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The calculus story : a mathematical adventure
Calculus is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn. In this book, David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day.
Book
When Computers Were Human
Before Palm Pilots and iPods, PCs and laptops, the term \"computer\" referred to the people who did scientific calculations by hand. These workers were neither calculating geniuses nor idiot savants but knowledgeable people who, in other circumstances, might have become scientists in their own right. When Computers Were Human represents the first in-depth account of this little-known, 200-year epoch in the history of science and technology. Beginning with the story of his own grandmother, who was trained as a human computer, David Alan Grier provides a poignant introduction to the wider world of women and men who did the hard computational labor of science. His grandmother's casual remark, \"I wish I'd used my calculus,\" hinted at a career deferred and an education forgotten, a secret life unappreciated; like many highly educated women of her generation, she studied to become a human computer because nothing else would offer her a place in the scientific world. The book begins with the return of Halley's comet in 1758 and the effort of three French astronomers to compute its orbit. It ends four cycles later, with a UNIVAC electronic computer projecting the 1986 orbit. In between, Grier tells us about the surveyors of the French Revolution, describes the calculating machines of Charles Babbage, and guides the reader through the Great Depression to marvel at the giant computing room of the Works Progress Administration. When Computers Were Human is the sad but lyrical story of workers who gladly did the hard labor of research calculation in the hope that they might be part of the scientific community. In the end, they were rewarded by a new electronic machine that took the place and the name of those who were, once, the computers.
eBook
Paleo-proteomic analysis of Iron Age dental calculus provides direct evidence of Scythian reliance on ruminant dairy
The Scythians, often described as mounted horse-back warriors of the Iron Age steppe with lavish burial goods, have attracted increasing scientific interest over the past years. Recent genetic and multi-isotopic studies have uncovered that the ‘Scythians’ were neither a homogenous political nor a cultural group, but rather diverse populations of heterogeneous origins with intricate socio-political systems. Although populational differences in agro-pastoral subsistence regimes of Northern Black Sea Region groups have previously been identified through stable isotope analysis, it remains unclear which animal products were consumed. Here we investigate the dietary systems of two Scythian-era populations in present-day Ukraine using protein analysis of ancient dental calculus. Various dietary proteins and their taxonomic origin were identified revealing the consumption of milk from ruminant and equine species. This study supplements previous findings that Scythians engaged in complex, agro-pastoralist subsistence strategies in forest-steppe and steppe environments.
Journal Article
The calculus gallery : masterpieces from Newton to Lebesgue
More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be. -- From publisher's description.
BOOK
Microbial differences between dental plaque and historic dental calculus are related to oral biofilm maturation stage
Background
Dental calculus, calcified oral plaque biofilm, contains microbial and host biomolecules that can be used to study historic microbiome communities and host responses. Dental calculus does not typically accumulate as much today as historically, and clinical oral microbiome research studies focus primarily on living dental plaque biofilm. However, plaque and calculus reflect different conditions of the oral biofilm, and the differences in microbial characteristics between the sample types have not yet been systematically explored. Here, we compare the microbial profiles of modern dental plaque, modern dental calculus, and historic dental calculus to establish expected differences between these substrates.
Results
Metagenomic data was generated from modern and historic calculus samples, and dental plaque metagenomic data was downloaded from the Human Microbiome Project. Microbial composition and functional profile were assessed. Metaproteomic data was obtained from a subset of historic calculus samples. Comparisons between microbial, protein, and metabolomic profiles revealed distinct taxonomic and metabolic functional profiles between plaque, modern calculus, and historic calculus, but not between calculus collected from healthy teeth and periodontal disease-affected teeth. Species co-exclusion was related to biofilm environment. Proteomic profiling revealed that healthy tooth samples contain low levels of bacterial virulence proteins and a robust innate immune response. Correlations between proteomic and metabolomic profiles suggest co-preservation of bacterial lipid membranes and membrane-associated proteins.
Conclusions
Overall, we find that there are systematic microbial differences between plaque and calculus related to biofilm physiology, and recognizing these differences is important for accurate data interpretation in studies comparing dental plaque and calculus.
