Journal articles on the topic 'Other homology theories'

Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us to show that our homology transfer coincides with the one given by L. Smith. With our definition of the homology transfer we can give simpler proofs of the properties of the known transfer and of some new ones. Our transfers can also be defined in Karoubi's approach to homology and cohomology. Furthermore, we show that one can define mixed transfers from other homology or cohomology theories to the ordinary ones.

One of the least understood properties of chromatin is the ability of its similar regions to recognize each other through weak interactions. Theories based on electrostatic interactions between helical macromolecules suggest that the ability to recognize sequence homology is an innate property of the non-ideal helical structure of DNA. However, this theory does not account for the nucleosomal packing of DNA. Can homologous DNA sequences recognize each other while wrapped up in the nucleosomes? Can structural homology arise at the level of nucleosome arrays? Here, we present a theoretical model for the recognition potential well between chromatin fibres sliding against each other. This well is different from the one predicted for bare DNA; the minima in energy do not correspond to literal juxtaposition, but are shifted by approximately half the nucleosome repeat length. The presence of this potential well suggests that nucleosome positioning may induce mutual sequence recognition between chromatin fibres and facilitate the formation of chromatin nanodomains. This has implications for nucleosome arrays enclosed between CTCF–cohesin boundaries, which may form stiffer stem-like structures instead of flexible entropically favourable loops. We also consider switches between chromatin states, e.g. through acetylation/deacetylation of histones, and discuss nucleosome-induced recognition as a precursory stage of genetic recombination.

We investigate a generalization to non-Witt stratified spaces of the intersection homology theory of Goresky–MacPherson. The second-named author has described the self-dual sheaves compatible with intersection homology, and the other authors have described a generalization of Cheeger's L2 de Rham cohomology. In this paper we first extend both of these cohomology theories by describing all sheaf complexes in the derived category of constructible sheaves that are compatible with middle perversity intersection cohomology, though not necessarily self-dual. Our main result is that this refined intersection cohomology theory coincides with the analytic de Rham theory on Thom–Mather stratified spaces. The word "refined" is motivated by the fact that the definition of this cohomology theory depends on the choice of an additional structure (mezzo-perversity) which is automatically zero in the case of a Witt space.

The following are personal reminiscences of my research years in algebraic K-theory and cyclic homology during which Dan Quillen was everyday present in my professional life.In the late sixties (of the twentieth century) the groups K0;K1;K2 were known and well-studied. The group K0 had been introduced by Alexander Grothendieck, then came K1 by Hyman Bass [2] (as a variation of the Whitehead group), permitting one to generalize the notion of determinant, and finally K2 by John Milnor [9] and Michel Kervaire. The big problem was: how about Kn? Having in mind topological K-theory and all the other generalized (co)homological theories, one was expecting higher K-groups which satisfy similar axioms, in particular the Mayer-Vietoris exact sequence. The discovery by Richard Swan of the existence of an obstruction for this property to hold shed some embarrassment. What kind of properties should we ask of Kn? There were various attempts, for instance by Max Karoubi and Orlando Villamayor [4]. And suddenly Dan Quillen came with a candidate sharing a lot of nice properties. He had even two different constructions of the same object: the “+” construction and the “Q” construction [14, 15]. Not only did he propose a candidate but he already got a computation: the higher K-theory of finite fields. This was a fantastic step forward and Hyman Bass organized a two week conference at the Battelle Institute in Seattle during the summer of 1972, which was attended by Bass, Borel, Husemoller, Karoubi, Priddy, Quillen, Segal, Stasheff, Tate, Waldhausen, Wall and sixty other mathematicians. The Proceedings appeared as Springer Lecture Notes 341, 342 and 343. I met Quillen for the first time on this occasion.

AbstractWe develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology ofU(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra= ℤ/2 n ⋊ Λ* ℝ2on the other side. We find that both TQFT's are SL(2; ℝ)-equivariant functors and, as such, are isomorphic. The SL(2; ℝ)-action in the Hennings construction comes from the natural action onand in the case of the Frohman–Nicas theory from the Hard–Lefschetz decomposition of theU(1)-moduli spaces given that they are naturally Kähler. The irreducible components of this TQFT, corresponding to simple representations of SL(2; ℤ) and Sp(2g; ℤ), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg–Witten theories, Casson type theories for homology circlesà laDonaldson, higher rank gauge theories following Frohman and Nicas, and the ℤ=pℤ reductions of Reshetikhin.Turaev theories over the cyclotomic integers ℤ[ζp]. We also conjecture that the Hennings TQFT for quantum-sl2is the product of the Reshetikhin–Turaev TQFT and such a homological TQFT.

A second family of highly repeated sequences has been identified on the B chromosome of rye (Secale cereale). The E3900 family was detected as a variant band in EcoRI digests of +B DNA. A clone of the basic repeat of the family was obtained, and the organization of the family was investigated by genomic hybridization. The E3900 family has no apparent homology to the A chromosome sequences of rye or other members of the Gramineae. The family has been localized by in situ hybridization to the end of the long arm of the rye B chromosome. The previously characterized E1100 sequence shows in situ hybridization to the same location as the E3900 family. These results are discussed in light of current theories of the origin of B chromosomes.Key words: B chromosome, Secale cereale, repeated sequence, cloning, in situ hybridization.

Abstract Pierre Bourdieu’s work has argued that there is a homology of social classes on the one hand and cultural consumption on the other. In contrast, theories of individualisation posit that social class plays only a minor role in shaping lifestyle in contemporary societies. In this paper we examine a) how much contemporary highbrow lifestyles in 27 European countries are structured by class membership, b) the extent to which highbrow consumption varies according to the level of modernisation of a society and c) whether the explanatory power of social class in relation to highbrow consumption decreases in more modernised European countries. The findings show that highbrow lifestyles are strongly influenced by social class, and that highbrow consumption is more common in more modernised societies. Moreover, the findings confirm the hypothesis that the formative power of social class on lifestyle decreases in highly modernised societies, albeit without disappearing completely.

In a spacetime divided into two regions U1 and U2 by a hypersurface Σ, a perturbation of the field in U1 is coupled to perturbations in U2 by means of the holographic imprint that it leaves on Σ. The linearized gluing field equation constrains perturbations on the two sides of a dividing hypersurface, and this linear operator may have a nontrivial null space. A nontrivial perturbation of the field leaving a holographic imprint on a dividing hypersurface which does not affect perturbations on the other side should be considered physically irrelevant. This consideration, together with a locality requirement, leads to the notion of gauge equivalence in Lagrangian field theory over confined spacetime domains. Physical observables in a spacetime domain U can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that ∂Σ⊂∂U. The set of observables of this type is sufficient to distinguish gauge inequivalent solutions. The integral of a conserved current on a hypersurface is sensitive only to its homology class [Σ], and if U is homeomorphic to a four ball the homology class is determined by its boundary S=∂Σ. We will see that a result of Anderson and Torre implies that for a class of theories including vacuum general relativity all local observables are holographic in the sense that they can be written as integrals of over the two-dimensional surface S. However, nonholographic observables are needed to distinguish between gauge inequivalent solutions.

Different theories have been proposed for explaining the evolution of language. One of this maintains that gestural communication has been the precursor of human speech. Here we present a series of neurophysiological evidences that support this hypothesis. Communication by gestures, defined as the capacity to emit and recognize meaningful actions, may have originated in the monkey motor cortex from a neural system whose basic function was action understanding. This system is made by neurons of monkey’s area F5, named mirror neurons, activated by both execution and observation of goal-related actions. Recently, two new categories of mirror neurons have been described. Neurons of one category respond to the sound of an action, neurons of the other category respond to the observation of mouth ingestive and communicative actions. The properties of these neurons indicate that monkey’s area F5 possesses the basic neural mechanisms for associating gestures and meaningful sounds as a pre-adaptation for the later emergence of articulated speech. The homology and the functional similarities between monkey area F5 and Broca’s area support this evolutionary scenario.

This paper attempts to clarify or to reposition some of the controversies generated by Burawoy’s defense of public sociology and by his vision of the mutually stimulating relationship between the different forms of sociology. Before arguing if, why, and how, sociology should or could be more ‘public’, it might be useful to reflect upon what it is we think we, as sociologists, know that ‘lay people’ do not. This paper thus explores the public sociology debate’s epistemological core, namely the issue of the relationship between sociologists’ and non-sociologists’ knowledge of the social world. Four positions regarding the status of sociologists’ knowledge versus lay people’s knowledge are explored: superiority (sociologists’ knowledge of the social world is more accurate, objective and reflexive than lay people’s knowledge, thanks to science’s methods and norms), homology (when they are made explicit, lay theories about the social world often parallel social scientists’ theories), complementarity (lay people’s and social scientists’ knowledge complement one another. The former’s local, embedded knowledge is essential to the latter’s general, disembedded knowledge), and circularity (sociologists’ knowledge continuously infuses commonsensical knowledge, and scientific knowledge about the social world is itself rooted in common sense knowledge. Each form of knowledge feeds the other). For each of these positions, implications are drawn regarding the terms, possibilities and conditions of a dialogue between sociologists and their publics, especially if we are to take the circularity thesis seriously. Conclusions point to the accountability we face towards the people we study, and to the idea that sociology is always performative, a point that has, to some extent, been obscured by Burawoy’s distinctions between professional, critical, policy and public sociologies.

AbstractThe chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the filtration levels of chains representing that class. These spectral numbers have been studied extensively in the case of Hamiltonian Floer homology by Oh, Schwarz and others. We prove that the spectral number associated to any nonzero Floer homology class is always finite, and that the infimum in the definition of the spectral number is always attained. In the Hamiltonian case, this implies that what is known as the ‘nondegenerate spectrality’ axiom holds on all closed symplectic manifolds. Our proofs are entirely algebraic and apply to any Floer-type theory (including Novikov homology) satisfying certain standard formal properties. The key ingredient is a theorem about the existence of best approximations of arbitrary elements of finitely generated free modules over Novikov rings by elements of prescribed submodules with respect to a certain family of non-Archimedean metrics.

We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky–MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity homology theory and a companion perversity cohomology theory based on generalized cocycle spaces. These theories lead to conditions on pairs of cycles which can be intersected and a suitable equivalence relation on cocycles/cycles enabling pairings on equivalence classes. We establish suspension and splitting theorems, as well as a localization property. Some examples of intersections on singular varieties are computed.

Abstract In network science, the non-homogeneity of node degrees has been a concerning issue for study. Yet, with today's modern web technologies, the traditional social communication topologies have evolved from node-central structures into online cycle-based communities, urgently requiring new network theories and tools. Switching the focus from node degrees to network cycles could reveal many interesting properties from the perspective of totally homogenous networks or sub-networks in a complex network, especially basic simplexes (cliques) such as links and triangles. Clearly, compared with node degrees, it is much more challenging to deal with network cycles. For studying the latter, a new clique vector-space framework is introduced in this paper, where the vector space with a basis consisting of links has a dimension equal to the number of links, that with a basis consisting of triangles has the dimension equal to the number of triangles and so on. These two vector spaces are related through a boundary operator, for example mapping the boundary of a triangle in one space to the sum of three links in the other space. Under the new framework, some important concepts and methodologies from algebraic topology, such as characteristic number, homology group and Betti number, will play a part in network science leading to foreseeable new research directions. As immediate applications, the paper illustrates some important characteristics affecting the collective behaviors of complex networks, some new cycle-dependent importance indexes of nodes and implications for network synchronization and brain-network analysis.

