptown to a little shack that served cheap food and I got my favorite, a soft-shell crab poor-boy. It reminded me of a cartoon I'd seen in Mad Magazine when I was a kid, a pizza with everything on it, including a live octopus or an alien, not clear which, a guy's cavernous mouthful of looming teeth ready to engulf the whole mess. The crab played the alien, legs and claws sticking out the sides; I loved chomping through the creature's fried and battered body squirting juices and dripping mayonnaise and sauce. The only problem was the mess on my face, but Lori licked it off when I let her.

Afterward we parked at her apartment and caught the streetcar. There was no easy way to park in the French Quarter, and this being the start of the weekend we'd not find anything in Marigny either. Parking in Treme was out of the question, neither of us feeling up to being shot.

Lori rested her hand on my thigh, then held my hand, uncharacteristic sentimentalities, and I felt her mood as the streetcar rocked and swayed around the long curve from Carrollton Avenue past Tulane and Audubon Park. I kept quiet. I guessed it was Steve, still dragging his feet about dissolving the marriage, but from what he'd told me it was not his doing. Deana didn't want a divorce though she knew Steve and Lori were getting it on. It incensed Lori that Deana referred to her as "that little girl." Steve had been sick of Deana for a long time, but he hadn't wanted any hassles until he passed his orals. That done, he plunged ahead in ridding himself of her, but she wasn't passing easily from his life.

Around Napoleon Avenue Lori began the soulful stare. Past Louisiana Avenue I asked if she'd ever eaten at Commander's Palace, trying to get past it all; she ignored the question. I told her it was the favorite restaurant of the department's resident gourmet, Professor Momus. She snorted and said Steve called him a lush. Maybe he drank, I replied, but he sure as hell knew a lot of stuff, even if he'd stopped creating. His advisor had been a founding member of Bourbaki.

As we made the circle around the statue of Robert E Lee she told me Deanna had decided to give Steve the divorce and moved out, but that he didn't want to live together yet; he wanted to remember living alone.

Not knowing what the hell to say, I lamely muttered to give him some time, that he was nuts about her, some bullshit about which I knew nothing. Steve and I discussed math and dope, the only interests he seemed to have besides porn films. He'd never said a thing about Lori to me, and the only woman I'd seen him hit on was the young one staying with Red, tall and athletic with a hard body and straight-legged walk, no hips, a round ass, a decent set of tits on a long torso, close set eyes, slightly gapped front teeth and a hell of a ski nose. I'd once seen her around some of his visiting friends from out of town, sporting a pair of tiny shorts and a leather vest open in front with nothing under it until he whispered to her and she disappeared, reappearing in jeans and wearing a t-shirt under the vest.

It had turned dusk and the Quarter lit up and came alive up as we walked up Bourbon Street blocked off from motorized vehicles for the night, Lori firmly gripping my free hand, my old black grip in the other, the macadam street sloping from the bald center towards broken lines of sidewalk. The buildings crowded flush against the sidewalks and hawkers for the strip joints standing in the doorways incited imagination to encourage entrance as bored topless girls standing behind them discouraged, the few on stage gyrating listlessly. GIRLS had been flipped from BOYS in LIVE ____ ON STAGE at Little Darlings. Knots of men and a few couples, most holding plastic cups of beer, stood gawking into the darkened dives.

We made St. Ann and hit my place, 839 Bourbon, passed through the iron gate into the brick passageway leading out to the courtyard and climbed the rickety spiral stairway to the top, the third floor. The landlord didn't call out "Good evening, Mr. Bouchée" from his second floor apartment and the French doors were shuttered behind the plank storm door, so I guessed he was out or with his boyfriend or some other man. I thought of him as Scarlet O'Hara with a bushy mustache; he always referred to me as Mister Bouchée in an exaggerated drawl, lending the name Butcher a gay Southern Louisiana French pronunciation.

