# Archives

- 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

# Studies in Mathematical Pornography: American Dream - 6

### By Jim Chaffee

### Chapter 6

Strong Deformation Retract

Twisted knot: pillow-sheet-limbs. Groping leg. Nothing: not pain not sensation. Clammy flesh. Untangling from the knot, flailing toward the lit world. Grab the unresponsive appendage like a block of scarred wood. Rub for germs of pins and needles. Nothing. Dead meat.

Drag the dead thing over to the edge of the bed and claw my way up to sit.

Burned a big-ass hole in the sheet. Pick up and revive the roach; inhale a deep toke.

With some care I raised up on the almost tingling leg. No pain: no control. I leaned against the edge of the bed and scooted back-to-wall for support; walking brought it grudgingly alive. Pacing until it felt real; rolling another joint; fixing coffee. The morphine had stifled my appetite, but the dope revived it. I boiled water and cooked macaroni, added the packaged powdered cheese-food, ate the stuff, showered and headed for campus, catching the minibus in the quarter to Canal, then the streetcar.

On the way in, I wondered why I hadn't heard from Lori. Thought she'd've wished me luck.

I stopped in the office to thank Joelle. She sat head down studying some scrawl of symbols I assumed she'd been assigned to type.

I'd always thought her hair black, but in the glow from the window the black highlighted like darkly roasted coffee. Her long face and noble nose straight as an arrow deceived the expectation of round face centered with a button. Perhaps the visage pulled long as illusion from her dense hair falling beyond her shoulders and piling onto the desk.

She looked up with a melancholy expression, natural sadness in her absent sloe-eyed stare, her full lips in a pout. On seeing me her eyes lit up with transformation of pout to smile, petite dimples at mouth-ends accentuating cheeks bosomy by contrast with the swooping line of chin.

"You're here! I didn't expect you to make it." Concern passed over her features, smile swapped for a neutral mouth I found beckoning, sexy.

"I'm fine. I said it would pass. It always does. It just wore out and I didn't notice. I hope one day to build the muscles back so it can deal with more standing and walking. It seems I lost a lot of muscle."

"I was so worried. I almost called a doctor."

"There wouldn't have been anything they could do except what I did: take morphine and sleep. But I wanted to thank you again. It was a great kindness."

"It was the least I could do. You almost died for me."

I wanted to tell her not for her, or anyone else for that matter. Not for anything; just a fuck-up, a cosmic joke on me. But she wouldn't have gotten it and I didn't want to antagonize her. I hadn't noticed how beautiful I found her. Her brows arched like streaks of the same dark roasted coffee, chiseled above shallow orbs emanating from the apex of the bridge of that regal nose.

"You didn't have any trouble with it this morning?"

"None. Woke up perfectly normal. Almost forgot all about it."

She smiled again and I could have kissed her. A mistake.

"I need to get ready for class."

I walked out of the office without showing any of the numbness that still dogged my leg. Once in the hallway I leaned against the wall for support for a moment, then made it almost to the graduate student carrels when I heard a voice from the office just opposite the doorway.

"Butcher. Congratulations."

I wandered into the office inhabited by a faculty member not more than a couple years my senior, a low-dimensional topologist. His forte was algebraic topology, a necessity in any real university no matter how small. His counterparts were a point-set descendent of R. L. Moore, second generation, a recently graduated differential topologist from Stanford, and an aging algebraic topologist who had taken to the bottle and prayed for guidance in proving new theorems. It seems the older professor had not made any recent mistakes, though neither had he written a paper in years. His work on yet one more calculus text for the textbook mill was kind of a joke with the graduate students; perhaps here would emerge finally the great American calculus book. Spivak claimed to have written the great American differential geometry book. It was fat, I gave him that, unlike his midge of a book *Calculus on Manifolds.* I thought that the great American calculus book.

Anyway, Ron Goldman had taken a liking to me, though I had not yet decided what to make of him. Not so solemn as the rest of his group, he nonetheless took this stuff more seriously than it merited. A fault of many of the younger faculty, it seemed, and some of the graduate students as well. Grandly beautiful and totally irrelevant, all this stuff.

"You heard?"

"Of course. The word is out. They said you did well. Surprised them with your grasp of Lie groups and differential geometry. Said you were going on about connections."

"They didn't ask shit about Lie groups. I think Oberst sandbagged me. Probably felt sorry for me."

"I heard you were limping. Big to-do from the secretaries about having to help you home. No one else would do it."

"It wasn't necessary, really; I'd have gotten home. They felt like mothering me."

"So anyway it came out about your war wounds."

"I was surprised Joelle knew."

"Most of the faculty knew, with the exception of your advisor it seems."

"I don't know how. Very few people I talked to about it."

