We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.

We describe a list of canonical functions from 2 to ℝ such that every Borel measurable function from 2 to ℝ, on some superperfect rectangle, induces the same equivalence relation as some canonical function.

We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results:1. The class of unions of rectangles is polynomial time learnable for constant dimension d.2. The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable.3. The (...) class of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses. (shrink)

Plimpton 322 is one of the most sophisticated and interesting mathematical objects from antiquity. It is often regarded as teacher’s list of school problems, however new analysis suggests that it relates to a particular geometric problem in contemporary surveying.

We present a theory of human artistic experience and the neural mechanisms that mediate it. Any theory of art has to ideally have three components. The logic of art: whether there are universal rules or principles; The evolutionary rationale: why did these rules evolve and why do they have the form that they do; What is the brain circuitry involved? Our paper begins with a quest for artistic universals and proposes a list of ‘Eight laws of artistic experience’ -- a (...) set of heuristics that artists either consciously or unconsciously deploy to optimally titillate the visual areas of the brain. One of these principles is a psychological phenomenon called the peak shift effect: If a rat is rewarded for discriminating a rectangle from a square, it will respond even more vigorously to a rectangle that is longer and skinnier that the prototype. We suggest that this principle explains not only caricatures, but many other aspects of art. Example: An evocative sketch of a female nude may be one which selectively accentuates those feminine form-attributes that allow one to discriminate it from a male figure; a Boucher, a Van Gogh, or a Monet may be a caricature in ‘colour space’ rather than form space. Even abstract art may employ ‘supernormal’ stimuli to excite form areas in the brain more strongly than natural stimuli. Second, we suggest that grouping is a very basic principle. The different extrastriate visual areas may have evolved specifically to extract correlations in different domains , and discovering and linking multiple features into unitary clusters -- objects -- is facilitated and reinforced by direct connections from these areas to limbic structures. In general, when object-like entities are partially discerned at any stage in the visual hierarchy, messages are sent back to earlier stages to alert them to certain locations or features in order to look for additional evidence for the object . Finally, given constraints on allocation of attentional resources, art is most appealing if it produces heightened activity in a single dimension rather than redundant activation of multiple modules. This idea may help explain the effectiveness of outline drawings and sketches, the savant syndrome in autists, and the sudden emergence of artistic talent in fronto-temporal dementia. In addition to these three basic principles we propose five others, constituting a total of ‘eight laws of aesthetic experience’. (shrink)

Generalization is a fundamental problem solved by every cognitive system in essentially every domain. Although it is known that how people generalize varies in complex ways depending on the context or domain, it is an open question how people learn the appropriate way to generalize for a new context. To understand this capability, we cast the problem of learning how to generalize as a problem of learning the appropriate hypothesis space for generalization. We propose a normative mathematical framework for learning (...) how to generalize by learning inductive biases for which properties are relevant for generalization in a domain from the statistical structure of features and concepts observed in that domain. More formally, the framework predicts that an ideal learner should learn to generalize by either taking the weighted average of the results of generalizing according to each hypothesis space, with weights given by how well each hypothesis space fits the previously observed concepts, or by using the most likely hypothesis space. We compare the predictions of this framework to human generalization behavior with three experiments in one perceptual (rectangles) and two conceptual (animals and numbers) domains. Across all three studies we find support for the framework's predictions, including individual‐level support for averaging in the third study. (shrink)

A set of visual search experiments tested the proposal that focused attention is needed to detect change. Displays were arrays of rectangles, with the target being the item that continually changed its orientation or contrast polarity. Five aspects of performance were examined: linearity of response, processing time, capacity, selectivity, and memory trace. Detection of change was found to be a self-terminating process requiring a time that increased linearly with the number of items in the display. Capacity for orientation was (...) found to be about 5 items, a value comparable to estimates of attentional capacity. Observers were able to filter out both static and dynamic variations in irrelevant properties. Analysis also indicated a memory for previously-attended locations. These results support the hypothesis that the process needed to detect change is much the same as the attentional process needed to detect complex static patterns. Interestingly, the features of orientation and polarity were found to be handled in somewhat different ways. Taken together, these results not only provide evidence that focused attention is needed to see change, but also show that change detection itself can provide new insights into the nature of attentional processing. (shrink)

Time–space synesthetes report that they experience the months of the year as having a spatial layout. In Study 1, we characterize the phenomenology of calendar sequences produced by synesthetes and non-synesthetes, and show a conservative estimate of time–space synesthesia at 2.2% of the population. We demonstrate that synesthetes most commonly experience the months in a circular path, while non-synesthetes default to linear rows or rectangles. Study 2 compared synesthetes’ and non-synesthetes’ ability to memorize a novel spatial calendar, and revealed (...) better performance in synesthetes. The capacity to learn mappings between arbitrary spatial forms and temporal sequences is present in all individuals, and time–space synesthetes’ enhanced visuo-spatial memory abilities may underlie their creation of idiosyncratic spatial calendar forms. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Twelve subjects provided shape and orientation judgments for a set of projectively equivalent, variously rotated rectangles under three viewing conditions—monoptic, dichoptic, and binocular—with and without the presence of a pattern mask. In the absence of the mask, partial constancy was exhibited under the first two conditions and near perfect constancy under the binocular condition. Orientation was discriminated. Presence of the mask produced projective shape matching and diminished orientation discrimination. It is argued that the site of masking was postchiasmal, and (...) the results are related to previous work with pattern masking of projectively equivalent ellipses. (shrink)

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

According to the spreading hypothesis of object-based attention, a subliminal cue that can successfully capture attention to a location within an object should also cause attention to spread throughout the whole cued object and lead to the same-object advantage. Instead, we propose that a subliminal cue favors shifts of attention between objects and strengthens the between-object link, which is coded primarily within the dorsal pathway that governs the visual guidance of action. By adopting the two-rectangle method and using an effective (...) subliminal cue to compare with the classic suprathreshold cue, we found a different result pattern with suprathreshold cues than with subliminal cues. The suprathreshold cue replicated the conventional location and object effects, whereas a subliminal cue led to a different-object advantage with a facilitatory location effect and a same-object advantage with an inhibitory location effect. These results support our consciousness-dependent shifting hypothesis but not the spreading hypothesis. (shrink)

The association between New York City’s all-over structure and the play that unfolds within it relative to difference and identity is very pertinent but is not specific enough, in my opinion. On the one hand, all of Mondrian’s neoplastic works are constituted by an opposition between the variable and the invariable . On the other hand, the type of identity produced in New York City relies on repetition, a principle which, we know, explicitly governs a whole range of paintings predating (...) neoplasticism. New York City differs from the “classic” neoplastic works, as well as from the 1918-19 modular paintings with which it seems to have a good deal in common. It is, in part, because he never discusses this last point that Masheck doesn’t entirely grasp the amplitude of the reversal that Mondrian effected in his New York works.In fact, as James Johnson Sweeney realized quite early, one must go back o the 1917 works, which gave rise to modular grids for the two years that followed, in order to understand what happens not only in New York City but also in the two Boogie-Woogie paintings.3Everyone is aware of the extraordinarily rapid evolution of Mondrian’s work during the years immediately preceding the foundation of neoplasticism: under the influence of Bart van der Leck, he dopted the colored plane and the black dash on a white background as elements of his composition for the two Compositions in Color, A and B . Mondrian, who had not yet found a means of perspicuously relating these diverse elements , tied both plane and dashes together by way of an optical dynamism, based largely on their superimposition. The immediate consequence was to make the background recede optically. The next step was the five Compositions , all entitled “With Colored Planes” . Here all superimposition was eliminated, as well as all “line.” In the last two of these canvases, the background itself is divided without remainder in to planes of different shades of white. The colored rectangles are on the way to alignment. In spite of this, the rectangles fluctuate and, consequently, the background is hollowed out behind them. 3. See James Johnson Sweeney, “Mondrian, the Dutch and De Stijl,” Art News 50 : 63. Meyer Schapiro made a similar remark, at about the same time, in his courses. 4. When I refer to a number accompanied by “Seuphor,” it refers to the “catalog by group” included in Michel Seuphor’s book on the artist. See Seuphor [Ferdinand Louis Berckelaers], Piet Mondrian; sa vie, son oeuvre, 2d ed. . Yve-Alain Bois is associate professor of art history at the Johns Hopkins University. He has published a number of essays on twentieth-century art, architecture, and criticism and is currently working on Mondrian’s neoplastic years and on a history of axonometric perspective. Amy Reiter-McIntosh is a lecturer at the University of Chicago. Her previous contribution to Critical Inquiry was a translation of Ernesto Laclau’s “Psychanalyse et marxisme”. (shrink)