After a couple joints, Lori and I commenced our prowl at a locals bar she favored for the pinball machines. Before she'd gotten her high-paying corporate job she'd done part-time programming of pinball machines. A wizard at communicating with computers in their basic instructions, she now programmed PDP-11s for real-time control, freed up for full time work after flunking her written exams the previous term. She didn't care shit for mathematics and I wondered why she'd bothered in the first place, but she took all three of the damned four-hour exams, wasting three full days of her life even as she spent the nights with me carousing and screwing. She didn't bother to register for the second semester.

We avoided tourist places and I made certain we steered clear of the gay bars, not wanting anyone to get the wrong idea. It was my neighborhood and I felt at home in the omnipresent crowds, but my apartment rested in the heart of the gayest neighborhood in the South, on Bourbon Street between St. Ann and Dumaine. Next door to my place, once sharing a courtyard before a wall had been erected, the Washing Well Laundryteria, and across Dumaine from the Washing Well, Lafitte's in Exile, a hardcore bar with music blaring twenty-four hours a day, every day, where men performed sex acts on the balcony and I'd been told in the bathrooms. It wasn't uncommon to see men in leathers, sometimes wearing chaps with no pants, their bare butts hanging out.

The local atmosphere abetted my favored garb of work shoes, baggy trousers and loose fitting t-shirts. Once walking to my apartment I heard the words "Not bad" from behind me. One of his companions replied in nelly drag, "If he would just lose those awful khaki pants," and I thought, That's why I wear them, cocksucker. Steve refused to come to the Quarter to visit because the gallery on the balcony at Lafitte's in Exile always hooted and whistled at his tight jeans, cowboy shirt and boots. I explained my approach but he couldn't bring himself to dress like a janitor.

I repeatedly lost to Lori at pinball, so after several beers and shots she tired of the routine and dragged me off to a place packed with women, a lot of them dressed like bikers; I saw no other men in the joint. We sat at the bar and she watched, then sidled up to some of them and struck up conversations. She kept moving until she came back with one in tow, a short thing who made little Lori look tall: pale and skinny with long hairy arms and sticks for legs, brows like inky wooly worms and jet-black stringy hair hanging to her shoulders.

We moved to a table and the girl, named Milly or something like that, giggled and showed tiny teeth inside a tiny oval opening overwhelmed by a humongous beezer swerving to the right from a hump at mid slope.

I ordered beers and shots of bourbon and poured a shot in her beer. She stared at me as if myopic and unable to focus. The bridge of her nose seemed to perch far above her giant round black peepers, maybe mid forehead, and the peepers themselves were perched a little askew in a concave visage creased at the bridge of her nose like a paper dessert plate. I guessed she was drunk.

The boiler-makers didn't enhance her sobriety; hauling her up the winding stairwell would have been a major problem had she not been so slight. In the quasi-light of the apartment I saw clown red daubed on her cheeks and smeared around her mouth to give an impression of lips, lashes coated with a purple viscous substance beaded into drops, all of it strewn above a receding chin with a crease on the bottom. Her flattened face suggested an asymmetry with respect to eyes set low and wide apart far down on the nose, well below the bridge and off center, the left one slightly higher than the right which seemed a smidge farther from the centerline of the nose. She had lesser boobs than Lori, no ass at all and elongated legs encased in tight jeans.

We smoked a joint on the narrow gallery perched a high three-floors above Bourbon Street, accessed via the bedroom window that ran from the floor to the steeply pitched roof sloping from the garret's high ceiling. The window opened like French doors but the ceiling swooped so low all but infants and elves had to duck through.

The view of queer Bourbon Street from on high mesmerized Millie; she steadied herself with the flimsy wrought iron handrail along the edge of the narrow outcropping. Lori took advantage of the moment to stand behind her and fondle her chest where breasts might have been. Millie turned and kissed her on the mouth. Lori dragged her to the living room, promising nose-candy. We snorted the stuff I kept for guests and they engaged in serious tongue probing. Lori helped her get naked from the waist down, then went to her knees and buried her face between her legs. Millie moaned and randomly emitted hysterical laughs like a hyena. Lori steered the wobbly half-naked creature back to the bedroom.

