數(shù)學(xué)和統(tǒng)計(jì)有助于解釋FBI的“失蹤科學(xué)家”案件，無(wú)需陰謀論

統(tǒng)計(jì)學(xué)原理表明，無(wú)需陰謀論也能解釋科學(xué)家和實(shí)驗(yàn)室工作人員大量失蹤的現(xiàn)象。

作者：費(fèi)伊·弗拉姆， 編輯：丹·韋爾加諾

J·埃德加·胡佛的聯(lián)邦調(diào)查局徽章位于聯(lián)邦調(diào)查局大樓側(cè)面。

四月份，一位作家朋友給我發(fā)了一封電子郵件，內(nèi)容是英國(guó)小報(bào)《每日郵報(bào)》的一篇報(bào)道——“第九位與美國(guó)機(jī)密有關(guān)的科學(xué)家之死疑云重重，令人不安的模式愈發(fā)明顯”——并評(píng)論道：“他們現(xiàn)在才開(kāi)始注意到嗎？”但我讀了兩遍也沒(méi)看出其中的模式。

現(xiàn)在，聯(lián)邦調(diào)查局已經(jīng)展開(kāi)調(diào)查，名單上的人似乎因?yàn)椤吧衩亍钡乃劳龌蚴й櫠?lián)系在一起，目前已增加到11人或12人。然而，一些簡(jiǎn)單的統(tǒng)計(jì)學(xué)原理表明，任何聯(lián)系都可能只是錯(cuò)覺(jué)。

在這種情況下，統(tǒng)計(jì)學(xué)家戴維·漢德提出的“概率不對(duì)稱(chēng)原理”就派上了用場(chǎng)。他指出，如果數(shù)量足夠大，隨機(jī)數(shù)字、詞語(yǔ)或事件分布就會(huì)呈現(xiàn)出聚集和聚集的模式。而這位科學(xué)家失蹤的事件，他認(rèn)為，“正是概率不對(duì)稱(chēng)原理的一個(gè)例證”。

這一原理源于漢德等人所稱(chēng)的“真正大數(shù)定律”。例如，在數(shù)萬(wàn)億個(gè)隨機(jī)數(shù)中，幾乎肯定會(huì)出現(xiàn)連續(xù)七個(gè)7。在一個(gè)擁有超過(guò)80億人口的繁忙世界里，總會(huì)有人偶遇遠(yuǎn)在異國(guó)他鄉(xiāng)的鄰居。世界如此復(fù)雜多變，以至于各種非凡甚至聞所未聞的事情時(shí)有發(fā)生。

每年有成千上萬(wàn)的美國(guó)人失蹤或被謀殺，其中不乏杰出的科學(xué)家或在大型實(shí)驗(yàn)室工作過(guò)的人，這并非特別不合情理。

漢德指出，有兩種錯(cuò)誤會(huì)使隨機(jī)出現(xiàn)的模式看起來(lái)像是相互關(guān)聯(lián)的，具有欺騙性。其中之一是“差不多就行”效應(yīng)。這種效應(yīng)經(jīng)常出現(xiàn)在一些令人驚訝的彩票中獎(jiǎng)?wù)吖适轮校绕涫窃趯ⅰ爸歇?jiǎng)”的定義擴(kuò)大到包括那些贏得二等獎(jiǎng)或三等獎(jiǎng)（金額相對(duì)較小）的人之后。突然間，兩次中獎(jiǎng)似乎就不再是天方夜譚了。

在科學(xué)家失蹤案的調(diào)查中，了解最初是如何發(fā)現(xiàn)這種令人不安的模式很有幫助。CNN曾報(bào)道過(guò)一篇頗有助益的文章，追溯了首例案件，發(fā)現(xiàn)其源頭是已故的麻省理工學(xué)院物理學(xué)家努諾·盧雷羅。12月16日，盧雷羅被同一人槍殺，此人幾天前曾在布朗大學(xué)向一群學(xué)生開(kāi)槍?zhuān)斐蓛扇怂劳觥屖趾芸毂淮_認(rèn)為盧雷羅的一位前物理系同學(xué)，據(jù)信他嫉妒盧雷羅的成就。

然而，也有人猜測(cè)，盧雷羅之所以成為襲擊目標(biāo)，是因?yàn)樗诤司圩冾I(lǐng)域的研究。核聚變——將小原子核結(jié)合成大原子核——一旦科學(xué)家們完善這項(xiàng)技術(shù)，有望帶來(lái)更豐富、更清潔的能源。雖然一些核聚變研究與武器相關(guān)，但盧雷羅是龐大科學(xué)家網(wǎng)絡(luò)中的一員，該網(wǎng)絡(luò)致力于大型實(shí)驗(yàn)反應(yīng)堆的研究，并在會(huì)議和論文中分享想法。如果一項(xiàng)突破性進(jìn)展是他遇害的動(dòng)機(jī)，那么他的同事們應(yīng)該知曉此事。

