- Home
- INVENTING ROOT LOCUS -TOC
- CHAPTER 1: REVOLUTION
- CHAPTER 2 SON OF ST LOUIS
- CHAPTER 3: WASHU
- CHAPTER 4: GE IN WWII YRS
- CHAPTER 5: FIRST PAPER
- CHAPTER 6 AEROPHYSICS
- CHAPTER 7: EUREKA
- CHAPTER 8: SECOND PAPER
- CHAPTER 9: FIRST SPIRULES
- CHAPTER 10: TEXTBOOK
- CHAPTER 11: AUTONETICS
- CHAPTER 12: SPIRULE INC.
- CHAPTER 13 INTO STABILITY
- CHAPTER 14: STROKE YEARS
- ARTWORK
- ROOT LOCUS EXPLANATIONS
- FIVE VIDEOS
1955-1959
CHAPTER 13: INTO STABILITY
THESE REMARKS ARE AN EDITED VERSION OF EVANS' SON, GREG'S, 1987 SPEECH ACCEPTING ON BEHALF OF HIS DAD, THE RUFUS OLDENBURGER MEDAL. HIS TALK ON THAT OCCASION WAS ENTITLED "LIFE IN THE LEFT HALF PLANE."
LEADING, LIVING, AND LOVING A LIFE IN THE LEFT HALF PLANE
INTO STABILITY
As a student, my father's first love was geometry. In fact, the root-locus method began, in a way, in his Soldan High School geometry class. There he discovered a formal discipline matched to his pictorial way of thinking. Years later, he wrote about geometry's appeal in a letter to my high school math teacher:
"Math has always been a game for me and now is a good part of my livelihood. Geometry used to provide (me) a steady diet of looking for a pattern that would lead to a solution before settling down to the detail of writing down all the steps."
His next academic step was a degree in Electrical Engineering at Washington University in St. Louis. (By the way, he abandoned his initial major, Engineering Administration, when one of his professor's recommended he prove himself as an engineer first and prepare for the vice presidency later.) [Post-speech note: His father, Gomer Evans, was an Engineering Vice President at the Wagner Electric Company.]
Twenty years later, in a letter to its Engineering School's former Dean, Alexander S. Langsdorf, my father, reflected on how he learns best and how his Wash. U. teachers helped him "I personally learn most effectively by starting from simple examples and working up. Washington University was excellent in that professor such as yourself, Professor (Roy) Glasgow, Dr. (Frank) Bubb, and Dr. Middlemiss could and did take a student all the way back to the beginning if necessary and work up to the question at hand."
His education continued at General Electric in Schenectady, New York, where he and his fellow students cooperated to survive the rigors of what was known simply as "The Advanced Course". Its particular appeal to him is evident in his later statement on the key to learning:
"The main key to learning in my opinion is to treat the problem as a game using all the simplifications possible to get the approximate answer. ... The General Electric Advanced Engineering Program put great emphasis on solving practical problems in approximate form starting from a few basic principles."
After completing the Advanced Course, my father returned to Washington University as an instructor. There, in one of his classes, a student asked him what would happen to a typical control system if a certain quadratic approximation broke down. My father credits this question as being the specific inspiration for root locus. Working from first principles, he obtained a graphical solution to what he referred to as the "slightly cubic system" envisioned by the student. It was the first root-locus plot. [Post-speech correction: this question was asked in a class at North American Aviation in 1948]
And so, it's no accident that Dad's approaches to problem solving-- starting from the beginning, applying basic principles and geometric reasoning to achieve approximate answers before proceeding to the mathematical detail are at the heart of his rapid graphical analysis technique root-locus method.
It was an unorthodox concept at the time, and as was true of many of his ideas, it did not catch on right away. Reflecting back thirty years later, as to why it eventually did, he wrote, I have had more than my share of luck in hitting it big with Root Locus. I mean luck because many other ideas, not directly I think that the servo, have failed to arouse any interest. The explanation is that I strive for a kind of understanding that most people don't seek. In the case of root locus, it provided a needed link to a complete solution of a system which many others did seek."
Dad, I remember some of your ideas that didn't catch on at the time: spray painting tennis balls bright yellow and orange to improve their visibility, mounting wheels on luggage to enhance their transportability, and staggering work hours to ease traffic congestion. Let's face it, you often were ahead of the times.