continent. 1.4 (2011): 286—310. This mad play of writing —Stéphane Mallarmé Somewhere in between mathematics and theory, light and dark, physicality and projection, oscillates the poetry of Alessandro De Francesco. The texts hold no periods or commas, not even a capital letter for reference. Each piece stands as an individual construction, and yet the poetry flows in and out of the frame. Images resurface from one poem to the next, haunting the reader with reincarnations of an object lost in the (...) grass or a representation of a pear in a Dutch still life, embedded in cycles of cinematic close ups and multiple dimensions. As a whole, De Francesco’s oeuvre suggests, to use the title of one of his works, a redefinition —linguistic, epistemological, personal. The poem The End (un’agenda) (The End (an agenda)) opens with a quote by literary theorist Maurice Blanchot, which may be translated as follows: Speaking is not seeing. Speaking frees thought from this optical imperative that in the Western tradition, for thousands of years, has subjugated out approach to things, and induced us to think under the guaranty of light or under the threat of its absence.[1] In writing, De Francesco seeks to redefine our approach to things. His poems, like Blanchot’s writings, speak to both illuminate and to obscure. The reader hangs in an absence of reality within language that necessitates an attempt at interpretation, yet renders such a search ultimately futile. De Francesco draws the anonymous images that appear in this poem from the city of Paris, his current home. The fragmented narrative depicts an inner doubt of realness, calling for a confirmation of a physical existence beyond verbalization and cogitation. Cyclical references to film throw into question the reliability of the reality he creates. The light, sometimes red and safe, other times absent and murky, cannot necessarily be trusted as a guaranteed means of illumination. Blanchot’s distinction between language and visualization, and the relationship of each to reality, though linked specifically to The End (un’agenda) , can be a lens through which to read any of the three works that follow. assente obliqua (absent oblique) is composed of descriptions of six still life paintings, ranging from Dutch masterpieces of the seventeenth century to 1960s minimalism. The actual images of the paintings are absent, and the text is the sole source and object of a virtual reality created around the artwork. “Absent oblique” refers to the light source placed outside of the frame, which both informs and distracts viewing of the scene. Although mere description can be unreliable and unsatisfying in its necessary limitation, the representational act of description is shown as more than just a human want. It is a need, a means by which to grapple with an unsure reality. As the illustrations progress, they descend into abstraction and chaos. The precariously placed plate triggers the movement: the bottle bursts and the objects collapse into the movement of a tracking film camera. corpo estraneo in moto ascensionale (foreign body in ascending motion) is prose poetry in action. Its objective tone of description is skewed by the subjectivity of the narrative as horrific images are relayed in fragmented but matter-of-fact manner. A “foreign body” is both a mass of cancerous cells, and a corporeal description, and the poem takes the reader on a journey back and forth between the two, destination unclear. Beyond a questioning of the real, corpo estraneo in moto ascensionale is an examination of the possible. De Francesco’s poetry becomes a camera obscura through which to observe the constant flux of light and dark that blurs our reality. His work is colored by the idea of apo koinou , a Greek term meaning “from the common” that involves a construction of two clauses with a shared word or phrase. Through such melting of meaning, De Francesco creates a fluid ambiguity that is nonetheless grounded in bodily concepts. In assente obliqua , the reader is confronted with a description of a still life that rapidly transforms into a more chilling scene: the membrane of the mushroom in the basket emerges behind the white cloth a body could hide itself that asks for help In the realm of pure description, there is a mushroom that peeks out from behind a white cloth in a basket. Behind the white cloth, too, there could be a body, hiding, asking for help. Such an elision elicits disorienting mistrust in temporality, but also expands the planar possibilities of syntactical meaning. A white cloth is not merely a construct in still life painting, but veil that both shields and reveals potential mysteries. It is a proposed alternative to a traditional Western binary of subjectivity and objectivity. The apo koinou construction is rare in modern English, having slipped out of use after its resurgence in Old English poetry. De Francesco reintroduces this blur of object and subject relations into a modern light. He draws inspiration from a device used by Gruppo 63 founder and avant-garde poet Antonio Porta tended toward repetition of phrases in third person perspective. In Italian, it is perfectly grammatically correct to omit the subject, including only a verb conjugation. Gender, even humanity unknown, the subject dissolves into the action, thus giving to the poetry the power to change the reader’s perception of who or what is actually acting. To further push the relative boundaries of experience, De Francesco expands his written poetry into what he calls “reading environments.” In these sound experiments, De Francesco’s voice reading his poetry is manipulated by real time digital voice processing. The written is transformed to the spoken, and then injected with currents of electric sound. “At each activation of word in the darkness,” (from The End (un’agenda) ) language is permutated into a nonphysical yet all-encompassing being. In these projects, realized all over Europe, De Francesco continues his examination of the word’s potency beyond the page and into an “n-dimensional space,” where the lines between nature and affect are intertwined. To publish excerpts of De Francesco’s oeuvre is to show screen shots of full-length film, to read pull quotes from a philosophy treatise. In these poems, there are questions, not to be answered, but to be questioned again. The words will oscillate in and out of the square construction found in his poems, out of the borders of the page, out of the rectangle of the laptop screen. NOTES (1) Blanchot, Maurice. The Infinite Conversation . Trans. Susan Hanson. Minneapolis: University of Minnesota Press, 1993. 27. EDITORS' NOTE The .pdf above contains about twenty pages of translation and the original Italian poetry. Below we provide only a brief account. The End (an agenda) Parler, ce n’est pas voir. Parler libère la pensée de cette exigence optique qui, dans la tradition occidentale, soumet depuis des millénaires notre approche des choses et nous invite à penser sous la garantie de la lumière ou sous la menace de l’absence de lumière. —Maurice Blanchot in this n-dimensional space i could spy on myself from the cracks while going back and forth from the summer to the wardrobe from the night to the parking lot but something filters in through the half-closed shutters becomes an event enunciation we stay without explanation like parallel curves on the back of a solid growing older she enters the garden always repeats certain phrases the elevator to be redone the neighbor’s music the steps the pavement furls like the leaves of a fern when touched she is framed from behind while she moves rocking she covers distances slowly a bag overflows from the wardrobe something stirs inside but then the suitcase comes open not even by my hand it’s the objects that are starting to filter out the little red haired monster watches idling the appointments written on one of your agendas two years old still seem urgent each letter holds itself upright on the page with flourishes and arabesques each angle has its own geography i’m trying to describe the path the fingers trace on the carpet the zipper takes the opposite route we are suspended on the stairs above the water in the center is the summer seen from above the darkness of the city passes from one headlight to the next the surfaces of our arms cohere and are shiny underneath the blinking of a sign each pore is an open expanse the body dreams the hair gives form to the possible some daring swimmers were throwing themselves into the seine they swam upstream up to the first quay look there could exist behind the screen a room where even when the lamp is out and the curtains drawn even when the suitcase wasn’t closed everything seemed red everything calm construction of a four-dimensional tetrahedron by R. Courant – H. Robbins, What is Mathematics? Oxford University Press, 1941  . (shrink)

The present essay questions at the same time it acknowledges the historical and logical conditions of existence of painting as an expanded field. The expanded field of painting is presented using a Greimas rectangle that incorporates the notions of uniqueness/reproducibility, multidimensional affine spaces, and history. The essay provides an understanding of the discipline and of the art-works that make it possible to locate different artistic manifestations taking place today in society.

One of the most frequently discussed passages from Locke's An Essay Concerning the Human Understanding is that which occurs in IV.vii.9, where he writes:… the Ideas first in the Mind, ‘tis evident, are those of particular Things, from whence, by slow degrees, the Understanding proceeds to some few general ones; which being taken from the ordinary and familiar Objects of Sense, are settled in the Mind, with general Names to them. Thus particular Ideas are first received and distinguished, and so (...) Knowledge got about them: and next to them, the less general, or specifick, which are next to particular. For abstract Ideas are not so obvious or easie to Children, or the yet unexercised Mind, as particular ones. If they seem so to grown Men, ’tis only because by constant and familiar use they are made so. For when we nicely reflect upon them, we shall find, that general Ideas are Fictions and Contrivances of the Mind, that carry difficulty with them, and do not so easily offer themselves, as we are apt to imagine. For example, Does it not require some pains and skill to form the general Idea of a Triangle, for it must be neither Oblique, nor Rectangle, neither Equilateral, Equicrural, nor Scalenon; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an Idea wherein some parts of several different and inconsistent Ideas are put together.I shall not pretend that what Locke is claiming in this passage is wholly clear, nor shall I try to defend the views expressed in it. My intention is to show that what he says here has been widely misinterpreted. It has become common to treat the contents of the passage as aberrant; as presenting a ridiculous variant on his main thesis on abstraction, or that very thesis elaborated with a foolish rhetorical flourish. But what is said in this passage is not something said elsewhere, nor is it an alternative to something said elsewhere. Here, and nowhere else, Locke shows awareness of implications for his doctrine of abstraction, of views he holds about simple ideas. (shrink)

What does it mean for a general term to be rigid? It is argued by some that if we take general terms to designate their extensions, then almost no empirical general term will turn out to be rigid; and if we take them to designate some abstract entity, such as a kind, then it turns out that almost all general terms will be rigid. Various authors who pursue this line of reasoning have attempted to capture Kripke’s intent by defining a (...) rigid general term as one that applies to the objects in its extension essentially. I argue that this account is significantly mistaken for various reasons: it conflates a metaphysical notion (essentialism) with a semantic one (rigidity); it fails to countenance the fact that any term can be introduced into a language by stipulating that it be a rigid designator; it limits the extension of rigid terms so much that terms such as ‘meter’, ‘rectangle’, ‘truth’, etc. do not turn out to be rigid, when they obviously are; and it wrongly concentrates on the predicative use of a general term in applying a certain test offered by Kripke to determine whether a term is rigid. (shrink)

