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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Self Related Processing --- Self Information --- Self Reference Processing --- Self Cognition

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Science: general issues --- Psychology --- Self Related Processing --- Self Information --- Self Reference Processing --- Self Cognition

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The risk of physical accident or injury to humans from horses is well understood. Now, there is increasing awareness of negative impacts on the physical and mental wellbeing of horses from living in fundamentally human environments and being subject to human management regimes. The 17 articles in this collection describe horse-related risks to humans and human-related risks to horses across a range of equestrian disciplines, sectors and activities. Not only do the authors take detailed approaches towards describing and calculating risk, they suggest solutions-focussed interventions for reducing the consequence and likelihood of harm to horses and humans in their relations with one another. Together, these important articles provide strategies for maximising the mutual benefits of humans and horses in each other’s lives. By considering human, animal and environmental aspects of horse-related risk, this collection provides a foundation for the development of an ‘Equestrian One Health’ framework to underpin future research into horse-related risks.

Research & information: general --- Biology, life sciences --- Animals & society --- horse-riding --- risk --- mitigation --- culture --- research --- review --- safety --- behavior change --- eque-culture --- motivator --- equestrian --- horse --- injury --- helmet --- online forum --- barriers --- enablers --- injury prevention --- horse-rider --- road safety --- decision-making vehicle --- Australia --- jockey --- economic --- costs --- insurance --- horse-related --- accident --- student --- education --- veterinary --- bedding material --- respiratory health --- peat --- wood shaving --- thoroughbred --- horse-racing --- steeplechase --- hurdles --- animal-human relationships --- media --- public debate --- horse stable --- management --- web tool --- transport --- journey duration --- season --- human–horse risk --- context-specificity --- attention --- cognitive error --- self-reference --- horses --- eventing --- falls --- riders --- human−animal relationships --- human−horse relationships --- protective behavior --- equestrians --- horse-related accidents --- safety equipment --- multiple regression analysis --- ethology --- equitation science --- learning theory --- behaviour change --- fireworks --- anxiety --- behaviour --- fear --- people --- WHS --- deaths --- workplace --- horse racing

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In today's unpredictable and chaotic world, we look to science to provide certainty and answers--and often blame it when things go wrong. The Blind Spot reveals why our faith in scientific certainty is a dangerous illusion, and how only by embracing science's inherent ambiguities and paradoxes can we truly appreciate its beauty and harness its potential. Crackling with insights into our most perplexing contemporary dilemmas, from climate change to the global financial meltdown, this book challenges our most sacredly held beliefs about science, technology, and progress. At the same time, it shows how the secret to better science can be found where we least expect it--in the uncertain, the ambiguous, and the inevitably unpredictable. William Byers explains why the subjective element in scientific inquiry is in fact what makes it so dynamic, and deftly balances the need for certainty and rigor in science with the equally important need for creativity, freedom, and downright wonder. Drawing on an array of fascinating examples--from Wall Street's overreliance on algorithms to provide certainty in uncertain markets, to undecidable problems in mathematics and computer science, to Georg Cantor's paradoxical but true assertion about infinity--Byers demonstrates how we can and must learn from the existence of blind spots in our scientific and mathematical understanding. The Blind Spot offers an entirely new way of thinking about science, one that highlights its strengths and limitations, its unrealized promise, and, above all, its unavoidable ambiguity. It also points to a more sophisticated approach to the most intractable problems of our time.