Street noise grinding outside poured in the open window and Millie confronted the monstrous ceiling-high, gilt-framed mirror behind the bed, taking an unsteady step back from the reflection of the three of us.

"Where did you get that mirror?" she squealed, pealing off her blouse.

"Was here when I moved in. Landlord says it was put here by some washed up silent movie star, Lola Montes or something like that, someone I never heard of. I don't understand how they got it in here. Won't fit in that window and would be impossible to bring up the stairwell."

Lori whispered in my ear to shut the fuck up. Millie squealed "Far out" and Lori kissed her on the mouth, pulling her down on the bed, backing away from the drawn-out kiss to suck the girl's nipples.

Millie on her back, straight and flat as a little boy, her dense sprout of pitch-black pubic hair narrowing at the mons pubis to thread up the middle of her stomach and branch to tufts of black sprouts like anemone scattered around puffy nipples the color of moles standing alone on a chest with no hint of tits. I reached out and stroked one; it felt like an erect fingertip sprouting from a knot the size of a golf ball.

She said something that sounded like "I never done nothing like this before," and Lori said to me, "Can't you put your dick in her mouth?" before diving into the lush growth between her legs.

I tried to push my dick in Millie's mouth but she made a lot of noise and held me back with her hand against my groin before relenting to suck the head like a lollypop. I ejected a wad in her mouth and that seemed to upset her, but Lori cleaned her up with her tongue, kissing her and cooing some kind of odd noises in her ear until Millie calmed down at which time Lori attacked her cunt again. Millie heated up to moaning punctuated by the hyena laugh and Lori encouraged me to fuck her. I entered with restraint, the constricted aperture wet but tight; she protested I was too big until Lori shut her up by kissing her. Lori thumbed the clit above my penis and the hole relaxed, easing around my dick as Millie fell into a rhythmic ride that brought me gradually to another ejaculation.

I sat on the edge of the bed as they lay face to crotch, parasites sucking and slurping amidst moans and cries and snorts. Lori rolled onto her back with Millie on top, mouths leeching cunts. With her tongue, she lubricated Millie's asshole which she found buried in long, luxurious black growth that clamored vine-like up over her ass and along her spine. She motioned for me to fuck that hairy sphincter while the two of them performed sixty-nine. This time Millie thrashed like a fish out of water and flailed against me as I slid in. With concentrated thrusts she drove our rhythm, her bony ass butting my pelvis until I felt stoking behind my scrotum the pressure of building orgasm. She wriggled free from between us before I could explode, landing on her butt on the floor.

"I'm hungry," she ejaculated. "Any food here?"

"Some sardines in the cabinet," I said as the urge dissipated. "Not much else."

"Too fishy!" Millie squeaked and Lori laughed out loud.

"Bring that fucking thing over here," Lori said, grabbing me around my hips and pulling me so my erection poked at her face. She licked and slobbered the length of it while Millie muttered to herself words that sounded like "It's too big." Once Lori'd slathered it with spit she said, "Come on, pretty boy, fuck my face" and offered me her mouth. I set to trying to finesse my hard-on down her throat in a motion staggered by the slow push at the end when she slid out her tongue and locked her lips attempting to inch to the base. I lost interest in this game and pulled her up to a position where I could steady her head with my hands, stepping up the pace to periodic forcing, speeding as the pressure grew again until I let go with my dick buried as deeply as I could cram it, grunting with the spasms rocking my pelvis. Lori ingested without a hitch, inspiring a piercing "Wow!" from Millie.

I wanted to sleep, but Millie would have none of it. She begged for food. We smoked more dope and snorted some coke and then Lori and I escorted her to Molly's Irish Pub, a twenty-four hour place that catered to a mixed crowd of locals and savvy tourists. We must have been a sight, a threesome careening across the quarter, Lori and I supporting Millie upright.

