Choice reaction tasks are performed faster when stimulus location corresponds to response location. This spatial stimulus–response compatibility effect affects performance at the level of action planning and execution. However, when response selection is completed before movement initiation, the Simon effect arises only at the planning level. The aim of this study was to ascertain whether when a precocious response selection is requested, the Simon effect can be detected on the kinematics characterizing the online control phase of a non-ballistic movement. Participants (...) were presented with red or green colored squares, which could appear on the right, left, above, or below a central cross. Depending on the square's color, participants had to release one of two buttons, then reach toward and press a corresponding lateral pad. We found evidence of the Simon effect on both action planning and on-line control. Moreover, the investigation of response conflict at the level of previous trials, a factor that might determine interference at the level of the current response, revealed a conflict adaptation process across trials. Results are discussed in terms of current theories concerned with the Simon effect and the distinction between action planning and control. (shrink)

. Computational chemistry grew in a new era of “desktop modeling,” which coincided with a growing demand for modeling software, especially from the pharmaceutical industry. Parameterization of models in computational chemistry is an arduous enterprise, and we argue that this activity leads, in this specific context, to tensions among scientists regarding the epistemic opacity transparency of parameterized methods and the software implementing them. We relate one flame war from the Computational Chemistry mailing List in order to assess in detail (...) the relationships between modeling methods, parameterization, software and the various forms of their enclosure or disclosure. Our claim is that parameterization issues are an important and often neglected source of epistemic opacity and that this opacity is entangled in methods and software alike. Models and software must be addressed together to understand the epistemological tensions at stake. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations (...) of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition (...) of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR) (1982). Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, (...) we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check the three new mathematically emerged Relativities 4.3, 4.4, and 4.5. (shrink)

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant Λ is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When Λ→∞, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c→∞ is further considered, the kinematical group in this case being a modified Galilei (...) group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology. (shrink)

Janssen argues that special relativity is preferable to Lorentzian dynamics due to its kinematic structure. Brown, along with others, raises an objection, arguing that a dynamical understanding of special relativity is explanatorily prior and hence more fundamental than the principle theory-based kinematic structure of Minkowski spacetime. This paper challenges this objection, arguing that both Janssen and Brown miss the essential aspect of the principles of special relativity which underwrite its interpretational success. It is not its kinematic structure, (...) but the constitutive nature of the principles it employs, by providing a coherent conceptual framework, which does the foundational work. (shrink)

Many parameterized problems ask, given an instance and a natural number k as parameter, whether there is a solution of size k. We analyze the relationship between the complexity of such a problem and the corresponding maximality problem asking for a solution of size k maximal with respect to set inclusion. As our results show, many maximality problems increase the parameterized complexity, while “in terms of the W-hierarchy” minimality problems do not increase the complexity. We also address the corresponding construction, (...) listing, and counting problems. (shrink)

Parameterized complexity has, so far, been largely confined to consideration of computational problems as decision or search problems. However, it is becoming evident that the parameterized point of view can lead to new insight into counting problems. The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems.

Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.

Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove that (...) theory of mind reasoning, so formalized, indeed is intractable. Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind. (shrink)

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

Contextualism is the view that knowledge ascriptions – utterances of sentences containing the word “knows” - express different propositions in different contexts of utterance. But what features of context determine the propositions expressed by knowledge ascriptions? According to a version of contextualism I call conversational contextualism, the conversational dynamics or kinematics determine the propositions expressed by knowledge ascriptions. In this paper I argue that the most sophisticated version of conversational contextualism, which is the view defended by Michael Blome-Tillmann (2009; 2014), (...) faces serious problems. My (very) tentative conclusion will be that conversational contextualism should be abandoned because of these problems. (shrink)

It’s recently been argued that biological fitness can’t change over the course of an organism’s life as a result of organisms’ behaviors. However, some characterizations of biological function and biological altruism tacitly or explicitly assume that an effect of a trait can change an organism’s fitness. In the first part of the paper, I explain that the core idea of changing fitness can be understood in terms of conditional probabilities defined over sequences of events in an organism’s life. The result (...) is a notion of “conditional fitness” which is static but which captures intuitions about apparent behavioral effects on fitness. The second part of the paper investigates the possibility of providing a systematic foundation for conditional fitness in terms of spaces of sequences of states of an organism and its environment. I argue that the resulting “organism–environment history conception” helps unify diverse biological perspectives, and may provide part of a metaphysics of natural selection. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with _different results._ We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge of the domain of (...) discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when the conditions (...) for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution. (shrink)

