In this paper we describe some first steps for bringing the framework of branching space-times (BST) to bear on quantum information theory. Our main application is quantum error correction. It is shown that BST offers a new perspective on quantum error correction: as a supplement to the orthodox slogan, “fight entanglement with entanglement”, we offer the new slogan, “fight indeterminism with indeterminism”.

In this paper, we study the lower semilattice of NP-subspaces of both the standard polynomial time representation and the tally polynomial time representation of a countably infinite dimensional vector space V∞ over a finite field F. We show that for both the standard and tally representation of V∞, there exists polynomial time subspaces U and W such that U + V is not recursive. We also study the NP analogues of simple and maximal subspaces. We show (...) that the existence of P-simple and NP-maximal subspaces is oracle dependent in both the tally and standard representations of V∞. This contrasts with the case of sets, where the existence of NP-simple sets is oracle dependent but NP-maximal sets do not exist. We also extend many results of Nerode and Remmel concerning the relationship of P bases and NP-subspaces in the tally representation of V∞ to the standard representation of V∞. (shrink)

We examine a condition in which units of time, such as months of the year, are associated with specific locations in space. For individuals with this time-space synaesthesia, contiguous time units such as months are spatially linked forming idiosyncratically shaped patterns such as ovals, oblongs or circles. For some individuals, each time unit appears in a highly specific colour. For instance, one of the synaesthetes we studied experienced December as a red area located at (...) arms length to the left of their body. For the same individual May was a blue area located roughly at arms length to the right of their body. We studied four synaesthetes who report spatial associations for the months of the year. We found that the time-space associations experienced by these individuals were consistent across test–retest. In addition, month names directed visual attention to particular locations in space. For some synaesthetes, this directing of spatial attention was quite rapid-in accord with their reports that month names involuntarily bring to mind spatial locations. (shrink)

There is no question, of course, that music is a temporal art. Stravinsky, noting that it is inconceivable apart from the elements of sound and time, classifies it quite simply as "a certain organization in time, a chrononomy."1 His definition stands as part of a long and honored tradition that encompasses such diverse figures as Racine, Lessing, and Schopenhauer. Schopenhauer, putting the case in its strongest terms, remarks that music is "perceived solely in and through time, to (...) the complete exclusion of space," thus making explicit the opposition between time and space and ruling out the latter as a possible area for legitimate musical experience. Yet anyone familiar with the philosophical and theoretical literature dealing with music must be struck by the persistence with which spatial terminology and categories appear. Indeed, it would seem to be impossible to talk about music at all without invoking spatial notions of one kind or another. Thus in discussing even the most elementary aspects of pitch organization—and among the musical elements, only pitch, we should remember, is uniquely musical—one finds it necessary to rely upon such spatially oriented oppositions as "up and down," "high and low," "small and large" , and so on. Space, then, pace Schopenhauer, apparently forms an inseparable part of the musical experience. · 1. Igor Stravinsky, Poetics of Music in the Form of Six Lessons, trans, Arthur Knodel and Ingolf Dahl , p. 28. Robert P. Morgan is active as both a music composer and theorist. A professor of music at the University of Chicago, he is currently composing a concerto for flute, oboe, and string orchestra to be performed at Swarthmore College. His previous contribution to Critical Inquiry, "On the Analysis of Recent Music," appeared in the Autumn 1977 issue. Anthony Gilbert responds to the current essay in "Musical Space: A Composer's View". (shrink)

What is the role of language in constructing knowledge? In this article, we ask whether learning new relational language can create new ways of thinking. In Experiment 1, we taught English speakers to talk about time using new vertical linguistic metaphors, saying things like “breakfast is above dinner” or “breakfast is below dinner”. In Experiment 2, rather than teaching people new metaphors, we relied on the left–right representations of time that our American college student participants have already internalized (...) through a lifetime of visuospatial experience reading and writing text from left to right. In both experiments, we asked whether the representations are susceptible to verbal interference. We found that learning new metaphors created new space–time associations that could be detected in a nonlinguistic implicit association task; these newly learned representations were not susceptible to verbal interference; and with respect to both verbal and visual interference, representations newly learned from linguistic metaphor behaved just like those on the left–right axis that our participants had acquired through years of visuospatial experience. Taken together, these results suggest that learning new relational language can be a powerful tool in constructing new representations and expanding our cognitive repertoire. (shrink)

