Representation is central to contemporary theorizing about the mind/brain. But the nature of representation--both in the mind/brain and more generally--is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received view is that analog representations vary smoothly, while digital representations vary in a step-wise manner. I argue that this characterization is inadequate to account for the ways in which representation is used in cognitive science; in its place, I (...) suggest an alternative taxonomy. I will defend and extend David Lewis's account of analog and digital representation, distinguishing analog from continuous representation, as well as digital from discrete representation. I will argue that the distinctions available in this four-fold account accord with representational features of theoretical interest in cognitive science more usefully than the received analog/digital dichotomy. (shrink)

Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of “analog” presupposed by these arguments for analog mental representation, and to open avenues for future research.

The distinction between analog and digital representation is reexamined; it emerges that a more fundamental distinction is that between symbolic and analog simulation. Analog simulation is analyzed in terms of a (near) isomorphism of causal structures between a simulating and a simulated process. It is then argued that a core concept, naturalistic analog simulation, may play a role in a bottom-up theory of adaptive behavior which provides an alternative to representational analyses. The appendix discusses some formal conditions for naturalistic analog (...) simulation. (shrink)

Newtonian and Machian aspects of the stationary gravitational field are brought into formal analogy with a stationary electromagnetic field. The electromagnetic vector potential equals (up to a factor) the timelike Killing vector field. The current density is given by the contraction of the Killing vector with the Ricci tensor. A coordinate-dependent split in electric and magnetic field vectors is given, and some results of classical electrodynamics are used to illustrate the analogy. In the linearized theory, the usual Maxwell equations are (...) obtained. The analogy also holds from the point of view of particle motion. The geodesic equation is brought into a special form that exhibits an analog to the Lorentz force. Two examples (which have played an important role in the theoretical discovery of Machian effects) are considered. (shrink)

The issue of symbol grounding is not essentially different in analog and digital computation. The principal difference between the two is that in analog computers continuous variables change continuously, whereas in digital computers discrete variables change in discrete steps (at the relevant level of analysis). Interpretations are imposed on analog computations just as on digital computations: by attaching meanings to the variables and the processes defined over them. As Harnad (2001) claims, states acquire intrinsic meaning through their relation to the (...) real (physical) environment, for example, through transduction. However, this is independent of the question of the continuity or discreteness of the variables or the transduction processes. (shrink)

In this paper, I argue for three claims. The first is that the difference between analog and digital representation lies in the format and not the medium of representation. The second is that whether a given system is analog or digital will sometimes depend on facts about the user of that system. The third is that the first two claims are implicit in Haugeland's (1998) account of the distinction.

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

Analog representation is often cast in terms of an engineering distinction between smooth and discrete systems. The engineering notion cuts across interesting representational categories, however, so it is poorly suited to thinking about kinds of representation. This paper suggests that analog representations support a pattern of interaction, specifically open-ended searches for content across levels of abstraction. They support the pattern by sharing a structure with what they represent. Continuous systems that satisfy the engineering notion are exemplars of this kind because (...) they are uninterpretable unless they are structure-preserving. Analog representations, so understood, include pictures, images, diagrams, and most graphs. This conception of analogicity also fits well with a line of thought about what makes perceptual states distinctive: they satisfy a “parts principle”. (shrink)

Characterizing different kinds of representation is of fundamental importance to cognitive science, and one traditional way of doing so is in terms of the analog–digital distinction. Indeed the distinction is often appealed to in ways both narrow and broad. In this paper I argue that the analog–digital distinction does not apply to representational schemes but only to representational systems, where a representational system is constituted by a representational scheme and its user, and that whether a representational system is analog or (...) non-analog depends on facts about that user. This aspect of the distinction has gone unnoticed, and I argue that the failure to notice it can be an impediment to scientific progress. (shrink)

Computationalism about the brain is the view that the brain literally performs computations. For the view to be interesting, we need an account of computation. The most well-developed account of computation is Turing Machine computation, the account provided by theoretical computer science which provides the basis for contemporary digital computers. Some have thought that, given the seemingly-close analogy between the all-or-nothing nature of neural spikes in brains and the binary nature of digital logic, neural computation could be a species of (...) digital computation. A few recent authors have offered arguments against this idea; here, I review recent findings in neuroscience that further cement the implausibility of this view. However, I argue that we can retain the view that the brain is a computer if we expand what we mean by “computation” to include analog computation. I articulate an account of analog computation as the manipulation of analog representations based on previous work on the difference between analog and non-analog representations, extending a view originally articulated in Shagrir :271–279, 2010). Given that analog computation constitutes a significant chapter in the history of computation, this revision of computationalism to include analog computation is not an ad hoc addition. Brains may well be computers, but of the analog kind, rather than the digital kind. (shrink)

