Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while (...) libertarianism pulls towards the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it. (shrink)

The lecture starts by considering analytic philosophy as a tradition, and its global spread over recent years, of which Disputatio’s success is itself evidence. The costs and benefits of the role of English as the international language of analytic philosophy are briefly assessed. The spread of analytic philosophy is welcomed as the best hope for scientific philosophy, in a sense of ‘science’ on which mathematics, history, and philosophy can all count as sciences, though not as natural sciences. Arguably, experimental philosophy (...) provides no plausible alternative methodology for philosophy, only a way of psychologizing it. However, it serves a useful purpose by highlighting the inadequacy of current methods for detecting errors in judgments on possible cases, which may result from reliance on possibly universal but imperfectly reliable cognitive heuristics. The problem is exacerbated by analytic philosophers’ tendency to regard increased flexibility in a theoretical framework as progress, where natural scientists would treat it as methodologically vicious profligacy with degrees of freedom. The result is a familiar type of bad science, overfitting theory to uncritically accepted data. The recent ‘hyperintensional revolution’ may be an example of such overfitting, it is suggested. The lecture ends with a call for a more miserly attitude to degrees of freedom. (shrink)

I propose a theory of freedom of choice on which it is a variable quality of individual conscious choices that has several dimensions that admit of degrees, even though - as many theorists have traditionally supposed - it also has as a necessary condition the possession of a capacity that is all or nothing. I argue that the proposed account better fits the phenomenology of ostensibly free actions, as well as empirical findings in the human sciences.

Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this limitation we (...) demonstrate that such systems exhibit a number of features, such as randomness, no-cloning, and non-commutativity, which are peculiarities attributed to quantum mechanics (QM). After demonstrating many astonishing parallels to quantum behavior, we postulate an interpretation of quantum physics as the physics of systems with a single degree of freedom. We then show how a number of other quantum conundrum can be understood by considering the informational properties of the systems and also resolve the EPR paradox. In the present work, we assume that the formalism of the QM is correct and well-supported by experimental verification and concentrate on the interpretational aspects of the theory. (shrink)

Some claim that Non- reductive Physicalism is an unstable position, on grounds that NRP either collapses into reductive physicalism, or expands into emergentism of a robust or ‘strong’ variety. I argue that this claim is unfounded, by attention to the notion of a degree of freedom—roughly, an independent parameter needed to characterize an entity as being in a state functionally relevant to its law-governed properties and behavior. I start by distinguishing three relations that may hold between the degrees (...) of freedom needed to characterize certain special science entities, and those needed to characterize their composing physical entities; these correspond to what I call ‘reductions’, ‘restrictions’, and ‘eliminations’ in degrees of freedom. I then argue that eliminations in degrees of freedom, in particular—when strictly fewer degrees of freedom are required to characterize certain special science entities than are required to characterize their composing physical entities—provide a basis for making sense of how certain special science entities can be both physically acceptable and ontologically irreducible to physical entities. (shrink)

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a “core basis problem.” To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and (...) their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus. (shrink)

THOMAS SCHELLING taught us that in ordinary human affairs, conflict and common interest are ubiquitously intertwined. For when it comes to variety, the occasion of pure conflict (known to some of its friends as the zerosum game) is as under-represented in human affairs as the occasion of undiluted common interest (known as the pure coordination game). The undiluted extremes are the exceptions, when it comes to counting kinds, while the mixed-motive kind of occasion is the rule. Things look a bit (...) different, however, when one looks at sheer numbers of true-life occasions, as I will explain. Schelling also taught us that in the diverse space of mixed-motive affairs, intermediate between pure conflict and pure coordination, there is more true-life collaborative behavior—more trustings and promise-keepings—than our prescriptive decision theories can accommodate, never mind explain. This collaborative behavior, as long ago another Thomas—Thomas Hobbes—was painfully aware, requires some explaining precisely because of the presence of ineliminable conflict of interest. The problem confronting those who aspire to explain such collaboration is to identify weighty motivations in its favor, in the face of the weighty, but countervailing motivations. What shall concern me here is not the collaboration that transpires in the face of conflict of interest, but the success which meets us more than halfway in those limiting cases of pure coordination, so as (for example) not to collide in roadways and corridors. For in sheer quantity, the occasions for pure coordination outnumber the occasions for anything else perhaps a hundredfold. (shrink)

