Two Bar was a name they gave a certain view of the Paris Basin, from their side of the river looking north past the clumps of muck and stranded flood wrack which would later host St. Chappel, Notre Dame and, set just upstream, the favorably disposed citydwellings of the anciently and permanently rich of present day Paris, but seeing then, instead, the place where by the wrestlings of chance and design it would become.

coil The controversial Barry Coat of Arms

The controversial
Barry Coat of Arms

coil

July forth

The word for it may have its known etymology. Certainly it had its first mouthing, some one moment of saying which gave, for whatever reason, the newly agreeable phonics of it to language. Fresh spoken, adopted, retransmitted, found once here and again here in the source material, becoming the acknowledged and proper beast for bearing the burden of the indicated reference into speech.

The word for it: once newmade, and by and by the categorically correct and telling thing.

Word, what word? Oh, any word; aye. Oh, yes, yes, any word at all.

July 31, 2005

July 31, 2005

On Synechdoche

Synechdoche names the part by its whole or names the whole by its part.

Metonymy names the whole by its attribute.

Thus in the sentence, "Today the White House applauded Russia for yah de yah yah," there is the specific metonymy of "The White House," the well–known building attributed to the well–known government staffing it, and also there is the more encompassingly syndechdochal "Russia" summarily rounding up in this case what we are persuaded is the current cast of criminal Russian overlords of that spacious land by the gesture of substituting in the sentence the name of the famously woe–begotten place for the name of its chief begetters, who, themselves attributes of Russia, are nevetheless metonymically incapable of representing it very well.

Unarguably, metonymy may by all rights darken the door of The White House in the sentence, but synecdoche, the naming of the whole by its part, is equally evident in the usage, the White House being a famously physical part of the whole of the indicated government and thus the naming of it properly a synechdochal substitute as well.

Metonymy may strike out on its own, as in the amended sentence, "Word comes from the land of the free and the home of the brave today that the White House applauds Russia for yah de yah yah."

Or it may be enough to metonomize the sentence:"Today the White House applauded the Kremlin for yah de yah yah."

Or synechdochalize: "The U.S. applauded Russia today for yah de yah yah."

July 19, 2005

July 19, 2005

A question we will seek to answer satisfactorily in the next few hours. Something simple really, the application of archived formulas to a simple question about cubes:

What's the increase of surface area of the arbitrary cube in relation to the increase in its volume as its volume is arbitrarily adjusted to some other given size? Setting the volume of the arbitrary cube to twice the volume of its arbitrarily chosen inferior, for example, how much has the surface area altered, and by reductio, how much has each equal edge, root of that area, altered in turn?

The surface of the cube is six times the square of any edge of the thing, the edge being at the arbitrary given root of the figure; six squares of just that edge placed just so in neat relation one to the other exhaust the surface of the cube's six-faceted face.

In two dimensions a square registers area. Six equal areas each formed by equal edges amount to the surface's constant relation to the volume taken up by the cube. Should the volume of the cube be doubled, the six equal surface areas bloat as well, to six times the square of that self-same newly bloated root.

Should a volume of root 2 of a cube be increased to a volume of root 4, the increase in volume is from 8 units of girth (2³ — refexively inches here at HCE, we must admit) to 64 units of girth (4³ units), unnecesarily more volume than the already expansively doubled amount originally sought. A cube 16 units in girth is twice the girth of a cube of root two in the above example, and its edges are by design ³√16, just as the edges of the smaller are ³√8.

The cube root of sixteen evokes the curiously precise number 2.5198421, the number we fall on when we try to figure the stretched surface of a doubled cube from its root here. The six adjoined square areas arrestingly disposed to fill the role of the cube's surface area in the above example would perforce be 6 × (³√16)², a surface area hardly different from 38 square units, all told. The doubled thing has a surface area now slightly greater than half again as big as the surface area of the original cube.

