Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk–Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in (...) several different circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system. (shrink)

Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of a spacetime, one can attempt to extend a local CTC-free patch of such a spacetime in a way that does not give rise to CTCs. One such procedure is informally known as unwrapping. However, changes in global identifications tend to lead to local effects, and (...) unwrapping is no exception, as it introduces a special kind of singularity, called quasi-regular. This “unwrapping” singularity is similar to the string singularities. We define an unwrapping of a (locally) axisymmetric spacetime as the universal cover of the spacetime after one or more of the local axes of symmetry is removed. We give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Gödel spacetime. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Gödel spacetime still contains CTCs through every point. A “multiple unwrapping” procedure is devised to remove the remaining circular CTCs. We conclude that, based on the given examples, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications. Alternative extensions of spacetimes with CTCs tend to lead to other pathologies, such as naked quasi-regular singularities. (shrink)

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (...) (phenomenological) action pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)

String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in this chapter that those two conspicuous characteristics of string physics are related to each other. What links them together is the fact that string theory has no dimensionless free parameters at a fundamental level. (...) The paper analyses possible implications of this situation for the long term prospects of theory building in fundamental physics. (shrink)

Gödel’s contention that closed timelike curves (CTC’s) are a necessary consequence of the Einstein equations for his metric is challenged. It is seen that the imposition of periodicity in a timelike coordinate is the actual source of CTC’s rather than the physics of general relativity. This conclusion is supported by the creation of Gödel-like CTC’s in flat space by the correct choice of coordinate system and identifications. Thus, the indications are that the notion of a time machine remains exclusively (...) an aspect of science fiction fantasy. The element of the identification of spacetime points is also seen to be the essential factor in the modern creation of CTC’s in the Gott model of moving cosmic strings. (shrink)

The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that (...) could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, something which the other methods lack, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambekʼs pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, the apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings, and also reflects the structure of the parse trees of the Lambek calculus. (shrink)

The long duration of the Communist regime cannot be explained without closely looking at the manners of creating shared meanings and agreement on explanations on the shared historical context. Narratives of legitimation, some easier to depict than others, were almost as important as the use of force in imposing the specific values of the regime. In other words, soft power was the buttress of hard power. But the nuances are numerous, once we put this otherwise obvious remark under closer scrutiny. (...) The case studies presented in this issue of the yearbook underline the practice of combining soft power with hard power: that is, legitimating narrative discourses transmitting sets of values and beliefs, backed up by policies of various forms of violence. (shrink)

We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order typeω,ω2orωω. We show that a familiar construction gives rise to continuum many such orderings of order typeω. We construct a new family of such orderings of order typeω2, and show that there are continuum many of these. We show that there are only four such orderings (...) of order typeωω, the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings onNnwhich are preserved under vector addition. We show that any such ordering must have order typeωkfor some 1 ≤k≤n. We show that ifkshrink)

We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order type $\omega, \omega^2$ or $\omega^\omega$. We show that a familiar construction gives rise to continuum many such orderings of order type $\omega$. We construct a new family of such orderings of order type $\omega^2$, and show that there are continuum many of these. We show that (...) there are only four such orderings of order type $\omega^\omega$, the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings on $\mathbf{N}^n$ which are preserved under vector addition. We show that any such ordering must have order type $\omega^k$ for some $1 \leq k \leq n$. We show that if $k < n$ there are continuum many such orderings, and if $k = n$ there are only $n$!, the $n$! lexicographic orderings. (shrink)

Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form S=∫ L 1 Φ d 4 x+∫ L 2 $\sqrt{-g}$ d 4 x where the volume element Φ d 4 x is independent of the metric. For global scale invariance, a “dilaton” φ has to be introduced, with non-trivial potentials V(φ)=f 1 eαφ in L 1 and U(φ)=f 2 e 2αφ in L 2 . This leads to non-trivial (...) mass generation and a potential for φ which is interesting for inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for “Quintessential models,” which are scale invariant but formulated with the use of volume element Φ d 4 x alone. For closed strings and branes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

This chapter explores the concept of time itself, as physicists understand it. Einstein's special theory of relativity requires worldlines of physical objects to be timelike; the field equations of his general theory of relativity predict that massive bodies such as stars and black holes distort space‐time and bend worldlines. Suppose space‐time becomes so distorted that some worldlines form closed loops. If one tried to follow such a closed timelike curve (or CTC) exactly, all the way around, one would (...) bump into ones former selves and get pushed aside. But by following part of a CTC, we could return to the past and participate in events there. According to a recent calculation by J. Richard Gott of Princeton, a cosmic string passing rapidly by another would generate CTCs. The chapter concludes that if time travel is impossible, then the reason has yet to be discovered. (shrink)

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the (...) intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles. (shrink)

The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived (...) from “modular localization” including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where “dynamic” means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4,2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d=9+1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. (shrink)

An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit (...) scales delineating the asymptotic regimes (Planck scale region and a smooth region of a quantum point oscillator). In the most interesting Planck scale regime, the solution recovers in an elementary fashion some basic relations of string theory (including string tension quantization and string uncertainty relation). It is shown that the degeneracy of the first collective excited state of the p-loop oscillator yields not only the well-known Bekenstein–Hawking area-entropy linear relation but also the logarithmic corrections therein. In addition we obtain for any number of dimensions the Hawking temperature, the Schwarschild radius, and the inequalities governing the area of a black hole formed in a fusion of two black holes. One of the interesting results is a demonstration that the evaporation of a black hole is limited by the upper bound on its temperature, the Planck temperature. (shrink)

Given two strings, text t of length n, and pattern p = p1…pk of length k, and given a natural number w, the subsequence matching problem consists in finding the number of size w windows of text t which contain pattern p as a subsequence, i.e. the letters p1,…,pk occur in the window, in the same order as in p, but not necessarily consecutively . Subsequence matching is used for finding frequent patterns and association rules in databases. We generalize the (...) Knuth–Morris–Pratt pattern matching algorithm; we define a non-conventional kind of RAM, the MP-RAMs which model more closely the microprocessor operations; we design an O on-line algorithm for solving the subsequence matching problem on MP-RAMs. (shrink)

This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument for (...) the ideality of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity. (shrink)

Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because (...) the true physical mass still obeys M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. A Born’s Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 GeV, we find a value for the magnitude $|\mathcal{M } | = 119.7\mbox{~MeV}$ that, coincidentally, is close to the mass of the muon m μ =105.7 MeV. (shrink)

This paper examines various philosophical arguments to do with time travel. It argues that time travel has not been shown to be logically impossible. It then considers whether time travel would give rise to improbable strings of coincidences, or closed causal loops. Finally, it considers whether we could ever be justified in believing someone who claimed to be a time traveller, or whether we would always be more justified in believing that the claimant was either deluded or trying to (...) deceive us. For this last issue the Terry Gilliam film ‘Twelve Monkeys’ is used as an example. (shrink)

Murray Gell-Mann has proposed the concept of effective complexity as a measure of information content. The effective complexity of a string of digits is defined as the algorithmic complexity of the regular component of the string. This paper argues that the effective complexity of a given string is not uniquely determined. The effective complexity of a string admitting a physical interpretation, such as an empirical data set, depends on the cognitive and practical interests of investigators. The (...) effective complexity of a string as a purely formal construct, lacking a physical interpretation, is either close to zero, or equal to the string's algorithmic complexity, or arbitrary, depending on the auxiliary criterion chosen to pick out the regular component of the string. Because of this flaw, the concept of effective complexity is unsuitable as a measure of information content. (shrink)

If the cortex is an associative memory, strongly connected cell assemblies will form when neurons in different cortical areas are frequently active at the same time. The cortical distributions of these assemblies must be a consequence of where in the cortex correlated neuronal activity occurred during learning. An assembly can be considered a functional unit exhibiting activity states such as full activation (“ignition”) after appropriate sensory stimulation (possibly related to perception) and continuous reverberation of excitation within the assembly (a putative (...) memory process). This has implications for cortical topographies and activity dynamics of cell assemblies forming during language acquisition, in particular for those representing words. Cortical topographies of assemblies should be related to aspects of the meaning of the words they represent, and physiological signs of cell assembly ignition should be followed by possible indicators of reverberation. The following postulates are discussed in detail: (1) assemblies representing phonological word forms are strongly lateralized and distributed over perisylvian cortices; (2) assemblies representing highly abstract words such as grammatical function words are also strongly lateralized and restricted to these perisylvian regions; (3) assemblies representing concrete content words include additional neurons in both hemispheres; (4) assemblies representing words referring to visual stimuli include neurons in visual cortices; and (5) assemblies representing words referring to actions include neurons in motor cortices. Two main sources of evidence are used to evaluate these proposals: (a) imaging studies focusing on localizing word processing in the brain, based on stimulus-triggered event-related potentials (ERPs), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI), and (b) studies of the temporal dynamics of fast activity changes in the brain, as revealed by high-frequency responses recorded in the electroencephalogram (EEG) and magnetoencephalogram (MEG). These data provide evidence for processing differences between words and matched meaningless pseudowords, and between word classes, such as concrete content and abstract function words, and words evoking visual or motor associations. There is evidence for early word class-specific spreading of neuronal activity and for equally specific high-frequency responses occurring later. These results support a neurobiological model of language in the Hebbian tradition. Competing large-scale neuronal theories of language are discussed in light of the data summarized. Neurobiological perspectives on the problem of serial order of words in syntactic strings are considered in closing. Key Words: associative learning; cell assembly; cognition; cortex; ERP; EEG; fMRI; language; lexicon; MEG; PET; word category. (shrink)

We propose a kernel method for using combinations of features across example pairs in learning pairwise classifiers. Pairwise classifiers, which identify whether two examples belong to the same class or not, are important components in duplicate detection, entity matching, and other clustering applications. Existing methods for learning pairwise classifiers from labeled training data are based on string edit distance or common features between two examples. However, if two examples from the same class have few common features, these methods have (...) difficulties in finding these pairs and achieving high recall. One typical example is to check whether two abbreviated author names in different citations refer to the same person or not. Since similarities between examples from the same class become close to zero, classifiers fail to distinguish positive pairs from negative pairs. One approach to avoiding the problem of zero similarities is using conjunctions of different features across examples, but implementing this idea straightforwardly makes the computational cost prohibitive for practical problems. Using a kernel on pair instances, our method can use feature conjunctions across examples without actually doing feature mappings, which are computationally expensive. The kernel is a tensor product of two inner products on the original feature space. The corresponding feature mapping generates conjunctions of features only across the two different examples while that of the conventional polynomial kernel also generates conjunctions of features from the same example, which are irrelevant to pairwise classification and cause deterioration of accuracy. Our experiments on the author matching problem show that this method can give a precision 4 to 8 times higher than that of previous methods at medium recall levels. (shrink)

In this interview, Boris Groys discusses his key cultural-theoretical ideas, positions his thought in relation to debates on the cultural economy and clarifies questions emerging from his work. The conversation focuses on his untranslated cultural-theoretical contributions, notably Über das Neue [On the New] and Topologie der Kunst [Topology of Art], but also touches on his writings available in English, for example Art Power. The interview contains three sections. The first revisits Groys’s challenge to the postmodern claim about the end of (...) cultural innovation. He problematizes this claim with reference to the current rise of digital archives and the loss of individual and collective memory. Groys goes on to elucidate the centrality of the ready-made method to cultural innovation. Cultural activity, he argues, constitutes a ritual which promises immortality in a world of perpetual change. Finally, Groys clarifies and illustrates the questions guiding his phenomenological investigation of the ‘scene of evidence’ and the ‘mode of suspicion’. The second section is dedicated to the topology of culture in 21st-century capitalism. Groys sets out from his observation of the privatization and fragmentation of archival space. Humanity is entering a ‘new virtual Middle Age’, where individuals are engaged in a series of self-installations, travelling through a string of heterogeneous valorizing spaces. The ‘chance’ of genuine art in these conditions lies in its withdrawal from exchange. As inexchangeable ‘commodity corpses’ demanding eternal preservation, artworks can provocatively indicate the possibility of a ‘life after capitalism’. His considerations also lead Groys to discuss his notion of Soviet Communism as an installation in pursuit of the wish to ‘step out of time’. The third section centres on the problems of politics and critique. Responding to a question about the political potential of art, Groys proposes consideration of the increasing intensity — presently illustrated by the conflict in the Middle East — with which politics acts in the realm of aesthetics. The interview closes with reflections on the possibility of intellectual resistance. Referring to Nietzsche and Adorno, Groys locates the potential of opposition in a resentful critique of time: a ‘rejection of everything’ and the insistence upon the possibility that what is will vanish. (shrink)