But getting back to the learning process, I'll never forget another of his ideas that's only now gaining acceptance using computers in the classroom. I won't forget it because it became my eighth grade science fair project. Together, we built an algebra teaching computer. Its opening message to the student reads as follows: "This is no ordinary machine. It is a teaching machine. can learn at (your) own individual pace. Depending upon the answer given, the machine advances to a more difficult question or to an explanation of why the answer given is wrong. (You) learn instantly whether you are right or wrong. button A to begin."
The questions were written on a roll of shelf paper (. patterns under each answer provided the appropriate counts to a stepping relay and direction to a motor drive. The motor engaged when the student closed a sliding wooden panel that triggered a microswitch. Building logic circuits proved to be a lot of fun, and, 27 years later, I'm still at it.
To my disappointment, Dad was only secondarily interested in the details of the electrical and mechanical design. His primary interests were the contents and structure of its questions and answers; how they could most whatever the state of his initial effectively respond to any student understanding of algebra. Well, I learned more than algebra from the experience. I learned that punching holes, writing programs, and connecting switching relays together were one hell of a lot simpler than aligning and maintaining uniform tension on a roll of shelf paper wrapped around a couple of rotating wooden spindles, and I've stayed as far away as possible from mechanical engineering problems ever since.
Dad's kind of problem solving, grounded in fundamental understanding, didn't always go down well with us kids. We were often content with a more superficial understanding. superficial understanding. Perhaps he was referring to those resistive encounters with us when he wrote again to Dean Langsdorf. "... I find that working with my children is a good testing ground for teaching methods because the subject matter is simple, the opportunities frequent, and the reaction clear."
Well, our occasional reaction may have been resistant but let me set the record straight. His four children went on to earn undergraduate degrees in physics, mathematics, computer science, and engineering. I think it's fair to say he was a role model to all four of us. My father's philosophy toward learning and teaching is, perhaps, best summarized in a 1965 letter he wrote to his favorite Wash. U. Professor, Roy Glasgow:
"it seems to me the real bulk of learning takes place in self-study and problem solving with a lot of positive feedback around that loop. The function of the teacher is to pressure the lazy, inspire the bored, deflate the cocky, encourage the timid, detect and correct individual flaws, and broaden the viewpoint of all."
I'd like to shift gears now and pick up the root-locus story where we left off in St. Louis. John R. Moore offered my father a summer job in Downey, California with North American Aviation. He accepted it and never turned back. There, with the support and encouragement of several auto-pilot designer colleagues (e.g., Jeff Schmidt, Bill Mullins, and others), another idea was born: a plastic tool that became known as the Spirule.
As the root-locus method provides a rapid means of plotting the roots of a servo-mechanism's characteristic equation, the Spirule simplifies the task of constructing accurate plots. Word of its utility spread more rapidly than he imagined. When the head of the University of Cincinnati's Electrical Engineering Department wrote him in 1950 to find out if any Spirules were available for instructional use, my father responded with the following note:“None are available because of the following costs: $30 for a single machine shop model, or 50 cents each for a stamped version in a lot of 500. It's not worth $30 and the demand is far short of 500."
Soon thereafter, however, professors from UCLA and U.C. Berkeley placed orders for 150 and the Spirule Company was born. Mom was the shipping and receiving department, the executive secretary, and the accounting department. Later my older brother and I became the assembly line inserting eyelets and stuffing instruction sheets into envelopes.
One Sunday morning I answered the front doorbell while in my pajamas, only to confront a bewildered looking engineering undergraduate student who asked, "Is this the Spirule Company?" Since they were readily available in college bookstores, I can only surmise that a student desperate enough to drive to our house was cramming on the weekend before his final exam.
At least one such student at UCLA, perhaps driven by his exasperation in mastering its use, was driven to rewrite the lyrics to Merle Travis's popular song, Sixteen Tons. I'll agree to read from just one of the stanzas, if you will agree to imagine Tennessee Ernie Ford singing it.
O, I was born one morning' as the root-locus flew.
Buried neck-deep in snow and a-turnin dark blue.
Raised in the Nyquist by an old zero--
Get a grade in this course and I'll be a hero.