Mathematics educators suggest that students of all ages need to participate in productive forms of mathematical argument (NCTM, 2000). Accordingly, we developed two complementary frameworks for analyzing the emergence of mathematical argumentation in one second‐grade classroom. Children attempted to resolve contesting claims about the “space covered” by three different‐looking rectangles of equal area measure. Our first analysis renders the topology of the semantic structure of the classroom conversation as a directed graph. The graph affords clear “at a glance” visualization (...) of how various senses of mathematics—as imagined, as performed, and as historically rooted—were interrelated. The graph represents the emergence and intercoordination between conceptual and procedural knowledge in the ebb and flow of classroom conversation. The graph has not just descriptive, but also predictive power: Interconnectedness among the nodes of the graph representing the first 40 min of conversation predicted the structure of recall in the final ten minutes by children who had played little overt role in the conversation up to that point. The second, complementary framework draws upon Goffman's expanded repertoire of roles in speech to demonstrate how the teacher orchestrated this classroom conversation to establish coherent argument. In this second analysis, we establish how the teacher mediated between the everyday talk of her students and the discourse of mathematics. Her revoicing of student talk created interstices for identity and participation in the formation of the argument. Together, the two forms of analysis illuminate the emergence of mathematical argument at two levels: as collective structure and concurrently, as individual activity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Putting French Studies on the MapTom Conley (bio)A good deal of work accomplished in new historicism over the last decade has opened new perspectives on the relations of literature to cartography. If new historicism tends to be affiliated with Shakespearean scholars who reconstruct the world of the Globe Theatre in the context of London and the Elizabethan world picture, it almost goes without saying that cartography, whose mobilization and (...) rapid growth occur from the beginnings of the printing press to the middle of the seventeenth century, plays a significant role in the analysis of print-culture in general. 1 The convergence of the two disciplines has shown that Renaissance authors, obsessed with the beginnings of writing, valorize both its geographical and spatial virtues and the ways that its pictogrammar constitutes “a grid for comprehension of the world” [Martin 14]. Humanists discovered that it simulated divisions of land in transactions devoted to their negotiation. What early archeologists of writing discovered is comparable today to what we gather about the meaning of the crosshatched rectangles and insignia we admire on the great prehistoric petroglyph of Bedolina standing over its arable valley below [Jacob 41–48; Thrower 4–5]. In the early modern age cartographical issues are central to broader inquiry about the power of writing.New historicists take up early modern cartography not just to assess the impact of Ptolemy on humanism but to develop agendas that concern how a sense of habitus was conceived, projected, and betrayed at a time of tumultuous change. They ask how the “world” could be both imagined and experienced when its boundaries were expanding at exponential rates. Cartographic studies have shown where the unknown, vital for any definition of consciousness or even the drives of life itself, was located and bracketed. 2 The unknown was an integral part of cartography prior to the eighteenth century. But to assert, as many have, that cartography sought to contain the unknown within the terrae incognitae it indicated on its maps does not solve the relation of the discipline with the [End Page 23] unknown. Evidence shows how much in the early modern age the unknown inhabits most written and schematic representations of the world. 3 Unnamed patches that we retrieve on maps printed in the sixteenth century prompt reverie of spaces that can be fancied as unknown by virtue of the maps themselves. The cartographical impulse in early modern studies cannot be dissociated from our own drive to find spots that can remove us from the regnum of nonplaces that define our world, that is, other places, whether heterotopical or “anywhere out of this world,” valorized when the “nonplace” has come to define contemporary human geography [see Augé 1992].Concurrently, the history of cartography remains one of the most immediate modes of access for what we can understand about the imagination of power, control, statecraft, and economy at a time when maps figured with increasing regularity in matters of administration. In broader terms, we can say that the unforeseen growth of map production and the consequent stress laid on fantasies of power that accompanied cartographic representations from the beginning of print culture to the establishment of “state reason” under Louis XIV bore witness to a greater spatialization of knowledge. What in the study of literature goes by the name of discourse is seen through a cartographical lens as patterns of utterances and exchanges that owe much to the influence of Ramism, monocular perspective, and diagrammatical logic. It is a truism to note that when the world became a function of cartographical representations made accessible to a public at large, the ways it was configured bore great impact on communication in general. 4In this issue of Diacritics, where the current plight and uncertain future of French studies is being pondered, it also goes without saying that many teachers and scholars are wondering what can be done to invigorate one of the richest of all literary canons. The assault that American media have led on French culture (among others, articles in the New Times by Roger Cohen and Craig Whitney) would lead us to believe that literature has [End Page 24] become equivalent to freeze-dried croissants, a... (shrink)

We consider the problem of quadrilaterizing an orthogonal polygon P, that is to decompose P into nonoverlapping convex quadrangles without adding new vertices. In this paper we present a CREW-algorithm for this problem which runs in O time using Θ processors if the rectangle decomposition of P is given, and Θ processors if not. Furthermore we will show that the latter result is optimal if the polygon is allowed to contain holes.

Inquiries of Wellstein, Grünbaum and others have proved that there are indefinitely many different spatial models of Euklidian geometry. The points, lines and planes of these models are related to each other as the points, straight lines and planes of Euklidian geometry, but they are obviously totally different from them. That means that the axiomatic Euklidian geometry does not clearly determine the spatial forms of their planes and straight lines. The constructive geometry basing on approaches of Hugo Dingler tries to (...) solve this problem of disambiguity so that a clear realization of the geometrical basic objects plane, straight line and rectangle and others is possible because of certain rules. On the one hand these rules are to pledge the techniques of realisation and on the other hand they are the basic for the deduction of statements on the technically realized geometrical basic objects. The rules are especially to pledge the selection of apt material that keep its form. The following will show that the disambiguity cannot be pledged by the mere laws established by the constructive geometry and especially that the problem of electing the material cannot be solved by these laws. Furthermore it proves to be necessary to analyze and reconstruct more circumstances describing the selection of apt material which exceed the present standard of constructive geometry. (shrink)