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when the conditions (...) for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with different results. We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge of the domain of (...) discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Sparse languages play an important role in classical structural complexity theory. In this paper we introduce a natural definition of sparse problems for parameterized complexity theory. We prove an analog of Mahaney's theorem: there is no sparse parameterized problem which is hard for the tth level of the W hierarchy, unless the W hierarchy itself collapses up to level t. The main result is proved for the most general form of parametric many:1 reducibility, where the parameter functions are not assumed (...) to be recursive. This provides one of the few instances in parameterized complexity theory of a full analog of a major classical theorem. The proof involves not only the standard technique of left sets, but also substantial circuit combinatorics to deal with the problem of small weft, and a diagonalization to cope with potentially nonrecursive parameter functions. The latter techniques are potentially of interest for further explorations of parameterized complexity analogs of classical structural results. (shrink)

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)

Restricted and repetitive behavior is a core symptom of autism spectrum disorder characterized by features of restrictedness, repetition, rigidity, and invariance. Few studies have investigated how restrictedness is manifested in motor behavior. This study aimed to address this question by instructing participants to perform the utmost complex movement. Twenty children with ASD and 23 children with typical development performed one-dimensional, left-right arm oscillations by demonstrating varying amplitudes and frequencies. The entropy of amplitude and velocity was calculated as an index of (...) kinematic complexity. Results showed that the velocity entropy, but not the amplitude entropy, was significantly lower in ASD than in TD, suggesting restricted kinematics. Further analysis demonstrated that a significantly higher proportion of the velocity values was allocated at a low-speed level in the children with ASD. A qualitative comparison of the complex movement with movement at preferred frequency suggested that the children with ASD might be less likely to shift away from the preferred movement. However, our study can be improved in terms of recruiting a larger sample of participants, measuring the level of motivation, and collecting both complex and preferred movements of the same participant. (shrink)

A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and (...) class='Hi'>kinematic geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge. Key Words: internalization of regularities; kinematic geometry; simplicity. (shrink)

Dynamical systems play a central role in explanations in cognitive neuroscience. The grounds for these explanations are hotly debated and generally fall under two approaches: non-mechanistic and mechanistic. In this paper, I first outline a neurodynamical explanatory schema that highlights the role of dynamical systems in cognitive phenomena. I next explore the mechanistic status of such neurodynamical explanations. I argue that these explanations satisfy only some of the constraints on mechanistic explanation and should be considered pseudomechanistic explanations. I defend this (...) argument against three alternative interpretations of the neurodynamical explanatory schema. The independent interpretation holds that neurodynamical explanations and mechanisms are independent. The constitutive interpretation holds that neurodynamical explanations are constitutive but otherwise non-mechanistic. Both the independent and constitutive interpretations fail to account for all the features of neurodynamical explanations. The partial interpretation assumes that the targets of dynamical systems models are mechanisms and so holds that neurodynamical explanations are incomplete because they lack mechanistic details. I contend instead that the targets of those models are dynamical systems distinct from mechanisms and defend this claim against several objections. I conclude with a defense of the pseudomechanistic interpretation and a discussion of the source of their explanatory power in relation to a causal-mechanical description of the world. (shrink)

In De gravitatione, Newton contends that Descartes' physics is fundamentally untenable since the "fixed" spatial landmarks required to ground the concept of inertial motion cannot be secured in the constantly changing Cartesian plenum. Likewise, it is has often been alleged that the collision rules in Descartes' Principles of Philosophy undermine the "relational" view of space and motion advanced in this text. This paper attempts to meet these challenges by investigating the theory of connected gears (or "kinematics of mechanisms") for a (...) potential Cartesian method of positing the permanent reference frames necessary to uphold Descartes' conservation law for the quantity of motion. In particular, the insights gained from an examination of the kinematics of mechanisms will provide the Cartesian with much needed resources to counter the two threats posed above. (shrink)

Bayesian, Jeffrey and Field conditionals are compared and it is shown why the last two cannot be reduced to the first. Maximum relative entropy is used in two kinds of justification of the Field conditional and the dispensability of entropy principles in general is discussed.

Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in Parallax, published by and copyright Routledge.

Kinematic properties of reaching movements reflect constraints imposed on the joint angles. Contemporary models present solutions to the redundancy problem by a pseudoinverse procedure (Whitney 1969) or without any inversion (Berkenblit et al. 1986). Feldman & Levin suggest a procedure based on a regular inversion. These procedures are considered as an outcome of a more general approach.

