There's a lot for astronomers to be smug about. But when it comes to understanding how the Universe began and grew up we are literally in the dark ages. In effect, we are missing the first one billion years from the timeline of the Universe.This brief but far-reaching period in the Universe's history, known to astrophysicists as the 'Epoch of Reionisation', represents the start of the cosmos as we experience it today. The time when the very first stars burst into life, when darkness gave way to light. After hundreds of millions of years of dark, uneventful expansion, one by the one these stars suddenly came into being. This was the point at which the chaos of the Big Bang first began to yield to the order of galaxies, black holes and stars, kick-starting the pathway to planets, to comets, to moons, and to life itself.Incorporating the very latest research into this branch of astrophysics, this book sheds light on this time of darkness, telling the story of these first stars, hundreds of times the size of the Sun and a million times brighter, lonely giants that lived fast and died young in powerful explosions that seeded the Universe with the heavy elements that we are made of. Emma Chapman tells us how these stars formed, why they were so unusual, and what they can teach us about the Universe today. She also offers a first-hand look at the immense telescopes about to come on line to peer into the past, searching for the echoes and footprints of these stars, to take this period in the Universe's history from the realm of theoretical physics towards the wonder of observational astronomy.

    In The Irrationals , the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them. That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random". Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    Everyday experience cannot prepare us for the sub-atomic world, where quantum effects become all-important. Here, particles can look like waves, and vice versa; electrons seem to lose their identity and instead take on a shifting, unpredictable appearance that depends on how they are being observed; and a single photon may sometimes behave as if it could be in two places at once. In the world of quantum mechanics, uncertainty and ambiguity become not just unavoidable, but essential ingredients of science -- a development so disturbing that to Einstein "it was as if God were playing dice with the universe." And there is no one better able to explain the quantum revolution as it approaches the century mark than David Lindley. He brings the quantum revolution full circle, showing how the familiar and trustworthy reality of the world around us is actually a consequence of the ineffable uncertainty of the subatomic quantum world -- the world we can't see.

    In addition, it discusses antennas and microwave techniques at a technician level and covers data communication techniques (modems, local area networks, fiber optics, satellite communication) and advanced applications (cellular telephones, facsimile and radar). The work is suitable for courses in Communications Technology.

    Over the next ten years the “Strange” books sold over 6,000,000 copies worldwide. Strange True Encounters & Unearthly Experiences is the first new book in the series in over three decades, and features: Robert M. Schoch, Ph.D. in Geology and Geophysics at Yale University on discoveries at Anatolia‘s Gobekli Tepe suggesting civilization is far older than previously believed. Gregory Sams on unfolding evidence that stars may be conscious. Janet Brennan on Europe’s mysterious Black Madonna statues. Martin Cadin, ex-member Federal Aviation Administration, on his personal experiments using telekinesis. Michio Kaku, Professor of Theoretical Physics at the City University of New York, on our ten-dimensional universe and paranormal phenomenon. Journalist Chris Friar on 19th century UFO sightings proving they are not a modern phenomenon. Actor Anthony Quinn on the “profound mystical experience” in the Sinai Desert that changed his life. Plus over a dozen other accounts, investigation and in-depth reports on the Ouija board, remote viewing, poltergeists, Kansas’ sacred sites, the U.S. warship that was saved by an angel, and much more. We believe this brand new entry in the “Strange” series – is in every way the equal of its predecessors. And will prove every bit as entertaining and enlightening as the earlier books did. (Asked where he got the ideas for his stories, Steven King credited FATE. “My mother used to read me FATE Magazine, which was about the paranormal, flying saucers…all that stuff. I was fascinated.”) Here is what Amazon readers have to say about classic reprints from FATE: “A book worth reading. I look forward to reading the other books in this series.” “FATE always comes through.” “Well written, short articles on a variety of paranormal events, many of which were unfamiliar to me. Interesting, unfamiliar and competently edited.” “Good stuff. Reminds us that stories like this have been happening for years. Not just a modern invention. Worth a read.” “Very good read. 5 stars.”

    But Shep Doeleman and a global coalition of scientists are on the cusp of doing just that.With exclusive access to the team, journalist Seth Fletcher spent five years following Shep and an extraordinary cast of characters as they assembled the Event Horizon Telescope, a virtual radio observatory the size of the Earth. He witnessed their struggles, setbacks, and breakthroughs, and along the way, he explored the latest thinking on the most profound questions about black holes. Do they represent a limit to our ability to understand reality? Or will they reveal the clues that lead to the long-sought Theory of Everything?Fletcher transforms astrophysics into something exciting, accessible, and immediate, taking us on an incredible adventure to better understand the complexity of our galaxy, the boundaries of human perception and knowledge, and how the messy human endeavor of science really works.Weaving a compelling narrative account of human ingenuity with excursions into cutting-edge science, Einstein’s Shadow is a tale of great minds on a mission to change the way we understand our universe—and our place in it.

    Geared to the layperson, a clear, concise, non-mathematical explanation of the Theory of Everything and its profound implications is followed by transcripts of interviews with most of the physicists involved in its development.