Reproduced with the kind permission of the author. Currently available in the collection I Looked Alive . © 2010 The Brooklyn Rail/Black Square Editions | ISBN 978-1934029-07-7 Originally published 2003 Four Walls Eight Windows. continent. 1.1 (2011): 43-51. Introduction Ben Segal What interests me is instigated language, language dishabituated from its ordinary doings, language startled by itself. I don't know where that sort of interest locates me, or leaves me, but a lot of the books I see in the stores (...) seem to lack language entirely. Gary Lutz (2006). This issue of continent.'s fiction section features a reprint of “This Is Nice of You” from the first edition of Gary Lutz's collection I Looked Alive . That book was originally released by Four Walls Eight Windows in 2003 and has since been reissued in 2010 by The Brooklyn Rail/Black Square Editions. Calamari Press has also reissued Lutz's Stories in the Worst Way (originally published by Knopf, largely forgotten and dismissed, and then re-issued by the too-short-lived 3rd Bed). “This Is Nice of You” was edited for the re-issue of I Looked Alive and, as the original book is out of print, the earlier version of the story has been hard to come by for some time. This initial version is a bit longer than the new version—Lutz is a master of tightening down his texts to their most linguistically intensified cores—but it is in no way sloppy. It is a great privilege for continent. to be able to make available rare texts of (first) aesthetic and (second) scholarly value. For those readers unfamiliar with Gary Lutz, I believe this story will serve as a worthy introduction. Like Raymond Carver, Diane Williams, Christine Schutt, and so many other important twentieth century and contemporary short story writers, Lutz studied with and was edited by Gordon Lish. This connection is apparent in his attention to sound and the sentence as compositional unit, but Lutz's is a unique voice. “This Is Nice of You” bears Lutz's trademark torqued and turning syntax, his sexed-but-nameless characters, his rendering of the human body and its emissions as utterly discomfiting. Lutz's preoccupations with the mundane raise ordinariness, via startling language and observation, to grandiosity and grotesquery. In the fall of 2008, Lutz delivered a lecture entitled “The Sentence is a Lonely Place” to writing students at Columbia University. The lecture was later printed in The Believer (and is linked below). In it, he spoke about the importance of the sentence as a compositional unit, as even the distinguishing formal characteristic of prose. Specifically, Lutz explained that, from Lish, he had developed a "poetics of the sentence." Accordingly, Lutz constructs his stories at the level of the sentence, paying extreme attention to the material of words- their letters and their sounds- and the way they abut one another and interact on this material level even before they are employed in the service of traditional aims of fiction like meaning or story. Lutz often uses a(n almost constraint-related) technique called consecution. Letters or sounds from one word are carried forward into the following, producing drama and movement in the language itself at a level entirely apart from that of plot. For example, you can see how the 't's in the first sentence of “This Is Nice of You” repeat fast and hard through met and then soften into the 'th's of brothers and they. This close attention to the specific material and characteristic conditions of prose means that Gary Lutz's work always involves both a happening in language and of language. “This Is Nice of You” has a richness and depth that is hidden not in symbolism or obscure reference but on the surface of the page, in the language of every sentence. FURTHER READING Lutz, Gary. “ The Sentence Is a Lonely Place. ” The Believer January, 2009. Web. Short stories and excerpts at Web del Sol . Web. Taylor, Justin. “ An Interview with Gary Lutz .” Bookslut. July, 2006. Web. THIS IS NICE OF YOU [156] [1] I was a man dropping already well through my forties, filthy with myself, when, taking a turn at the toilets one afternoon, I met two brothers-they said they were brothers-who swore they had a sister, a schoolteacher, an officer of instruction at the county college, a whirlwind midlife turmoil of everything already put to ruin, who had gone off from a new marriage in an old car, an upkept and ennobling sedan, but had returned now to the apartment and [157] was living there alone with the little runoff there was from the marriage-some outcurved appliances, apparently, and low-posted furniture promoting its own mystery but becoming figurable in certain concentrations of TV light-and, above all, a telephone (on a pedestal, they insisted), the handpiece of which she gripped in lieu of exercise, or in fury, and I thus let out my little, reliable cry that I was in fact a student of the telephone, that it was a debasing apparatus in the main, with its meager economy of bells and tones, and the intimacy of the mouthpiece that sent your breath, tiny aftervapors of it, back toward your lips, so that regardless of the party accepting the outgoing products of your voice, you were, at most, in a further, rivaling exchange with yourself alone, and this is what must have brought the two of them around, the men who proclaimed brotherhood with the woman, because they offered me her phone number, put it at my disposal on a piece of paper one of them had already committed it to, a tearing from a menu, and the looks the men were now giving me had deletions in them, already, of my exact, beanpole shape and size. So off I went to a pay phone, the nearest canopied one I could find. The woman answered after the second ring and said she needed a lift right that very moment into the little, unlevel city close by. She was idling in the doorway of the building when I pulled up in front, and I helped her into the car, then got back in myself. I had always had a way of not having to look at people that nonetheless brought them to me in full, and so I still am certain of the susceptive and impressible comp-[158]lexion, the shimmer on the mouth, a lipstick of low brilliance, a difficulty around the eyes, the hair short and rayed out exclamation ally, skin bagged up over the elbow bone, conflict even in how her arms stayed at her sides—in sum, a spinal loveliness for me, an off-blonde quantity with shadowed, thumbworn hollows that put me out of as much as I might have ever known of women before. I set the two of us into the narrow traffic, and I remember telling her, by way of explaining the little burden which I had shifted, by now, from the shelf of the dashboard and onto my lap, that when you lived in filth, as I then did, a daily newspaper came to count for a lot, although instead of the thick-supplemented local paper I bought a trimmer one from a backlying town—not, of course, for any affluences of native data it carried, but as an article of house ware: a rough immaculacy in four lank sections, a set of fresh, hygienic surfaces to come between the table, say, and whatever I had going for me at the table, if the table was where I was going forward—because what else so cheap comes so clean and far-spreading? The woman told me that her own trouble with paper was that through a modest hole, no larger than a quarter, that had been drilled a foot or so above the floor (the standard height, she had reasoned, of legitimate electrical outlets), and by means of which her faculty office had at last gained communication with the roomier but unoccupied office next door, more and more often shot a single sheet of paper, plain copier paper she had rolled just barely into a tube, [159] so that after landing on the floor of the neighboring office the paper would preserve little if any of the curl, and there would be nothing written or typed on it, of course, and it was always a blank sheet that had been ageing on her desk for some time and had already been moved around, or advanced, from station to station on the desktop, coming into further creaselets and crimps and other infirmities—paper, in short, still too bare and unfraught to be thrown responsibly and forgettably away, and yet too seasoned and beset with irritations of the surface (a molelike blemish, say, or what looked like a tiny hair, an eyelash, sunk into it, or frecklings, or notational pressings of a fingernail), too wrought, in sum, for the paper to be appointed to any secure curricular purpose. Her office, she claimed, was in fact full of such paper, much-handled and singularized sheets of it by the loose, functionless hundred. I had to get it across to the woman that I myself no longer had an office, or any other place to divide me reliably from everybody else, and that for much of the daylight I thus appeared to be among people because I kept putting myself where people came together into even closer-fitting assortments, the viewing areas and showrooms and rotundas and such: I took in the lean-to look of the women, the tongues coming and going in what the men kept thinking of to say—whole families of low knees for me to bark my shins against during the crowded and involving way out. At home afterward, in the one room where my life was packed down, I would keep my nose stuck in the safehold of the phone [160] book, where the names of people suffered reduction to mere episodes of the alphabet and underwent humbling declensions down every column (Lail, Lain, Laine, Lainerd), and he names of streets, of the towns and townships, got docked in crude, heedless abbreviations (the vowels almost always the first to get poked out), and I would run my eyes over the telephone numbers themselves, each sequence of digits another fallible run of the infinite. I thus corrected my feelings for people and assembled myself emotionally into whatever else I had at hand—the obligating arms of the clothes hangers, usually, or the keen-angled understructure, the guardian legginess, of the ironing board. The woman said that in her case, though, it was more a matter of making slow circuits of the classroom where she had to put across the Emporial Sciences, retail theory and methods, to heat-giving and suggestive young women, some of them world cruelties already. There was the cooing of empty stomachs in the hour just before lunch, and the braying and fizzle of loaded stomachs in the low hours of the afternoon. She would recite her notes in a voice barely loyal to anyone octave, a tiny alluvium of slaver hardening at the corners of her mouth on the days she gave the glassy lozenges a slow, warming suck, and she would take lowering notice of how whatever she said succumbed at once to freak spellings and razzing paraphrase in the big, dividered notebooks; and because in midafternoon light the world looked as thorough, as filled in, as it was ever going to get, a better way to set about ruining her eyes was to review how hair had [161] established itself on the arms of the young women, because almost every arm had brought across itself a welcome and diversifying shadow. On one girl it would be a fine, driftless haze afloat above the white of the arm, never seeming to touch down on the skin itself. (An atmosphere, at most, of chestnut brown.) On another, it was as if copper wire, the narrowmost lengthlets of it, had been stuck into the fleshy batter of the thick, freckled forearms. On a third: a field of it–wheat-colored, thin-spun. On a fourth; a differencing, darkish updrift that shaded off as it approached the inner bend of the elbow, then re-emerged at the base of the upper arm as whiskery fringe. On others it was a brassy or rust-colored frizz, or it was as coarse as cornsilk, or it looked fussed on, as if the arm had been slowly stroked with charcoal. But here the woman broke off, or I may well have made an interruption of my own—I think I must have asked whether she was hungry, and she said if I was, and so on one of the lesser streets I parked the car and led her down into a belowstairs eating house I still remembered. Sandwiches were presently lowered in front of us. I watched her remove the festooned toothpick from hers and then play her fingers over the toasted planes before she took a fond first bite. "This is nice of you," she said. I must have looked at her in the way I then had of getting people to speak so they would not seem to be dwelling any longer on my features, because if on the well-set face the mouth and eyes are said to seem frozen in elegant orbit about the til) of the nose, then mine was a face that behold-[162]ers, regarders, could not help trying to round off with greater success, to goad the particulars of it back into the arcs they had wandered away from—the mouth, for instance, having been pursed and pinched suchwise that it seemed resident more on one side of the face than the other—and there were other signs of original strife to be busied with (slapdash eyebrows unbunched, it appeared, from reserves of hair elsewhere on my person; a showing of adult acne, a shrivelly little relevance of it, confined to the declivity of my nose); and so to be polite, the woman thus sank her gaze into her sandwich, and told me, in a voice lowered accordingly, that, one late-childhood summer, she had devoted herself to collecting postage stamps: it was a tongue-involving sideline to early-arriving puberty, and she liked having to lick the pale, gummed hinges instead of the sticky backs of the stamps themselves before entering everything into the hosting album; and once, during some foul weather between her and a brother (the older, thrown-over one, who had already made a habit of fooling the underside of his arm across the top of hers and calling her "pussified"), she reached for the shoe box in which she had let duplicate stamps accumulate—Spanish ones, mostly, of a fading orange—and sent the box slooshing through the lower air so that the stamps showered onto the brother's bare legs with a full, delicate harm. The woman was now touching up the surface of her iced tea with tiny activities, initiatives, of the longspun spoon. I myself was good at getting my touch onto things, although in a way that seemed to mix up the motive atoms inside [163] them, but I was satisfied that for the moment my sandwich, the unbitten-at half of it, was displayable and fit and local to my plate. The woman went on to say that, as a child, she had been bundled off, many an afternoon, to the slope-ceilinged quarters of a bachelor uncle who, when speaking of anybody not immediately present, could not bring himself to use the person's name but instead would say "an acquaintance of mine in ..." and then mention the name of some lapsed homeland, or little-loved rural orchestra, or backset building about to come down; and it was never a riddle, this device of his (not once could the girl have been expected to identify any of the subjects), and no matter how often and aloud he insisted that particularizing persons any further—bringing even a first name down upon anyone of them—would have been indecent, he claimed, much like doing things to people while they slept, the girl accepted all of the uncle's prim and extravagant evasion for what he surely must have intended it to be: a neat, protective trick to space the world out a little further in her favor, to scatter the population so that wherever her hand might at last come down, it would have to be on herself alone. And here I could sense that the woman wanted from my mouth an account of as much as I myself might have ever managed of attachment, so I told her I had once owned a house (a rising, really, of much-fingered, handwrought architecture that amounted to a little family of rooms above garages: a boxlike building with a rattly thorax of downspouts [164] and drainpipes and an unfolded but full-toned fire escape), and I had had for a time a boarder, a student, a high-colored, loose-packed representative of declining girlhood, hung with necklaces and barrettes, a girl of precise but shifting leanings and inclinations; and the afternoon she had come round to ask after the room, I stood in the entranceway, handshaken and asweat, and from what would later be my memory of the girl, I made off with, first, how every pore of her nose seemed to be sheltering within itself a tiny dark seedlet, a grain of something immediately, enormously valuable. And an almost lipless mouth (just a slit, practically), the teeth inside looking wet, watered-it was my life's chore, at that instant, to keep from sending the back of my thumb blotterlike across the line of them (I was later to learn she drank everything cold and through the narrowest of straws). And her hair: it was tea-colored hair she had, long and reachful, an unstopped downcome of it. Tall for a girl, but she managed to stay out of much of her height and put herself across as somebody backward, or behind. I must have told the girl, as best I could, that I of course had a wife, a full-faced, imperishable partner, though for the moment she was gone otherwhere in the marriage, and here the woman, my present companion, my tablemate, whose feet were now parked, in parallel, on the grade of my upper leg, interrupted to say that her husband, too, had been such a liar, and what could I bring up by way of reply other than that a lie is a truth struck through with other, further truth, or that a lie is the present multiplied by the past or that a lie [165] is an outcry of borrowed