Plamondon's kinematic theory is very powerful from a descriptive point of view. Unfortunately, the fact that it neglects some fundamental features of the motor system, such as nonlinear inertial torque interactions or joint redundancies, limits its explanatory power and biological validity. As a consequence, the data presented by Plamondon & Alimi should be analyzed and interpreted with caution. There appears to be a gap between the observations reported by the authors and some of the conclusions they draw.

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line (...) elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

ABSTRACTPrevious research has revealed a stable preference for words with inward consonantal-articulation patterns, over outward-words. Following the oral approach-avoidance account suggesting that the in–out effect is due to the resemblance between consonantal-articulations patterns and ingestion/expectoration, recent findings have shown that when judging inward-outward names for objects with particular oral functions, valence did not modulate the effect while the oral function did. To replicate and examine further the role of edibility and valence in shaping the in–out effect, we asked participants to (...) rate inward and outward names for edible and non-edible products while controlling for valence. Results revealed that the motor-to-affect link was only observed for edible products, regardless of valence. (shrink)

It has been established that the kinematics of the Voigt transformation, which lacks group structure, is different from that of the Lorentz transformation, and that the apparent kinematic asymmetry of the Voigt coordinate transformations may be understood as a conformally symmetric kinematics. Phenomena such as the kinetic energy of a moving body and the Doppler effect are not quite the same under the conformal Voigt transformation as they are for the usual theory developed with respect to the Lorentz group. (...) Yet the massenergy conservation law under the Voigt coordinate transformations and the mass-energy conservation law under the group of Lorentz transformations are identically the same. (shrink)

In Plamondon & Alimi's target article, a bell-shaped velocity profile typically observed in fast movements is used as a basis for the of motor control. In our opinion, kinematics is a necessary but insufficient ground for a theory of motor control. Relationships between different kinematic characteristics are an emergent property of the system dynamics controlled by the brain in a specific way. In particular, bell-shaped velocity profiles with or without additional waves are a trivial consequence of shifts in the (...) equilibrium state of the system as suggested, for example, in the [lambda]-model of motor control. (shrink)

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

The aim of the present study was to investigate the effect of observing other’s movements on subsequent performance in bottlenose dolphins. The imitative ability of non-human animals has intrigued a number of researchers. So far, however, studies in dolphins have been confined to intentional imitation concerned with the explicit request to imitate other agents. In the absence of instruction to imitate, do dolphins (un)intentionally replicate other’s movement features? To test this, dolphins were filmed while reaching and touching a stimulus before (...) and after observing another dolphin (i.e., model) performing the same action. All videos were reviewed and segmented in order to extract the relevant movements. A marker was inserted post-hoc via software on the videos upon the anatomical landmark of interest (i.e. rostrum) and was tracked throughout the time course of the movement sequence. The movement was analyzed using an in-house software developed to perform two-dimensional (2D) post-hoc kinematic analysis. The results indicate that dolphins’ kinematics is sensitive to other’s movement features. Movements performed for the ‘visuomotor priming’ condition were characterized by a kinematic pattern similar to that performed by the observed dolphin (i.e., model). Addressing the issue of spontaneous imitation in bottlenose dolphins might allow ascertaining whether the potential or impulse to produce an imitative action is generated, not just when they intend to imitate, but whenever they watch another conspecific’s behavior. In closing, this will clarify whether motor representational capacity is a by-product of factors specific to humans or whether more general characteristics such as processes of associative learning prompted by high level of encephalization could help to explain the evolution of this ability. (shrink)

To cover as much as possible the various questions raised by the commentators, I have divided my Response into three major sections. In section R1, I reply to the major comments and remarks dealing with the basic hypothesis upon which the kinematic theory is built (Plamondon 1993b; 1993c; 1995a; 1995b). I focus on linearity, determinism, kinematics, and the biological significance of the model parameters. I conclude this section by showing how, from a practical point of view, the delta-lognormal law (...) can be used to group similar data prior to proceeding with further statistical analysis. In section R2, I address the main comments and remarks dealing with the speed/accuracy tradeoffs. First, I focus on the origin of speed/accuracy tradeoffs and the effect of visual feedback. Then I clarify some terminology problems and mathematical misinterpretations prior to providing new support for the theory using the experiments and data referred to by some commentators. I devote section R3 to a generalization of the kinematic theory and to some potential applications. I first provide new explanations of some classical experiments; then I show how more complex movements can be analyzed using the delta-lognormal law. I focus on perturbed and oscillatory movements as well as on cursive script and signature analysis. I conclude this section and my Response by showing some possible applications to the study of movement learning in children as well as to the study of aging phenomena in movement control. I complete my Response by recalling some technical problems that still need further analysis. Throughout the text, I try to convince the reader that the kinematic theory provides a new window on old and new data in the field. (shrink)