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09-01-2012
The Gospel of Wealth: Towards a New Generation of American Consumership By Jim Chaffee
08-01-2011
Rick Perry leads Baal worshippers in prayer meeting By Pig Bodine M.Sc., Ph.D., BM2, BEM, MAD, MDMA
02-01-2011
A Film Too Far: The Battle of the Strait of Hormuz By Jim Chaffee
08-01-2010
Maurice Stoker quasireviews The Vicious Circulation of Dr. Catastrophe: A Polemical Ensemble by Kane X. Faucher By Maurice Stoker
06-01-2010
Boozer Allan Hamilton Justifies the Tea Party By Boozer Allan Hamilton
04-15-2010
Keith Olbermann Freaks Out Pig Bodine By Pig Bodine
06-15-2009
Saving California: Secession and the Reagan Scheme By Pig Bodine
05-15-2009
Maurice Stoker on Tom Bradley's Even the Dog Won't Touch Me By Maurice Stoker
12-15-2008
Two Glad Tidings from The Marshall By Marshall Smith
11-01-2008
Sarah Palin's Party of God By Maurice Stoker
09-15-2008
Double-Ended Dildos Manufactured at Cosmodrome By Kane X. Faucher
07-15-2008
At the Airport By Tom Bradley
05-01-2008
Building the Perfect Weapon By Thomas Sullivan
04-01-2008
CNBC Wins Pequod Institute Award for Excellence in High School Journalism By Pig Bodine, M.Sc., Ph.D., BM2, BEM, MAD, MDMA
03-01-2008
Pig Bodine's Funky Financial Cooze Network Topological Finance for Aging Bald Dudes By Pig Bodine, M.Sc., Ph.D., BM2, BEM, MAD, MDMA
12-01-2007
Un Mensaje Navideño del Director General Por Sandra Ramos Rossi
Christmas Parades are a Deadly Derangement of Culture and other Seasonal Asides by Kane X. Faucher
11-01-2007
Euphotan, Protoplasmic Flash, and their Properties by Nail, with commentary by Chevy the Scientist
10-01-2007
Suggested reading, Universitatis Merdalina Literature 734.5, Advanced Topics in Mathematical Literature: Pseudo-British/American/Pidgin English Literature, Tensor Products of Novels and Poetry for Quasi-Conformal Plagiarism in Modern Genre and its Relationship to Sexual Identity and Morphisms by Maurice Stoker
08-01-2007
The Unexamined Life in Hell: Peregrinations Across The Diagnosis by Alan Lightman by Maurice Stoker
06-01-2007
Presidential Politics in the Year of the Toad by Boozer Allan Hamilton Ph.D.
04-01-2007
An Eleventh Tonkin Scenario by Donald Dickerson
03-01-2007
The Second Annual Howard Littlefield Boosterism Award for Economic Forecasting Awarded to Boozer Allan Hamilton by Pig Bodine, M.Sc., Ph.D., BM2, BEM, MAD, MDMA
12-01-2006
Maurice Stoker On Writing a Prize Winning Best Seller by Maurice Stoker
11-01-2006
¿Study says lack of talent? by Pig Bodine M.S., Ph.D., BM2, BEM, MAD, MDMA
08-01-2006
US Cracks International Terrorist Ring by Maurice Stoker
06-01-2006
Pig Bodine Solves the US Immigration and Education Dilemmas in One Blow by Pig Bodine M.S., Ph.D., BM2, BEM, MAD, MDMA
05-01-2006
Maurice Stoker Anent Two Errors in Thomas Pynchon’s Mason and Dixon by Maurice Stoker
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Maurice Stoker Anent Two Errors in Thomas Pynchon’s Mason and Dixon - 3