In the brightness of Molly's, Millie turned out to be a horror. The pale complexion turned pasty, almost greenish in contrast to the ultra black of hair on her head and face. Smeared makeup mixed with dried bodily excretions didn't add to her appeal. Or maybe they did.

The kitchen was closed but there were sandwiches and Millie gobbled her way through a chicken salad dripping mayonnaise and washed it down with a mug of beer into which I'd dumped a shot of bourbon. As I chased shots with Guinness draft, Lori disappeared at the bar and returned with two nondescript guys from Australia. She must have clued them to what she had in mind, because they were all over Millie who seemed oblivious to everything but their "funny accents" which elicited her hyena laugh. Gibbering repeatedly about how pretty was their talk, Millie snuggled up against one of them while the other rubbed the nape of her neck. The five of us left together; at the door they peeled off for their hotel, sustaining Millie barely afoot between them.

Lori pulled my face down and kissed me on the mouth, exploring with her tongue. The earthy flavor mingled with the beer recalled for me where my dick had been before she had cleaned it so thoroughly; I started to pull back but she held me insistently.

"I like ass juice on dick," she said when she let go. "And I'm ready for a fuck now. I wanted to go with those two Aussies. They were cute. I was afraid you wouldn't have tagged along."

We trudged back across the quarter, now deserted in the lower blocks where tourists predominated. Most places shuttered already, even the tourist strip joints, and it would be desolate until we hit Bourbon and St. Ann where the gay crowd still yo-yoed between their twenty-four hour bars.

"Maybe you should have."

She snuggled up and took my arm in hers.

"Would you have come along?"

"I'm pretty tapped out. I need to sleep."

"I want some action before we sleep."

"May not be anything left."

"We'll find something."

"You might wish you'd gone with those two."

"I like doing two guys. Or three. Never done more than three together. But I like the idea."

"Pulling a train?"

"That. Or just all together."

"Cluster fuck. Gang bang. Orgies?"

"Not really. Like to, but Steve isn't into it."

"No?"

"No other guys. Just girls. I wanted to do a threesome with him and a guy and he wouldn't have it. Doesn't care if I do it, but he won't join."

"Makes sense."

"Why, are you that way?"

"I never really thought about it. I doubt it'd bother me if there weren't guy on guy stuff. Not into that."

"A lot of people think you're gay, living down here. You're the only person in the entire department who lives in the Quarter."

"I don't care. Let them think what they want."

"Would you have come with us tonight?"

"Probably if I weren't so fucking tired. I'm whipped."

We hit St. Ann and made our way to the apartment. Bourbon had been opened to traffic again and the stream of guys wandering my block was joined by cars cruising for hustlers, young men and boys standing on the corners from St. Ann to Esplanade.

Once inside the passageway, the heavy iron gate secured behind us, Lori pulled my face down for another kiss, then knelt and unzipped my pants and fellated me beside the gate. No one on the street noticed but the idea they might brought me to attention right away.

She stood. "Those fucking bricks are wet and hard," she said, and led me by my erection to the bench in the courtyard. She pulled off her jeans and climbed on top and stuffed my dick in her cunt, lowering herself gradually.

"See," saying another long kiss, "you can't help yourself."

"Sometimes it works on its own."

"Like autopilot."

"That chick was weird, don't you think? Ugly."

"You think she was ugly?"

"No tits, no ass."

"Did you see the hair? Her pubic hair was nicer than the hair on her head."

"Almost as long."

"Like silk. Soft as silk."

"Never seen such a hairy woman. Black hair on her stomach, her chest, her asshole. Her back."

"Her back too? And those eyebrows. And skinny arms covered with long black hair. Her legs too, if she didn't shave. And armpits. Legs and armpits full of coarse stubble."

