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      "text": "拉弗曲线",
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      "text": "国家发展的倒U形曲线",
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      "text": "时间函数",
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      "depth": 2,
      "text": "我们普通人在生活上遇到的最大挑战就是短视，最近一段时间的境遇会极大的影响我们对未来的判断",
      "anchor": "我们普通人在生活上遇到的最大挑战就是短视最近一段时间的境遇会极大的影响我们对未来的判断",
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      "depth": 2,
      "text": "穿透时间预测未来的上帝视角",
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      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%A9%BF%E9%80%8F%E6%97%B6%E9%97%B4%E9%A2%84%E6%B5%8B%E6%9C%AA%E6%9D%A5%E7%9A%84%E4%B8%8A%E5%B8%9D%E8%A7%86%E8%A7%92"
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    {
      "depth": 2,
      "text": "高特纳曲线",
      "anchor": "高特纳曲线",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E9%AB%98%E7%89%B9%E7%BA%B3%E6%9B%B2%E7%BA%BF"
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      "depth": 2,
      "text": "时间—期望曲线：新技术->高度乐观->过度悲观->逐步走向成熟",
      "anchor": "时间期望曲线新技术-高度乐观-过度悲观-逐步走向成熟",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%97%B6%E9%97%B4%E6%9C%9F%E6%9C%9B%E6%9B%B2%E7%BA%BF%E6%96%B0%E6%8A%80%E6%9C%AF-%E9%AB%98%E5%BA%A6%E4%B9%90%E8%A7%82-%E8%BF%87%E5%BA%A6%E6%82%B2%E8%A7%82-%E9%80%90%E6%AD%A5%E8%B5%B0%E5%90%91%E6%88%90%E7%86%9F"
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      "text": "世界毒打曲线",
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      "text": "人性曲线与物性曲线",
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      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%BA%BA%E6%80%A7%E6%9B%B2%E7%BA%BF%E4%B8%8E%E7%89%A9%E6%80%A7%E6%9B%B2%E7%BA%BF"
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      "depth": 2,
      "text": "人性函数",
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      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%BA%BA%E6%80%A7%E5%87%BD%E6%95%B0"
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    {
      "depth": 3,
      "text": "细胞膜电位与时间关系函数图",
      "anchor": "细胞膜电位与时间关系函数图",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%BB%86%E8%83%9E%E8%86%9C%E7%94%B5%E4%BD%8D%E4%B8%8E%E6%97%B6%E9%97%B4%E5%85%B3%E7%B3%BB%E5%87%BD%E6%95%B0%E5%9B%BE"
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      "depth": 4,
      "text": "人类遇到各种刺激情况下的缩影",
      "anchor": "人类遇到各种刺激情况下的缩影",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%BA%BA%E7%B1%BB%E9%81%87%E5%88%B0%E5%90%84%E7%A7%8D%E5%88%BA%E6%BF%80%E6%83%85%E5%86%B5%E4%B8%8B%E7%9A%84%E7%BC%A9%E5%BD%B1"
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      "depth": 3,
      "text": "逻辑斯蒂函数",
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      "text": "理想状态下的指数增长与环境阻力的限制作用",