Part III Cutting off Your Nose to Linearize Your Stochastic Dynamical System

boat on pond

The perceived complexity of Mr. Pynchon’s work is exacerbated by a glaring oversight apparent when reading exegeses of his novels like Ophelia Legg’s Pynchon for Pedestrians. Miss Legg, as all the other exegetes, misses the obvious fact that Mr. Pynchon linearizes. More engineer than mathematician, and though there be much ado about nonlinearity in his work, like all engineers he loathes nonlinearity and attempts to linearize it away. Of course, were he to express the gory higher-order effects his work would be clearer but harder to understand, more so as the neglected second-order terms arising from the stochastic dynamics be not so easily rid of. Like the engineer who believes the extended Kalman filter to be optimal, an illusion since linearization about prior estimates requires the nonlinear second-order terms arising from Ito’s lemma appear as the neglected gradient of the gain iterating into an overly optimistic propagated covariance feeding back into the new gain ad infinitum, so the too happy view of the world presented the reader by Pynchon is not representative of the world in which the reader finds him- (or her-) self immersed. This be rather like the vision of happy Iraqis greeting US troops as liberators with flowers instead of blowing them and everyone else in sight to smithereens; in fact more like insisting that the Iraqis do love the US troops and the mayhem and carnage are nothing more than normal adjuncts to Democracy. The missing second-order terms in Mr. Pynchon’s expansion are essential, and like the Ghost in the Machine haunt the reader, akin to claiming terms to be tensorial when in fact they are neither covariant nor contravariant. Ignoring second–order terms doesn’t make them vanish, flattening a globally bumpy surface rather by lopping than smoothing. Moreover, Pynchon linearizes about a nominal trajectory skirting the edge of stability, passing betwixt nonlinear protuberances and crevasses alike, giving the reader that characteristic sense of impending doom, of danger and dissociation and alienation.

Mr. Pynchon needs to learn that One cannot force tensorial transformation by ignoring second-order terms, tensors arising from more indirect connections upon the bundles like covariant differentiation. Obscurity compounds directly from this blissful ignoring of second-order effects. Tensor products live in a number of settings, including the tortured tensor products of Hilbert spaces, and One ignores noncommutative random variables, particularly in free harmonic analysis, at peril.

wild water buffalo

As over-simplistic example, consider that perhaps cabin is stochastic, in fact standard Brownian motion (BM), in which case integral cabin dcabin would become cabin squared over two minus t over two: might this imply that integral one over cabin dcabin be log cabin minus t over two, that is, half a crumpet? (Left to the reader as an exercise, with the hint to use Ito’s lemma for log b sub t, b standard BM, and of course pay attention to the quadratic variation: remember BM not be of quadratic variation in any interval and so leaves this ghostly second-order trail of undying wiggles. The answer is of course no, but the instructive D---l is in the details.)

So Mason and Dixon, newly finished with an adventure among the Dutch of South Africa, find themselves in the New World immersed in nothing if not second-order effects, largely ignored by Pynchon. For example, the loony religious immigrants founding the nation, besides being murderous real-estate hustlers on the take, are spiritual refugees from the Thirty Years War which, though seemingly settled a century prior, lingers with the suspicions of Jesuit plots and other paranoid and not-so-paranoid possible delusions (in fact migrating from pornographic comic books to the camp followers of Mason and Dixon, sort of an M. C. Escher meets Hogarth meets Guido Crepax (see Chapter Fifty-Three)), but what is shown are but first-order effects. T’is the second-order effects that drive the nation as we find it today, best expressed with the superstitious sects’ occult prayer, left over from prior religious wars: Lord, deliver me from other Christians.

Part IV Epsilonics Meets GPS

GPS marker on hill 38

Howbeit anticipating the second error the setup of context and connection needs be given, the spatiotemporal Kabala wending its way through the sequence of odd Pynchon novels engraved upon the underlying theory of this work. Ineluctable facts are horometry, positioning, the heavens and bad Feng Shui leading, One supposes, to Civil War. My kingdom for a rubidium oscillator!

GPS marker on hill 38

To get directly to the point (please don’t run into me), the second problem is the anachronism expressed by Ethelmer, DePugh and perhaps even Cherrycoke himself. This temporal error cannot but be intentional, as for a fact Everyone knows that Mr. Pynchon has read Judith Grabiner’s The Origins of Cauchy’s Rigorous Calculus and so knows that the bemoaned epsilonics (Cauchy’s abbreviation for erreur, his error estimates around the damnable ghosts of departed quantities, so much like Pynchon’s overlooked second-order terms) are not yet about in 1786, in fact not making their way into mathematical discourse until likely the first and possibly second decade of the 19th century. But here the suspicions compound like Christmastide 1954 parachuted bags of dehydrated wine at Dien Bien Phu.