In the 1980s, a number of philosophers argued that perception is analog. In the ensuing years, these arguments were forcefully criticized, leaving the thesis in doubt. This paper draws on Weber’s Law, a well-entrenched finding from psychophysics, to advance a new argument that perception is analog. This new argument is an adaptation of an argument that cognitive scientists have leveraged in support of the contention that primitive numerical representations are analog. But the argument here is extended to the representation of (...) non-numerical magnitudes, such as luminance and distance, and shown to apply to perception and not just cognition. The relevant sense of ‘analog’ is also clarified, and two powerful objections are addressed. Finally, the question whether perception’s analog vehicles are located in conscious experience is explored and related to a well-known controversy within psychophysics. (shrink)

Building on Christopher Peacocke’s account of analog perceptual contentand my own account of analog perceptual vehicles, I defend three claims: that theperception of magnitudes often has analog contents; that the perception of magni-tudes often has analog vehicles; and that the first claim is true in virtue of the second—that is, the analog vehicles help to ground the analog contents.

This encyclopaedia entry defines ‘analog(ue) photography’ as a construct of the digital age. After first situating the concept’s history in relation to that of the larger field of ‘the analog’, thereby exposing its connection to the American field of cybernetics, the entry describes how analog photography’s identity as a synonym for film was initially constructed and has subsequently evolved. Then it elaborates on the category’s formulation as a site of resistance to emerging technologies. Analog photography’s ongoing usage, the entry suggests, (...) is a testament to the way that information-age epistemologies have organized the shape and scope of the photographic field. (shrink)

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with computing, (...) which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine. (shrink)

It is fairly well-known that certain hard computational problems (that is, 'difficult' problems for a digital processor to solve) can in fact be solved much more easily with an analog machine. This raises questions about the true nature of the distinction between analog and digital computation (if such a distinction exists). I try to analyze the source of the observed difference in terms of (1) expanding parallelism and (2) more generally, infinite-state Turing machines. The issue of discreteness vs continuity will (...) also be touched upon, although it is not so important for analyzing these particular problems. (shrink)

The ‘received view’ of the analog–digital distinction holds that analog representations are continuous while digital representations are discrete. In this paper I first provide support for the received view by showing how it (1) emerges from the theory of computation, and (2) explains engineering practices. Second, I critically assess several recently offered alternatives, arguing that to the degree they are justified they demonstrate not that the received view is incorrect, but rather that distinct senses of the terms have become entrenched (...) specific fields, perhaps most notably in the cognitive psychology of mental imagery. (shrink)

Flanders will complete the migration from analog to digital terrestrial television by the end of 2008. Despite the cable dominated television landscape, the Flemish government is aiming at a smooth transition from analog to digital terrestrial television. Therefore, a multi-methodical study has been set up by order of the Flemish government to understand the specific features and needs of analog antenna viewers and their expectations for the analog switch-off. The study shows that there are three distinctive types of analog antenna (...) viewers. The results demonstrate that the antenna viewers are rather badly informed about the upcoming analog switch-off, which may lead to a negative attitude and may impede a smooth transition. Finally, antenna viewers seem to be rather conservative viewers: they wish to keep on watching the same television programs from the same channels. Moreover, digital terrestrial television is their preferred alternative. (shrink)

