Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been (...) shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

The fundamental solution of the Schrödinger equation for a free particle is modified by the inclusion of an arbitrary scalar and an arbitrary vector, both imaginary. This gives a field free from singularities. By choosing the scalar small and the vector large, one obtains a model of a wavepacket which moves fast and remains concentrated over a long range.

Over the history of research on sign languages, much scholarship has highlighted the pervasive presence of signs whose forms relate to their meaning in a non-arbitrary way. The presence of these forms suggests that sign language vocabularies are shaped, at least in part, by a pressure toward maintaining a link between form and meaning in wordforms. We use a vector space approach to test the ways this pressure might shape sign language vocabularies, examining how non-arbitrary forms are (...) distributed within the lexicons of two unrelated sign languages. Vector space models situate the representations of words in a multi-dimensional space where the distance between words indexes their relatedness in meaning. Using phonological information from the vocabularies of American Sign Language and British Sign Language, we tested whether increased similarity between the semantic representations of signs corresponds to increased phonological similarity. The results of the computational analysis showed a significant positive relationship between phonological form and semantic meaning for both sign languages, which was strongest when the sign language lexicons were organized into clusters of semantically related signs. The analysis also revealed variation in the strength of patterns across the form-meaning relationships seen between phonological parameters within each sign language, as well as between the two languages. This shows that while the connection between form and meaning is not entirely language specific, there are cross-linguistic differences in how these mappings are realized for signs in each language, suggesting that arbitrariness as well as cognitive or cultural influences may play a role in how these patterns are realized. The results of this analysis not only contribute to our understanding of the distribution of non-arbitrariness in sign language lexicons, but also demonstrate a new way that computational modeling can be harnessed in lexicon-wide investigations of sign languages. (shrink)

Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions (...) of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018). (shrink)

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.

The equation for the fundamental field quantity ϱ is obtained. It is Div $\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } $,where h is an arbitrary function oft andr, and [,]− is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ϱ.(2) Relativistic covariance of the equations governing ϱ.(3) Principle of continguous action.(4) Conservation of total amount (...) of ϱ. The equation appears to be unique. It is suggested that the physical world corresponds to ϱ being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential Aμ is identified with ε ρμ dΩ. Conservation laws on various measures of ϱ are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ϱ to the metric is made via Einstein's gravitational equation Gμυ =KTμυ. (shrink)

Let R be a real closed field, and X⊆Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq R^m}$$\end{document} semi-algebraic and 1-dimensional. We consider complete first-order theories of modules over the ring of continuous semi-algebraic functions X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\to R}$$\end{document} definable with parameters in R. As a tool we introduce -piecewise vector bundles on X and show that the category of piecewise vector bundles on X is equivalent to the category of (...) syzygies of finitely generated submodules of free modules. We give an explicit method to determine the Baur–Monk invariants of free modules in terms of pre-piecewise vector bundles. When R is a recursive real closed field this yields the decidability of the theory of free modules. Where it makes sense, we address the same questions for continuous definable functions in o-minimal expansions of a real closed field. From the free module case we are able to deduce generalisations of some results to arbitrary modules over the ring. We present a geometrically motivated quantifier elimination result down to the level of positive primitive formulae with a certain block decomposition of the matrix of coefficients. (shrink)

Concept learning becomes possible only when existing representations fail to account for experience. Most models of learning and inference, however, presuppose a fixed representational basis within which belief updating occurs. In this paper, I address a prior question: under what structural conditions can the representational basis itself expand in a principled and selective way? I propose a geometric framework in which conceptual growth is modeled as admissible basis extension evaluated under a Minimum Description Length (MDL) criterion. Experience, whether externally observed (...) or internally simulated, is represented as vectors relative to a current conceptual subspace. Residual components capture systematic representational failure, and candidate conceptual extensions are restricted to low-rank, admissible transformations. I show that any MDL-accepted extension can be chosen so that its novel directions lie entirely within the residual span induced by experience, while extensions orthogonal to this span strictly increase description length and are therefore rejected. This yields a conservative account of imagination and conceptual innovation. Internally generated counterfactual representations contribute to learning only insofar as they expose or amplify structured residual error, and cannot introduce arbitrary novelty. I further distinguish representational counterfactuals--counterfactuals over an agent's conceptual basis--from causal or value-level counterfactuals, and show how MDL provides a normative selection principle governing representational change. Overall, the framework characterizes conceptual development as an error-driven, geometry-constrained process of basis extension, clarifying both the role and the limits of imagination in learning and theory change. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

This is the formal capstone of the Cosmological Codas of the Principia Cybernetica 2025. Contemporary physics remains haunted by the apparent arbitrariness of nature’s fundamental constants: the fine-structure constant α⁻¹ ≈ 137, the baryon asymmetry ∼10⁻⁹, the MOND acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s², and the dark energy fraction ∼68%. Standard models treat these as free parameters—numerological inputs without causal explanation. This final entry of the Cosmological Coda series replaces numerology with geometric necessity, demonstrating that all constants emerge (...) from a single structural principle: the universe is a tetrahedral lattice in continuous self-organization. We posit that the vacuum is not a smooth continuum but a dynamical, pixelated geometry undergoing perpetual “Jitterbug” collapse from vector equilibrium to tetrahedral stability. This living lattice imposes two competing imperatives: perfect packing at the irrational golden angle (137.508°, solving the Thomson Problem) and quantization into rational harmonic closure (137.036°). The geometric strain between these angles—approximately α—becomes the fundamental incompleteness that manifests as physical phenomena. From this strain we derive: α⁻¹ ≈ 137 as the crystallized golden angle—the resonant closure of infinite potential into finite structure; the baryon asymmetry ∼10⁻⁹ as the exponential residue of chiral filtration through the lattice; dark energy (Ω_Λ ≈ 68.17%) as the tensegrity recoil of the lattice, geometrically fixed as 1 − 1/π; the MOND scale a₀ = c H₀ / 2π as the critical acceleration where inertial wavelengths exceed the cosmic cavity circumference; and gravity as the entropic cost of maintaining geometric strain, unifying Landauer’s principle with Hawking temperature. The framework resolves long-standing anomalies without new particles or fields: dark matter effects arise from holographic inertia below a₀; the Hubble tension reflects varying lattice strain in voids versus structures; the hierarchy problem is the scale gap between Planckian pixels and hadronic standing waves. Time itself is discrete, emerging as the “click rate” of the Jitterbug at the Planck frequency. We predict precise convergence of Ω_Λ to 1 − 1/π, a geometric origin for Chern–Simons terms in electroweak knots, and laboratory signatures of lattice thermodynamics. The constants are not random; they are the immutable signature of a universe wrestling infinite potential into finite, stable form—a cosmic geometry writing its own laws. (shrink)

