Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the Weinberg-Salam theory of weak and electromagnetic interactions. It follows that internal symmetries of the weak interactions can be interpreted as space-time symmetries of spinor fields in the Dirac algebra. The possibilities for interpreting strong interaction symmetries in a similar way are highly restricted.

In this paper I analyze the temporal structures that are appropriate to study the notion of point of view. When we analyze the points of view and their structure, it seems clear that we must take into account the time t in which a point of view is attributed to a subject. A two-dimensional temporal logic which combines a modal dimension for possibilities and a temporal one for the flow of time, offers a clear view of the (...) temporary location of a point of view. In this logic, we have histories, thanks to the temporal dimension, and evaluation is in two indices, time and history. These stories can be seen as different scenarios, providing a clear advantage when applying to the analysis of the notion of point of view. The conclusion is that, in order to give a proper approach for the notion of point of view, all these aspects should be combined. (shrink)

It is proposed that quantum mechanical systems may spontaneously develop collective modes and other cooperative behavior which lead to a rich structuring of their Hilbert spaces and the consequent appearance ofobjective parameters for their description, in addition to the more familiar wave function description. The paper discusses the time evolution of these objective parameters, both the terms of non-unitary operators and through the dynamical effects of the quantum system's environment. A brief exploration is also made of the way in (...) which the objective parameters corresponding to two quantum systems can “measure” and interact with each other. The significance of a non-unitary time evolution for the origin of the universe is also discussed. (shrink)

At first sight the interrelation between the two main themes of this paper, time structuring and time measurement, seems to be simple enough. Time is something that we measure and that we measure with. But what is it that we measure and how is it constructed that we come to think of it as being measurable? As Leach has pointed out, in any society the prevailing ideas about the nature of time and space are closely linked (...) up with the kinds of measuring scales which are thought to be appropriate. If we alter the scales and dimensions with which we measure, we seem to alter the nature of that which is being measured, as well. (shrink)

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in (...) the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

This chapter contains sections titled: Coordinate Systems: Euclidean Space Invariant Quantities Classical Space‐times Special Relativity Consequences of the Lorentz Transformation Lorentz Invariant Quantities.

General relativity is commonly thought to imply the existence of a unique metric structure for space-time. A simple example is presented of a general relativistic theory with ambiguous metric structure. Brans-Dicke theory is then presented as a further example of a space-time theory in which the metric structure is ambiguous. Other examples of theories with ambiguous metrical structure are mentioned. Finally, it is suggested that several new and interesting philosophical questions arise from the sorts (...) of theories discussed. (shrink)

Gödel's conclusion that time-travel is possible in his models of Einstein's gravitational theory has been questioned by Chandrasekhar and Wright, and treated as doubtful in the recent philosophical literature. The present note is intended to remove this doubt: a review of Gödel's construction shows that his arguments are entirely correct; and the objection is seen to rest upon a misunderstanding. Computational points treated succinctly by Gödel are here presented in fuller detail. The philosophical significance of Gödel's results is briefly (...) considered, and a set of technical questions is posed whose answers would clarify this significance. (shrink)

An axiomatic foundation of a quantum theory for microsystems in the presence of external fields is developed. The space-time structure is introduced by considering the invariance of the theory under a kinematic invariance group. The formalism is illustrated by the example of charged particles in electromagnetic potentials. In the example, gauge invariance is discussed.

Published online: 01 Dec 2006 See pg. 7-9 of pdf to view this book review.

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three different accessibility (...) relations between spatio-temporal points. (shrink)

The two books discussed here make important contributions to our understanding of the role of spacetime concepts in physical theories and how that understanding has changed during the evolution of physics. Both emphasize what can be called a ‘dynamical’ account, according to which geometric structures should be understood in terms of their roles in the laws governing matter and force. I explore how the books contribute to such a project; while generally sympathetic, I offer criticisms of some historical claims concerning (...) Newton, and argue that the dynamical account does not undercut ontological issues as the books claim. (shrink)

The two books discussed here make important contributions to our understanding of the role of spacetime concepts in physical theories and how that understanding has changed during the evolution of physics. Both emphasize what can be called a ‘dynamical’ account, according to which geometric structures should be understood in terms of their roles in the laws governing matter and force. I explore how the books contribute to such a project; while generally sympathetic, I offer criticisms of some historical claims concerning (...) Newton, and argue that the dynamical account does not undercut ontological issues as the books claim. *Received January 2009; revised March 2009. †To contact the author, please write to: Department of Philosophy, 1423 University Hall MC 267, University of Illinois at Chicago, 601 S. Morgan Street, Chicago, IL 60607; e‐mail: [email protected]. (shrink)

The application of the general theory of relativity to the cosmological plane has led to a significant change in traditional notions on the space-time structure of the universe. This has been expressed in a new formulation and solution of cosmological problems such as that of a single world space and time, the problem of selection of a cosmological model for description of the universe, and the problem of the infinity of the universe.