"Well, if it hadn't been for people like you, we wouldn't have had a war."

"If it hadn't been for people like me, we'd have won the war."

He laughed and I joined him, but his remark surprised me. The differential topologist seemed hostile, as did his two hippy grad students, but I hadn't expected such a remark from Goldman. Most knew better than to blame the people who went as if they'd had a real choice.

"Good answer."

"Well, it wasn't as if most of us had much choice other than jail."

"Canada."

"Too fucking cold for me."

"If you want to talk about Lie groups let me know. I used group actions to prove some theorems in low dimensional manifolds. People have said good things about the work. The theorems are getting used. And I know some algebraic topology, particularly homology. You will likely at some point need the Mayer-Vietoris sequence."

"I need to learn jet bundles. And cohomology, too."

"I can help with fibre bundles and cohomology but don't know anything about jet bundles. Never even heard of them."

"Well, chances are it will take some book learning. Can't always be avoided. But I will likely come to you for a run down of cohomology and other tools."

"If you have to get it from books, it probably won’t be useful."

My leg still not fully alive, I left his office walking carefully and crossed the hallway without betraying a limp. At my carrel, a cane leaned against the back of my chair.

"Anyone know who left this cane here?"

A head popped up above the rows of carrels, one of the crisp shiny-blonde German students.

"It was left by Professor Momus. He said you might find a use for it."

"Thanks, Klaus."

I trudged off down the hall to Momus's office using the cane for support. The door slightly ajar, I caught him napping at his desk. He jolted awake at my knock.

"Ah, come in Mr. Butcher. I wanted to congratulate you on a splendid performance yesterday. You comported yourself with exceptional aplomb."

His bulbous nose seemed especially red and porous today.

"You wanted me to have this?" I held up the cane, a long, thin stick with a gold knob.

I noticed that he seldom cleared his throat before making normal conversation, though he projected the speechifying tone no matter what.

"Yes. Consider it a token of my appreciation for your efforts on our behalf in Southeast Asia. I know there exist those here who would diminish those efforts, some even perhaps displaying hostility."

"Well, I must admit it is not what I consider to have been a worthy effort on the part of the US."

"I can appreciate that. I have not been a whole-hearted supporter either, but I also appreciate many didn't have a choice and some perhaps adventured out of duty."

"I'm surprised people knew about it. I didn't make much noise about it."

"No, but there are ways for all these things to become public knowledge. Besides which you are obviously not cut from the same cloth as the great majority of our candidates. You stand out, Mr. Butcher. There is a look in your eyes that does not go unnoticed. A faraway expression sometimes that seems to transport you to a polar region, as in a singularity."

"This is a beautiful cane. Light, just the right length. I think the round knob may take a bit of getting used to, though."

"Yes. A handle or crook would be more comfortable for extended leaning, but on the other hand it has simpler lines. Straight like a toothpick, I always think."

"Rather a large circumferential cross section for a toothpick, sir. Perhaps Godzilla? It has a nice heft. Could be a decent cudgel."

"Well" and here he cleared his throat "given its girth it would be a toothpick for a rather large creature. It is ebonized hickory, darkened the old-fashioned way with ammonia fumes. The rose gold cap bears the engraving of a mask. The ferrule is gold too and proclaims the inscription 'Rei Momo' which is Portuguese though I don't think it came from Brazil or Portugal. King Momus. Maybe someone thought it was Latin. But you know Momus of course."

He'd interrupted his speech several times to formally cough or clear his throat, his tone inflating as if lecturing.

"No, don't know except the Mardi Gras krewe called that, but I'm not aware of the meaning."

"The Greek god of ridicule. But more often than not a carping critic, one who is not constructive or pleasant."

"Critics are necessary."

"But unwelcome. There was an element of Momus with the chorus during your exam. But that is more common than you think. Particularly when the candidate is apt himself to ask many questions. And when the candidate is not likely to fail, in which case the chorus is more circumspect."

"No hard feelings, dude, but you failed."

"Yes, along those lines. There is seldom hooting at debacles."

"The date on here, 1856, is that legit?"

"It seems unlikely to have been backdated, unless there existed an interest in forging an antique. In any case, it is now a genuine antique."

"I imagine it’s worth money."

"I had it appraised at a bit more than one thousand dollars. But please don't sell it."

"Of course not, but I will be afraid to let it out of my sight. It’s more than twice my own net worth."

"It looks quite common. That is the beauty of it. Unless you realize the two bits of metal are gold. It has grayed some. A straight stick, with an apparent grain, hickory with certainty, but hickory canes are quite common. And it makes a lovely knobkerrie for whacking belligerents, though it may be a bit long and hard to grasp from the end."