We will immediately recognize the surface of a cube when the surface area is six times the area formed by the square of its edge: six times the square of the measured edge, to be blunt, or 6x² to be absolutely curt about it in the manner of the new sciences, which rightfully have little interest in revisiting usefully settled arguments of the past however crucial to the enterprise of classical geometry of Euclid and his ilk such arguments may have been, since the forceful application of the archived formula relieves the user from the bother of engaging in all the steps originally taken to reach the argument's resolution, codified now in the readily accessible formula that puts a stop to all that redundant talk.

image of the standard definition of frustum

Anciently the smartallecks attending the talk of mathematics posed this question:

I want to build an altar shaped like a frustum that's exactly twice as big in volume as that altar shaped like a frustum over there. How much bigger do I make the edges of the frustum to achieve this, eh?

The frustum has fallen far out of favor as a topic of mathematical conversation, so far that the word for it is hardly used, though the shape of the thing is given in specie on the back of every dollar bill in the truncated pyramid surmounted by the the famously observant eye that's so meaningfully attached to the commonest legal tender of the United States of America.

image of the frustum on the back of the dollar

That shape, the truncated pyramid pictured on the back of every dollar bill, is the frustum.

The square base below, the square altar on top, and the equal tilted inclination of the sides of it extending from one squared value to the other. Frustum.

For our purposes we will say that the frustum exists in literature in the witnessed shape given everyone (may their tribe increase) who holds the good paper of a dollar bill in a most fortunate paw, without the word for it itself having any obvious currency whatever in the vocabulary of that paper's common holder.

Unnamed, the frustum is. Yet, and in spite of this, a happy many are well enough aware.

Frustum, once the notorious shape for raising up the mathematical argument, now reduced to bare mention by the succinct summarizing formula for the thing that, as it proves, is itself but a byway in the modern maze of mathematical discourses of the new sciences. The frustum as subject of sustained investigation has seen its day, its matter long–settled into the background of the stuff mathemeticians are on about in our own age.

Some thousands of years ago the Egyptians had at the frustum, calculating the volume of the area encompassed by such a thing, making it out to be equal to one third of the measure found by multiplying the proposed distance between base and altar resting on respective parallel planes times the sum of the areas of base and altar added to the square root of the product of the areas of base and altar, and there you have it, the volume of the frustum, one third height times the sum of the square of the base's edge plus the square of the altar's edge plus the square root of the product of base and altar.

Over time the discourse was battened down by shortening the way of saying it, in keeping with the brusque concision typical of mathematical dictions. It was observed early on that the square root of the product of base and altar described a measure indistinguishable from the plainer product revealed by multiplying the altar's edge by the base's edge directly.

figure of the frustum

Volume of some frustum = V
Base = some square B
(length of the edge of the Base) = b
Altar= some square A
(length of the edge of the Altar) = a
constant distance from A to B= some height h

V = 1/3 h(a² + b² + ab ) or even
V = 1/3 h(A + B + √AB)

The formula for the volume of a frustum is a special case of the Heronian mean, which that famously reputed Alexandrian Heron is credited with incorporating into the distinct Greek idioms of Book II of his Metrica, an exhaustive and thoroughgoing rifling through the lore of Middle Eastern mathematics on the matter of the volume of regular solids.

All Heron had to say on the matter of Heron's mean between two positive numbers is now crisply cut short by the perfected paraphrase of the thing in the curt notation of the new sciences —:

(x + y + √xy)/3.

(Though the Egyptian mathematics of the frustum brought full stop to Egyptian argument over the volume of certain solid figures, and Heron astuely analogized this argument-stopping manuever in the diction of the geometrically disposed mathematics of the Greeks, we are reduced to the other shorter and more comprehensive paraphrase of the new sciences of our age in speaking of the thing at all, losing the flavor of the frusta as well as the word for it, admittedly, as we wend a thoroughly algebraic path along the distance between two cubed values without much need for reference to frusta at all, on which the literature of Egyptian and Greek mathematics so fully depended. The frustum was the badge of the settled thing in the mathematical lore of Egyptians and Greeks, a badge which when shown once again would settle once again the foregone argument of its origin).

The formula 1/3 h(a² + b² + ab ) for the volume of a frustum covers that special view of Heron's mean arising when a and b are taken to be the square roots of numbers A and B as shown above. They are the respective squares of edges a and b, with B the base of the figured frustum, and A the altar of the thing.