You do sixteen tons, and what do you learn?
Slide-rule busted and the Spirule won't turn.
Well, you get the idea. Despite this student's travail, Spirule orders poured in. My father set prices over the years barely above his costs out of consideration for cash-poor students. Orders continue to this day, arriving at the same address that first appeared in his 1954 Control Systems Dynamics book 9728 El Venado, Whittier, California. My parents still live there and that's where my roots are. Roots not in the reckless fast lane, but roots in the stable left half plane.
By now Mom has personally wrapped, packed, and delivered to Whittier's post office over 100,000 Spirules for shipment to universities and engineers around the world -- 65 countries in all. Over the years she's received a lot of interesting correspondence, including two letters in 1973 from a Philippino Ho Hwa Hui. In the first, he simply asked what a Spirule cost. Mom took it as a typical order and sent him one the same day. He was delighted and included this note with his return payment:
"You have unknowingly given me a two-fold surprise package. First, you sent the Spirule to a complete stranger thousands of miles away without even a guarantee that you'll get paid! Secondly, you are Mrs. W. R. Evans, wife of one of the most respected and prestigious control engineers in the forefront of the W. R. Evans! Of course I don't this highly technical field have to tell you."
Yes, Ho Hwa, you're right. You didn't have to tell her, his colleagues, or the ASME. Today, by bestowing upon him the 1987 Rufus Oldenburger Medal, you recognize him for his method of plotting roots of characteristic equations. My brothers, sister, and I love him for planting in us the roots of character. Both you and we honor the same man, Walter Richard Evans, who today it can truly be said, takes his rightful place among the giants of Control Theory. Congratulations, Dad, and thank you all for coming today to acknowledge what many of us, even Ho Hwa Hui, have known for a long, long time.
Memories of DAD
Each paragraph is a memory I have of Dad
Sports
Dad wasn’t just athletic—he was fearless, physical, and unselfconscious. Mom often mentioned how his high school principal at Soldan High told him to slow down, likely after watching him run energetically through the hallways between classes. His strength was remarkable. While living in Nashville, he tied a rope to the balcony outside his second-story bedroom and climbed up and down with ease. Even in his early 40s, at his heaviest weight of 180 pounds, he was filmed climbing a 12-foot rope outside our Houston home—a feat that left no doubt about his fitness and determination.
Our backyard became a sports haven, all thanks to Dad. Every summer, he set up a 24-foot above-ground swimming pool with a rim four feet off the ground. Dad would sprint across the lawn and dive straight into the pool without hesitation. Beyond the pool, he transformed our yard into a veritable sports park, complete with a large lawn, blacktop area, and a backboard for practicing tennis. He even installed four tall poles with floodlights so we could practice late into the evening.
When my brothers and I took up sports—Randy with basketball, Greg with golf and tennis, and all of us with baseball and touch football—Dad was always there. Despite his own work commitments, he never hesitated to drop what he was doing to join in. He often rounded out teams for games, like two-on-two basketball, and gave his all when playing. I’ll never forget watching Randy practice layups and three-pointers for hours under the floodlights—something we took for granted but only existed because of Dad’s vision and effort.
Dad’s love for sports wasn’t confined to our backyard. He made sure we experienced professional games, and those outings became some of my favorite memories. We’d drive into Los Angeles to watch the Rams at the Coliseum (Bill Wade, Norm Van Brocklin, Elroy “Crazy Legs” Hirsch, Jon Arnett), the Lakers (Jerry West, Elgin Baylor), and the Dodgers (Duke Snider, Don Drysdale, Sandy Koufax, Jim Gilliam). My birthday often coincided with a Sunday doubleheader featuring the St. Louis Cardinals, and seeing my hero, Stan Musial, step into his signature crouch at the plate remains a highlight of my childhood.
One especially unforgettable game was the exhibition at the Coliseum to honor Dodgers catcher Roy Campanella after a paralyzing accident ended his career. Dad and I sat in the top row, far from home plate, but the atmosphere was electrifying. When the lights dimmed and the crowd lit matches, the sight was awe-inspiring. Though we relied more on Vin Scully’s iconic commentary than our own eyes to follow the game, it was an experience I’ll never forget.
