Infinitesimal

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出版者:Scientific American / Farrar, Straus and Giroux
作者:Amir Alexander
出品人:
页数:368
译者:
出版时间:2014-4-8
价格:USD 27.00
装帧:Hardcover
isbn号码:9780374176815
丛书系列:
图书标签:
  • 数学史
  • 数学
  • 科普
  • 历史
  • 好奇
  • 台湾
  • 微积分
  • 数学分析
  • 极限
  • 无穷小
  • 微量
  • 函数
  • 导数
  • 积分
  • 数学
  • 理论
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具体描述

Pulsing with drama and excitement, Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line.

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On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.

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In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.

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The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.

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From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

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【From Booklist】

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*Starred Review* Convinced that it opened the Royal Road through the mathematical thicket, seventeenth-century mathematician Evangelista Torricelli trumpeted the method of indivisibles. Yet in recounting how that method originated, provoked vigorous resistance, and finally prevailed, Alexander tells a story with implications far beyond mathematics. Premised on the definition of a line as a composite of countless infinitesimally small elements, the method of indivisibles opened the door to calculus. But it also subverted Aristotelian philosophical principles, so alarming defenders of the status quo. Alexander compellingly chronicles the clashes as Galileo squares off with Pope Urban VIII in Italy, and royalist Thomas Hobbes crosses swords with puritan John Wallis in England. Beyond what it teaches about mathematics, the intellectual combat illuminates the tempestuous birth of modernity. Alexander credits the champions of indivisibles with helping to usher in an era of progressive tolerance and democracy, and he indicts their foes as hidebound authoritarians. But as readers explore the personalities and life trajectories of the combatants, they will recognize complexities that do not fit into Alexander’s overall script: Bonaventura Cavalieri (one of the discoverers of indivisibles) was a cautious monk, while RenéDescartes (the father of modern philosophy) rejected the new mathematics. A bracing reminder of the human drama behind mathematical formulas.

--Bryce Christensen

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【Review】

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“You probably don't think of the development of calculus as ripe material for a political thriller, but Amir Alexander has given us just that in Infinitesimal.”

―Jordan Ellenberg, The Wall Street Journal

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“Packed with vivid detail and founded on solid scholarship, [Infinitesimal] is both a rich history and a gripping page turner.”

―Jennifer Ouellette, The New York Times Book Review

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“[A] finely detailed, dramatic story.”

―John Allen Paulos, The New York Times

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“Alexander pulls off the impressive feat of putting a subtle mathematical concept centre stage in a ripping historical narrative . . . this is a complex story told with skill and verve, and overall Alexander does an excellent job . . . There is much in this fascinating book.”

―Times Higher Education

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“A triumph.”

―Nature

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“Every page of this book displays Alexander's passionate love of the history of mathematics. He helps readers refigure problems from over the centuries with him, creating pleasurable excursions through Euclid, Archimedes, Galileo, Cavalieri, Torricelli, Hobbes, and Wallis while explaining how seemingly timeless and abstract problems were deeply rooted in different worldviews. Infinitesimal captures beautifully a world on the cusp of inventing calculus but not quite there, struggling with what might be lost in the process of rendering mathematics less certain and familiar.”

―Paula E. Findlen, The Chronicle of Higher Education

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“With a sure hand, Mr. Alexander links mathematical principles to seminal events in Western cultural history, and has produced a vibrant account of a disputatious era of human thought, propelled in no small part by the smallest part there is.”

―Alan Hirshfeld, The Wall Street Journal

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“Infinitesimal is a gripping and thorough history of the ultimate triumph of [a] mathematical tool . . . If you are fascinated by numbers, Infinitesimal will inspire you to dig deeper into the implications of the philosophy of mathematics and of knowledge.”

―New Scientist

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“Brilliantly documented . . . Alexander shines . . . the story of the infinitesimals is fascinating.”

―Owen Gingerich, The American Scholar

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“Back in the 17th century, the unorthodox idea [of infinitesimals], which dared to suggest the universe was an imperfect place full of mathematical paradoxes, was considered dangerous and even heretical . . . Alexander puts readers in the middle of European intellectuals' public and widespread battles over the theory, filling the book's pages with both formulas and juicy character development.”