In good faith any number can be granted the property of being the product of some other number self-multiplied (simply enough 4 is 2 self-multiplied, and 2 is itself something or other else self-multplied, and whatever else that something or other else might be by actual count, it is the square root, easily enough illustrated in practice even though the formation of the word for it in the most basic syntax of the new sciences must regrettably elude completion).

The volume of pyramid or cube is easily enough realized by use of the frustrum's generative formula.

Setting a, the length of the altar's edge, to zero in the formula for the frustum makes the special case V = 1/3hb², the volume of a pyramid. Floridly, the altar of the truncated pyramid of the frustum provides the locus for the self-defining sacrifice of the rest of the matter presumed of some completed pyramidal figure, the frustum's altar being that square spot of frustum on which the integrity of that likely pyramid's ascension to its one fine point on top, immanent, is foreborne in favor of the defined benefits of the given frustum instead.

Square prisms arise when a, the length of the altar's edge, equals b, the length of the base's edge. V = a²h, and when a equals h as well, V = a³, the cube.

Six certain equal frusta, nested so that their square bases form the square areas of the six–faceted face of a cube, will fall snuggly inward toward the center of that suggested cube and occupy all the volume of that larger cube except for the volume of some other smaller cube marked by the regular intersection of the relatively narrowed edges of each fustrum's altar, the six altars edging together inside the enclosing cube to form the six necessarily square surfaces of the six–faced lesser cube inside it.

Unpacking the difference in volume between one cube and another from the formula of the frustum, we acknowledge that no matter the relative size of the smaller cube, six equal frusta must define the difference between the volume of that cube and any larger cube which might enclose it. If there is a larger cube, six equal fustra of some certain size added to the given smaller cube must amount to the same thing.

Admittedly, unless the height of the appropriate frustum is some discernable length less than half the length b, outfitting the cube in this way is impossible.

Concievably there might be an altar A half the size of its base B placed so many parsecs distant that, given the luxury of such height, examined by whatever rude tools our age makes available, the sloped sides of the frustum would never be quite distinguishable by our best measure from the slopes reputedly uniquely available to only the most rigourously orthogonal of objects, our insufficient measure blurring the distinction between the two unlike forms for all practical purposes.

Oh, we might yet presume in spite of our failed measure and with no certain way of knowing, that at that prodigous height the altar of a frustum continues to exist, that the sacrifice of the rest of the matter of the pyramid is made there, that the sacrificed matter includes the necessarily implied point to which all the lines of the surface of the frustum would otherwise inexorably rise and converge if not for the altar's manifest sacrifice, a singular point denied the surfaces of the resolutely orthogonal figure of a square prism, for example, its own surfaces even at that far–flung pyramid–topping height still rightly separated by the originally construed distances of its base.

For all the good it may do beyond the bounds of measurement the realized choice between these disparate figures becomes a matter of optimism rather than observation, founded on faith in the pragmatic pracitices available in either case rather than on the solid result of a good clean count.

Likewise, the absence in the formula for the frustum of any discernable height at all leaves but two squares, a² and b², whose famous complicities have recieved the chronic attention of humans for all the other reasons down the ages but aren't particularly amenable to the suasions of the formula for the frustum, which seeks a volume which is never present between them.

Such limiting considerations as these are usefully avoided by the suggested construct of the cube. The possible height of the class of frustum found there is constrained by but ranges freely between nothing at all and half the value of b.

Our formula for some bigger cube in relation to some smaller cube always comes out volume of the bigger cube equals six equal frusta plus the volume of the smaller cube in which h, the frustum's constant of distance between altar and base, is identical to the difference in length between half the altar's edge, a, and half the edge of the base, b:

h = (b/2-a/2), [(b-a)/2], ½(b-a).

The difference between the two cubes can thus be entirely expressed in terms of the roots a and b.

Six equal frusta surrounding the smaller cube contain the difference in volume between the smaller cube and the larger.