hope? The woman gave me an allowed look of disgust, her eyes lowered but still popular with me, and on I went with what had now become the girl of my story. For there had been a great, gainful carpet in the room I put the girl into, a matty expanse of coarse, grabby piles, an engrossing affair that took things into itself and held them tight, misered them, and I of course insisted that the girl not bother herself with its upkeep, that I enjoyed weekly access to a prestigious, upstanding vacuum cleaner; but no sooner was the girl out of the house each morning than I would withdraw from my room, where time was unportionable, and loose myself into the ticktock impertinence of the girl's room and get down on my knees, and, going after the carpet first with my fingers, then with a forceps, and finally by unspooling lengths of clear package-sealing tape and pressing them against the tufts in neat rectangles to catch what I might have missed, I brought vast tracts of the carpet to depletion, recovering not simply the girlinesses, the girleries, one would expect (buttons, straight pins, downed jewelry), but flirtier personalia in the form, say, of a stray confetto brought into the world when a page had been wrung with out caution from a spiral-bound notebook, or some pleated paper shells of the chocolates she required, or one of the bargain antihistamines she took to get her naps going, or a trash-bag tie ragged enough to show the kinked line of the wire within (this I would get wound around my finger), or a cough drop enwrapped like a bonbon (I would undo the [166] wings of the wrapper and have to decide whether to suck the drop all down or begin chewing it midway)—I became the following, the public, that these things, these off-faIlings, had come to have; but mostly there was hair, afloat above the uppermost pushings of the fabric of the carpet an almost continuous haziness of loose hairs of all lengths and sources, and I would have to set them out on a fresh sheet of paper and assort them according to the regions of the body they had taken their departure from, and in no time I had nest-like filiations of broken filaments and smaller involvements of the hairs that made me think of hooks, of barbs, of treble clefs, and each pile required a separate envelope, to be filed in a separate shoe box for every sector of the body until, I hoped, the boxes themselves would no longer be enough and I would have raised something semblable, brought up something equal in volume to the comprehensive girl herself. And her wastebasket! For every bit of rubbish, every dreariment she tossed into the thing, I would, in secret, deposit a reciprocal discard of my own, matching a spotted, confessory tissue of hers with a lurid throwaway after my own heart–the cardboard substructions of a fresh parcel of underwear, maybe, or tearings from pantyhose I now and again pressed against a span of my forearm to work onto it the complications of female shading I otherwise made do, choosily, without. I thus built the two of us up together in her trash! One afternoon-it was another of those lifeful, unsam-[167]pled days on which the world humors us each a little differently to keep us nicely on our last legs—I discovered in the wastebasket an inch-deep textbook of hers, a paperback with a celery-colored cover that had come partly unglued, and this dilapidation I paired off, naturally, with a name-your baby guide to whose pages, during my recurrent turnings of them, in bed or at table, I had contributed dried produces of my person, a chemical splendor entirely mine. This coupling sent a sudden spigoty thrill from me that forced an unbuckling and an unzipping and a cleanup with a handkerchief I then ventured responsively into the wastebasket as well. It was in the bathroom afterward that I found a suds-clouded puddle on the unlevel floor of the tub, a little undrained remainder, rimmed with offscum, of the girl's prolonged early-morning soak, and this was as much as I needed to get on my hands; I pressed them flat against the wet porcelain, then flapped them around in the air, and that was when I noticed it—in the amphitheater of the toilet bowl, an orange-yellow tint, or value, to the waters. When the girl arrived home that evening, I told her, of course, that I had discovered fresh, unforeseen trouble within the tank of thelet (a misalignment of the trip lever, a waywardness of the float ball, a ulation of the lift wires, kinks and defects, really, throughout the entire system) and that in fine it was an apparatus now operable only by means of advanced and strenuous equilibrial manipulations that it would be unseemly, inhospitable, of me to pre-[168]sume to burd to burden her with–so that from here on out, following any leak or evacuation she need merely lower the lid and then, before quitting the room, ring the handbell that had been placed on the would seeeverythinghing else. But the bell never rang, not even once, and from my window the next morning I watched the girl carry from the house a little plastic bag distended balloonishly, much like those bags you will remember having seen in the hands of children bearing homeward their solitary carnival-prize goldfish. In fact, I never ran across the likes of the girl again. The man who came to collect her things-not the father, apparently, but an advocate, an upholder-l found to be dull-eared and lax in his speech, and the better part of his face seemed to have already begun making tiny, rotational departures from whatever it was that the eyes, themselves impressively mobile, were just that moment having to take in. (Was there a lamp in the house that was not that night slopping its wattage over everything?) I guess I was waiting for the man to take a laggard, last-minute interest in me, and by now I was pushing everything out into the paired first person–it was, I said, “Our night shot,” and I began including the two of us in whatever it might be doing out, the expected sprinkles and such—but he was no friendship buff, and he paid no heed to my telling him that the only dress of hers I'd ever twidged myself into even part of the way had been the simplest of them all, a large-buttoned wonder of depthless blue, and then only on the principle that one naturally fits whatever one has into whatever somebody else [169] had first, or how else would the world keep getting any taller with people? The man just went about the removal of the girl's things without having to be reminded too noticeably, I guess, of how every dick hangs by a thread. My listener, though, had by this time brought about some becoming slowings of her arm—it was an arm inclinable to langorous diagonals and magicianly swoops through the air above the tabletop—but it no longer was involving itself with her plate, so I suggested we shove off, I made payment for the food, and on our way to the car, and then in the car as I took to following her pointings, the directional tilts of her head, she said that you naturally kept putting more and more of yourself into another person, at first wondering how much she can take, how much of you is accumulable and how much she can hold, and you're letting things out, disbursing yourself, and you've soon got things set up in her, and room is being made for even more of you, and if you bring this off with enough people, even two or three, what you've got is at first a comfort, because you can pass yourself along and move a little more widely through the world and leave it to these others to man your grievances, your disappointments; and what brought this to mind, the woman said, was a term of financial hardship she had contrived for herself a few years back, an unpaid leave of absence from scrupling letter grades onto quiz papers (propped-up As, and upended Bs made to look, rather, like fannies; all As and Bs, no Cs or anything lower, the difference between an A and a B having less to do with the accuracy of whatever facts might [170] have been impounded in provided for an answer than with anything recallable about the way the enrollee ad conformed her body to the confining perpendiculars of her chair and the navel-level writing surface that projected from it, or the way there might one day have been an unignorable blush on the instep of a once-moseying foot, disburdened of its shoe, that had got itself trapped in the grillwork of that cagelike involvement, intended for books, that was welded to, or otherwise schemed into, the underworks of the chair)—this had been a duration, in short, of controlled difficulty when the misexpenditure of even a twenty-dollar bill had set her thrilling, gloating, over everything she would miss out on, and one afternoon she had made an engagement for a haircut, just a trim, and very early in the session the haircutter, a woman ill-defined in the face but otherwise full of conspicuities of emotion, set down the prevailing scissors and pressed the flat of a lukewarm hand against the woman's cheek, held it there for a good minute or longer, while the other hand eventually found its way into a drawer, a shallow treasury of slender specialty scissors, one pair of which the cutter withdrew and began routing deductively through the woman's hair, the other hand staying put on the cheek, longer and longer, and the woman went home and for afterward the bathtub was now a more likely destination than any of the upright furniture, and it got easier to fill the tub with further clarifying volumes than to clear space on the difficult heights of the sofa, and she was hardly claiming to have become a cleaner [171] person in result—she in fact would often discover, voyaging about her body, a browned, fractionary detail of a larger crepe of toilet tissue that must have got itself stuck in some assy crevice and was impossible to get plucked out of the revolving suds—she was saying only that she spent more and more of her time thus immersed, ill off in water, and the haircutter had surely had a hand in it, the woman was doing some of the cutter's life now, coming into some of its wrong, because you sometimes have to look to somebody else's life to get dimensions set back even part of the way around your own, and it should not have to be any less your own life when it comes from somebody else, and you could surely fudge a society out of anyone available person and get this person doubling for the many, so that in the little run of things perpetuable from one person to the next, every loose moment stood to become a complete, active finality. But by now this was a new day, with only an hour or so off it already, and the place the woman had made me bring us to, the man's place, with a promise that the man was elsewhere—this was on a little offshoot of a street, a stewy efficiency apartment the color had long ago gone out of; and when, once in bed, still clothed, I found among the sheets and blankets a spoiling pair of the man's underpants, one of the leg openings of which was puckered into an avid, sloppy mouth, I held myself accountable for redisposing the fabric until I got a befitting featurelessness back onto it; but all the while, I am sure I had to make myself go over again in my mind that if the body is the porter of as many organs of affec-[172]tion as there might one day turn out to be, then the idea was to let the thing carry you to where you would otherwise never have any reason to arrive, because I listened for the unmelodiof the the thede ofthe woman's zipper, and then the woman made me put myself out of my own clothes, the attritional corduroys and overshirt, and got herself up at last onto the topic not of the man whose apartment it was (because his story was scarcely the story of how the boy who decides he is half a girl no sooner starts to worry about where the other half might than he gets careless with where he rests his eyes, or what he gives even the feeblest of fingerholds to, and anything, even a crumbly triangle of pie offered on a saucer instead of on a pie plate proper, comes in easy, ready, wronging answer), but of her husband, and how, no more than a couple of months into the marriage, he had begun snugging away in his undershorts a little source of chanc, reliable frictions to nudge him onward through the workday—anything company-keeping that could be counted on not to slide out of the elasticky leg holes: a half-dollar packet of chocolate tittles, maybe, that was barely noticeable in the baggy surround of the widecut trousers so popular at the time. For by now the woman had at last brought what is usually called the other mouth to within only inches of my lips, but it is not a mouth, obviously, although I let myself go along with the goodwill behind the comparison, the way I will remain loyal to anything deliberately and faithfully misunderstood, and I fussed my tongue against the vital trifles hung inside of her, as much of the curtailed finery as I could find, [173] and gave the whole insimplicity of it a slow-circling, examinational lick, until I was taking a sudden tepid downwash on the tongue. It was a familiar, latrine in dribble that must have tasted, no doubt, like trouble just starting out.p [1] Editor's Note: Original pagination from first edition print denoted with bracketed page numbers. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:From Politics to Philosophy and Theology:Some Remarks about Foucault's Interpretation of Parrêsia in Two Recently Published SeminarsCarlos LévyAt the beginning of his seminar entitled Le courage de la vérité, Foucault gives a first definition of parrêsia (2009, 10–12), which I take as my point of departure.Parrêsia is a fundamental political concept; it denotes outspokenness, and Foucault distinguishes between two versions of it, one negative, the other positive. The first (...) meaning implies the articulation of everything, "n'importe quoi" (whatever), an expression that in French is indeed derogatory. For Foucault this meaning finds an illustration in a passage from Plato's Republic in which the philosopher describes the appalling state of the democratic city, where everyone tries to impose their own desires on others.1 The positive meaning implies that truth will be stated "without dissimulation, reservation, set clause, or rhetorical ornament that could encode or hide it" (2009, 11). But Foucault says that to effectuate this positive meaning it is not enough to merely state everything and state it truthfully. It is also necessary for the speaker of parrêsia, the parrêsiastês, to personally involve himself in what he says and to take a risk. As Foucault says himself, this is to speak "truth while taking the risk of violence" (2009, 12). [End Page 313] This risk is nonetheless attenuated by what Foucault calls "the parrêsiastic play," that is, the capacity of the interlocutor (assembly, tyrant) to tolerate outspokenness.Even though Foucault never sets the problem out in these terms, one may construe parrêsia as both a passion, since it entails an emotional investment, and a virtue, insofar as it is still linked to courage. It is common to say that somebody has "a passion for the truth" or that he has "the courage of his convictions." However, Foucault uses the term "passion" very sparingly. An analysis of word frequency in his seminars for the period 1982 to 1984 reveals that the term "virtue" occurs often, while "passion" is almost entirely absent, except about tragedy (2008, 105–35). By refraining from speaking of the "passion of truth," Foucault rejects the possibility of analyzing the concept of parrêsia in a more unitary way. For him, there is a good and a bad parrêsia, a situation that emphasizes the difficulties usually inherent in dualism: how can two opposite realities coexist, especially within the same concept? These difficulties are carefully analyzed in the seminars, but there is also a methodological difficulty: do historical sources force us to accept the dualistic interpretation or, better, the reconstruction proposed by Foucault in such a persuasive way? Or do they prompt us to introduce the notion of passion, somehow or other, as being present even in the "good" parrêsia?In my view, one does not compromise Foucault's position by saying that, for him, the dualism inherent in political parrêsia has a functional nature. It is linked to what he calls the right functioning and the worsening functioning of democracy, as they are articulated in his seminar of 2 February 1983 (2008, 157–69). In his exposé some postulates are expounded using the metaphor of the rectangle: the existence of parrêsia requires democracy, and thus democracy forms the first vertex of this rectangle. But one of the most interesting elements in Foucault's subsequent seminars is his effort to demonstrate that parrêsia can nevertheless exist under tyranny without its most essential features being undermined.Democracy, in Foucault's opinion, can't be lively and dynamic without the second vertex, which he calls "le pôle de l'ascendant"—the pole of ascending leadership; that is, in his own words, "the problem of those who, speaking before others and above them, are heard by them, persuade them, lead them, and have control over them" (2008, 157). Foucault's use of the term "problem" is itself somewhat... problematic. It is not clear why the existence of this ascendancy is a problem to the extent that it can be seen as the condition of a democratic and parrêsiastic functioning. In Foucault's [End Page 314] own words, the... (shrink)