      "anchor": "理想状态下的指数增长与环境阻力的限制作用",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%90%86%E6%83%B3%E7%8A%B6%E6%80%81%E4%B8%8B%E7%9A%84%E6%8C%87%E6%95%B0%E5%A2%9E%E9%95%BF%E4%B8%8E%E7%8E%AF%E5%A2%83%E9%98%BB%E5%8A%9B%E7%9A%84%E9%99%90%E5%88%B6%E4%BD%9C%E7%94%A8"
    },
    {
      "depth": 4,
      "text": "人类历史人口增长",
      "anchor": "人类历史人口增长",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%BA%BA%E7%B1%BB%E5%8E%86%E5%8F%B2%E4%BA%BA%E5%8F%A3%E5%A2%9E%E9%95%BF"
    },
    {
      "depth": 2,
      "text": "正余弦函数",
      "anchor": "正余弦函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%AD%A3%E4%BD%99%E5%BC%A6%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 2,
      "text": "黎明前的黑暗",
      "anchor": "黎明前的黑暗",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E9%BB%8E%E6%98%8E%E5%89%8D%E7%9A%84%E9%BB%91%E6%9A%97"
    },
    {
      "depth": 3,
      "text": "不要在遇到挫折的时候，就退出朝阳赛道",
      "anchor": "不要在遇到挫折的时候就退出朝阳赛道",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%B8%8D%E8%A6%81%E5%9C%A8%E9%81%87%E5%88%B0%E6%8C%AB%E6%8A%98%E7%9A%84%E6%97%B6%E5%80%99%E5%B0%B1%E9%80%80%E5%87%BA%E6%9C%9D%E9%98%B3%E8%B5%9B%E9%81%93"
    },
    {
      "depth": 4,
      "text": "一叶障目，不见泰山",
      "anchor": "一叶障目不见泰山",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%B8%80%E5%8F%B6%E9%9A%9C%E7%9B%AE%E4%B8%8D%E8%A7%81%E6%B3%B0%E5%B1%B1"
    },
    {
      "depth": 2,
      "text": "黑夜前的黄昏",
      "anchor": "黑夜前的黄昏",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E9%BB%91%E5%A4%9C%E5%89%8D%E7%9A%84%E9%BB%84%E6%98%8F"
    },
    {
      "depth": 2,
      "text": "黑夜中的雷鸣",
      "anchor": "黑夜中的雷鸣",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E9%BB%91%E5%A4%9C%E4%B8%AD%E7%9A%84%E9%9B%B7%E9%B8%A3"
    },
    {
      "depth": 3,
      "text": "不要因为短期看起来光鲜亮丽的形式，就忽略了整体下降的大趋势",
      "anchor": "不要因为短期看起来光鲜亮丽的形式就忽略了整体下降的大趋势",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%B8%8D%E8%A6%81%E5%9B%A0%E4%B8%BA%E7%9F%AD%E6%9C%9F%E7%9C%8B%E8%B5%B7%E6%9D%A5%E5%85%89%E9%B2%9C%E4%BA%AE%E4%B8%BD%E7%9A%84%E5%BD%A2%E5%BC%8F%E5%B0%B1%E5%BF%BD%E7%95%A5%E4%BA%86%E6%95%B4%E4%BD%93%E4%B8%8B%E9%99%8D%E7%9A%84%E5%A4%A7%E8%B6%8B%E5%8A%BF"
    },
    {
      "depth": 2,
      "text": "大趋势要多个学科相互印证",
      "anchor": "大趋势要多个学科相互印证",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%A4%A7%E8%B6%8B%E5%8A%BF%E8%A6%81%E5%A4%9A%E4%B8%AA%E5%AD%A6%E7%A7%91%E7%9B%B8%E4%BA%92%E5%8D%B0%E8%AF%81"
    },
    {
      "depth": 2,
      "text": "瑞达利欧产业发展大小周期曲线",
      "anchor": "瑞达利欧产业发展大小周期曲线",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%91%9E%E8%BE%BE%E5%88%A9%E6%AC%A7%E4%BA%A7%E4%B8%9A%E5%8F%91%E5%B1%95%E5%A4%A7%E5%B0%8F%E5%91%A8%E6%9C%9F%E6%9B%B2%E7%BA%BF"
    },
    {
      "depth": 2,
      "text": "指数函数",
      "anchor": "指数函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 2,
      "text": "指数级裂变",
      "anchor": "指数级裂变",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%8C%87%E6%95%B0%E7%BA%A7%E8%A3%82%E5%8F%98"
    },
    {
      "depth": 2,
      "text": "指数函数",