"Really? Stubble?" I hadn't noticed the stubble. "I didn't get that close. She had tits like knobs with tubes on the end."

"Those dark hard knobs were the areola. Huge areolas, no boobs."

"Like a tarantula with those skinny extremities."

"Four legged spider. We ought to have called her spider woman."

"—"

"Don't stop," she said. "I need this; I deserve this."

"Why deserve?"

"You know how hard it is to get a chick from a gay bar to go home with a man and woman together?"

"No. That was a gay bar?"

"You didn't notice you were the only guy there?"

"No."

She hadn't let up dragging her cunt up and down my cock and I was wearing out supporting her. My right leg nagged at me with dull throbs.

"Let's go upstairs," I said. "I need to do this in bed."

She dismounted. "Listen," she said standing awash with moonlight in her white tennies, no pants, hands on hips, "Steve and I prowl for girls like that sometimes. But not lesbian bars. Usually places where I know some bi women go. We had luck only twice. Usually we do threesomes with women I already know."

"Interesting. Wonder how that happened?"

"I think she really wanted to hook up but not many takers. Maybe they knew her. She was alone, dikes all around her and no one talking to her. She's a submissive, I think."

"Should be popular?"

"Depends. There is some kind of code. Probably true for guys, too. I have friends tell me that effeminate men aren't respected."

I shrugged. "Nellies they call them."

"Anyway," Lori said, "I asked if she wanted to go to an apartment on Bourbon Street with my boyfriend and me and she said, 'I don't do guys.' Then she looked over at you and she couldn't stop staring. 'He's pretty,' she said. 'You sure he’s a boy?'"

"That's where that fucking 'pretty boy' you called me came from?"

"Yeah. She said, 'That pretty boy over there? He's just a big boy, isn't he?'"

"You tell her I was a killer?"

"Course not. I said you were a sweet guy. Gentle. I said she didn't have to do anything with you if she didn't want to, but I think she wanted to. Your white hair and blue eyes—"

"Not white. I'm a towhead."

"Looks white; not like in old-man-white. Not snow white. Blonde white. You look so harmless."

"Cute? Like the two Aussies?"

"Not cute. Sweet and pretty. You're a pretty boy. With a big dick."

"Really?"

"You must've been told that before. I thought she'd freak more when she met it."

"I heard it once or twice. A whore in Okinawa said I was too big, wouldn't let me fuck her. But I always took it as an excuse or just some kind of flattery. Like telling an ugly chick she has pretty eyes."

"It's true. You must have noticed around guys in locker rooms—"

"I don't notice other guy's equipment. Not something men do."

"Well, I have sampled more than a few and it's the biggest I've encountered."

"Your sample isn't that significant. Come on, let's go up…"

I started dragging her up the stairs, she carrying her pants, me with my bare erection drooling from the wet spot on the front of my khakis.

"I never thought of myself as looking harmless. Or sweet. Or cute."

She zipped around me and ran up to the top of the stairs.

"I will admit," she said as she waited for me on the solarium, "it is a trick for someone your size to look harmless. But you do. Maybe it’s the short hair. You look like a clean cut Republican dork."

I pondered this as I unlocked the yellow front door, a solid barrier built from long planks to cover the flimsy French doors. I pushed Lori through the living room to the bedroom, onto the bed, and took off my clothes.

"Wonder what's up with her right now," I said. "If she really meant she didn't do guys, she's got two of them probably fucking the shit out of her now. Probably using her like an old rag doll…"

"She might be puking by now. You pouring bourbon in her beer wasn't going to help much…"

"Not to mention that chicken salad. I couldn't eat that on so much booze. Just watching her made me wanna puke."

"Her eating habits were disgusting."

"You think she takes birth control?"

Lori laughed. "No. Now forget her," she said. "You're making me think you're more interested in her than me."

I undressed and climbed on the bed to perform my duty.