The two‐dimensional version of the classical Mycielski theorem says that for every comeager or conull set there exists a perfect set such that. We consider a strengthening of this theorem by replacing a perfect square with a rectangle, where A and B are bodies of some types of trees with. In particular, we show that for every comeager Gδ set there exist a Miller tree and a uniformly perfect tree such that and that cannot be a Miller tree. In the (...) case of measure we show that for every subset F of of full measure there exists a uniformly perfect tree such that and no side of such a rectangle can be a body of a Silver tree or a Miller tree. We also show some properties of forcing extensions from which we derive nonstandard proofs of Mycielski‐like theorems via the Shoenfield Absoluteness Theorem. (shrink)

It is commonly the case that a problem concerning a mathematical or physical system can be solved in two quite different ways--by an internal or an external approach. For example, the area of a triangle can be found by integration or by showing it to be half that of a certain rectangle. In general, the first approach is, to analyse the given system into component parts, and the second approach is to deal with the system as a whole. It seems (...) that even in cases where solutions to physical problems obtained according to these two approaches are equally valid, and are equally good as explanations, scientists prefer the solution obtained by the internal approach. The reasons for this preference are examined. And it is suggested that whatever the reasons, this preference may have been partly responsible for the 19th century preference for the Kinetic Theory rather than Thermodynamics. (shrink)

The present paper describes a joint action paradigm in which individuals or pairs utilized two computer keys to keep a dot stimulus moving inside a larger rectangle. Members of a pair could neither see nor hear each other. This paradigm allowed us to combine the discrete-trial type dependent variables commonly utilized by representational theorists, with the continuous, temporal dependence variables utilized by dynamical theorists. Analysis revealed that individuals kept the dot in the rectangle longer than dyads and did so by (...) moving it back and forth within the rectangle. Dyads, however, pressed their individual buttons as quickly as possible in order to keep the dot near the middle of the rectangle. These findings indicate that joint action constitutes a multi-scale phenomena that is best investigated via multiple, complementary methodologies versus single-measure, competing theories. (shrink)