I grabbed near the tip and swung as if braining a slew of combatants.

"It seems you have gained the knack already," he said.

"Let's say I've been in disagreements at close quarter before. My last job was dispensing misery and death. But I wasn't all that good at it really. That's the true story."

"It is rumored that you were highly decorated."

"The operative word is rumor. It isn't true at all. I was a trouble-maker. What the Marine Corps called a shit-bird. It seems to be my nature."

"So you were not decorated."

"Purple heart, twice. An award given for being in the wrong place at the wrong time. And I would just as soon any discussion out there regarding my war exploits die."

"I see that such speculations and innuendoes focus undue and unwanted attention on you from these pipsqueaks around here."

"Exactly. I am already a freak. I would be super freak, with no way to mitigate it, if someone thought I had won some gallantry medal. Any decorations for gallantry happened to someone else."

"I assume you accept my gift?"

"Certainly. It's a true honor. I can say nothing that would describe how I feel about this."

"It is my honor to bestow it upon you. I have taught at some of the finest universities in the world and never have I met such a character."

"Thanks. I hope I can live up to your words."

"You already have. With that, let me change the subject. What have you been reading for geometry? It seems you moved far beyond what was on your list."

"Kobayashi and Nomizu. Through the first two chapters of the second volume. I find it slipping away now. Can't seem to tie it to anything."

"I recall you wrote well on multilinear algebra on the algebra qualifying examination. You displayed a firm grasp of the basics of modules, tensor products, and alternating algebras."

"I liked the multilinear algebra course. We did it all over modules. I also took both semesters of the advanced module course Bolyai gave last term."

"You are an analyst. Go to the book by Postnikov, *Variational Theory of Geodesics.* He utilizes multilinear algebra to determine tensorial properties without dragging the reader through the orgy of indices. He also contrasts the global and the local properties while concentrating on analysis to prove the theorems. It concludes with a thorough discussion of Morse theory and includes a technique of Bott's."

"I hate reading books." I decided not to ask him who was Bott.

"I must admit that I love them. But I am unusual in that regard here. There are not many of us who like to read as much."

"I like that math's transmitted mostly orally. And papers are always short. That is a good thing."

"Of course, mathematics is largely an oral art form. A form of conceptual art, really. The innovative insight and ingenious argument. Literary form plays a small part really," and with this throat clearing I realized he was set to deliver a lecture, his formal tone rising to new heights, "except for the terse exposition presented often without helpful guide posts; it's rather the directness of expression and the inroads and explanations of one area via another, as with J. Frank Adams and the relationship between non-vanishing vector fields and division algebras, extending the classical theorem of Frobenius, for example. To explain some geometry with algebra or vice-versa, or to see much broader swathes of the mathematical landscape, as with the interplay in several complex variables of algebraic geometry and function theory…"

"Or between partial differential equations and probability." I had began backing towards the door; once more he cleared his throat.

"One often confronts the beauty when the mystery falls away, as when seemingly eccentric behavior in one dimension becomes clear with the structure of higher dimensional complex manifolds. You are aware that there is a relationship between martingales and non-probabilistic analysis, as with potential theory or the recent work of people like Fefferman and Burkholder relating functions of bounded mean oscillation and H-pee spaces with martingales. It seems there is excitement regarding these new results."

"I've heard the names but no one here is working with it. Except for the relationship to PDEs, which I discussed yesterday."

"Ah yes, a lovely explication of the Dirichlet problem using Brownian motion. You are aware this goes back to Kakutani?"

"No. Actually never heard of him."

I had reached the doorway, ready to duck out.

"Ahem. I knew him at Yale, of course—"

"I really have to prepare for class. I teach a class—"

He cleared his throat yet again. I worried I might have missed the bell.

"This book by Postnikov is a small book, really. More like a paper. He writes as if talking, without a lot of verbiage. And also without a lot of symbols. It is as if he is at the board. I saw how you present your material. You say it and write very little. He also works like this. Try it."

"Does he do cohomology?"

"No, but there are a plethora of viewpoints of cohomology represented at your disposal. Mine of course emanates from algebraic topology and algebraic geometry as used in several complex variables. The topology group has a slightly different viewpoint. You have an ally in that group."

I didn't mention that ally had just accused me of being a war-monger.

The conversation had played out though Momus displayed his usual lack of enthusiasm for disengagement. I took my opportunity and prattled again about needing to get to class, a true statement, thanked him profusely once more for the gift and extricated myself. His voice followed me, admonishing more careful board skills in my expositions. Fuck that, I decided as I headed away.

I practiced ambling to class, swiveling my cane with a flourish as I entered the room. I leaned into it and scoped out the faces. The cheerleader up front smiled and shook her head like I was a certifiable loony. Her breasts strained against their sleek container.