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, (...) we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real. (shrink)

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...) pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms. (shrink)

Undoubtedly the Penrose-Hameroff Orch OR model may be considered as a good theory for describing information processing mechanisms and holistic phenomena in the human brain, but it doesn’t give us satisfactory explanation of human perception. In this work a new approach explaining our perception is introduced, which is in good agreement with Orch OR model and other mainstream science theories such as string theory, loop quantum gravity and holographic principle. It is shown that human perception cannot be explained in (...) the terms of elementary particles and we should introduce new indivisible holistic objects with geometry based on smooth infinitesimal analysis - elastic membranes. The example of such a membrane is our Universe which is an indivisible whole. It is shown that our perception may be considered as the result of elastic oscillations of two dimensional (2D) elastic membranes with closed topology embedded in our bodies. Only one elastic membrane responsible for its perceptions will correspond to the selected organism, but there may be other membranes, even at the cell level. In other words, reality may be considered as the process of time evolution of holistic energetically very weak macro objects - elastic membranes with the geometry based on smooth infinitesimal analysis. An embedded membrane in this multidimensional world will look different for the external and internal observers: from the outside it will look like a material object with smooth infinitesimal geometry, while from the inside our Universe-like space-time fabric. When interacting with elementary particles and other membranes, a membrane will transform their energy into its elastic energy (a new form of energy) - the energy of stretching of the infinitesimal segments. The theory postulates that these elastic deformations will not be observable from the point of view of the internal observer. Heisenberg’s uncertainty principle will work in this physics only from the point of view of the internal observer. For the external observer each embedded elastic membrane may be stretched and even a very small region will become observable. For example, living organisms play the role of internal observers of the Universe, and at the same time they serve as external observers for 2D membranes embedded into our Universe. We can observe our 2D self-membranes through our perceptions, which are encoded in elastic oscillations of the elastic membrane. According to the theory, elastic membranes occupy energetically favorable positions around microtubules involved into Orch OR. The theory not only gives us a really multidimensional holistic picture of reality, but it also provides us with a new method for understanding such phenomena as perception, self-awareness and will. (shrink)

I outline some of my work and results on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system’s matter-gravity entanglement entropy. The main arguments presented are: that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; that the black hole information loss puzzle (...) may be regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; that the black hole thermal atmosphere puzzle can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states ; that the Susskind–Horowitz–Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which ) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.’s ‘canonical typicality’ result to systems which are not necessarily small. (shrink)

The Middle Way was first taught explicitly by the Buddha. It is the first teaching offered by the Buddha in his first address, and the basis of his practical method in meditation, ethics, and wisdom. It is often mentioned in connection with Buddhist teachings, yet the full case for its importance has not yet been made. This book aims to make that case. -/- The Middle Way can be understood from the Buddha's life and metaphors as well as his teachings, (...) and it is these that are used to provide an accessible way into it. In the traditional story, he moved from Palace to Forest, finally realising that neither offered the whole story. The acceptance of rice-porridge marks the moment of recognition. The Middle Way can also be found in the Buddha's practice throughout the rest of his life: his teaching, his politics, even his death. Well-known similes such as the raft, the lute-strings, the arrow, and the blind people with the elephant also offer a profound source of the Middle Way. They are not just allegories of Buddhist teachings, but relate closely to universal judgement in human experience. -/- This book emphasises a positive case, but also has a critical one. Although it has transmitted the Middle Way, the Buddhist tradition has also often ignored or distorted it. The Middle Way is experiential, authentic and creative, and thus threatening to the power of a tradition that has instead emphasised the Buddha's authority as a source of revelation. That authority is allegedly based on the Buddha's enlightenment, which is often interpreted as abstract, discontinuous and absolute. Too many other Buddhist teachings are routinely interpreted in these absolute terms, when they would be much more helpful and universal interpreted in the terms of the Middle Way. -/- Although it engages fully with Buddhist material, this book shows the Middle Way to be a principle of experiential judgement based on awareness that goes far beyond Buddhism. Because it's about how humans judge things, it's universal, not a Buddhist monopoly. In its final section it offers ten alternative non-Buddhist sources for the Middle Way, many of them recent. (shrink)

The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a (...) new paradigm is hindered by the Strong Church–Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation more expressive than TMs are impossible. In this paper, we show that SCT reinterprets the original Church–Turing Thesis (CTT) in a way that Turing never intended; its commonly assumed equivalence to the original is a myth. We identify and analyze the historical reasons for the widespread belief in SCT. Only by accepting that it is false can we begin to adopt interaction as an alternative paradigm of computation. We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction. PTMs allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of TMs and of the CTT. The paradigm shift to interaction provides an alternative understanding of the nature of computing that better reflects the services provided by today’s computing technology. (shrink)

McTaggart distinguished two conceptions of time: the A-series, according to which events are either past, present or future; and the B-series, according to which events are merely earlier or later than other events. Elsewhere, I have argued that these two views, ostensibly about the nature of time, need to be reinterpreted as two views about the nature of the universe. According to the so-called A-theory, the universe is three dimensional, with a past and future; according to the B-theory, the universe (...) is four dimensional. Given special relativity (SR), we are obliged, it seems, to accept (a modified version of) the B-series, four dimensional view, and reject the A-series, three dimensional view, because SR denies that there is a privileged, instantaneous cosmic "now" which seems to be required by the A-theory. Whether this is correct or not, it is important to remember that the fundamental problem, here, is not "What does SR imply?", but rather "What is the best guess about the ultimate nature of the universe in the light of current theoretical knowledge in physics?". In order to know how to answer this question, we need to have some inkling as to how the correct theory of quantum gravity incorporates quantum theory, probability and time. This is, at present, an entirely open question. String theory, or M-theory, seems to evade the issue, and other approaches to quantum gravity seem equally evasive. However, if probabilism is a fundamental feature of ultimate physical reality, then it may well be that the A-theory, or rather a closely related doctrine I call “objectism”, is built into the ultimate constitution of things. (shrink)

