数学和统计有助于解释FBI的“失踪科学家”案件，无需阴谋论

统计学原理表明，无需阴谋论也能解释科学家和实验室工作人员大量失踪的现象。

作者：费伊·弗拉姆， 编辑：丹·韦尔加诺

J·埃德加·胡佛的联邦调查局徽章位于联邦调查局大楼侧面。

四月份，一位作家朋友给我发了一封电子邮件，内容是英国小报《每日邮报》的一篇报道——“第九位与美国机密有关的科学家之死疑云重重，令人不安的模式愈发明显”——并评论道：“他们现在才开始注意到吗？”但我读了两遍也没看出其中的模式。

现在，联邦调查局已经展开调查，名单上的人似乎因为“神秘”的死亡或失踪而联系在一起，目前已增加到11人或12人。然而，一些简单的统计学原理表明，任何联系都可能只是错觉。

在这种情况下，统计学家戴维·汉德提出的“概率不对称原理”就派上了用场。他指出，如果数量足够大，随机数字、词语或事件分布就会呈现出聚集和聚集的模式。而这位科学家失踪的事件，他认为，“正是概率不对称原理的一个例证”。

这一原理源于汉德等人所称的“真正大数定律”。例如，在数万亿个随机数中，几乎肯定会出现连续七个7。在一个拥有超过80亿人口的繁忙世界里，总会有人偶遇远在异国他乡的邻居。世界如此复杂多变，以至于各种非凡甚至闻所未闻的事情时有发生。

每年有成千上万的美国人失踪或被谋杀，其中不乏杰出的科学家或在大型实验室工作过的人，这并非特别不合情理。

汉德指出，有两种错误会使随机出现的模式看起来像是相互关联的，具有欺骗性。其中之一是“差不多就行”效应。这种效应经常出现在一些令人惊讶的彩票中奖者故事中，尤其是在将“中奖”的定义扩大到包括那些赢得二等奖或三等奖（金额相对较小）的人之后。突然间，两次中奖似乎就不再是天方夜谭了。

在科学家失踪案的调查中，了解最初是如何发现这种令人不安的模式很有帮助。CNN曾报道过一篇颇有助益的文章，追溯了首例案件，发现其源头是已故的麻省理工学院物理学家努诺·卢雷罗。12月16日，卢雷罗被同一人枪杀，此人几天前曾在布朗大学向一群学生开枪，造成两人死亡。枪手很快被确认为卢雷罗的一位前物理系同学，据信他嫉妒卢雷罗的成就。

然而，也有人猜测，卢雷罗之所以成为袭击目标，是因为他在核聚变领域的研究。核聚变——将小原子核结合成大原子核——一旦科学家们完善这项技术，有望带来更丰富、更清洁的能源。虽然一些核聚变研究与武器相关，但卢雷罗是庞大科学家网络中的一员，该网络致力于大型实验反应堆的研究，并在会议和论文中分享想法。如果一项突破性进展是他遇害的动机，那么他的同事们应该知晓此事。

其他聚变科学家也遭到谋杀了吗？一位名叫杰西卡·里德·克劳斯的作家指出，另一位科学家卡尔·格里尔迈尔于二月份在洛杉矶北部家中被枪杀。然而，格里尔迈尔是一位天体物理学家，他的研究方向是系外行星——围绕银河系中其他恒星运行的行星。

克劳斯写道，这两位遇害的科学家都“精通行星灾难”。核聚变和系外行星与行星灾难有何关联尚不清楚，但对某些人来说，两者关系密切。

据《每日邮报》报道，受害者名单增加到了“第九位”，这源于另一个概率原理错误，即所谓的“另寻他处效应”。粒子物理学家们用这个术语来解释他们在对撞机实验中，试图解读粒子碰撞产生的碎片数据时所面临的风险。粒子物理学家并不直接观测新粒子，而是寻找具有某些预期特性的碎片簇或“峰值”。如果他们没有看到预期的结果，有时会忍不住将目光转向数据的其他部分，并提出类似这样的想法：“嘿，看看这边这个较小的峰值——也许那是一种会彻底改变物理学的新粒子！”

但正如一些人惨痛的教训所表明的那样，随机事物看似形成某种模式的倾向意味着另一个峰值可能只是噪音。在科学家失踪案中，一些热心的侦探将目光转向其他方向，结果发现新墨西哥州有四人在过去一年内失踪，至今下落不明。其中一人是退役空军将领，另外两人并非科学家，但曾在洛斯阿拉莫斯国家实验室工作，还有一人拥有安全许可，但在其他地方工作。

另一起疑似聚集性死亡事件出现在与加州喷气推进实验室有关联的人群中，但只有一人失踪——一位材料工程师，据信于2025年6月徒步旅行时迷路。另外两人曾在该实验室担任科学家，分别于2023年和2024年去世，享年59岁和61岁，他们的家人没有透露死因。这种“近似效应”再次发挥作用，将其他地方发现的聚集性死亡事件与其他一些零星死亡事件联系起来。

汉德说，如果美国每年约有20万成年人失踪，而约有7万人从事与核能相关的工作，那么预计每年大约会有50名从事核能相关工作的人失踪。但鉴于这一谜团已经蔓延到各个行业和各种类型的悲剧中，我们无法找到关于美国在特定时期内，究竟有多少科学家和科学相关人员被枪杀、失踪、徒步旅行迷路或以家属不愿透露的方式死亡的统计数据。