―Bill Andrews, Discover

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“In Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander successfully weaves a gripping narrative of the historical struggle over the seemingly innocuous topic of infinitesimals. He does an excellent job exploring the links between the contrasting religious and political motivations that lead to acceptance or refusal of the mathematical theory, skillfully breathing life into a potentially dry subject. Infinitesimal will certainly leave its readers with a newfound appreciation for the simple line, occasion for such controversy in the emergence of modern Europe.”

―Emilie Robert Wong, The Harvard Book Review

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“Fluent and richly informative”

―Jonathan Rée, Literary Review (UK)

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“Alexander tells this story of intellectual strife with the high drama and thrilling tension it deserves, weaving a history of mathematics through the social and religious upheavals that marked much of the era . . .The author navigates even the most abstract mathematical concepts as deftly as he does the layered social history, and the result is a book about math that is actually fun to read. A fast-paced history of the singular idea that shaped a multitude of modern achievements.”

―Kirkus (starred review)

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“[Infinitesimal] gives readers insight into a real-world Da Vinci Code–like intrigue with this look at the history of a simple, yet pivotal, mathematical concept . . . Alexander explores [a] war of ideas in the context of a world seething with political and social unrest. This in-depth history offers a unique view into the mathematical idea that became the foundation of our open, modern world.”

―Publishers Weekly

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“A bracing reminder of the human drama behind mathematical formulas.”

―Bryce Christensen, Booklist

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“A gripping account of the power of a mathematical idea to change the world. Amir Alexander writes with elegance and verve about how passion, politics, and the pursuit of knowledge collided in the arena of mathematics to shape the face of modernity. A page-turner full of fascinating stories about remarkable individuals and ideas, Infinitesimal will help you understand the world at a deeper level.”

―Edward Frenkel, Professor of Mathematics, University of California, Berkeley, and author of Love and Math

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“In this fascinating book, Amir Alexander vividly re-creates a wonderfully strange chapter of scientific history, when fine-grained arguments about the foundations of mathematical analysis were literally matters of life and death, and fanatical Jesuits and English philosophers battled over the nature of geometry, with the fate of their societies hanging in the balance. You will never look at calculus the same way again.”

―Jordan Ellenberg, Professor of Mathematics, University of Wisconsin–Madison, and author of How Not to Be Wrong

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“You may find it hard to believe that illustrious mathematicians, philosophers, and religious thinkers would engage in a bitter dispute over infinitely small quantities. Yet this is precisely what happened in the seventeenth century. In Infinitesimal, Amir Alexander puts this fascinating battle in historical and intellectual context.”

―Mario Livio, astrophysicist, Space Telescope Science Institute, and author of Brilliant Blunders

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“With considerable wit and unusual energy, Amir Alexander charts the great debate about whether mathematics could be reduced to a rigorous pattern of logical and orderly deductions or whether, instead, it could be an open-ended and exciting endeavor to explore the world's mysteries. Infinitesimal shows why the lessons of mathematics count so much in the modern world.”

―Simon Schaffer, Professor of the History of Science, University of Cambridge

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“In Infinitesimal, Amir Alexander offers a new reading of the beginning of the modern period in which mathematics plays a starring role. He brings to life the protagonists of the battle over infinitesimals as if they were our contemporaries, while preserving historical authenticity. The result is a seamless synthesis of cultural history and storytelling in which mathematical concepts and personalities emerge in parallel. The history of mathematics has rarely been so readable.”

―Michael Harris, Professor of Mathematics, Columbia University and Université Paris Diderot

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“We thought we knew the whole story: Copernicus, Galileo, the sun in the center, the Church rushing to condemn. Now this remarkable book puts the deeply subversive doctrine of atomism and its accompanying mathematics at the heart of modern science.”

