A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes (...) the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology. (shrink)

Humans have undergone a long evolutionary history of violent agonistic exchanges, which would have placed selective pressures on greater body size and the psychophysical systems that detect them. The present work showed that greater body size in humans predicted increased knockout power during combative contests (Study 1a-1b: total N = 5,866; Study 2: N = 44 openweight fights). In agonistic exchanges reflective of ancestral size asymmetries, heavier combatants were 200% more likely to win against their lighter counterparts because they were (...) 200% more likely to knock them out (Study 2). Human dominance judgments (total N = 500 MTurkers) accurately tracked the frequency with which men (N = 516) knocked out similar-sized adversaries (Study 3). Humans were able to directly perceive a man’s knockout power because they were attending to cues of a man’s body size. Human dominance judgments—which are important across numerous psychological domains, including attractiveness, leadership, and legal decision-making—accurately predict the likelihood with which a potential mate, ally, or rival can incapacitate their adversaries. (shrink)

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e. those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with (...) continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss--Markov (``\OU'') processes and show how such \textit{OU networks} can express complex dynamic phenomena such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world. (shrink)

Over-flexibility in the definition of Friston blankets obscures a key distinction between observational and interventional inference. The latter requires cognizers form not just a causal representation of the world but also of their own boundary and relationship with it, in order to diagnose the consequences of their actions. We suggest this locates the blanket in the eye of the beholder.

The Democratic Republic of the Congo is facing two crises: a potentially explosive Ebola epidemic and a major insurgency. But they are not wholly distinct from each other: the first is intertwined with the second, and public mistrust and political violence add a dangerous dimension to the Ebola epidemic. The World Health Organization and other health emergency responders will increasingly find themselves fighting outbreaks in insecure, misgoverned or ungoverned zones, possibly experiencing active conflict. Yet the WHO has neither the mission (...) nor the capabilities to navigate these security threats. We cannot expect that the usual public health strategy will succeed when health workers’ lives are directly imperiled and community resistance runs deep. Tackling health emergencies amidst complex humanitarian crises requires fresh thinking. Here, we offer a blueprint for fighting diseases in complex humanitarian emergencies. The building blocks of security and trust include high‐level political support, street‐level diplomacy, community engagement, enhanced funding, and protection of health professionals working in conflict or disaster zones. (shrink)

The Patient Self-Determination Act (PSDA) requires hospitals to ask patients upon admission whether they have an advance directive. Although the PSDA has received extensive criticism, little attention has been paid to the cost of the law, either during its legislative course or following its implementation. Nonetheless, several tangible and intangible costs are associated with the PSDA. Such costs may be incurred by different parties. This paper examines the costs and benefits of the PSDA and illustrates the extent of some of (...) its tangible costs. The incremental start-up cost for one institution's response to the PSDA is estimated to be $49,304 ($1.31 per admission) and the total implementation cost of the program to be $114,528. In addition, the national incremental start-up cost for hospitals to implement the PSDA is estimated to be between $43,625,114 and $101,569,922. Finally, the potential implications of the PSDA for future governmental health care ethics regulation are discussed. (shrink)

We examine deceptive impression management's effect on a supervisor's ratings of promotability and relationship quality (i.e., leader-member exchange) via the mediating role of the supervisor's recognition of deception. Extending ego depletion theory using social information processing theory, we argue that deceptive impression management in a supervisor-subordinate relationship is difficult to accomplish and the degree that deception is detected will negatively impact desired outcomes. Data collected from a matched sample of 171 public sector employees and their supervisors supported this model and (...) indicated that recognition fully mediated the negative relationships between deceptive impression management with supervisor's rating of promotability and relationship quality. (shrink)

Generalization does not come from repeatedly observing phenomena in numerous settings, but from theories explaining what is general in those phenomena. Expecting future behavior to look like past observations is especially problematic in psychology, where behaviors change when people's knowledge changes. Psychology should thus focus on theories of people's capacity to create and apply new representations of their environments.

It is widely held that there is an important distinction between the notion of consciousness as it is applied to creatures and, on the other hand, the notion of consciousness as it applies to mental states. McBride has recently argued in this journal that whilst there may be a grammatical distinction between state consciousness and creature consciousness, there is no parallel ontological distinction. It is argued here that whilst state consciousness and creature consciousness are indeed related, they are distinct properties. (...) Conscious creatures can have, at one time, both conscious and unconscious mental states. This raises the question of what distinguishes the conscious from unconscious mental states of a subject: a question about what state consciousness consists in. Whilst the state/creature distinction may not be of use in explaining every aspect of a subject's consciousness, it does provide a key part of the explanandum for theories of consciousness and mind. The state/creature consciousness distinction is a real one and should not be dropped from our psychological taxonomy. (shrink)

Researchers from diverse disciplines, including organismal and cellular physiology, sports science, human nutrition, evolution and ecology, have sought to understand the causes and consequences of the surprising variation in metabolic rate found among and within individual animals of the same species. Research in this area has been hampered by differences in approach, terminology and methodology, and the context in which measurements are made. Recent advances provide important opportunities to identify and address the key questions in the field. By bringing together (...) researchers from different areas of biology and biomedicine, we describe and evaluate these developments and the insights they could yield, highlighting the need for more standardisation across disciplines. We conclude with a list of important questions that can now be addressed by developing a common conceptual and methodological toolkit for studies on metabolic variation in animals. (shrink)