Big V = 6 × (b/2-a/2) × 1/3 × (a² +ab+ b²) + little v

V - v = 6 × ½(b-a) × 1/3 × (a² +ab+ b²)

V - v = (b-a)(a² +ab+ b²)

(A curiosity of the six nested frusta of the cube is that in practice each four–sided frustum snuggles up to four equally disposed frusta to form five of the six faces of the larger cube, needing yet but one other equal, symmetrically reversed frustum across the way to attach itself to the far reaches of those same four frusta met by its untouched partner to constitute the larger cube. The frustum across the way never meets its opposite, but always shares edges with the same four frusta common to both. Each opposite frustum shares the same four neighbors with its unmet partner. Opposites, they have the same neighbors, but are by design never neighborly themselves. Irreducibly and curiously contrary they are.)

For all the good it will do, any number may be thought of as the product of some other number self–multiplied however many times, if convenient to the mathematics. Saying a² + b² +ab rather than A + B + √AB is certainly convenient to the modern slang of mathematics we are hobbled with here at HCE, where at best a rude paraphrase of the Egyptian mathematics of the frustum might arise. Gazing at the Heronian mean

(x + y + √xy)/3

in our own scrip, we mark the hinted Heronian amount in the volume of a frustum

V = 1/3 h(A + B + √AB) or its alternate

V = 1/3 h(a² + b² + ab )

Six gathered equal frusta make the difference between two cubes, V and v. As any number may be taken to be the square of some other number, so it may be taken to be the cube of some other number still, emboldening us to accept the fact that the difference between any two positive numbers considered as cubes will reveal the injunctions placed on that difference by the Heronian mean.

distance between numbers

Any two numbers will differ by an amount lifted directly up out of the Heronian mean between them. In the event, any number a smaller than b procedes to become b by the simple addition of an amount ruled by the Heronian mean between the two. The greater amount is lacking just that Heronian amount in the smaller amount to enjoy perfect equality with it. Added to the smaller, the Heronian amount arises instantly to make up any difference between them.

The literature of the frustum assumed by Heron, let alone the one recorded by Egyptians before him, lies characteristically inert in the present age alongside its unused name.

There it is, but unheeded. Few people crack wise anymore about an altar twice as big, the sting taken out of that nettling challenge to the mathematics by the successful resolution of the matter long, long ago. Some specialist might wander by to pick away at what remains of that literature with the modern tools, but otherwise, the subject, signalled by the unused word for it, is closed.

All the probable bother of mathematical nattering leading up to the revelation of the novel statement of the frustum's necessary volume was blunted early on in Egypt, at least in that direction. Whatever ancillary argument may have led Egyptians in the end to cap the whole thing with their comprehensive formulation, blessedly scant record remains of credible certainties composed and then frustrated in the Egyptian literature of the frustum down all the centuries and centuries before the formally agreed solution finally managed to be reached.

In The Crest of the Peacock Non–European Roots of Mathematics George Cheverghese Joseph quotes E.T. Bell dubbing the solution of the frustum's volume "the greatest Egyptian pyramid." It serves as well as a monument to the assiduously pragmatic demonstrations of Middle Eastern mathematics.

Even absent records it is almost certain how the drift of mathematical talk of Egypt went back then, for it is unargued that the lot of them were irrefragably empirical in handling any question a mathematician might drag in the door. Their mathematics counted stuff, recognizing the profound power of subscribing to the ageless pragmatic belief that the counted thing will return in time something or other of value, a belief fundamental to all the sciences but hardly limited to them.

There are two major results which we obtain from the study of Egyptian mathematics. The first consists in the establishment of the fact that the whole procedure of Egyptian mathematics is essentially additive.
— O. Nuegebauer in The Exact Sciences in Antiquity

Any argument was pragmatically addressed by the equal but ever–fruitful bother of compiling the potentially exhausting count of each and every observed instance of the matter in question until the papyrus went groaning under the inherent implications of the sufficiently exhaustive list as gathered in the the subscribed count.

Egyptian mathematics leaves a literature of the counted thing, expressed in tables giving lists of observed answers to the implicitly understood matter at hand.

The counted thing, with the suggestive powers of its primordially pragmatic tactic subscribed to by all the humans, admits a wider literature including but not limited to what literature there ever was of Egytian mathematics. Especially among the Egyptians the literature of the practiced count was congenitally deployed by a wide variety of practitioners for their own condign usages, practitioners who we well imagine would not willingly in that age have touched the literature of Egyptian mathematics, per se, with a stick.