―Margaret C. Jacob, Distinguished Professor of History, University of California, Los Angeles

《Infinitesimal》是一部引人入胜的科幻小说,它将读者带入一个充满惊奇与未知的宇宙,探索人类在浩瀚星辰中的存在意义。故事围绕着一位名叫艾莉亚的年轻天体物理学家展开,她一直被宇宙的奥秘所吸引,尤其是那些尚未被理解的微小尺度下的物理规律。 艾莉亚在一个偏远的天文观测站工作,那里拥有一台先进的望远镜,能够观测到极其遥远的星系,捕捉到光线经过数百万年才能抵达地球的信号。她的人生目标是找到一种能够统一量子力学与广义相对论的理论,一种能够解释从黑洞奇点到宇宙大爆炸最初瞬间的统一法则。 一天晚上,当她观测一个异常平静的深空区域时,望远镜捕捉到了一个前所未有的信号。这个信号的模式极其复杂,不像是任何已知的自然现象。起初,艾莉亚认为这只是设备故障或是某种罕见的宇宙辐射。然而,随着她深入分析,她发现这个信号似乎携带着一种信息,一种以她从未见过的方式编码的信息。 她全身心地投入到对这个信号的破译工作中。日以继夜,她试图理解信号的逻辑结构,尝试用各种数学模型和物理理论来解读。这个过程异常艰难,信号的复杂性超出了她现有的知识体系。它似乎来自一个比我们所知的宇宙更古老、更基础的层面,触及到了她所追求的“无限小”的领域。 随着她对信号的理解逐渐深入,艾莉亚开始意识到,这个信号并非来自任何已知的文明,而是来自某种更根本的宇宙意识或是一种尚未被发现的宇宙规律的体现。信号中蕴含的知识,让她开始质疑她所熟知的物理学定律,甚至是对现实本身的认知。它揭示了一个隐藏在宏观宇宙表面之下的微观宇宙,一个充满了可能性和结构的领域,其复杂程度远远超越了人类的想象。 这个信号让她接触到了一些颠覆性的概念,比如,时间并非是线性的流逝,而是一种可以被操纵或感知的维度;空间也并非是空无一物的背景,而是充满了动态的能量场和潜藏的相互作用。她开始理解,我们所观测到的宇宙,可能只是一个更庞大、更精妙的系统中的一个层面,而那个信号,则是通往更深层现实的钥匙。 艾莉亚的发现并没有引起她同事的广泛重视,他们更关注于数据分析的准确性和已有的理论模型。然而,艾莉亚知道,她正在触及一个可能改变人类对宇宙认知的秘密。她必须独自面对这个挑战,独自去探索这个信号所指向的未知领域。 在这个过程中,她遇到了许多意想不到的困难。信号的解析让她进入了一种近乎“超现实”的思考模式,她的思维方式开始发生变化,对世界的感知也变得不同。她开始经历一些“非寻常”的体验,仿佛能够“看到”那些构成物质的微小粒子之间的联系,甚至能够“感知”到宇宙的脉动。 随着她越来越接近信号的真相,她也开始感受到一种来自未知源头的“回应”。这种回应并非是字面上的对话,而是一种更加深邃的、基于数学和逻辑的交流。她意识到,这个信号背后所代表的,可能是一种超越了人类理解范畴的智慧,一种对宇宙基本构成有着深刻洞察的存在。 故事的高潮部分,艾莉亚通过对信号的深入解读,成功地“连接”到了这个未知源头。她获得的知识,让她得以窥见宇宙的终极奥秘。她发现,所谓的“无限小”并非是虚无,而是包含了无限的潜能和信息。我们所处的宇宙,就像一个巨大的、精密的计算系统,而她所接收到的信号,则是这个系统中最底层、最核心的代码。 然而,这份知识也带来了巨大的责任。她明白,一旦将这份信息公之于众,可能会引起巨大的混乱,甚至可能对人类社会产生难以预料的影响。她必须决定,是否要将这个秘密分享出去,或者选择将它深深地埋藏在心底。 《Infinitesimal》不仅仅是一个关于科学发现的故事,它更深入地探讨了人类在宇宙中的位置,以及我们对未知的好奇心和探索精神。它引导读者思考,我们所理解的现实是否是唯一的,以及在浩瀚的宇宙中,是否存在着超越我们想象的智慧和规律。艾莉亚的旅程,是对人类认知边界的一次挑战,也是对我们探索宇宙奥秘的永恒追求的一次致敬。这部小说以其深刻的思想、严谨的科学推演和扣人心弦的情节,为读者提供了一次难忘的精神体验。

作者简介

Amir Alexander teaches history at UCLA. He is the author of Geometrical Landscapes and Duel at Dawn. His work has been featured in Nature, The Guardian, and other publications. He lives in Los Angeles, California.