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...) the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. (shrink)

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL 2(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL 2(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable (...) trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism. (shrink)

We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear (...) Logic, we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

continent. 2.1 (2012): 29–35. Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "Politieke Poëzie: Enige aantekeningen, Poëtica bij N30 (versie 2006)." In Weerstandbeleid: Nieuwe kritiek . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. L’égalité veut d’autres lois . —Eugène Pottier The modern poem does not have form but consistency (that is sensed), no content but a problem (that is developed). Consistency + problem = composition. The problem of modern poetry is capitalism. Capitalism—which has no (...) image: the unrepresentable Idea of “everything.” The problem is that a poem cannot be justified. There is no excuse for it. Political poetry— pure poetry—has to be problematic, though not in a mannerist way. Yes, its problem is first its own problem—poetry’s existence in the same world as the newspaper—but therefore also always everybody’s problem (the problem of any world at all). The cult of the sublime points at a suspect desire for transcendence, nostalgia for paradise lost (the womb?). Melancholia of the post-. But a problem neither sorrows nor mourns, it is alive, and the fact that it is alive is the problem—the problem for death (rigidity, the status quo). Our symbols and ideologies do not hide any god: symbolic = state; imaginary = human; real = money. Problem: the possibility of communal speech (poetry) in the absence of a “we.” Or: what is a “we” that is not a collective subject (or in any case is not a volonté générale )? What is a universal history that is not a History? This work was started in the shade of the anti-globalization protests at the end of November 1999. I considered N30 to be the closure of the nineties, of my adolescence, and of the a seemingly total extinction of social desire. From the beginning I was skeptical about the alterglobalization movement as the avant-garde of a new politics, but something was happening . Maybe this event did not show that, as the slogan would have it, “another world” is possible, but for me it indicated that such possibility was at least still possible. That naked possibility is carrying forward. And if the fundamental tone of this work sounds more desperate than utopian, this is not caused by the catastrophic sequence that since 1999 has plunged us ever deeper into the right-wing nightmare—a nightmare that this work also gives an account for—but because my hope as yet remains empty. Composition . Composition is no design, but the production of an autonomous block of affects (i.e. a POEM), rhythmically subtracted from the language of a community. A poem does something. Is something. New Sentence . Choosing the non sequitur as compositional unit has the advantage that an abstract composition is subjected to the stress of concrete, social references. Where there is a sentence, there is always a world. (This does not hold necessarily for words on their own.) And where sentences collide, something akin to a textual civil war takes place. It is not about “undermining” whatever, or de-scribing the raging global civil war, but about writing social (or even: ontological) antagonism -- including all its catastrophic and utopian possibilities. Minor resistance. Why would poetry be the no protest zone par excellence? It is nothing but protest, not simply qua “content,” but in its most fundamental essence: rhythm. Rhythm is resistance against language, time, and space, and the basis of (what we will continue to call) autonomy. Rhythm starts with the anti-rhythmic caesura as Hölderlin remarked about Sophocles, a disruption of the quotidian drone. The destruction of everything that is dead inside of us. The noise of the avant-garde has never been the representation of the noise of (post)modernity (from the television or shopping mall), but the sober noise of the systematic exchange of an unbearable worldview. The poet does not describe, but looks for a way out: There is a Grain of Sand in Lambeth that Satan cannot find Nor can his Watch Fiends find it, tis translucent & has many Angles But he who finds it will find Oothoons palace, for within Opening into Beulah every angle is a lovely heaven William Blake was not mad. And there has always been only one poetry: the poetry of paradise. The principle is that there is something in art (the essentially creative element) that is disgusted by that which, unlike art, does not aim for the supreme. Wonder is not supreme, tranquility is not supreme, beauty is not supreme. Even amusement is not supreme! The supreme is supremely open, “das Einfache,/ Das Schwer zu machen ist” 1 : paradise. That is abstract. Literally. For me it is not about a concrete imagination, an idyll or utopia. There is no doubt a need for that, but it is not so much the supposed lack of imagination or ideals (human rights are ideals), but a fundamental lack of desire (human rights are no desires) that we suffer from, and from which we do not need to remove Nietzsche’s label of “nihilism.” “We.” George Oppen: “ Of Being Numerous asks the question whether or not we can deal with humanity as something which actually exists.” What is less actual than humanity? Nowadays it appears as a lifeless ideology of cynical power politics. Or as what makes one think. It is a shame to be human. The event is the caesura that defines rhythm. Writing toward the event is not the description of the event, but marking an abstract and intense space in which the event may unfold and keep itself. It is a task. “Remember that thou blesseth the day on which I seized thee, because such is thy obligation.” The event is a contraction (or a series of contractions) with its own rhythm and unique qualities. It is more than an explosion or demonstration. But at the same time less. The endless repetition of images and stories in the media points to a fear for the indeterminate and indeterminable void of the event. In the end there is nothing to see. We do not live in disaster’s shade or miracle’s light, but rather in the rhythm, which is contracted time, having little to do with omnipresent representations. For this book I did not intend a rhythm of evental representations (a narrative rhythm), but a rhythm which would be an event itself , because it draws the border between artwork and history. My desire for a direct engagement with the “extra-textual reality” has nothing to do with the representation of “rumor in the streets.” (What has less street cred than representation?) Naturally, a poem is no historical event and