“Two Bits, Four Bits, Six Bits, a

Dollar…all for

Pascal, Pythagoras,

and Euclid stand up and holler!”

 

 

Jerry Woodfill

Former NASA Apollo Warning System Engineer

 

 

 

 

 

Reflections on the Space Race and  how mathematics helped America ultimately win.

 

Contact Jerry Woodfill to schedule this free 30 minute talk for your school or professional organization at 281-474-2974

 

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For more about Space Mathematics try:

http://er.jsc.nasa.gov/seh/math.html

by clicking here.

 

     This recollection was prompted by an invitation to keynote the opening of a math and science center at Stephen F. Austin University in Nacogdoches, Texas.  My message was to be a slide show titled: How America Got to the Moon First.  The well-rehearsed program  promised to be  altogether perfunctory.  However,  a brief closing comment from the University academic coordinator of the event changed all that:  “Could you include something about how math benefited you, your career, and NASA?”   Taking no thought of how I might do that, I half-heartedly  agreed.

     Forgotten until a few days before the engagement, that promise had a way of  launching feelings about my character, ethics, and trustworthiness.  My thought had been to conveniently brush aside the request in the heat of my Space Race presentation.  But  I hadn’t been invited to  inaugurate a space education center.  These educators and attendees would come to hear about math learning and its familiar friend science education.

     My wife’s off-hand comment heightened my guilt, “I can’t remember one time that you’ve mentioned using math on your job at NASA.”  I’d only worked at the Johnson Space Center 37 years.  Her follow-up remark simply buried any hope of waving off the professor’s challenge, “For that matter, I don’t know that you’ve ever talked about any engineering either.”  (I hold two degrees from Rice University in electrical engineering.) So that’s the background for these  reflections about math, NASA, and me during the past half century. 

 

 

     The first page of this treatise begins in the year 1948.  The scene opens at the blackboard of Mrs. Geisen’s first grade class at Lincoln Grade School,  Highland, Indiana. I’m holding a chalk in my left hand (Yes, I’m left handed.) waiting for Mrs. Geisen to voice the arithmetic problem I am to scratch on the board. This will be a crude display of my mathematical talents.  A sense of alarm overwhelms me.  I am not alone.   A classmate, my adversary, stands with chalk in hand, ten feet to my right.  He is poised to devour me before  a thirty member congregation of my six year old peers. I am in a math contest!

     Though five decades past, that moment remains as humiliating as it was that morning so long ago…a paralysis of fear consumed me. Sweating hands were the least of my afflictions.  No need to grip the chalk anyway.  The thought of defeat clouded my thinking. Confused by anxiety, I lost on the first problem of the contest.   What happened next will never be forgotten by my classmates.  Slowly placing the wet chalk stick on the blackboard’s  metal ledge,  I burst into tears.  Head bowed, weeping aloud, I returned to my seat wholly dejected, embarrassed, and forlorn.

     Sensing I needed a measure of encouragement, Mrs. Geisen invited me to have lunch at her desk, even giving me her desert in hopes of restoring my confidence and self worth.  I can still remember that small hexagonal white paper cup of  Mrs. Geisen’s  cherry  desert.  This was my humble introduction to the world of mathematics.

     Flash forward to the fall of  1955, two years prior to the October 4, 1957 launch of the Soviet Sputnik. Those 30 classmates and I had separated.  Of all those who graduated from Lincoln School, I was the lone Highland student among 500 freshmen attending the 2000 student Hammond High School, a large metropolitan school in northwest Indiana. Hammond High was on my father’s route to work.  His daily drive to the office made attending the city school possible while hometown friends took a school bus to the much smaller Griffith High School nearer home.  Predictably, the academic and athletic competition was greater at the large city school.  Nevertheless, I made the frosh basketball squad and concluded a 16-0 season as the third high scorer.

       But the recollection which comes to mind that fall occurred on the final day of my freshman Algebra class.  I opened my report card.  Though I’d mostly recovered from that first grade humiliation by making an A on  three successive periods, my teacher Katie Williams had written something in the margin.  It said,  Jerry is a careful thinker.  He will make something of himself.”  I was vindicated!  I had made a comeback from the depths of mathematical defeat.  “I had a future in math after all, despite my dismal beginnings!”

       The building of the first high school in Highland brought me home. Those first graders were now my sophomore classmates, the future graduates of 1960.  Then came October 4, 1957, Sputnik, and the ensuing Cold War. On a cerebral level, I joined the host of Americans wondering about our international status in science and math, but on a more visceral level, I ached to be a star basketball player with a college basketball scholarship. 

     Perhaps, it was Sputnik, the advent of Communist Cuba, or the Cold War which led to the establishment of Highland High School’s first math squad.  Coach Donald Clark recruited four of us from his Geometry classes as the first members. As juniors, (There were no seniors.) we had only Algebra, Geometry, and some Trigonometry as completed disciplines.  Predictably, our performance that first year was sobering.  Among the 700 plus schools in the state of Indiana, we held no ranking in math or basketball though our “round-ballers” had ended with a 16-5 record despite the dearth of seniors. 

     So distressing was my showing at that first math contest that had my first grade classmates been present, Mrs. Geisen’s desert would have been needed once more. But the same resolve America found in the face of Sputnik ignited our math and basketball teams.  A  routine was begun that senior year which promised victory.  The motto was, “PRACTICE, PRACTICE, PRACTICE…STUDY, STUDY, STUDY!” 

