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)

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)

We examine the interrelationships between analog computational modelling and analogue (physical) modelling. To this end, we attempt a regimentation of the informal distinction between analog and digital, which turns on the consideration of computing in a broader context. We argue that in doing so one comes to see that (scientific) computation is better conceptualised as an epistemic process relative to agents, wherein representations play a key role. We distinguish between two, conceptually distinct, kinds of representation that, we argue, (...) are both involved in each case of computing. Based on the semantic and syntactic properties of each of these representations, we put forward a new account of the distinction between analog and digital computing. We discuss how the developed account is able to explain various properties of different models of computation, and we finish by conceptually comparing analog computational modelling to analogue (scale) modelling. It is concluded that, contrary to the standard view, the two practices are orthogonal, differing both in their foundations and in the epistemic functions they fulfil. (shrink)

Recent years have seen an increasing amount of attention devoted to the subject of structural representation. Is there one type of structural representation or many? How do they differ from other types of representation? Are they really a genuine type of representation in the first place? All good questions, which I will address indirectly by arguing that structural representations are nothing more than analog representations. Understanding them as such provides some much needed theoretical clarity about this type of representation. (...) Typical analog representations (e.g., liquid thermometers or analog clocks) are often "one-dimensional;" the corresponding one-dimensional characterization of these representations can be extended into multiple dimensions, which elucidates the structure of more complex analog representations, such as photographs, maps, or three-dimensional models. However, this analysis applies to structural representations without remainder. The upshot is that we can directly apply what we have learned about analog representation to our understanding of structural representation, which, if not directly answering these recent questions, greatly adds to our theoretical resources for doing so. The analog wheel has already been invented; we need not reinvent it for structural representation. (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.

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)

This article intends to establish a comparison between technical analog objects—which were the objects of the epoch when the French philosopher Gilbert Simondon elaborated his philosophical reflection—and digital devices that emerged in the last few decades of the 1900s. First, I define the main features of Simondon’s technical objects in order to understand what the necessary conditions are for there to be technical progress, which is based on what he called the process of concretization. Then, I analyze the relationship (...) between digital objects—as understood by Yuk Hui—and digital devices that take over from analog objects, without necessarily presenting continuity in an evolutionary process. Finally, I intend to expose the role that both analog objects and digital devices play as mediators with the world in a digital era, and to address the question of technical culture nowadays. (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)

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)

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)

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)

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)

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)

In this study, a low-power analog integrated classifier for biomedical applications based on an ANN is introduced. The proposed architecture consists of four analog circuits as building blocks. All circuits operate in sub-threshold region in order to achieve low-power consumption. Post-layout simulations using the Cadence IC Suite and the TSMC 90 nm CMOS technology demonstrate that the proposed analog classifier operates properly with good sensitivity. The implemented classifier is trained using software and it is compared with related (...) classifiers. It can be used as a building block for biomedical monitoring. (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.

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)

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)

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)

This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. (...) Finally, it is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function. (shrink)

It will always remain a remarkable phenomenon in the history of philosophy, that there was a time, when even mathematicians, who at the same time were philosophers, began to doubt, not of the accuracy of their geometrical propositions so far as they concerned space, but of their objective validity and the applicability of this concept itself, and of all its corollaries, to nature. They showed much concern whether a line in nature might not consist of physical points, and consequently that (...) true space in the object might consist of simple [discrete] parts, while the space which the geometer has in his mind [being continuous] cannot be such. (shrink)

1.1 The predominant approach to cognitive modeling is still what has come to be called "computationalism" (Dietrich 1990, Harnad 1990b), the hypothesis that cognition is computation. The more recent rival approach is "connectionism" (Hanson & Burr 1990, McClelland & Rumelhart 1986), the hypothesis that cognition is a dynamic pattern of connections and activations in a "neural net." Are computationalism and connectionism really deeply different from one another, and if so, should they compete for cognitive hegemony, or should they collaborate? These (...) questions will be addressed here, in the context of an obstacle that is faced by computationalism (as well as by connectionism if it is either computational or seeks cognitive hegemony on its own): The symbol grounding problem (Harnad 1990). (shrink)

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space, cancer therapy up to the sky. This paper may be the first attempt towards such a complete description of the Universe based on classical wave equation of sound. It is argued that one can (...) arrive at a consistent description of space, elementary particles, Sachs-Wolfe acoustic theorem, up to a novel approach for cancer therapy, starting from this simple classical wave equation of sound. We also discuss a plausible extension of Acoustic Sachs-Wolfe theorem based on its analogue with Klein-Gordon equation to become Acoustic Sachs-Wolfe-Christianto-Smarandache-Umniyati (ASWoCSU) equation. It is our hope that the new proposed equation can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)

The traditional model theory of first-order logic assumes that the interpretation of a formula can be given without reference to its deductive context. This paper investigates an interpretation which depends on a formula's location within a derivation. The key step is to drop the assumption that all quantified variables must have the same range and to require only that the ranges of variables in a derivation must be related in such way as to preserve the soundness of the inference rules. (...) With each (consistent) derivation there is associated a Buridan-Volpin (orBV) structure [M, {r(x)}] which is simply a Tarski structureM for the language and a map giving the ranger(x) of each variablex in the derivation. IfLK* is (approximately) the classical sequent calculusLK of Gentzen from which the structural contraction rules have been dropped, then our main result reads: If a set of first-ordered formulas has a Tarski modelM, then from any normal derivationD inLK* of can be constructed aBV modelM D=[M, {r(x)}] of where each ranger(x) is finite. (shrink)