"Steve," she said lying on her stomach as I climbed aboard, "alternate between my ass and my pussy."

b) Parallel Displacement

I awoke removed from Lori and the sheets. I didn't remember finishing with her; probably I'd fallen asleep after she'd climbed on top.

She slept as I went about morning business, coffee, shit, shower, shave. By the time I came out of the bathroom she sat at the black lacquer table on the solarium nursing a steaming cup of instant coffee.

"Want a blow job before I clean up?" she asked.

"Good morning," I said.

"It looks cloudy," she said.

She worked at looking sad and serious while we traipsed through the quarter to Jackson Square for coffee and pastries at La Marquise. I wasn't up for her mood and didn't take the bait, sitting quietly probing for deficiencies in my grasp of Ito's construction of his stochastic integral. She gave up on me and left soon after, not even returning to the apartment for a final fuck. Just as well; I dragged around most of the day doing nothing, went out for a sandwich later, and turned in early Saturday night.

Sunday my head cleared and I worried about the upcoming exam Thursday afternoon. I had no interest in reading books, but after lining up several joints to help me along I skimmed some of the material on the reading list. Fortunately, all were short and to the point, and I skimmed McKean's Stochastic Integrals and Folland's Introduction to Partial Differential Equations, hitting the high spots with the intent of making certain I understood the big picture, some details of approach and how hypotheses tied to major proofs. No memorization, impossible with so much material anyway, but understanding enough to reproduce the highlights of essential arguments without fatal holes.

My advisor's papers were not an issue, since only he knew what was in them and he wasn't going to try to trip me up.

Lie groups loomed as the big worry. I needed to smoke a lot of dope to review that stuff again. Problem was, my advisor cared for no more than the local approach, local Lie groups and their associated Lie algebras with a view towards symmetries of PDEs. But Professor Karl Oberst, the big gun from the topological algebra group, would come after me, maybe, since I had of necessity taken his course in Lie algebras. With no interest in our point of view or problems, he nonetheless was an international authority and could not be left off my committee.

I'd absorbed the viewpoint from Kobayashi and Nomizu since I figured differential geometry would be the last approach anyone there would take. Tulane being small, the math department concentrated on one uniting area, groups, so that there were groups and semigroups and modules and group rings in all sorts of settings, algebraic, topological, analytical. But not geometric; no geometers on the faculty.

The topological algebra point of view would be topological groups and that hideous functorial approach; I would tiptoe through geometry instead, getting the topological stuff as a side show on the way to the Montgomery-Zippin theory with results on the compact-open topology for transformation groups. Then I'd hit the high points of connections, sketching an argument about parallel displacements to show that the holonomy group for a connection in a principle fibre bundle turned out to be a Lie group.

The problem was I hadn't tied any of it to the viewpoint of either my advisor or Oberst.

Assigned reading on Lie theory was a single chapter on Lie groups from a fat book on symmetry groups, a fat book I didn't care about since most of it was superfluous and the whole approach ugly. It relied on local theory in a neighborhood of the identity, the exponential map to the Lie algebra gained mostly via matrix groups, the so-called linear Lie groups and the classical groups. Heavy on computation, it stressed the Campbell-Baker-Hausdorff theorem, analytic groups more than c-infinity, expansions in terms of Lie brackets. It wouldn't satisfy Oberst. Still, differential equations and one-parameter groups were the natural tie to Kobayashi and Nomizu, adjoints and inner automorphisms raw meat for the group theorists.

I smoked a couple joints while plowing through the mimeographed notes from Oberst's course. The path would of necessity jump off Oberst's theme in the categorical world, the exponential map from the algebra to the group, and the differential equations would play their part since Lie algebra = tangent space for Lie group as manifold. After bringing up Ado's theorem regarding realizations of abstract Lie algebras as matrix Lie algebras, I could dance around the matrix exponential as a solution to the ordinary differential equation using the constant coefficients case as an example and then do Campbell-Baker-Hausdorff with the time-varying case by looking at the logarithm. The problem that there existed no constructive process to build the associated matrix algebra could be brushed off. The bigger problem would be if Oberst asked about a proof of Ado's theorem; I had no idea of how it went. It wasn't in my readings. It's essential to not come off as shallow, the major danger of bringing up outside shit.