continent. 2.1 (2012): 22–28. Jeroen Mettes burst onto the Dutch poetry scene twice. First, in 2005, when he became a strong presence on the nascent Dutch poetry blogosphere overnight as he embarked on his critical project Dichtersalfabet (Poet’s Alphabet). And again in 2011, when to great critical acclaim (and some bafflement) his complete writings were published – almost five years after his far too early death. 2005 was the year in which Dutch poetry blogging exploded. That year saw the foundation (...) of the influential, polemical, and populistically inclined weblog De Contrabas (The Double Bass), which became a strong force for internet poetry in Dutch in the years to follow. In the summer of that year, a lively debate raged in the aftermath of Bas Belleman’s article “ Doet poëzie er nu eindelijk toe ?” (“Does poetry finally matter now?”), on a blog specifically devoted to this question. Up to that point, the poetical debate in the Netherlands had largely been confined to literary reviews (which were often subsidized), having become mostly marginalized in more mainstream media, where poetry could be covered by only a small number of so-called authorities. As a result, literary debate had acquired a rather placid quality. Though a variety of camps with different aesthetics could be discerned, most poetical positions shared a general acceptance of poetry as a form of art somewhat apart from fundamental political concerns. Late modernists would pursue subtlety and density of reference. Others would insist poetry was best understood as a form of entertainment that should ideally be accessible and work well on the stage. Still others would insist that poetry is mostly a play with forms. Linguistically disruptive strategies were valued highly by some, but mostly for their aesthetic effect. Values of disinterested playfulness reigned supreme everywhere. Any idea that poetry could be a field in which one confronts politics and the world was decidedly marginal. This led to a climate in which most attempts at polemics were DOA, often based on far too superficial positioning and analysis. The greatest polemical debates were revolving around the question of whether poetry should be difficult or easy, with both camps defining their ideas of difficulty and accessibility in ways that were so utterly shallow as to make the entire point moot. Debates were performed, rather than engaged with. It was a postmodern hell of underarticulated poetics. Half-consciously, people were yearning for new forms of criticism that could put the oomph back into poetry. Weblogs provided for ways to explore debate directly outside of the clotted older channels of the reviews and the newspapers. Belleman’s essay and the resulting online activity had shown that there was a widespread eagerness to take poetry more seriously as a social art form. It was in this environment that Mettes started his remarkable project Dichtersalfabet . At that moment, Mettes was active mostly in academic circles, having become noted at Leiden University as a particularly gifted student of literary theory. Within the Netherlands, the field of literary theory has a very odd relationship to literature as it is practiced in the country. Academic theory tends to have a mostly international view and engage with international debates of cultural criticism, literary theory, and philosophy, with academics often publishing in English and attending conferences around the world. Literature itself however is much more concerned with domestic traditions. Consequently, in the Netherlands, there exists a language gap between academic theoretical practice (as it is studied in the literary theory departments) and literary practice (which, academically, gets studied in specialized departments of Dutch literature). The Dichtersalfabet can be seen as Mettes’s attempt to close this gap. It is also an attempt to bridge the divide between theory and practice, in which he could apply his theoretical knowledge in a very unorthodox and unacademic critical mode that moreover could reach far beyond the domain of conventional criticism. Mettes’s goal was to trace a diagonal through Dutch poetic culture, to “strangle” what he perceived to be its dominant oppressive traditions of agreeable irrelevance, in order to see whatever might be able to survive his critical assaults. But he could only do so by means of a very serious engagement with poetry itself. To this end, he would go systematically through the poetry bookshelf of the Verwijs bookshop (part of a mainstream chain of booksellers) in The Hague, buying one publication per blog item, starting from A and working his way through the alphabet, reading whatever he might encounter that way in the restaurant of the HEMA store (another big commercial chain in the country). He would subsequently write down his reading experiences, refraining however from trying to write a nuanced book review. Rather, he would write about anything that caught his attention and sparked his critical interest. This way of working would yield vast, at times somewhat rambling, dense, lively, and generally brilliant essays, in which he held no punches. He never hesitated to pull out his entire arsenal of concepts from the international theory traditions, while never degenerating into mere academic exercise and pointless intertextualities. The attempt was rather to live the poetry that he read, and to engage it with the full range of political, academic, cultural, and personal references that he had at his disposal—all that composed the individual named Jeroen Mettes as a reader. Often what he wrote would not be according to the standards of what we usually think of as a critical review of a book of poetry. Sometimes he would even be a little sloppy in his judgments of poets or representations of the books he read, for example by basing an entire essay on the blurb of a book rather than its poetry content. But what he did was always brilliant writing nonetheless—virtuoso riffs on poetic fragments randomly found within capitalist society, exposing an incisive and insistent poetical sensibility. Mettes read poetry for political reasons, to see whether poetry could offer him a way to deal with a political world he detested. The right-wing horrors of the Bush years, the Iraq war, and the turn of Dutch public opinion towards ever more conservative, narrow-minded, and xenophobic views alongside a complete failure of the political left to present any credible alternative, were weighing heavily on the times in which Mettes reported on his reading. Poetry was to measure this world, diagram it, to lay bare its inconsistencies and faults, to indicate where lines of flight might be found. Amid the ruins of a world wrecked by imperialist policies, corporate capitalism, and doctrinal neoliberalism it would have to show the possibility of a new community. And it was, through its rhythmical workings, to release the reading subject from his confinement to ideologically conditioned individuality and lead him into the immanent paradise of reading. The stakes were high. Much higher than anything Dutch poetry had seen for many years. Mettes’s blog was widely read from the start. His posts sparked lively debates. Some of these subsequently led to the publication of extensive essays on a few key poets in some literary journals, particularly Parmentier and the Flemish journal yang , for which Mettes would become a member of the editorial board, a few months after starting the Dichtersalfabet . This could have been the start of a brilliant career, but this was not to be. The initial manic energy that fueled the blog gradually subsided. The Alfabet was updated less and less regularly. Mettes sometimes just disappeared for many weeks, then suddenly returning with a brilliant essay. Until, on September 21, 2006, he posted his final blogpost, consisting of no text whatsoever. That night I learned from his mentor at Leiden University that he had committed suicide. Mettes and I had had some fruitful exchanges on poetry, rhythm, music, and form, mostly on the blogs, but also by email. Three weeks before his death was the last time I heard from him: a very sudden, uncharacteristically curt note saying “My old new sentence epic.” Attached to that message I found a DOC-file of a work so major that I felt intimidated. This was N30 , a text he had been working on for over five years. After his death, it took me a long time before I dared to read it in its entirety. In the meantime, the work of preparing the manuscript for publication was entrusted by his relatives to his colleagues at yang magazine. It took them a few years to brush up the text and to edit the Dichtersalfabet -blog (which, apart from the Alphabet project itself, incorporated many other fragments of political, polemical, and theoretical writing) into book form along with the essays. The result of this labor was finally published in 2011 as a two-book set, and Mettes burst onto the Dutch poetry scene for the second time. The work was widely reviewed, on blogs, in journals, magazines, and newspapers. Many critics who had not followed the blogs in 2005 showed themselves surprised, baffled even, by the intensity of Mettes’s critical writing. But for those who had read the blog, the main surprise was in the poetry. During Mettes’s lifetime, some of his poems had already been published in Parmentier . Although these were strong texts by themselves, in no way did they prepare readers for N30 . Nothing like it had been written in Dutch before. Instead, N30 explicitly follows the American tradition of Language Writing, directly referencing Ron Silliman and his concept of The New Sentence. However, it would seem that much of the poetical thinking around his use of this technique puts him closer to a writer such as Bruce Andrews. For Mettes, using non sequiturs as a unit of poetic construction was not only a way of reinventing formal textual construction, but it was another way of finding the fault lines in the social fabric. From the perspective of the Language tradition, one may put N30 somewhere between Silliman and Andrews. N30 shares an autobiographical element with Silliman’s New Sentence projects, and as in Andrews, there is a concern for mapping out social totality within text—what Mettes refers to as a “textual world civil war.” Again this shows a formal textual strategy for allowing the person “Jeroen Mettes” to be absorbed by the world, which here appears as a whirlwind of demotic and demonic chatter, full of violence, humor, intensity, beauty, disgust, sex, commerce, and strife. Influenced as it may by American precursors, Mettes’s tone and form end up quite different from his American counterparts, consistently referencing a world that is Dutch, all too Dutch, taking on the oppressive orderliness of Dutch society with its endemic penchant for consensus by introducing chaos into its daily life and laying bare its implicit aggressions. The work’s 31 chapters each have a different feel and rhythmical outline, but none of them follow a predetermined pattern. Rather, Mettes would consistently edit and reedit the text, randomly rewriting parts of it, as he explains in his poetical creed Politieke Poëzie (Political Poetry). N30 – referring to the 1999 antiglobalist protest in Seattle – was to be the first text of a trilogy. The work itself was written “in the mode of the present.” A second text was to be written in the mode of the future, and a third one, in the mode of the past, was going to be an epic poem about the Paris Commune, and to form an alternative poetic constitution for the European project. I still deeply regret that Jeroen Mettes never got to complete those projects, just as I would be very keen on knowing what he might have had to say about more recent political developments. Instead, in 2006, he remained stuck in the horrors of the present, that ended up consuming him completely. He left Dutch literature with some of its most piercing criticism and its most profoundly moving, exciting and powerful poetry. Excerpts from N30 Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "N30." In N30+ . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. Chapter 1 1999. A day is a space too. And another man, who had chained himself, had his ribs crushed, and a motor has driven over somebody’s legs. Dutch health care system spends ±145 million guilders per year on worriers. A spiderweb vibrates as I pass by. Randstad renovating. She slaps her bag against her ass: “Hurry up!” OPINION IS TRUE FRIENDSHIP Your skin. It doesn’t express anything. “But the use of the sword, that’s what I learned, and you’ll need nothing more for the moment.” Just try to interrogate a guy like that. Gullit in Sierra Leone. Codes silently lying all around. But that’s simply what belongs to “that it’s just allowed”: that sigh of “world” (a word expressing that the trees are now standing along the water like black men with white bags in their hair); that’s nothing else right? And you see how everything has to move, and first of all what cannot do so. Without Elysium and without savings, barbarians lashing out, horny for an enemy, staring across the water, staring into the air—staring to get out of it. “You’ve never showed me more than the mall,” she said. All those “dreams” in the end—and now? It was lying on the stairway, so I picked it up and took it upstairs. Chapter 3 “You know what?” Telecommunication. For love… I don’t really like that cheap cultural pessimism, but… The holy city is on pilgrimage in the earthly bodies of the faithful until the time of the heavenly kingdom has come. The end of an exhausting autumn day behind the computer, my eyes filled with tears of fatigue. KITCHEN / INSTALLATION / SPECIALIST. Network integration. In the sun, stretched out on a sheet. (…) I don’t believe what I’m reading, because I want to believe something else. An illusion? Suits me. There’s a variety of shapes and tastes… “So what?” you may think. 102 dalmatians can’t be wrong. But I want more, dear… A feel good movie. I’m smashing the burned body. So what? We continue to save the European civilization. What’s there to win? Plato with poets = Stalin without gulag? Ball against the crossbar. No wonder. She comes straight to her point. She’s standing in the kitchen eating an apple. (…) The godless Napoleon had used her as a stable and wanted to have her taken down. “Our” Rutger Hauer. Ready or not here I come. Psst… are you also wearing a string? Nobody understands our desire. Cliffs breaking the waves and shattering the sunset. I used to be a real romantic (as a poet). A typical fantasy used to be the one in which I brutally raped mother and daughter Seaver from the sitcom Growing Pains . Nevertheless you only contain bad words. Eyelashes. Automatic or manual? That your skin always in the afternoon. Integration. The air is empty. Too bad! Hand in hand on their lonely way. Alaska! Chapter 12 May 5, 2001 [10:00-10:30] A dust cloud on a hill. Globe. Indian (British) (tie) / pope. Damascus. Rape. We’re carrying the ayatollah’s portrait through the streets. At the moment the girl is mostly suede jacket with white ribbons on her sleeves. A small explosion flares up/impact. Camouflage. Close up. We’re analyzing the situation. He’s dead right? Dead dead. Dead. Everything without, these, and only with the body. Indices signal death. Dollar bills are printed in factories. Holes. Light patch. Globe in a box. Microphone. What’s the situation? Grey impact on a green hill (field?). The water is blue. He has no lips. Interns on the background with skirts that are too long. This is an example of a sonnet. An Islamic woman pushes against the door of an electronics shop. Arrows (percentages (prices)). Is this what awaits the American? Touch screen interface. The word, an island, can only be a sign in that situation. We pull up a chair, join in on the fun. On the shelves only books about computers. One glance in the distance is enough to lighten up a luna park in the distance. She’s really desperate, especially when she laughs. Click. Ah. Next. And now it’s raining, but that’s ok. Yellow stains sliding over the south. Shallow caves light: clothes, boots, electrical equipment. 45. 22:10. Nothing gives you the right to eat more than people starving to death. The Hague. Slam dunk. Traffic light. Two H’s, one L (standing for the L (little prick)). We’re happy to say something. Clouds, small suns, temperatures, cities. The truth is never an excuse. Yellow. Yellow. Green. Yellow. Yellow. Yellow. Yellow. Green. Green. Yellow. Will you email me? Skeleton: “No.” Ex-nerds in brand-new and brightly red sport cars. $$$. I love. Shihab. Hooves in the sand. Skinny senior with over-sized sunglasses; old jockey (cap, trophy) smiling in slow motion. And there I am again, flashback, crying with my head in between my hands. Sometimes I’ve got the feeling that cannibals. Eyes: blue. Cancer. Why would I wait until tomorrow? Golden beams protruding from the lifted/lit earth. May 5, 2001 [11:30-12:45] You’ll remember this for the rest of your life. Graphs, diagrams. Bu$ine$$. Blue shirt, white collar, no neck (porn star). A name lights up. I’m hysteric. Will you join us? Letters falling in their words. Fingers set up a tent and start to dance. Young entrepreneurs from poor neighborhoods (read: black) guided by Microsoft. Kinda makes me happy, that sort of kitsch. A sense of exhaustion/impotence to see anything but the present. (…) Wouldn’t you like to? Orange explosion in an industrial zone. YOU’RE DOING THIS FOR AMNESTY INTERNATIONAL. Would you. A familiar face. Clouds and blossom. Sunflowers. Supermodels. Mountainous area in a rectangle: shades of brown, from dark to beige, more green toward the south. Tents and next to them (it’s all a blur) people. Plane. Stadium. Geometrical block of people. No, I ain’t crying. I don’t speak no more. I just want. Quote + photo. (Positive:) screaming crowd. Three-piece suit, seen from the back, before entering the arena. On the back: “Daddy abused me.” Oh, bummer. State of emergency has been declared and everyone has to cooperate. She’s cut her wrists. What we do know (…) is that there’s never been a unique word, an imperative name, nor will there ever be. [Click here for work that suits you.] Barefooted children are watching it (coherent pieces revelation of what’s lying below). Who knows how she’s changed during those two years. “Everything used to be better” + sigh. And here we are. An empty field of parquet. A city lying behind it. Explosion. Blue. A rain drop falling in my coffee. May 5, 2001 [14:30-15:30] A young Arafat on video speaking with raised finger. “I’m calling from my convertible.” Names on walls, victims, numbers… Tourists. Yellow. Yellow. “Your own child! Really, what kind of human are you?” I don’t want to hear it no more. A woman jumping out of the water in a yellow bikini against a background of fireworks and the Cheops pyramid. Thy sorrow shall become good fortune, thy complaints laudation. All planets will float and wander. Wo die Welt zum Bild wird, kommt das System (…) zur Herrschaft. It is something, but is it? May 5, 2001 [18:30-19:00] Iris. Leaves. NASDAQ. Open / and white and. For the one who’s doing nothing, just waiting. (…) NO DEFEAT is made entirely up of defeat -- since / the world it opens is always a place / formerly / unsuspected. October 2002. “Jeroen, I’m leaving for the cemetery, byeeee.” The rise of the middle class. My entire oeuvre is an ode to the. My entire head is a fight against the. God always demands what you cannot sacrifice. You may take that the easy way, but… “The state hasn’t made us, but we make the state” (Hitler). A stork exits the elevator. Skeletons of. Moscow. Helsinki. Palermo. Paris. Chapter 30 Like your paradises: nothing. United Desire, as only remaining superpower. And even though the sea is now calmer and the wind is blowing pleasantly in my face… Heart! Who determines whether a tradition is “alive”? The yellow leaf or the white branch? Mars. This sentence is a typical example. Most Dutch people are happy. No consolation. When I see a girl sitting at a table with a book, a notepad, a pen, a bottle of mineral water, her hand writing in the light—then I consider that one thing. “Presents,” “poetry,” “classics.” We are what we cannot make from ourselves. “Left”: mendicant orders, missionaries. Saint-Just: “A republic is founded on the destruction of its enemies.” She crosses the street with a banana peel between her fingers. (…) We chose our own wardens, torturers, it was us who called all this insanity upon ourselves, we created this nightmare… But “no”? Girl (just like a beach ball) talking rapid Spanish (Portuguese?) in a mobile phone. Do I have a chance now that her boyfriend is getting bold? CLIO, horny bitch. What else do you want? An old woman, between the doors of the C1000, is suddenly unable to go on; her husband stretches out his hand, speaking a few encouraging words. Selection from. Der Führer schenkt den Jüden ein Stadt. How can it reach us if we haven’t been already reached somehow? It doesn’t “speak.” No problem. Each word she uses is a small miracle, as if she doesn’t belong to it, to language, but wanders around with a pocket light looking for the exit; she’s never desperate (maybe a little nervous), lighting up heavy words from the inside. But indeed, we’re free. But the predicate is not an attribute, but an event, and the subject is not a subject, but a shell. That’s why also samurai, knights, and warriors raised the blossom as emblem: they knew how to die. Locked up in a baby carriage with a McDonald’s balloon. Blue helicopter, the blue sky. Whether you want to refer? The point is. How / Motherfucker can I sing a sad song / When I remember Zion? You’ll feel so miserable and worthless that you think: “If only I were dead!,” or: “Just put an end to it!” “So you’re an economist?” Her card—two little birds building a nest, her handwriting shaking—is still on the mantelpiece. Guevara: “No, a communist.” A straw fire, such was our life: rapidly it flared up, rapidly it passed. I’m fleeing, coming from nowhere. (…) Eazy-E drinking coffee with the American president. If I’d scream, would that be an event? Drown it: the cleaner it will rise up from the depths. No! The night, so fast… As if there’s something opened up in that face. Come on, we may not curse life. He shows me his methadone: “If you drink that all at once, you’ll die instantly.” The last one dictates how we should behave to deserve happiness. One shine / above the earth. “I want to go to Bosnia,” I said bluntly. I don’t even know the name of the current mayor. Let’s despise our success! “There is no future; this is the future. Hope is a weakness that we've overcome. We have found happiness!” Sun. Sushi. Volvo. I feel like a bomb about to explode at any moment. Makes a difference for the reconstruction right? The decor moves forward. Daughter of Nereus, you nymphs of the sea, and you Thetis, you should have kept his tired head above the waves! Alas! This sentence has been written wearing a green cap. I receive my orders from the future. A frog jumps into it. Her husband has turned the Intifada, which he follows daily on CCN, into his hobby, “to forget that he doesn’t have his driver’s license yet." Suddenly the sun slides over the crosswalk. Her (his?) foot is playing with the slipper under the table. Is this how I’m writing this book now? I’m not a fellow man. I hate you and I want to hurt you. These are my people. Their screaming doesn’t rise above the constantly wailing sirens which we've learned to ignore. My whole body became warm and suddenly started to tremble. Unfortunate is he who is standing on the threshold of the most beautiful time, but awaits a better one. Arafat’s “removal” is contrary to American interests. Jeep drives into boy. What you can do alone, you should do alone. A food gift from the people of the United States of America. Two seagulls. [...]. (shrink)

