We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another (...) type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω = ϵ0) in the Veblen hierarchy of ordinals. (shrink)

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to (...) Lev Beklemishev is also presented. (shrink)

Through a phenomenological study of horse-human relations, this article explores the ways in which, as embodied beings, we live relationally, rather than as separate human identities. Conceptually this challenges oppositional logic and humanist assumptions, but where poststructuralist treatments of these issues tend to remain abstract, this article is concerned with an embodied demonstration of the ways in which we experience a relational or in-between logic in our everyday lives.

We argue that pedagogic authority relies on love, which is misunderstood if seen as a matter of actions and subjects. Love is based not on finite subjects and objects existing in Euclidean space and linear time, but, rather, on the non-finite ontology, space and time of relations. Loving authority is a matter of calling and vocation, arising from the spontaneous and simultaneous call-and-response of a lively relation. We make this argument through a reading of Buber’s I–You relation and Murdoch’ s (...) account of the responsiveness of ascetic discipline. In presenting this analysis, we draw upon a case study from a research project on Australian teachers and students. (shrink)

Prior research suggests brokers do not always act in the best interests of clients, although morally obligated to do so. We empirically investigated this issue focusing on trades executed at best execution price, before and after the introduction of electronic limit-order trading, on the London Stock Exchange. As a result of limit-order trading, the proportion of trades executed at the best execution price for the customer significantly increased. We attribute this to a sustained increase in the liquidity of stocks as (...) a result of limit-order trading, regardless of market capitalisation. We discuss the ethical implications of our findings and conclude that market structures that enhance market competitiveness may help reconcile broker and client interests. (shrink)

This study examined the link between employees’ adult attachment orientations and perceptions of line managers’ interpersonal justice behaviors, and the moderating effect of national culture. Participants from countries categorized as low collectivistic and high collectivistic completed an online survey. Attachment anxiety and avoidance were negatively related to interpersonal justice perceptions. Cultural differences did not moderate the effects of avoidance. However, the relationship between attachment anxiety and interpersonal justice was non-significant in the Southern Asia cultural cluster. Our findings indicate the importance (...) of ‘fit’ between cultural relational values and individual attachment orientations in shaping interpersonal justice perceptions, and highlight the need for more non-western organizational justice research. (shrink)

Abstract In this article we develop a relational understanding of sociality, that is, an account of social life that takes relation as primary. This stands in contrast to the common assumption that relations arise when subjects interact, an account that gives logical priority to separation. We will develop this relational understanding through a reading of the work of Martin Buber, a social philosopher primarily interested in dialogue, meeting, relationship, and the irreducibility and incomparability of reality. In particular, the article contrasts (...) Buber’s work with that of poststructuralist theorists who take as their starting point the deconstruction of the Hegelian logic of binary oppositions. Deconstruction understands difference as the excess that undoes the binary, but Buber, we argue, shows how difference derives from the primacy and ontological undefinability of relation. Relational logic does not exclude the logic of separations and oppositions: relation is the primal ground that makes separations possible. Content Type Journal Article Pages 1-13 DOI 10.1007/s11841-011-0278-9 Authors Andrew Metcalfe, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Ann Game, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Journal Sophia Online ISSN 1873-930X Print ISSN 0038-1527. (shrink)

The mechanisms responsible for the fine tuning of development, where the wildtype phenotype is reproduced with high fidelity, are not well understood. The difficulty in approaching this problem is the identification of mutant phenotypes indicative of a defect in these fine‐tuning control mechanisms. Evolutionary biologists have used asymmetry as a measure of developmental homeostasis. The rationale for this was that, since the same genome controls the development of the left and right sides of a bilaterally symmetrical organism, departures from symmetry (...) can be used to measure genetic or environmental perturbations. This paper examines the relationship between asymmtry and resistance to organophosphorous insecticides in the Australian sheep blowfly, Lucilia cuprina. A resistance gene, Rop‐1, which encodes a carboxylesterase enzyme, also confers a significant increase in asymmetry. Continued exposure of resistant populations to insecticide has selected a dominant suppressor of the asymmetry phenotype. Genetic evidence indicates that the modifier is the L. cuprina Notch homologue. (shrink)

This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly universality and renormalization (...) issues in this context. Finally, we indicate how regularity properties of ordinal count functions can be used to prove logical limit laws. (shrink)