其他聚變科學(xué)家也遭到謀殺了嗎？一位名叫杰西卡·里德·克勞斯的作家指出，另一位科學(xué)家卡爾·格里爾邁爾于二月份在洛杉磯北部家中被槍殺。然而，格里爾邁爾是一位天體物理學(xué)家，他的研究方向是系外行星——圍繞銀河系中其他恒星運(yùn)行的行星。

克勞斯寫(xiě)道，這兩位遇害的科學(xué)家都“精通行星災(zāi)難”。核聚變和系外行星與行星災(zāi)難有何關(guān)聯(lián)尚不清楚，但對(duì)某些人來(lái)說(shuō)，兩者關(guān)系密切。

據(jù)《每日郵報(bào)》報(bào)道，受害者名單增加到了“第九位”，這源于另一個(gè)概率原理錯(cuò)誤，即所謂的“另尋他處效應(yīng)”。粒子物理學(xué)家們用這個(gè)術(shù)語(yǔ)來(lái)解釋他們?cè)趯?duì)撞機(jī)實(shí)驗(yàn)中，試圖解讀粒子碰撞產(chǎn)生的碎片數(shù)據(jù)時(shí)所面臨的風(fēng)險(xiǎn)。粒子物理學(xué)家并不直接觀測(cè)新粒子，而是尋找具有某些預(yù)期特性的碎片簇或“峰值”。如果他們沒(méi)有看到預(yù)期的結(jié)果，有時(shí)會(huì)忍不住將目光轉(zhuǎn)向數(shù)據(jù)的其他部分，并提出類(lèi)似這樣的想法：“嘿，看看這邊這個(gè)較小的峰值——也許那是一種會(huì)徹底改變物理學(xué)的新粒子！”

但正如一些人慘痛的教訓(xùn)所表明的那樣，隨機(jī)事物看似形成某種模式的傾向意味著另一個(gè)峰值可能只是噪音。在科學(xué)家失蹤案中，一些熱心的偵探將目光轉(zhuǎn)向其他方向，結(jié)果發(fā)現(xiàn)新墨西哥州有四人在過(guò)去一年內(nèi)失蹤，至今下落不明。其中一人是退役空軍將領(lǐng)，另外兩人并非科學(xué)家，但曾在洛斯阿拉莫斯國(guó)家實(shí)驗(yàn)室工作，還有一人擁有安全許可，但在其他地方工作。

另一起疑似聚集性死亡事件出現(xiàn)在與加州噴氣推進(jìn)實(shí)驗(yàn)室有關(guān)聯(lián)的人群中，但只有一人失蹤——一位材料工程師，據(jù)信于2025年6月徒步旅行時(shí)迷路。另外兩人曾在該實(shí)驗(yàn)室擔(dān)任科學(xué)家，分別于2023年和2024年去世，享年59歲和61歲，他們的家人沒(méi)有透露死因。這種“近似效應(yīng)”再次發(fā)揮作用，將其他地方發(fā)現(xiàn)的聚集性死亡事件與其他一些零星死亡事件聯(lián)系起來(lái)。

漢德說(shuō)，如果美國(guó)每年約有20萬(wàn)成年人失蹤，而約有7萬(wàn)人從事與核能相關(guān)的工作，那么預(yù)計(jì)每年大約會(huì)有50名從事核能相關(guān)工作的人失蹤。但鑒于這一謎團(tuán)已經(jīng)蔓延到各個(gè)行業(yè)和各種類(lèi)型的悲劇中，我們無(wú)法找到關(guān)于美國(guó)在特定時(shí)期內(nèi)，究竟有多少科學(xué)家和科學(xué)相關(guān)人員被槍殺、失蹤、徒步旅行迷路或以家屬不愿透露的方式死亡的統(tǒng)計(jì)數(shù)據(jù)。

“我并不認(rèn)為這有什么神秘之處，或者說(shuō)有什么可疑之處需要解釋?zhuān)彼f(shuō)。

然而，這些陷阱很容易讓人感到震驚。著名物理學(xué)家加來(lái)道雄最近在接受福克斯新聞采訪(fǎng)時(shí)談到此事：“這聞所未聞，”他說(shuō)，“以前從未發(fā)生過(guò)。”他的說(shuō)法沒(méi)錯(cuò)，但根據(jù)漢德概率原理，從未發(fā)生過(guò)的事件組合每天都在發(fā)生——即使是對(duì)科學(xué)家來(lái)說(shuō)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 “l(fā)ook-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.