GPS marker on hill 38

First of all, this be temporal, not spatial as the first "slip," and so ties to a host of occult meanings, crypto-temporal-spatial inexorably linked into the future in part through (advanced action again?) Dixon’s obsession with electricity and magnetism to be expressed in Maxwell’s not-yet-existing (existing but not yet discovered or invented?) partial differential equations, leading to invariance problems with Galilean transformations (can this very name be a mistake in so religiously charged a setting?) thereby scrapped for Lorenz transforms and relativity? Or later still the NAVSTAR Global Positioning System and its pseudorange equations so often mistaken for trilateration and hence the elliptic geometry of ranges (see the misguided comic book by Trimble Navigation) when instead related to the Minkowski metric and hyperbolic geometry (what would be the effect upon Mason of swapping sin and cos for sinh and cosh?) and in fact hyperbolic navigation, like a four dimensional LORAN (time being explicit coordinate)? More: unlike ranging in which time is wasted in exchange for improved zenith (given the same emitter geometry relative to receiver) GPS trades the zenith error (along average line of sight) for time, with the atomic clocks and careful synchronous time-transfer accurate to nanoseconds. Information costs, as does ignoring second-order effects. (Relevant authors are J. Abel and J. Chaffee, in a sequence of papers in the IEEE Transaction on Aerospace and Electronic Systems (AES) and a host of different Institute of Navigation Conference Proceedings, following up on a 1985 IEEE AES paper by S. Bancroft. For a relevant historical discussion going back to the third century BC see J. Hoshen, The GPS Equations and the Problem of Apollonius, IEEE AES 1996.)

GPS marker on hill 38

And of course all leading back to spread spectrum, tying Mason and Dixon directly to the GPS signal itself.

By now the reader is feeling a little edgy, looking over the Old Shoulder, and it is imperative to stress that this be no time to wander. Stay on the path, this geodesic losing all its second-order terms with differentiation, not covariant differentiation, either, and skating by parallel transport along this geodesic. Much like Mason and Dixon approaching the Warrior Path.

GPS marker on hill 38

So skip a couple centuries and find that indeed time and position warp into sinister twines, time being distance (as with ten nanoseconds approximately three meters) and in particular with the hard coupling of time into the GPS pseudorange equations. What more natural than the tree-infested nation surveyed by Mason and Dixon becoming the dominant colonial power foisting its Sha upon the globe, combining the power of Olinde Rodrigues’ quaternionic formulae in inertial navigation, Bradford Parkinson’s Air Force backed initiative stealing the Navy’s Transit for a new beginning at a lonely outpost near Lompoc on a windswept hill overlooking the Pacific, and the mighty computing engine the size of a pinhead or so. Pass through the bombing tests upon the dry deserts of Arizona; the battles of Senior Masters over matters trivial for Undergraduate Statistics Students concerning least squares, eigenvalues and singular value decompositions; the wild flights of Satzap by the carousing K-squared; the inventor of carrier phase penning Escape from Einstein? Zoom in on a squad of Geordie surveyors from Racal Group Surveying Ltd Sky Fix, spiritual descendents of Dixon, with one Brit mathematician plus a Yank or two in tow, carousing at a conference in Kansas City, in Salt Lake City scattered around a long table in a brewpub drinking weak beer when their leader in thick brogue asks the waitress if they have single malt whisky and she answering, Now that you ask, we can sell it but we can’t list it on the menu, a cherubic baby-face asking, Do you have any hoors then? Enter this impish Buddha, curved meerschaum belching some blend of perique and dirty socks, shoulder-length hair and waist-long beard crinkled like a zig zag perm, asking eyes atwinkle What do you get when you dig up the grave of Stephen Banach? The residue of a pole, smiling What is Batman’s favorite geometry? Lobatchaveskian. What is Differential Geometry? The study of invariants under change of Notation.

GPS marker on hill 38

These scattered among second-order effects swept away by pretensions of tensoriality where there be none.

Let’s go there, then, to GPS and the world of inertial platforms wherein Dixon’s gravity vector would be a crux, as well Mason’s earthly rotation and the oblateness of the spheroid with its crucial higher-order harmonic terms and let us not forget the terrible Sha visited upon current generations with the destructive power of combined GPS and inertial devices for guidance and navigation. Accurate local gravity (mapping the locally mass-perturbed normal bundle) and classified higher-order tesseral harmonics for oblateness together with proper accounting for that polar hula dancer guiding a bomb down the smokestack or missile through the window.