That i) there is a somehow determined chronology of Plato’s dialogues among all the chronologies of the last century and ii) this theory is subject to many objections, are points this article intends to discuss. Almost all the main suggested chronologies of the last century agree that Parmenides and Theaetetus should be located after dialogues like Meno, Phaedo and Republic and before Sophist, Politicus, Timaeus, Laws and Philebus. The eight objections we brought against this arrangement claim that to place the (...) dialogues like Meno, Phaedo and Republic both immediately after the early ones and before Parmenides and Theaetetus is epistemologically and ontologically problematic. -/- Key Words: Plato; chronology; knowledge; being; Parmenides -/- Introduction While the ancient philosophers, doxographers and commentators from Aristotle onward considered, more or less, the question of the date and arrangement of the dialogues (cf. Irwin 2008, 77 n. 69), they would not observe a firm necessity to consider the progress of Plato’s theories in dialogues, maybe because they did not think of any essential shift in there. We might be able to say, nevertheless, that the most prominent feature of the ancient attitude to Plato was its peculiar attention to the Republic and the Timaeus as the most mature works in his philosophy and also the consideration of Laws as a later work. This tendency can be discovered from the general viewpoint of the first chronologies of the early 19th century after starting to deal with the issue. That Schleiermacher observed Republic as the culmination of Plato’s philosophy and as one of the latest dialogues besides Laws and Timaeus could reflex the implicit chronology of the tradition in the first mirrors it found. Another tendency in Schleiermacher is taking the triology of Theaetetus, Sophist and Politicus as relatively early. From the last quarter of 19th century onward, stylometry helped scholars to establish a new framework to constructa new arrangement between the dialogues. Based on stylistic as well as literary findings, Campbell (1867, xxxff.) argued for the closeness of the style of Sophist and Politicus with Timaeus, Critias, Philebus and Lawsthat, especially because of the certain evidence about this last dialogue’s lateness, led to the consideration of all as late dialogues. Almost every other stylistic effort after Campbell approved the similarities between Sophist and Politicus with Timaeus, Critias, Philebus and Laws. The result of all such investigations led to a new chronology that, despite some differences, has a fixed structure in all its appearances. 1. The Standard Chronology of the Dialogues The chronologies that are now commonly accepted are mostly based on the arrangement of dialogues to three groups corresponding to three periods of Plato’s life, which became predominant after applying stylistic features in assessing the similarities between dialogues. The fact that all the stylometric considerations reached to the similar results about the date of dialogues while they were assessing different stylistic aspects helped the new chronology become prevailing not only among stylistic chronologies but also between those like Fine, Kahn and Vlastos who were inclined more to the content-based arrangements. Even this latter group could not neglect the apparently certain results of using the method of stylometry. This was the main reason, I think, that made what they called content-based chronology be under the domination of stylometry much more than they could expect. The division of the dialogues into three separate groups became something that most of the scholars took for granted so far as Kahn thinks this division 'can be regarded as a fixed point of departure in any speculation about the chronology of the dialogues' (1996, 44). Thereafter, all the chronologists are accustomed to divide the dialogues to three groups of early, middle and late corresponding to the three stages of Plato’s life. Nevertheless, some of them tried to make subdivisions among each group and introduce some of the dialogues as transitional between different periods and thus reached to a fourfold classification of the dialogues. Although theycould never achieve to a consensus about the place of some dialogues, about which we will discuss soon, the whole spirit of theirchronological arrangements is the same and thus compelling enough for us to unify all of them with the label of 'Standard Chronology of Dialogues' (SCD). We brought together some of the most famous chronologies in the table below to make a comparison easier and to show how all are approximately of the same opinion about the place of some dialogues. The following points must be noted about this table: 1. I divided the dialogues to eight groups of early, late early, transitional, early middle, late middle, post-middle, early late, and late. Although none of the chronologists applies this classification, it can be helpful to compare them. In this table, for example, if one of the chronologist’s beholds one of the dialogues as later than all the dialogues of middle group, it is considered here as late middle. Otherwise, if it is emphasized that it is after all of them, it is considered as post-middle. The same is true about the dialogues of the late group in which I regarded the first dialogues of that period as early late only in those who explicitly considered some dialogues as earlier than other ones in the late group. Though, therefore, some of the dialogues might have not been considered as forming a distinct class, they are distinguished here. A. SCD’s Early and Transitional Dialogues When we move from stylometric to content-based chronologies, the homogeneity between the dialogues of each group is more understandable. Guthrie (1975, v. 4, 50) distinguishes three groups, the first of them includes Apology, Crito, Laches, Lysis, Charmides, Euthyphro, Hippias Minor, Hippias Major, Protagoras, Gorgiasand Ion. In addition to Meno, Phaedo and Euthydems, his first group does not include Cratylus and Menexenus. Unlike Guthrie, almost all the other content-based chronologiesof our study desire to distinguish two categories inside the first group of which the latter must be considered as the transitional group leading to the dialogues of the middle period. Kahn distinguishes four groups of dialogues and arranges two of them before middle period dialogues. The first group including Apology, Crito, Ion, Hippias Minor, Gorgiasand Menexenus he calls 'early' or 'presystematic' dialogues (1998, 124). The second group he calls the 'threshold', 'pre-middle' or 'Socratic' dialogues including seven: Laches, Charmides, Lysis, Euthyphro, Protagoras, Euthydemus and Meno. Based on Vlastos’ arrangement we must distinguish Euthydemus, Hippias Major, Lysis, Menexenus and Meno as 'transitional' dialogues from the 'elenctic' dialogues that are the other dialogues of Kahn’smentioned first two groups plus the first book of theRepublic. Fine also distinguishes 'transitional' dialogues from early or 'Socratic' dialogues,but her transitional dialogues are Gorgias, Meno, Hippias Major, Euthydemus and Cratylus of which she thinks the last two dialogues are 'controversial' (2003, 1). Her Socratic dialogues are all the remaining dialogues of Kahn’s first two groups. In spite of all the differences between the mentioned chronologies, it can be seen that all of them are inclined to arrange the early dialogues in a way that: i) Besides the dialogues that are considered as late, it never includes Republic II-X, Theaetetus, Phaedrus and Parmenides. ii) It intends to consider the dialogues like Euthydemus and Hippias Majorthat look more critical as later among the earlier dialogues or as transitional group. iii) Those who do not consider Meno as a middle period dialogue place it in their second or transitional group. iv) None of the content-based chronologies considers Phaedo and Symposium as early. Stylometric chronologies also intend to put them either as last dialogues among their early ones or as middle. B. SCD’s Middle Period Dialogues Campbell listed Republic, Phaedrus, Parmenides and Theaetetus as his second group of dialogues, an idea thatwas accepted by Brandwood. Ledger’smiddle period dialogueshad Euthydemus, Symposium and Cratylus in addition to the dialogues that Campbell and Brandwood had mentioned as middle. Among content-based chronologies, Guthrie’s list of middle period dialogues did not include Parmenides but some dialogues which had been considered as early in stylometric ones: Meno, Phaedo, Republic, Symposium, Phaedrus, Euthydemus, Menexenus and Cratylus. In sofar as I know, Euthydemus and Menexenus have not been considered as middle by other content-based chronologists and Guthrie is an exception among them. That Phaedo, Phaedrus, Symposium and Republic were middle period dialogues almost all the philosophical chronologists like Kahn, Fine, Vlastos (except Rep.I), Irwin andKraut came along. The dialogues they do not string along about are Meno, Cratylus, Parmenides and Theaetetus. Those like Guthrie, Kraut and Irwin who did not consider Meno as early presumably posit it among middles. The same can be said about Cratylus in the suggested chronologies of Guthrie, Kahn, Vlastos and Kraut. Nonetheless, it is different in case of Parmenides and Theaetetus. Whereas all the mentioned stylometric chronologists like Campbell, Brandwood and Ledger set them among middle period dialogues,the philosophical chronologists, it might seem at first, did not arrive at a consensus about them. While Guthrie and Fine put them as the first dialogues of the late group, Vlastos and Kraut set them as the latest of the middle group, as well as Kahn who puts them as post-middle and amongst the late period dialogues. Regardless the way they classify their groups, their disagreement does not affect the arrangement of the dialogues: they all posit Parmenides and Theaetetus after the series of Meno, Phaedo, Phaedrus, Symposium and Republic and before Sophist, Politicus, Timaeus, Philebus and Laws. To sum up SCD’s arrangement of the middle period dialogues we can add: v) Republic and Phaedrus have been considered by all the mentioned chronologists as dialogues of the middle period. vi) All the philosophical chronologies have reached a consensus about setting Phaedo and Symposium alongside with Republic and Phaedrus as middle. vii) While Stylometric alongside some philosophic chronologists arrange Parmenides and Theaetetus among their middle period dialogues and mostly as the latest among them, other philosophical chronologists put them as the early among the late dialogues. We can conclude then that SCD intends to locate these two dialogues at the boundary between the middle and late period dialogues. -/- . (shrink)