The aim of the first part of this paper is to make some reflections on the role of geometrical and topological concepts in the developments of theoretical physics, especially in gauge theory and string theory, and we show the great significance of these concepts for a better understanding of the dynamics of physics. We will claim that physical phenomena essentially emerge from the geometrical and topological structure of space–time. The attempts to solve one of the central problems in 20th theoretical physics, i.e. how to combine gravity and the other forces into an unitary theoretical explanation of the physical world, essentially depends on the possibility of building a new geometrical framework conceptually richer than Riemannian geometry. In fact, it still plays a fundamental role in non-Abelian gauge theories and in superstring theory, thanks to which a great variety of new mathematical structures has emerged. The scope of this presentation is to highlight the importance of these mathematical structures for theoretical physics. A very interesting hypothesis is that the global topological properties of the manifold's model of space–time play a major role in quantum field theory (QFT) and that, consequently, several physical quantum effects arise from the nonlocal changing metrical and topological structure of these manifold. Thus the unification of general relativity and quantum theory require some fundamental breakthrough in our understanding of the relationship between space–time and quantum process. In particular the superstring theories lead to the guess that the usual structure of space–time at the quantum scale must be dropped out from physical thought. Non-Abelian gauge theories satisfy the basic physical requirements pertaining to the symmetries of particle physics because they are geometric in character. They profoundly elucidate the fundamental role played by bundles, connections, and curvature in explaining the essential laws of nature. Kaluza–Klein theories and more remarkably superstring theory showed that space–time symmetries and internal (quantum) symmetries might be unified through the introduction of new structures of space with a different topology. This essentially means, in our view, that "hidden" symmetries of fundamental physics can be related to the phenomenon of topological change of certain class of (presumably) nonsmooth manifolds. In the second part of this paper, we address the subject of topological quantum field theories (TQFTs), which constitute a remarkably important meeting ground for physicists and mathematicians. TQFTs can be used as a powerful tool to probe geometry and topology in low dimensions. Chern–Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of QFTs which can be exactly (nonperturbatively) and explicitly solved. Abelian Chern–Simons theory provides a field theoretic interpretation of the linking and self-linking numbers of a link (i.e. the union of a finite number of disjoint knots). In non-Abelian theories, vacuum expectation values of Wilson link operators yield a class of polynomial link invariants; the simplest of them is the well-known Jones polynomial. Powerful methods for complete analytical and nonperturbative computation of these knot and link invariants have been developed. From these invariants for unoriented and framed links in S3, an invariant for any three-manifold can be easily constructed by exploiting the Lickorish–Wallace surgery presentation of three-manifolds. This invariant up to a normalization is the partition function of the Chern–Simons field theory. Even perturbative analysis of Chern–Simons theories are rich in their mathematical structure; these provide a field theoretic interpretation of Vassiliev knot invariants. In Donaldson–Witten theory perturbative methods have proved their relations to Donaldson invariants. Nonperturbative methods have been applied after the work by Seiberg and Witten on N = 2 supersymmetric Yang–Mills theory. The outcome of this application is a totally unexpected relation between Donaldson invariants and a new set of topological invariants called Seiberg–Witten invariants. Not only in mathematics, Chern–Simons theories find important applications in three- and four-dimensional quantum gravity also. Work on TQFT suggests that a quantum gravity theory can be formulated in three-dimensional space–time. Attempts have been made in the last years to formulate a theory of quantum gravity in four-dimensional space–time using "spin networks" and "spin foams". More generally, the developments of TQFTs represent a sort of renaissance in the relation between geometry and physics. The most important (new) feature of present developments is that links are being established between quantum physics and topology. Maybe this link essentially rests on the fact that both quantum theory and topology are characterized by discrete phenomena emerging from a continuous background. One very interesting example is the super-symmetric quantum mechanics theory, which has a deep geometric meaning. In the Witten super-symmetric quantum mechanics theory, where the Hamiltonian is just the Hodge–Laplacian (whereas the quantum Hamiltonian corresponding to a classical particle moving on a Riemannian manifold is just the Laplace–Beltrami differential operator), differential forms are bosons or fermions depending on the parity of their degrees. Witten went to introduce a modified Hodge–Laplacian, depending on a real-valued function f. He was then able to derive the Morse theory (relating critical points of f to the Betti numbers of the manifold) by using the standard limiting procedures relating the quantum and classical theories. Super-symmetric QFTs essentially should be viewed as the differential geometry of certain infinite-dimensional manifolds, including the associated analysis (e.g. Hodge theory) and topology (e.g. Betti numbers). A further comment is that the QFTs of interest are inherently nonlinear, but the nonlinearities have a natural origin, e.g. coming from non-Abelian Lie groups. Moreover there is usually some scaling or coupling parameter in the theory which in the limit relates to the classical theory. Fundamental topological aspects of such a quantum theory should be independent of the parameters and it is therefore reasonable to expect them to be computable (in some sense) by examining the classical limit. This means that such topological information is essentially robust and should be independent of the fine analytical details (and difficulties) of the full quantum theory. In the last decade much effort has been done to use these QFTs as a conceptual tool to suggest new mathematical results. In particular, they have led to spectacular progress in our understanding of geometry in low dimensions. It is most likely no accident that the usual QFTs can only be renormalized in (space–time) dimensions ≤4, and this is precisely the range in which difficult phenomena arise leading to deep and beautiful theories (e.g. the work of Thurston in three dimensions and Donaldson in four dimensions). It now seems clear that the way to investigate the subtleties of low-dimensional manifolds is to associate to them suitable infinite-dimensional manifolds (e.g. spaces of connections) and to study these by standard linear methods (homology, etc.). In other words we use QFT as a refined tool to study low-dimensional manifolds.

The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over the rationals) of type m (resp. T-type m) invariants of integral homology 3-spheres are finite dimensional. These results have already been obtained by [Oh] and [GL2] respectively; our derivation however is simpler, conceptual and relates to several other applications of the lantern identity.

In [6] and [9] the second author and Bill Richter showed that the natural ‘degree’ filtration on the homology of ΩSU(n) has a geometric realization, and that this filtration stably splits (as conjectured by M. Hopkins and M. Mahowald). The purpose of the present paper is to prove the real and quaternionic analogues of these results. To explain what this means, consider the following two ways of viewing the filtration and splitting for ΩSU(n). Whenn= ∞, ΩSU=BU. The filtration isBU(1)⊆BU(2)⊆… and the splittingBU≅ V1≤<∞is a theorem of Snaith[14]. The result for ΩSU(n) may then be viewed as a ‘restriction’ of the result forBU. On the other hand there is a well-known inclusion ℂPn−1. This extends to a map ΩΣℂPn−1→ΩSU(n), and the filtration (or splitting) may be viewed, at least algebraically, as a ‘quotient’ of the James filtration (or splitting) of ΩΣℂPn−1. It is now clear what is meant by the ‘real and quaternionic analogues’. In the quaternionic case, we replaceBUbyBSp=Ω(SU/SP), ΩSU(n) by Ω(SU(2n)/SP(n))and ℂPn−1by ℍPn−1. The integral homology of Ω(SU(2n)/SP(n)) is the symmetric algebra on the homology of ℍPn−1, and may be filtered by the various symmetric powers. We show that this filtration can be realized geometrically, and that the spaces of the filtration are certain (singular) real algebraic varieties (exactly as in the complex case). The strata of the filtration are vector bundles over filtrations of Ω(SU(2n−2)/SP(n−1)), and the filtration stably splits. See Theorems (1·7) and (2·1) for the precise statement. In the real case we replaceBUby Ω(SU/SO), Ω(SU(n)/SO(n)) and ℂPn−1by ℝPn−1. Here integral homology must be replaced by mod 2 homology, and splitting is only obtained after localization at 2. (Snaith's splitting ofBOin [14] can be refined [2, 8] so as to be exactly analogous to the splitting ofBU:BO≅V1≤<∞MO(k).)

In this paper we study the homology of groups with coefficients in metabelian Lie powers, and apply the results to obtain information about elements of finite order in certain free central extensions of groups. Perhaps the most prominent example to which our results apply is the relatively free groupwhere Fd is the (absolutely) free group of rank d. Thus Fd(Bc) is the free group of rank d in the variety Bc of all groups which are both centre-by-(nilpotent of class ≤ c − 1)-by-abelian and soluble of derived length ≤ 3. It was pointed out in [1] that the order of any torsion element in Fd(Bc) divides c if c is odd and 2c if c is even. This, however, is a conditional result as it does not answer the question of whether or not there are any torsion elements in (1·1). Up to now, this question had only been answered in case when c is a prime number [1] or c = 4 [8]. In these cases Fd (Bc) is torsion-free if d ≤ 3, and elements of finite order do occur in Fd(Bc) if d ≥ 4. Moreover, the torsion elements in Fd(Bc) form a subgroup, and the precise structure of this torsion subgroup was exhibited in [1] in the case when c is a prime and in [8] for c = 4. In the present paper we add to this knowledge. On the one hand, we show that for any prime p dividing c the group Fd(Bc) has no elements of order p for all d up to a certain upper bound, which takes arbitrarily large values as c varies over all multiples of p. On the other hand, we show that for prime powers does contain elements of order p whenever d ≥ 4. Finally, we exhibit the precise structure of the p-torsion subgroup of when p ≠ 2. Precise statements are given below (Corollaries 1 and 2). Our results on (1·1) are a special case of more general results (Theorems 1′−3′) which refer to a much wider class of groups, and which are, in their turn, a consequence of our main results on the homology of metabelian Lie powers (Theorems 1–3).

Abstract The human T-cell lymphotropic virus type I (HTLV-I) is causally associated with adult T-cell leukemia, but its role in mycosis fungoides (MF) has remained enigmatic. The virus is suspect because a small percentage of patients with MF have antibodies to it, the cells of others harbor deleted HTLV-I proviral sequences, and particles resembling HTLV-I emerge in cultured blood lymphocytes obtained from most patients. An alternative possibility is that disparate lymphotropic retroviruses may infect or affect a population of epidermotropic lymphocytes, leading to the same outcome, ie, MF. In studies designed to identify the particles detected in lymphocyte cultures of nine patients with a diagnosis of skin involvement characteristic of MF, this concept has gained support. While the cells of four patients provided evidence of HTLV-I infection, molecular hybridization with HTLV-II-specific pol probes showed HTLV-II in the cells of another patient. The 103-bp fragment amplified by the HTLV-II- specific probe was sequenced and proved to have greater than 90% homology with the same fragment amplified from cells known to be infected with HTLV-II. A role for HTLV-II in MF has not been suggested heretofore. Therefore, HTLV-I, HTLV-II, and their incomplete forms may be found in cells of MF patients, suggesting new theories regarding the pathogenesis of this disease.