Stroke
Sitting at my desk on a Friday afternoon when the phone rang. I recognized the voice, my brother, but not the tone, “Dad is at Presbyterian hospital,” his voice cracking. The next thing I remember was walking into his hospital room that evening and being shocked at his appearance. “Corpse-ike” comes to mind, His face was lifeless, pale, and totally expressionless. Randy was there. “Mom has gone home, “ he said. And so, when the neurologist came in with the results of the brain scan, it was just the two fo us. Perhaps around 9 pm. His report was blunt and to the point. He stated categorically Dad would not walk again or be capable of speech. The stroke had killed his brain cells encompassing a large region of Dad’s left hemisphere, including an area called Broca’s region. How will Mom react to this?
Early the next morning, in the bedroom she had shared with Dad for 26 years, I shared with Mom what the doctor had shared with Randy and me the night before, “I’m afraid he will kill himself,” Mom said. The next thing I remember was calling people on the phone. Doctor’s prognosis, several asked whether it had anything to do with Dad’s stammer. I knew Dad loved his work, but these calls informed me of something I had not known. These men loved Dad. Years later, in the course of doing research for this book, this insight has been reinforced many times over in their letters.
Stammer
Dad stammered. While noticeable, it was not a defining feature of his voice nor a topic of discussion. Recordings of his speech reveal a monotonic quality—he spoke quickly and softly, requiring careful listening. His stammer must have been frustrating, yet he never discussed it or complained, nor did it keep him from engaging in conversation.
Modern science suggests that stammering (or stuttering) arises from disruptions in the neural processes that coordinate speech. Persistent stammering into adulthood is thought to result from a combination of genetic predispositions and differences in brain activity, particularly in areas responsible for speech and motor control. In Dad’s case, I wonder if his mind and mouth operated at such different speeds that the disfluency stemmed from speech not keeping pace with his rapid thoughts. Research has found that stammering may become more pronounced under time pressure or stress—moments when the need for quick articulation could intensify the disconnect between thought and speech production.
Despite these challenges, Dad’s stammer never held him back. I remember attending a lecture with him where, after the speaker concluded with the customary “Any questions?” an awkward silence followed. Seeing no hands raised, Dad would raise his own and ask the first question, despite his stammer occasionally impeding his phrasing. This small act, repeated on other occasions, demonstrated his resilience and willingness to speak up, regardless of the obstacle.
Far from limiting him, his stammer became part of his voice—not a hindrance, but a marker of his determination and ability to rise above the challenge.
Shopsmith
I was in fifth grade, sixth at the latest—possibly even fourth—when Dad bought the Shopsmith. For those unfamiliar, a Shopsmith is the Swiss Army knife of power tools. With remarkable versatility, it could transform from one function to another with relative ease. One moment, it was a table saw: the next, a drill press, then a band saw, or even a lathe. Its accessories supported ripping and cross-cutting, and its design allowed for both vertical and horizontal operations. One of its most useful features was its variable-speed motor, controlled by a dial ranging from A (the slowest) to Z (the fastest). It even came with a laminated card specifying the optimal speeds for various materials and operations. Of course, there was also a user manual packed with helpful how-to’s and safety guidance on every page. But, heck, Dad was an engineer—he could figure it all out, right? Right. And he did. Safety measures, however, were largely ignored. I count myself lucky to still have ten fingers and two eyes, let me tell you.
I distinctly remember the very first woodworking project we tackled with the Shopsmith: a four-drawer desk. It featured a top drawer and three side drawers, the bottom-most deep enough for file folders. Every visible surface was covered with a 1/16-inch veneer of hardwood, finished with two or three coats of clear varnish. The desk measured about 42 inches wide, 30 inches deep, and 32 inches high. And it was mine for the next ten years.
This wasn’t a simple project—not by any stretch. But, unless my memory fails me, we started on Saturday morning and completed it by Sunday night, all in that first weekend the Shopsmith graced our garage. I can still recall the hum of the motor, the scent of sawdust filling the air, and the sense of triumph as we attached the last drawer pull. I was a kid, barely ten years old, and I had just helped build a real piece of furniture from scratch. The pride I felt was overwhelming.
That desk wasn’t just a functional piece of furniture—it was a badge of honor; a tangible reminder of what Dad and I had accomplished together. Countless hours and projects followed with the Shopsmith, but none were as memorable as that desk we built between 1956 and 1958. It was the first, and it set the tone for everything that came after.