     By March of 1960, both the state math contest and basketball tournament were imminent: 700 schools competing, thousands of students  vying for recognition and victory, academically and athletically.   And the formula worked!  No, we won neither contest as far as becoming number one in the state, but our basketball team finished the season at 19-1 ranked in the top twenty among those 700 plus schools…and took the ultimate winning team to task in the final game of the sectional, the fourth game of the state tournament, scoring more points against them than any other team in the tournament. 

     But most impressive was the Trojan math team.  I, as a senior,  finished 14th in the state in my division and my teammate, a junior, in the top 10 of his. So based on our collective performance,  we just might have won the state math contest for Highland High School.

     Having the best game of my career  in the state tournament led to a basketball scholarship at Rice University in Houston, Texas.  However, I soon found both college basketball and mathematics  daunting challenges.  To that extent, I possess a pair of records:  the lowest shooting percentage in Rice basketball history - one of 18 shots (The shot I made was actually a bad pass.) and the lowest grade ever made at Rice in Math 310, Differential Equations.  I made an F minus.

     One might ask,  How can you make an F minus?”  The answer is by never scoring, i.e., in Math 310, as on the hardwood, I never scored!  I’m zero for twelve.  There  were three one hour tests with three problems each and a final with three problems.   That’s 12 altogether, and I never answered one correctly.   The fact is,  I GAVE UP AFTER THE FIRST TEST.  Where was Mrs. Geisen when I needed her?

     Despite this, a merciful electrical engineering professor allowed me to take a summer make-up course elsewhere at a less difficult university math-wise. Nevertheless, I did graduate from Rice in 1965. 

     Lest you think too ill of me as a math and science speaker,  I did make an A on the make-up course at the anonymous college, a school well thought of in engineering circles.  Though you may be thinking of Texas or Texas A&M, it was neither. Rationalizing my athletic/academic failings at Rice, I attributed it to Providence.  Finishing 11th out of 13 in my  Rice electrical engineering class was a divine sign of my work as the Apollo 11 and Apollo 13 warning system engineer.

     These reflections have departed from their original intent which was to refute my wife’s doubt about mathematics in my career at NASA.  Additionally, I have not shown  math’s contribution to the Space Race.  In the interest of restoring a measure of respectability to my narrative, I want to show proof that some kind of cloud hung over my Rice basketball and math endeavors. 

     There is this evidence: The national Scholastic Aptitude Test (SAT)  math achievement exam had 800 as the highest possible score.  Shortly before entering Rice,  I made 770 which registered me well above the top 1% of those taking the test.  Years after graduation, my oldest son brought a math problem home from high school with the comment,  The math instructor said no parent in his years of experience at Clear Lake High School had ever solved the problem.”   That week I became the first, sending the solution to school with my son. 

     As for basketball:  Entering the NASA industrial league comprised of numerous recent college players, some of whom were all-conference performers, I averaged over 20 points per game as one of the three best players in the league.  It was as though  a curse  had existed during my Rice years, a curse which had lifted on graduation.  But I believe  the academic and athletic foundations established during high school carried me in those early years at NASA, years when I needed help from the past in designing the alarm systems for the manned spacecraft which would carry men to the  Moon.  

     How was math used?  I remember the warning system used Boolean Algebra and voting logic to determine which of the lander’s sixteen thrusters failed.  Then there were those probability equations which determined what parts were criticality ONE, i.e., apt to threaten the lives of the crew.  How can I ever forget the mathematics of program control where flow charts integrated the intricate schedules of thousands of components and systems through a math framework to determine which were “pacing” items?  My warning system often appeared as that pacing item in the early years.

     Though those ancient electrical engineering text books were half vacuum tube - half transistor technology, there was one digital chip in the warning system. It was a binary counter. The mathematics of set theory and binary counting were used to denote hardware failures.  In reality, mathematics was so very much a part of going to the Moon that most failed to consider its value in our quest to win the Moon Race.

     The science of going to the Moon, the engineering of the Columbia and Eagle, the ultimate winning of the space race could not have succeeded without the bedrock of mathematics: From the simplest of arithmetic problems through intricate geometric principles to the farthest reaches of the Calculus with its unfathomable concepts of infinity, all contributed to putting the first men on the Moon.

     No astronaut who ever rode a rocket into space could not help but appreciate the power of mathematics to make it happen. The very discovery of the “Rocket Equation” and the measure of specific impulse tells the story,  Will It Make Orbit?”  Without mathematics,  the answer is assured, “No it won’t.”  So that every Russian cosmonaut, NASA astronaut, and future spacefarer will, like my Highland High School math squad, cheer…

 

“Two Bits, Four Bits, Six Bits, a Dollar…

all for Pascal, Pythagoras, and Euclid stand up and holler!”

 

…and thank you Mrs. Geisen.  Wherever you are.

 

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Jerry Woodfill

 

     Jerry Woodfill graduated from Rice University in 1965 with  BAEE and BSEE degrees.  Attending Rice on a basketball scholarship, Jerry joined NASA after graduation becoming the warning system engineer for the Apollo Program.  In this capacity, he was monitoring Neil Armstrong’s Eagle and Jim Lovell’s Apollo 13 craft when his warning system sounded  alarms. 

     For his role in the rescue of Apollo 13, Jerry shared the Presidential Medal of Freedom as part of the Apollo 13 Mission Operations Team at the Manned Spacecraft Center.  A NASA employee for 43  years,  he  speaks to diverse venues about the rescue of Apollo 13  and how America won the Moon Race (which includes a recreation of President Kennedy’s Rice Moon Speech which Jerry attended on September 12, 1962  as a Rice student). His appearances include Rotary clubs, technical societies, AARP chapters, professional and business  meetings, grade schools, Christian schools, and churches of all denominations.

 

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