Implicitly some succinct and general formula for generating every instance of the matter at hand might be proposed, certain to speed the process of aquiring the exhaustive list of the valued thing.

The peremptory and brusque Greek practice was just this, leading the rhetoric of its literature bluntly to the goal of the succinct and general formula and leaving it to its user to operate the thing successfully.

Concise, that, but by no means to the taste of Egyptians, inclined as they were by their assiduously pragmatic mathematics to create a literature whose goal was pragmatically enough to take that one further step and deliver to the user not the machinery for succesfully generating the good answer, but the fruitful answer itself, arrived at by means implicity available to someone marking up the good answer to the succinct and general formula.

In this the mathematician who made the Moscow papyrus followed the practice of Chaldeans, who millennia before had pragmatically enough recorded on something now called the Plimpton Tablet a nice list of useful answers implicitly consistent with a thoroughly sophisticated knowledge of the general formula much later to be made widely available in the the argument for a² + b² = c², colloquially called Pythagorean. Implicitly, the Chaldeans knew the general formula for seeking what are known as Pythagorean triplets, but did not seek to give it. Fundamentally pragmatic, they succeded in making a literature to their own taste delivering to the immediate grasp of its user the practical result generated by that formal operation, its listed values in that literature implicating that operation without naming it.

The Egyptian mathematician who noted the volume of a frustum in the Moscow papyrus likewise wrote down the process for finding the volume of a very particular and singularly representative frustum, the listing of that answer being inextricably bound to the very expression of the subject in that literature, so that even at its most succinct, at least one good sample of an answer needed listing for mathematics to be mentionable at all.

Not surprisingly, The Egyptian mathematician, who by temperament and training would as soon count answer after answer to the question, pragmatically observing and recording all the most likely values for the matter at hand, when pressed for space, or time, or availing of the mathematical equivalent of metonymy piled on synecdoche in that literature which allows for the named part representing one answer to revealingly display the essential attibute of all answers to the matter at hand, sought to record pragmatically enough the one answer among all the potentially counted likely answers most likely by its singular expression to exemplify the formally settled argument. Thus the Egyptian mathematician gives in the Moscow papyrus the process for finding the volume of a specific frustum of base 4, altar 2, and height 6, leaving it to the user to discover the reasons this particularly satisfying example among all others should be chosen.

Following the Chaldeans, the Egyptians were fundamentally inclined to count stars and shares of land and shares of this bounty or that bale of the other matter entirely.

Notoriously in that ancient time along the Nile constraints of manpower were no obstacle to gratuitously expressive projects fundamentally counting on the supremely effective deployment of well–ordered processes; counting quite literally on this ordered process followed by that ordered process followed by your other ordered process still, until by the additive inherencies in the comprehensive count of any quantity, each process counting as an essential distinguishable portion of the sequence leading to the whole, the desired result was had.

For all the reasons, any good count based society will perpetuate a literature of counted things if staffed by the critical number of counters spared for that pragmatically useful endeavor. The Egyptians of that time had staff to spare for counting and recording unsparingly all the specific stars and lands and bounties and peoples so ordered to be counted in that land and surplus staff left over to tend directly to the tools and training needed to perpetuate the useful good works of counting among succeeding generations.

Undoubtedly some certain Egyptians recognized the agreeable personal advantage of joining those who staffed their practice of mathematics in that ancient age, of availing themselves of the opportunity, should it presented itself, of taking up the clever craftings of those marvelously developed tools instead of devoting themselves to the kit of another occupation whose staffing needs might call them entirely away.

Contrarily, the common preference among people of every age, even that age experienced anciently by Egyptians, would be to gang up willing enough with others commanding all the robust tools available to that otherwise disposed sort of staff, to dress a rock up out of the ground, e.g., and move it precisely to some other given place on command, rather than acquiese at the prospect of resting in some however leafy glade among the sort of people likely to go on about mathematics.

When it came time again to take up staff to build another pyramid and the actual likelihood of working on a pyramid increased accordingly among them, the majority of Egyptians might yet hold to that common preference, gasping out "…Saved from mathematics, at least!" in face of the most daunting burdens a rock–based organization might provide.