What do exotic area rugs, handcrafted steel-string guitars, and fiddling have in common today? Many contemporary tradition bearers embrace complexity in form and content. They construct objects and performances that draw on the past and evoke nostalgia effectively but also reward close attention. In Rugs, Guitars, and Fiddling: Intensification and the Rich Modern Lives of Traditional Arts, author Chris Goertzen argues that this entails three types of change that can be grouped under an umbrella term: intensification. First, traditional creativity (...) can be intensified through virtuosity, through doing hard things extra fluently. Second, performances can be intensified through addition, by packing increased amounts of traditional materials into the conventionally sized packages. Third, in intensification through selection, artistic impact can grow even if amount of information recedes by emphasizing compelling ideas-e.g., crafting a red and black viper poised to strike rather than a pretty duck decoy featuring more colors and contours. Rugs handwoven in southern Mexico, luthier-made guitars, and southern US fiddle styles experience parallel changes, all absorbing just enough of the complex flavors, dynamics, and rhythms of modern life to translate inherited folklore into traditions that can be widely celebrated today. New mosaics of details and skeins of nuances don't transform craft into esoteric fine art, but rather enlist the twists and turns and endless variety of the contemporary world therapeutically, helping transform our daily chaos into parades of negotiable jigsaw puzzles. Intensification helps make crafts and traditional performances more accessible and understandable and thus more effective, bringing past and present closer together, helping folk arts continue to perform their magic today. (shrink)

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements, identifies four possible options for a Theory of Everything. Quotes from prominent physicists express divergent views on (...) each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery. (shrink)

This paper offers a defense of Charles Parsons’ appeal to mathematical intuition as a fundamental factor in solving Benacerraf’s problem for a non-eliminative structuralist version of Platonism. The literature is replete with challenges to his well-known argument that mathematical intuition justifies our knowledge of the infinitude of the natural numbers, in particular his demonstration that any member of a Hilbertian stroke string ω-sequence has a successor. On Parsons’ Kantian approach, this amounts to demonstrating that for an “arbitrary” or “vaguely (...) represented” string of strokes, we can always “add” one more stroke. Critics have contested the cogency of a notion of an arbitrary object, our capacity to vaguely represent a definite object, and the role of spatial and temporal representation in the demonstration that we can “add” one more. The bulk of this paper is devoted to demonstrating how to meet all extant criticisms of his key argument. Critics have also suggested that Parsons’ whole approach is misbegotten because the appeal to mathematical intuition inevitably falls short of providing a complete solution to Benacerraf’s problem. Since the natural numbers are essentially and exclusively characterized by their structural properties, they cannot be identified with any particular model of arithmetic, and thus a notion of intuition will fail to capture the universality of arithmetic, its applicability to all entities. This paper also explains why we should not reject appeal to mathematical intuition even though it is not itself sufficient to fully “close the gap” on Benacerraf’s challenge. (shrink)

Abstract There appears to be very close link between globalization and imperialism. Both seem to have domineering character. Globalization could be likened to a new wave of imperialism as it could be adjudged the process by which the so called superior powers of the West dominate and influence developing countries like Nigeria. They are expansionist in nature. Christianity has the same expansionist features as globalization and imperialism. The imperialist nature of globalization could be assessed from the expansionist activities of Christianity (...) that equally originates from the West. This paper is an attempt to discuss globalization, imperialism and Christianity as expansionist realities from the Nigerian perspective. Information is gathered from content analyses of the concepts of globalization, imperialism and Christianity and simple observation of what Nigeria experiences with regard to Christianity. It is observed that much of what Christianity favours are materials from the West. The paper concludes that Christianity more than ever before rides on the crest of globalization to further imperialism. It suggests that Christianity in the twenty-first century should be more inculturated than hanging on the apron strings of the West especially with regard to religious wares. (shrink)