目录信息

读后感

评分

尝试记下读《无穷小》这本书学到的东西。只是其中的数学知识懂得很少,因此也很可能理解错了。包涵则个。欢迎指教。 无穷小的概念是这样的:假设一条线,是由无数个不能再细分的点组成,这些点如果有厚度,则这条线无限长,如果没有厚度,则这条线的长度为零。所以在(常识)逻...

评分

尝试记下读《无穷小》这本书学到的东西。只是其中的数学知识懂得很少,因此也很可能理解错了。包涵则个。欢迎指教。 无穷小的概念是这样的:假设一条线,是由无数个不能再细分的点组成,这些点如果有厚度,则这条线无限长,如果没有厚度,则这条线的长度为零。所以在(常识)逻...

评分

尝试记下读《无穷小》这本书学到的东西。只是其中的数学知识懂得很少,因此也很可能理解错了。包涵则个。欢迎指教。 无穷小的概念是这样的:假设一条线,是由无数个不能再细分的点组成,这些点如果有厚度,则这条线无限长,如果没有厚度,则这条线的长度为零。所以在(常识)逻...

评分

尝试记下读《无穷小》这本书学到的东西。只是其中的数学知识懂得很少,因此也很可能理解错了。包涵则个。欢迎指教。 无穷小的概念是这样的:假设一条线,是由无数个不能再细分的点组成,这些点如果有厚度,则这条线无限长,如果没有厚度,则这条线的长度为零。所以在(常识)逻...

评分

尝试记下读《无穷小》这本书学到的东西。只是其中的数学知识懂得很少,因此也很可能理解错了。包涵则个。欢迎指教。 无穷小的概念是这样的:假设一条线,是由无数个不能再细分的点组成,这些点如果有厚度,则这条线无限长,如果没有厚度,则这条线的长度为零。所以在(常识)逻...

用户评价

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我怀着一种近乎朝圣的心情,一页一页地翻阅着《Infinitesimal》。这本书的魅力,在于它所构建的那个宏大而细腻的世界。作者笔下的每一个人物,每一个场景,都仿佛拥有独立的生命,鲜活地跃然纸上。我能感受到人物内心的挣扎与成长,能体会到他们之间错综复杂的情感纠葛。故事的发展出人意料,却又合情合理,仿佛是命运的齿轮在精准地转动。我被深深地吸引,沉浸其中,甚至会忘记自己身在何处。书中对于人性的探讨,尤为深刻。作者并没有简单地将人物脸谱化,而是展现了人性的多面性,那些光明与阴影,那些善良与自私,都交织在一起,构成了真实而复杂的人类群像。我常常会在读到某个情节时,陷入沉思,反思自己的人生,反思自己与他人的关系。这本书不仅仅是一个故事,它更是一面镜子,映照出我们内心深处的渴望与恐惧。我喜欢作者的叙事节奏,不疾不徐,张弛有度,总能在最恰当的时候,抛出最令人回味的情节。我常常会把书合上,久久地凝视着封面,试图将书中世界的每一个细节,都深深地刻在脑海里。这本书是一次心灵的洗礼,它让我更加懂得,生命的意义并非只有一种,而是在于我们如何去经历,去感受,去爱。我真诚地推荐这本书给所有热爱故事,热爱生活,渴望在文字中寻找共鸣的读者。

