Many real-world optimization problems usually require a large number of conflicting objectives to be optimized simultaneously to obtain solution. It has been observed that these kinds of many-objective optimization problems often pose several performance challenges to the traditional multi-objective optimization algorithms. To address the performance issue caused by the different types of MaOPs, recently, a variety of many-objective particle swarm optimization has been proposed. However, external archive maintenance and selection of leaders for designing the MaOPSO to real-world MaOPs (...) are still challenging issues. This work presents a MaOPSO based on entropy-driven global best selection strategy to solve the many-objective software package restructuring problem. EMPSO makes use of the entropy and quality indicator for the selection of global best particle. To evaluate the performance of the proposed approach, we applied it over the five MaOSPR problems. We compared it with eight variants of MaOPSO, which are based on eight different global best selection strategies. The results indicate that the proposed EMPSO is competitive with respect to the existing global best selection strategies based on variants of MaOPSO approaches. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This (...) construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This (...) construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we (...) show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. (shrink)

In our current era, a new rapidly spreading pandemic disease called coronavirus disease, caused by a virus identified as a novel coronavirus, is becoming a crucial threat for the whole world. Currently, the number of patients infected by the virus is expanding exponentially, but there is no commercially available COVID-19 medication for this pandemic. However, numerous antiviral drugs are utilized for the treatment of the COVID-19 disease. Identification of the appropriate antivirus medicine to treat the infection of COVID-19 is (...) still a complicated and uncertain decision. This study’s key objective is to develop a novel approach called _q_-rung orthopair probabilistic hesitant fuzzy rough set, which incorporates the _q_-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set structures. New _q_-ROPHFR aggregation operators have been established: the _q_-ROPHFR Einstein weighted averaging operator and the _q_-ROPHFR Einstein weighted geometric operator. In this study, we explored some basic features of the developed operators. Afterward, to demonstrate the viability and feasibility of the established decision-making approach in real-world applications, a case study related to selecting drugs for COVID-19 pandemic is addressed. Furthermore, a comprehensive comparison with the _q_-rung orthopair probabilistic hesitant fuzzy rough TOPSIS technique is also presented to illustrate the benefits of the new framework. The obtained results confirm the reliability and effectiveness of the proposed approach for finding uncertainty in real-world decision-making. (shrink)

With the increasing volume of data transmission through insecure communication channels, big data security has become one of the important concerns in the cybersecurity domain. To address these concerns and keep data safe, a robust privacy-preserving cryptosystem is necessary. Such a solution relies on chaos encryption algorithms over standard cryptographic methods that possess multistage encryption levels, including high speed, high security, low compute overheads, and procedural power, among other characteristics. In this work, a secure image encryption scheme is proposed using (...) linear feedback shift register and chaos-based quantum chaotic map. The focus of the scheme is mainly dependent on the secret keys from the input of the algorithm. The threat landscape, the statistical test analysis, along critical comparisons with other schemes indicate that the presented algorithm is significantly secure and is resistant to a wide range of different attacks such as differential and statistical attacks. The proposed method has sufficiently higher sensitivity and security when compared to existing encryption algorithms. Several security parameters validated the security of proposed work such as correlation coefficient analyses among the neighboring pixels, entropy, the number of pixels change rate, unified average change intensity, mean square error, brute force, key sensitivity, and peak signal to noise ratio analyses. The randomness of the ciphers produced by the proposed technique is also passed through NIST-800-22. The results of NIST indicate that the ciphers are highly random and do not produce any type of periodicity or pattern. (shrink)

The 3D Prandtl fluid flow through a bidirectional extending surface is analytically investigated. Cattaneo–Christov fluid model is employed to govern the heat and mass flux during fluid motion. The Prandtl fluid motion is mathematically modeled using the law of conservations of mass, momentum, and energy. The set of coupled nonlinear PDEs is converted to ODEs by employing appropriate similarity relations. The system of coupled ODEs is analytically solved using the well-established mathematical technique of HAM. The impacts of various physical parameters (...) over the fluid state variables are investigated by displaying their corresponding plots. The augmenting Prandtl parameter enhances the fluid velocity and reduces the temperature and concentration of the fluid. The momentum boundary layer boosts while the thermal boundary layer mitigates with the rising elastic parameter strength. Furthermore, the enhancing thermal relaxation parameter ) reduces the temperature distribution, whereas the augmenting concentration parameter drops the strength of the concentration profile. The increasing Prandtl parameter declines the fluid temperature while the augmenting Schmidt number drops the fluid concentration. The comparison of the HAM technique with the numerical solution shows an excellent agreement and hence ascertains the accuracy of the applied analytical technique. This work finds applications in numerous fields involving the flow of non-Newtonian fluids. (shrink)

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F ¦ –¦dF/dt=gG =k 1,G=k 2 as ¦– ¦ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower.A solution of the system satisfying the boundary conditions is constructed so that specified limiting conditions are fulfilled.