The recently celebrated discovery of the Higgs boson has captivated the public's imagination with the promise that it can explain the origins of everything in the universe. It's no wonder that the media refers to it grandly as the "God particle." Yet behind closed doors, physicists are admitting that there is much more to this story, and even years of gunning the Large Hadron Collider and herculean number crunching may still not lead to a deep understanding of the laws (...) of nature. In this fascinating and eye-opening account, theoretical physicist Alexander Unzicker and science writer Sheilla Jones offer a polemic. They question whether the large-scale, multinational enterprises actually lead us to the promised land of understanding the universe. The two scientists take us on a tour of contemporary physics and show how a series of highly publicized theories met a dead end. Unzicker and Jones systematically unpack the recent hot theories such as "parallel universes," "string theory," and "inflationary cosmology," and provide an accessible explanation of each. They argue that physics has abandoned its evidence-based roots and shifted to untestable mathematical theories, and they issue a clarion call for the science to return to its experimental foundation. (shrink)

Aravind Joshi famously hypothesized that natural language syntax was characterized (in part) by mildly context-sensitive generative power. Subsequent work in mathematical linguistics over the past three decades has revealed surprising convergences among a wide variety of grammatical formalisms, all of which can be said to be mildly context-sensitive. But this convergence is not absolute. Not all mildly context-sensitive formalisms can generate exactly the same stringsets (i.e. they are not all weakly equivalent), and even when two formalisms can both generate a (...) certain stringset, there might be differences in the structural descriptions they use to do so. It has generally been difficult to find cases where such differences in structural descriptions can be pinpointed in a way that allows linguistic considerations to be brought to bear on choices between formalisms, but in this paper we present one such case. The empirical pattern of interest involves wh-movement dependencies in languages that do not enforce the wh-island constraint. This pattern draws attention to two related dimensions of variation among formalisms: whether structures grow monotonically from one end to another, and whether structure-building operations are conditioned by only a finite amount of derivational state. From this perspective, we show that one class of formalisms generates the crucial empirical pattern using structures that align with mainstream syntactic analysis, and another class can only generate that same string pattern in a linguistically unnatural way. This is particularly interesting given that (i) the structurally-inadequate formalisms are strictly more powerful than the structurally-adequate ones from the perspective of weak generative capacity, and (ii) the formalism based on derivational operations that appear on the surface to align most closely with the mechanisms adopted in contemporary work in syntactic theory (merge and move) are the formalisms that fail to align with the analyses proposed in that work when the phenomenon is considered in full generality. (shrink)

Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier series" and the so-called (...) "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work. (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)

Theo C. Meyering, in “Mind Matters: Physicalism and the Autonomy of the Person,” takes yet a third approach to the issue of reduction. He states that “if (true, downward) mental causation implies nonreducibility [as Stoeger and Murphy argue] and physicalism implies the converse, it is hard to see how these two views could be compatible.” Meyering distinguishes three versions of reductionism: radical (industrial strength) physicalism; ideal (regular strength) physicalism, and mild or token physicalism. Radical physicalism asserts that all special sciences (...) are reducible to physics in the sense that their laws can be deduced via bridge laws from those of physics. Ideal physicalism asserts that while it is practically impossible to reduce the special sciences, such reduction would be possible were there an ideally complete physics" (Note: This distinction parallels Stoeger’s recognition that epistemological reducibility is relative to the meaning of “laws of nature). Token physicalism is ontologically reductionist: there are no events that are not “token-identical” with some physical event or other (Note: See above, sec. 3.3). However, there are no identities between higher-level and lower- level types of events; consequently some events described by the special sciences have no physical explanation at all. -/- All of these reductionist positions are to be contrasted with compositional (milder than mild) physicalism, which asserts that some higher-level events are not even token-identical with physical events because the higher-level event (say, a crash in the stock market) is constituted by innumerable physical particulars in all sorts of states and interactions. -/- Meyering then surveys some of the existing arguments for the nonreducibility of the special sciences. One of the most important is the argument from multiple realizability. The claim is that economics, for example, is not reducible to physics because economic concepts (for example, monetary exchange) are “wildly multiply realizable” (for example, using coins, strings of wampum, signing a check). Thus, there can be no bridge laws and no reduction. Such an argument, however, only cuts against radical physicalism, not the weaker (and a priori more plausible) ideal physicalism. -/- A stronger argument for the indispensability of special-science explanations is based on the role of functional explanations. For example, the functional description of aspirin as an analgesic is in some instances a more useful explanation of its causal role (relieving a headache) than is its description as the chemical level. -/- Meyering’s own contribution focuses neither on multiple realizability of supervenient properties nor on multiple “fillers” of functional roles, but on “multiple supervenience.” In particular, a single subvenient state of affairs (for example, a cloud of free electrons permeating the metal of which a ladder is constructed) may realize a variety of supervenient dispositional properties (in this case, electrical conductivity, thermal conductivity, opacity). An explanation (say, of the cause of a deadly accident) requires reference to the dispositional property (electrical conductivity), not merely to the subvenient property. Meyering argues that it is this possibility of multiple supervenience, not multiple realizability, that gives arguments against reduction based on functional properties their real force. Downward causation, then, can be understood in terms of selective activation of one of several dispositional properties of a lower-level state, and thus can be assigned a stable place in our picture of how the world is organized without upsetting our conception of physics as constituting a closed and complete system of physical events. (shrink)

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for (...) 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in [28] by improving both the lower and the upper bounds. (shrink)