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我必须承认,当我拿起《Infinitesimal》这本书时,我对它并没有抱有太高的期望。然而,它却以一种令人惊喜的方式,彻底颠覆了我之前的认知。这本书的独特之处,在于它敢于挑战传统的思维模式,并以一种全新的视角,去探索那些我们习以为常的领域。作者的想象力天马行空,却又牢牢地根植于现实,他能够将看似不可能的想法,描绘得栩栩如生,引人入胜。每一次阅读,都像是在进行一次头脑的风暴,我的思绪被书中奇妙的构思所点燃,开始进行各种各样的联想。我尤其喜欢作者对于未知世界的探索,他用一种充满好奇与敬畏的态度,带领我们去窥探那些隐藏在表象之下的秘密。这本书让我重新认识到了知识的边界,也激发了我对未知世界的无限遐想。作者的语言,充满了一种独特的韵味,它既有科学的精确,又不失艺术的灵动,仿佛是一场思想的盛宴。我常常会在阅读过程中,感到一种强烈的求知欲,想要去了解更多,去探索更远。这本书是一本能够激发你无限创造力的书籍,它让你敢于跳出思维的定势,去拥抱那些令人兴奋的可能性。我毫不保留地将这本书推荐给所有对创新充满热情,对未知世界充满好奇的读者。

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这本书给我带来的震撼,远超我的想象。我原本以为它会是一本严肃的学术著作,充斥着晦涩难懂的理论,但事实恰恰相反,它以一种极其生动有趣的方式,向我展示了一个我从未接触过的领域。作者的逻辑思维严谨而清晰,仿佛一把锋利的解剖刀,将复杂的概念层层剥开,展现出其内在的精妙结构。然而,最令人称赞的是,他并没有因此而牺牲掉作品的趣味性。每一次阅读,都像是在进行一场智力探险,我被书中层出不穷的观点和案例所吸引,仿佛置身于一个充满智慧的迷宫,一边摸索,一边惊喜于每一个转角的发现。我常常会在阅读过程中,拿出纸笔,记录下那些触动我的想法,并尝试着去思考它们与我自身经历的联系。这本书挑战了我固有的认知,也拓展了我的思维边界。我开始用一种全新的视角去审视周围的世界,那些曾经看似平淡无奇的事物,如今都充满了值得探索的奥秘。作者的叙述方式非常具有感染力,他善于运用比喻和类比,将抽象的概念具象化,让读者能够轻松理解。即使是对于非专业人士,也能从中获得极大的启发。这本书不仅仅是知识的传递,更是一种思维方式的启迪。它让我学会了如何更深入地思考问题,如何更批判性地看待信息,如何在纷繁复杂的现象中抓住本质。我毫不犹豫地将这本书推荐给所有渴望提升自己认知能力,寻求更深层次理解世界的朋友。

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《Infinitesimal》这本书,就像一股清泉,在我干涸的心田里缓缓流淌,带来生机与活力。我一直以来都对某个特定的领域充满好奇,但总感觉缺乏一个清晰的入口。这本书的出现,恰好填补了我的空白。作者以一种极其系统且易于理解的方式,为我展开了这个领域的画卷。我惊叹于作者知识的广博,更折服于他梳理知识脉络的清晰度。每一次翻阅,都像是在进行一次知识的“考古”,我不断地发现新的宝藏,并尝试着将它们与已有的认知融会贯通。书中关于某个观点的阐述,让我茅塞顿开,仿佛一直以来困扰我的难题,瞬间迎刃而解。我特别喜欢作者在书中穿插的那些生动有趣的案例,它们让枯燥的理论变得鲜活起来,也让抽象的概念变得更容易理解。这本书不仅增长了我的见识,更重要的是,它激发了我对这个领域更深层次的探索欲望。我开始主动去寻找相关的资料,去思考书中提出的问题,一切都变得那样自然而然。我推荐这本书给所有渴望在某个领域获得系统性知识,并对学习充满热情的朋友,相信你们也会像我一样,在这本书中找到属于自己的“启蒙之光”。