The emoluments of staff in the Egyptian practice of mathematics would have been of no matter to those we imagine most resolutely averse to the practice among the class of pyramid workers of that age, although those rest of them among that class, speaking comparatively from their own mitigated perspective, might allow the subtle argument that, exept for the mathematics, the job itself was not a bad job at all.

Which is not to say that all who would staff could staff the practice of Egyptian mathematics in that distant age. Not at all.

Surely among those who ganged the pyramid when staff was called to build it in what amounted to yet another new order of the ages, were workers there who would rather square a root than square a rock but were by fortune pressed to the requirements of that other calling instead by the squalid suasions of personal circumstance. Missing a chance at mathematics that sort would be, and mixing perforce directly with those most resolutely averse to the stuff as well.

This is not to suggest in the least (or even to suggest in some lesser amount should it be proved necessary) that mathematics alone constitutes the full range of a priori antipathies automatically arising in a staff of sufficient size, which given the needs of pyramid construction at times in Egypt included a necessary motley of all the disparately disposed resources of personnel and all their baggage of prestressed conflicts that could be commanded in that age, ensuring staff a wealth of ready–made topics eminently more disputable than mathematics.

July 12, 2005

July 12, 2005

From the reportedly acephalous Scott Eric Kaufman:

An ersatz theoretical ecumenicalism channels critical works through the same limited set of thinkers, as is borne out by the introduction to Bhabha in the The Nortion:

Although “the wit and wisdom of Jacques Derrida” (as he calls it in another essay) is fundamental to his work, Bhabha draws on a wide array of twentieth-century theorists throughout “The Commitment to Theory.” Building on the influential concept of nations set forth by Benedict Anderson in Imagined Communities (1983), Bhabha stresses how nationality is narratively produced, rather than arising from an intrinsic essence. From Mikhail Bakhtin, he takes the concept of dialogue to stress that colonialism is not a one-way street but entails an interaction between colonizer and colonized. Regarding identity, he draws on Frantz Fanon’s psychoanalytic model of colonialism and Jacque Lacan’s concepts of “mimicry” and the split subject, arguing that there is always an “excess” in the cultural imitation that the colonial subject is forced to produce.[29]

I could continue, but the unchallenged nature of the claims attributed to Bhabha here speaks volumes about the current state of Theory. My point is a simple one: the more debate about the fundamental claims of theoretical approaches the less likely the next generation of critics will be as philosophically incoherent as Bhabha. In the classroom, Theory’s Empire could function as a simulation of the debates that created critics as rigorous and justifiably eclectic--i.e. the critic him- or herself can justify the applicability of a given theoretical approach to a given literary work--as Miller and Jameson. No one, I believe, advocates the return to New Criticism or to the production of philosophical and theoretical curiosities. But everyone, I believe, should desire the return to theoretical responsibility a collection like Theory’s Empire can facilitate.

No one knows what would come of shouting out Helmholtz in a crowded theater, though the result of shouting out Foucault, say, or Jameson, or any of a number of other theoretically controversial names of a certain stripe, given the sort of people who frequent theater, must be met with instant certain voice from knowing quarters of the crowd in that electric moment when the signified is publicly apprehended.

An esnured moan shall greet the muttered Derrida in such spaces, followed quickly by that moan's rejoinder. Or the order may be reversed, and a pip of praise from the audience precede its puncture by those otherwise inclined instead, with the quickest lip settling the arbitrary priority of the terms.

However turned toward the arguably mentioned Derrida, once joined, the conversation of the audience, spurred by the mere mention, will incline in its own characteristic direction, so that an argument starting with a moaned "Oh, Jayz! " or a spurt of praise will in either case be satisfied to end or not depending precisely on the likely disposition of the crowd in the matter's equable resolution.

