Old Game, New Rules: Rethinking The Form of Physics

We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wave-function in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.Comment: 23 pages, no figure

Abstract Interpretation of Supermodular Games

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework

Abstracting Nash equilibria of supermodular games

Supermodular games are a well known class of noncooperative games which find significant applications in a variety of models, especially in operations research and economic applications. Supermodular games always have Nash equilibria which are characterized as fixed points of multivalued functions on complete lattices. Abstract interpretation is here applied to set up an approximation framework for Nash equilibria of supermodular games. This is achieved by extending the theory of abstract interpretation in order to cope with approximations of multivalued functions and by providing some methods for abstracting supermodular games, thus obtaining approximate Nash equilibria which are shown to be correct within the abstract interpretation framework

Focusing in Asynchronous Games

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear logic, of very different flavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic

The logic of forbidden colours

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects

Sound for Fantasy and Freedom

Sound is an integral part of our everyday lives. Sound tells us about physical events in the environ- ment, and we use our voices to share ideas and emotions through sound. When navigating the world on a day-to-day basis, most of us use a balanced mix of stimuli from our eyes, ears and other senses to get along. We do this totally naturally and without effort. In the design of computer game experiences, traditionally, most attention has been given to vision rather than the balanced mix of stimuli from our eyes, ears and other senses most of us use to navigate the world on a day to day basis. The risk is that this emphasis neglects types of interaction with the game needed to create an immersive experience. This chapter summarizes the relationship between sound properties, GameFlow and immersive experience and discusses two projects in which Interactive Institute, Sonic Studio has balanced perceptual stimuli and game mechanics to inspire and create new game concepts that liberate users and their imagination

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc