Concise Summary简洁概述
A 17th-century witch-trial manual shows the classic trap: every possible observation is declared proof of guilt, so the accused can never win. Probability theory forbids this. The Conservation of Expected Evidence — a theorem derived directly from Bayes's rule — says the expected value of your posterior belief, before you see any evidence, must equal your current prior. This means for every way evidence could push you toward a hypothesis, there is an equally weighted way it could push you away. You cannot, even in principle, design an investigation whose expected outcome is to raise your confidence without risk of lowering it. The only honest use of evidence is to test a theory, never to confirm it.
一本 17 世纪的猎巫审判手册揭示了经典陷阱：任何可能的观察都被宣布为罪证，被告永无翻案之日。概率论不允许这一点。预期证据守恒——直接由贝叶斯定理推导出的定理——指出：在看到任何证据之前，你后验信念的期望值必须等于你当前的先验概率。这意味着，对于证据可能把你推向某假设的每一种方式，都存在一种等权重的方式把你推离它。你不可能——甚至在原则上也不可能——设计出一个预期结果是提高你信心却不冒降低风险的调查。证据唯一诚实的用途是检验理论，而非确证它。
Infographic信息图
You can't have it both ways
鱼与熊掌不可兼得
If 'no sabotage' counts as evidence for a Fifth Column, then 'sabotage' must count as evidence against one. Every claim of confirmation has an obligatory mirror.
若「没有破坏行动」能证明第五纵队存在，则「有破坏行动」就必须证明第五纵队不存在。每一个确证主张都有其强制性的镜像。
A theorem, not just fairness
这是定理，不只是公平
Conservation of Expected Evidence is derived directly from the law of total probability — it's a mathematical constraint, not a moral preference.
预期证据守恒直接由全概率公式推导而来——它是数学约束，而非道德偏好。
Test, never confirm
检验，而非确证
No clever strategy can legitimately make you expect, before seeing the data, that your confidence will increase on average. You can only test, not confirm.
没有任何聪明策略能让你在看到数据之前，合理地预期自己的信心会平均提高。你只能检验，不能确证。
Relaxation follows
随之而来的是释然
Knowing this law is liberating: you needn't worry about spinning every result to fit your theory, because mathematically you never can.
知道这条定律令人释怀：你无需操心如何把每个结果都解释成支持自己的理论，因为从数学上讲，你永远做不到。
Detailed Summary详细概述
The Witch-Trial Opening
Yudkowsky opens with Friedrich Spee von Langenfeld, a Jesuit priest who heard the last confessions of condemned witches in 1631 and recorded the decision tree prosecutors used. The accused's life was virtuous? — proof of witchcraft, for witches dissemble. Evil life? — direct proof of guilt. Imprisoned and afraid? — guilty. Calm and unbothered? — guilty, for witches pretend innocence. Tried to flee? — guilty. Stayed put? — the devil detained her. Spee's singular vantage point was that he sat at every branch: he could see that no possible behavior could exonerate the accused. Scientists write down experimental predictions in advance for exactly this reason — to prevent the investigator from retroactively claiming every outcome as confirmation.
The Mathematical Law
But this isn't merely an ethical complaint about unfairness. It is a theorem.
P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E)
This is just the law of total probability. It says: the expectation of your posterior belief — weighted by the probability of each possible observation — must equal your prior. Yudkowsky names this the Conservation of Expected Evidence.
The corollary is unavoidable: for every expectation of evidence, there is an equal and opposite expectation of counterevidence. If you are confident and expect to see a result matching your hypothesis, that match can only nudge you a tiny bit (you were already near 1); but the surprising failure of your prediction must deal you a proportionally crushing blow. The math is exact and zero-sum.
Three Forced Consequences
The essay enumerates three cases where the law bites:
- Fifth Column: If "no sabotage" counts as evidence that a Japanese-American Fifth Column exists and is hiding, then actual sabotage must be evidence against its existence.
- Witches: If a good life proves a woman is a witch (dissembling), then an evil life must prove she is not a witch.
- God testing faith: If God hiding His existence is held to test humanity's faith, then the biblical miracles must argue against God's existence.