does not change anything. But a poem is a part of history that wants to be repeated forever, constructed in such a way that it is worthy of repetition. It is a part of desire (composition) made consistent (durable). The “historical event” flares up and burns down, and has to burn down to be effective. The leftovers are images and stories (representations), History—no event. The artwork—that is the ambition— remains event (though monumental and inefficient/inoperable). (No wonder that a historical singularity, a revolution, reminds us of a work of art; the resurrection yearns for a judgment, an affirmation; everything depends on it.) Hence the title does not summarize the book, let alone contract its “content” into a quasi-transcendental signifier. The title is juxtaposed to the book, like everything else inside the book, and in that relation it precisely forms a part of it. The ideal work is an open whole, lacking nothing but to which everything may be added. I have been interested in this “everything,” the world, or as I said above: capitalism. “Everything” is not the space for “wonder”—a code word, a shibboleth for petty bourgeois imagination (I recognize myself in the strangest things, a speaking dog, a canal, a pond standing straight—oh my god). No. The world is a social world, not YOUR world, poet. Power is number one. I will call “Dutch,” or “shitty,” whatever denies this power. That hurts, but this pain is an expression of the desire in the world to write another world, or as Blanchot says, “the other of all worlds” 2 : the world. Not as what “is there,” but rather as that which urges for an escape from what “is.” This is a testament of how radical reality has become, for me—or rather, a writing body—in a having-been-written. I am not interested in the problem of “meaning” as misunderstood by literary scholarsi: “order” in “chaos,” “symbolization.” Bullshit. What is there, hop, hope, now: the meaning of the taste in my mouth. Bullshit. I am not interested in the frustration of interpretation; I am writing for readers who do not want to interpret. I do not know how many “professional readers” will hear the music of a paragraph like: Sun. Sushi. Volvo. I hope more than I would think. There is a suggestion (or rather, an actual production) of speed and infinitive owing to the absence of plosives, i.e. articulations such as /k/, /t/, or /p/. Can you hear the slick suaveness? Driving car dark, vocal chiaroscuro of the word “sushi.” The unstressed /i/ stands in the middle of dark vowels and thus acquires its own special out of focus , like a momentary flash or brilliance—an obscure light. It is not about recognizing a story, but about avoiding any story whatsoever: the car disappears in the glow, cars and raw fish have nothing in common except their articulation in a language that brings them together, blurring them. A world appears in its disappearance. For a moment, light is a metaphor for language, though it cannot be reduced to tenor. It is not necessary to be a linguist or philosopher to hear this—a “difficult” poem all too often becomes an allegory of its own impenetrable being-language. The only demand: leave your hermeneutical fetish at home. This was no interpretation. Most shit has been stolen etcetera. That is no longer interesting. You cannot shoot the body with information and let your lawyers reclaim the bullets. So every sentence has been stolen. Also the ones “out” “of” “my” “head.” Why would I be allowed to steal from myself and not from others? Man takes what he needs to move forward. Whatever he encounters, finds in front of him, “occurs” to him. The writer as text editor, or singing pirate. Nothing new here. Important difference with for example Sybren Polet’s 4 montage technique: anti-thematicism. Most of the time ferocious citation from whatever I was reading, listening to, ended up in, and so on. I wrote chapter 12 on my laptop while watching CNN. On the air instead of en plein air . I often employed search engines to generate material. Chapter 20 offers the purest example of this. Often I stop recognizing a particular citation after some time. It is not uncommon for a stolen sentence to conform itself to the paragraph in which it finds itself. Sometimes I nearly arbitrarily replace words. Arbitrariness as a guarantee for absolute democracy. It is a poetics of the non sequitur : a conclusion that does not follow from the premises, the strange element in the discourse. A discourse of strangers. No logical, narrative, thematic unity. There is unity in speed/flight. It has to be read linearly, but not necessarily (not preferably) from beginning to end. The shortest distance between two points is a straight line, but this line precedes every point. The middle, the acceleration, comes first. A point occurs where two lines cross. It has been written from up close, at the level of the tension between sentences. Nothing to be seen from a distance: no form except the exchange of form, no geometrical or mythical meaning. You have to get in, “groping toward a continuous present, a using everything a beginning again and again” (Stein). 5 In Dutch, experimental poetry has been mainly dense: a small rectangular form filled with a maximum amount of poetic possibility. But at the moment the poem starts to relax, the anecdotical content seems to increase. This is what is called “epic”: long, narrative. I believe that an epic is more than that, in fact something completely different. An epic is “a poem including history,” 6 a long poem tied up with the life of community, that as a whole does not need to be narrative. The American poets of the twentieth century (Pound, Williams, Zukofsky, Oppen, Olson, Silliman) have put the epic back on the map by interpreting the poem itself as a map, and writing it as navigation. They have invented the experimental epic, a genre that has generated little original following in “our” poetry. N30 is the middle part—“always start in the middle”—of a trilogy, the contours of which remain as of yet unclear, although each episode investigates one of the three “ecstasies of time”—past, present, future—concerning society X. N30 concerns itself with the PRESENT: not with the description of actual facts but of the rhythm and the intense depth in which facts appear to us. Where are we? We are camping in the desert. Sometimes we are looking at the stars. As opposed to maximum density and minimal tension (a characteristic of most (post-)experimental lyricism), I have sought a minimal density and maximum tension in this book, considered as a long non-narrative prose poem. On the one hand, the minimal density is obtained by the inherent formlessness of prose, on the other hand by the conscious refusal of any active (formal, non-rhythmic) synthesis: the poem tells nothing, shows nothing, has no theme. I did not seek maximum tension either by loading the quotidian with epiphanic radioactivity (“wonder,” confirmation