Nick Huggett and Robert Weingard (1994) have recently proposed a novel approach to interpreting field theories in physics, one which makes central use of the fact that a field generally has an infinite number of degrees of freedom in any finite region of space it occupies. Their characterization, they argue, (i) reproduces our intuitive categorizations of fields in the classical domain and thereby (ii) provides a basis for arguing that the quantum field is a field. Furthermore, (iii) it (...) accomplishes these tasks better than does a well-known rival approach due to Paul Teller (1990, 1995). This paper contends that all three of these claims are mistaken, and suggests that Huggett and Weingard have not shown how counting degrees of freedom provides any insight into the interpretation or the formal properties of field theories in physics. (shrink)

This paper argues that the doctrines of determinism and supervenience, while logically independent, are importantly linked in physical mechanics—and quite interestingly so. For it is possible to formulate classical mechanics in such a way as to take advantage of the existence of mathematical devices that represent the advance of time—and which are such as to inspire confidence in the truth of determinism—in order to prevent violation of supervenience. It is also possible to formulate classical mechanics-and to do so in an (...) observationally equivalent, and thus equally empirically respectable, way—such that violations of supervenience are (on the one hand) routine, and (on the other hand) necessary for achieving complete descriptions of the motions of mechanical systems—necessary, therefore, for achieving a deterministic mechanical theory. Two such formulations—only one of which preserves supervenience universally—will conceive of mechanical law in quite different ways. What's more, they will not admit of being extended to treat thermodynamical questions in the same way. Thus we will find that supervenience is a contingent matter, in the following rather surprising and philosophically interesting way: we cannot in mechanics separate our decisions to conceive of physical law in certain ways from our decisions to treat macroscopic quantities in certain ways. (shrink)

While the issue of standards has received attention from analysts in science and technology studies, this attention has tended to focus on either units of measurement or compatibility standards. Much less attention has been devoted to equally important standards of practice. These are the procedural or process standards which govern how technologists go about designing and constructing artifacts. Such standards have a substantial documented history in the form of engineering codes of practice. As the embodiment of judgments rendered by a (...) particular community of technological practi tioners, these standards both reflect and shape the exercise of practitioner judgment. This article explores both these functions through examples drawn from structural and software engineering. These examples yield insights regarding both the role of formal procedural standards in technological practice and the unusual nature of software technology. (shrink)

We show that in the Maxwell–Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological (...) status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology. (shrink)

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a (...) single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated. (shrink)

Some claim that Non-reductive Physicalism is an unstable position, on grounds that NRP either collapses into reductive physicalism, or expands into emergentism of a robust or ‘strong’ variety. I argue that this claim is unfounded, by attention to the notion of a degree of freedom—roughly, an independent parameter needed to characterize an entity as being in a state functionally relevant to its law-governed properties and behavior. I start by distinguishing three relations that may hold between the degrees of (...) freedom needed to characterize certain special science entities, and those needed to characterize their composing physical entities; these correspond to what I call ‘reductions’, ‘restrictions’, and ‘eliminations’ in degrees of freedom. I then argue that eliminations in degrees of freedom, in particular—when strictly fewer degrees of freedom are required to characterize certain special science entities than are required to characterize their composing physical entities—provide a basis for making sense of how certain special science entities can be both physically acceptable and ontologically irreducible to physical entities. (shrink)

In an influential article, Anthony Kenny charged that (a) the view of freedom in Descartes’ “1645 letter to Mesland” is incoherent, and (b) that this incoherence was present in Descartes’ thought from the beginning. Against (b), I argue that such incoherence would rather support Gilson’s suspicions that the 1645 letter is dishonest. Against (a), I offer a close reading of the letter, showing that Kenny’s objection seems plausible only if we misconstrue a key ambiguity in the text. I close (...) by defending Descartes against some related worries of my own about the degrees of Cartesian freedom. I conclude that there is really no good reason to deny that Descartes’ view in the 1645 letter is both internally coherent and a genuine explication of the Meditations’ account of freedom. (shrink)

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter (...) fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. (shrink)