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim (...) of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require “renormalization” or “dressing” of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described. (shrink)

Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle–antiparticle amplitude. This process differs from conventional on-shell Mandelstam s, t, u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the (...) Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle–antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum. (shrink)

We show that if is not in the field generated by α1,…,αn, then no restriction of the function xβ to an interval is definable in . We also prove that if the real and imaginary parts of a complex analytic function are definable in Rexp or in the expansion of by functions xα, for irrational α, then they are already definable in . We conclude with some conjectures and open questions.

This paper contains a proposal for a free, nonzero-rest-mass particle’s proper spacetime, determined exclusively by the particle’s rest mass \ and numbers. The approach defines proper time as de Broglie time, which is isomorphic to a sequence of natural numbers \ that count de Broglie time units \\). The approach is based on defining the spatial coordinate as proper following the constructive definition of positive and negative integers as all possible differences of ordered pairs of natural numbers multiplied (...) by the Compton unit \\). The spatial and temporal coordinates that form the particle’s proper spacetime are constructed as Euclidean projections of the de Broglie time. The corresponding expression in the form of an energy-momentum relation reveals the existence, aside from the rest energy term \, of an additional energy term of the same order of magnitude, which is related to large intervals of the \-particle’s proper space. The relation of the numbers-based approach to the foundations of the special theory of relativity and of quantum mechanics is discussed. (shrink)

Recently, Michael Redhead has argued that the grouping of particles into multiplets by grand unified gauge theories (GUT's) does not, by itself, imply an ontological reduction in the number of elementary particles. While sympathetic to Redhead's argument, in this note I argue that under certain conditions involving Kaluza-Klein theories, GUT's would provide such an ontological reduction.

There have been two attempts in the history of human speculation to estimate the number of particles in the universe. The first was that of Archimedes of Syracuse about 216 B. C., and the second that of Sir Arthur Eddington nearly two thousand years later. What is surprising is that they both arrive at the same number. This is the number obtained by multiplying ten by itself seventy-nine times.

There have been two attempts in the history of human speculation to estimate the number of particles in the universe. The first was that of Archimedes of Syracuse about 216 B. C., and the second that of Sir Arthur Eddington nearly two thousand years later. What is surprising is that they both arrive at the same number. This is the number obtained by multiplying ten by itself seventy-nine times.

Six years ago, the Singer lab published a landmark paper which described how individual mRNA particles cross the nuclear pore complex in mammalian tissue culture cells. This involved the simultaneous imaging of mRNAs, each labeled by a large number of tethered fluorescent proteins and fluorescently tagged nuclear pore components. Now two groups have applied this technique to the budding yeast Saccharomyces cerevisiae. Their results indicate that in the course of nuclear export, mRNAs likely engage complexes that are present on (...) either side of the pore and that these interactions are modulated by proteins present in the messenger ribonucleoprotein (mRNP) complex. These findings lend support to the notion that just before and/or after the completion of nuclear export, mRNPs undergo one or more maturation steps that prepare the packaged mRNAs for translation. These results represent new and exciting insights into the mechanism of mRNA nuclear export. (shrink)

We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy for expansions of Presburger arithmetic on the integers. Combining these two results, we obtain that the expansion of the ordered group of integers by any number of sets of powers does not define multiplication.

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s (...) formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model. (shrink)

A number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical ħ→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbar \rightarrow 0$$\end{document} limit can aid our understanding of the particle content of quantum field theories. In particular, we demonstrate that for the massive Klein–Gordon field, the classical limits of number operators can be understood to encode local (...) information about particles in the corresponding classical field theory. (shrink)

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of “electric” or “magnetic” type, according as the radial component of the magnetic or electric field (...) vanishes in the rest frame, and each has an “antiparticle.” Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (κ, ω0, σ,l, m), where ω0 is the mean of the angular frequencies of the plane waves making up the configuration, σ is the variance of those frequencies, κ is a positive constant with dimensions of action, andl, m are angular momentum “quantum numbers” withl a positive integer andm an integer such that ‖m‖≤l. The rest energy of the “particle” is κω0, its spin is κ ‖m‖, and its lifetime is of the order of 1/σ. Its antiparticle has ω0 replaced by −ω0. (shrink)

