Scientists of many disciplines use theoretical models to explain and predict the dynamics of the world. They often have to rely on digital computer simulations to draw predictions fromthe model. But to deliver phenomenologically adequate results, simulations deviate from the assumptions of the theoretical model. Therefore the role of simulations in scientific explanation demands itself an explanation. This paper analyzes the relation between real-world system, theoretical model, and simulation. It is argued that simulations do not explain processes in the (...) real world directly. The way in which simulations help explaining real-world processes is conceived as indirect, mediated by the theoretical model. Simulacra are characterized further, and turn out to be a priori measurable. This gives a clue to a better understanding of the epistemic role of computer simulations in scientific research. (shrink)

There are currently considerable confusion and disarray about just how we should view computationalism, connectionism and dynamicism as explanatory frameworks in cognitive science. A key source of this ongoing conflict among the central paradigms in cognitive science is an equivocation on the notion of computation simpliciter. ‘Computation’ is construed differently by computationalism, connectionism, dynamicism and computational neuroscience. I claim that these central paradigms, properly understood, can contribute to an integrated cognitive science. Yet, before this claim can be defended, (...) a better understanding of ‘computation’ is required. ‘Digital computation’ is an ambiguous concept. It is not just the classical dichotomy between analogue and digital computation that is the basis for the equivocation on ‘computation’ simpliciter in cognitive science, but also the diversity of extant accounts of digital computation. There are many answers on what it takes for a system to perform digital computation. Answers to this problem range from Turing machine computation, through the formal manipulation of symbols, the execution of algorithms and others, to the strong-pancomputational thesis, according to which every physical system computes every Turing-computable function. Despite some overlap among them, extant accounts of concrete digital computation are non-equivalent, thus, rendering ‘digital computation’ ambiguous. The objective of this dissertation is twofold. First, it is to promote a clearer understanding of concrete digital computation. Accordingly, my main thesis is that not only are extant accounts of concrete digital computation non-equivalent, but most of them are inadequate. I show that these accounts are not just intensionally different (this is quite trivially the case), but also extensionally distinct. In the course of examining several key accounts of concrete digital computation, I propose the instructional information processing account, according to which digital computation is the processing of discrete data in accordance with finite instructional information. The second objective is to establish the foundational role of computation in cognitive science whilst rejecting the purported representational nature of computation. (shrink)

Stevan Harnad correctly perceives a deep problem in computationalism, the hypothesis that cognition is computation, namely, that the symbols manipulated by a computational entity do not automatically mean anything. Perhaps, he proposes, transducers and neural nets will not have this problem. His analysis goes wrong from the start, because computationalism is not as rigid a set of theories as he thinks. Transducers and neural nets are just two kinds of computational system, among many, and any solution to the semantic (...) problem that works for them will work for most other computational systems. (shrink)

The concept of ‘digital phenotyping’ was originally developed by researchers in the mental health field, but it has travelled to other disciplines and areas. This commentary draws upon our experiences of working in two scientific projects that are based at the University of Oxford’s Big Data Institute – The RADAR-AD project and The Minerva Initiative – which are developing algorithmic phenotyping technologies. We describe and analyse the concepts of digital biomarkers and computational phenotyping that underlie these projects, explain (...) how they are linked to other research in digital phenotyping and compare and contrast some of their epistemological and ethical implications. In particular, we argue that the phenotyping paradigm in both projects is grounded on an assumption of ‘objectivity’ that is articulated in different ways depending on the role that is given to the computational/digital tools. Using the concept of ‘affordance’, we show how specific functionalities relate to potential uses and social implications of these technologies and argue that it is important to distinguish among them as the concept of digital phenotyping is increasingly being used with a variety of meanings. (shrink)

The distinction at the heart of van Gelder’s target article is one between digital computers and dynamical systems. But this distinction conflates two more fundamental distinctions in cognitive science that should be keep apart. When this conflation is undone, it becomes apparent that the “computational hypothesis” (CH) is not as dominant in contemporary cognitive science as van Gelder contends; nor has the “dynamical hypothesis” (DH) been neglected.

There are different ways to present a Presidential Address to the APA; the one I have chosen is simply to report on work that I am doing right now, on work in progress. I am going to present some of my further explorations into the computational model of the mind.\**.

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring (...) to digital computation simply adhere to Turing’s notion of computability . Classical computability theory studies what functions on the natural numbers are computable and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon . There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: (1) Turing’s account ; (2) The triviality “account”; (3) Reconstructing Smith’s account of participatory computation ; (4) The Algorithm Execution account . My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation. (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)

As a device used by scientists in the course of performing research, the digital computer might be considered a scientific instrument. But if so, what is it an instrument for? This paper explores a number of answers to this question, focusing on the use of computers in a simulating mode.

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)

ABSTRACTIs the brain a digital computer? What about your own brain? This article will examine these questions, some possible answers, and what persistent disagreement on the topic might indicate. Along the way we explore the metaphor at the heart of the question and assess how observer relativity features in it. We also reflect on the role of models in scientific endeavour. By the end you should have a sense of why the question matters, what some answers to it might (...) be, and why your preferred answer is highly pertinent to any discussion. (shrink)

What is nontrivial digital computation? It is the processing of discrete data through discrete state transitions in accordance with finite instructional information. The motivation for our account is that many previous attempts to answer this question are inadequate, and also that this account accords with the common intuition that digital computation is a type of information processing. We use the notion of reachability in a graph to defend this characterization in memory-based systems and underscore the importance (...) of instructional information for digital computation. We argue that our account evaluates positively against adequacy criteria for accounts of computation. (shrink)