In back sat my dumpy fan. "Miss Cone, I missed you last time."

She blushed and smiled at me. "I was unavoidably detained."

I knew exactly why. "If you need a fill-in, let me know."

I launched into a rambling excursion regarding the statistical properties of the sample mean as an estimator for the expected value of a distribution, driving mercilessly through the distributional properties and ending with the example of sampling a normal distribution. I showed that the variance of the mean went to zero as the size increased to infinity. I used the cane as intimidating pointer and leaning stick.

The cheerleader frowned and shook her blonde head. After class she cornered me. "How can a statistic be a statistic?"

"Well," I said, "two different uses of the word. Consider each sample as a draw from a normal distribution. The more draws you make the more you know about the shape of the distribution. And since they are drawn at random, they are also distributed normally, but the more of them you draw the less uncertain you are about the shape. That is the variance going to zero. I suggest you do those exercises I assigned. They are about sampling with and without replacement from urns filled with balls. Pay attention to the distribution of the samples. That will help get the idea. The rest will follow from what we studied about sums of random variables. And remember sums of independent normal variables are normal. If you still don't get it, come to office hours."

Behind her stood Miss Cone. "Did you mean what you said about filling me in?"

"Of course. Come to office hours and I'll give you what you need."

"Thanks." We walked out together and she left me where I ran into Steve at the foot of the steps in front of the mathematics building. Straight and lean wearing cowboy boots and long sleeved shirt, long legs embedded within a pair of denim stovepipes that slouched behind the knees making them appear bandy, he tilted his head back dripping Visine into each eye, sure sign he'd just come from home fully loaded.

"Damn, Steve, you look like you might bleed to death through those roadmaps you call eyes."

He shrugged. "Well, it's good shit. Second round of drops."

"Want a cigarette?" I asked, pulling the case of Perique hash-laced specials from my pants pocket.

"Too strong. Can't cut it."

"Laced with good hash," I said.

"Wish you'd put that stuff in something smokable." But he stood near while I smoked it down. Neither of us brought up Lori.

"Heard you passed," he said.

"Yep. Got a present from Momus," holding up the cane.

"That old drunk."

"Maybe so, but he knows a lot of shit. He's a smart guy."

"He's finished. Just taking up a chair. Ought to retire."

I shrugged and we made our way up to the department. I stopped by my advisor's office.

"Good job yesterday," he said. "It seems your leg is better, too."

"Its fine. Momus gave me this and it is helpful when I am standing. I used it as pointer-intimidator in my class."

He seemed to relish the image, chuckling shy acknowledgement.

"I want you to focus now on the conversation laws."

"Sure, but we're doing it in class."

"Yes, but maybe more computationally. See if there is something we can do along those lines. Maybe with a computer."

"Well, I don't know shit about computers. Never worked with one."

"I understand MACSYMA isn't hard to learn."

"I prefer to concentrate on the geometric aspects. This variational stuff and Noether's theorem seem to point to some interesting connections between the symmetries and conserved quantities. No one has done a lot of with the differential geometric aspects of diffusion processes on manifolds, and that is a natural place to look at conserved quantities. I think there is something beneath all this tied to the quadratic variation of these processes. And people keep looking at the Laplacian on manifolds. Let me do some reading and thinking and discuss what I have come up with in a couple weeks. Is that acceptable?"

"Okay, but just don't get off on too deep a tangent. "

He referred to the legendary graduate student in the department who sat in classes correcting the lectures while taking notes. About to run out of time, his long tether stretched by years as a graduate student without a viable thesis. Knowing a lot of stuff wasn't the end goal.

"Don't worry. I have an intuition. If it doesn't play out, I'll drop it."

Before class I went to the library and found Postnikov. Two hundred pages of large type, including the index. Read breezily, like Momus said, almost like talking at a board.

A phone message at my carrel from Gudrun Ball reminded me of the party Saturday. I guessed I wasn't going with Bobbi.

I sat out office hours in my carrel without a single visitor. To date, there'd been no visitors. I got lost in Postnikov and didn't notice the time.

My advisor had already started his lecture as I entered the room, moving on from Noether's Theorem with some discussion of symmetry algebras of self-adjoint operators before plowing ahead with Hamiltonian vector fields and a bit of geometry with a definition of the Poisson bracket of one-forms and a proof it was exact. He wrote a slug of problems on the board and promised for next class the proof of another version of Noether's theorem, this time for two-forms on even dimensional manifolds related somehow to one-forms. What he wrote on the board didn't make sense to me at all, but I figured he'd start there next time so it didn't matter.

I got the hell out as soon as he seemed finished, grabbing my bag and heading for the gym.

© Jim Chaffee 2011