Mind & Society

Spotting the Sunk Cost in Disguise

Sunk costs distort decisions in recognizable, patterned ways — and a few targeted self-questions can expose them before they pull you in.

Real Options vs. Irreversibility

Irreversibility creates a quantifiable cost that option value must clear before action becomes rational, turning 'just decide' into 'compare a threshold to the expected upside'.

The Sunk-Cost Double Count

A precise picture of how sunk costs get re-injected into opportunity-cost comparisons, the standard double-count pattern that produces it, and a simple test that exposes the error.

When Does Irreversibility Change a Decision?

Irreversibility is the loss of the option to recover the foregone alternative, and once that option is destroyed, rational choice depends on the value of waiting under uncertainty rather than on the size of the payoffs alone.

When Opportunity Cost Misleads

Opportunity cost gives wrong guidance when the forgone option is misidentified, when sunk costs are double-counted, or when the alternative was never realistically available — and a quick 'would I actually choose this if nothing else were on the table?' test reveals most of these traps.

When Opportunity Cost Fails

Opportunity cost reliably frames decisions between measurable alternatives of similar scope, but loses explanatory power when options involve incommensurable values, sunk commitments, or irreversible consequences.

Where Does 1/√n Shrinkage Show Up?

The standard error of a mean shrinks as 1/√n, and this same scaling shows up visibly in dice averages, polling margins, and physics timing experiments.

When Opportunity Cost Breaks Down

Opportunity cost delivers sharp answers only inside a narrow boundary of comparable, reversible, scale-compatible choices — and it breaks down precisely when decisions become identity-laden, irreversible, or incommensurable.

What You Give Up vs. What You Pay

Opportunity cost is the value of the next-best alternative you forgo, while price is the money exchanged; the two diverge whenever time, attention, or forgone options carry value beyond the transaction itself.

The Real Cost of a Choice

The cost of a choice is the value of the next-best alternative you gave up, not the price you paid.

How Machines Judge Similarity

Machines judge similarity by representing items as numerical vectors and computing the distance between them in a feature space.

TikTok FYP vs Instagram Explore

TikTok's For You Page learns you from pure watch behavior on strangers' videos, while Instagram's Explore learns you from likes and saves blended with your social graph — that's why they feel different.

Why We Enjoy Sad Songs

We enjoy sad songs because the brain simulates loss in a safe context, triggering consolation neurochemistry such as prolactin that real sorrow does not provide.

流星雨是怎么发生的

流星雨是地球穿过彗星遗留的碎片带时产生的，辐射点是透视造成的视错觉。

镜像反转：艺术中的对称魔法

镜像反转不是简单的复制粘贴，而是一种把同一形状分成两个对立的'世界'的装置——它制造意义，靠的是让差异在对称中现身。

镜像反转的视觉与心理效应

镜像反转揭示了大脑对'自我视角'的偏好：熟悉的方向会被当作真实，反向则显得陌生，而艺术家和心理学家正是利用这种不对称来制造意义。

How Borda Count Crowns a Loser

Borda count collapses the *ordering* of preferences into *points*, so the size of the margin at each rank — not just the ranking itself — decides the winner, and this lets a candidate who is last against every rival still win overall.

When Elections Misbehave: Arrow's Impossibility in Practice

Arrow's impossibility becomes tangible when a single set of ballots reveals three different failures: plurality violates Independence of Irrelevant Alternatives through a spoiler, Borda count violates Condorcet/transitivity via a reversal, and instant-runoff voting fails transitivity through a cycle.

夜里的魔法师：噩梦在帮我们整理心情

孩子的噩梦，是在悄悄完成一件重要的事

夜里的小烦恼，自己会变小

Arrow's Impossibility Theorem

Arrow's theorem proves that no ranked-ballot voting rule with three or more options can simultaneously satisfy every basic fairness condition—at least one must be sacrificed.

噩梦在整理情绪

噩梦是睡眠在把白天的情绪记忆重新打开、降低强度再归档，大脑借此把情绪从「当下正在发生」搬到「已经发生」。

为什么有些梦记得清，有些忘光？

梦的留存不取决于梦本身有多强烈，而取决于醒来后那几十秒里你是否把梦境翻译成了语言——大脑只在“刚醒”这个极短的窗口里，把视觉化的梦境转写成可以长期储存的语言记忆。