There is a debate in philosophy of mind about the nature of reason explanations of action, and this volume is testament to a resurgence of interest in non-causal accounts. In Teleological Realism: Mind, Agency, and Explanation,2 I have proposed a non-causal account according to which common-sense reason explanations of action are irreducibly teleological in form. I claim that we explain behavior by citing the state of affairs towards which the agent was directing her behavior, i. e., by citing the purpose (...) or goal of the behavior. I will not be defending that account of action explanation here, but will be assuming it and applying it to the free will debate. I will argue that the teleological account of action explanation leads to a view of free will with some interesting and attractive features. Philosophical accounts of free will typically propose some sort of criterion for determining which behaviors count as free, e. g., that the agent could have done otherwise, or that the behavior was in accord with the agent’s second-order volitions. The account is then usually used to answer the question of whether we have free will, and especially whether we can have free will even if determinism is true. To test these accounts, philosophers make arguments of various sorts, but the primary method is with cases. Here’s the recipe for an objection to an account of free will: come up with a case where the theory says that the agent is free, but our intuition says that the agent is unfree, or vice versa. I won’t question the method of cases in principle; it’s what we have and it makes some sense. On the picture of analytic philosophy as conceptual analysis, it makes perfect sense. Philosophers put forward a precisely spelled out version of our concept of free will; but if such an account is at odds with firm intuitions in particular cases, then it can’t be what we mean. We know that the situation is not really so simple as that. Our ordinary concept of free will might be messy and not perfectly consistent; accordingly, any particular theory might get a few cases ›wrong‹ as judged by our intuitions.. (shrink)

There are at least three different notions of degrees of freedom that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the other to the structure of the system and the third to the properties of dynamical orbits. In this paper, definitions and comparison in classical and quantum systems of the tree types of DF are formulated and discussed. In particular, we concentrate on comparison (...) of the number of the so called dynamical DF in a quantum system and its classical model. The comparison involves analyzes of relations between integrability of the classical model, dynamical symmetry and separability of the quantum and the corresponding classical systems and dynamical generation of appropriately defined quantumness. The analyzes is conducted using illustrative typical systems. A conjecture summarizing the observed relation between generation of quantumness by the quantum dynamics and dynamical properties of the classical model is formulated. (shrink)

A theory is presented to explain how accurate, single-joint movements are controlled. The theory applies to movements across different distances, with different inertial loads, toward targets of different widths over a wide range of experimentally manipulated velocities. The theory is based on three propositions. (1) Movements are planned according to “strategies” of which there are at least two: a speed-insensitive (SI) and a speed-sensitive (SS) one. (2) These strategies can be equated with sets of rules for performing diverse movement tasks. (...) The choice between SI and SS depends on whether movement speed and/or movement time (and hence appropriate muscle forces) must be constrained to meet task requirements. (3) The electromyogram can be interpreted as a low-pass filtered version of the controlling signal to the motoneuron pools. This controlling signal can be modelled as a rectangular excitation pulse in which modulation occurs in either pulse amplitude or pulse width. Movements to different distances and with loads are controlled by the SI strategy, which modulates pulse width. Movements in which speed must be explicitly regulated are controlled by the SS strategy, which modulates pulse amplitude. The distinction between the two movement strategies reconciles many apparent conflicts in the motor control literature. (shrink)

In the paper it will be shown that Reichenbach’s Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ , respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ and commuting with (...) the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models. (shrink)

Tsuda examines the potential contribution of nonlinear dynamical systems, with many degrees of freedom, to understanding brain function. We offer suggestions concerning symmetry and transients to strengthen the physiological motivation and theoretical consistency of this novel research direction: Symmetry plays a fundamental role, theoretically and in relation to real brains. We also highlight a distinction between chaotic “transience” and “itineracy.”.

Quantum degrees of freedom greatly enrich nonlinear systems, which can support nonlocal control and superposition of states. Basing my discussion on Yasue’s quantum brain dynamics, I suggest that the Cartesian subject is a cybernetic process rather than a substance: I am nonlocal control and my meanings are cybernetic variables. Meanings as nonlocal attunements are not mechanically determined, thus is it concluded we have freedom to mean.

Cognition means different things to different psychologists depending on the position held on the mind-matter problem. Ecological psychologists reject the implied mind-matter dualism as an ill-posed theoretic problem because the assumed mind-matter incommensurability precludes a solution to the degrees of freedom problem. This fundamental problem was posed by both Nicolai Bernstein and James J. Gibson independently. It replaces mind-matter dualism with animal-environment duality -- a better posed scientific problem because commensurability is assured. Furthermore, when properly posed this way, (...) a conservation law is suggested that encompasses a psychology of transactional systems, a biology of self-actional systems, and a physics of interactional systems. For such a solution, a theory of cognition for goal-directed behaviour is needed. A sketch is supplied for how such a theory might be pursued in the spirit of the new physics of evolving complex systems. (shrink)