This paper proposes an account of the distribution and role of a set of particles in Hungarian dubbed `polarity particles', which include igen `yes', nem `no', and de `but'. These particles occur at the leftmost edge of a class of assertions uttered as reactions to an immediately preceding assertion or polar question. It is argued that they express two sets of features typical of the class of reactive assertions they occur in, one set encoding the polarity of the asserted sentence, (...) and the other encoding the relation of the asserted sentence to the immediately preceding utterance. The discussion is set against an explicit approach to context structure and to assertive and polar questioning speech acts that draws on a number of pre-existing proposals in the literature. (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. (...) We take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of (...) mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature. (shrink)

This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag's theorem. Finally, a recent argument due to Redhead, Malament and Arageorgis against the concept of localized particle states is addressed. Briefly, the (...) argument observes that the Reeh-Schlieder theorem entails that correlations between spacelike separated vacuum expectation values of local field operators are always present, and this, according to the above authors, dictates against the notion of a localized particle state. I claim that this moral is excessive and that a coherent notion of localized particles is given by the LSZ approach. The underlying moral to be drawn from this analysis is that questions concerning the ontology of interacting QFT cannot be appropriately addressed if one restricts oneself to the free theory. (shrink)

Flow prediction in a vegetated channel has been extensively studied in the past few decades. A number of equations that essentially differ from each other in derivation and form have been developed. Because the process is extremely complex, getting the deterministic or analytical form of the process phenomena is too difficult. Hybrid neural network model is particularly useful in modeling processes where an adequate knowledge of the physics is limited. This hybrid model is presented here as a complementary tool (...) to model channel flow–vegetation interactions in submerged vegetation conditions. The hybrid model is used to overcome the local minima limitations of a feed-forward neural network. The prediction capability of model has been found to be better than past empirical predictors. The model developed herein showed significantly better results in several model performance criteria compared with empirical models. (shrink)

Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor and scalar fields. There seems to be no physical principle to determine these parameters as long as they stay within certain domains dictated by the renormalization group. Here however, reasons are given to demand that, when gravity is coupled to the system, local (...) conformal invariance should be a spontaneously broken exact symmetry. The argument has to do with the requirement that black holes obey a complementarity principle relating ingoing observers to outside observers, or equivalently, initial states to final states. This condition fixes all parameters, including masses and the cosmological constant. We suspect that only examples can be found where these are all of order one in Planck units, but the values depend on the algebra chosen. This paper combines findings reported in two previous preprints (G. ’t Hooft in arXiv:1009.0669 [gr-qc], 2010; arXiv:1011.0061 [gr-qc], 2010) and puts these in a clearer perspective by shifting the emphasis towards the implications for particle models. (shrink)

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means of (...) subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

This paper develops a means–end analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden (...) particles. Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions—including prescriptions for when exactly to introduce hidden particles. (shrink)

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events is (...) due to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be "inapplicable" (or "undefined") in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b = d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the 'influence-at-a-distance', quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that "hidden variables" are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. (shrink)

Effective and personalized treatment relies heavily on skin disease categorization. In the stratification of skin disorders, it is crucial to identify the subtypes of illnesses to provide an efficient therapy. To attain this aim, researchers have focused their attention on cluster algorithms for the stratification of skin disorders in recent decades. But, cluster algorithms have real-world drawbacks, including experimental noises, a large number of dimensions, and a poor ability to comprehend. Cluster algorithms, in particular, determine the quality of clusters (...) using a single internal evaluation operation in the majority of cases. A single internal assessment procedure is difficult to design and robust for all datasets, which is a problem. The multi-objective particle swarm obtained high sensitivity in the existing work, but it is not able to anticipate all kinds of classes. An optimized cluster distance parameter for K-means clustering is determined using a hybrid particle swarm and moth flame optimization. Multi-objective is guided by two cluster value indices, including the K-means clustering misclassification rate and neural network classification rate. Hybrid PSO will solve the multi-objective problem to identify the optimal cluster for clustering. On the dermatological dataset from the UCI repository, MATLAB R2020a will be used to evaluate the proposed method. This will be followed by an evaluation of the proposed method’s performance using the cluster evaluation indices. (shrink)

