Dreyfus is not a single case, but rather a series of connected military, civil and criminal proceedings. They began in 1894 with a court-martial that convicted Dreyfus of transmitting military secrets to Germany and sentenced him to life imprisonment on Devil's Island. The verdict, which was tainted by a secret dossier, fabricated evidence and widespread anti-Semitism in the French army and populace, became an international cause célèbre . As evidence of Dreyfus's innocence began to mount and as it became known that French military authorities had manufactured additional evidence to keep the case from being reopened, the army and the government were shaken. The discovery of one forgery, purporting to be a letter from an Italian military attaché, prompted the suicide of the colonel working in military intelligence who had prepared it and produced the resignations of the chief of the Army's General Staff and the Minister of War.
France's highest court, the Cour de Cassation , sitting en banc as a result of special legislation, vacated the judgment of the military court. After five years of brutal conditions on Devil's Island, Dreyfus returned to a second court-martial. At Rennes in 1899, this court again found Dreyfus guilty of treason. Issuing a compromise verdict referring to extenuating circumstances (and prompting Dreyfus to ask "Since when are there extenuating circumstances for treason?"), it sentenced Dreyfus, to another five years confinement. The verdict was so poorly received that within two weeks, the president of the republic pardoned Dreyfus. After further political upheavals and a War Office report finding that most of the evidence at Rennes either did not relate to Dreyfus or had been altered to make it appear that it did, the Cour de Cassation granted a petition for review. In 1906, declaring that no credible evidence of treason ever existed, the court annulled the verdict of the Rennes court-martial. Dreyfus, the man twice convicted of treason, returned to the army and was awarded the cross of the Legion of Honor.
Bertillon's Analysis of the Bordereau
The document that initiated the 1894 prosecution was a letter, known as the bordereau . Retrieved from a wastepaper basket in the German embassy, the bordereau listed several relatively unimportant accompanying documents about French artillery and troops. French intelligence officers decided that Dreyfus was the culprit. (Why not? He was a Jew and an Alsatian.) They collected and contrived evidence to support this thesis and ignored or suppressed all contrary evidence. The resulting dossier was enough to convince the French government to convene the 1894 court-martial.
Handwriting experts contacted by the army and the Ministry of Justice who studied the bordereau came to conflicting conclusions. The most notorious analysis came from the anthropologist Alphonse Bertillon, who claimed that Dreyfus wrote it in a way that would make it look like a forgery of his own handwriting. Bertillon advanced this "self-forgery" theory at both the military trials and at the criminal libel trial of the novelist, Emile Zola, for his vitriolic public letter, J'accuse , which denounced the army for "one of the greatest iniquities of the century" in its handling of the case.
To Bertillon, the proof of "self-forgery" was scientific, incontestable and infallible ) in a word, geométrique . This proof included computations of the probabilities of selected coincidences between the lengths of certain words and letters in this document and the lengths of certain words and letters in correspondence taken from Dreyfus's home. Furthermore, from obscure lexicographical and graphological coincidences within the document itself, Bertillon divined that the letter contained coded information. For example, he stressed the presence of four coincidences out of the 26 initial and final letters of the 13 repeated polysyllabic words in the bordereau . He evaluated at .2 the probability of an isolated coincidence and calculated a probability of .2 4 = .0016 that four such coincidences would occur in normal writing. 16 Likewise, to establish that the letters had been traced over the word intérêt as it appeared in a letter in Dreyfus's brother's handwriting, Bertillon computed the "amazing" frequency with which certain letters in the bordereau appeared over the same letters of the word chain constructed by repeating intérêt a number of times, once a variety of complex and ad hoc adjustments had been made.
The Impact of Bertillon's Testimony
Bertillon's recondite analysis may have had some impact in the first courtmartial before the defense had the opportunity to examine his work carefully. The principal exponent of this view is the novelist, Armand Charpentier, who wrote that Dreyfus's counsel, two observers from the General Staff, and the prosecuting attorney "said afterwards that they understood nothing of Bertillon's testimony." As for the judges, Charpentier merely states that "one may think that it was the same," and he remarks that "in any event, they allowed themselves to be impressed by the scientific phraseology of the system."
Since the 1894 proceedings were closed to the public and were not transcribed, Charpentier's attributions seem somewhat speculative. Moreover, most accounts of the court-martial identify a dramatic announcement by a high-ranking intelligence official that an "honorable person" informed him that Dreyfus was a traitor as the event that swayed the previously doubtful tribunal.
Although the actual impact of Bertillon's pseudo-science in the first courtmartial is difficult to gauge, in all the subsequent proceedings, other experts exposed Bertillon's "proofs" as vacuous. In the Rennes court-martial, for example, a letter provided by the world-renowned mathematician, Henri Poincaré, identified "colossal errors" in Bertillon's analysis and flatly declared that no unprejudiced person with a scientific education could possibly find any merit in it. In a meticulous report prepared at the request of the Cour de Cassation , Poincaré and two other distinguished scholars showed that the supposedly improbable coincidences said to confirm Dreyfus's authorship of the bordereau were of the type and frequency to be expected when one searches for any and all coincidences. For instance, the relevant probability for the four coincidences in the initial and final letters of the 13 polysyllabic words is not .0016. That figure is the probability of exactly four coincidences in four words. The probability of four or more out of 13 is approximately .7, indicating that such "coincidences" are common.
Thus, the Dreyfus case is a clear example of an early abuse of probability theory, but it is not a compelling example of judges or jurors beguiled and bemused by mathematics into convicting an innocent person. The courts-martial and related proceedings were so imbued with anti-Semitism, political machinations, and outright perjury, forgery and fabrications that the mathematical errors pale in significance. Bertillon's forensic forays were more often greeted with ridicule than respect. In the Zola trial, for instance, the reaction to Bertillon's testimony about the "infallible and transcendent method of graphology" was "laughter from the audience." It is not surprising, then, that most accounts do not identify the mathematical testimony as an important cause of the convictions. The opposite view that Professor Tribe injected into the legal literature and case law is based on an obvious misreading of one of these accounts.
Flimsy accusations, supported only by vague character evidence, fabricated hearsay, forged documents and pathological science, make the Dreyfus affair a fascinating chapter in legal history. But it is a poor example of the supposed power o f mathematics to paralyze critical thought and to insulate itself from effective refutation. If anything, the Dreyfus cases demonstrate that forensic abuses of applied probability can be detected and corrected.
This reconstruction of the events in Dreyfus does not mean that "probability evidence" is innocuous and should be routinely admitted. A single set of proceedings, conducted under the glare of publicity in a highly politicized atmosphere, could hardly support so sweeping a claim. But neither can the Dreyfus cases be relied on for the proposition that "probability evidence" is too mystifying to be admissible. The apparent consensus in the legal literature that the convictions are paradigmatic of the paralysis of "critical examination" induced by "mathematical evidence" is, on balance, inconsistent with the historical record. Whether the dangers of such evidence are any greater than those of more conventional modes of proof remains an important question for the law of evidence, but the resolution of this issue should no longer be influenced by a dubious reconstruction of the past.