The human T-cell lymphotropic virus type I (HTLV-I) is causally associated with adult T-cell leukemia, but its role in mycosis fungoides (MF) has remained enigmatic. The virus is suspect because a small percentage of patients with MF have antibodies to it, the cells of others harbor deleted HTLV-I proviral sequences, and particles resembling HTLV-I emerge in cultured blood lymphocytes obtained from most patients. An alternative possibility is that disparate lymphotropic retroviruses may infect or affect a population of epidermotropic lymphocytes, leading to the same outcome, ie, MF. In studies designed to identify the particles detected in lymphocyte cultures of nine patients with a diagnosis of skin involvement characteristic of MF, this concept has gained support. While the cells of four patients provided evidence of HTLV-I infection, molecular hybridization with HTLV-II-specific pol probes showed HTLV-II in the cells of another patient. The 103-bp fragment amplified by the HTLV-II- specific probe was sequenced and proved to have greater than 90% homology with the same fragment amplified from cells known to be infected with HTLV-II. A role for HTLV-II in MF has not been suggested heretofore. Therefore, HTLV-I, HTLV-II, and their incomplete forms may be found in cells of MF patients, suggesting new theories regarding the pathogenesis of this disease.

AbstractThe last universal common ancestor (LUCA) has been considered as the branching point on which Bacteria, Archaea and Eukaryotes have diverged. However, the increased information relating to viruses’ genomes and the perception that many virus genes do not have homologs in other organisms opened a new discussion. Based on these facts, there has emerged the idea of an early LUCA that should be moved further into the past to include viruses, implicating that life should have originated before the appearance of cellular life forms. Another point of view from advocates of the RNA-world suggests that the origin of life happened a long time before organisms were capable of organizing themselves into cellular entities. Relevant data about the origin of ribosomes indicate that the catalytic unit of the large ribosomal subunit is what should actually be considered as the turning point that separated chemistry from biology. Other researchers seem to think that a tRNA was probably some sort of a strange attractor on which life has originated. Here we propose a theoretical synthesis that tries to provide a crosstalk among the theories and define important points on which the origin of life could have been originated and made more complex, taking into account gradualist assumptions. Thus, discussions involving the origin of biological activities in the RNA-world might lead into a world of progenotes on which viruses have been taken part until the appearance of the very first cells. Along this route of complexification, we identified some key points on which researchers may consider life as an emerging principle.

AbstractThis work establishes a comparison between functions on derived loop spaces (Toën and Vezzosi,Chern character, loop spaces and derived algebraic geometry, inAlgebraic topology: the Abel symposium 2007, Abel Symposia, vol. 4, eds N. Baas, E. M. Friedlander, B. Jahren and P. A. Østvær (Springer, 2009), ISBN:978-3-642-01199-3) and de Rham theory. IfAis a smooth commutativek-algebra andkhas characteristic 0, we show that two objects,S1⊗Aand ϵ(A), determine one another, functorially inA. The objectS1⊗Ais theS1-equivariant simplicialk-algebra obtained by tensoringAby the simplicial groupS1:=Bℤ, while the object ϵ(A) is the de Rham algebra ofA, endowed with the de Rham differential, and viewed as aϵ-dg-algebra(see the main text). We define an equivalence φ between the homotopy theory of simplicial commutativeS1-equivariantk-algebras and the homotopy theory of ϵ-dg-algebras, and we show the existence of a functorial equivalence ϕ(S1⊗A)∼ϵ(A) . We deduce from this the comparison mentioned above, identifying theS1-equivariant functions on the derived loop spaceLXof a smoothk-schemeXwith the algebraic de Rham cohomology of X/k. As corollaries, we obtainfunctorialandmultiplicativeversions of decomposition theorems for Hochschild homology (in the spirit of Hochschild–Kostant–Rosenberg) for arbitrary semi-separatedk-schemes. By construction, these decompositions aremoreovercompatible with theS1-action on the Hochschild complex, on one hand, and with the de Rham differential, on the other hand.

A worldwide coronavirus pandemic is in full swing and, at the time of writing, there are only few treatments that have been successful in clinical trials, but no effective antiviral treatment has been approved. Because of its lethality, it is important to understand the current strain’s effects and mechanisms not only in the respiratory system but also in other affected organ systems as well. Past coronavirus outbreaks caused by SARS-CoV and MERS-CoV inflicted life-threatening acute kidney injuries (AKI) on their hosts leading to significant mortality rates, which went somewhat overlooked in the face of the severe respiratory effects. Recent evidence has emphasized renal involvement in SARS-CoV-2, stressing that kidneys are damaged in patients with COVID-19. The mechanism by which this virus inflicts AKI is still unclear, but evidence from other coronavirus strains may hold some clues. Two theories exist for the proposed mechanism of AKI: 1) the AKI is a secondary effect to reduced blood and oxygen levels causing hyperinflammation and 2) the AKI is due to cytotoxic effects. Kidneys express angiotensin-converting enzyme-2 (ACE2), the confirmed SARS-CoV-2 target receptor as well as collectrin, an ACE2 homologue that localizes to the primary cilium, an organelle historically targeted by coronaviruses. Although the available literature suggests that kidney damage is leading to higher mortality rates in patients with COVID-19, especially in those with preexisting kidney and cardiovascular diseases, the pathogenesis of COVID-19 is still being investigated. Here, we present brief literature review supporting our proposed hypothesis of a possible link between SARS-CoV-2 cellular infection and cilia.

The biliary recovery and effect on bile flow and biliary bicarbonate secretion of infused norchenodeoxycholate (nor-CDC), the synthetically prepared C23 homologue of chenodeoxycholate (CDC), were defined in the anesthetized biliary fistula hamster, rat, and guinea pig and compared with those of its taurine conjugate as well as those of the natural C24 bile acid, CDC. In the hamster and rat, nor-CDC was recovered slowly in bile in contrast to its taurine conjugate or CDC. Hepatic biotransformation of nor-CDC was complex. Little amidation with glycine or taurine occurred and the compound was recovered in bile in unchanged form, in the form of hydroxylated derivatives as well as glucuronates and sulfates, the proportion varying in the different species. In contrast, CDC was efficiently amidated with glycine or taurine. The taurine conjugate of nor-CDC was secreted largely unchanged. Nor-CDC infusion caused a striking hypercholeresis in the hamster (108 microliters bile/mumol bile acid in bile) and in the rat (220 microliters/mumol); these values for bile acid-dependent flow far exceed those reported for any other natural bile acid to date in these species. The induced hypercholeresis was of canalicular origin and was accompanied by an enrichment in bicarbonate ion concentration as well as increased bicarbonate output. The taurine conjugate of nor-CDC did not display hypercholeretic properties in the hamster. In the guinea pig, whose native bile is bicarbonate-rich relative to other species, nor-CDC was only mildly hypercholeretic relative to CDC and caused no change in bicarbonate concentration. Thus shortening the side chain of a natural dihydroxy bile acid by a single carbon atom formed a compound that underwent a different hepatic biotransformation than that of most natural bile acids and induced a bicarbonate-rich canalicular choleresis far greater than that which can be explained by current theories of bile formation.

According to a recent hypothesis, the holothurians originated by a process of extreme paedomorphism as "giant larvae", with "<i>de novo</i>" developed radial systems. However, the present approach, which follows the principles of constructional morphology, supports former views that the holothurian predecessor must have been echinoid-like. After constitution of a (reliable) early predecessor construction as a model with machine analogies, subsequent steps of structural transformation are explained by functional improvement and economy. Following results are discussed: (i) Holothurians have to be derived from a postlarval precursor; (ii) "Apodida" (as molecular-genetically derived first holothurians) must originally have been pedate; (iii) ophiocistioids would not be cladistic “holothurians” but a precursor construction of the taxon echinoids plus holothurians; (iv) the Lovenian structure of the calcareous ring of <i>Nudicorona</i> (Middle Devonian), possible radial series in <i>Palaeocucumaria</i> (Lower Devonian), and distribution of the podia in two new holothurian body fossils from the Lower and Middle Devonian (preliminary description as <i>Prokrustia tabulifera</i> n. gen., n. sp. and <i>Podolepithuria walliseri</i> n. gen., n. sp.) obviously corroborate homology of holothurian and other echinoderm radial systems; (v) different extent of podial and body wall skeletonization suggests the existence of respiratory trees by no later than the Middle Devonian. <br><br> Nach einer neueren Erklärung, die sich auf eine Theorie zur Homologisierung von larvalen und adulten Strukturen von Echinodermen stützt, sollen die Holothurien über extreme Paedomorphose, d.h. über „Riesen-Larven” mit neugebildeten postoralen Radial-Systemen entstanden sein. Dagegen läßt sich anhand eines konstruktions-morphologischen Verfahrens zeigen, daß Holothurien auf einen Echiniden-artigen Vorläufer zurückzuführen sind. So wird zunächst eine (wahrscheinliche) frühe Vorläufer-Konstruktion der Echinozoen nach Maschinen-Analogien konstituiert. Die daran anschließenden strukturellen Transformationen werden nach funktionellen und energetischen Kriterien begründet. Sie führen zwanglos zu Konstruktionen, die nicht nur rezenten Formen entsprechen, sondern offensichtlich auch durch bekannte und neue paläozoische Fossilien bestätigt werden. Im Einzelnen werden folgende Ergebnisse zur Diskussion gestellt: (i) Holothurien sind von einer post-larvalen Vorläufer-Konstruktion abzuleiten; (ii) die füßchenlosen „Apodida” (als molekulargenetisch früheste Holothurien) müssen zunächst vollständige Radien mit Podia besessen haben; (iii) bei den (nur paläozoischen) Ophiocistioiden handelt es sich nicht kladistisch um „Holothurien”, sondern sie repräsentieren eine Vorläufer-Konstruktion des Taxon Echiniden plus Holothurien; (iv) die Loven'sche Struktur des Schlundrings von <i>Nudicorona</i> (Mittel-Devon), die möglicherweise radialen Strukturen bei <i>Palaeocucumaria</i> (Unter-Devon) und die Verteilung der Podia in zwei neuen, vollständig erhaltenen Holothurien aus dem Unter- und Mittel-Devon (vorläufige Beschreibung als <i>Prokrustia tabulifera</i> n. gen., n. sp. und <i>Podolepithuria walliseri</i> n. gen., n. sp.) stützen die konstruktions-morphologische Begründung der Homologie der Radial-Systeme bei Holothurien und den übrigen Echinodermen; (v) das deutlich unterschiedliche Ausmaß der Skelettierung von Podia bei den neuen Holothurien-Funden scheint anzudeuten, daß die analen Respirations-Strukturen der Holothurien spätestens ab dem Mittel-Devon vorhanden sind. <br><br> doi:<a href="http://dx.doi.org/10.1002/mmng.20020050110" target="_blank">10.1002/mmng.20020050110</a>

Abstract In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology parallel to the Loday–Pirashvili construction of higher Hochschild homology; in fact, we establish a direct geometric relation between the two theories by proving that the representation homology of the suspension of a (pointed connected) space is isomorphic to its higher Hochschild homology. We also construct some natural maps and spectral sequences relating representation homology to other homology theories associated with spaces (such as Pontryagin algebras, ${{\mathbb{S}}}^1$-equivariant homology of the free loop space, and stable homology of automorphism groups of f.g. free groups). We compute representation homology explicitly (in terms of known invariants) in a number of interesting cases, including spheres, suspensions, complex projective spaces, Riemann surfaces, and some 3-dimensional manifolds, such as link complements in ${\mathbb{R}}^3$ and the lens spaces $ L(p,q) $. In the case of link complements, we identify the representation homology in terms of ordinary Hochschild homology, which gives a new algebraic invariant of links in ${\mathbb{R}}^3$.