Classical particles of the same kind are distinguishable: they can be labeled by their positions and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated (...) as indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox. (shrink)

The first volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles, consisting of four sets of lectures. Every summer since 1959 Brandeis University has conducted a lecture series centered on various areas of theoretical physics. The areas are sufficiently broad to interest a large number of physicists and the lecturers are among the original explorers of these areas. The 1970 lectures, presented in two volumes, are on theories of interacting elementary particles. (...) The four lecturers of Volume 1, and the range of the topics they cover, are as follows: Stephen L. Adler on "Perturbation Theory Anomalies": introduction and review of perturbation theory; the VVA triangle anomaly; absence of radiative corrections; generalizations of our results; connection between Ward identity anomalies and commutator anomalies; applications of the Bjorken limit; and breakdown of the Bjorken limit in perturbation theory. Stanley Mandelstam on "Dynamical Applications of the Veneziano formula for the four-point scalar amplitude; factorization; the operator formalism; Veneziano-type quark models; and higher-order Feynman-like diagrams. Steven Weinberg on "Dynamic and Algebraic Symmetries": Introduction; hadron electrodynamics; local symmetries; and chirality. Wolfhart Zimmermann on "Local Operator Products and Renormalization in Quantum Field Theory": introduction; renormalization; operator product expansions; and local field equations. The second volume contains lectures by Rudolf Haag on observables and fields, by Maurice Jacob on duality, by Michael Reed on non-Fock representations, and by Bruno Zumino on effective Lagrangians and broken symmetries. (shrink)

This dissertation reconsiders some traditional issues in the foundations of quantum mechanics in the context of relativistic quantum field theory (RQFT); and it considers some novel foundational issues that arise first in the context of RQFT. The first part of the dissertation considers quantum nonlocality in RQFT. Here I show that the generic state of RQFT displays Bell correlations relative to measurements performed in any pair of spacelike separated regions, no matter how distant. I also show that local systems in (...) RQFT are "open" to influence from their environment, in the sense that it is generally impossible to perform local operations that would remove the entanglement between a local system and any other spacelike separated system. The second part of the dissertation argues that RQFT does not support a particle ontology -- at least if particles are understood to be localizable objects. In particular, while RQFT permits us to describe situations in which a determinate number of particles are present, it does not permit us to speak of the location of any individual particle, nor of the number of particles in any particular region of space. Nonetheless, the absence of localizable particles in RQFT does not threaten the integrity of our commonsense concept of a localized object. Indeed, RQFT itself predicts that descriptions in terms of localized objects can be quite accurate on the macroscopic level. The third part of the dissertation examines the so-called observer-dependence of the particle concept in RQFT -- that is, whether there are any particles present must be relativized to an observer's state of motion. Now, it is not uncommon for modern physical theories to subsume observer-dependent descriptions under a more general observer-independent description of some underlying state of affairs. However, I show that the conflicting accounts concerning the particle content of the field cannot be reconciled in this way. In fact, I argue that these conflicting accounts should be thought of as "complementary" in the same sense that position and momentum descriptions are complementary in elementary quantum mechanics. (shrink)

This paper and its predecessor () are about the question: 'Are the events in the entire universe encoded in and predictable from any of its parts?' To approach a positive answer in classical physics, the following result is proved and commented on: in Newton's theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving-provided that there is only a finite number of particles and (...) that their speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed. (shrink)

The success of particle detection in high energy physics colliders critically depends on the criteria for selecting a small number of interactions from an overwhelming number that occur in the detector. It also depends on the selection of the exact data to be analyzed and the techniques of analysis. The introduction of automation into the detection process has traded the direct involvement of the physicist at each stage of selection and analysis for the efficient handling of vast (...) amounts of data. This tradeoff, in combination with the organizational changes in laboratories of increasing size and complexity, has resulted in automated and semi-automated systems of detection. Various aspects of the semi-automated regime were greatly diminished in more generic automated systems, but turned out to be essential to a number of surprising discoveries of anomalous processes that led to theoretical breakthroughs, notably the establishment of the Standard Model of particle physics. The automated systems are much more efficient in confirming specific hypothesis in narrow energy domains than in performing broad exploratory searches. Thus, in the main, detection processes relying excessively on automation are more likely to miss potential anomalies and impede potential theoretical advances. I suggest that putting substantially more effort into the study of electron–positron colliders and increasing its funding could minimize the likelihood of missing potential anomalies, because detection in such an environment can be handled by the semi-automated regime—unlike detection in hadron colliders. Despite virtually unavoidable excessive reliance on automated detection in hadron colliders, their development has been deemed a priority because they can operate at currently highest energy levels. I suggest, however, that a focus on collisions at the highest achievable energy levels diverts funds from searches for potential anomalies overlooked due to tradeoffs at the previous energy thresholds. I also note that even in the same collision environment, different research strategies will opt for different tradeoffs and thus achieve different experimental outcomes. Finally, I briefly discuss current searches for anomalous process in the context of the previous analysis. (shrink)