“我并不认为这有什么神秘之处，或者说有什么可疑之处需要解释，”他说。

然而，这些陷阱很容易让人感到震惊。著名物理学家加来道雄最近在接受福克斯新闻采访时谈到此事：“这闻所未闻，”他说，“以前从未发生过。”他的说法没错，但根据汉德概率原理，从未发生过的事件组合每天都在发生——即使是对科学家来说也是如此。

Math and statistics help explain the FBI's ‘missing scientists’ cases

Statistical principles show you don’t need a nefarious plot to explain clusters of missing scientists and lab workers

BY FAYE FLAM EDITED BY DAN VERGANO

J. Edgar Hoover FBI wall emblem on the side of the FBI Building.

wingedwolf/Getty Images

Statistics

In April a writer friend e-mailed me a story from the U.K.-based tabloid Daily Mail—“Mystery surrounds death of NINTH scientist tied to US secrets as disturbing pattern grows”—with the comment, “and they’re just starting to notice?” But I didn’t see the pattern, even after reading it twice.

Now the FBI has launched an investigation, and the list has grown to 11 or maybe 12 people seemingly linked through their “mysterious” deaths or disappearances. Yet some simple statistical principles suggest any connection is likely an illusion.

One idea that comes in handy in cases like this is statistician David Hand’s “improbability principle.” Random numbers, words or distributions of events, he says, can appear to clump and cluster in patterns if you make the numbers big enough. And the missing scientist situation, he says, “is a case for the improbability principle.”

The principle is rooted in what Hand and others have called the law of truly large numbers. In a series of trillions of random numbers, for example, a string of seven 7’s would be almost certain to show up. In a world of more than eight billion busy people, a few will bump into a neighbor traveling in a distant country, for example. The world has so many moving parts that extraordinary and even unheard-of things happen all the time.

It’s not even particularly improbable that of the thousands of Americans who disappear or are murdered every year, a few would include prominent scientists or people who’ve worked at large laboratories.

Hand says that a couple of errors that can make randomly occurring patterns look deceptively connected. One is the “near-enough” effect. This often shows up in surprising stories about repeat lottery winners when the definition of “win” is expanded to include people who won second or third prizes of relatively small value. Suddenly a double win doesn’t seem astronomically improbable at all.

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In the missing scientist investigation, it helps to consider how the allegedly disturbing pattern was first identified. CNN ran a helpful story tracing the index case to the late Massachusetts Institute of Technology physicist Nuno Loureiro. He died on December 16 after being shot by the same person who had opened fire on a group of students at Brown University days earlier, killing two people. The shooter was soon identified as a former physics classmate thought to have been jealous of Loureiro’s success.

Elsewhere, however, people speculated that Loureiro was targeted because of his work in nuclear fusion. Fusion—uniting small atomic nuclei into larger ones—promises more abundant, cleaner energy once scientists perfect it. Some fusion research is connected to weapons, but Loureiro was part of a large network of scientists working on big experimental reactors and sharing ideas at meetings and in papers. If a breakthrough had motivated his murder, his colleagues should have known about it.

Were other fusion scientists being murdered? A writer named Jessica Reed Kraus noted that another scientist, Carl Grillmair, was shot at his home north of Los Angeles in February. Grillmair, however, was an astrophysicist who worked on observations of exoplanets—planets orbiting other stars in the galaxy.

Kraus wrote that both murdered scientists were “versed in planetary catastrophes.” What fusion and exoplanets have to do with planetary catastrophes is unclear, but for some, it’s near enough.

The victim list grew to a “NINTH” person, as the Daily Mail would have it, through another improbability principle error called the “look-elsewhere” effect, which was named by particle physicists to explain a hazard of attempting to interpret the debris they capture by smashing particles together in collider experiments. Particle physicists don’t observe new particles directly but look for a cluster or “peak” of debris with some predicted properties. If they don’t see what they expected, they are sometimes tempted to look elsewhere in the data and say something like, “Hey, what about this smaller peak over here—maybe that’s a new particle that will revolutionize physics!”

But as some have learned the hard way, that tendency of random things to appear to form patterns means that the other peak might be just noise. In the missing scientist case, would-be sleuths looked elsewhere and found a cluster of four people in New Mexico who went missing within the past year and have not been found. One was a retired Air Force general, two others were not scientists but had worked at Los Alamos National Laboratory, and another had a security clearance but worked elsewhere.

Another alleged cluster turned up among people with ties to the Jet Propulsion Laboratory in California, but only one had disappeared—a materials engineer who is thought to have become lost on a hike in June 2025. The other two had worked as scientists at the lab and died at age 59 in 2023 and age 61 in 2024, respectively, and their families didn’t disclose the causes. The near-enough effect comes back into play in the weaving together of these clusters found elsewhere and adding a few other sporadic deaths.

If about 200,000 adults go missing every year in the U.S., Hand says, and about 70,000 people work in areas associated with nuclear energy, you’d expect roughly 50 people involved in that work to annually go missing. But given the way this mystery has sprawled across professions and forms of tragedy, it’s impossible to find statistics on the expected number of scientists and science-related people who were shot or disappeared or been lost hiking or died in a way the family chose not to disclose within a given time period in the U.S.

“I don’t really think there’s a mystery or, indeed, anything suspicious that needs to be explained,” he says.

Still, these pitfalls are easy to find alarming. Celebrity physicist Michio Kaku recently spoke to Fox News about the case: “This is unheard of,” he said. “This has never happened before.” He’s not wrong, but according to Hand’s improbability principle, unheard-of combinations of things that never happened before happen every day—even to scientists.