A Markovian slot machine and Parrondo's paradox

The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here, we evaluate the stationary distribution of the Markov chain, and this leads to a strong law of large numbers and a central limit theorem for the sequence of payouts. Following a suggestion of Pyke [In Mathematical Statistics and Applications: Festschrift for Constance van Eeden (2003) 185--216 Institute of Mathematical Statistics], we address the question of whether there exists a two-armed version of this ``one-armed bandit'' that obeys Parrondo's paradox. More precisely, is there such a machine with the property that the casino can honestly advertise that both arms are fair, yet when players alternate arms in certain random or nonrandom ways, the casino makes money in the long run? The answer is a qualified yes. Although this ``history-dependent'' game is conceptually simpler than the original such games of Parrondo, Harmer and Abbott [Phys. Rev. Lett. (2000) 85 5226--5229], it is nearly as complicated analytically, and open problems remain.Comment: Published in at http://dx.doi.org/10.1214/09-AAP653 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Future Tense

Nature - Humans - Past - Future - Presence - Absence These familiar terms are the stepping stones of thought that went into my thesis work. While some may pair these words together as dichotomies, I concentrate on the balancing act that exists between them. Since the first Industrial Revolution beginning in the mid-18th century, human activities have significantly altered the rest of the natural world. Other species have evolved in reaction to circumstances produced by human actions. Through my own observations of nature and research into how humans have impacted nature’s evolution, speculation began to swell as to what does the future look like? My thesis work presents found objects from human life intermingled with my own ceramic pieces that are inspired by nature but have elements of peculiarity. The relics represent a human existence and the ceramic components act as a symbol of other forms of life. These familiar, yet odd growth forms imply futurity, a continued existence. This futurity is stemming from a human element that is clearly from the past, combined with this altered view of nature. Are humans of the past too? Are these growths something of the future? At a fundamental level, the work I make as an artist is intended to imply that life will continue in some form, with or without us. My work evokes a glimpse of how things may evolve in the future in order to stress the importance of mindful consideration of how the decisions we make impact the environment

On McTaggart’s Theory of Time

J. McTaggart argues that the philosophical conception of time is constituted by the notions of fluid and static time. Since, on his view, neither notion is philosophically viable, he concludes that time is nothing but an illusion that arises from our distorted perception of essentially atemporal reality. In the paper, I argue that despite McTaggart’s failure to prove the unreality of time as such, he does succeed in establishing his lesser claim that the concept of fluid time is without any ontological import whatsoever

What is the ‘Future’ of Greek? Towards a Pragmatic Analysis

The paper investigates the problems related to futurity and modality in modern Greek. The discussion of Greek temporal future expressions is conducted with reference to relevant literature from the areas of English linguistics, cognitive studies and pragmatics. The focus is on the status of future-oriented expressions and the question whether they are primarily epistemic in nature, whether they are tense-based, or modality-based. It is argued that the future tense in Greek has a modal semantic base conveying epistemic modality and that the preferred future prospective reading is a pragmatic development of the semantic modal base. The author further suggests that the future reading is a kind of presumptive meaning which follows from the neo-Gricean Principle of Informativeness, known as the I-principle (Levinson 2000) being a generalised interpretation which does not depend on contextual information