Sociologists often imagine society as spaces, yet how social spaces are related remains ambiguous in most theories. In developing his field theory, Bourdieu used extensively the concept of homology to describe the structural similarities across fields, but he had not taken seriously the spaces between fields or how fields are related to each other. Adopting the Simmelian approach of formal sociology, this article outlines six basic social forms by which social spaces are related. It argues that relations between social spaces can be understood along two dimensions: heterogeneity and social distance. In terms of heterogeneity, social spaces can be kindred, symbiotic or oppositional. In terms of social distance, they can be linked, nested or overlapping. These social forms of interspatial relations are constituted by the boundary work of a variety of actors, including guardians, brokers and space travellers. The article provides a general vocabulary for thinking about how social spaces are related and how they interact across boundaries.

Introduction The genealogy of Feminist Standpoint Theory in the 1970s prioritised “locationality”, particularly the recognition of social and historical locations as valuable contribution to knowledge production. Pioneering figures such as Sandra Harding, Dorothy Smith, Patricia Hill Collins, Alison Jaggar, and Donna Haraway have argued that the oppressed must have some means (such as language, cultural practices) to enter the world of the oppressor in order to access some understanding of how the world works from the privileged perspective. In the essay “Meeting at the Edge of Fear: Theory on a World Scale”, the Australian social scientist Raewyn Connell explains that the production of feminist theory almost always comes from the global North. Connell critiques the hegemony of mainstream Northern feminism in her pyramidal model (59), showing how theory/knowledge is produced at the apex (global North) of a pyramid structure and “trickles down” (59) to the global South. Connell refers to a second model called mosaic epistemology which shows that multiple feminist ideologies across global North/South are juxtaposed against each other like tiles, with each specific culture making its own claims to validity.However, Nigerian feminist Bibi Bakare-Yusuf’s reflection on the fluidity of culture in her essay “Fabricating Identities” (5) suggests that fixing knowledge as Northern and Southern—disparate, discrete, and rigidly structured tiles—is also problematic. Connell proposes a third model called solidarity-based epistemology which involves mutual learning and critiquing with a focus on solidarity across differences. However, this is impractical in implementation especially given that feminist nomenclature relies on problematic terms such as “international”, “global North/South”, “transnational”, and “planetary” to categorise difference, spatiality, and temporality, often creating more distance than reciprocal exchange. Geographical specificity can be too limiting, but we also need to acknowledge that it is geographical locationality which becomes disadvantageous to overcome racial, cultural, and gender biases — and here are few examples.Nomenclatures: Global-North and Global South ParadigmThe global North/South terminology differentiating the two regions according to means of trade and relative wealth emerged from the Brandt Report’s delineation of the North as wealthy and South as impoverished in 1980s. Initially, these terms were a welcome repudiation of the hierarchical nomenclature of “developed” and “developing” nations. Nevertheless, the categories of North and South are problematic because of increased socio-economic heterogeneity causing erasure of local specificities without reflecting microscopic conflicts among feminists within the global North and the global South. Some feminist terms such as “Third World feminism” (Narayan), “global feminism” (Morgan), or “local feminisms” (Basu) aim to centre women's movements originating outside the West or in the postcolonial context, other labels attempt to making feminism more inclusive or reflective of cross-border linkages. These include “transnational feminism” (Grewal and Kaplan) and “feminism without borders” (Mohanty). In the 1980s, Kimberlé Williams Crenshaw’s concept of intersectionality garnered attention in the US along with Gloria Anzaldúa’s Borderlands/La Frontera: The New Mestiza (1987), which raised feminists’ awareness of educational, healthcare, and financial disparities among women and the experiences of marginalised people across the globe, leading to an interrogation of the aims and purposes of mainstream feminism. In general, global North feminism refers to white middle class feminist movements further expanded by concerns about civil rights and contemporary queer theory while global South feminism focusses on decolonisation, economic justice, and disarmament. However, the history of colonialism demonstrates that this paradigm is inadequate because the oppression and marginalisation of Black, Indigenous, and Queer activists have been avoided purposely in the homogenous models of women’s oppression depicted by white radical and liberal feminists. A poignant example is from Audre Lorde’s personal account:I wheeled my two-year-old daughter in a shopping cart through a supermarket in Eastchester in 1967, and a little white girl riding past in her mother’s cart calls out excitedly, ‘oh look, Mommy, a baby maid!’ And your mother shushes you, but does not correct you, and so fifteen years later, at a conference on racism, you can still find that story humorous. But I hear your laughter is full of terror and disease. (Lorde)This exemplifies how the terminology global North/South is a problem because there are inequities within the North that are parallel to the division of power and resources between North and South. Additionally, Susan Friedman in Planetary Modernisms observes that although the terms “Global North” and “Global South” are “rhetorically spatial” they are “as geographically imprecise and ideologically weighted as East/West” because “Global North” signifies “modern global hegemony” and “Global South” signifies the “subaltern, … —a binary construction that continues to place the West at the controlling centre of the plot” (Friedman, 123).Focussing on research-activism debate among US feminists, Sondra Hale takes another tack, emphasising that feminism in the global South is more pragmatic than the theory-oriented feminist discourse of the North (Hale). Just as the research-scholarship binary implies myopic assumption that scholarship is a privileged activity, Hale’s observations reveal a reductive assumption in the global North and global South nomenclature that feminism at the margins is theoretically inadequate. In other words, recognising the “North” as the site of theoretical processing is a euphemism for Northern feminists’ intellectual supremacy and the inferiority of Southern feminist praxis. To wit, theories emanating from the South are often overlooked or rejected outright for not aligning with Eurocentric framings of knowledge production, thereby limiting the scope of feminist theories to those that originate in the North. For example, while discussing Indigenous women’s craft-autobiography, the standard feminist approach is to apply Susan Sontag’s theory of gender and photography to these artefacts even though it may not be applicable given the different cultural, social, and class contexts in which they are produced. Consequently, Moroccan feminist Fatima Mernissi’s Islamic methodology (Mernissi), the discourse of land rights, gender equality, kinship, and rituals found in Bina Agarwal’s A Field of One’s Own, Marcia Langton’s “Grandmothers’ Law”, and the reflection on military intervention are missing from Northern feminist theoretical discussions. Moreover, “outsiders within” feminist scholars fit into Western feminist canonical requirements by publishing their works in leading Western journals or seeking higher degrees from Western institutions. In the process, Northern feminists’ intellectual hegemony is normalised and regularised. An example of the wealth of the materials outside of mainstream Western feminist theories may be found in the work of Girindrasekhar Bose, a contemporary of Sigmund Freud, founder of the Indian Psychoanalytic Society and author of the book Concept of Repression (1921). Bose developed the “vagina envy theory” long before the neo-Freudian psychiatrist Karen Horney proposed it, but it is largely unknown in the West. Bose’s article “The Genesis and Adjustment of the Oedipus Wish” discarded Freud’s theory of castration and explained how in the Indian cultural context, men can cherish an unconscious desire to bear a child and to be castrated, implicitly overturning Freud’s correlative theory of “penis envy.” Indeed, the case of India shows that the birth of theory can be traced back to as early as eighth century when study of verbal ornamentation and literary semantics based on the notion of dbvani or suggestion, and the aesthetic theory of rasa or "sentiment" is developed. If theory means systematic reasoning and conceptualising the structure of thought, methods, and epistemology, it exists in all cultures but unfortunately non-Western theory is largely invisible in classroom courses.In the recent book Queer Activism in India, Naisargi Dev shows that the theory is rooted in activism. Similarly, in her essay “Seed and Earth”, Leela Dube reveals how Eastern theories are distorted as they are Westernised. For instance, the “Purusha-Prakriti” concept in Hinduism where Purusha stands for pure consciousness and Prakriti stands for the entire phenomenal world is almost universally misinterpreted in terms of Western binary oppositions as masculine consciousness and feminine creative principle which has led to disastrous consequences including the legitimisation of male control over female sexuality. Dube argues how heteropatriarchy has twisted the Purusha-Prakriti philosophy to frame the reproductive metaphor of the male seed germinating in the female field for the advantage of patrilineal agrarian economies and to influence a homology between reproductive metaphors and cultural and institutional sexism (Dube 22-24). Attempting to reverse such distortions, ecofeminist Vandana Shiva rejects dualistic and exploitative “contemporary Western views of nature” (37) and employs the original Prakriti-Purusha cosmology to construct feminist vision and environmental ethics. Shiva argues that unlike Cartesian binaries where nature or Prakriti is inert and passive, in Hindu Philosophy, Purusha and Prakriti are inseparable and inviolable (Shiva 37-39). She refers to Kalika Purana where it is explained how rivers and mountains have a dual nature. “A river is a form of water, yet is has a distinct body … . We cannot know, when looking at a lifeless shell, that it contains a living being. Similarly, within the apparently inanimate rivers and mountains there dwells a hidden consciousness. Rivers and mountains take the forms they wish” (38).Scholars on the periphery who never migrated to the North find it difficult to achieve international audiences unless they colonise themselves, steeping their work in concepts and methods recognised by Western institutions and mimicking the style and format that western feminist journals follow. The best remedy for this would be to interpret border relations and economic flow between countries and across time through the prism of gender and race, an idea similar to what Sarah Radcliffe, Nina Laurie and Robert Andolina have called the “transnationalization of gender” (160).Migration between Global North and Global SouthReformulation of feminist epistemology might reasonably begin with a focus on migration and gender politics because international and interregional migration have played a crucial role in the production of feminist theories. While some white mainstream feminists acknowledge the long history of feminist imperialism, they need to be more assertive in centralising non-Western theories, scholarship, and institutions in order to resist economic inequalities and racist, patriarchal global hierarchies of military and organisational power. But these possibilities are stymied by migrants’ “de-skilling”, which maintains unequal power dynamics: when migrants move from the global South to global North, many end up in jobs for which they are overqualified because of their cultural, educational, racial, or religious alterity.In the face of a global trend of movement from South to North in search of a “better life”, visual artist Naiza Khan chose to return to Pakistan after spending her childhood in Lebanon before being trained at the University of Oxford. Living in Karachi over twenty years, Khan travels globally, researching, delivering lectures, and holding exhibitions on her art work. Auj Khan’s essay “Peripheries of Thought and Practise in Naiza Khan’s Work” argues: “Khan seems to be going through a perpetual diaspora within an ownership of her hybridity, without having really left any of her abodes. This agitated space of modern hybrid existence is a rich and ripe ground for resolution and understanding. This multiple consciousness is an edge for anyone in that space, which could be effectively made use of to establish new ground”. Naiza Khan’s works embrace loss or nostalgia and a sense of choice and autonomy within the context of unrestricted liminal geographical boundaries.Early work such as “Chastity Belt,” “Heavenly Ornaments”, “Dream”, and “The Skin She Wears” deal with the female body though Khan resists the “feminist artist” category, essentially because of limited Western associations and on account of her paradoxical, diasporic subjectivity: of “the self and the non-self, the doable and the undoable and the anxiety of possibility and choice” (Khan Webpage). Instead, Khan theorises “gender” as “personal sexuality”. The symbolic elements in her work such as corsets, skirts, and slips, though apparently Western, are purposely destabilised as she engages in re-constructing the cartography of the body in search of personal space. In “The Wardrobe”, Khan establishes a path for expressing women’s power that Western feminism barely acknowledges. Responding to the 2007 Islamabad Lal Masjid siege by militants, Khan reveals the power of the burqa to protect Muslim men by disguising their gender and sexuality; women escape the Orientalist gaze. For Khan, home is where her art is—beyond the global North and South dichotomy.In another example of de-centring Western feminist theory, the Indian-British sitar player Anoushka Shankar, who identifies as a radical pro-feminist, in her recent musical album “Land of Gold” produces what Chilla Bulbeck calls “braiding at the borderlands”. As a humanitarian response to the trauma of displacement and the plight of refugees, Shankar focusses on women giving birth during migration and the trauma of being unable to provide stability and security to their children. Grounded in maternal humility, Shankar’s album, composed by artists of diverse background as Akram Khan, singer Alev Lenz, and poet Pavana Reddy, attempts to dissolve boundaries in the midst of chaos—the dislocation, vulnerability and uncertainty experienced by migrants. The album is “a bit of this, and a bit of that” (borrowing Salman Rushdie’s definition of migration in Satanic Verses), both in terms of musical genre and cultural identities, which evokes emotion and subjective fluidity. An encouraging example of truly transnational feminist ethics, Shankar’s album reveals the chasm between global North and global South represented in the tension of a nascent friendship between a white, Western little girl and a migrant refugee child. Unlike mainstream feminism, where migration is often sympathetically feminised and exotified—or, to paraphrase bell hooks, difference is commodified (hooks 373) — Shankar’s album simultaneously exhibits regional, national, and transnational elements. The album inhabits multiple borderlands through musical genres, literature and politics, orality and text, and ethnographic and intercultural encounters. The message