Class, Party, Social Movement - Class, « Race », Gender The ruling class is a hydra with two heads : “finance” and “elite”. The popular struggle for emancipation is thus not merely a confrontation between two classes. It is rather a game with three players. Itsultimate horizon is not “socialism”, a term which still carries the connotation of a “top-down” process,but “communism”. It presupposes the convergence between the apparently disparate conflicts whichare being played out in modern society. And, (...) to begin, the struggle calls for the deciphering – drawing on a concept from contemporary materialist feminism- of the “consubstiantiality” of the socialrelations of class, “race”, and gender. In such conditions, the party of emancipation is not merely aclass-based organisation. It is also, and equally, a feminist, an internationalist, and an ecological party.This party of social movement presupposes a “new ethos of party”. (shrink)

The beginning of the journey -- What this book is about : using ideas from mathematics, economics, and physics to tackle the big questions in philosophy : what is real? what can we know? what is the difference between right and wrong? and how should we live? -- Reality and unreality -- On what there is -- Why is there something instead of nothing? the best answer I have : mathematics exists because it must and everything else exists because it (...) is made of mathematics, with an excursion into artificial intelligence -- Unfinished business -- Unfinished business from chapter two : the nature and purpose of economic models -- How Richard Dawkins got it wrong -- Why Dawkins's argument against intelligent design can't be right and a mathematical analysis of the arguments for the existence of God -- Belief -- Daydream believers -- Most beliefs are ill-considered because most false beliefs are costless to hold -- The next several chapters will explore the consequences of this observation before we return to the question of where our beliefs and knowledge come from -- Unfinished business -- Unfinished business from the preceding chapter : how color vision works, sound, and water waves, the sheer craziness of economic protectionism -- Do believers believe? -- Our ill-considered beliefs about religion : why I believe that almost nobody is deeply religious -- On what there obviously is -- Our ill-considered beliefs about free will, ESP, and life after death -- Diogenes's nightmare -- How is legitimate disagreement possible if you're arguing with someone who is as intelligent and informed as you are, shouldn't you put just as much weight on your opponent's arguments as your own? -- The fact that we persist in disagreeing is strong evidence that we don't really care what's true -- Knowledge -- Knowing your math -- Where mathematical knowledge comes from and logic and why evidence and logic are not enough -- Unfinished business -- Unfinished business from the preceding chapter : the tale of hercules and the hydra, with an excursion into the lore of very large numbers -- Incomplete thinking -- Godel's incompleteness theorem and what it doesn't say about the limits of human knowledge -- The rules of logic and the tale of a Potbellied pig -- The power of logical thought, with excursions into the most counterintuitive theorem in all of mathematics and the tale of a potbellied pig -- The rules of evidence -- What we can and can't learn from evidence, with excursions into the value of preschool and how internet porn prevents rape -- The limits to knowledge -- What physics does and doesn't tell us about what we can and cannot know -- Understanding Heisenberg's uncertainty principle -- Unfinished business -- The oddness of the quantum world and why it matters to game theorists -- Right and wrong -- Telling right from wrong -- Some hard questions about right and wrong and about life and death -- The economist's golden rule -- A rule of thumb for good behavior -- How to be socially responsible -- Putting the rule of thumb into practice -- On not being a jerk -- Goofus and gallant on immigration policy -- The economist on the playground -- Our ill-considered beliefs about fairness in the market place and in the voting booth, contrasted with our carefully considered beliefs about fairness on the playground -- Unfinished business -- How ancient talmudic scholars anticipated modern economic theory -- The life of the mind -- How to think -- Some basic rules for clear thinking, mostly about economics, but also about arithmetic, neurobiology, sin, and eschewing blather -- What to study -- Advice to college students : stay away from the English department and approach the philosophy department with caution, with an excursion into the remarkable life of Frank Ramsey. (shrink)

Hydra are remarkable because they are immortal. Much of immortality can be ascribed to the asexual mode of reproduction by budding, which requires a tissue consisting of stem cells with continuous self‐renewal capacity. Emerging novel technologies and the availability of genomic resources enable for the first time to analyse these cells in vivo. Stem cell differentiation in Hydra is governed through the coordinated actions of conserved signaling pathways. Studies of stem cells in Hydra, therefore, promise critical insights (...) of general relevance into stem cell biology including cellular senescence, lineage programming and reprogramming, the role of extrinsic signals in fate determination and tissue homeostasis, and the evolutionary origin of these cells. With these new facts as a backdrop, this review traces the history of studying stem cells in Hydra and offers a view of what the future may hold. (shrink)