Uncertainty (Information theory) --- Science --- Measure of uncertainty (Information theory) --- Shannon's measure of uncertainty --- System uncertainty --- Information measurement --- Probabilities --- Questions and answers --- Science and society --- Sociology of science --- Social aspects. --- Acknowledgment (creative arts and sciences). --- Algorithm. --- Ambiguity. --- Analogy. --- Approximation. --- Axiom. --- Axiomatic system. --- Basic research. --- Big O notation. --- Calculation. --- Certainty. --- Chaos theory. --- Circumference. --- Computation. --- Concept. --- Conjecture. --- Consciousness. --- Consistency. --- Contingency (philosophy). --- Continuous function. --- Continuum hypothesis. --- Contradiction. --- Counting. --- David Bohm. --- Dynamism (metaphysics). --- Emergence. --- Euclidean geometry. --- Explanation. --- Feeling. --- Fermat's Last Theorem. --- Geometry. --- Gestalt psychology. --- Gregory Chaitin. --- Gödel's incompleteness theorems. --- Human behavior. --- Human intelligence. --- Hypothesis. --- Ideology. --- Inference. --- Integer. --- Irrational number. --- Learning. --- Logic. --- Logical reasoning. --- Mathematician. --- Mathematics. --- Measurement. --- Methodology. --- Modernity. --- Molecule. --- Natural number. --- Nature. --- Paradigm shift. --- Paradox. --- Participant. --- Phenomenon. --- Philosopher. --- Philosophy of mathematics. --- Philosophy of science. --- Philosophy. --- Platonism. --- Prediction. --- Principle. --- Probability. --- Pythagoreanism. --- Qualitative property. --- Quantification (science). --- Quantity. --- Quantum mechanics. --- Randomness. --- Rational number. --- Rationality. --- Real number. --- Reality. --- Reason. --- Reductionism. --- Relationship between religion and science. --- Result. --- Science. --- Scientific method. --- Scientific progress. --- Scientific theory. --- Scientist. --- Self-reference. --- Set theory. --- Special case. --- Subatomic particle. --- Subjectivity. --- Suggestion. --- Technology. --- The Philosopher. --- Theorem. --- Theoretical physics. --- Theory of everything. --- Theory. --- Thomas Kuhn. --- Thought. --- Uncertainty. --- Universality (philosophy). --- Writing. --- Sociology of knowledge

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How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.

Proof theory. --- Mathematicians. --- Scientists --- Logic, Symbolic and mathematical --- Accuracy and precision. --- Addition. --- Aleph number. --- Algorithm. --- Analogy. --- Analysis. --- Archimedean property. --- Associative property. --- Axiom of choice. --- Axiom schema. --- Axiom. --- Bijection. --- Calculation. --- Certainty. --- Coefficient. --- Commutative property. --- Computability theory. --- Computability. --- Computable function. --- Computation. --- Constructible number. --- Constructive analysis. --- Continuous function (set theory). --- Corollary. --- Countable set. --- Credential. --- Dedekind cut. --- Desargues's theorem. --- Determinant. --- Direct proof. --- Equation. --- Equinumerosity. --- Estimation. --- Estimator. --- Extreme value theorem. --- Fundamental theorem. --- Gentzen's consistency proof. --- Geometry. --- Hypotenuse. --- Hypothesis. --- Identifiability. --- Inference. --- Infimum and supremum. --- Infinitesimal. --- Intermediate value theorem. --- Intuitionism. --- Logic. --- Logical connective. --- Mathematical induction. --- Mathematician. --- Mathematics. --- Maximal element. --- Natural number. --- Number theory. --- Obstacle. --- Ordinal number. --- Peano axioms. --- Permutation group. --- Permutation. --- Planarity. --- Playfair's axiom. --- Polygon. --- Polynomial. --- Power set. --- Predicate logic. --- Prediction. --- Prime factor. --- Prime number. --- Proof by infinite descent. --- Pythagorean theorem. --- Quantifier (logic). --- Quantity. --- Quaternion. --- Quintic function. --- Rational number. --- Real number. --- Reason. --- Recursively enumerable set. --- Rule of inference. --- Satisfiability. --- Self-reference. --- Sequence. --- Set theory. --- Special case. --- Staffing. --- Subsequence. --- Subset. --- Summation. --- Symbolic computation. --- Symmetry group. --- Theorem. --- Theory. --- Total order. --- Truth value. --- Turing machine. --- Unit square. --- Vector space. --- Well-order. --- Zorn's lemma.