(Oh, and "Jameson, gaah!" would surely sound out from the throats of myrmidons of your other man entirely who abjured Jameson from the first, not that Jameson wouldn't have his own cadre capable of carrying on in his behalf should it come to it, that sort being as likely to attend the theater for their own condign reasons as his detractors are for theirs, thus introducing the bother of a well–staffed agrument to what could otherwise have been a very nice night out)

The merest suasive slogan suggests argument enough for any crowd, a word for it perfectly capable of engendering instant predictable engagement of enough of them to have just the argument the crowd is capable of. Say, with some force, Derrida in a crowded theater, for example.

Clearly, a rapture might be proposed to possess one member of that audience whose attention, focused forcefully on the study of electrical engineering, more's the pity, is in that instant riveted by an epiphany of the place of Helmholtz in a chain of settled argument leading inexorably to the universally understood electronic age of today.

This proposal proposes as a singularity some member shouting Helmoholtz in a crowded theater during the course of such a rapture. Admittedly a theater might contain sufficient electrical engineers in its audience grappling likwise with that self–same electricity for which Helmoltz is such a byword that the overt mention of the name would bring about the same sort of characteristic public intervention expected of the more normal distribution of the previously mentioned audience at the shouted out Derrida, though ideally there are never that many electrical engineers in one place. In a normal crowd the singularity of the uttered Helmoltz can be expected to be met at most by the familiarly arched language of eyebrows.

Argument

[Editor's note: Mr. Kaufman's error in spelling the word "Norton" (purposely emphasized in the above selection from his essay prompted by the book Theory's Empire) might be easily avoided in the future if other than what we suspect is no more than a simple nonce in a text rarely discommoded in its attempted adherence to the standard comonalities of grammars and spellings by the easy mnemonic aid of Jackie Gleason pronouncing the very word, an aid which Mr. Kaufman might legitimately call upon to resolve what is to all but Mr. Kaufman in this errant instance the settled thing. Norton, of course. Not Nortion at all.]

Mr Kaufman chides Bhabha as if the writer were the very type of the current crop of Theorists who wrankle the contributors to Theory's Empire so. Having the pleasure of never reading Bahbha, we here at HCE cannot say whether Mr. Kaufman's characterization is justified, though we are willing to let him have his way in this. He finds Bhabha's writing irresponsible, and this may be so. Eyeballs may roll everywhere Bhabha passes for all we can tell. A great deal of Mr. Kaufman's argument against what he construes as Theory depends in this short essay on how typical Bhabha is of writers of Theory generally and how readily the criticism rolled out against him spreads itself equally among the lot of them.

Bhabha's work appears to Mr. Kaufman to rely on a promiscuous use of the appeal to authority, a practice which inclines its overuser inexorably toward fallacy, but is generally considered a necessary venial sin of scholarship, by which the agument presumed won in some previous discourse is truncated by reference solely to the name of its champion in extending the debatable subject matter. The implicit presumption is made by such appeal that the argument is over, previously settled by by someone its arguer claims to be qualified to address the matter. This presumtion may founder on the shoal of fallacy for all the many reasons, or it may prove just the concise reference needed to spark some fresh consideration on the part of the arguer.

The nortorious calculus of the famous Newton survived and thrived for scores of years in the hands of those whose promiscuous uses of it extended mathematics with profound practical result in spite of the fact that no sound foundational argument could be made at the time to buttress the appeal to that authority or to the pursuasive alternate authority of Leibnitz in the matter of the calculus for all those many years. Presumptuously, mathematicians did appeal to authority in this instance, granting what was yet to be earned in the name of Newton or Leibnitz.

Mathematicians following Newton or Leibnitz behaved as if the foundational argument was settled by their authority, committing to the venial sin of a logical fallacy in the expectation, realized by their investigations, of immensely fruitful results from endorsing the admittedly as–yet–baseless legitimacy of the calculus.

Sometimes you can get away with that, assuming the proof of the yet unproven by developing the claims of an unfinished argument as if the claims were settled, but it is not best practice.

July 11, 2005

July 11, 2005

Giants ½ Way

page D1, San Francisco Chronicle, July 11, 2005

The San Francisco Giants are the favored squad here at HCE.

We've known all the many irritations of disappointed alliegiance meted out by that club to those who've bothered to attend hopefully to its activities down the decades.

Our extreme hope for a championship won by the San Francisco Giants is never extinguished in a season until each and every chance for its happening is gone as well.