Each sounds absurd — Yudkowsky says to pay attention to that feeling of this seems a little forced, because that instinct is tracking something real.
You Can Only Test, Never Confirm
For a true Bayesian, it is impossible to seek evidence that confirms a theory. No plan, no clever strategy, no cunning scheme can legitimately produce an expected net increase in confidence (on average). Trying to weaken counterevidence only weakens the confirming evidence by the same amount; it is a zero-sum game.
The liberating conclusion: you need not worry about interpreting every possible result favorably. You can't do it even if you try. The correct posture is to test a theory and simply wait for the evidence.
The closing line punctures the relief: "...Human psychology is so screwed up." The whole essay exists because people routinely violate this law — the witch-trial is not a historical curiosity but a template still in active use.
猎巫审判的开场
Yudkowsky 以弗里德里希·斯佩·冯·朗根费尔德开篇——一位 1631 年为被定罪的女巫听临终忏悔的耶稣会神父。斯佩记录了检察官所用的判罪决策树：被告生活贤淑？——女巫善于伪装，故此为证。生活邪恶？——直接罪证。被关押后恐惧害怕？——有罪。镇定自若？——有罪，因为女巫会假装无辜。试图逃跑？——有罪。留下没跑？——是魔鬼将她拘押。斯佩的独特视角在于他坐遍了每一个分支：他能看出，被告无论怎么做都无法洗脱罪名。科学家提前记下实验预测，正是出于同样的原因——防止调查者在事后声称每一个结果都是对自己的确证。
数学定律
但这不仅是对不公平的伦理抱怨，它是一条定理。
P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E)
这正是全概率公式。它说的是：你后验信念的期望值——以每个可能观察的概率为权重——必须等于你的先验概率。 Yudkowsky 将此命名为预期证据守恒。
推论不可回避：对于每一份预期中的证据，都存在一份等量而相反的预期反证。 若你十分有把握、预期会看到与假设吻合的结果，该吻合也只能将你微推一步（你已接近 1）；但你预测出人意料地失败，必须给你造成相应程度的重创。数学是精确的，是零和的。
三个被迫的推论
文章列举了三个定律「咬人」的案例：
- 第五纵队： 若「没有破坏活动」能证明日裔美国人第五纵队的存在（并在潜伏），则实际发生的破坏活动就必须是反对其存在的证据。
- 女巫： 若贤淑的生活证明一名女性是女巫（在伪装），则邪恶的生活就必须证明她不是女巫。
- 上帝考验信仰： 若上帝隐藏自身存在被视为对人类信仰的考验，则《圣经》中的奇迹就必须是反对上帝存在的证据。
每一条听起来都荒诞不经——Yudkowsky 说要注意那种这话感觉有点别扭的感觉，因为这种直觉正在追踪某种真实的东西。
你只能检验，无法确证
对于真正的贝叶斯主义者而言，寻求确证理论的证据是不可能的。没有任何计划、没有任何聪明策略、没有任何精巧方案，能合法地产生信心的预期净增益（平均而言）。试图削弱反证只会以相同量削弱确证证据，这是一场零和博弈。
由此得出令人释怀的结论：你无需担心如何把每个可能的结果都解读为有利。就算你想这么做，也做不到。正确的姿态是检验一个理论，然后静待证据的到来。
结尾那句话刺破了这种释然："……人类心理真的一塌糊涂。"整篇文章存在的原因正是因为人们常规性地违反这条定律——猎巫审判不是一段历史奇闻，而是一个至今仍在活跃使用的模板。
FAQ常见问答
What exactly is "Conservation of Expected Evidence"?「预期证据守恒」究竟是什么？
It is a direct theorem from the law of total probability: P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E). Before you observe any evidence, the weighted average of what your belief would become after seeing all possible outcomes must equal what your belief is now. Your expected belief cannot shift on average — every possible confirmation is exactly offset by a possible disconfirmation.
