Hermann Grassmann's Ausdehnungslehre of 1844 and his Lehrbuch der Arithmetik of 1861 are landmark works in mathematics; the former not only developed new mathematical fields but also both contributed to the setting of modern standards of rigor. Their very modernity, however, may obscure features of Grassmann's view of the foundations of mathematics that were not adopted since. Grassmann gave a key role to the learning of mathematics that affected his method of presentation, including his emphasis on making initial assumptions explicit. (...) In order to better understand this less well-known aspect of his work it will help to examine why some commentators have overlooked his theme of unifying logic, pedagogy and foundations, while others have recognised it. (shrink)

C. S. Lewis takes us on a profound journey through both heaven and hell in this engaging allegorical tale. Using his extraordinary descriptive powers, Lewis introduces us to supernatural beings who will change the way we think about good and evil.

C. S. Lewis sets out to persuade his audience of the importance and relevance of universal values such as courage and honor in contemporary society.

Given a set of objects characterized by a number of attributes, hidden patterns can be discovered in them for the grouping of similar objects into clusters. If each of these clusters can be considered as exemplifying a certain concept, then the problem concerned can be referred to as a concept discovery problem. This concept discovery problem can be solved to some extent by existing data clustering techniques. However, they may not be applicable when the concept involved is vague in nature (...) or when the attributes characterizing the objects can be qualitative, quantitative, and fuzzy at the same time. To discover such concepts from objects with such characteristics, we propose a Genetic-Algorithm-based technique. By encoding a specific object grouping in a chromosome and a fitness measure to evaluate the cluster quality, the proposed technique is able to discover meaningful fuzzy clusters and assign membership degrees to objects that do not fully exemplify a certain concept. For evaluation, we tested the proposed technique with simulated and real data and the results are found to be very promising. (shrink)

Given a set of objects characterized by a number of attributes, hidden patterns can be discovered in them for the grouping of similar objects into clusters. If each of these clusters can be considered as exemplifying a certain concept, then the problem concerned can be referred to as a concept discovery problem. This concept discovery problem can be solved to some extent by existing data clustering techniques. However, they may not be applicable when the concept involved is vague in nature (...) or when the attributes characterizing the objects can be qualitative, quantitative, and fuzzy at the same time. To discover such concepts from objects with such characteristics, we propose a Genetic-Algorithm-based technique. By encoding a specific object grouping in a chromosome and a fitness measure to evaluate the cluster quality, the proposed technique is able to discover meaningful fuzzy clusters and assign membership degrees to objects that do not fully exemplify a certain concept. For evaluation, we tested the proposed technique with simulated and real data and the results are found to be very promising. (shrink)

C. S. Lewis sets out to persuade his audience of the importance and relevance of universal values such as courage and honor in contemporary society.

A repackaged edition of the revered author's classic work that examines the four types of human love: affection, friendship, erotic love, and the love of God—part of the C. S. Lewis Signature Classics series. C.S. Lewis—the great British writer, scholar, lay theologian, broadcaster, Christian apologist, and bestselling author of Mere Christianity, The Screwtape Letters, The Great Divorce, The Chronicles of Narnia, and many other beloved classics—contemplates the essence of love and how it works in our daily lives in one of (...) his most famous works of nonfiction. Lewis examines four varieties of human love: affection, the most basic form; friendship, the rarest and perhaps most insightful; Eros, passionate love; charity, the greatest and least selfish. Throughout this compassionate and reasoned study, he encourages readers to open themselves to all forms of love—the key to understanding that brings us closer to God. (shrink)

C. S. Lewis sets out to disentangle this knotty issue but wisely adds that in the end no intellectual solution can dispense with the necessity for patience and ...

Despite a large and multifaceted effort to understand the vast landscape of phenotypic data, their current form inhibits productive data analysis. The lack of a community-wide, consensus-based, human- and machine-interpretable language for describing phenotypes and their genomic and environmental contexts is perhaps the most pressing scientific bottleneck to integration across many key fields in biology, including genomics, systems biology, development, medicine, evolution, ecology, and systematics. Here we survey the current phenomics landscape, including data resources and handling, and the progress that (...) has been made to accurately capture relevant data descriptions for phenotypes. We present an example of the kind of integration across domains that computable phenotypes would enable, and we call upon the broader biology community, publishers, and relevant funding agencies to support efforts to surmount today's data barriers and facilitate analytical reproducibility. (shrink)

On the occasion of the 50th anniversary of C. S. Lewis’s death, a special annotated edition of his Christian classic, The Screwtape Letters, with notes and excerpts from his other works that help illuminate this diabolical masterpiece. Since its publication in 1942, The Screwtape Letters has sold millions of copies worldwide and is recognized as a milestone in the history of popular theology. A masterpiece of satire, it offers a sly and ironic portrayal of human life and foibles from the (...) vantage point of Screwtape, a highly placed assistant to “Our Father Below.” At once wildly comic, deadly serious, and strikingly original, The Screwtape Letters comprises the correspondence of the worldly-wise devil Screwtape and his nephew Wormwood, a novice demon in charge of securing the damnation of an ordinary young man. For the first time, The Screwtape Letters will be presented in full-text accompanied by helpful annotations in a striking two-color format. These annotations will give fans a deeper, more nuanced understanding of the popular book, providing background information, explanations of terms, historical significance, and excerpts from Lewis’s other works that more fully explain the ideas in this volume. For both expert Lewis fans and casual readers, The Screwtape Letters: Annotated Edition will be a beautiful and insightful guide to a beloved classic. (shrink)

A repackaged edition of the revered author’s spiritual memoir, in which he recounts the story of his divine journey and eventual conversion to Christianity. C. S. Lewis—the great British writer, scholar, lay theologian, broadcaster, Christian apologist, and bestselling author of Mere Christianity, The Screwtape Letters, The Great Divorce, The Chronicles of Narnia, and many other beloved classics—takes readers on a spiritual journey through his early life and eventual embrace of the Christian faith. Lewis begins with his childhood in Belfast, surveys (...) his boarding school years and his youthful atheism in England, reflects on his experience in World War I, and ends at Oxford, where he became "the most dejected and reluctant convert in all England." As he recounts his lifelong search for joy, Lewis demonstrates its role in guiding him to find God. (shrink)

Biological ontologies are used to organize, curate, and interpret the vast quantities of data arising from biological experiments. While this works well when using a single ontology, integrating multiple ontologies can be problematic, as they are developed independently, which can lead to incompatibilities. The Open Biological and Biomedical Ontologies Foundry was created to address this by facilitating the development, harmonization, application, and sharing of ontologies, guided by a set of overarching principles. One challenge in reaching these goals was that the (...) OBO principles were not originally encoded in a precise fashion, and interpretation was subjective. Here we show how we have addressed this by formally encoding the OBO principles as operational rules and implementing a suite of automated validation checks and a dashboard for objectively evaluating each ontology’s compliance with each principle. This entailed a substantial effort to curate metadata across all ontologies and to coordinate with individual stakeholders. We have applied these checks across the full OBO suite of ontologies, revealing areas where individual ontologies require changes to conform to our principles. Our work demonstrates how a sizable federated community can be organized and evaluated on objective criteria that help improve overall quality and interoperability, which is vital for the sustenance of the OBO project and towards the overall goals of making data FAIR. Competing Interest StatementThe authors have declared no competing interest. (shrink)