Proofiness: The Dark Arts of Mathematical Deception


Charles Seife - 2010
     According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.

Mathematics: From the Birth of Numbers


Jan Gullberg - 1997
    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

Fermat's Enigma


Simon Singh - 1997
    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

QED: The Strange Theory of Light and Matter


Richard P. Feynman - 1985
    QED--the edited version of four lectures on quantum electrodynamics that Feynman gave to the general public at UCLA as part of the Alix G. Mautner Memorial Lecture series--is perhaps the best example of his ability to communicate both the substance and the spirit of science to the layperson.The focus, as the title suggests, is quantum electrodynamics (QED), the part of the quantum theory of fields that describes the interactions of the quanta of the electromagnetic field-light, X rays, gamma rays--with matter and those of charged particles with one another. By extending the formalism developed by Dirac in 1933, which related quantum and classical descriptions of the motion of particles, Feynman revolutionized the quantum mechanical understanding of the nature of particles and waves. And, by incorporating his own readily visualizable formulation of quantum mechanics, Feynman created a diagrammatic version of QED that made calculations much simpler and also provided visual insights into the mechanisms of quantum electrodynamic processes.In this book, using everyday language, spatial concepts, visualizations, and his renowned "Feynman diagrams" instead of advanced mathematics, Feynman successfully provides a definitive introduction to QED for a lay readership without any distortion of the basic science. Characterized by Feynman's famously original clarity and humor, this popular book on QED has not been equaled since its publication.

The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life


Alex Bellos - 2014
    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

The Enigma of Reason


Hugo Mercier - 2017
    If reason is so useful, why didn't it also evolve in other animals? If reason is that reliable, why do we produce so much thoroughly reasoned nonsense? In their groundbreaking account of the evolution and workings of reason, Hugo Mercier and Dan Sperber set out to solve this double enigma. Reason, they argue with a compelling mix of real-life and experimental evidence, is not geared to solitary use, to arriving at better beliefs and decisions on our own. What reason does, rather, is help us justify our beliefs and actions to others, convince them through argumentation, and evaluate the justifications and arguments that others address to us.In other words, reason helps humans better exploit their uniquely rich social environment. This interactionist interpretation explains why reason may have evolved and how it fits with other cognitive mechanisms. It makes sense of strengths and weaknesses that have long puzzled philosophers and psychologists--why reason is biased in favor of what we already believe, why it may lead to terrible ideas and yet is indispensable to spreading good ones.Ambitious, provocative, and entertaining, The Enigma of Reason will spark debate among psychologists and philosophers, and make many reasonable people rethink their own thinking.

Consciousness: Confessions of a Romantic Reductionist


Christof Koch - 2012
    This engaging book--part scientific overview, part memoir, part futurist speculation--describes Koch's search for an empirical explanation for consciousness. Koch recounts not only the birth of the modern science of consciousness but also the subterranean motivation for his quest--his instinctual (if "romantic") belief that life is meaningful.Koch describes his own groundbreaking work with Francis Crick in the 1990s and 2000s and the gradual emergence of consciousness (once considered a "fringy" subject) as a legitimate topic for scientific investigation. Present at this paradigm shift were Koch and a handful of colleagues, including Ned Block, David Chalmers, Stanislas Dehaene, Giulio Tononi, Wolf Singer, and others. Aiding and abetting it were new techniques to listen in on the activity of individual nerve cells, clinical studies, and brain-imaging technologies that allowed safe and noninvasive study of the human brain in action.Koch gives us stories from the front lines of modern research into the neurobiology of consciousness as well as his own reflections on a variety of topics, including the distinction between attention and awareness, the unconscious, how neurons respond to Homer Simpson, the physics and biology of free will, dogs, Der Ring des Nibelungen, sentient machines, the loss of his belief in a personal God, and sadness. All of them are signposts in the pursuit of his life's work--to uncover the roots of consciousness.

An Anthropologist on Mars: Seven Paradoxical Tales


Oliver Sacks - 1995
    Paradoxical portraits of seven neurological patients, including a surgeon consumed by the compulsive tics of Tourette's syndrome unless he is operating; an artist who loses all sense of color in a car accident, but finds new creative power in black & white; & others.