As you might have guessed, when I bought my first house in Mountain View in 1978, one of my first purchases was a Shopsmith of my own. And now, nearly 47 years later, it still finds its way into my projects. When I need to rip something that a chop saw or saber saw just can’t handle, the Shopsmith roars back to life, a steadfast companion through decades of craftsmanship.
Lessons in Learning
Dad had a lifelong fascination with education. He sought understanding—true understanding—not mere memorization. This passion is evident across many decades of his life:
· 1930s:At Washington University, Dad’s favorite professor was Roy Glasgow, who inspired him by encouraging students to solve problems independently while providing guidance and coaching.
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· 1940s:While at GE, Dad's passion for education was evident in the letters he wrote for the company’s engineering newsletter, where he emphasized learning and understanding.
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· 1950s:When McGraw-Hill reviewers questioned his decision to omit the Laplace Transform from his development of the root locus method, Dad stood firm. His classroom experience had shown him that students often memorized the Laplace Transform without truly understanding it. Despite pushback from multiple reviewers, he developed the concept in a way he believed was more comprehensible.
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· 1960s:Dad voiced concerns to my high school math teacher about the “New Math” curriculum, which emphasized memorization over understanding. At the same time, the district-wide annual mathematics contest, featuring practical problems written by engineers and applied mathematicians, encouraged real-world problem-solving. My brother Randy and I each won the contest, competing against students from half a dozen high schools. When I attended Caltech, Dad took great interest in Richard Feynman’s Lectures on Physics, finding their emphasis on fundamental principles far more illuminating than the physics he had studied in college.
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· 1970s:Dad built home computers from Heath kits and experimented with primitive links—precursors to modern hyperlinks. He saw this as a way to enhance learning, enabling readers to skip familiar content and quickly access explanations for unfamiliar terms.
Dad’s lifelong dedication to fostering understanding over rote memorization left a profound impact on those around him.
Accidental Deaths of my Evans ancestors
I was 32 years old when my dad was struck down by a stroke at age 60. As shocking as his stroke was, I later learned that tragic losses were a recurring theme in my paternal Evans lineage When my dad was just 14, his father died at the age of 49 from internal bleeding following routine operation. His father, in turn, faced tragedy early in life, losing his own father at the age of 13. That man, Gomer Daniel Evans, a locomotive engineer, perished when his train slid into the Missouri River after heavy rains weakened the track bed. The pattern continued further back in the family history. In 1851, my second great-grandfather, Daniel Evans, lost his father in an accidental drowning when he slipped off a dock in Llanelli, Wales. None of these Evans males died of natural causes.
The line between heroism and misfortune often blurs in the tapestry of life. A locomotive engineer guiding his train despite the inherent risks, or a man working hard to provide for his family, embodies everyday heroism. Conversely, slipping off a dock or succumbing to post-surgical complications highlights life’s capriciousness. Their heroism lies in their perseverance, their contributions to their communities and families, and their ability to navigate the unpredictability of their times. Recognizing them as such not only honors their memory but also inspires the current generation to find strength and purpose in their own journeys.
A Legacy of Strength:
These ancestors faced untimely ends, yet their lives—and the legacy they left behind—paved the way for future generations. Reflecting on their stories, one can sense their quiet heroism in navigating challenges and building a life despite knowing the fragility of existence.
A Reminder of Vulnerability:
While the circumstances may seem rooted in misfortune, they underline the inherent unpredictability of life. This realization can inspire today's Evans males to live purposefully, valuing health, relationships, and the moments often taken for granted.
A Call to Resilience:
The pattern also highlights resilience—the ability to continue, adapt, and grow despite losses. Honoring this trait can bring meaning to the lives of their descendants.
Preserve Their Stories:
Documenting and sharing their histories—whether through a book, a family tree, or even a short film—ensures their lives are remembered and valued. Highlight their professions, sacrifices, and dreams to celebrate their humanity.
Their heroism lies in their perseverance, their contributions to their communities and families, and their ability to navigate the unpredictability of their times. Recognizing them as such not only honors their memory but also inspires the current generation to find strength and purpose in their own journeys.