Turing's analysis of the concept of computation is indisputably the foundation of computationalism, which is, in turn, the foundation of cognitive science. What is disputed is whether computationalism is explanatorily bankrupt. For Turing, all computers are digital computers and something becomes a computer just in case its 'behavior' is interpreted as implementing, executing, or satisfying some function 'f'. As 'computer' names a nonnatural kind, almost everyone agrees that a computational interpretation of this sort is necessary for something to (...) be a computer. But because everything in the universe satisfies at least one function, it is the sufficiency of such interpretations that is the problem. If, as anticomputationalists are fond of pointing out, computationalists are wedded to the view that a computational interpretation is sufficient for something to be a computer, then everything becomes a digital computer. This not only renders computer-talk vacuous, it strips computationalism of any empirical or explanatory import. My aim is to defend computationalism against charges that it is explanatorily bankrupt. I reexamine several fundamental questions about computers. One effect of this computation-related soul-searching will be a framework within which 'Is the brain a computer?' will be meaningful. Another effect will be a fracture in the supposed link between computationalism and symbolic-digital processing. (shrink)

I do not wish at this time to dispute either or. I do not believe, however, that the intermediate step can be adequately justified, and hence remain unconvinced by the purported conclusion. The most recent presentation of this argument is in Professor Dreyfus' article "Why Computers must have Bodies in order to be Intelligent," a discussion of which will serve to explain my lack of confidence in any argument of this general form.

It is common in cognitive science to equate computation (and in particular digital computation) with information processing. Yet, it is hard to find a comprehensive explicit account of concrete digital computation in information processing terms. An information processing account seems like a natural candidate to explain digital computation. But when ‘information’ comes under scrutiny, this account becomes a less obvious candidate. Four interpretations of information are examined here as the basis for an information (...) processing account of digital computation, namely Shannon information, algorithmic information, factual information and instructional information. I argue that any plausible account of concrete computation has to be capable of explaining at least the three key algorithmic notions of input, output and procedures. Whist algorithmic information fares better than Shannon information, the most plausible candidate for an information processing account is instructional information. (shrink)

Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence (the manifest causal effectiveness of application programs) to (...) occur. Although synchronic emergence of higher levels from lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables. (shrink)

Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence to occur. Although synchronic emergence of higher levels (...) from lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables. (shrink)

In 1965, John A. Pope presented a paper entitled 'Two-Dimensional Chart of Quantum Chemistry' to illustrate the inverse relationship between the sophistication of computational methods and the size of molecules under study. This chart, later called the 'hyperbola of quantum chemistry', succinctly summarized the growing tension between the proponents of two different approaches to computation–the ab initio method and semiempirical method–in the early years of electronic digital computers. Examining the development of quantum chemistry after World War II, I (...) focus on the role of computers in shaping disciplinary identity. The availability of high-speed computers in the early 1950s attracted much attention from quantum chemists, and their community took shape through a series of conferences and personal networking. However, this emerging community soon encountered the problem of communication between groups that differed in the degree of reliance they placed on computers. I show the complexity of interactions between computing technology and a scientific discipline, in terms of both forming and splitting the community of quantum chemistry. (shrink)

In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts. Ancient debates in natural philosophy on atomism versus the continuum are deeply involved in modern research on digital and computational physics. This example underlines that modern physics, in the tradition of Newton’s Principia Mathematica Philosophiae Naturalis, is a further development of natural philosophy with the rigorous methods of (...) mathematics, measuring, and computing. We consider fundamental concepts of natural philosophy with mathematical and computational methods and ask for their ontological and epistemic status. The following article refers to the author’s book, “The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy.”. (shrink)

Technologies of communication condition human sense-making. They do so by creating the social environment we inhabit and extending their structural biases and logics through human use. As such, this essay inquires into the prevailing habits of mind in the digital era. Employing a media ecology of communication, I argue that digital computers and microprocessors are defined by three structural properties and, hence, underlying logics: digitization (binary code), algorithmic execution (input/output), and efficiency (machine logic). Repeated exposure to these logics (...) cultivates a digital mind, a model of thinking, communicating, and sense-making characterized by intransigence, impertinence, and impulsivity. I conclude the essay by exploring the broader implications of a digital mind, paying particular attention to the challenges it poses to democratic politics. (shrink)

Our digital technologies have inspired new ways of thinking about old religious topics. Digitalists include computer scientists, transhumanists, singularitarians, and futurists. Digitalists have worked out novel and entirely naturalistic ways of thinking about bodies, minds, souls, universes, gods, and life after death. Your Digital Afterlives starts with three digitalist theories of life after death. It examines personality capture, body uploading, and promotion to higher levels of simulation. It then examines the idea that reality itself is ultimately a system (...) of self-surpassing computations. On that view, you will have infinitely many digital lives across infinitely many digital worlds. Your Digital Afterlives looks at superhuman bodies and infinite bodies. Thinking of nature in purely computational terms has the potential to radically and positively change our understanding of life after death. (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)

Recent findings indicate that the constituting digits of multi-digit numbers are processed, decomposed into units, tens, and so on, rather than integrated into one entity. This is suggested by interfering effects of unit digit processing on two-digit number comparison. In the present study, we extended the computational model for two-digit number magnitude comparison of Moeller, Huber, Nuerk, and Willmes (2011a) to the case of three-digit number comparison (e.g., 371_826). In a second step, we evaluated how hundred-decade and hundred-unit compatibility effects (...) were moderated by varying the percentage of within-hundred (e.g., 539_582) and within-hundred-and-decade filler items (e.g., 483_489). From the results we predict that numerical distance as well as compatibility effects should indeed be modulated by the relevance of tens and units in three-digit number magnitude comparison: While in particular the hundred distance effect should decrease, we predict hundred-decade and hundred-unit compatibility effects to increase with the relevance of tens and units. (shrink)