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, (...) inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

The aim of this paper is to discuss the relation between the observation basis and the theoretical principles of General Relativity. More specifically, this relation is analyzed with respect to constructive axiomatizations of the observation basis of space-time theories, on the one hand, and in attempts to complete them, on the other. The two approaches exclude one another so that a choice between them is necessary. I argue that the completeness approach is preferable for methodological reasons.

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the (...) topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought. (shrink)

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

Time underlies many interesting human behaviors. Thus, the question of how to represent time in connectionist models is very important. One approach is to represent time implicitly by its effects on processing rather than explicitly (as in a spatial representation). The current report develops a proposal along these lines first described by Jordan (1986) which involves the use of recurrent links in order to provide networks with a dynamic memory. In this approach, hidden unit patterns are fed (...) back to themselves: the internal representations which develop thus reflect task demands in the context of prior internal states. A set of simulations is reported which range from relatively simple problems (temporal version of XOR) to discovering syntactic/semantic features for words. The networks are able to learn interesting internal representations which incorporate task demands with memory demands: indeed, in this approach the notion of memory is inextricably bound up with task processing. These representations reveal a rich structure, which allows them to be highly context‐dependent, while also expressing generalizations across classes of items. These representations suggest a method for representing lexical categories and the type/token distinction. (shrink)

In the existing expositions of the Károlyházy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.

Drawing on findings in psychology, neuroscience, and utilising the perspective of cognitive linguistics, this work argues that our experience of time may...

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural (...) realism. In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. (shrink)

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. (...) These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

The temporal structure of behavior contains a rich source of information about its dynamic organization, origins, and development. Today, advances in sensing and data storage allow researchers to collect multiple dimensions of behavioral data at a fine temporal scale both in and out of the laboratory, leading to the curation of massive multimodal corpora of behavior. However, along with these new opportunities come new challenges. Theories are often underspecified as to the exact nature of these unfolding interactions, and psychologists (...) have limited ready-to-use methods and training for quantifying structures and patterns in behavioral time series. In this paper, we will introduce four techniques to interpret and analyze high-density multi-modal behavior data, namely, to: (1) visualize the raw time series, (2) describe the overall distributional structure of temporal events (Burstiness calculation), (3) characterize the nonlinear dynamics over multiple timescales with Chromatic and Anisotropic Cross-Recurrence Quantification Analysis (CRQA), (4) and quantify the directional relations among a set of interdependent multimodal behavioral variables with Granger Causality. Each technique is introduced in a module with conceptual background, sample data drawn from empirical studies and ready-to-use Matlab scripts. The code modules showcase each technique’s application with detailed documentation to allow more advanced users to adapt them to their own datasets. Additionally, to make our modules more accessible to beginner programmers, we provide a “Programming Basics” module that introduces common functions for working with behavioral timeseries data in Matlab. Together, the materials provide a practical introduction to a range of analyses that psychologists can use to discover temporal structure in high-density behavioral data. (shrink)

Memory structures range across the dimensions that distinguish language-like thought. Recent work suggests agent- or situation-specific information is embedded in these structures. Understanding why this is, and pulling these structures apart, requires observing what happens under major changes. The evidence presented for the language-of-thought (LoT) does not look broadly enough across time to capture the function of representational structure.

Much of ordinary memory is autobiographical; memory of what one saw and did, where and when. It may derive from your own past experiences, or from what other people told you about your past life. It may be phenomenologically rich, redolent of that autumn afternoon so long ago, or a few austere reports of what happened. But all autobiographical memory is first-person memory, stateable using ‘I’. It is a memory you would express by saying, ‘I remember I . . .’.

In this paper I wish to make some headway on understanding what \emph{kind} of problem the ``problem of time'' is, and offer a possible resolution---or, rather, a new way of understanding an old resolution. The response I give is a variation on a theme of Rovelli's \emph{evolving constants of motion} strategy. I argue that by giving correlation strategies a \emph{structuralist} basis, a number of objections to the standard account can be blunted. Moreover, I show that the account I offer (...) provides a suitable ontology for time in both classical and quantum canonical general relativity. (shrink)

Originally published in 1980. What is time? How is its structure determined? The enduring controversy about the nature and structure of time has traditionally been a diametrical argument between those who see time as a container into which events are placed, and those for whom time cannot exist without events. This controversy between the absolutist and the relativist theories of time is a central theme of this study. The author's impressive arguments provide grounds (...) for rejecting both these theories, firstly by establishing that 'empty' time is possible, and secondly by showing, through a discussion of the structure of time which involves considering whether time might be cyclical, branching, beginning or non-beginning, that the absolutist theory of time is untenable. This book then advances two new theories, and succeeds in shifting the traditional debate about time to a consideration of time as a theoretical structure and as a theoretical framework. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at (...) least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

The theory of general relativity has produced some great insights into the nature of space and time. Unfortunately, its relevance to the problem of the direction of time has been overestimated. This paper points out that the problem of the direction of time can be formulated in purely local ways, and that in this kind of formulation considerations of general relativity are of little or no importance. On the basis of this, positions which assume that relativistic considerations (...) are always relevant are criticised. (shrink)