      "anchor": "指数函数-1",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0-1"
    },
    {
      "depth": 2,
      "text": "指数函数增长的脆弱性",
      "anchor": "指数函数增长的脆弱性",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0%E5%A2%9E%E9%95%BF%E7%9A%84%E8%84%86%E5%BC%B1%E6%80%A7"
    },
    {
      "depth": 2,
      "text": "初期难以理解难以注意到",
      "anchor": "初期难以理解难以注意到",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%88%9D%E6%9C%9F%E9%9A%BE%E4%BB%A5%E7%90%86%E8%A7%A3%E9%9A%BE%E4%BB%A5%E6%B3%A8%E6%84%8F%E5%88%B0"
    },
    {
      "depth": 2,
      "text": "对数函数",
      "anchor": "对数函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 2,
      "text": "出道即巅峰",
      "anchor": "出道即巅峰",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%87%BA%E9%81%93%E5%8D%B3%E5%B7%85%E5%B3%B0"
    },
    {
      "depth": 2,
      "text": "玻璃顶约束",
      "anchor": "玻璃顶约束",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%8E%BB%E7%92%83%E9%A1%B6%E7%BA%A6%E6%9D%9F"
    },
    {
      "depth": 2,
      "text": "幂函数",
      "anchor": "幂函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%B9%82%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 2,
      "text": "凹型幂函数",
      "anchor": "凹型幂函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%87%B9%E5%9E%8B%E5%B9%82%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 3,
      "text": "不会遇到玻璃顶的一种函数形态",
      "anchor": "不会遇到玻璃顶的一种函数形态",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E4%B8%8D%E4%BC%9A%E9%81%87%E5%88%B0%E7%8E%BB%E7%92%83%E9%A1%B6%E7%9A%84%E4%B8%80%E7%A7%8D%E5%87%BD%E6%95%B0%E5%BD%A2%E6%80%81"
    },
    {
      "depth": 3,
      "text": "头部国家和头部城市国家所符合的函数",
      "anchor": "头部国家和头部城市国家所符合的函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%A4%B4%E9%83%A8%E5%9B%BD%E5%AE%B6%E5%92%8C%E5%A4%B4%E9%83%A8%E5%9F%8E%E5%B8%82%E5%9B%BD%E5%AE%B6%E6%89%80%E7%AC%A6%E5%90%88%E7%9A%84%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 3,
      "text": "引用书籍：《规模》——杰弗里.韦斯特",
      "anchor": "引用书籍规模杰弗里韦斯特",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%BC%95%E7%94%A8%E4%B9%A6%E7%B1%8D%E8%A7%84%E6%A8%A1%E6%9D%B0%E5%BC%97%E9%87%8C%E9%9F%A6%E6%96%AF%E7%89%B9"
    },
    {
      "depth": 2,
      "text": "凸型幂函数",
      "anchor": "凸型幂函数",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%87%B8%E5%9E%8B%E5%B9%82%E5%87%BD%E6%95%B0"
    },
    {
      "depth": 2,
      "text": "逻辑斯蒂函数、指数函数、对数函数、幂函数对比",
      "anchor": "逻辑斯蒂函数指数函数对数函数幂函数对比",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E9%80%BB%E8%BE%91%E6%96%AF%E8%92%82%E5%87%BD%E6%95%B0%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0%E5%B9%82%E5%87%BD%E6%95%B0%E5%AF%B9%E6%AF%94"
    },
    {
      "depth": 2,
      "text": "对比图",
      "anchor": "对比图",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%AF%B9%E6%AF%94%E5%9B%BE"
    },
    {
      "depth": 2,
      "text": "四大人生职业类型",
