Bringing together scholars from around the world, this collection examines many of the historical developments in making data visible through charts, graphs, thematic maps, and now interactive displays. Today, we are used to seeing data portrayed in a dizzying array of graphic forms. Virtually any quantified knowledge, from social and physical science to engineering and medicine, as well as business, government, or personal activity, has been visualized. Yet the methods of making data visible are relatively new innovations, most stemming from eighteenth- and nineteenth-century innovations that arose as a logical response to a growing desire to quantify everything-from science, economics, and industry to population, health, and crime. Innovators such as Playfair, Alexander von Humboldt, Heinrich Berghaus, John Snow, Florence Nightingale, Francis Galton, and Charles Minard began to develop graphical methods to make data and their relations more visible. In the twentieth century, data design became both increasingly specialized within new and existing disciplines-science, engineering, social science, and medicine-and at the same time became further democratized, with new forms that make statistical, business, and government data more accessible to the public. At the close of the twentieth century and the beginning of the twenty-first, an explosion in interactive digital data design has exponentially increased our access to data. The contributors analyze this fascinating history through a variety of critical approaches, including visual rhetoric, visual culture, genre theory, and fully contextualized historical scholarship.

The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance children′s learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing children′s number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes: a clearly defined purpose detailed instructions, activities, learning tasks and reinforcing games lists of responses which children may make application in whole class, small group and individualised settings a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each country′s numeracy strategy. Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.

In Numerals in Early Greek New Testament Manuscripts, Zachary J. Cole provides the first in-depth examination of the seemingly obscure, yet important topic: how early Christian scribes wrote numbers and why. While scholars have long been aware that Christian scribes occasionally used numerical abbreviations in their books, few have been able to make much sense of it. This detailed analysis of numerals in manuscripts up through the fifth century CE uncovers a wealth of palaeographical and codicological data. Among other findings, Zachary J. Cole shows that some numerals can function as “visual links” between witnesses, that numbers sometimes—though rarely—functioned like nomina sacra, and that Christians uniquely adapted their numbering system to suit the needs of public reading.

Shapes of Time explores how concepts of time and history were spatialized in early twentieth-century German thought. Michael McGillen locates efforts in German modernism to conceive of alternative shapes of time—beyond those of historicism and nineteenth-century philosophies of history—at the boundary between secular and theological discourses. By analyzing canonical works of German modernism—those of Karl Barth, Franz Rosenzweig, Siegfried Kracauer, and Robert Musil—he identifies the ways in which spatial imagery and metaphors were employed to both separate the end of history from a narrative framework and to map the liminal relation between history and eschatology. Drawing on theories and practices as disparate as constructivism, non-Euclidean geometry, photography, and urban architecture, Shapes of Time presents original connections between modernism, theology, and mathematics as played out within the canon of twentieth-century German letters. Concepts of temporal and spatial form, McGillen contends, contribute to the understanding not only of modernist literature but also of larger theoretical concerns within modern cultural and intellectual history.

How do we really think about the world? We may use words to tell stories about it or draw pictures to represent it, but one thing we do far more than either of those is make calculations of the things that are in it—and to do that we use numbers. Numbers give shape and texture to almost everything we feel, say, dream, and do, a fact that Steven Connor explores in this qualitative assessment of the quantifiable. Looking at how numbers play a part in nearly every aspect of our lives, he offers a fascinating portrait of the world as a world of numbers. Connor explores a host of thought-provoking aspects of our numerical existence. He looks at the unexpected oddities that shape the loneliest number—the number one. He looks at counting as a human phenomenon and the ways we negotiate crowds, swarms, and multitudes. He demonstrates the work of calculation as it lies at the heart of poetry, jokes, painting, and music. He shows how we use numbers to adjust to uncertainty and chance and how they help us visualize the world in diagrammatic ways, and he unveils how numbers even help us think about death. Altogether, Connor brings into relief an aspect of our lives so ubiquitous that we often can’t see it, unveiling a rich new way of thinking about our existence.

In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career. Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.