早期指数增长无法告诉我们的关于失控过程的事情
1 分•作者: jamespropp•3 个月前
这是一篇关于一个简单但（我认为）被低估的观点的文章：
如果一个过程遵循逻辑斯谛曲线，那么早期的行为几乎与指数增长无法区分，这意味着你通常无法从早期数据推断其最终的承载能力。
换句话说，即使有非常好的数据，非常不同的长期结果也可能都与相同的初始“失控”阶段一致。
我使用《火星救援》作为框架（基本上是数学同人小说），但真正的问题是推断和模型选择。
好奇大家是否认为这是一个公正的评价，或者我是否夸大了此类问题在实践中有多么病态。
https://mathenchant.wordpress.com/2026/04/18/sorry-mary
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This is an essay about a simple but (I think) underappreciated point:<p>If a process follows a logistic curve, then early behavior is almost indistinguishable from exponential growth, which means you generally can’t infer its eventual carrying capacity from early data.<p>In other words, very different long-term outcomes can all be consistent with the same initial “runaway” phase, even with very good data.<p>I use <i>Project Hail Mary</i> as a framing device (basically mathematical fanfiction), but the real issues are inference and model choice.<p>Curious whether people think this is a fair critique, or whether I’m overstating how ill-conditioned such problems are in practice.<p>https://mathenchant.wordpress.com/2026/04/18/sorry-mary