这是全概率公式直接推导出的定理：P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E)。在你观察到任何证据之前，所有可能结果出现后你信念将会变成的加权平均，必须等于你信念目前是的值。你的预期信念不可能平均地发生偏移——每一种可能的确证都被一种可能的否证精确抵消。
Why does Yudkowsky say absence of evidence is evidence of absence?为什么 Yudkowsky 说「缺乏证据确实是缺席的证据」？
Because Conservation of Expected Evidence forces it. If finding evidence E would raise your belief in H, then not finding E must lower your belief in H (to maintain the average). The magnitude depends on how probable you thought E was; weak expected evidence means its absence is only mildly exculpatory, but strong expected evidence means its absence is genuinely damning.
因为预期证据守恒迫使这一点成立。若发现证据 E 会提升你对 H 的信念，则未发现 E 就必须降低你对 H 的信念（以维持平均值）。降低的幅度取决于你原本认为 E 有多大可能出现；预期证据弱意味着其缺席只是轻微的免罪因素，但预期证据强则意味着其缺席真的相当致命。
How does this apply to the witch-trial example specifically?这如何具体适用于猎巫审判的例子？
Each branch of the accusation tree ('virtuous life' → guilty; 'evil life' → guilty) violates the law. If 'virtuous life' is evidence of guilt (witches dissemble), then by Conservation, 'evil life' must be evidence of innocence — but the witch-finders deny that too. You cannot claim every possible observation increases guilt. Spee saw all branches simultaneously and recognized that no outcome could ever exonerate the accused.
指控决策树的每个分支（「贤淑生活」→有罪；「邪恶生活」→有罪）都违反了这条定律。若「贤淑生活」是有罪的证据（女巫善于伪装），则按守恒定律，「邪恶生活」就必须是无辜的证据——但猎巫者同样否认这一点。你不能声称每一个可能的观察都增加了有罪的可能性。斯佩同时看到了所有分支，由此认识到没有任何结果能为被告洗脱。
Does this mean a very confident scientist should feel no pressure from confirming evidence?这是否意味着一位非常有把握的科学家，对确证证据不应感到多大压力？
Correct, and deliberately so. If you already have 99% confidence in a theory, a successful prediction can only nudge you to perhaps 99.1% — the math gives it very little room. But a failed prediction must drop your confidence severely, perhaps to 50% or lower. A scientist who feels great relief at every confirmation but shrugs off failures is violating this symmetry.
是的，而且这是刻意如此。若你对某理论已有 99% 的把握，一次成功的预测只能将你推到或许 99.1%——数学上留给它的空间极小。但一次预测失败必须大幅降低你的信心，或许到 50% 甚至更低。一位对每次确证都大感宽慰、却对失败满不在乎的科学家，正在违背这种对称性。
If confirmation is mathematically impossible to "engineer," why do people keep trying?若「设计确证」在数学上不可能，人们为何还是不断尝试？
Yudkowsky's closing line answers this: human psychology is deeply screwed up. We are motivated reasoners who feel the pull of desired conclusions. The witch-trial template — where every observation gets spun as confirmation — is not a historical relic; it is a live cognitive pattern. The essay's purpose is precisely to let readers see the impossibility clearly enough that the pattern becomes recognizable when they do it themselves.
Yudkowsky 的结尾一句话回答了这个问题：人类心理被深深地搞砸了。我们是受动机驱动的推理者，受到期望结论的牵引。猎巫审判的模板——每一个观察都被扭曲为确证——并非历史遗迹，而是一种活跃的认知模式。这篇文章的目的，正是让读者看清这种不可能性，清晰到足以在自己身上实施时能够认出来。
Is the law purely negative — just a constraint — or does it have a positive use?这条定律纯粹是消极的约束，还是也有积极用途？
Both. As a constraint, it rules out entire classes of motivated reasoning. As a positive tool, it tells you how to design a genuine test: figure out what observations would change your mind and in which direction, commit to that in advance, and then let the evidence come in. Yudkowsky's closing image — sitting back and relaxing while you wait — is the correct posture once you've designed an honest test.