7 lectures, Torquay, UK, August 12-20, 1924 (CW 311) These seven intimate, aphoristic talks were presented to a small group on Steiner's final visit to England. Because they were given to "pioneers" dedicated to opening a new Waldorf school, these talks are often considered one of the best introductions to Waldorf education. Steiner shows the necessity for teachers to work on themselves first, in order to transform their own inherent gifts. He explains the need to use humor to keep their (...) teaching lively and imaginative. Above all, he stresses the tremendous importance of doing everything in the knowledge that children are citizens of both the spiritual and the earthly worlds. And, throughout these lectures, he continually returns to the practical value of Waldorf education. These talks are filled with practical illustrations and revolve around certain themes--the need for observation in teachers; the dangers of stressing the intellect too early; children's need for teaching that is concrete and pictorial; the education of children's souls through wonder and reverence; the importance of first presenting the "whole," then the parts, to the children's imagination. Here is one of the best introductions to Waldorf education, straight from the man who started it all. German source: Die Kunst des Erziehens aus dem Erfassen der Menschenwesenhiet (GA 311). ∞ ∞ ∞ SYNOPSIS OF THE LECTURES LECTURE 1: The need for a new art of education. The whole of life must be considered. Process of incarnation as a stupendous task of the spirit. Fundamental changes at seven and fourteen. At seven, the forming of the "new body" out of the "model body" inherited at birth. After birth, the bodily milk as sole nourishment. The teacher's task to give "soul milk" at the change of teeth and "spiritual milk" at puberty. LECTURE 2: In first epoch of life child is wholly sense organ. Nature of child's environment and conduct of surrounding adults of paramount importance. Detailed observation of children and its significance. In second epoch, seven to fourteen, fantasy and imagination as life blood of all education, e.g., in teaching of writing and reading, based on free creative activity of each teacher. The child as integral part of the environment until nine. Teaching about nature must be based on this. The "higher truths" in fairy tales and myths. How the teacher can guide the child through the critical moment of the ninth year. LECTURE 3: How to teach about plants and animals (seven to fourteen). Plants must always be considered, not as specimens, but growing in the soil. The plant belongs to the earth. This is the true picture and gives the child an inward joy. Animals must be spoken of always in connection with humans. All animal qualities and physical characteristics are to be found, in some form, in the human being. Humans as synthesis of the whole animal kingdom. Minerals should not be introduced until twelfth year. History should first be presented in living, imaginative pictures, through legends, myths, and stories. Only at eleven or twelve should any teaching be based on cause and effect, which is foreign to the young child's nature. Some thoughts on punishment, with examples. LECTURE 4: Development of imaginative qualities in the teacher. The story of the violet and the blue sky. Children's questions. Discipline dependent on the right mood of soul. The teacher's own preparation for this. Seating of children according to temperament. Retelling of stories. Importance of imaginative stories that can be recalled in later school life. Drawing of diagrams, from ninth year. Completion and metamorphosis of simple figures, to give children feeling of form and symmetry. Concentration exercises to awaken an active thinking as basis of wisdom for later life. Simple color exercises. A Waldorf school timetable. The "main lesson." LECTURE 5: All teaching matter must be intimately connected with life. In counting, each different number should be connected with the child or what the child sees in the environment. Counting and stepping in rhythm. The body counts. The head looks on. Counting with fingers and toes is good (also writing with the feet). The ONE is the whole. Other numbers proceed from it. Building with bricks is against the child's nature, whose impulse is to proceed from whole to parts, as in medieval thinking. Contrast atomic theory. In real life we have first a basket of apples, a purse of coins. In teaching addition, proceed from the whole. In subtraction, start with minuend and remainder; in multiplication, with product and one factor. Theorem of Pythagoras (eleven-twelve years). Details given of a clear, visual proof, based on practical thinking. This will arouse fresh wonder every time. LECTURE 6: In first seven years etheric body is an inward sculptor. After seven, child has impulse to model and to paint. Teacher must learn anatomy by modeling the organs. Teaching of physiology (nine to twelve years) should be based on modeling. Between seven and fourteen astral body gradually draws into physical body, carrying the breathing by way of nerves, as playing on a lyre. Importance of singing. Child's experience of well being like that of cows chewing the cud. Instrumental music from beginning of school life, wind or strings. Teaching of languages; up to nine through imitation, then beginnings of grammar, as little translation as possible. Vowels are expression of feeling, consonants are imitation of external processes. Each language expresses a different conception. Compare head, Kopf, testa. The parts of speech in relation to the life after death. If language is rightly taught, out of feeling, eurythmy will develop naturally, expressing inner and outer experiences in ordered movements--"visible speech." Finding relationship to space in gymnastics. LECTURE 7: Between seven and fourteen soul qualities are paramount. Beginnings of science teaching from twelfth year only, and connected with real phenomena of life. The problem of fatigue. Wrong conceptions of psychologists. The rhythmic system, predominant in second period, never tires. Rhythm and fantasy. Composition. Sums from real life, not abstractions. Einstein's theory. The kindergarten--imitation of life. Teachers' meetings, the heart of the school. Every child to be in the right class for its age. Importance of some knowledge of trades, e.g., shoemaking, handwork, and embroidery. Children's reports-- characterization, but no grading. Contact with the parents. QUESTIONS AND ANSWERS: The close relationship of Multiplication and Division. How to deal with both together. Transition from the concrete to the abstract in Arithmetic. Not before the ninth year. Healthiness of English weights and measures as related to real life. Decimal system as an intellectual abstraction. Drawing. Lines have no reality in drawing and painting, only boundaries. How to teach children to draw a tree in shading, speaking only of light and color. (Illustration). Line drawing belongs only to geometry. Gymnastics and Sport. Sport is of no educational value, but necessary as belonging to English life. Gymnastics should be taught by demonstration. Religious Instruction. Religion lessons in the Waldorf school given by Catholic priest and Protestant pastor. "Free" religion lessons provided for the other children. Plan of such teaching described, of which the fundamental aim is an understanding of Christianity. The Sunday services. Modern Language Lessons. Choice of languages must be guided by the demands of English life. These can be introduced at an early age. Direct method in language teaching. Closing words by Dr. Steiner on the seriousness of this first attempt to found a school in England. (shrink)

We interpret the concept of determinism for a classical system as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally believed to hold for all autonomous classical systems. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension provides counterexamples of this belief. Given the initial conditions of a particular type, the Cauchy problem may have an infinite set of solutions. Therefore, (...) random behavior of closed classical systems is indeed possible. With this finding, we give a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems. (shrink)

The classification of grammars that became known as the Chomsky hierarchy was an exploration of what kinds of regularities could arise from grammars that had various conditions imposed on their structure. Intersubstitutability is closely related to the way different levels on the Chomsky hierarchy correspond to different kinds of memory. This chapter deals with the general concept of a string‐rewriting grammar, which provides the setting in which the Chomsky hierarchy can be formulated. An unrestricted rewriting grammar works with a (...) specified set of nonterminal symbols, and specified set of terminal symbols. From the very outset there were doubts about about whether context‐free grammars (CFGs) could form the basis of a theory of natural language syntax. The grammar's rewrite rules correspond to the automaton's transitions. Chomsky argued that even if the generative capacity of CFGs turned out to be sufficient for English, the resulting grammars would be unreasonably complex. (shrink)

We study a theory PTO of polynomial time computability on the type of binary strings, as embedded in full lambda calculus with total application and extensionality. We prove that the closed terms of type W → W are exactly the polynomial time operations. This answers a conjecture of Strahm [13].