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我必须承认,《Infinitesimal》这本书,以一种我从未预料到的方式,深深地触动了我。它并非以情节的曲折取胜,也非以语言的华丽见长,但其所蕴含的深沉的情感力量,足以让我为之动容。作者似乎拥有一种能够洞察人心的魔力,他能够精准地捕捉到那些我们内心深处最柔软,也最隐秘的情感。我在这本书中,读到了关于孤独,关于爱,关于失去的真实写照。那些平凡而又充满力量的文字,勾勒出了一个个鲜活的人物形象,让我仿佛置身于他们的世界,与他们一同经历喜怒哀乐。我尤其喜欢作者对于情感细微之处的刻画,那些不易察觉的眼神,那些欲言又止的沉默,都充满了故事的张力。这本书让我更加懂得,生命中最动人的时刻,往往隐藏在那些看似平淡的日子里。作者的叙事风格,有一种不动声色的力量,它不会刻意煽情,却能在不经意间,引发读者内心深处的情感共鸣。我常常会在阅读过程中,眼眶湿润,却又感到一种被理解的温暖。这本书是一次关于情感的深度体验,它让你重新审视自己与他人的关系,并更加懂得去珍惜身边的人。我强烈推荐这本书给所有渴望在文字中寻找情感慰藉,并希望与书中人物产生深刻连接的读者。

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《Infinitesimal》这本书,就像是我在漫长人生旅途中,遇到的一位智者,他用一种平静而深邃的目光,引导我去看透世事的繁华与喧嚣。它没有激烈的冲突,也没有惊心动魄的转折,却蕴含着一种淡泊而持久的智慧。我在这本书中,读到了关于人生哲理,关于生命意义的深刻思考。作者以一种抽离而又充满关怀的视角,审视着人类的生存状态,并提出了许多发人深省的观点。我常常会在阅读过程中,停下脚步,陷入沉思,尝试着去理解作者所要传达的深意。这本书让我更加懂得,生命的价值,并非在于追求外在的物质,而在于内心的宁静与丰盈。作者的语言,简洁而富有力量,他用最朴实的词语,道出了最深刻的哲理。我喜欢这种“大道至简”的写作风格,它能够让读者在喧嚣的世界中,找到内心的平静。这本书是一次关于智慧的启迪,它让你学会如何去面对人生的起伏,如何去寻找内心的安宁。我推荐这本书给所有在人生道路上寻求指引,渴望获得精神力量的朋友。

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《Infinitesimal》这本书,就像是我在茫茫书海中偶然拾得的一颗璀璨的珍珠,它的光芒,足以照亮我前行的道路。我曾几何时,对某些领域感到迷茫,对某些问题感到困惑,但正是通过这本书,我找到了方向,找到了答案。作者的文字,带着一种穿透人心的力量,它能够直击问题的核心,并以一种温和而坚定的方式,引导我去思考。我尤其欣赏作者对于细节的把握,那些看似微不足道的描写,却往往蕴含着深刻的哲理。每一次阅读,我都能从中获得新的感悟,就像是在不断地挖掘宝藏。这本书给我带来的,不仅仅是知识的增益,更是一种精神上的升华。它让我学会了如何以更广阔的视野去看待事物,如何以更包容的心态去接纳他人。我常常会在阅读这本书的时候,感到一种前所未有的平静与安宁,仿佛所有的烦恼都被抛诸脑后。作者的语言风格,既有学术的严谨,又不失文学的优美,形成了一种独特的魅力,让人爱不释手。我常常会反复阅读某些章节,每一次都能从中品味出不同的滋味。这本书是一本值得反复品味的“慢读”之书,它需要你静下心来,用心去感受,去体会。我强烈推荐这本书给所有渴望在精神世界获得滋养,在知识海洋中遨游的读者。

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我迫不及待地想要分享我对《Infinitesimal》这本书的感受。它绝对是一本能够让你沉浸其中,久久不能自拔的作品。作者的写作功底毋庸置疑,他能够将看似复杂的主题,以一种清晰明了的方式呈现出来。然而,这本书最吸引我的地方,在于它所蕴含的深刻的哲学思考。作者并没有给出明确的答案,而是通过引导性的提问和发人深省的论述,鼓励读者进行自我探索。我常常会在阅读过程中,停下来,反复咀嚼作者提出的观点,并尝试着去联系自己的生活经验,进行更深入的思考。这本书就像是一位睿智的导师,它循循善诱,让你在不知不觉中,完成了思想的飞跃。我尤其欣赏作者的逻辑严谨性,他能够从一个看似微小的切入点,层层递进,最终构建出一个宏大而完整的思想体系。这本书不仅仅是知识的传递,更是一种思维方式的训练。它让你学会如何去质疑,如何去反思,如何去构建属于自己的知识体系。我强烈推荐这本书给所有对深度思考感兴趣,渴望提升自己认知能力,并勇于挑战自身固有观念的读者。