from above), or by means of the intensity of the linguistic structure. I want an abstract tension, but social in its abstraction, in other words, not neutralized by and subjected to Form. Instead of form (transcendent): composition (immanent). The concept is series. Ideal: every unit is necessary for the efficacy of the others and the whole, their relation is purely linear, i.e. non-hierarchic, non-syllogistic, non-discursive, non-narrative. Sentence related to sentence like paragraph to paragraph and chapter to chapter; the whole means nothing and represents nothing. Inside the sentence: syntax (Chomsky’s tree, a type of parallel circuit), outside: parataxis (coordination, an asyntactic line through language and world). I consider duration—the energy of duration (rhythm)—to be the fundament of a poem, the temporal inclination to delimit a “space.” Being as consistency, its consistency. A spatial part of time is not merely a metaphor for an inevitable trajectory, an inescapable time, something like “our time.” Not merely—because rhythm comes from language and is not projected onto it; the poem derives from the world like a scent and a color and a life from a flower. A series, a sequence: nothing potential, but truly infinite—the movement of an infinitude. The infinite series = everything minus totality. That means that there is no container—no Form, no Self, no Image, no Structure, not even a Fragment—just “the prose of the world.” No representation, but also no staging of the impossibility of representation (the postmodern sublime). These are no fragments, no image of a fragmented world or personality, no cautious incantations around the Void. It does not exist. It is a movement. Buying bread, a flock of birds, a bomb falling—they do not depict or represent anything, not literally, not metaphorically. There is an Idea, which is however nothing more than a rhythm, in the same way that capitalism is nothing more than a pure function. Parataxis: the white space between two sentences stresses, which is nevertheless always there, also between words, even between letters: the out of focus of idle talk, the gutter, the irreducible Mallarméan mist which renders even the seemingly most transparent text legible. The white space suggests a neutral medium for free signification, a substance of language. A non sequitur is an element from a foreign discourse, which stresses the white space as space, and problematizes freedom for supra-sentential signification. I start by withdrawing material, leaving the initiative to the sentences. In general a word presupposes less often a discourse than a sentence. What discourse is presupposed by “dog”? We could think of several, but why would we? It is more probable that, when faced with the naked word, we think of its naked (dictionary) meaning, of its denotative signified. By means of two simple interventions we may also write the word as sentence: Dog. In no way this suggests the discourse from which this sentence originates, but in any case we’re presupposing one. This is shown by questions like: “Whose dog? Who’s a dog? What kind of dog?” Etc. (Sentences are question marks.) A sentence implies/is a microcosm—a subject, a verb, an object, and so on. Even an incomplete or ungrammatical sentence does so. My main fascination while writing this book is the worldly and social aspect of language, an aspect that often becomes invisible, or rather, transparent in narrativity—the stretching of sentences into stories. Narrativity organizes a new discourse and a new world, and places a sometimes all too dispersing relation of transparence in between. The conventional novel is the brothel of being. I do not intend to prohibit brothels, and I have certainly not intended to write an anti-novel (THIS IS A POEM), but I do consider narrativity (in general, in poetry, in the news, in daily life) to be ontologically secondary with regard to an immediate being in the world through sentences, also if the latter have been withdrawn from a narrative or otherwise externally structured discourse (which in that case would therefore be chronologically primary ). Naturally, two or more sentences are always in danger of telling stories or arguing, just like the world is always in danger of becoming an objective representation, facing us, strangers. That is why need to wage war—against representation and against the interface, against interaction. AGAINST THE “READER.” To the extent that a sentence is worldly, writing is a condensed global war, and in so far as there is ultimately only one world and one open continuum of languages, it is a global civil war. Nice subject for an epic. The elaboration of a singular problem—prose as the outside of poetry, the form of the novel as purely prosodic composition scheme—“expresses” the universal problem: capitalism as Idea of the world vs. poetry as language of an (im)possible community. The paragraphs are blocks of rhythmically contracted social material. By choosing the sentence as the basic compositional component, an abstract whole may contain social sounds, without telling a story or showing an image. Composition is subrepresentative —a rhythmic, passive synthesis, or rather: a synthesis of syntheses. I never write large blocks of prose in one sitting, because there is no obvious organizational vector —plot, theme, conscience—outside the inherent qualities of the material itself. Usually I write down one sentence, sometimes two, but rarely more than three. Those sentences are usually placed in the text which I am editing at the time. In fact, there is no original composition, new chapters split off from chapters which became too long during the editing process. (Revision mainly consists of adding and inserting, displacing and dividing; only during the last phase, when the text has gained enough consistency, there may be subtraction to tighten the composition; each chapter requires a season of daily revision). This constant revision, accompanied by a continuous influx of collective background noise (to speak with Van Bastelaere), 7 makes every chapter a block condensed (“historical” and “personal”) time. The block itself is a-personal and a-historic; it is ontologically autonomous. If there is such a thing as a spirit of the times, I do not try to offer an image of it, but rather to cancel something of it by erecting a monument of its own excrement within its own boundaries. Tuning and dis-tuning , “in de taal der neerslachtigen een eigen geluid doen klinken,” 8 in other words, desiring in an Elysian way. In this sense I have intended to be able to write a political poetry. The ultimate political poem is the epic, “the tale of the tribe.” I consider N30 to be a prolegomenon to a future epic (of which it in the end will form a part a structural moment, as introduction-in-the-middle), an extended pile on top of an epic as narrative, a question of the tribe and question of its history. I was burdened