“Two Bits, Four Bits, Six Bits, a
Former NASA Apollo Warning System Engineer
Reflections on the Space Race and how mathematics helped
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This recollection was prompted by an
invitation to keynote the opening of a math and science center at
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
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
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
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
Perhaps, it was Sputnik, the advent of Communist
Cuba, or the Cold War which led to the establishment of
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
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
we just might have won the state math contest for
Having the best game of my career in the state
tournament led to a basketball scholarship at
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
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
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
“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 graduated from
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