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question (...) whether or not space-time is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space- (...) class='Hi'>time realism" pertains to modal scope. Constructivism takes a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

Is synaesthesia cognitively useful? Individuals with time–space synaesthesia experience time units as idiosyncratic spatial forms, and report that these forms aid them in mentally organising their time. In the present study, we hypothesised that time–space synaesthesia would facilitate performance on a time-related cognitive task. Synaesthetes were not specifically recruited for participation; instead, likelihood of time–space synaesthesia was assessed on a continuous scale based on participants’ responses during a semi-structured interview. Participants performed (...) a month-manipulation task, which involved naming every second month or every third month in reverse-chronological order, beginning and ending with a target month. Using hierarchical multiple regression, we found that time–space synaesthesia corresponded with faster performance on both versions of the task. We propose that time–space synaesthesia may expedite the cognitive manipulation of time-based information. Our results also indicate that synaesthesia is far less unusual than widely believed. (shrink)

A perverted space-time geodesy results from the notions of variable rods and clocks, which are taken to have their length and rates affected by the gravitational field. On the other hand, what we might call a concrete geodesy relies on the notions of invariable unit-measuring rods and clocks. In fact, this is a basic assumption of general relativity. Variable rods and clocks lead to a perverted geodesy in the sense that a curved space-time might be seen (...) as arising from the departure from the Minkowskian space-time as an effect of the gravitational field on the rate of clocks and the length of rods. In the case of a concrete geodesy we have “directly” a curved space-time whose curvature can be determined using (invariable) unit-measuring rods and clocks. In this paper, we will make the case for the plausibility that Einstein's views on geometry in relation to general relativity are permeated by a perverted geodesy. (shrink)

Roderich Tumulka’s GRWf theory offers a simple, realist and relativistic solution to the measurement problem of quantum mechanics. It is achieved by the introduction of a stochastic dynamical collapse of the wavefunction. An issue with dynamical collapse theories is that they involve an amendment to the Schrodinger equation; amending the dynamics of such a tried and tested theory is seen by some as problematic. This paper proposes an alteration to GRWf that avoids the need to amend the Schrodinger equation via (...) what might be seen as a primary set of solutions to the Schrodinger equation that satisfy a normalisation condition over space and time. The traditional Born-normalised solutions are shown to be conditionalisations of these primary solutions. (shrink)

Greenberger. Horne. Shimony, and Zeilinger gave a new version of the Bell theorem without using inequalities (probabilities). Mermin summarized it concisely; but Bohm and Hiley criticized Mermin's proof from contextualists' point of view. Using the branching space-time language, in this paper a proof will be given that is free of these difficulties. At the same time we will also clarify the limits of the validity of the theorem when it is taken as a proof that quantum mechanics (...) is not compatible with a deterministic world nor with a world that permits correlated space-related events without a common cause. (shrink)

It is taken for granted that the explanation of the Universe’s space-time dimension belongs to the host of the arguments that exhibit the superiority of modern (inflationary) cosmology over the standard model. In the present paper some doubts are expressed . They are based upon the fact superstring theory is too formal to represent genuine unification of general relativity and quantum field theory. Neveretheless, the fact cannot exclude the opportunity that in future the superstring theory can become more (...) physical. Hence this paper does not aim to query neither string cosmology, nor superstring theory; it asks for “tolerance in the matters cosmological”. It advices the researchers not to dwell on the common way of unification and to take into consideration the other ways as well. (shrink)