The impossibility of an indeterministic evolution for standard relativistic quantum field theories, that is, theories in which all fields satisfy the condition that the generators of space-time translation have spectra in the forward light-cone, is demonstrated. The demonstration proceeds by arguing that a relativistically invariant theory must have a stable vacuum and then showing that stability of the vacuum, together with the requirements imposed by relativistic causality, entails deterministic evolution, if all degrees of freedom are standard degrees (...) of freedom. (shrink)

The minimum-uncertainty states for systems with many degrees of freedom are investigated. The limiting situation, relevant to the electromagnetic field, is discussed and it is pointed out that the states that minimize Δp Δq do not tend to the coherent states. These latter, including the vacuum state, are minimum-uncertainty states for the transverse electric and magnetic fields. In an appendix a direct method to obtain the wave functional for the vacuum is presented.

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

The Bell–Kochen–Specker theorem shows that, in any Hilbert space of dimension of at least 3, it is impossible to assign noncontextual definite values to all observables in such a way that the quantum-mechanical predictions are reproduced. This leaves open the issue of what subsets of observables may be assigned definite values. Clifton has shown that, for a system of at least two continuous degrees of freedom, it is not possible to assign simultaneous noncontextual values to two coordinates and (...) their conjugate momenta. In this Letter, it is shown that, for a system of a single continuous degree of freedom, it is not possible to assign noncontextual values to the coordinate and its conjugate momenta that satisfy a continuity assumption herein called the ‘ -Product Rule’.  2002 Elsevier Science B.V. All rights reserved. (shrink)

One of the most efficient nondestructive methods for pipeline in-line inspection is magnetic flux leakage inspection. Estimating the size of the defect from MFL signal is one of the key problems of MFL inspection. As the inspection signal is usually contaminated by noise, sizing the defect is an ill-posed inverse problem, especially when sizing the depth as a complex shape. An actor-critic structure-based algorithm is proposed in this paper for sizing complex depth profiles. By learning with more information from the (...) depth profile without knowing the corresponding MFL signal, the algorithm proposed saves computational costs and is robust. A pinning strategy is embedded in the reconstruction process, which highly reduces the dimension of action space. The pinning actor-critic structure helps to make the reward for critic network more efficient when reconstructing the depth profiles with high degrees of freedom. A nonlinear FEM model is used to test the effectiveness of algorithm proposed under 20 dB noise. The results show that the algorithm reconstructs the depth profile of defects with good accuracy and is robust against noise. (shrink)

A Greenberger, Horne and Zeilinger - type construction is realized in the position properties of three particles whose wave functions are distributed over three two - chambered boxes. The same system is modeled more realistically using three spatially separated, singly ionized hydrogen molecules.

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

We are told that we live in a scientific world. All about us are the fruits of scientific research, and the products of scientific industry. But, in spite of this transformation of our material surroundings, scientific thought, or the scientific method as such, has had no effect upon the everyday thought and behaviour of our people. To be sure, along with the scientific gadgets a few scientific truths have been disseminated. They know the earth is round and moves about the (...) sun; they could know that bacteria cause disease and that they are themselves descended from less articulate forms of animal life. Even when such conclusions are accepted, it is on the basis of authority with no understanding as to how they arose and on what basis they stand. For the large majority, science has merely acquired a cloak of respectability; it is a stronger magic than that of our forebears, and our modern alchemy is known as a powerful though mysterious source of pecuniary profit. (shrink)

Aboitiz et al. suggest that the mammalian isocortex is derived from the dorsal cortex of reptiles and birds, and that there has been a major divergence in the connectivity patterns (and hence function) of the mammalian and reptilian/avian hippocampus. There is considerable evidence to suggest, however, that the avian hippocampus serves the exact same function as the mammalian hippocampus.

In modern physics nonlinear systems with a lot of heterogeneity and anisotropy which are in strong fields and processes of crossings of electromechanical, spinor-mechanical, termo-magnetic and other ones are actual. Correct building with the help of mathematics of the given theories is possible only with the attraction geometry of the stratified spaces. The geometry of the stratified spaces chow its power by examining these systems and processes. Noncontradictional, covarianty theory of the single whole field of matter can be built only (...) with the attraction the geometry of the stratified spaces. Introduction the stratified spaces into physics of geometry is a continuation of works of Hamiltone, Langrange, Aler and other scientists. The problem is multivariate spaces of internal degrees offreedom. The ideas, positions of geometry of stratified spaces and their supplements demand a new philosophical sense of understanding. (shrink)