Clinician scientists have gained institutional support in the era of translational research, as the key solution to closing the ‘translational gap’ between biomedical research and medical practice. However, clinician scientists remain an ‘endangered species’ in search of a secure niche, while new grants and training programs attempt to counteract their measurable decline in numbers over the past decades. Our study asks how an occupational space for clinician scientists is currently situated between the politics of translation, professional dynamics, and the specialization (...) of academic disciplines. We interviewed clinician scientists, their adjacent professions—clinicians and biomedical researchers—, and contrast their views with expectations from the discourse on clinician scientists in the biomedical and policy literature. We identify professionalizable work and tasks that relate to, first, being able to speak the two languages of both clinic and research, second, translating patients’ needs and clinical experience for further research, and third, counteracting the trends towards specialization by providing an inclusive point of view. We find that clinician scientists are overburdened with fulfilling a hybrid role of simultaneously being clinicians and scientists. Based on these findings, we suggest a path for the future professional development of clinician scientists towards the role of a translator. (shrink)

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential (...) property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated. (shrink)

In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=∞, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.

We discuss two supertasks invented recently by Laraudogoitia [1996, 1997], Both involve an infinite number of particle collisions within a finite amount of time and both compromise determinism. We point out that the sources of the indeterminism are rather different in the two cases - one involves unbounded particle velocities, the other involves particles with no lower bound to their sizes - and consequently that the implications for determinism are rather different - one form of indeterminism affects (...) Newtonian but not relativistic physics, while the other form is insensitive to the classical vs relativistic distinction. We also note some interesting linkages among supertasks, indeterminism and foundations problems in the general theory of relativity. (shrink)

Even though hesitations (e.g., um/uh) were historically perceived as involuntary non-linguistic items (e.g., Maclay & Osgood 1959), more recently, a number of scholars have suggested that hesitations can behave like (a) lexical items (e.g., Clark & Fox Tree 2002), and (b) at least in some contexts and with some functions as grammatical items like suffixes/clitics (Kirjavainen, Crible & Beeching 2022; Tottie 2017). The current study contributes to this body of work and presents two spoken language corpus analyses (frequency analysis; (...) network analysis) investigating the nature of the Finnish planning particle tota. Our results suggest that tota is more similar to grammatical items than lexical items. (shrink)

According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for nonrelativistic QFTs. I argue that this is due to (...) the absolute structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs. (shrink)

Discourse particles have received a considerable amount of scholarly attention in linguistic research. Although their use in specific text types has been discussed, few studies have actually attempted to look at the effect of text type on their use. Therefore, how the use of discourse particles is related to the situational context in which they are produced remains a largely unexplored area. In this article, the use of one of the most frequently occurring yet often overlooked discourse particles, so, in (...) a number of monologic and dialogic texts is examined. Drawing on data from a spoken corpus of Hong Kong English, the present study shows that the frequency rates and functions of so as a discourse particle vary according to the text type in which it occurs. Findings from the study thus argue that the full range of functions realized by so as a discourse particle cannot be determined without taking into account the wide range of communicative events in which the particle is used. This highlights the fact that contextual cues are indispensable in the interpretation of the pragmatic meanings of discourse particles. (shrink)

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature β become small. Thus, microscopic particles (...) like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2πħ)3 are reduced to points in the phase space, the partition functionTr{exp(−βĤ) for N identical bosons (fermions) approaches (2πħ)−3N(N!) ∫ ... ∫ d3r1 d3p1 ... d3rN d3pN exp(−βH). The two factors, (2πħ)−3N and (N!)−1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles. (shrink)

A number of papers on wave-particle duality has appeared since the two-prism experiment was performed by Mizobuchi and Ohtake, based on a suggestion by Ghose, Home, and Agarwal. Against this backdrop, the present paper provides further clarification of the key issues involved in the analysis of the two-prism experiment. In the process, we present an overview of wave-particle duality vis-a vis Bohr's complementarity principle.