This paper interrogates Hölderlin's effort to deconstruct the speculative matrix of tragedy, with a particular focus on his "Remarks on Antigone," which are appended to his translation of the Sophoclean tragedy. In focus are, firstly, the separative force of the caesura, which stems tragic transport and is here analyzed, in terms of Hölderlin's understanding of Greece in relation to "Hesperia," as an incipiently Hesperian poetic gesture. Secondly, Hölderlin's key thought of the mutual "unfaithfulness" of God and man is at issue: (...) the god here is revealed as sheer time, while man is thrown back upon the bare moment. This "unfaithfulness" must be tempered by a striving that turns back from the quest for transcendence to the measures of fmitude and to this world. By attentiveness to the singular (which is not the particular), the tragic poet, unlike the speculative philosopher, reveals time's agonal spacing. (shrink)

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of \,\varpi )\), where \\) is a 1-form with coefficients in (...) the Lie algebra of the Poincaré group and \ is an 8-form with coefficients in the dual of this Lie algebra. The dynamical equations derive from a simple variational principle and imply that the 10-dimensional manifold looks locally like the total space of a fiber bundle over a 4-dimensional base manifold. Moreover this base manifold inherits a metric and a connection which are solutions of a system of Einstein–Cartan equations. (shrink)

Hardly any other problem has been discussed more than that of the status of time in modem physics. This is only natural since there are not many other more important problems in philosophy of science and in philosophy in general. There are also few other areas where controversies as well as confusion were more frequent. This is true not only of popular and semi-popular expositions of the Minkowski concept of space-time but also of a number of its (...) philosophical interpretations. Generally we do not find anything of this kind in the writings of physicists, at least as long as they confine themselves to strictly mathematical and physical expositions; but when they sometimes venture beyond a strictly mathematical approach, they often do not escape certain unconscious or semi-conscious prejudices which are contrary not only to the spirit but sometimes even to the letter of relativity. The true significance of the relativistic fusion of space and time can be understood only when we contrast it with its classical counterpart, i.e., with what may be called the Newtonian space-time. Only on such a contrasting background will the revolutionary meaning of the new concept clearly stand out. (shrink)

This paper begins by asking a simple question: can a farmer own and fully utilise precisely five tractors and precisely six tractors at the same time? Of course not. He can own five or he can own six but he cannot own five and six at the same. The answer to this simple question eventually led this author to Alfred Marshall's historically-ignored, linguistically-depicted 'cardboard model' where my goal was to construct a picture based on his written words. More precisely, (...) in this paper the overall goal is to convert Marshall's ('three-dimensional') words into a three-dimensional picture so that the full import of his insight can be appreciated by all readers. After a brief digression necessary to introduce Euclidean three-dimensional space, plus a brief digression to illustrate the pictorial problem with extant theory, the paper turns to Marshall's historically- ignored words. Specifically, it slowly constructs a visual depiction of Marshall's 'cardboard model'. Unfortunately (for all purveyors of extant economic theory), this visual depiction suddenly opens the door to all manner of Copernican heresy. For example, it suddenly becomes obvious that we can join the lowest points on a firm's series of SRAC curves and thereby form its LRAC curve; it suddenly becomes obvious that the firm's series of SRAC curves only appear to intersect because mainstream theory has naively forced our three-dimensional economic reality into a two-dimensional economic sketch; and it suddenly becomes obvious that a two-dimensional sketch is analytically useless because the 'short run' (SR) never turns into the 'long run' (LR) no matter how long we wait. (shrink)

We gratefully thank Filipa Matos Wunderlich for the permission to republish this text, which was first published in a shorter version in KOHT ja PAIK/PLACE and LOCATION Studies in Environmental Aesthetics and Semiotics VI, 2008.: Temporality is a fundamental characteristic of urban places. An attribute of nature, people and space, place-temporality consolidates and emerges out of their dynamic relationship in urban space. Temporality is place-specific and a result of compounds - Urbanisme – Nouvel article.

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

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)

This chapter contains section titled: Discussion.

A number of models of general relativity seem to contain “holes” that are thought to be “physically unreasonable.” One seeks a condition to rule out these models. We examine a number of possibilities already in use. We then introduce a new condition: epistemic hole-freeness. Epistemic hole-freeness is not just a new condition—it is new in kind. In particular, it does not presuppose a distinction between space-times that are “physically reasonable” and those that are not.