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's "relations of uncertainty." The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one solution with (...) the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty. (shrink)

Ramachandran and Hirstein offer a number of interesting ideas about aesthetic preference. In this commentary I shall focus mainly on their ideas concerning peak shift and prototypicality. The authors give the example of a rat rewarded for responding to a rectangle and not rewarded for responding to a longer triangle . They argue that the rat will respond even more to a more elongated rectangle. In fact, two phenomena are involved here. Peak shift refers to the fact that the rat (...) responds more to a supernormal stimulus . Behavioural contrast refers to the fact that the rat responds more to the S++ than it did to the S+ before discrimination training took place. It does not detract from the authors’ main point, but we would be unlikely to find peak shift in the hypothetical experiment described. Peak shift only occurs when the S+ and the S- are very similar to each other . Let us say that we train a rat to respond to a 1000 Hz tone and not to respond to a 500 Hz tone. No peak shift will be found. We will find peak shift if the S+ is 1000 Hz and the S- is 950 Hz. The conventional explanation for this is that the animal shows generalization. A rat trained simply to respond to a 1000 Hz tone will also respond a bit less to one of 990 Hz, even less to one of 980 Hz, and so on. In discrimination training, our rat would have a strong tendency to respond to a 1000 Hz tone but, because of generalization from the 950 Hz tone, it would also have some tendency not to respond to it. If we subtract the inhibitory gradient around 950 Hz from the excitatory gradient around 1000 Hz, we will end up with maximal responding around, say, 1010 Hz . Intuitively, we would expect the rat to respond more to the S++ but also less vigorously than it had to the S+ before discrimination training was begun. This is because the inhibitory gradient has been subtracted from the excitatory gradient. Surprisingly, we find behavioural contrast; the rat responds more vigorously to the S++ than it had to the S+. Grossberg argues that this is because there is a tendency to keep amount of activation on a layer of cortex constant. (shrink)

One of the mathematical topics examined in the Old Babylonian period consisted of calculating the size of a reed which was used to measure either a longitude or the perimeter of a rectangle or trapezium. These subjects were solved, probably, applying the geometric construction called completing the square. In this paper, we analyse the problem texts on the tablets AO 6770 (5), Str 368, VAT 7532, and VAT 7535.

In this paper we investigate conditions for Lp-computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ⊂ ℝq, we show that an Lp function f ∈ Lp is LP-computable if and only if f is sequentially computable as a linear functional and the Lp-modulus function of f is effectively continuous at the origin of ℝq.

I link together the nuptial number, that ‘whole geometric number', represented as the areas of two distinct figures -- a square and a rectangle -- with the ‘triangles in ascending order'. I locate an indeterminancy in the conditions for the production of the ‘divine creature', which I take to be a philosopher , and suggest a new interpretation of the breakdown of the eugenics programme. I try to show how and why that breakdown is metaphysically necessary. I argue that Plato (...) uses mathematical indeterminancy not only to suggest that the decline is necessary, but also to issue an epistemic warning to us, to the effect that we should avoid trying to come to a philosophical understanding of forms by focusing on even very fine particulars. (shrink)

The Erlanger Program of F. Klein ensures a ground for the ὲ́κθεσις procedure, which has not been much studied in the recent debates about geometrical analysis, but refers to a more general problem: the identity of a sign within a sign system, and the attempts of reduction of the mentioned system by another one. The exampIe considered is the reduction of the conics to characteristic rectangles realized by Apollonius. Starting from Klein and Apollonius, as weIl as from cartesian geometry, (...) the figures are considered as geometric signs, and the proposed analysis of sign identity are conceived as models to follow in the analysis of identity of mathematical signs in general. (shrink)

One of the most frequently discussed passages from Locke's An Essay Concerning the Human Understanding is that which occurs in IV.vii.9, where he writes:… the Ideas first in the Mind, ‘tis evident, are those of particular Things, from whence, by slow degrees, the Understanding proceeds to some few general ones; which being taken from the ordinary and familiar Objects of Sense, are settled in the Mind, with general Names to them. Thus particular Ideas are first received and distinguished, and so (...) Knowledge got about them: and next to them, the less general, or specifick, which are next to particular. For abstract Ideas are not so obvious or easie to Children, or the yet unexercised Mind, as particular ones. If they seem so to grown Men, ’tis only because by constant and familiar use they are made so. For when we nicely reflect upon them, we shall find, that general Ideas are Fictions and Contrivances of the Mind, that carry difficulty with them, and do not so easily offer themselves, as we are apt to imagine. For example, Does it not require some pains and skill to form the general Idea of a Triangle, for it must be neither Oblique, nor Rectangle, neither Equilateral, Equicrural, nor Scalenon; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an Idea wherein some parts of several different and inconsistent Ideas are put together.I shall not pretend that what Locke is claiming in this passage is wholly clear, nor shall I try to defend the views expressed in it. My intention is to show that what he says here has been widely misinterpreted. It has become common to treat the contents of the passage as aberrant; as presenting a ridiculous variant on his main thesis on abstraction, or that very thesis elaborated with a foolish rhetorical flourish. But what is said in this passage is not something said elsewhere, nor is it an alternative to something said elsewhere. Here, and nowhere else, Locke shows awareness of implications for his doctrine of abstraction, of views he holds about simple ideas. (shrink)

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

La publication, par J. Bousquet, du trésor de Cyrène dans le fascicule II des Fouilles de Delphes proposait d'assigner à ce bâtiment la fondation XIII (Atlas 203). L'auteur avait cependant relevé de nombreuses non-correspondances entre cette fondation et la crépis du trésor, qu'il expliquait par une interruption des travaux due à la troisième guerre sacrée. Un nouvel examen de la fondation XIV (Atlas 302), située immédiatement au-dessus de XIII, permet d'y replacer sans difficulté le trésor, dont le plan s'inscrit, au (...) pied des murs, dans un rectangle de 20 x 30 pieds. La date d'érection du trésor est précisée : entre 334 et 323 avant J.-C. La restitution du système de couronnement du péribole, sur lequel le trésor s'appuyait à l'Est, indique les niveaux de sols antiques autour de l'édifice. (shrink)

In this article the authors intend to present a very important topic of the geometry of space: the polyhedra. After having introduced their definition, their presence will be shown in nature, in everyday life and in art, starting from ancient Greece up to the present day. First of all, we will deal with regular polyhedra; subsequently we will introduce the important family, especially in the applications, of the Archimedean polyhedra. Finally, the interesting Goldberg polyhedra will be presented.

In a case-history, Ben, a university-graduate blind adult, is shown to draw a cube as if it were folded out, but with slim rectangles for the sides around a central square. This form is drawn by sighted 8-year-olds. It might involve foreshortening and parallel projection, despite the presence of more sides than would be present in parallel projection in a single direction. Also, Ben drew a glass’s brim as both a straight line and as an ellipse, a form common (...) in drawings by sighted 8-year-olds that may include the circular brim foreshortened to an ellipse in a ¾ view. In several drawings made later in the testing session Ben only showed aspects of the depicted object facing one direction. In elevation and plan drawings, he showed aspects facing to the side of the object or above the object. Also, Ben’s use of foreshortening advanced in sophistication in the testing session. We hypothesize that the blind and the sighted are on the same drawing developmental trajectory. (shrink)