两者皆有。作为约束，它排除了整类受动机驱动的推理。作为积极工具，它告诉你如何设计真正的检验：弄清哪些观察会改变你的想法以及朝哪个方向改变，提前承诺这一点，然后让证据自行到来。Yudkowsky 结尾的意象——坐下来放松等待——正是在你设计了一个诚实的检验之后，正确的姿态。
In-depth Analysis · Pros & Cons深入解读 · 优缺点
This 740-word piece does something rare: it turns a moral intuition ("you can't have it both ways") into a mathematical theorem and then extracts practical consequences. The witch-trial framing is historically vivid and the core equation is one of the most load-bearing in all of Bayesian epistemology.
这篇 740 词的文章做到了一件罕见的事：它将一种道德直觉（「你不能脚踩两只船」）转化为数学定理，然后提取出实践推论。猎巫审判的框架历史生动，而核心等式是整个贝叶斯认识论中最承重的等式之一。
- The historical opener is pitch-perfect历史开场无懈可击Spee's decision tree is not just an analogy; it is a precise illustration of the conservation law's violation. Every branch of the tree claims confirmation, which is exactly what the math forbids.斯佩的决策树不仅仅是一个类比，它是违反守恒定律的精确图示。树的每个分支都声称确证，而这恰恰是数学所禁止的。
- The math is unusually clear数学推导异常清晰Yudkowsky 实际写出了等式 P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E) 并将其标注为原则的来源而非装饰。论证是可追溯、可核查的。Yudkowsky 实际写出了等式 P(H) = P(H|E)·P(E) + P(H|¬E)·P(¬E) 并将其标注为原则的来源而非装饰。论证是可追溯、可核查的。
- "Test, never confirm" is actionable「检验，而非确证」切实可操作The essay ends with a concrete behavioral upshot: you can stop worrying about how to spin results, because the law makes spinning mathematically futile. The liberation is real.文章以一个具体的行为要点收尾：你可以停止担忧如何扭曲结果，因为这条定律使扭曲在数学上毫无意义。这种释然是真实的。
- The three examples land precisely三个例子精准落点Fifth Column, witch, and God-hiding-for-faith are chosen because each one is a case where the conservation violation is actually used as rhetorical cover — making the absurdity viscerally apparent.第五纵队、女巫和上帝隐藏以考验信仰，被选中是因为每一个都是守恒违背实际被用作修辞掩护的案例——使其荒谬性触目惊心地显现。
- The law is about rational agents, not psychology这条定律关乎理性的 agent，而非心理学The Conservation principle holds for coherent Bayesian reasoners. Real people do not update as Bayes dictates; they anchor, weight vivid evidence too heavily, and update asymmetrically. The essay gestures at this ("human psychology is so screwed up") but doesn't bridge the gap between the normative theorem and descriptive human behavior.守恒原则对连贯的贝叶斯推理者成立。真实的人并不按贝叶斯定理更新信念；他们锚定、过度权重生动证据、非对称地更新。文章对此有所暗示（「人类心理真的一塌糊涂」），但并未弥合规范定理与描述性人类行为之间的鸿沟。
- "Absence of evidence" deserves more nuance「缺乏证据」值得更多细究The claim that absence of evidence is always evidence of absence is mathematically true, but the magnitude depends entirely on how hard you looked. A cursory glance finding nothing is very different from an exhaustive search finding nothing. The essay doesn't address how to calibrate this — a significant practical gap.「缺乏证据总是缺席的证据」这一主张在数学上是正确的，但其程度完全取决于你调查得多深入。粗略一瞥什么都没发现，与穷尽搜索什么都没发现，是截然不同的。文章没有讨论如何校准这一点——这是一个重大的实践缺口。
- The essay overstates how liberating the insight is文章过度渲染了这一洞见的解放感"You might as well sit back and relax" works rhetorically but is misleading as practical advice. Knowing you can't engineer confirmation doesn't tell you how to design a genuinely informative test, how to set priors, or how to aggregate evidence across multiple experiments — the hard parts of actual inquiry.「你大可坐下来放松」作为修辞很有力，但作为实践建议是误导性的。知道你无法设计确证，并不能告诉你如何设计真正有信息量的检验、如何设定先验、或如何跨多个实验综合证据——这些才是实际探究的困难部分。
- The witch-trial example conflates bad epistemology with bad faith猎巫审判例子将糟糕的认识论与恶意混为一谈Spee's torturers were not just epistemically confused — they were operating a system of social control with motivated conclusions. The essay treats the conservation violation as the cause of the injustice, when it may be more accurately a symptom of motivated reasoning in service of power. This conflation can mislead readers into thinking purely epistemic fixes would solve such problems.斯佩时代的刑讯者不仅是认识论上的混乱者——他们在运作一套带有预定结论的社会控制系统。文章把守恒定律的违背视为不公义的原因，而实际上它更准确地说只是权力驱动的动机推理的症状。这种混淆可能误导读者，以为纯粹的认识论修正就能解决此类问题。
An elegant and rigorous short essay that converts a mathematical truism into a genuine epistemic virtue: the discipline of designing tests rather than confirmations. Its weakness lies in overconfidence about how easily the insight translates into better human reasoning — the distance between knowing the law and internalizing it is exactly what the rest of the Sequences struggles to close.
