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If you prefer to wait until the paperback version of a top seller comes out, you need wait no longer for Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality. Because of its popularity, the book that was predicted to become the standard reference for aerospace engineering has exhausted its fourth printing and will soon be out in paperback. That’s almost unheard of for a book that is intended for mathematicians, engineers and physicists and for the rest of us, even the title sounds like a foreign language. The success has astounded author Jack Kuipers, a retired Calvin math professor who many regard as the founder of virtual reality. He spent ten years typing every word of the 384page book and drew all 121 diagrams. The book, which was highly regarded at the time of its initial printing in 1998 and is available worldwide, makes quaternion algebra and resulting calculations involving rotating objects accessible to “aerospacetype people.” “People have written about quaternions before,” said Kuipers. “But a lot of what has been written is not very palatable. I’m an applied person, not a theoretician. That’s what makes this book different.” In fact, it’s Kuipers’ background, before spending 20 years teaching mathematics as Calvin, that makes his take on numbers and equations and formulas so unique. A 17year career in industrial engineering helped Kuipers develop his skill in mathematical modeling. His early career involved working for defense and aerospace contractors to develop complex weapons systems for the U.S. Air Force. He is known as the inventor of “Spasyn,” a patented space synchronizer system that allows pilots to simply look at a target, push a button and direct bombs on target. The system works from a sensor embedded in the pilot’s helmet sending waves electro magnetically to a source in the cockpit. “It was revolutionary because it made dive bombing unnecessary,” said Kuipers. “It was very fortunate for pilots because it made their missions much less risky. It gave the aircraft the flexibility of a handgun.” Much of the employment of Kuipers’ technology has been defense related, though he has worked persistently at finding more civilian uses for it. He is currently working on patenting a system that will make two aircrafts aware of each other even though they can’t see each other. “I didn’t expect my technology would be used so prominently in the military,” he said. “As I began my career I found it very interesting that it (the technology) could be used to support the rendezvous of satellites. Its primary focus is relating two bodies in space.” Yet, much of Kuipers’ work occurred during the Cold War. “You have to understand the mind of the nation,” he said. “We were worried about Russia and communism. We were very concerned about being able to respond if somebody attacked us.” Still it was talk of “kill ratios” and “kill efficiency” that led Kuipers to return to his alma mater in 1966. “I needed to get away from that. I had been moving in circles that I never wanted to get familiar with.” Kuipers graduated from Calvin in 1942 and it was here that he first realized his love for mathematics. “I’m not a scholar type,” said Kuipers. “I never expected to go to college, but when I couldn’t find a job that’s where I ended up.” In fact, he went on to earn three additional degrees from the University of Michigan before returning to Calvin to teach. “I am grateful to Calvin for taking me in when my family so needed it,” he said. Calvin allowed Kuipers to align mathematics with his faith and teach it in that way. For example, in a portion of Kuipers’ book, he links his formulas and sequences to an explanation of the seasons. “Using mathematics you can explain why and precisely compute how much the length of each day increases in the summer and decreases in the winter,” he said. “The appropriate celestial mechanics are modeled using rotation sequences. One can explain it very nicely mathematically, but the effort often generates awe and inspires a spiritual view of things. “It’s fun and often beautiful to work things out and see how they all fit together. I see much beauty in mathematics. Yet, much of what I see around me is pure mystery. We live very presumptuously—we think we understand things, and in some limited, often pious sense we do, but when pressed we do not.” Upon coming to Calvin, Kuipers never gave up his love for applied mathematics. He continued to work as a consultant to the aerospace industry throughout his teaching career. “Jack just has this ability to put mathematics to life,” said Ernie Blood, a former colleague of Kuipers, in a 1998 Grand Rapids Press article. “A lot of professors, they can prove this theory or that on paper, but then give them a practical problem…. “He would sit down and write a mathematical solution to something practical and do it very elegantly.” He did this in developing his simulation for what is real or “virtual reality.” Kuipers began experimenting
with the mathematics used to produce simulations for air force pilots
in the 1950s.
He later developed a sixdimensional graphics system which gained him
the reputation as the founder of virtual reality. The technology is now widely used in the aerospace, defense and entertainment industries. He discounts recognition for his achievements saying, “It is a great honor, but in that context who really deserves that honor if all of us are just what doing what we love to do?” Kuipers, now 81, lives in Grand Rapids with his wife, Lois Holtrop Kuipers ’46. All of their five children graduated from Calvin. He comes to his office on campus on a daily basis to continue working on useful applications for his research. He holds several patents for a variety of products around the world, but continues to work his mathematical genius on more formulas and equations taking this mathematical language and translating it for practical use in society. 


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