Is it ever morally wrong to enjoy fantasizing about immoral things? Many video games allow players to commit numerous violent and immoral acts. But, should players worry about the morality of their virtual actions? A common argument is that games offer merely the virtual representation of violence. No one is actually harmed by committing a violent act in a game. So, it cannot be morally wrong to perform such acts. While this is an intuitive argument, it does not resolve (...) the issue. -/- Focusing on why individual players are motivated to entertain immoral and violent fantasies, Video Games, Violence, and the Ethics of Fantasy advances debates about the ethical criticism of art, not only by shining light on the interesting and under-examined case of virtual fantasies, but also by its novel application of a virtue ethical account. Video games are works of fiction that enable players to entertain a fantasy. So, a full understanding of the ethical criticism of video games must focus attention on why individual players are motivated to entertain immoral and violent fantasies. -/- Video Games, Violence, and the Ethics of Fantasy engages with debates and critical discussions of games in both the popular media and recent work in philosophy, psychology, media studies, and game studies. (shrink)

The convergence of morphogenesis into viable organisms under variable conditions suggests closed‐loop dynamics involving multiscale functional feedback. We develop the idea that morphogenesis is based on synergy between mechanical and bio‐signaling processes, spanning all levels of organization: molecular, cellular, tissue, up to the whole organism. This synergy provides feedback within and between all levels of organization, to close the loop between the dynamics of the morphogenesis process and its robust functional outcome. Hydra offer a powerful platform to explore this (...) direction, thanks to their simple body plan, extraordinary regeneration capabilities, and the accessibility and flexibility of their tissues. Our recent experiments show that structural inheritance of the actomyosin organization directs body‐axis formation during Hydra regeneration. Morphogenesis is then stabilized through dynamic cytoskeletal reorganization induced by the inherited structure. The observed cytoskeletal stability and reorganization capabilities suggest that mechanical feedback integrates with biochemical processes to establish viable patterns and ensure canalization. (shrink)

Almost nobody favors long consent forms for prospective research subjects. Almost everybody thinks they interfere with informed consent’s purpose—good decisions. Nevertheless, almost everybody believes consent forms have long been getting longer. Years ago, Paul Appelbaum lamented the “tendency to cram ever more information into consent forms.”1 Weeks ago, Ilene Albala and her colleagues (one of them Appelbaum) reported in IRB: Ethics & Human Research that the length of one institutional review board’s forms “increased roughly linearly by an average of 1.5 (...) pages per decade. In the 1970s, the average consent form was less than one page long and often only a paragraph or two, but by the mid-1990s the .. (shrink)

The microbiome of human hair follicles (HFs) has emerged as an important player in different HF and skin pathologies, yet awaits in‐depth exploration. This raises questions regarding the tightly linked interactions between host environment, nutrient dependency of host‐associated microbes, microbial metabolism, microbe‐microbe interactions and host immunity. The use of simple model systems facilitates addressing generally important questions and testing overarching, therapeutically relevant principles that likely transcend obvious interspecies differences. Here, we evaluate the potential of the freshwater polyp Hydra, to (...) dissect fundamental principles of microbiome regulation by the host, that is the human HF. In particular, we focus on therapeutically targetable host‐microbiome interactions, such as nutrient dependency, microbial interactions and host defence. Offering a new lens into the study of HF – microbiota interactions, we argue that general principles of how Hydra manages its microbiota can inform the development of novel, microbiome‐targeting therapeutic interventions in human skin disease. (shrink)

The introductory personal remarks refer to my motivations for choosing research projects, and for moving from physics to molecular biology and then to development, with Hydra as a model system. Historically, Trembley’s discovery of Hydra regeneration in 1744 was the begin¬ning of developmental biology as we understand it, with passionate debates about preformation versus de novo generation, mechanisms versus organisms. In fact, seemingly conflicting bottom-up and top-down concepts are both required in combination to understand development. In modern terms, (...) this means analysing the molecules involved, as well as searching for physical principles underlying development within systems of molecules, cells and tissues. During the last decade, molecular biology has provided surprising and impressive evidence that the same types of mol¬ecules and molecular systems are involved in pattern formation in a wide range of organisms, including coelenterates like Hydra, and thus appear to have been “invented” early in evolution. Likewise, the features of certain systems, especially those of developmental regulation, are found in many different organisms. This includes the generation of spatial structures by the interplay of self-enhancing activation and “lateral” inhibitory effects of wider range, which is a main topic of my essay. Hydra regeneration is a particularly clear model for the formation of defined patterns within initially near-uniform tissues. In conclusion, this essay emphasizes the analysis of development in terms of physical laws, including the application of mathematics, and insists that Hydra was, and will continue to be, a rewarding model for understanding general features of embryogenesis and regeneration. -/- -/- . (shrink)