一篇优雅而严谨的短文，将一个数学定理转化为真正的认识论美德：设计检验而非确证的自律。其弱点在于对这一洞见多容易转化为更好的人类推理过于自信——知道这条定律与将其内化之间的距离，正是后续整个系列试图弥合的。
Original Text原文
Friedrich Spee von Langenfeld, a priest who heard the confessions of condemned witches, wrote in 1631 the Cautio Criminalis (“prudence in criminal cases”), in which he bitingly described the decision tree for condemning accused witches: If the witch had led an evil and improper life, she was guilty; if she had led a good and proper life, this too was a proof, for witches dissemble and try to appear especially virtuous. After the woman was put in prison: if she was afraid, this proved her guilt; if she was not afraid, this proved her guilt, for witches characteristically pretend innocence and wear a bold front. Or on hearing of a denunciation of witchcraft against her, she might seek flight or remain; if she ran, that proved her guilt; if she remained, the devil had detained her so she could not get away.
Spee acted as confessor to many witches; he was thus in a position to observe every branch of the accusation tree, that no matter what the accused witch said or did, it was held as proof against her. In any individual case, you would only hear one branch of the dilemma. It is for this reason that scientists write down their experimental predictions in advance.
But you can’t have it both ways —as a matter of probability theory, not mere fairness. The rule that “absence of evidence is evidence of absence” is a special case of a more general law, which I would name Conservation of Expected Evidence: the expectation of the posterior probability, after viewing the evidence, must equal the prior probability.
P(H) = P(H) P(H) = P(H,E) + P(H,~E) **P(H) = P(H|E)\P(E) + P(H|~E)\P(~E)**
Therefore, for every expectation of evidence, there is an equal and opposite expectation of counterevidence.
If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. If you’re very confident in your theory, and therefore anticipate seeing an outcome that matches your hypothesis, this can only provide a very small increment to your belief (it is already close to 1); but the unexpected failure of your prediction would (and must) deal your confidence a huge blow. On average, you must expect to be exactly as confident as when you started out. Equivalently, the mere expectation of encountering evidence—before you’ve actually seen it—should not shift your prior beliefs.
So if you claim that “no sabotage” is evidence for the existence of a Japanese-American Fifth Column, you must conversely hold that seeing sabotage would argue against a Fifth Column. If you claim that “a good and proper life” is evidence that a woman is a witch, then an evil and improper life must be evidence that she is not a witch. If you argue that God, to test humanity’s faith, refuses to reveal His existence, then the miracles described in the Bible must argue against the existence of God.
Doesn’t quite sound right, does it? Pay attention to that feeling of this seems a little forced, that quiet strain in the back of your mind. It’s important.
For a true Bayesian, it is impossible to seek evidence that confirms a theory. There is no possible plan you can devise, no clever strategy, no cunning device, by which you can legitimately expect your confidence in a fixed proposition to be higher (on average) than before. You can only ever seek evidence to test a theory, not to confirm it.
This realization can take quite a load off your mind. You need not worry about how to interpret every possible experimental result to confirm your theory. You needn’t bother planning how to make any given iota of evidence confirm your theory, because you know that for every expectation of evidence, there is an equal and oppositive expectation of counterevidence. If you try to weaken the counterevidence of a possible “abnormal” observation, you can only do it by weakening the support of a “normal” observation, to a precisely equal and opposite degree. It is a zero-sum game. No matter how you connive, no matter how you argue, no matter how you strategize, you can’t possibly expect the resulting game plan to shift your beliefs (on average) in a particular direction.