by too much satire, too much bullshit. But: satire willy-nilly = the only justifiable satire. Against the abstract universalism of the market (“globalism”): concrete disgust, a positive way of saying “No.” Moreover, disgust is a specifically total attitude, which ultimately concerns the world as a whole. I hate this or that, but I am disgusted by EVERYTHING (when I am disgusted), and so it appears that satire is in fact related to the epic, in so far as it concerns society, the cosmos, history. Maybe it is no coincidence that the Dutch literary canon knows no great poet of disgust; what could be more fearful to us than society, the cosmos, and history? The T-tendency (T from Tollens 9 ) clearly points into the direction of the small, friendly, ironic, melancholic, acquiescent, wondrous, and so on. The anti-political, anti-cosmic, anti-historical. (Why am I so philosophical? To scare away the Dutchies.) And most of all: the “poetical” (the pseudo-mysticism from the backyard). Yes, the N in N30 also stands for the Netherlands (just like 30 indicates the number of chapters). I was not in Seattle, I do not live in Iraq. But is not the whole world bleeding to death on Dutch paving stones? Let’s hope that we mowed away something with this total satire, also “in myself.” The arrogant stupidity that definitely thinks to know the essence of freedom (the free development of esthetic needs inside the void), that cannot take anything serious, only believes in the disciplined bestiality of the individual (“norms and values”) and the mere functioning of a social factory which finds no justification whatsoever outside its functioning (“get to work”)… Who knows. A certain aimed destruction leaves grooves and craters, mapping out a next adventure. Pound’s periplum : sailing while mapping the coasts. Immanent orientation. The terrain changes with the map, history changes with the poem. Maps never merely organize the chaos, transcendent schemes imposed on a formless Ding-an-sich . They organize from within, surfing. But they are most of all routes back into the chaos or forward to paradise (final identity of chaos and paradise; Schlegel: “ Nur diejenige Verworrenheit ist ein Chaos aus der eine Welt entspringen kann ”10). A poem is not only a piece of history, it is also a flight from history. Maps give chaos to the form of reality , open escape routes, break through representations, make us shivery and dazed. Paradise is immanent to a fleeting desire. History is the history of labor—this is Adam’s curse—and the poet works too: For to articulate sweet sounds together Is to work harder than all these, and yet Be thought an idler by the noisy set Of bankers, school masters, and clergymen The martyrs call the world 11 But: the poet works in paradise. The paradox of the artwork, the work that is no work, the piece of history that cannot be reduced to History—this is explained by The Space of Literature , a virtual space, an autonomous rhythm, not outside, but in the midst of the noise, a piece of paradise in hell, a postcard from the vale of tears addressed to paradise, to X. Political poetry means: a poetry that dares to think about itself, about its language and about its world and about the problematic relation between both, which is this relation as problem. A poetry that thinks at all, articulates its problem. It has nothing to do with journalism or morality or debate, let alone the law or the state. It has nothing to do with “criticism” if this means the replacement of incorrect representations by other, more correct representations. It has something to do with ethics in the sense of learning to live. It has something to do with the community and the language of the community (whichever that may be) and the role of the poet regarding the community. It concerns justice without judgement or measure. In the end the just word is just a word , to paraphrase Godard: it is from a future that is unimaginable. It Is no rational engagement, but an aversion against everything that obstructs life, and love for everything what is worthy of having been loved. The world is engaged with me, not the other way round. First Exodus, then Sinai. A desire does not start with an agenda. To answer the question whether I am really so naive as to want to change the world: “We only want the world.” Justice is the world appealing to us to liberate it from all possible chains, from each organization and inequality, to be it, smooth, equal, under a clear sky—a desert and a people in a desert. That moment between Egypt and the Law. It is not a revolution, but the sky above the revolution. Poetry = the science of escape. There is no art that we already know. The weakness of modernistic epic poetry seems to me to be the unwillingness to completely abandon narrative as a structural principle, in favor of a composition “around” or from an event. The China Cantos and Adams Cantos are the low point, and the Pisan Cantos the high point of Pound’s poetry. Two types of research: archival representation of the past vs. ontology of the present (which virtually presupposes the entire history). Presupposing an event means that it is impossible for the poet to stage his own absence, but in no way makes the work personal. An event is the unknown, the new invading into the business as usual, so also the personal. The question heading this research is not: “Who am I?” but “What is happening?” The book is as little illegible as Mondrian’s work is invisible. Form is of interest only to the extent that it empowers liberation. Ron Silliman So no formalism, but what it means to live in this world and to have a future in it. I want something that holds together that’s not smooth. Bruce Andrews The past above, the future below and the present pouring down: the roar, the roar of the present, a speech— William Carlos Williams If my confreres wanted to write a work with all history in its maw, I wished, from the beginning to start all over again, attempting to know nothing but a will to create, and matter at hand. Ronald Johnson NOTES 1) “The easy thing/ that is difficult to make.” Bertold Brecht, Lob des Kommunismus . (All footnotes are the translator’s) 2) Maurice Blanchot, The Space of Literature , trans. Ann Smock. Lincoln/London: University of Nebraska Press (1989), 75. 3) Mettes uses the word “Neerlandicus,” which refers to scholars of Dutch language and literature. 4) Dutch poet. 5) Gertrude Stein. “Composition as Explanation.” A Stein Reader . Ed. Ulla E. Dydo. Evanston, IL: Northwestern University Press (1993), 495-503. 6) Ezra Pound. 7) Flemish poet. 8) “Resounding an original sound in the language of the despondent.” A. Roland Holst, De afspraak . 9) Dutch poet. 10) “Only such a confusion is a chaos which can give rise to a world.” 11) W.B. Yeats, “Adam’s Curse.&rdquo. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of (...) class='Hi'>arbitrary spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

