Escher and composer Johann Sebastian Bach , GEB expounds concepts fundamental to mathematics , symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.
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TensorFlow 2. Our brain's job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories. Why did two-year-old Camille proudly exclaim, "I undressed the banana! Why do people who hear a story often blurt out, "Exactly the same thing happened to me!
How do we recognize an aggressive driver from a split-second glance in our rearview mirror? What in a friend's remark triggers the offhand reply, "That's just sour grapes"? What did Albert Einstein see that made him suspect that light consists of particles when a century of research had driven the final nail in the coffin of that long-dead idea? The answer to all these questions, of course, is analogy-making -- the meat and potatoes, the heart and soul, the fuel and fire, the gist and the crux, the lifeblood and the wellsprings of thought.
Analogy-making, far from happening at rare intervals, occurs at all moments, defining thinking from top to toe, from the tiniest and most fleeting thoughts to the most creative scientific insights. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core -- the incessant, unconscious quest for strong analogical links to past experiences -- this book puts forth a radical and deeply surprising new vision of the act of thinking.
Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever approach the intricacy of the human mind. A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.
Alone in a cube that's glowing in the darkness, X is content within its little universe of infinite thought. This solitude is disturbed by the appearance of Y, who insists on exposing X to the richness of the physical world.
Each begins to long for what the other has, luring them into a strange loop. In this play for two variables, Marcus du Sautoy and Victoria Gould use mathematics and theatre to navigate the furthest reaches of our world.
Through a series of surreal episodes, X and Y tackle some of life's greatest questions: where did the universe come from, does time have an end, do we have free will? Also, to look for structure - but also look for meta-structures. Especially in the music of Bach. Oh, wait. Escher does the same thing - a pattern, repeated a layer up, and again repeated a layer up again in his art!
And if you can follow mathematics, you will understand why you can't "use just mathematics to understand mathematics, because there is 'higher math. In the beginning, he has you do some rather simple games and puzzles. You don't have a CHANCE of following the later stuff unless you learn to "feel" and recognize the mental steps he walks you around during the most simple stuff in the beginning.
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