THE FIGHTING EPSILONS
By James F. Epperson

The following piece of wistful humor was composed by Jim Epperson, a Civil War enthusiast with a mathematical background.  One may see his serious websites at:  

http://members.aol.com/jfepperson/causes.html
and
http://members.aol.com/siege1864

        The Civil War (or, if you prefer, War Between the States) is well-known for the large number of distinctive and colorful regiments and brigades on both sides. Students and buffs are all familiar with the exploits of such units as the Iron Brigade, the Stonewall Brigade, the Orphan Brigade, the 20th Maine, the Louisiana Tigers, the 1st Minnesota, and the 5th N.Y. Interior Decorators. One of the less-well-known regiments -- in fact, their story has only recently been discovered by a researcher at Princeton University -- was the 1st United States Mathematicians, known as the "Fighting Epsilons."
        The idea for a regiment of mathematically trained soldiers came to Peter Fairmaht, a German immigrant school teacher working in the St. Louis area. Educated at the best German schools, under men such as Jacobi and Gauss, Fairmaht was convinced that a corps of men, trained to think precisely and analytically, and skilled at computation, would be of invaluable service to the Federal war effort. In the fall of 1862, he took his proposal to President Lincoln himself. Always intrigued by interesting ideas, Lincoln gave Fairmaht permission to recruit for the Federal service regiment of men "trained in the analytical and deductive arts and sciences." (There are some indications among John Hay's papers that Lincoln agreed only to get Fairmaht out of his office, as the President lived in mortal fear that the German professor would ask him to do an algebra problem.)
        Fairmaht was expected to concentrate his recruiting efforts among the New England and New York universities, but his European training had convinced him that these schools were vastly over-rated, so he concentrated his efforts in the new colleges emerging in the Midwest. By the end of the spring, 1863, semester, he had nearly 300 men ready for service. (He would have had more, but the men from Ohio Agricultural College had all flunked their final exams.)
        To Fairmaht's eternal disgust, the War Department split the regiment up into small detachments, each one assigned to a field headquarters. Fairmaht's dream of demonstrating the superior combat abilities of the analytical mind were forever dashed, and his troops were forced to serve in small driblets (hence their nickname, "Fighting Epsilons," for the small sizes of each detachment) scattered across the country.
        Still, they did good service. The improvement in the Army of the Potomac's intelligence service can be directly tied to the arrival of the men from the 1st USM, who were able to correct the woefully exaggerating estimation techniques held over from the McClellan regime. (McClellan, an advocate of all things French, had ignored the more recent work on approximation and estimation being done at Heidelberg.) It was the detachment of Epsilons that was able to accurately estimate the ranges to Pickett's men during the charge at Gettysburg, thus resulting in the heavy casualties among the Rebel troops before they were able to close with the Yankee lines.
        In the west, Col. Fairmaht himself led the detachment that served with Grant in the Vicksburg campaign, where controversy continued to dog the good colonel. It was Fairmaht's analysis which convinced Grant that paroling the prisoners would maximize the cost-benefit utility function, and thus lead to the optimum result for the Federals, a conclusion that foundered when the Rebels unilaterally released the men from parole early that fall. Fairmaht's claims that "the proof of the theorem is entirely valid, those damned Rebels refused to satisfy the hypotheses!" did not sit well in Washington, although Grant remained supportive of the German's work.
        Not all of the Epsilons' efforts paid off. The detachment serving with the Army of the James argued strenuously that Maj. Gen. Ben Butler's effort to blow up Fort Fisher by exploding a boat filled with gunpowder would be a failure. But the Massachusetts politician-general scoffed at their analysis. "Bah! did any of you graduate from Harvard? No! Then why should we listen to you?" Before this, the Epsilons had tried to convince Army of Potomac headquarters that Burnside's mine was a sound idea, but were unable to overcome the prejudices that existed. Maj. James Duane, the Army of the Potomac Chief Engineer, still held a grudge against the Epsilons for showing that McClellan, far from being badly outnumbered at Antietam, had in fact outnumbered Lee. If Col. Fairmaht had been serving in the east, he might have been able to convince Grant, who liked and trusted the German scholar, but Fairmaht was still serving in the west.
        During Sherman's campaigns, the Epsilons continued their strong efforts. It was a ballistic analysis by the 1st USM that helped target the artillery round that killed Confederate Lt. Gen. Leonidas Polk, and a brilliant, extemporaneous, heat and fluid flow analysis that helped Sherman turn the tide of the devastating fire in Columbia, South Carolina. The effort was so intense and fatiguing that Col. Fairmaht -- who did most of it himself -- spent much of the time throwing up while he worked. Of course, the logistic support efforts for Sherman's army, including the March to the Sea, were all based on mathematical analyses carried out by the Epsilons.
        Confederate efforts to use mathematical talent were more mixed and are still shrouded in mystery. A young British scholar, brought to the South in the 1850's to impart Euclid and other subjects to the children of a Louisiana planter, served in some capacity throughout the early western campaigns. It appears to have been this man -- whose precise identity is unknown, although he did seem to have an affinity for the planter's youngest daughter, named Alice -- who sited Fort Henry on the flood plain of the Tennessee River, and who placed Bragg's line of defense along Missionary Ridge. A devotee of the more abstract areas of mathematics, he appears to have been uncomfortable with the egalitarian nature of applications, and spoke mostly in convoluted riddles, thus hampering communication with his superiors. He was last seen during the rout from Missionary Ridge, running wildly through the melee screaming, "I'm late! I'm late!"
        On the other hand, Confederate efforts in the east scored a number of major coups. This group became known as the "Deltas," because most of them had been working as tutors to planters in the Mississippi Delta region. Desperately short of resources, the Deltas had to depend on battlefield scavenging for their slide rules and trig tables. There are even claims that Harry Heth's division was directed to march on Gettysburg for the express purpose of seizing the collection of trig and log tables held by the Mathematics Department at Pennsylvania College.
        A team of Delta cryptographers was able to crack the Federal codes easily, thus giving General Lee intimate knowledge of what was happening at Federal headquarters. Their decoding of a message from Hooker's headquarters during the Chancellorsville Campaign -- "Butterfield: Make sure Miss LaTour is brought to my tent tonight. Will you and yours be able to join us?" -- is thought to have influenced Lee's decision to stand and fight. It is also believed that McClellan's own intelligence staff was badly infiltrated by Confederate mathematicians, who were able to leave behind a flawed methodological legacy that was not corrected until the arrival of the Fighting Epsilons soon after Chancellorsville.
        It was the presence of the Deltas in the eastern theatre that, in Col. Fairmaht's mind, proved the foolishness of splitting his unit into detachments. "They had parity with us in a critical theatre," he wrote after the war, "and we were unable to exploit our advantages. Every time we tried to undertake an analysis, one of them was on hand to thwart us. For every Epsilon, there was a Delta, and this limited out effectiveness at first." But eventually, the Epsilons' superior training won out.
        Until recently, the only hint of the existence of the Fighting Epsilons was a curious note about the Columbia fire. In his personal copy of Sherman's Memoirs, Col. Fairmaht had made an odd marginal notation: "I have a wonderful anecdote to tell about this incident, but the margin of this book is too small to contain it." Scholars searched for years for Fairmaht's story, but it wasn't until 1993 that a wily Princeton professor looked among some ungraded homework papers found among Fairmaht's effects, and there found the manuscript history of the "Fighting Epsilons."

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