Scholarship has grown increasingly nuanced in its grappling with the intersections of religion, science, and technology but requires a new paradigm. Contemporary approaches to specific technologies reveal a wide variety of perspectives but remain too often committed to typological classification. To be vigilant of our obligation to understand and reveal, scholars in the study of religion, science, and technology can adopt a hydra‐logical stance: we can recognize that there are cultural monsters possessing scientific, technological, and religious heads. These heads (...) may work with a common agenda or they might not. They might disagree, pulling their shared body back and forth in a public commotion that lays waste to their surroundings. They might see past one another or move in tandem—purposively or not. Evaluations of climate response and AI benefit from seeing how the various heads are inseparable: indeed, cutting one off simply promotes the growth of new heads. Methodological and analytical clarity, therefore, emerges in the transition from schemes of classification to the recognition of hydras. (shrink)

Games occupy a unique and valuable place in our lives. Game designers do not simply create worlds; they design temporary selves. Game designers set what our motivations are in the game and what our abilities will be. Thus: games are the art form of agency. By working in the artistic medium of agency, games can offer a distinctive aesthetic value. They support aesthetic experiences of deciding and doing. -/- And the fact that we play games shows something (...) remarkable about us. Our agency is more fluid than we might have thought. In playing a game, we take on temporary ends; we submerge ourselves temporarily in an alternate agency. Games turn out to be a vessel for communicating different modes of agency, for writing them down and storing them. Games create an archive of agencies. And playing games is how we familiarize ourselves with different modes of agency, which helps us develop our capacity to fluidly change our own style of agency. (shrink)

Games may seem like a waste of time, where we struggle under artificial rules for arbitrary goals. The author suggests that the rules and goals of games are not arbitrary at all. They are a way of specifying particular modes of agency. This is what make games a distinctive art form. Game designers designate goals and abilities for the player; they shape the agential skeleton which the player will inhabit during the game. Game designers work in the (...) medium of agency. Game-playing, then, illuminates a distinctive human capacity. We can take on ends temporarily for the sake of the experience of pursuing them. Game play shows that our agency is significantly more modular and more fluid than we might have thought. It also demonstrates our capacity to take on an inverted motivational structure. Sometimes we can take on an end for the sake of the activity of pursuing that end. (shrink)

Deianira complains that Hercules, as a slave of Omphale, did not refrain from telling to the Lydian queen his famous labours; among them, the Hydra: quaeque redundabat fecundo vulnere serpens fertilis et damnis dives ab ipsa suis ‘It will be admitted that redundabat, which usually means to “overflow”’ can only be applied to the Hydra by a very strong metaphor; but it is not only a strong one, it is quite unexampled: so A. Palmer in The Academy 49 (...) , 160. But his own emendation rebellabat has not convinced anybody – rightly, as I think. Still, his remark was not otiose: redundabat refers to the ‘growing again’ of Hydra's heads, that seem to ‘spring’ from the wounds like water's spurts; it is not impossible, but nevertheless it is strange. Why does Ovid use this metaphor ‘a fluctibus desumpta’ here? I suggest that there is a precise reason: Ovid does not mention the name of the serpens, but of course his reader knows it and also knows why the Hydra is so called: πò τν δτων. (shrink)

Cells isolated from this freshwater polyp can aggregate and form a complete new animal. Experiments with the system lend support to a physico-chemical scheme for the creation of biological pattern.

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

Binmore argues that game theory provides a systematic tool for investigating ethical matters.

This article is the introduction of the volume The Many-Headed Hydra. The Hidden History of the Revolutionary Atlantic, to be published by Amsterdam, a historical investigation of the multi-ethnique class which formed the cheap workforce which made possible the rising of capitalism and of modern transatlantic economy, since the beginning of 17th century. A motley crowd made by merchants, pirates, workers, women, soldiers, convicted criminals, religious radicals, etc. developed forms of resistence and mutual cooperations, in order to escape the (...) deep exploitation of the workforce, taking place in an economy already globalised. The authors tell the story of the role played by these wretched of modern world and of their fight for liberty. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping (...) causal patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

• Aggregates of previously isolated cells of Hydra are capable, under suitable solvant conditions, of regeneration forming complete animals. In a first stage, ecto- and endodermal cells sort out, producing the bilayered hollow structure characteristic of Hydra tissue; thereafter, heads are formed (even if the original cell preparation contained no head cells), eventually leading to the separation of normal animals with head, body column and foot. Hydra appears to be the highest type of organism that allows for (...) regeneration of the entire structure from random cell aggregates. The system is particularly useful for studying cell interactions, tissue polarity, pattern formation, and cell differentiation. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)