In this paper, the stability of switched neural networks with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the (...) robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature. (shrink)

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schrödinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent space to scale-invariant spacetimes. Convergence and measurability on this tangent tower are guaranteed using a scale-invariant norm, restricted to conformally self-dual vectors. Maps on the resulting (...) Hilbert space are correspondingly restricted to semi-definite conformal weight. We find the maximally- and minimally-commuting, complete Lie algebras of definite-weight operators. The projective symmetry of the tower gives these algebras central charges, giving the canonical commutator and quantum Virasoro algebras, respectively. Using a continuous, m-parameter representation for rank-m tower tensors, we show that the parallel transport equation for the momentum-vector of a particle is the Schrödinger equation, while the associated definite-weight operators obey canonical commutation relations. Generalizing to the set of integral curves of general timelike, self-dual vector-valued weight maps gives a lifting such that the action of the curves parallel transports arbitrary tower vectors. We prove that the full set of Schrödinger-lifted integral curves of a general self-dual map gives an immersion of its 2-dim parameter space into spacetime, inducing a Lorentzian metric on the parameter space. This immersion is shown to satisfy the full variational equations of open string. (shrink)

The electron-optical phase shift induced in the electron beam due to the interaction with the electromagnetic field of magnetized nanoparticles of defined shape and arbitrary dimensions is calculated, presented and discussed. Together with the computable knowledge of vector potential and magnetic induction, including the demagnetizing field, and with the extension to more realistic geometries which will be presented in part II, this theoretical framework can be employed for the interpretation of transmission electron microscopy experiments on magnetic particles on (...) the nanometre scale. (shrink)

The two-component spinor theory of van der Waerden is put into a convenient matrix notation. The mathematical relations among various types of matrices and the rule for forming covariant expressions are developed. Relativistic equations of classical mechanics and electricity and magnetism are expressed in this notation. In this formulation the distinction between time and space coordinates in the four-dimensional space-time continuum falls out naturally from the assumption that a four-vector is represented by a Hermitian matrix. The indefinite metric of (...) tensor analysis is a derived result rather than an arbitrary ad hoc assumption. The relation to four-component spinor theory is also discussed. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) (...) class='Hi'>vector potential that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive (...) the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned. (shrink)

Assuming the fact that science, at the present stage of its development, is not able to say anything concrete about the Universe, on the basis of the generalisation of the second thermodynamical principle, the authors of the article propose a new, in a way inverse, approach. From what modern cosmology states concerning the Universe taken as a whole, they endeavour to draw conclusions as to the applicability* of thermodynamic laws to it.. In other words, far from building a new „model" (...) of the Universe by extrapolation of the increase of entropy principle, they try to assertain whether the theory of „thermic death" comes within the compass of ready models offered by cosmology.Thermodynamic principles can be safely applied to such systems only as have been, at least relatively, isolated, and the parameters of which, defining their state, are known. Hence it appears more reasonable not to start any study of „Universe thermodynamics" until after cosmological of the Universe have been apprehended as kind of system, i. e., within the framework of a concrete model.Such a method has been exemplarily applied to some relativistic models and to the steady state model of the Universe.It seems that, in relativistic cosmology, since the evaluation of the four-vector momentum for the ęntire space of a finished model results in the banal identity 0 : 0, the question of the maximal entropy characteristic of the „thermic death", is devoid of any physical sense.The excellent cosmological principle, assumed by the steady state model, prescribes to extend the lack of thermic equilibrium, observed in our immediate astronomic vicinity, to all cosmic spaces and to arbitrary periods, past or future. Thus, according to the steady state model, the „thermic death" will never happen.Modern cosmology knows observation tests permitting to envision a possible determination of which of the various models of the Universe corresponds the most to reality. That is why, to link the question of „thermic death" with a cosmological model is not only more correct from the point of view of thermodynamics itself, but appears also as a step forwards in a discussion that has been kept so far at a deadlock. (shrink)

A rational approach to the Fermi-Walker transport equation is proposed by deriving it from a condition of “non-rotation”. First, the condition is applied to a tetrad basis and then generalized to an arbitrary space-time four-vector. The method is conceptually simple and apart from the use of tetrad bases in four-dimensional space-time, does not require the effort of visualizing abstract geometrical constructs in spaces of more than three dimensions. The argument develops in the context of the flat space-time of (...) special relativity theory but the final result can be immediately extended to curved space-time. (shrink)

The program of the evolution of the base of knowledge in machines' mechanisms on the example of technical systems of arbitrary purpose and structure with the aim of formalization and structurization of knowledge for creation of new techniques of automatized projecting in suggested. The program is declared as the process of transference of the base of knowledge from its initial state into final one, at the permissible restrictions in quality and resources in real time. The program's concept is based (...) on the introduction of N-measured structural space. Discrete coordinates of the multi-measured vector of this space are: flathierarchical sets of languages, objects, problems, estimations, resources, restrictions, types of working areas, etc. The vectors' co-ordinates define the set of the program projects. The possibility of choice of the optimal program strategies' realization is discussed. The concept can be applied to objects of arbitrary purpose. (shrink)

In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor and corresponds (...) to a generalized Minkowski “double” light cone in the parameter space. A general description of finite spatial rotations, which utilizes the Baker-Campbell-Hausdorff formula, generalizes the usual infinitesimal treatments of the rotation group. We derive an explicit expression for the angle corresponding to two successive finite rotations in any direction. We also discuss Lorentz transformations and duality rotations of the electromagnetic field and exhibit a relationship between the algebraic inverse and a duality rotated field. Using a combined transformation, one can always transform an arbitrary electromagnetic field (E≠0) into a pure electric field, but never into a pure magnetic field. (shrink)

The mechanical aspect of momentum, basically its role as a tangent vector of the trajectory of the particle, is related to properties of the momentum found in the contexts of Hamilton's optico-mechanical analogy, de Broglie's matter waves, and quantum mechanics. These properties are treated in a systematic way by considering an approximation of the particle mechanical action of the particle by a step function. A special method of discretizing partial differential equations is shown to be required. Using this method, (...) a discrete dynamics is developed. It is shown that particle dynamics can be regarded as the limit case of the discrete dynamics as the step functions tend to the continuous ones. The equation of motion of a free particle in an arbitrary reference system is deduced in two ways: (i) in continuous dynamics by making use of the invariance of action within changes of reference systems, and (ii) by taking the mentioned limit in discrete dynamics of an equation which expresses that the mechanical and wave-theoretical aspects of the momentum are interrelated in specific way. (shrink)

Let D be a division ring such that the number of conjugacy classes of the multiplicative group D ∗ is equal to the power of D ∗ . Suppose that H is the group GL or PGL, where V is a vector space of infinite dimension ϰ over D . We prove, in particular, that, uniformly in κ and D , the first-order theory of H is mutually syntactically interpretable with the theory of the two-sorted structure 〈κ,D〉 in the (...) second-order logic with quantification over arbitrary relations of power ⩽κ . A certain analogue of this results is proved for the groups ΓL and PΓL . These results imply criteria of elementary equivalence for infinite-dimensional classical groups of types H= ΓL , PΓL , GL, PGL over division rings, and solve, for these groups, a problem posed by U. Felgner. It follows from the criteria that if H≡H then κ 1 and κ 2 are second-order equivalent as sets. (shrink)

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer Architecture approach (...) to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition. (shrink)

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called (...) holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function. (shrink)

We introduce a new convolution kernel for labeled ordered trees with arbitrary subgraph features, and an efficient algorithm for computing the kernel with the same time complexity as that of the parse tree kernel. The proposed kernel is extended to allow mutations of labels and structures without increasing the order of computation time. Moreover, as a limit of generalization of the tree kernels, we show a hardness result in computing kernels for unordered rooted labeled trees with arbitrary subgraph (...) features. (shrink)

Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac’s canonical commutation rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson (...) brackets between any linear function of phase space and the sum of an arbitrary function of only configuration space with one of only momentum space. Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not only is that so, but this slightly stronger canonical commutation rule also unambiguously determines the order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by E.H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse, which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization, i.e., its unique deterministic classical “shadow world” which can manifest negative densities in phase space. (shrink)

The remarkable performance of large language models (LLMs) on complex linguistic tasks has sparked debate about their capabilities. Unlike humans, these models learn language solely from textual data without directly interacting with the world. Yet they generate seemingly meaningful text on diverse topics. This achievement has renewed interest in the classical `Symbol Grounding Problem' -- the question of whether the internal representations and outputs of symbolic AI systems can possess intrinsic meaning that is not parasitic on external interpretation. Although modern (...) LLMs compute over vectors rather than symbols, an analogous problem arises for these systems, which we call the Vector Grounding Problem. This paper has two main goals. First, we distinguish five main notions of grounding that are often conflated in the literature, and argue that only one of them, which we call referential grounding, is relevant to the Vector Grounding Problem. Second, drawing on philosophical theories of representational content, we provide two arguments for the claim that LLMs and related systems can achieve referential grounding: (1) through preference fine-tuning methods that explicitly establish world-involving functions, and (2) through pre-training alone, which in limited domains may select for internal states with world-involving content, as mechanistic interpretability research suggests. Through these pathways, LLMs can establish connections to the world sufficient for intrinsic meaning. One potentially surprising implication of our discussion is that that multimodality and embodiment are neither necessary nor sufficient to overcome the Grounding Problem. *Note: this is an updated and improved version of the preprint originally made available on ArXiv in 2023.*. (shrink)

Support vector machines (SVMs) are being used increasingly in affective science as a data-driven classification method and feature reduction technique. Whereas traditional statistical methods typically compare group averages on selected variables, SVMs use a predictive algorithm to learn multivariate patterns that optimally discriminate between groups. In this review, we provide a framework for understanding the methods of SVM-based analyses and summarize the findings of seminal studies that use SVMs for classification or data reduction in the behavioral and neural study (...) of emotion and affective disorders. We conclude by discussing promising directions and potential applications of SVMs in future research in affective science. (shrink)

Excerpt from Vector Analysis and the Theory of Relativity One of the most striking effects of the publication of Einstein's papers on generalized relativity and of the discussions which arose in connection with the subsequent astronomical observations was to make students of physics renew their study of mathematics. At first they attempted to learn simply the technique, but soon there was a demand to understand more; real mathematical insight was sought. Unfortunately there were no books available, not even papers. (...) Dr. Murnaghan's little book is a most successful attempt to supply what is a definite need. Every physicist can read it with profit. He will learn the meaning of a vector for the first time. He will learn methods which are available for every field of mathematical physics. He will see which of the processes used by Einstein and others are strictly mathematical and which are physical. Every chapter is illuminating, and the treatment of the subject is that of a student of mathematics and is not developed ad hoc. The extension of surface and line integrals is most interesting for physicists and the discussion of the space relations in a four-dimensional geometry is one most needed. This is specially true concerning the case of point-symmetry which forms the basis of Einstein's formulae for gravitation as applied to the solar system. I feel personally that I owe to this book a great debt. I have read it with care and shall read it again. It has given me a definiteness of understanding which I never had before, and a vision of a field of knowledge which before was remote. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Arbitrary objects play an important role in both ordinary and mathematical reasoning. The reason for that is their distinct behavior: an arbitrary object presents those properties common to all individual objects in its range - what, following Kit Fine, has become known as the "Principle of Generic Attribution", or simply "PGA". Many philosophers have argued this precise quality to be contradictory, therefore rejecting arbitrary objects altogether - of which the most famous is George Berkeley's argument against Locke's (...) general ideas. However, all the arguments that have been offered assume rejecting properties of an arbitrary object to be expressible in terms of asserting something of it - a unilateral setting. This paper has two main purposes: first, to show how, in the propositional bilateral system of Weak Rejectivist Logic, introduced by Luca Incurvati and Julian Schloder (2017), the PGA does not fall prey to the counter arguments which rise in tension with the nature of the logical connectives; second, to argue understanding sentences about arbitrary objects in terms of assertions which preserve (or not) generality better frames our reasoning about them, and is reflected by the Weak Rejectivist Logic. Then, following the relation between this propositional system and arbitrary objects, a further goal of this paper is to offer a characterization result for the Weak Rejectivist Logic with respect to first-order logic. (shrink)

Vector autoregression (VAR) modeling allows probing bidirectional relationships in gender/sex development and may support hypothesis testing following multi-modal data collection. We show VAR in three lights: supporting a hypothesis, rejecting a hypothesis, and opening up new questions. To illustrate these capacities of VAR, we reanalyzed longitudinal data that recorded dyadic mother-infant interactions for 15 boys and 15 girls aged 3 to 11 months of age. We examined monthly counts of 15 infant behaviors and 13 maternal behaviors (Seifert et al., (...) 1994). VAR models demonstrated that infant crawling predicted a subsequently close feedback loop from mothers of boys but a subsequently open ended, branched response from mothers of girls. A different finding showed that boys’ standing independently later predicted significant later increases of four maternal behaviors: rocking/jiggling, lifting, affectionate touching, and stimulation of infant gross-motor activity. In contrast, crawling by girls led mothers to later decrease the same maternal behaviors. Thus, VAR might allow us to identify how mothers respond differently during daily interactions depending on infant gender/sex. The present work intends mainly to showcase the VAR method in the specific context of the empirical study of gender/sex development. (shrink)

In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two (...) opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the (...) class='Hi'>vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

It is widely held that entities have moral status if they possess a status-conferring property to a sufficient degree. However, this means that for at least one degree to which an entity can possess the status-conferring property and that grounds moral status, there is some incrementally lower degree of possessing the property that does not ground moral status. Critics maintain that this renders any threshold for moral status arbitrary. In this paper, we reject common responses to this arbitrariness objection, (...) such as that moral status thresholds are not arbitrary but merely vague. Instead, we defend the moderate discontinuity view. This view holds that thresholds denote moderate rather than radical shifts in moral status and that significant shifts in the moral status of entities on opposite sides of the threshold are a function of their distance from the threshold rather than of the threshold itself. Crucially, it follows from this that there is no principled way to reconcile the commitment to the moral equality of persons with the commitment to the moral superiority of persons over nonhuman animals. (shrink)

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the (...) ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore the (...) experiment should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

We investigate the deductive strength of statements concerning vector spaces over specific fields in the hierarchy of various choice principles.

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. (...) In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)

This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map linguistic expressions to truth conditions, while distributional semantics represents meaning through word vectors derived from contextual usage. By constructing injective mappings that preserve semantic relationships, we show that every semantic function in an extensional model corresponds to a compatible vector space operation. This result respects compositionality and extends to function compositions, (...) constant interpretations, and n-ary relations. Rather than pursuing unification, we highlight a mathematical foundation for hybrid cognitive models that integrate symbolic and sub-symbolic reasoning and semantics. These findings support multimodal language processing, aligning ‘meaning as reference’ (Frege, Tarski) with ‘meaning as use’ (Wittgenstein, Firth). (shrink)

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.

Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. Which (...) one? We do not and cannot know, because the reference of ‘n’ is fixed arbitrarily. Underlying this proposal is a more general thesis: Arbitrary Reference : It is possible to fix the reference of an expression arbitrarily. When we do so, the expression receives its ordinary kind of semantic-value, though we do not and cannot know which value in particular it receives. Our aim in this paper is defend AR. In particular, we argue that AR can be used to provide an account of instantial reasoning, and we suggest that AR can also figure in offering new solutions to a range of difficult philosophical puzzles. (shrink)

This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's (...) four equations expressed as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated. (shrink)

Critics of reliability theories of epistemic justificationoften claim that the `generality problem' is an insurmountabledifficulty for such theories. The generality problem is theproblem of specifying the level of generality at which abelief-forming process is to be described for the purposeof assessing its reliability. This problem is not asintractable as it seems. There are illuminating solutionsto analogous problems in the ethics literature. Reliabilistsought to attend to utilitarian approaches to choices betweeninfinite utility streams; they also ought to attend towelfarist approaches to social (...) choice situations that donot demand full aggregation of individual welfares.These analogies suggest that the traditional `single number'approach to reliability is misguided. I argue that a newapproach – the `vector reliability' approach – is preferable.Vector reliability theories associate target beliefs withreliability vectors – that is, structured collections ofreliability numbers – and construct criteria of epistemicjustification that appeal to these vectors. The bulk of thetheoretical labor involved in a reliability account of epistemicjustification is thus transferred from picking a uniquereliability number to constructing a plausible criterionof epistemic justification. (shrink)