Social: Why Our Brains Are Wired to Connect


Matthew D. Lieberman - 2013
    It is believed that we must commit 10,000 hours to master a skill.  According to Lieberman, each of us has spent 10,000 hours learning to make sense of people and groups by the time we are ten.  Social argues that our need to reach out to and connect with others is a primary driver behind our behavior.  We believe that pain and pleasure alone guide our actions.  Yet, new research using fMRI – including a great deal of original research conducted by Lieberman and his UCLA lab -- shows that our brains react to social pain and pleasure in much the same way as they do to physical pain and pleasure.  Fortunately, the brain has evolved sophisticated mechanisms for securing our place in the social world.  We have a unique ability to read other people’s minds, to figure out their hopes, fears, and motivations, allowing us to effectively coordinate our lives with one another.  And our most private sense of who we are is intimately linked to the important people and groups in our lives.  This wiring often leads us to restrain our selfish impulses for the greater good.  These mechanisms lead to behavior that might seem irrational, but is really just the result of our deep social wiring and necessary for our success as a species.   Based on the latest cutting edge research, the findings in Social have important real-world implications.  Our schools and businesses, for example, attempt to minimalize social distractions.  But this is exactly the wrong thing to do to encourage engagement and learning, and literally shuts down the social brain, leaving powerful neuro-cognitive resources untapped.  The insights revealed in this pioneering book suggest ways to improve learning in schools, make the workplace more productive, and improve our overall well-being.

The Knowledge Illusion: Why We Never Think Alone


Steven Sloman - 2017
    How have we achieved so much despite understanding so little? Cognitive scientists Steven Sloman and Philip Fernbach argue that we survive and thrive despite our mental shortcomings because we live in a rich community of knowledge. The key to our intelligence lies in the people and things around us. We're constantly drawing on information and expertise stored outside our heads: in our bodies, our environment, our possessions, and the community with which we interact--and usually we don't even realize we're doing it. The human mind is both brilliant and pathetic. We have mastered fire, created democratic institutions, stood on the moon, and sequenced our genome. And yet each of us is error prone, sometimes irrational, and often ignorant. The fundamentally communal nature of intelligence and knowledge explains why we often assume we know more than we really do, why political opinions and false beliefs are so hard to change, and why individually oriented approaches to education and management frequently fail. But our collaborative minds also enable us to do amazing things. This book contends that true genius can be found in the ways we create intelligence using the world around us.

Kluge: The Haphazard Construction of the Human Mind


Gary F. Marcus - 2008
    In this lucid and revealing book, Marcus argues that the mind is not an elegantly designed organ but rather a “kluge,” a clumsy, cobbled-together contraption. He unveils a fundamentally new way of looking at the human mind -- think duct tape, not supercomputer -- that sheds light on some of the most mysterious aspects of human nature.Taking us on a tour of the fundamental areas of human experience -- memory, belief, decision-making, language, and happiness -- Marcus reveals the myriad ways our minds fall short. He examines why people often vote against their own interests, why money can’t buy happiness, why leaders often stick to bad decisions, and why a sentence like “people people left left” ties us in knots even though it’s only four words long.Marcus also offers surprisingly effective ways to outwit our inner kluge, for the betterment of ourselves and society. Throughout, he shows how only evolution -- haphazard and undirected -- could have produced the minds we humans have, while making a brilliant case for the power and usefulness of imperfection.

Gödel's Proof


Ernest Nagel - 1958
    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics


Roger Penrose - 1989
    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

The Symbolic Species: The Co-evolution of Language and the Brain


Terrence W. Deacon - 1998
    Drawing on his breakthrough research in comparative neuroscience, Terrence Deacon offers a wealth of insights into the significance of symbolic thinking: from the co-evolutionary exchange between language and brains over two million years of hominid evolution to the ethical repercussions that followed man's newfound access to other people's thoughts and emotions.Informing these insights is a new understanding of how Darwinian processes underlie the brain's development and function as well as its evolution. In contrast to much contemporary neuroscience that treats the brain as no more or less than a computer, Deacon provides a new clarity of vision into the mechanism of mind. It injects a renewed sense of adventure into the experience of being human.

Math with Bad Drawings


Ben Orlin - 2018
     In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone.Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.