      "anchor": "四大人生职业类型",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E5%9B%9B%E5%A4%A7%E4%BA%BA%E7%94%9F%E8%81%8C%E4%B8%9A%E7%B1%BB%E5%9E%8B"
    },
    {
      "depth": 2,
      "text": "熵增定律的约束力，逆水行舟，不进则退",
      "anchor": "熵增定律的约束力逆水行舟不进则退",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E7%86%B5%E5%A2%9E%E5%AE%9A%E5%BE%8B%E7%9A%84%E7%BA%A6%E6%9D%9F%E5%8A%9B%E9%80%86%E6%B0%B4%E8%A1%8C%E8%88%9F%E4%B8%8D%E8%BF%9B%E5%88%99%E9%80%80"
    },
    {
      "depth": 2,
      "text": "指数函数与其他函数对比（找到风口）",
      "anchor": "指数函数与其他函数对比找到风口",
      "citation": "https://www.pystone.net/notes/mental-models-04-functions-math/#%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0%E4%B8%8E%E5%85%B6%E4%BB%96%E5%87%BD%E6%95%B0%E5%AF%B9%E6%AF%94%E6%89%BE%E5%88%B0%E9%A3%8E%E5%8F%A3"
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  "contentMarkdown": "学科04：函数重要模型\n\n# 学科04：函数重要模型\n![](assets/164119723096352_Copy_50.png)\n\n## 1：深奥复杂\n\n## 2：深奥简单\n\n### 极度有用\n\n### 非常直观\n\n## 3：浅显简单\n\n## 4：浅显复杂\n\n## 拉弗曲线\n\n![](assets/164119673472134_Copy_32.png)\n\n## 物极必反\n\n## 国家发展的倒U形曲线\n\n![](assets/164119961196559_Copy_57.png)\n\n## 时间函数\n\n## 我们普通人在生活上遇到的最大挑战就是短视，最近一段时间的境遇会极大的影响我们对未来的判断\n\n## 穿透时间预测未来的上帝视角\n\n## 高特纳曲线\n\n![](assets/164119676759835_Copy_33.png)\n\n## 时间—期望曲线：新技术->高度乐观->过度悲观->逐步走向成熟\n\n## 世界毒打曲线\n\n![](assets/164119679914936_Copy_34.png)\n\n## 人性曲线与物性曲线\n\n![](assets/164119803774558_Copy_56.png)\n\n## 人性函数\n\n### 细胞膜电位与时间关系函数图\n\n![](assets/164119684661537_Copy_35.png)\n\n#### 人类遇到各种刺激情况下的缩影\n\n## 物性函数\n\n### 逻辑斯蒂函数\n\n#### 人口增长模型\n\n![](assets/164119688946038_Copy_36.png)\n\n- L表示整个逻辑斯蒂函数的增长边界\n\n#### 理想状态下的指数增长与环境阻力的限制作用\n\n![](assets/164119690891639_Copy_37.png)\n\n#### 人类历史人口增长\n\n![](assets/164119692438040_Copy_38.png)\n\n## 正余弦函数\n\n![](assets/164119696679641_Copy_39.png)\n\n## 黎明前的黑暗\n\n![](assets/164120041010560_Copy_58.png)\n\n### 不要在遇到挫折的时候，就退出朝阳赛道\n\n#### 一叶障目，不见泰山\n\n## 黑夜前的黄昏\n\n![](assets/164120042491561_Copy_59.png)\n\n## 黑夜中的雷鸣\n\n![](assets/164119704012844_Copy_42.png)\n\n### 不要因为短期看起来光鲜亮丽的形式，就忽略了整体下降的大趋势\n\n## 大趋势要多个学科相互印证\n\n![](assets/164119698265242_Copy_40.png)\n\n## 瑞达利欧产业发展大小周期曲线\n\n![](assets/164119706498845_Copy_43.png)\n\n## 指数函数\n\n## 指数级裂变\n\n![](assets/164119708345646_Copy_44.png)\n\n## 指数函数\n\n![](assets/164119709822047_Copy_45.png)\n\n## 指数函数增长的脆弱性\n\n![](assets/164119711401648_Copy_46.png)\n\n## 初期难以理解难以注意到\n\n![](assets/164119713266949_Copy_47.png)\n\n## 对数函数\n\n## 出道即巅峰\n\n![](assets/164119717113550_Copy_48.png)\n\n## 玻璃顶约束\n\n![](assets/164119718911451_Copy_49.png)\n\n## 幂函数\n\n![](assets/164119726411853_Copy_51.png)\n\n## 凹型幂函数\n\n### 不会遇到玻璃顶的一种函数形态\n\n### 头部国家和头部城市国家所符合的函数\n\n### 引用书籍：《规模》——杰弗里.韦斯特\n\n## 凸型幂函数\n\n## 逻辑斯蒂函数、指数函数、对数函数、幂函数对比\n\n## 对比图\n\n![](assets/164119728178254_Copy_52.png)\n\n## 四大人生职业类型\n\n![](assets/164119730763155_Copy_53.png)\n\n## 熵增定律的约束力，逆水行舟，不进则退\n\n![](assets/164119732330256_Copy_54.png)\n\n## 指数函数与其他函数对比（找到风口）\n\n![](assets/164119734120257_Copy_55.png)\n"
}