Digital and analog: What do these terms mean today? The use and meaning of such terms change through time. The analog, in particular, seems to go through various phases of popularity and disuse, its appeal pegged most frequently to nostalgic longings for nontechnical or romantic modes of art and culture. The definition of the digital vacillates as well, its precise definition often eclipsed by a kind of fever-pitched industrial bonanza around the latest technologies and the latest commercial ventures. One common (...) response to the question of the digital is to make reference to things like Twitter, Playstation, or computers in general. Here one might be correct, but only coincidentally, for the basic order of digitality (the digitality of digitality) has not yet been demonstrated through mere denotation. And the second question—the question of the analog—is harder still, with responses often also consisting of mere denotations of things: sound waves, the phonograph needle, magnetic tape, a sundial. At least denotation itself is analogical. This article will aim to define the analog explicitly and argue, perhaps counterintuitively, that the golden age of analog thinking was not a few decades past, prior to the wide-spread adoption of the computer. In fact, the fields of structuralism and poststructuralism that emerged in the middle to late twentieth century, concurrent with the deployment of the digital computer, were characteristically digital, what with their focus on the symbolic order and logical economies. If anything, the golden age of analog is happening today, all around us, as evidenced by the proliferation of characteristically analog concerns: sensation, materiality, experience, affect, ethics, and aesthetics. (shrink)

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term ‘analog-model’ (...) does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing task.Keywords: Computation; Computational neuroscience; Analog computers; Representation; Simulation. (shrink)

In their target article, Hutto and Satne eloquently articulate the failings of most current attempts to naturalize mental content. Furthermore, we think they are correct in their insistence that the only way forward is by drawing a distinction between two kinds of intentionality, one of which is considerably weaker than—and should be deployed to explain—the propositional variety most philosophers take for granted. The problem is that their own rendering of this weaker form of intentionality—contentless intentionality—is too weak. What’s needed is (...) a species of intentionality distinct from both the industrial-strength version beloved by philosophers and the intentionality lite recommended by Hutto and Satne. We briefly motivate and sketch this alternative, and say a few words about the account of cognition that it spawns. (shrink)

Church's thesis, that all reasonable definitions of “computability” are equivalent, is not usually thought of in terms of computability by acontinuouscomputer, of which the general-purpose analog computer (GPAC) is a prototype. Here we prove, under a hypothesis of determinism, that the analytic outputs of aC∞GPAC are computable by a digital computer.In [POE, Theorems 5, 6, 7, and 8], Pour-El obtained some related results. (The proof there of Theorem 7 depends on her Theorem 2, for which the proof in [POE] is (...) incorrect, but for which a correct proof is given in [LIR]. Also, the proof in [POE] of Theorem 8 depends on the unproved assertion that a solution of an algebraic differential equation must be analytic on an open subset of its domain. However, this assertion was later proved in [BRR].) As in [POE], we reduce the problem to a problem about solutions of certain systems of algebraic differential equations (ADE's). If such a system is nonsingular (i.e. if the “separant” does not vanish along the given solution), then the argument is very easy (see [VSD] for an even simpler situation), so that the essential difficulties arise fromsingularsystems. Our main tools in handling these difficulties are drawn from the excellent (and difficult) paper [DEL] by Denef and Lipshitz. The author especially wants to thank Leonard Lipshitz for his kind help in the preparation of the present paper.We emphasize here that our proof of the simulation result applies only to the GPAC as described below. The GPAC's form a natural subclass of the class of all analog computers, and are based on certain idealized components (“black boxes”), mostly associated with the technology of past decades. One can easily envisage other kinds of black boxes of an input-output character that would lead to different kinds of analog computers. (For example, one could incorporate delays, or spatial integrators in addition to the present temporal integrators, etc.) Whether digital simulation is possible for these “extended” analog computers poses a rich and challenging set of research questions. (shrink)

This seminar report discusses the low-voltage current-mode analog circuits and their various aspects. The need of high speed, high performance, low power circuits because of the advent of the portable electronic and mobile communication systems and difficulties faced in achieving that in today’s scenario are presented. Current mode circuits are the best suited candidates for the above. Their advantages are discussed here and a comparison with the conventional voltage mode circuits has been presented. The principle and the implementation of the (...) most common current mode circuits i.e. the current conveyors, has been described. The basic device level techniques also play important role in the design of smarter and efficient circuits. Some of those techniques have also been discussed here. For illustration of these techniques, low power V-I converter using current mirrors and a low- voltage power efficient operational amplifier cell topology is presented. (shrink)

Chaotic dynamics can be related to analog computation. A possibility of electronically implementing the chaos -driven contracting system in the target article is explored with an analog electronic circuit with inevitable noise from the viewpoint of analog computation with chaotic neurons.

