Chapter 1: Mathematics & Probability Models
（数学与概率思维模型）
- Compound Interest（复利模型）
• Principle 原理:
Small gains compounded over time create extraordinary results.
微小的收益经过时间的复合增长，会产生惊人的结果。
• Practical Tips 实践建议:
Start saving or learning early; even small daily improvements accumulate significantly over time.
提早储蓄或学习；每天的小进步经过时间积累，会产生巨大效果。
• Keywords 关键词: Growth, Patience, Accumulation
增长、耐心、积累 - Expected Value（期望值模型）
• Principle 原理:
Rational decisions depend on probability × potential payoff.
理性决策基于“概率 × 潜在收益”的乘积。
• Practical Tips 实践建议:
Evaluate options based on long-term expected outcomes, not immediate results.
根据长期期望收益评估选择，而非短期结果。
• Keywords 关键词: Probability, Decision-making, Risk
概率、决策、风险 - Opportunity Cost（机会成本）
• Principle 原理:
The true cost of anything is what you give up to get it.
任何选择的真正成本，是你放弃的那个更好的机会。
• Practical Tips 实践建议:
Consider alternatives before committing; always ask, “What am I sacrificing?”
做决策前考虑替代方案，始终问自己：“我放弃了什么？”
• Keywords 关键词: Choice, Trade-off, Prioritization
选择、权衡、优先级 - Bayesian Updating（贝叶斯推理）
• Principle 原理:
Continuously update your beliefs as new evidence appears.
随着新证据出现，不断修正自己的信念与判断。
• Practical Tips 实践建议:
Be flexible; adapt your opinions when presented with reliable new information.
保持灵活；面对可靠新信息时及时调整观点。
• Keywords 关键词: Adaptation, Flexibility, Learning
适应、灵活、学习 - Critical Mass（临界质量）
• Principle 原理:
A system often requires a tipping point to trigger exponential growth.
系统常需要达到临界点后才会发生指数级变化。
• Practical Tips 实践建议:
Focus effort on building momentum; small actions alone may not suffice.
专注于积累势能；单独的小行动可能不足以引发大变化。
• Keywords 关键词: Momentum, Threshold, Growth
势能、门槛、增长 - Regression to the Mean（均值回归）
• Principle 原理:
Extreme outcomes tend to move back toward average over time.
极端结果随着时间会趋向平均水平。
• Practical Tips 实践建议:
Don’t overreact to outliers; focus on long-term trends.
不要对异常值过度反应；关注长期趋势。
• Keywords 关键词: Statistics, Trend, Perspective
统计、趋势、视角 - Diminishing Returns（边际效用递减）
• Principle 原理:
Each additional input yields less and less output.
每增加一单位投入，带来的收益递减。
• Practical Tips 实践建议:
Stop when additional effort produces minimal benefit; optimize resource allocation.
当额外努力带来收益微乎其微时停下；优化资源分配。
• Keywords 关键词: Efficiency, Optimization, Limits
效率、优化、界限 - Arithmetic vs Geometric Mean（算术平均与几何平均）
• Principle 原理:
Long-term returns depend on geometric, not arithmetic, averages.
长期收益取决于几何平均而非算术平均。
• Practical Tips 实践建议:
Evaluate growth multiplicatively; small differences compound over time.
按复利方式评估增长；微小差异会随时间积累。
• Keywords 关键词: Growth, Compounding, Long-term
增长、复利、长期 - Multiplicative Systems（乘法效应）
• Principle 原理:
Success multiplies with synergy; errors multiply through compounding.
成功会因协同而倍增；错误也会通过连锁反应被放大。
• Practical Tips 实践建议:
Focus on positive synergies; minimize small mistakes that can compound.
注重正向协同；尽量减少会积累的微小错误。
• Keywords 关键词: Synergy, Risk, Amplification
协同、风险、放大 - Zero-Sum Game（零和博弈）
• Principle 原理:
One party’s gain is another’s loss.
一方的收益就是另一方的损失。
• Practical Tips 实践建议:
Avoid unnecessary conflict; look for win-win alternatives in life and work.
避免无谓冲突；寻找生活与工作中的双赢机会。
• Keywords 关键词: Competition, Strategy, Balance
竞争、策略、平衡