Journal Article
Vector : a surprising story of space, time, and mathematical transformation
\"The stars of the latest book by award-winning science writer and mathematician Robyn Arianrhod are unlikely celebrities--vectors and tensors. If you took a high school physics course, the word \"vector\" might remind you of the mathematics needed to determine forces on an amusement park ride, say; or of cross products, a special kind of multiplication using a bespoke table and a right-hand rule. You might also remember the introductory definition of a vector as a quantity that has magnitude and (this is the key) direction. Velocity--for example, 25 miles per hour northwest--is a vector; speed, such as 25 miles per hour, is not. Put another way, a velocity vector in space contains not one number, but three-a measurement of speed along each of three dimensions. It sounds simple, in hindsight--yet, as Arianrhod shows in this intriguing story, the idea of a single symbol expressing several things at once is a sophisticated one, millennia in the making. Vectors are examples of an even more sophisticated idea, the tensor. And it's not just space that vectors and tensors can represent, but information, too. Which means that whenever you use a search engine, say, or AI bot, computer graphics, or a host of other digital applications, vectors and tensors are there somewhere in the software. As for physics, there's much more to it than velocities and simple forces! Arianrhod shows how the discovery of vectors and tensors enabled physicists and mathematicians to think brand new thoughts-such as Maxwell did when he ushered in the wireless electromagnetic age, and Einstein when he predicted the curving of four-dimensional space-time and the existence of gravitational waves. Quantum theory, too, makes fine use of these ideas. In other words, vectors and tensors have been critical not only to the way we see our universe, but also to the invention of Wi-Fi, GPS, micro-technology, and so much else that we take for granted today. In exploring the history and significance of vectors and tensors-and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. A celebration of an idea, Vector shows the genius required to imagine the world in new dimensions-and how a clever mathematical construct can direct the future of discovery\"-- Provided by publisher.
BOOK
Insights into demographic and cultural influences on the oral microbiome from historical Japanese dental calculus
Recent advances in genomic technologies have enabled detailed analyses of ancient microbiomes using dental calculus. While most studies have focused on European and North American populations, ancient Japanese oral microbiomes remain largely unexplored. Here, we analyzed dental calculus primarily from Edo period individuals (17th–19th centuries) to investigate the compositional, functional, and phylogenetic diversity of ancient oral microbiomes. Our results revealed clear differences between ancient and modern Japanese microbiomes, as well as phylogenetic divergence between the Final Jomon (ca. 1000 BCE) and Edo periods. We also identified regional variation in ancient oral microbiomes and clade-level diversity within the periodontitis-associated archaeon
Methanobrevibacter oralis
. Interestingly, individuals with traces of tooth blackening (
ohaguro
), a custom practiced by Edo period women, were all assigned to the same clade, suggesting cultural influences on the oral microbiome. These findings highlight the important role of human culture and demography in shaping the evolutionary dynamics of microbiomes.
Journal Article
The tales teeth tell : development, evolution, behavior
\"Why do anthropologists study teeth? Teeth contain detailed records of growth, health, and diet, as well as our evolutionary history. So what are the tales teeth tell? The French naturalist George Cuvier famously remarked, \"Show me your teeth and I will tell you who you are.\" In this book, we will explore the intimate precision, striking beauty, and integrative power of incremental growth rhythms in teeth. We will also consider the surprising records of behavior that remain on their surfaces for millennia. For example, the plaque our hygienists carefully remove traps food particles, bacteria, and DNA from our own cells in a sticky layer that can fossilize over time into dental calculus. While calculus doesn't show the same faithful records as enamel and dentine, it captures human activity after our teeth finish growing, continuing the story of our behavior and health into adulthood and old age. We'll learn how complementary clues such as microscopic scratches and pits formed during chewing have spawned serious debates about the evolution of the human diet. And we'll see how evidence from teeth may point to the uniqueness of our own species, Homo sapiens, with our long childhoods, remarkably diverse diets, and complex behaviors\"-- Provided by publisher.
Book
Pathogens and host immunity in the ancient human oral cavity
Christina Warinner and colleagues report a high-resolution characterization of the oral microbiome isolated from the dental tissues of adult skeletons dating to 1100 CE and showing evidence of periodontal disease. They show the long-term carriage of a diverse range of opportunistic pathogens in the oral cavity and reconstruct the genome of the periodontal pathogen
Tannerella forsythia
.
Calcified dental plaque (dental calculus) preserves for millennia and entraps biomolecules from all domains of life and viruses. We report the first, to our knowledge, high-resolution taxonomic and protein functional characterization of the ancient oral microbiome and demonstrate that the oral cavity has long served as a reservoir for bacteria implicated in both local and systemic disease. We characterize (i) the ancient oral microbiome in a diseased state, (ii) 40 opportunistic pathogens, (iii) ancient human–associated putative antibiotic resistance genes, (iv) a genome reconstruction of the periodontal pathogen
Tannerella forsythia
, (v) 239 bacterial and 43 human proteins, allowing confirmation of a long-term association between host immune factors, 'red complex' pathogens and periodontal disease, and (vi) DNA sequences matching dietary sources. Directly datable and nearly ubiquitous, dental calculus permits the simultaneous investigation of pathogen activity, host immunity and diet, thereby extending direct investigation of common diseases into the human evolutionary past.
Journal Article