You might as well sit back and relax while you wait for the evidence to come in.
. . . Human psychology is so screwed up.
弗里德里希·斯佩·冯·朗根费尔德，一位曾为被定罪的女巫聆听临终忏悔的神父，于 1631 年撰写了《刑事案件中的审慎》（Cautio Criminalis），在书中他辛辣地描述了定罪被指控女巫的决策树：若该女巫过着邪恶而不检点的生活，她有罪；若她过着善良而检点的生活，这同样是证据，因为女巫善于伪装，总是竭力显得格外贞洁。女人被关进监狱之后：若她害怕，这证明了她的罪行；若她不害怕，这也证明了她的罪行，因为女巫以假装无辜、摆出一副大胆无惧的面孔为特征。或者，当她听说针对她的巫术指控时，她可能会试图逃跑或留下；若她逃跑，那证明了她的罪行；若她留下，是魔鬼拘押了她，让她无法离开。
斯佩担任许多女巫的忏悔神父；因此他处于一个能够观察到指控树每一个分支的位置——无论被指控的女巫说什么或做什么，都被视为对她不利的证据。在任何单独的案例中，你只会听到这一进退两难困境的某一个分支。正是出于这个原因，科学家们才提前写下他们的实验预测。
但你不能脚踩两只船——这不仅是公平问题，更是概率论问题。「缺乏证据确实是缺席的证据」这一规则，是一条更普遍定律的特殊情形，我将其命名为预期证据守恒：在看到证据之后，后验概率的期望值必须等于先验概率。
P(H) = P(H) P(H) = P(H,E) + P(H,~E) **P(H) = P(H|E)\P(E) + P(H|~E)\P(~E)**
因此，对于每一份预期中的证据，都存在一份等量而相反的预期反证。
若你预期以相当大的概率看到某方向上的弱证据，那么它必然被以相当小的概率看到另一方向上的强证据所平衡。若你对自己的理论非常有信心，因此预计会看到与假设相符的结果，这只能给你的信念带来非常微小的增量（它已接近 1）；但你预测出乎意料地失败，将会（且必须）给你的信心以沉重打击。平均而言，你必须预期自己的信心与开始时完全相同。等价地说，在你真正看到证据之前，仅仅是预期遭遇证据，就不应该改变你的先验信念。
因此，若你声称「没有破坏活动」是支持日裔美国人第五纵队存在的证据，那么你相应地必须认为，看到破坏活动将会反驳第五纵队的存在。若你声称「善良而检点的生活」是一名女性是女巫的证据，那么邪恶而不检点的生活就必须是她不是女巫的证据。若你论证说上帝为了考验人类的信仰而拒绝显示自身存在，那么《圣经》中描述的奇迹就必然反对上帝的存在。
这听起来不太对，不是吗？注意那种这话感觉有点别扭的感觉，那是你脑后那种轻微的紧绷感。这很重要。
对于真正的贝叶斯主义者而言，寻求确证理论的证据是不可能的。没有任何你能设计的计划，没有任何聪明的策略，没有任何精巧的装置，能让你合法地预期自己对某一固定命题的信心（平均而言）会高于之前。你只能寻求检验理论的证据，而非确证它。
这一认识能让你卸下心头一大块重担。你不必再操心如何解释每一种可能的实验结果来确证你的理论。你无需费心计划如何让任何一丁点证据来确证你的理论，因为你知道对于每一份预期中的证据，都存在一份等量而相反的预期反证。若你试图削弱某个可能「异常」观察的反证力，你只能通过等量削弱某个「正常」观察的支撑来做到。这是一场零和博弈。无论你如何谋划，无论你如何论证，无论你如何制定策略，你都不可能预期最终的博弈计划会（平均而言）将你的信念推向某个特定方向。
你大可坐下来放松，等着证据自行到来。
……人类心理真的一塌糊涂。