We argue that living systems process information such that functionality emerges in them on a continuous basis. We then provide a framework that can explain and model the normativity of biological functionality. In addition we offer an explanation of the anticipatory nature of functionality within our overall approach. We adopt a Peircean approach to Biosemiotics, and a dynamical approach to Digital-Analog relations and to the interplay between different levels of functionality in autonomous systems, taking an integrative approach. We then apply (...) the underlying biosemiotic logic to a particular biological system, giving a model of the B-Cell Receptor signaling system, in order to demonstrate how biosemiotic concepts can be used to build an account of biological information and functionality. Next we show how this framework can be used to explain and model more complex aspects of biological normativity, for example, how cross-talk between different signaling pathways can be avoided. Overall, we describe an integrated theoretical framework for the emergence of normative functions and, consequently, for the way information is transduced across several interconnected organizational levels in an autonomous system, and we demonstrate how this can be applied in real biological phenomena. Our aim is to open the way towards realistic tools for the modeling of information and normativity in autonomous biological agents. (shrink)

This article investigates the analogy of the “laws of nature” through Graham Harman’s Object-Oriented Ontology (OOO) and Gilbert Simondon’s ontogenetic naturalism (ON). Both thinkers challenge the literalist interpretation of scientific knowledge by emphasizing the indirect nature of relation and the primacy of the autonomy of discrete beings over pre-established physical laws. Harman’s OOO defends this autonomy as the irreducible independence of objects from their relations, while Simondon focuses on the modulation of information in shaping the laws of nature through individuation. (...) The article argues that while science remains the best recursive triangulation between logic and empirical evidence, its grasp of an ultimate, literal Truth is constricted by an epistemological relation to autonomous realities, grounded in analogy. Consequently, the laws of nature are considered as legislated by discrete autonomies, with space and time emerging from the things themselves. The article concludes by discussing the consequences of this reframing in light of the ancient conception of díkēkosmos (cosmic justice). (shrink)

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by (...) examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

We live in an era characterized by technology as an integral part of the overall experiences. Non-hierarchic access to communication and virtual contacts in the metaverse, experienced as no less real than those in the brick-and-mortar world. The global health crisis has further highlighted the understanding that the integration of technology into our lives is inevitable, and when it comes to teaching and learning, the right use of technology can take teachers and learners to new, exciting places. The social distancing (...) regulations imposed worldwide provided educators with an opportunity to try out a variety of technological tools that enable surprising collaborations and access to information that encourages cognitive flexibility and a reexamination of our assumptions on knowledge, learning, teaching, human interaction, and space-time’s limitations. However, one great challenge within this ongoing transition concerns underprepared educators, feeling the pressure to make a successful shift while sustaining their educational inner compass regarding what constitutes adequate education. In this teacher’s self-study, I examined my teaching experience while teaching online. Informed by existing research, critical reflections, dialogue with a critical friend, a community of colleagues, and students’ artifacts, I inquire whether—and how—I can practice dialogical pedagogy while teaching online. (shrink)

This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having noisy (...) or fuzzy numerical content, it is suggested that the ANS has exquisitely precise numerical content that is subject to epistemic limitations. Similar considerations will arise for other analog representations. The chapter discusses how this new understanding of ANS representations recasts the learnability problem for number and the conceptual changes that children must accomplish in the number domain. (shrink)

The principle of bivalence is the assertion that every statement is either true or else false. Its legal analog, however, must be formulated relative to particular legal systems and in terms of validity rather than truth. It asserts that every statement of law that can be formulated in the vocabulary of a given legal system is valid or else invalid in that system. A line of New York cases is traced, beginning with Thomas v. Winchester . This case, which involved (...) a poison mislabeled as a medicine, established an exception to the rule that a manufacturer or supplier is never liable for negligence to a remote purchaser. The court made an exception because a poison is an “imminently dangerous” thing. How far may this exception be applied to other fact‐situations? Some subsequent cases are examined, and it is considered whether there is no correct answer in these instances and, more dramatically, whether more than one correct answer is tenable. In either event the legal analog of bivalence would seem to fail. (shrink)

A novel current-mode analog multiplier/divider based on voltage translinear principle is proposed, featuring favorable precision and wide dynamic range. It is suitable for VLSI implementation and can be successfully applied in a wide range of analog systems such as analog neural network and RMS-to-DC converter.