is: “the body is a continent / But may your heart always remain the sea" (Shankar). The human rights advocate and lawyer Randa Abdel-Fattah, in her autobiographical novel Does My Head Look Big in This?, depicts herself as “colourful adjectives” (such as “darkies”, “towel-heads”, or the “salami eaters”), painful identities imposed on her for being a Muslim woman of colour. These ultimately empower her to embrace her identity as a Palestinian-Egyptian-Australian Muslim writer (Abdel-Fattah 359). In the process, Abdel-Fattah reveals how mainstream feminism participates in her marginalisation: “You’re constantly made to feel as you’re commenting as a Muslim, and somehow your views are a little bit inferior or you’re somehow a little bit more brainwashed” (Abdel-Fattah, interviewed in 2015).With her parental roots in the global South (Egyptian mother and Palestinian father), Abdel-Fattah was born and brought up in the global North, Australia (although geographically located in global South, Australia is categorised as global North for being above the world average GDP per capita) where she embraced her faith and religious identity apparently because of Islamophobia:I refuse to be an apologist, to minimise this appalling state of affairs… While I'm sick to death, as a Muslim woman, of the hypocrisy and nonsensical fatwas, I confess that I'm also tired of white women who think the answer is flashing a bit of breast so that those "poor," "infantilised" Muslim women can be "rescued" by the "enlightened" West - as if freedom was the sole preserve of secular feminists. (Abdel-Fattah, "Ending Oppression")Abdel-Fattah’s residency in the global North while advocating for justice and equality for Muslim women in both the global North and South is a classic example of the mutual dependency between the feminists in global North and global South, and the need to recognise and resist neoliberal policies applied in by the North to the South. In her novel, sixteen-year-old Amal Mohamed chooses to become a “full-time” hijab wearer in an elite school in Melbourne just after the 9/11 tragedy, the Bali bombings which killed 88 Australians, and the threat by Algerian-born Abdel Nacer Benbrika, who planned to attack popular places in Sydney and Melbourne. In such turmoil, Amal’s decision to wear the hijab amounts to more than resistance to Islamophobia: it is a passionate search for the true meaning of Islam, an attempt to embrace her hybridity as an Australian Muslim girl and above all a step towards seeking spiritual self-fulfilment. As the novel depicts Amal’s challenging journey amidst discouraging and painful, humiliating experiences, the socially constructed “bloody confusing identity hyphens” collapse (5). What remains is the beautiful veil that stands for Amal’s multi-valence subjectivity. The different shades of her hijab reflect different moods and multiple “selves” which are variously tentative, rebellious, romantic, argumentative, spiritual, and ambitious: “I am experiencing a new identity, a new expression of who I am on the inside” (25).In Griffith Review, Randa-Abdel Fattah strongly criticises the book Nine Parts of Desire by Geraldine Brooks, a Wall-Street Journal reporter who travelled from global North to the South to cover Muslim women in the Middle East. Recognising the liberal feminist’s desire to explore the Orient, Randa-Abdel calls the book an example of feminist Orientalism because of the author’s inability to understand the nuanced diversity in the Muslim world, Muslim women’s purposeful downplay of agency, and, most importantly, Brooks’s inevitable veil fetishism in her trip to Gaza and lack of interest in human rights violations of Palestinian women or their lack of access to education and health services. Though Brooks travelled from Australia to the Middle East, she failed to develop partnerships with the women she met and distanced herself from them. This underscores the veracity of Amal’s observation in Abdel Fattah’s novel: “It’s mainly the migrants in my life who have inspired me to understand what it means to be an Aussie” (340). It also suggests that the transnational feminist ethic lies not in the global North and global South paradigm but in the fluidity of migration between and among cultures rather than geographical boundaries and military borders. All this argues that across the imperial cartography of discrimination and oppression, women’s solidarity is only possible through intercultural and syncretistic negotiation that respects the individual and the community.ReferencesAbdel-Fattah, Randa. Does My Head Look Big in This? Sydney: Pan MacMillan Australia, 2005.———. “Ending Oppression in the Middle East: A Muslim Feminist Call to Arms.” ABC Religion and Ethics, 29 April 2013. <http://www.abc.net.au/religion/articles/2013/04/29/3747543.htm>.———. “On ‘Nine Parts Of Desire’, by Geraldine Brooks.” Griffith Review. <https://griffithreview.com/on-nine-parts-of-desire-by-geraldine-brooks/>.Agarwal, Bina. A Field of One’s Own: Gender and Land Rights in South Asia. Cambridge: Cambridge University, 1994.Amissah, Edith Kohrs. Aspects of Feminism and Gender in the Novels of Three West African Women Writers. Nairobi: Africa Resource Center, 1999.Andolina, Robert, Nina Laurie, and Sarah A. Radcliffe. Indigenous Development in the Andes: Culture, Power, and Transnationalism. Durham, NC: Duke University Press, 2009.Anzaldúa, Gloria E. Borderlands/La Frontera: The New Mestiza. San Francisco: Aunt Lute Books, 1987.Bakare-Yusuf, Bibi. “Fabricating Identities: Survival and the Imagination in Jamaican Dancehall Culture.” Fashion Theory 10.3 (2006): 1–24.Basu, Amrita (ed.). Women's Movements in the Global Era: The Power of Local Feminisms. Philadelphia: Westview Press, 2010.Bulbeck, Chilla. Re-Orienting Western Feminisms: Women's Diversity in a Postcolonial World. 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Melbourne: Macmillan, 2003.Lazreg, Marnia. “Feminism and Difference: The Perils of Writing as a Woman on Women in Algeria.” Feminist Studies 14.1 (Spring 1988): 81-107.Liew, Stephanie. “Subtle Racism Is More Problematic in Australia.” Interview. music.com.au 2015. <http://themusic.com.au/interviews/all/2015/03/06/randa-abdel-fattah/>.Lorde, Audre. “The Uses of Anger: Women Responding to Racism.” Keynoted presented at National Women’s Studies Association Conference, Storrs, Conn., 1981.Mernissi, Fatima. The Veil and the Male Elite: A Feminist Interpretation of Women’s Rights in Islam. Trans. Mary Jo Lakeland. New York: Basic Books, 1991.Moghadam, Valentine. Modernizing Women: Gender and Social Change in the Middle East. London: Lynne Rienner Publishers, 2003.Mohanty, Chandra Talpade. Feminism without Borders: Decolonizing Theory, Practicing Solidarity. Durham, NC: Duke University Press, 2003.Moreton-Robinson, Aileen. Talkin' Up to the White Woman: Aboriginal Women and Feminism. 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‘Bitzer,’ said Thomas Gradgrind. ‘Your definition of a horse.’‘Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.’ Thus (and much more) Bitzer.‘Now girl number twenty,’ said Mr. Gradgrind. ‘You know what a horse is.’— Charles Dickens, Hard Times (1854)Dickens’s famous pedant, Thomas Gradgrind, was not an anomaly. He is the pedagogical manifestation of the rise of quantification in modernism that was the necessary adjunct to massive urbanisation and industrialisation. His classroom caricatures the dominant epistemic modality of modern global democracies, our unwavering trust in numbers, “data”, and reproductive predictability. This brief quotation from Hard Times both presents and parodies the 19th century’s displacement of what were previously more commonly living and heterogeneous existential encounters with events and things. The world had not yet been made predictably repetitive through industrialisation, standardisation, law, and ubiquitous codes of construction. Theirs was much more a world of unique events and not the homogenised and orthodox iteration of standardised knowledge. Horses and, by extension, all entities and events gradually were displaced by their rote definitions: individuals of a so-called natural kind were reduced to identicals. Further, these mechanical standardisations were and still are underwritten by mapping them into a numerical and extensive characterisation. On top of standardised objects and procedures appeared assigned numerical equivalents which lent standardisation the seemingly apodictic certainty of deductive demonstrations. The algebraic becomes the socially enforced criterion for the previously more sensory, qualitative, and experiential encounters with becoming that were more likely in pre-industrial life. Here too, we see that the function of this reproductive protocol is not just notational but is the sine qua non for, in Althusser’s famous phrase, the manufacture of citizens as “subject subjects”, those concrete individuals who are educated to understand themselves ideologically in an imaginary relation with their real position in any society’s self-reproduction. Here, however, ideology performs that operation through that nominally least political of cognitive modes, the supposed friend of classical Marxism’s social science, the mathematical. The historical onset of this social and political reproductive hegemony, this uniform supplanting of time’s ineluctable differencing with the parasite of its associated model, can partial be found in the formation of metrics. Before the 19th century, the measures of space and time were local. Units of length and weight varied not just between nations but often by municipality. These parochial standards reflected indigenous traditions, actualities, personalities, and needs. This variation in measurement standards suggested that every exchange or judgment of kind and value relied upon the specificity of that instance. Every evaluation of an instance required perceptual acuity and not the banality of enumeration constituted by commodification and the accounting practices intrinsic to centralised governance. This variability in measure was complicated by similar variability in the currencies of the day. Thus, barter presented the participants with complexities and engagements of skills and discrete observation completely alien to the modern purchase of duplicate consumer objects with stable currencies. Almost nothing of life was iterative: every exchange was, more or less, an anomaly. However, in 1790, immediately following the French Revolution and as a central manifestation of its movement to rational democratisation, Charles Maurice de Talleyrand proposed a metrical system to the French National Assembly. The units of this metric system, based originally on observable features of nature, are now formally codified in all scientific practice by seven physical constants. Further, they are ubiquitous now in almost all public exchanges between individuals, corporations, and states. These units form a coherent and extensible structure whose elements and rules are subject to seemingly lossless symbolic exchange in a mathematic coherence aided by their conformity to decimal representation. From 1960, their basic contemporary form was established as the International System of Units (SI). Since then, all but three of the countries of the world (Myanmar, Liberia, and the United States), regardless of political organisation and individual history, have adopted these standards for commerce and general measurement. The uniformity and rational advantage of this system is easily demonstrable in just the absurd variation in the numeric bases of the Imperial / British system which uses base 16 for ounces/pounds, base 12 for inches/feet, base three for feet/yards, base 180 for degrees between freezing and cooling, 43,560 square feet per acre, eights for division of inches, etc. Even with its abiding antagonism to the French, Britain officially adopted the metric system as was required by its admission to the EU in 1973. The United States is the last great holdout in the public use of the metric system even though SI has long been the standard wanted by the federal government. At first, the move toward U.S. adoption was promising. Following France and rejecting England’s practice, America was founded on a decimal currency system in 1792. In 1793, Jefferson requested a copy of the standard kilogram from France in a first attempt to move to the metric system: however, the ship carrying the copy was captured by pirates. Indeed, The Metric Conversion Act of 1975 expressed a more serious national intention to adopt SI, but after some abortive efforts, the nation fell back into the more archaic measurements dominant since before its revolution. However, the central point remains that while the U.S. is unique in its public measurement standard among dominant powers, it is equally committed to the hegemonic application of a numerical rendition of events.The massive importance of this underlying uniformity is that it supplies the central global mechanism whereby the world’s chaotic variation is continuously parsed and supplanted into comparable, intelligible, and predictable units that understand individuating difference as anomaly. Difference, then, is understood in this method not as qualitative and intensive, which it necessarily is, but quantitative and extensive. Like Gradgrind’s “horse”, the living and unique thing is rendered through the Apollonian dream of standardisation and enumeration. While differencing is the only inherent quality of time’s chaotic flow, accounting and management requite iteration. To order the reproduction of modern society, the unique individuating differences that render an object as “this one”, what the Medieval logicians called haecceities, are only seen as “accidental” and “non-essential” deviations. This is not just odd but illogical since these very differences allow events to be individuated items so to appear as countable at all. As Leibniz’s principle, the indiscernibility of identicals, suggests, the application of the metrical same to different occasions is inherently paradoxical: if each unit were truly the same, there could only be one. As the etymology of “anomaly” suggests, it is that which is unexpected, irregular, out of line, or, going back to the Greek, nomos, at variance with the law. However, as the only “law” that always is at hand is the so-called “Second Law of Thermodynamics”, the inconsistently consistent roiling of entropy, the evident theoretical question might be, “how is anomaly possible when regularity itself is impossible?” The answer lies not in events “themselves” but exactly in the deductive valorisations projected by that most durable invention of the French Revolution adumbrated above, the metric system. This seemingly innocuous system has formed the reproductive and iterative bias of modern post-industrial perceptual homogenisation. Metrical modeling allows – indeed, requires – that one mistake the metrical changeling for the experiential event it replaces. Gilles Deleuze, that most powerful French metaphysician (1925-1995) offers some theories to understand the seminal production (not reproduction) of disparity that is intrinsic to time and to distinguish it from its homogenised representation. For him, and his sometime co-author, Felix Guattari, time’s “chaosmosis” is the host constantly parasitised by its symbolic model. This problem, however, of standardisation in the face of time’s originality, is obscured by its very ubiquity; we must first denaturalise the seemingly self-evident metrical concept of countable and uniform units.A central disagreement in ancient Greece was between the proponents of physis (often translated as “nature” but etymologically indicative of growth and becoming, process and not fixed form) and nomos (law or custom). This is one of the first ethical and so political debates in Western philosophy. For Heraclitus and other pre-Socratics, the emphatic character of nature was change, its differencing dynamism, its processual but not iterative character. In anticipation of Hume, Sophists disparaged nomos (νόμος) as simply the habituated application of synthetic law and custom to the fluidity of natural phenomena. The historical winners of this debate, Plato and the scientific attitudes of regularity and taxonomy characteristic of his best pupil, Aristotle, have dominated ever since, but not without opponents.In the modern era, anti-enlightenment figures such as Hamann, Herder, and the Schlegel brothers gave theoretical voice to romanticism’s repudiation of the paradoxical impulses of the democratic state for regulation and uniformity that Talleyrand’s “revolutionary” metrical proposal personified. They saw the correlationalism (as adumbrated by Meillassoux) between thought and thing based upon their hypothetical equitability as a betrayal of the dynamic physis that experience presented. Variable infinity might come either from the character of God or nature or, as famously in Spinoza’s Ethics, both (“deus sive natura”). In any case, the plenum of nature was never iterative. This rejection of metrical regularity finds its synoptic expression in Nietzsche. As a classicist, Nietzsche supplies the bridge between the pre-Socratics and the “post-structuralists”. His early mobilisation of the Apollonian, the dream of regularity embodied in the sun god, and the Dionysian, the drunken but inarticulate inexpression of the universe’s changing manifold, gives voice to a new resistance to the already dominate metrical system. His is a new spin of the mythic representatives of Nomos and physis. For him, this pair, however, are not – as they are often mischaracterised – in dialectical dialogue. To place them into the thesis / antithesis formulation would be to give them the very binary character that they cannot share and to, tacitly, place both under Apollo’s procedure of analysis. Their modalities are not antithetical but mutually exclusive. To represent the chaotic and non-iterative processes of becoming, of physis, under the rubric of a common metrics, nomos, is to mistake the parasite for the host. In its structural hubris, the ideological placebo of metrical knowing thinks it non-reductively captures the multiplicity it only interpellates. In short, the polyvalent, fluid, and inductive phenomena that empiricists try to render are, in their intrinsic character, unavailable to deductive method except, first, under the reductive equivalence (the Gradgrind pedagogy) of metrical modeling. This incompatibility of physis and nomos was made manifest by David Hume in A Treatise of Human Nature (1739-40) just before the cooptation of the 18th century’s democratic revolutions by “representative” governments. There, Hume displays the Apollonian dream’s inability to accurately and non-reductively capture a phenomenon in the wild, free from the stringent requirements of synthetic reproduction. His argument in Book I is succinct.Now as we call every thing custom, which proceeds from a past repetition, without any new reasoning or conclusion, we may establish it as a certain truth, that all the belief, which follows upon any present impression, is deriv'd solely from that origin. (Part 3, Section 8)There is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; ... even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience. (Part 3, Section 12)The rest of mankind ... are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. (Part 4, Section 6)In sum, then, nomos is nothing but habit, a Pavlovian response codified into a symbolic representation and, pragmatically, into a reproductive protocol specifically ordered to exclude anomaly, the inherent chaotic variation that is the hallmark of physis. The Apollonian dream that there can be an adequate metric of unrestricted natural phenomena in their full, open, turbulent, and manifold becoming is just that, a dream. Order, not chaos, is the anomaly. Of course, Kant felt he had overcome this unacceptable challenge to rational application to induction after Hume woke him from his “dogmatic slumber”. But what is perhaps one of the most important assertions of the critiques may be only an evasion of Hume’s radical empiricism: “there are only two ways we can account for the necessary agreement of experience with the concepts of its objects: either experience makes these concepts possible or these concepts make experience possible. The former supposition does not hold of the categories (nor of pure sensible intuition) ... . There remains ... only the second—a system ... of the epigenesis of pure reason” (B167). Unless “necessary agreement” means the dictatorial and unrelenting insistence in a symbolic model of perception of the equivalence of concept and appearance, this assertion appears circular. This “reading” of Kant’s evasion of the very Humean crux, the necessary inequivalence of a metric or concept to the metered or defined, is manifest in Nietzsche.In his early “On Truth and Lies in a Nonmoral Sense” (1873), Nietzsche suggests that there is no possible equivalence between a concept and its objects, or, to use Frege’s vocabulary, between sense or reference. We speak of a "snake" [see “horse” in Dickens]: this designation touches only upon its ability to twist itself and could therefore also fit a worm. What arbitrary differentiations! What one-sided preferences, first for this, then for that property of a thing! The various languages placed side by side show that with words it is never a question of truth, never a question of adequate expression; otherwise, there would not be so many languages. The "thing in itself" (which is precisely what the pure truth, apart from any of its consequences, would be) is likewise something quite incomprehensible to the creator of language and something not in the least worth striving for. This creator only designates the relations of things to men, and for expressing these relations he lays hold of the boldest metaphors.The literal is always already a reductive—as opposed to literature’s sometimes expansive agency—metaphorisation of events as “one of those” (a token of “its” type). The “necessary” equivalence in nomos is uncovered but demanded. The same is reproduced by the habitual projection of certain “essential qualities” at the expense of all those others residing in every experiential multiplicity. Only in this prison of nomos can anomaly appear: otherwise all experience would appear as it is, anomalous. With this paradoxical metaphor of the straight and equal, Nietzsche inverts the paradigm of scientific expression. He reveals as a repressive social and political obligation the symbolic assertion homology where actually none can be. Supposed equality and measurement all transpire within an Apollonian “dream within a dream”. The concept captures not the manifold of chaotic experience but supplies its placebo instead by an analytic tautology worthy of Gradgrind. The equivalence of event and definition is always nothing but a symbolic iteration. Such nominal equivalence is nothing more than shifting events into a symbolic frame where they can be commodified, owned, and controlled in pursuit of that tertiary equivalence which has become the primary repressive modality of modern societies: money. This article has attempted, with absurd rapidity, to hint why some ubiquitous concepts, which are generally considered self-evident and philosophically unassailable, are open not only to metaphysical, political, and ethical challenge, but are existentially unjustified. All this was done to defend the smaller thesis that the concept of anomaly is itself a reflection of a global misrepresentation of the chaos of becoming. This global substitution expresses a conservative model and measure of the world in the place of the world’s intrinsic heterogenesis, a misrepresentation convenient for those who control the representational powers of governance. In conclusion, let us look, again too briefly, at a philosopher who neither accepts this normative world picture of regularity nor surrenders to Nietzschean irony, Gilles Deleuze.Throughout his career, Deleuze uses the word “pure” with senses antithetical to so-called common sense and, even more, Kant. In its traditional concept, pure means an entity or substance whose essence is not mixed or adulterated with any other substance or material, uncontaminated by physical pollution, clean and immaculate. The pure is that which is itself itself. To insure intelligibility, that which is elemental, alphabetic, must be what it is itself and no other. This discrete character forms the necessary, if often tacit, precondition to any analysis and decomposition of beings into their delimited “parts” that are subject to measurement and measured disaggregation. Any entity available for structural decomposition, then, must be pictured as constituted exhaustively by extensive ones, measurable units, its metrically available components. Dualism having established as its primary axiomatic hypothesis the separability of extension and thought must now overcome that very separation with an adequacy, a one to one correspondence, between a supposedly neatly measurable world and ideological hegemony that presents itself as rational governance. Thus, what is needed is not only a purity of substance but a matching purity of reason, and it is this clarification of thought, then, which, as indicated above, is the central concern of Kant’s influential and grand opus, The Critique of Pure Reason.Deleuze heard a repressed alternative to the purity of the measured self-same and equivalent that, as he said about Plato, “rumbled” under the metaphysics of analysis. This was the dark tradition he teased out of the Stoics, Ockham, Gregory of Rimini, Nicholas d’Autrecourt, Spinoza, Meinong, Bergson, Nietzsche, and McLuhan. This is not the purity of identity, A = A, of metrical uniformity and its shadow, anomaly. Rather than repressing, Deleuze revels in the perverse purity of differencing, difference constituted by becoming without the Apollonian imposition of normalcy or definitional identity. One cannot say “difference in itself” because its ontology, its genesis, is not that of anything itself but exactly the impossibility of such a manner of constitution: universal anomaly. No thing or idea can be iterative, separate, or discrete.In his Difference and Repetition, the idea of the purely same is undone: the Ding an sich is a paradox. While the dogmatic image of thought portrays the possibility of the purely self-same, Deleuze never does. His notions of individuation without individuals, of modulation without models, of simulacra without originals, always finds a reflection in his attitudes toward, not language as logical structure, but what necessarily forms the differential making of events, the heterogenesis of ontological symptoms. His theory has none of the categories of Pierce’s triadic construction: not the arbitrary of symbols, the “self-representation” of icons, or even the causal relation of indices. His “signs” are symptoms: the non-representational consequences of the forces that are concurrently producing them. Events, then, are the symptoms of the heterogenetic forces that produce, not reproduce them. To measure them is to export them into a representational modality that is ontologically inapplicable as they are not themselves themselves but the consequences of the ongoing differences of their genesis. Thus, the temperature associated with a fever is neither the body nor the disease.Every event, then, is a diaphora, the pure consequent of the multiplicity of the forces it cannot resemble, an original dynamic anomaly without standard. This term, diaphora, appears at the conclusion of that dialogue some consider Plato’s best, the Theaetetus. There we find perhaps the most important discussion of knowledge in Western metaphysics, which in its final moments attempts to understand how knowledge can be “True Judgement with an Account” (201d-210a). Following this idea leads to a theory, usually known as the “Dream of Socrates”, which posits two kinds of existents, complexes and simples, and proposes that “an account” means “an account of the complexes that analyses them into their simple components … the primary elements (prôta stoikheia)” of which we and everything else are composed (201e2). This—it will be noticed—suggests the ancient heritage of Kant’s own attempted purification of mereological (part/whole relations) nested elementals. He attempts the coordination of pure speculative reason to pure practical reason and, thus, attempts to supply the root of measurement and scientific regularity. However, as adumbrated by the Platonic dialogue, the attempted decompositions, speculative and pragmatic, lead to an impasse, an aporia, as the rational is based upon a correspondence and not the self-synthesis of the diaphorae by their own dynamic disequilibrium. Thus the dialogue ends inconclusively; Socrates rejects the solution, which is the problem itself, and leaves to meet his accusers and quaff his hemlock. The proposal in this article is that the diaphorae are all that exists in Deleuze’s world and indeed any world, including ours. Nor is this production decomposable into pure measured and defined elementals, as such decomposition is indeed exactly opposite what differential production is doing. For Deleuze, what exists is disparate conjunction. But in intensive conjunction the same cannot be the same except in so far as it differs. The diaphorae of events are irremediably asymmetric to their inputs: the actual does not resemble the virtual matrix that is its cause. Indeed, any recourse to those supposedly disaggregate inputs, the supposedly intelligible constituents of the measured image, will always but repeat the problematic of metrical representation at another remove. This is not, however, the traditional postmodern trap of infinite meta-shifting, as the diaphoric always is in each instance the very presentation that is sought. Heterogenesis can never be undone, but it can be affirmed. In a heterogenetic monism, what was the insoluble problem of correspondence in dualism is now its paradoxical solution: the problematic per se. What manifests in becoming is not, nor can be, an object or thought as separate or even separable, measured in units of the self-same. Dogmatic thought habitually translates intensity, the differential medium of chaosmosis, into the nominally same or similar so as to suit the Apollonian illusions of “correlational adequacy”. However, as the measured cannot be other than a calculation’s placebo, the correlation is but the shadow of a shadow. Every diaphora is an event born of an active conjunction of differential forces that give rise to this, their product, an interference pattern. Whatever we know and are is not the correlation of pure entities and thoughts subject to measured analysis but the confused and chaotic confluence of the specific, material, aleatory, differential, and unrepresentable forces under which we subsist not as ourselves but as the always changing product of our milieu. In short, only anomaly without a nominal becomes, and we should view any assertion that maps experience into the “objective” modality of the same, self-evident, and normal as a political prestidigitation motivated, not by “truth”, but by established political interest. ReferencesDella Volpe, Galvano. Logic as a Positive Science. London: NLB, 1980.Deleuze, Gilles. Difference and Repetition. Trans. Paul Patton. New York: Columbia UP, 1994.———. The Logic of Sense. Trans. Mark Lester. New York: Columbia UP, 1990.Guenon, René. The Reign of Quantity. New York: Penguin, 1972.Hawley, K. "Identity and Indiscernibility." Mind 118 (2009): 101-9.Hume, David. A Treatise of Human Nature. Oxford: Clarendon, 2014.Kant, Immanuel. Critique of Pure Reason. Trans. Norman Kemp Smith. London: Palgrave Macmillan, 1929.Meillassoux, Quentin. After Finitude: An Essay on the Necessity of Contingency. Trans. Ray Brassier. New York: Continuum, 2008.Naddaf, Gerard. The Greek Concept of Nature. Albany: SUNY, 2005. Nietzsche, Friedrich. The Birth of Tragedy. Trans. Douglas Smith. Oxford: Oxford UP, 2008.———. “On Truth and Lies in a Nonmoral Sense.” Trans. Walter Kaufmann. The Portable Nietzsche. New York: Viking, 1976.Welch, Kathleen Ethel. "Keywords from Classical Rhetoric: The Example of Physis." Rhetoric Society Quarterly 17.2 (1987): 193–204.