The exponential, that would be the key. Oberst loved that baby as a functor.

I reviewed my advisors point of view with the one parameter groups, going into details on some of the preprints and works in progress on the list, more to do with symmetry groups and their application to partial differential equations. The other fat source, a machine translation of a book by a Russian named Ovsiannikov weighing about ten pounds, we both agreed I'd skip. The damned thing was impossible and no one but he had an inkling of its internals.

It sounded like a plan, but in the back of my head lingered doubts about how the geometric approach would interlock with the two other divergent approaches. The differential equation, tangent space = Lie algebra, and one parameter groups would hook up with our approach, but Obert's way left me cold.

I smoked another joint, by now quite fucked up, and went out to find some food. I settled on a kabob and egg roll with beer at the nearest Takee-Outee and wolfed it down on the way back.

I didn't remember falling asleep but I woke up standing on a machine-quaking mound of sand vibrating an endless stream of waves, each grain a wave colliding with other grains training in original form in new phase, a mountain of solitons turned liquid and I slipping inside and towards the pit, the maw. I sat up and reached for a grip on the sky, clammy with sweat and shaking.

"Son of a bitch."

Son of a bitch. Oberst would know all that fucking geometry. Who was I kidding? He would know all that shit. He might even know a lot of the PDE shit. What he wouldn't know, probably, was the stochastic processes and for sure the stochastic differential equations (SDEs) and stochastic integrals. I lit up a joint and shuffled off to make a cup of instant coffee before the shit-shower-shave routine.

Forgoing my leisurely buzzed ride uptown on the streetcar, I grabbed the Freret Street bus and got there in half the time, approaching the math building from behind. I'd left early enough to spend time in the library looking up a proof of Ado's theorem. Two hours before I had to teach, no seminars this week, and I considered skipping the only class I took this term. But I'd missed the previous week. Not polite, not politically correct. It was acceptable to not do shit, not pay any attention, but it was bad form to make it obvious.

The department occupied the top floor of the building, the second floor. The first floor was admin, and there was a basement, a scary idea in flood-prone New Orleans where they had to pump water from every hole they dug, though it only appeared to be underground from the back.

The library filled a large room at the end of a wide corridor paneled in dark wood that split the top of the massive stone building across its considerable width. Like all the reasonable libraries at Tulane, it belonged to the department and stayed off limits to undergraduates without permission from a professor. I had seen the university's main library, devoid of anything of much substance for undergraduate use but with a damned fine collection of ancient texts, including some Lewis Carroll.

Professor Momus waylaid me before I could make it. I could tell he was a bit lit up, but not like I was. He wanted to chat, saying he looked forward to my exam, that he loved the Malleus Maleficuram, had missed his historical period, would have been a masterful grand inquisitor.

Shit, he was coming to my orals; I prayed he'd be the only representative from the several complex variables group. Those fuckers knew differential geometry. The Denjoy integral, the only question on the analysis written exam I didn't know squat about, I'd been assured was his doing. He made certain it stayed on the syllabus though he was likely the only person in the department who knew shit about it. He was going to be there Thursday.

His visible words didn't make it to my ears, dying on the way, falling to the floor and forming waves, superpositioning their wiggly asses around my feet; I might fall through the suddenly insubstantial atomic wiggles mixing with his squirming words. I remembered he'd kept me one day talking about music and religion, about Bach and Shinto, and when I tuned in again he was going on about the St. Matthew's Passion, humming for Christ's sake. I didn't want to insult him but had to get away.