We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ (...) sets X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements, identifies four possible options for a Theory of Everything. Quotes from prominent physicists express divergent views on (...) each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery. (shrink)

The paper explores the philosophical treatment of sacrifice in four of Jiří Menzel’s films of the 1960’s, Closely observed trains (Ostře sledované vlaky), Capricious summer (Rozmarné léto), Mr Balthazar’s death (Smrt pana Baltazara), his short film contribution to the anthology film of the New Wave, Pearls of the deep (Perličky na dně), and Larks on a string (Skřivánci na niti). The paper argues that Menzel problematizes romanticized versions of messianic sacrifice as they all too easily disregard the moral significance (...) of mundane relations. By analysing the treatment of sacrifice in each of these films, the paper makes a case for the significance of Menzel’s treatment of sacrifice for current philosophical debates. (shrink)

There is a family of questions in relativized complexity theory--weak analogs of the Friedberg Jump-Inversion Theorem--that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper defines aw2-generic sets. i.e., sets which meet every dense set of strings that is r.e. in some incomplete r.e. set. Aw2-generic sets are very close to 1-generic sets in strength, but are too weak to resolve these questions. In particular, it is shown that for any (...) set X there is an aw2-generic set G such that $\mathbf{NP}^G \cap co-\mathbf{NP}^G \nsubseteq \mathbf{P}^{G \oplus X}$ . (On the other hand, if G is 1-generic, then $\mathbf{NP}^G \cap co-\mathbf{NP}^G \subseteq \mathbf{P}^{G \oplus \mathrm{SAT}}$ . where SAT is the NP-complete satisfiability problem [6].) This result runs counter to the fact that most finite extension constructions in complexity theory can be made effective. These results imply that any finite extension construction that ensures any of the Friedberg analogs must be noneffective, even relative to an arbitrary incomplete r.e. set. It is then shown that the recursion theoretic properties of aw2-generic sets differ radically from those of 1-generic sets: every degree above O' contains an aw2-generic set: no aw2-generic set exists below any incomplete r.e. set; there is an aw2-generic set which is the join of two Turing equivalent aw2-generic sets. Finally, a result of Shore is presented [30] which states that every degree above 0' is the jump of an aw2-generic degree. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:From the Front NICOLAS ALIFERIS (Translated by Avi Sharon) The poems in Nicolas Aliferis’s 1998 collection “From the Front” offer a panorama of postcard views and epistolary voices from across the Greek oikoumene during the years 1897 through 1922. While the title has military tones, they are not all soldier’s letters. In point of fact, this was a period when the territorial limits of Greece, “the Front,” were undergoing (...) near constant alteration—“like the ink drunk in by blotting paper” as Seferis wrote in a poem about Europe at the beginning of the Second World War. The front, therefore, could be almost anywhere during this period, and certainly in the minds of almost every Greek. The Greco-Turkish War of 1897, stemming from irredentist forces in Crete, was the earliest outbreak, and put that island on a path toward union with the mainland. After that came the string of Balkan conflagrations before, during, and after ww i, that would more than double the land mass and population of Greece. The sequence of Treaties that, one by one, concluded each stage in these disputes (from that of Constantinople in 1897, to Sevres in 1920) brought Crete, Epirus, much of Macedonia, and then Thrace and the Dodecanese islands within the limits of Greece proper. The “front” was therefore more an idea than a line on a map, and the experience of it was not limited to actual soldiers in real trenches. The distinct personae that animate each poem range from conscripts in training camps to villagers turned mercenaries to city-bound merchants and other figures, high and low. The poems themselves are drawn from various sources: some were personal letters in the poet’s own family archive, others were drawn from written history arion 28.2 fall 2020 124 from the front and newspaper scraps, while some are more purely hypothetical. They present an imaginary memento of the experiences and voices of that period, and the struggle, personal and national, that helped inform the shape and meaning of what Greece is today. Nicolas Aliferis 125 the death of chakalarov We did away with Chakalarov and Popov, those terrors to the villages. They’d collect our lira then make their way to the north. When word reached Macedonia it was a huge relief. Now we’re in the mountains, all sixteen of us, walking the trails covered in fog, holed up in the rocks, always on lookout. The cold is fierce: ice, snow, gnashing teeth. Our enemies raging and the Bulgarians wild as bears. So much blood, deep red. Beyond to the east, gleaming peacefully, the lakes, Ostrovou and Sorovitz. 126 from the front dombro betser I received your letter. With so much happening here there was little time to write. But we haven’t forgotten you; every day there’s some mention of your name. How are you finding Macedonia— her mountains, her rivers? You were not joking with our neighbors, I see. Where will this story end for us? The teacher from the Monastery, she asks about you: “And Mr. Pelopidas...” she begins, then lowers her eyes. Here the knives are out. Oh Lord, will we ever get over it? Nicolas Aliferis 127 adrianople 1920 I am well and wish you the same. Living is cheap here— a chicken costs just two and a half drachmas. Lately I’ve gotten to know all the upper level subordinates and quite a few merchants, Turks and Jews. In the evening there’s either study or cards. As for what you write: I say we should learn from the Belgians, Pantelis, just a little. Otherwise, I’m afraid, our race is finished! 128 from the front training camp, 1918 I’ve sent three letters and received none. Only yesterday I heard news from the trenches: the deeds of Yanni and Bicha, how they died. It rained today and is raining still. I sit alone (it’s been a while...) and write you. My comrades are outside, their eyes glued to the open spaces. How necessary for the soul— amid this solitude— to feel human. The need to hear the breath of a comrade, to stand above his gaze, to half close your... (shrink)