IntroductionThe common origin of the adjective “corporeal” and the noun “corpse” in the Latin root corpus points to the value of mortuary practices for investigating how the human body is objectified. In post-mortem rituals, the body—formerly the manipulator of objects—becomes itself the object that is manipulated. Thus, these funerary rituals provide a type of double reflexivity, where the object and subject of manipulation can be used to reciprocally illuminate one another. To this extent, any consideration of corporeality can only benefit from a discussion of how the body is objectified through mortuary practices. This paper offers just such a discussion with respect to a selection of two contrasting mortuary practices, in the context of the prehistoric past and the Classical Era respectively. At the most general level, we are motivated by the same intellectual impulse that has stimulated expositions on corporeality, materiality, and incarnation in areas like phenomenology (Merleau-Ponty 77–234), Marxism (Adorno 112–119), gender studies (Grosz vii–xvi), history (Laqueur 193–244), and theology (Henry 33–53). That is to say, our goal is to show that the body, far from being a transparent frame through which we encounter the world, is in fact a locus where historical, social, cultural, and psychological forces intersect. On this view, “the body vanishes as a biological entity and becomes an infinitely malleable and highly unstable culturally constructed product” (Shilling 78). However, for all that the cited paradigms offer culturally situated appreciations of corporeality; our particular intellectual framework will be provided by cognitive science. Two reasons impel us towards this methodological choice.In the first instance, the study of ritual has, after several decades of stagnation, been rewarded—even revolutionised—by the application of insights from the new sciences of the mind (Whitehouse 1–12; McCauley and Lawson 1–37). Thus, there are good reasons to think that ritual treatments of the body will refract historical and social forces through empirically attested tendencies in human cognition. In the present connection, this means that knowledge of these tendencies will reward any attempt to theorise the objectification of the body in mortuary rituals.In the second instance, because beliefs concerning the afterlife can never be definitively judged to be true or false, they give free expression to tendencies in cognition that are otherwise constrained by the need to reflect external realities accurately. To this extent, they grant direct access to the intuitive ideas and biases that shape how we think about the world. Already, this idea has been exploited to good effect in areas like the cognitive anthropology of religion, which explores how counterfactual beings like ghosts, spirits, and gods conform to (and deviate from) pre-reflective cognitive patterns (Atran 83–112; Barrett and Keil 219–224; Barrett and Reed 252–255; Boyer 876–886). Necessarily, this implies that targeting post-mortem treatments of the body will offer unmediated access to some of the conceptual schemes that inform thinking about human corporeality.At a more detailed level, the specific methodology we propose to use will be provided by conceptual blending theory—a framework developed by Gilles Fauconnier, Mark Turner, and others to describe how structures from different areas of experience are creatively blended to form a new conceptual frame. In this system, a generic space provides the ground for coordinating two or more input spaces into a blended space that synthesises them into a single output. Here this would entail using natural or technological processes to structure mortuary practices in a way that satisfies various psychological needs.Take, for instance, W.B. Yeats’s famous claim that “Too long a sacrifice / Can make a stone of the heart” (“Easter 1916” in Yeats 57-8). Here, the poet exploits a generic space—that of everyday objects and the effort involved in manipulating them—to coordinate an organic input from that taxonomy (the heart) with an inorganic input (a stone) to create the blended idea that too energetic a pursuit of an abstract ideal turns a person into an unfeeling object (the heart-as-stone). Although this particular example corresponds to a familiar rhetorical figure (the metaphor), the value of conceptual blending theory is that it cuts across distinctions of genre, media, language, and discourse level to provide a versatile framework for expressing how one area of human experience is related to another.As indicated, we will exploit this versatility to investigate two ways of objectifying the body through the examination of two contrasting mortuary practices—cremation and inhumation—against different cultural horizons. The first of these is the conceptualisation of the body as an object of a technical process, where the post-mortem cremation of the corpse is analogically correlated with the metallurgical refining of ore into base metal. Our area of focus here will be Bronze Age cremation practices. The second conceptual scheme we will investigate focuses on treatments of the body as a vegetable object; here, the relevant analogy likens the inhumation of the corpse to the planting of a seed in the soil from which future growth will come. This discussion will centre on the Classical Era. Burning: The Body as Manufactured ObjectThe Early and Middle Bronze Age in Western Europe (2500-1200 BCE) represented a period of change in funerary practices relative to the preceding Neolithic, exemplified by a move away from the use of Megalithic monuments, a proliferation of grave goods, and an increase in the use of cremation (Barrett 38-9; Cooney and Grogan 105-121; Brück, Material Metaphors 308; Waddell, Bronze Age 141-149). Moreover, the Western European Bronze Age is characterised by a shift away from communal burial towards single interment (Barrett 32; Bradley 158-168). Equally, the Bronze Age in Western Europe provides us with evidence of an increased use of cist and pit cremation burials concentrated in low-lying areas (Woodman 254; Waddell, Prehistoric 16; Cooney and Grogan 105-121; Bettencourt 103). This greater preference for lower-lying location appears to reflect a distinctive change in comparison to the distribution patterns of the Neolithic burials; these are often located on prominent, visible aspects of a landscape (Cooney and Grogan 53-61). These new Bronze Age burial practices appear to reflect a distancing in relation to the territories of the “old ancestors” typified by Megalithic monuments (Bettencourt 101-103). Crucially, the Bronze Age archaeological record provides us with evidence that indicates that cremation was becoming the dominant form of deposition of human remains throughout Central and Western Europe (Sørensen and Rebay 59-60).The activities associated with Bronze Age cremations such as the burning of the body and the fragmentation of the remains have often been considered as corporeal equivalents (or expressions) of the activities involved in metal (bronze) production (Brück, Death 84-86; Sørensen and Rebay 60–1; Rebay-Salisbury, Cremations 66-67). There are unequivocal similarities between the practices of cremation and contemporary bronze production technologies—particularly as both processes involve the transformation of material through the application of fire at temperatures between 700 ºC to 1000 ºC (Musgrove 272-276; Walker et al. 132; de Becdelievre et al. 222-223).We assert that the technologies that define the European Bronze Age—those involved in alloying copper and tin to produce bronze—offered a new conceptual frame that enabled the body to be objectified in new ways. The fundamental idea explored here is that the displacement of inhumation by cremation in the European Bronze Age was motivated by a cognitive shift, where new smelting technologies provided novel conceptual metaphors for thinking about age-old problems concerning human mortality and post-mortem survival. The increased use of cremation in the European Bronze Age contrasts with the archaeological record of the Near Eastern—where, despite the earlier emergence of metallurgy (3300–3000 BCE), we do not see a notable proliferation in the use of cremation in this region. Thus, mortuary practices (i.e. cremation) provide us with an insight into how Western European Bronze Age cultures mediated the body through changes in technological objects and processes.In the terminology of conceptual blending, the generic space in question centres on the technical manipulation of the material world. The first input space is associated with the anxiety attending mortality—specifically, the cessation of personal identity and the extinction of interpersonal relationships. The second input space represents the technical knowledge associated with bronze production; in particular, the extraction of ore from source material and its mixing with other metals to form an alloy. The blended space coordinates these inputs to objectify the human body as an object that is ritually transformed into a new but more durable substance via the cremation process. In this contention we use the archaeological record to draw a conceptual parallel between the emergence of bronze production technology—centring on transition of naturally occurring material to a new subsistence (bronze)—and the transitional nature of the cremation process.In this theoretical framework, treating the body as a mixture of substances that can be reduced to its constituents and transformed through technologies of cremation enabled Western European Bronze Age society to intervene in the natural process of putrefaction and transform the organic matter into something more permanent. This transformative aspect of the cremation is seen in the evidence we have for secondary burial practices involving the curation and circulation of cremated bones of deceased members of a group (Brück, Death 87-93). This evidence allows us to assert that cremated human remains and objects were considered products of the same transformation into a more permanent state via burning, fragmentation, dispersal, and curation. Sofaer (62-69) states that the living body is regarded as a person, but as soon as the transition to death is made, the body becomes an object; this is an “ontological shift in the perception of the body that assumes a sudden change in its qualities” (62).Moreover, some authors have proposed that the exchange of fragmented human remains was central to mortuary practices and was central in establishing and maintaining social relations (Brück, Death 76-88). It is suggested that in the Early Bronze Age the perceptions of the human body mirrored the perceptions of objects associated with the arrival of the new bronze technology (Brück, Death 88-92). This idea is more pronounced if we consider the emergence of bronze technology as the beginning of a period of capital intensification of natural resources. Through this connection, the Bronze Age can be regarded as the point at which a particular natural resource—in this case, copper—went through myriad intensive manufacturing stages, which are still present today (intensive extraction, production/manufacturing, and distribution). Unlike stone tool production, bronze production had the addition of fire as the explicit method of transformation (Brück, Death 88-92). Thus, such views maintain that the transition achieved by