信念不是非黑即白，而是有程度的。贝叶斯主义提供了一套用概率推理的工具包。本文通过医学测试、NBA投篮、大学录取等生活化案例， 教你如何在不确定性面前做出更好的决策。无论你是在为孩子规划教育投资，还是在做重要的职业选择，贝叶斯思维都能帮你更好地让观点与 证据相称。 别人问你相信什么。相信鬼神吗？相信全球变暖吗？相信爱吗？人们说，你的信念决定了你是谁，也决定了你该做什么：「做你认为正确的事。」 这些问题要求非黑即白的答案。但生活远不是这样。对于很多重要问题，三个选项都不够。现在，我正在研究孩子的教育规划，学校的取决于很多变量： 他们能进什么学校？什么学校适合他们？如果我们换种方式投资，未来两年、五年、十年会有什么回报？ 假设有人试图帮我：「很简单。你相信你大女儿会被 xx 大学录取吗？」我不知道该怎么回答。我不相信她一定会被录取，也不相信她一定不会。我觉得 概率略高于 50%，但远谈不上确定。 过去几十年有个重要的概念突破：信念是有程度的。我们不只是「相信」或「不相信」某事。我们的大部分思考和决策，都由不同程度的信心驱动。这些 信心程度可以用概率衡量，从 0 到 100%。当我为孩子的教育投资时，只问「我相信股票 ...

Core Idea - The book "The Logic of the World" by Professor Ma Zhaoyuan explores the evolution of human understanding of the world, emphasizing the impact of ancient Greek civilization, the nature of uncertainty in mathematics, and the implications of AI on human existence and reasoning [1]. Group 1: Influence of Ancient Greek Civilization - Ancient Greek civilization has a unique historical position, shaping the way humans understand the world and laying the foundation for philosophy, science, and art [12][14]. - The scientific spirit originating from ancient Greece encourages a courageous confrontation with ambiguity, viewing it as a motivation for further exploration [12][15]. - The development of a complete logical system in ancient Greece allowed knowledge to be accumulated and transmitted stably, which was crucial for the subsequent scientific revolution [16]. Group 2: Mathematical Crises and Uncertainty - The book discusses three crises in mathematics that shifted the focus from the pursuit of certainty to the acceptance of uncertainty [22]. - The first crisis relates to the Pythagorean crisis regarding irrational numbers, the second to the study of infinitesimals, and the third to set theory, particularly the foundational difficulties posed by Bertrand Russell [22][23]. - Gödel's incompleteness theorem is highlighted as a pivotal moment in human cognitive history, indicating that any finite, describable system is inherently flawed [23]. Group 3: AI and Modern Understanding - The rise of AI and the rediscovery of Bayesian statistics provide new methodologies that align more closely with human subjective cognitive processes [25]. - The book aims to explore the implications of Gödel's work on AI, deterministic computation, information theory, and chaos theory, revealing a new logical framework that challenges traditional notions of certainty [26]. - The interplay between uncertainty and modern scientific inquiry is presented as a profound and promising topic, reshaping our understanding of computation, information, and logic [26].