Year after year, that moment has come when any and all hope of achieving our desire in this regard is utterly deadened. An out is made, a game decided, and the Giants are done for and our hopes vexed once again. Thus it has ever been, despite our ingrained wishes.

In the 1970's we had so much else to attend to that the consistent inartful failure of the San Francisco Giants ballclub each and every season was often enough a mere sidelight to the foregrounded failures of our own and others during that period of time.

And yet those failures of our own or others then were often enough partial or incomplete in contrast to the absolutely completed failure visited on the San Francisco Giants of that age, when characteristically hope for the club's fortunes would be regularly expunged from the realm of likelihood by their play with more than a month left in the baseball season each year.

The proximate causes of denied hope lounged everywhere about the clubhouse all through that era: a sad collection of players not adequately equipped to compete successfully in Major League, as borne out in actual play.

July 9, 2005

July 9, 2005

Drawing of flowers and hearts by five and a half year old Sophie , signed

Here is a detail of the image created by Sophie of numerous heart-shaped flowers, signed in her name by her in the upper left quadrant of the image in what was announced at the time of its creation as cursive.

The original image is considerably larger than that represented here on this page; the signature of Sophie itself routed through a rectangular area fully 4(and a half) by three (and a half) inches broad in the original creation.

the S in Sophie, magnified

The signature of Sophie is enscribed using a special tool: a pencil whose central cylinder of multi–colored lead leaves its own discrete distinctive multicolored track along the path to the signature's completion. Such pencils are easy enough to find, howevermuch the market is overwhelmend by the prodigously greater number of plainer pencils with their singular deep gray graphite shading everywhere available to the pencil–seeking paw, a pencil–seeking paw which would as soon reach for some arbitrary hue or even collection of color to scribe its lines given choice for all we can tell here at HCE, but satisfies its gross utlitarian need with the universally nearby tool of the plain pencil instead. The plain pencil is mostly present, the colorful one must generally be sought. Pragmatically enough, in practice the plain pencil is found to be most often used.

Here, for example, is a place where such multicolored pencils are in stock.

Breadth, as exhibited by the twists of color of the multi–colored pencil specifically chosen by the author for the task is of course a quality denied the ideal singular line cursive writing claims to represent: the ideal of "S" in cursive writing as instigated by its author assures the bloom of all the purposive argle-bargle of languages of communication connected to that claimed cursiveness. To anyone attending, given the cursive "S," "Sophie" must ensue.

July 5, 2005

July 5, 2005

Irregular stubs of fennel clumped like remnant teeth in a broken boxer's maw, though countably more of the things poking out there from the soil than might remain in the maw of even the most unsuccessful human combatant.

The twelve–foot fennelstalks of it are removed for now, hacked down and hauled away elsewhere. The gums of the boxer having no further teeth to offer up, what's done is done: relict toothroots remain of that previously happy regime of dentition with all its storied ease of gnawing and socially acceptable smile, all now forever subdued except in wistful memory. We do not credit the theory that "happiness is a worn gum" in the least.

As to the fennel, it is not yet done at all. Paused, yes, subdued; but only just.

In principle disposed as we are here at HCE to the long–term eradication of the stuff from the paddock which surrounds us, still, we have not yet taken to the chemical warfare, the methodology ever mentioned in the assured opinion of those, called gardeners, who make a living growing, or alternately, resisting the growth, of the citizens of the famous plant kingdom.

The cunning of the gardeners is a cunning we have never known, a relation to the ways of plants, with their knowledges and tools of art which we here at HCE, yet following in the abarboreal pathway of the Barry Family, do not posses.

We are told of feeding some planted thing, a bush of roses as example, of spreading some dusty something or dousing some liquid other on it, or alternately, in another season, of the pressing need to cut back what has been previously gained from the uses of those dusts and liquids. We listen, we hear with fresh surprise. It is a plan, we admit, but yet foreign to our way.

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Bogsniffings:

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Volume III: 03.03.05 to —;

Collected incompletions of the current year, by monthname.

Volume II: 03.03.04 to 03.02.05

Accumulated incompletions of the indicated annum.

Volume I: 03.03.03 to 03.02.04

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