cremation—i.e. reducing the human remains to objects or tokens that could be exchanged and curated relatively soon after the death of the individual—is equivalent to the framework of commodification connected with bronze production.A sample of cremated remains from Castlehyde in County Cork, Ireland, provides us with an example of a Bronze Age cremation burial in a Western European context (McCarthy). This is chosen because it is a typical example of a Bronze Age cremation burial in the context of Western Europe; also, one of the authors (MG) has first-hand experience in the analysis of its associated remains. The Castlehyde cremation burial consisted of a rectangular, stone-lined cist (McCarthy). The cist contained cremated, calcined human remains, with the fragments generally ranging from a greyish white to white in colour; this indicates that the bones were subject to a temperature range of 700-900ºC. The organic content of bone was destroyed during the cremation process, leaving only the inorganic matrix (brittle bone which is, often, described as metallic in consistency—e.g. Gejvall 470-475). There is evidence that remains may have been circulated in a manner akin to valuable metal objects. First of all, the absence of long bones indicates that there may have been a practice of removing salient remains as curatable records of ancestral ties. Secondly, remains show traces of metal staining from objects that are no longer extant, which suggests that graves were subject to secondary burial practices involving the removal of metal objects and/or human bone. To this extent, we can discern that human remains were being processed, curated, and circulated in a similar manner to metal objects.Thus, there are remarkable similarities between the treatment of the human body in cremation and bronze metal production technologies in the European Bronze Age. On the one hand, the parallel between smelting and cremation allowed death to be understood as a process of transformation in which the individual was removed from processes of organic decay. On the other hand, the circulation of the transformed remains conferred a type of post-mortem survival on the deceased. In this way, cremation practices may have enabled Bronze Age society to symbolically overcome the existential anxiety concerning the loss of personhood and the breaking of human relationships through death. In relation to the former point, the resurgence of cremation in nineteenth century Europe provides us with an example of how the disposal of a human body can be contextualised in relation to socio-technological advancements. The (re)emergence of cremation in this period reflects the post-Enlightenment shift from an understanding of the world through religious beliefs to the use of rational, scientific approaches to examine the natural world, including the human body (and death). The controlled use of fire in the cremation process, as well as the architecture of crematories, reflected the industrial context of the period (Rebay-Salisbury, Inhumation 16).With respect to the circulation of cremated remains, Smith suggests that Early Medieval Christian relics of individual bones or bone fragments reflect a reconceptualised continuation of pre-Christian practices (beginning in Christian areas of the Roman Empire). In this context, it is claimed, firstly, that the curation of bone relics and the use of mobile bone relics of important, saintly individuals provided an embodied connection between the sacred sphere and the earthly world; and secondly, that the use of individual bones or fragments of bone made the Christian message something portable, which could be used to reinforce individual or collective adherence to Christianity (Smith 143-167). Using the example of the Christian bone relics, we can thus propose that the curation and circulation of Bronze Age cremated material may have served a role similar to tools for focusing religiously oriented cognition. Burying: The Body as a Vegetable ObjectGiven that the designation “the Classical Era” nominates the entirety of the Graeco-Roman world (including the Near East and North Africa) from about 800 BCE to 600 CE, there were obviously no mortuary practices common to all cultures. Nevertheless, in both classical Greece and Rome, we have examples of periods when either cremation or inhumation was the principal funerary custom (Rebay-Salisbury, Inhumation 19-21).For instance, the ancient Homeric texts inform us that the ancient Greeks believed that “the spirit of the departed was sentient and still in the world of the living as long as the flesh was in existence […] and would rather have the body devoured by purifying fire than by dogs or worms” (Mylonas 484). However, the primary sources and archaeological record indicate that cremation practices declined in Athens circa 400 BCE (Rebay-Salisbury, Inhumation 20). With respect to the Roman Empire, scholarly opinion argues that inhumation was the dominant funerary rite in the eastern part of the Empire (Rebay-Salisbury, Inhumation 17-21; Morris 52). Complementing this, the archaeological and historical record indicates that inhumation became the primary rite throughout the Roman Empire in the first century CE. Inhumation was considered to be an essential rite in the context of an emerging belief that a peaceful afterlife was reflected by a peaceful burial in which bodily integrity was maintained (Rebay-Salisbury, Inhumation 19-21; Morris 52; Toynbee 41). The question that this poses is how these beliefs were framed in the broader discourses of Classical culture.In this regard, our claim is that the growth in inhumation was driven (at least in part) by the spread of a conceptual scheme, implicit in Greek fertility myths that objectify the body as a seed. The conceptual logic here is that the post-mortem continuation of personal identity is (symbolically) achieved by objectifying the body as a vegetable object that will re-grow from its own physical remains. Although the dominant metaphor here is vegetable, there is no doubt that the motivating concern of this mythological fabulation is human mortality. As Jon Davies notes, “the myths of Hades, Persephone and Demeter, of Orpheus and Eurydice, of Adonis and Aphrodite, of Selene and Endymion, of Herakles and Dionysus, are myths of death and rebirth, of journeys into and out of the underworld, of transactions and transformations between gods and humans” (128). Thus, such myths reveal important patterns in how the post-mortem fate of the body was conceptualised.In the terminology of mental mapping, the generic space relevant to inhumation contains knowledge pertaining to folk biology—specifically, pre-theoretical ideas concerning regeneration, survival, and mortality. The first input space attaches to human mortality; it departs from the anxiety associated with the seeming cessation of personal identity and dissolution of kin relationships subsequent to death. The second input space is the subset of knowledge concerning vegetable life, and how the immersion of seeds in the soil produces a new generation of plants with the passage of time. The blended space combines the two input spaces by way of the funerary script, which involves depositing the body in the soil with a view to securing its eventual rebirth by analogy with the sprouting of a planted seed.As indicated, the most important illustration of this conceptual pattern can be found in the fertility myths of ancient Greece. The Homeric Hymns, in particular, provide a number of narratives that trace out correspondences between vegetation cycles, human mortality, and inhumation, which inform ritual practice (Frazer 223–404; Carney 355–65; Sowa 121–44). The Homeric Hymn to Demeter, for instance, charts how Persephone is abducted by Hades, god of the dead, and taken to his underground kingdom. While searching for her missing daughter, Demeter, goddess of fertility, neglects the earth, causing widespread devastation. Matters are resolved when Zeus intervenes to restore Persephone to Demeter. However, having ingested part of Hades’s kingdom (a pomegranate seed), Persephone is obliged to spend half the year below ground with her captor and the other half above ground with her mother.The objectification of Persephone as both a seed and a corpse in this narrative is clearly signalled by her seasonal inhumation in Hades’ chthonic realm, which is at once both the soil and the grave. And, just as the planting of seeds in autumn ensures rebirth in spring, Persephone’s seasonal passage from the Kingdom of the Dead nominates the individual human life as just one season in an endless cycle of death and rebirth. A further signifying element is added by the ingestion of the pomegranate seed. This is evocative of her being inseminated by Hades; thus, the coordination of vegetation cycles with life and death is correlated with secondary transition—that from childhood to adulthood (Kerényi 119–183).In the examples given, we can see how the Homeric Hymn objectifies both the mortal and sexual destiny of the body in terms of thresholds derived from the vegetable world. Moreover, this mapping is not merely an intellectual exercise. Its emotional and social appeal is visible in the fact that the Eleusinian mysteries—which offered the ritual homologue to the Homeric Hymn to Demeter—persisted from the Mycenaean period to 396 CE, one of the longest recorded durations for any ritual (Ferguson 254–9; Cosmopoulos 1–24). In sum, then, classical myth provided a precedent for treating the body as a vegetable object—most often, a seed—that would, in turn, have driven the move towards inhumation as an important mortuary practice. The result is to create a ritual form that makes key aspects of human experience intelligible by connecting them with cyclical processes like the seasons of the year, the harvesting of crops, and the intergenerational oscillation between the roles of parent and child. Indeed, this pattern remains visible in the germination metaphors and burial practices of contemporary religions such as Christianity, which draw heavily on the symbolism associated with mystery cults like that at Eleusis (Nock 177–213).ConclusionWe acknowledge that our examples offer a limited reflection of the ethnographic and archaeological data, and that they need to be expanded to a much greater degree if they are to be more than merely suggestive. Nevertheless, suggestiveness has its value, too, and we submit that the speculations explored here may well offer a useful starting point for a larger survey. In particular, they showcase how a recurring existential anxiety concerning death—involving the fear of loss of personal identity and kinship relations—is addressed by different ways of objectifying the body. Given that the body is not reducible to the objects with which it is identified, these objectifications can never be entirely successful in negotiating the boundary between life and death. In the words of Jon Davies, “there is simply no let-up in the efforts by human beings to transcend this boundary, no matter how poignantly each failure seemed to reinforce it” (128). For this reason, we can expect that the record will be replete with conceptual and cognitive schemes that mediate the experience of death.At a more general level, it should also be clear that our understanding of human corporeality is rewarded by the study of mortuary practices. 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