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《Infinitesimal》这本书,就像是一位阅历丰富的老者,用他饱经风霜的眼睛,向我讲述着人生的种种际遇。它没有华丽的辞藻,没有惊心动魄的情节,却有一种朴实无华的力量,能够直击人心。我在这本书中,读到了许多关于成长,关于失去,关于爱的故事。作者以一种极其真诚的态度,展现了生命的脆弱与坚韧,那些平凡人的生活,在作者的笔下,都闪烁着动人的光辉。我常常会在阅读过程中,感到一种深深的共鸣,仿佛书中的每一个人物,都曾是我生命中的一部分。这本书让我更加懂得,生命的意义,并非在于轰轰烈烈,而是在于那些细微之处的坚持与守护。作者的叙述方式,平淡却又充满力量,他用最简洁的语言,道出了最深刻的道理。我喜欢这种“润物细无声”的写作风格,它能够让读者在不经意间,获得心灵的触动。这本书是一次关于人性的探索,它让我们看到了生命中最真实,也最动人的一面。我推荐这本书给所有在生活中感到迷茫,渴望寻找力量和慰藉的朋友。

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这本书就像一个静谧的午后,阳光穿过树叶的缝隙,洒下一片斑驳的光影,让人忍不住想要驻足,细细品味。我翻开《Infinitesimal》的瞬间,就被一股难以言喻的氛围所吸引,仿佛进入了一个充满诗意的世界。书中的字里行间,流淌着作者对生活细微之处的敏锐洞察,那些我们日常生活中常常忽略的点滴,在作者笔下却被赋予了生命,变得鲜活而动人。每一次阅读,都像是在进行一场心灵的对话,那些细腻的情感,那些深刻的思考,都随着文字的脉络,一点点地渗透进我的内心深处。我尤其喜欢作者对于意境的营造,那种淡淡的忧伤,那种隐约的希望,就像一首悠扬的乐曲,在脑海中久久回荡。我会在夜晚,点上一盏昏黄的灯,静静地翻阅,让自己的思绪随着书中的情节自由飞翔。有时,我会因为书中某个场景而潸然泪下,有时,又会因为某个哲理性的思考而豁然开朗。这本书的语言是那样优美,却又不失力量,它像一位智者,在用最温和的方式,向你诉说着生命的真谛。我常常会停下来,反复咀嚼某些句子,感受其中的韵味,仿佛从中汲取到了前行的力量。这本书不仅仅是一部作品,更像是一位知己,它陪伴我度过了许多孤独的时光,它让我更加懂得去爱,去感受,去珍惜生命中的每一个瞬间。我推荐这本书给所有对生活怀有热情,对内心世界有所追求的朋友,相信你们也会和我一样,在这本书中找到属于自己的那份宁静与启迪。

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Amir讲故事可真漂亮,但是确实没法面面俱到,讨论到infini的形而上学问题的时候,涉及的太少了。和雅克布克莱因完全是两种思路。

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Amir讲故事可真漂亮,但是确实没法面面俱到,讨论到infini的形而上学问题的时候,涉及的太少了。和雅克布克莱因完全是两种思路。

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Just a warm-over of the history of science and calculus. A summarizing note for the religious history of Europe; a crude intro to Hobbes’ work and some key notions for math approaches. Great command of language and pacing, though trapped in repetition and paraphrasing sometimes. Recommended for those knowing nothing about Middle Ages and science.

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Just a warm-over of the history of science and calculus. A summarizing note for the religious history of Europe; a crude intro to Hobbes’ work and some key notions for math approaches. Great command of language and pacing, though trapped in repetition and paraphrasing sometimes. Recommended for those knowing nothing about Middle Ages and science.

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读完啦。读了一个月。16-17世纪欧洲的数学家神学家们就“无穷小”这个概念而展开的斗争。这是一本对我来说完全“无用”的书。不容易读,读完有种满足感。

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