"I love Bach," I said, "but more the Mass in B Minor…"

"Ah, H-Moll-Messe," he said and began speaking German, clearing his throat and then making his point in a pedantic style at odds with his roly-poly shortness, sporting above his sport coat and tie the round bulbous nose made famous by W. C. Fields. Floating above it all I saw the ludicrous image of the two of us, a panic-stricken graduate student and a W. C. Fields mathematics near-genius discussing Bach and inquisitions. "One time at Yale I recall a performance in the…" and I tuned out again and when I came back it was "…in Dusseldorf at the university as a visiting faculty member for a year the famous…" and I dropped out again. He liked to tell about having Gian-Carlo Rota as a student at Yale, of Rota solving an unsolved problem he'd stuck on a final exam in topology.

One of the secretaries, Joelle, came out of the department office set off the middle of the long somber corridor and called him, "Professor Momus, can I have a minute please?" and he smiled, "See you Thursday afternoon," waddling off with a fat-man gait.

I ducked inside the library and picked up Jacobson's Lie Algebras. The statement of Ado's theorem read that every finite-dimensional Lie algebra with characteristic zero had a faithful finite-dimensional representation. I didn't know what the hell a faithful representation was. The index didn't have a listing for faithful, either alone or under representation, so I went to the basic definition for representation. It seemed it was a homomorphism into the linear algebra of homorphisms of a vector space, in other words into the general linear group. Faithful meant it was an isomorphism of the space, so a faithful representation was a one-to-one homomorphism into the general linear group, that is, a monomorphism.

All this intricate instrumentation came off as beating around the fucking bush, though I knew better. It pissed me off anyway. I wanted a joint, but would have to settle for a hash-laced cigarette before I taught my class. For now I had to buckle down and glean the idea of the proof.

Leading up to it four lemmas and a theorem. The set-up included a new piece of machinery, a universal enveloping algebra. I seemed to recall Oberst bringing them up in his class, but it hadn't stuck. It'd been in his notes and I'd skipped over it. Now here, waiting in ambush. Along with solvable ideals tied to a direct sum representation related to the kernel of an adjoint representation came some stuff about nilpotent ideals of finite co-dimension invariant under derivation. I'd not considered so damned much heavy equipment, but decided to push on.

Jacobson had a chapter on universal algebras in his book; they turned out to be nothing more than a giant algebraic object allowing the fill-in of a leg of the standard commutative diagram triangle. Big deal. Probably some kind of tensor algebra. But the chapter went on and on, leading into the Campbell-Hausdorff Theorem, leaving out old Baker whoever the hell he was. A new twist on this formula for the product of exponentials in the algebra, obtained by extending some free algebra generated by some finite set to an algebra of power series in the set. And suddenly section six:

Cohomology of Lie algebras. The standard complex

It was just too goddamn much. The big picture began to crumble into a heap of algebraic enginery far from the local one-parameter groups I needed for the PDEs, far from the geometry of manifolds and connections, deep in the Cartan-Eilenberg world of abstract nonsense I'd been warned would rear its ugly head in several complex variables with the famous Theorems A and B. But not here. I'd not expected it here, though I should have.

A mountain of debris rose up as I thumbed through, looking in vain for smoothness conditions and charts, finally coming upon derivations and the Killing form. More algebraic appliances.

I shut the book and left the library.

Outside in the humid New Orleans beginning of an afternoon I smoked a hashish-laced cigarette and let the whole thing deflate. Too late for all that shit. I needn't compound the plethora of heavy equipment with more machines, more isolated conceptual constructions of great beauty and complexity. It would be for better men than I to tie them together, find the cat walks or rope bridges linking one to the other. I hadn't time or inclination now, so close to the exam, to walk those dizzying heights, finding out who had already built the enveloping equipment, whether by rope or even more humongous mechanisms of the mind.

Humbled, my machination fell apart. If asked about proof of Ado's theorem, I'd shrug my shoulders and say I'd looked at one, but hadn't the machinery to grasp the essentials.

© Jim Chaffee 2011