Well, yes. Elements is the most important maths book of all time not because of the subject matter, but because of its revolutionary method. The book invented how mathematicians do mathematics. Elements begins with a list: 23 definitions, five postulates and five common notions. The definitions describe the geometrical objects Euclid will be writing about, such as points and lines. The postulates tell us the procedures that are allowed, for example, that given any two points you can draw a line between them.
Euclid allows us only what we can draw with a straight edge and a compass. And the common notions clarify basic concepts, for example, that if object A is the same as object X, and if object B is the same as object X, then object A is the same as object B. From that moment on, Euclid assumes nothing else. He builds up from these simple basics to construct a remarkable edifice of mathematical knowledge.
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All the theorems in Elements are deduced logically from his small set of assumed truths. The beauty in Elements is in its rigour and ingenuity. It establishes a standard for mathematical proof to which every subsequent mathematical work aspires.
Unlike other sciences, where new models and theories supersede earlier ones, the theorems in Elements remain as true now as they were in ancient Greece. The book was translated from Greek into Latin, and also into Arabic, where it initially had a much greater influence in Islamic culture and science.
Not everyone was a fan. If you were to dip into it now, you may not find it an easy read. And there has been barely a leak in 2, years. Euclid is the only great mathematician not credited with the discovery of an important theorem. His reputation is not based on what he did, but on how he did it in Elements.
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Alex Bellos. The long series of prefaces and the extended and rather arid first chapter on the history of dream interpretation put off many readers. Freud distinguished between a wish and a desire. A dream can be organised around a wish — say, to pass an exam — and unconscious desire will act like a hitchhiker, using the wish to smuggle itself into the dream.
We might pass or fail the exam, but the clues to desire lie in the details of the room we are in, the tie the examiner is wearing, the sounds in the background. These seemingly unimportant elements allow us to track unconscious material. Freud shows the central place of sexuality and violence in our mental lives. Writers and poets have always been alert to the troubling and darker sides of the psyche, but it was the dream book that showed so carefully how exactly these currents are forged and encrypted, how they undergo distortion and censorship and how they are formed and shaped by language.
The danger of the book was quickly apparent to Freud. Just as a femme fatale can lead you astray, so the book could set readers on a fruitless quest for hidden symbolism. All his later work on dreams was an effort to correct this. The search for hidden meaning is ultimately unhelpful, and, as he wrote in , there is a navel to the dream, a point that cannot be interpreted and where meaning fails.
The dream book opened up both of these worlds to future generations: that of meaning, so exciting to the early analysts, and that of non-meaning, crucial to the whole intellectual landscape of the 20th century and beyond. Darian Leader. It helped to transform what had been an essentially conservative, utilitarian conservation movement into the first stirrings of an ecologically centred green movement in the west. It is wrong when it tends otherwise. Humans, said Leopold, whatever they might like to think, were not above nature: they were part of it.
They could either understand that and act accordingly, or they could continue to destroy, and probably perish themselves. Back in , even conservationists saw their task as opening up wilderness areas for hunters. Leopold himself had been part of this work as a young man. But after seeing the green fire die, I sensed that neither the wolf nor the mountain agreed with such a view. Nature was the green fire in the eyes of the wolf, the skeins of geese across the sand county lakes, the flowering of the Arizona juniper or the bark of the young white pine.
You had to step outside to see it, and you had to remain humble. It is a lesson we still have to learn. And, in a different guise, the same spectre has haunted Europe at moments of crisis ever since Marx and Engels wrote it.
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It is not the spectre merely of working-class revolt: the factory workers of Manchester had been organising revolts for 30 years before the Manifesto came out. The threat was political: that working-class unrest would detach itself from the spontaneous ideology of the early 19th century — republican socialism — and embrace communism instead.
Marx and Engels had inherited the objective from the atheist left intelligentsia of the s, but, after Engels arrived in Manchester in , they came to understand the industrial proletariat as the only social force capable of achieving it. But the Manifesto is not about the proletariat.
Its whole first section is a eulogy to capitalism, which has played a revolutionary role by replacing all partial and informal attempts at a market economy with a pure one. Not only that, it is a eulogy to the bourgeoisie. If you only ever read one paragraph of the work itself, it should be this:. All that is solid melts into air, all that is holy is profaned, and man is at last compelled to face with sober senses his real conditions of life, and his relations with his kind.
The business class of the early industrial era, then, had brought about not only the conditions for constant technological improvement, but the demise of religious obscurantism and the emergence of sociological realism. From now on Marx and Engels thought — observing the acute social war raging in cities such as Lille and Manchester — the only problem would be to equip the proletariat with the political maturity to wield power.
The Manifesto was published a few weeks before the revolution in France, and shipped via Paris to Germany, where a full-scale revolutionary war promptly broke out. Here the minuscule communist sects, composed of skilled workers and radical students, found themselves having to side with radical democrats against, first, the toppled monarchy and then the bourgeoisie, which, on first sight of armed workers, became distinctly un-revolutionary. From then on, all revolutions became a dirty business for communists, involving the complex interplay of radical social objectives and radical democratic ones, around which the alliance of class forces was often unstable.
But the manifesto has shone through, in large part because its prose shines with unsullied logical clarity. Capitalism produces its own gravediggers and gives them the means to free themselves, and humanity, from economic necessity. As an idea it was powerful enough to sustain generations of people through the experience of exile, torture, imprisonment and concentration camps.
Paul Mason. The women in the house knew it and so did the children. I felt instinctively that Toni Morrison had broken open a hell as no one — not even great writers such as Richard Wright, James Baldwin and Alice Walker — had done before.
She achieved with Beloved what her four previous books had only hinted at: she put you there. To read it is to live in the haunted Ohio house of Sethe, the escaped slave who had decided to kill her child rather than let her go back into slavery. I finally read the book because I was writing a memoir and I wanted to understand how my mother and my grandmother saw the world.
Set in an alt-Mediterranean sort of world, with a Germanicish tribe at war with Greekish colonisers. Two enemy soldiers save one another post battle then hole up in a temple to recuperate, falling in love on the way. Beautifully written, with fascinating worldbuilding that supports the characters, a lovely romance that manages to be both moving and unsentimental, and lots of chewy and intriguing thoughts.https://inidonces.tk
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Plus, it pulls off the rare trick of making you feel better about people. I read it in a sitting and enjoyed every minute. An absolute stormer of a sexy romance. Doctor daughter of a Republican scumbag politician meets supersexy high flying architect and they agree on a no-strings no-stress sexual relationship. Yeah right.
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Wild Sweet Love by Beverly Jenkins. Teresa July, outlaw bank robber, is fresh out of jail on parole, and forced to live with a do-gooder to reform. She must learn manners and ladylike ways to avoid going back to prison. Fail Seven Times by Kris Ripper. He loves them; they love him and want him to join them in bedwith hope of a proper relationship. A glorious, affirming book of happiness achieved in the teeth of a lot of stuff.