Zeno-machines And The Metaphysics Of Time

This paper aims to explore the nature of Zeno-machines by examining their conceptual coherence, from the perspective of contemporary theories on the passage of time. More specifically, it will analyse the following questions: Are Zeno-machines and supertasks coherent if we adopt the eternalist theory of time? What conclusions can be drawn from choosing the eternalist thesis, or the presentist thesis, when examining Zeno-machines? To this end, an overview of the opposing theories of time is provided, alongside the usual objections to Zeno-machines and their theoretical foundations from Zeno's dichotomy paradox.17216116

Zeno-machines and the metaphysics of time

This paper aims to explore the nature of Zeno-machines by examining their conceptual coherence, from the perspective of contemporary theories on the passage of time. More specifically, it will analyse the following questions: Are Zeno-machines and supertasks coherent if we adopt the eternalist theory of time? What conclusions can be drawn from choosing the eternalist thesis, or the presentist thesis, when examining Zeno-machines? To this end, an overview of the opposing theories of time is provided, alongside the usual objections to Zeno-machines and their theoretical foundations from Zeno’s dichotomy paradox.Keywords: Zeno-machines, philosophy of time, supertasks, Zeno’s paradox

What is morphological computation? On how the body contributes to cognition and control

The contribution of the body to cognition and control in natural and artificial agents is increasingly described as “off-loading computation from the brain to the body”, where the body is said to perform “morphological computation”. Our investigation of four characteristic cases of morphological computation in animals and robots shows that the ‘off-loading’ perspective is misleading. Actually, the contribution of body morphology to cognition and control is rarely computational, in any useful sense of the word. We thus distinguish (1) morphology that facilitates control, (2) morphology that facilitates perception and the rare cases of (3) morphological computation proper, such as ‘reservoir computing.’ where the body is actually used for computation. This result contributes to the understanding of the relation between embodiment and computation: The question for robot design and cognitive science is not whether computation is offloaded to the body, but to what extent the body facilitates cognition and control – how it contributes to the overall ‘orchestration’ of intelligent behavior

Indeterministic finite-precision physics and intuitionistic mathematics

In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin and Del Santo, which suggests that physical quantities can equivalently be thought of as being only determined up to finite precision at each point in time, and that doing so naturally leads to indeterminism. Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see, such attempts are thwarted by conceptual contradictions. Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics

On the Possibilities of Hypercomputing Supertasks

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation