Chapter 1
IN THE BEGINNING
First memories should probably be family, but I confess first being aware of distances. It was a long way to the next place of interest. After one got there, the model T Ford was slow to somewhere else. My mother once told me that she would put me in the Model T when I needed sleep, for I was happy there. That makes sense.
The cattle across the creek actually looked small. Each vista, however, was filled with wonders of all sorts. There were cows, and milk, and potato patches, and wheat fields, and two barns, and the tall, tall silo. There were things to learn, but one memory better than almost any other is that of a sea horizon. Those Kansas prairies were magnificent. Here they are, though the picture was taken “recently” when trees surround every farm house.
Located 2.7 miles south and 0.7 miles east of Zenith, my “home town”, the farm house was the site of my birth and youth, the center of my world. But the world was a big one; see that wonderful horizon! In the upper right portion one can see the granaries of Stafford, Kansas—the location of my high school. Those are located 7 miles west of Zenith. The trees on the north side of the house--north is to the right in this picture--are “shelter belts” where trees were planted by the government in 1934 and shortly thereafter if the farmers would donate the land. Most of the remaining trees one sees were planted, though there are numerous volunteers. Once there was sufficient population to put out all prairie fires, trees could grow.
Kansas prairies are flat. Stafford County, where I was born, is reputed to be the flattest county in Kansas. There, rain water tends to pool--they are called “mud holes”--and if there is a lot of water, it can drain from the flatter fields in a direction depending on the wind. Flat land, with very few trees, permits one to anticipate views of an ocean.
Growing up with a “sea horizon” has some real merit. By standing in the same place, I noted that each star rises in the very same spot on the horizon, though at different times each night—about four minutes earlier. Now, why was that? And I soon learned that planets wandered around, seemingly in mystical ways. Because there was no electricity, nor near neighbors, the nights could really be dark, leaving bright skies to incite many new questions about the heavens. Dad supplied good explanations and I came to appreciate regularity, and precision. Astronomy became important to me.
Barn sitting was a regular big time activity. From the top of the barn, the horizon was considerably more distant, and day dreaming was easy, and avoiding work was easier yet! How pleased I was to discover some years later that the distance to the horizon for a round world was, in nautical miles, about equal to the square root of the height of the eye, in feet! Higher was better, and I could now calculate it whenever I chose!
As a devotee of the comic strip BUCK ROGERS, with its subtitle of “Twenty-fifth Century”, I was always saddened by the knowledge that I was born 500 years too soon for space travel. That did not hinder me having visions of the world in space, or what marvels might be found there, or what it might be like to travel there.
Kansas was surveyed as settlers arrived, and for most of the state was laid off in square miles, or “sections”. The settlers were given a quarter-section or 160 acres when they homesteaded. Across the section to the north lived a bachelor, Wilmer Learned. I would walk to see him at regular intervals, and he had a piano, and played it, much to my delight. It was only natural that he would teach me to play it. He was of an age that he knew a lot about the civil war, as did my father, so he taught me to play “Marching through Georgia”. It was a delightful tune, and I gave it my all.
I began to play the piano when I was four. That year being 1928, it was 63 years after the end of the civil war. As I write this, in 2008, it will soon be 67 years since Pearl Harbor! Being so close to the civil war, it is no wonder that I heard so much about it from Wilmer and my father.
One day we went somewhere in the community where there was a piano, and I now had an opportunity to play my tune. My parents were astounded, and a year or so later, when they concluded I was serious about music, they borrowed a piano from a relative, and I was in business. Sometime later when I was in elementary school, I took some piano lessons from a wonderful lady in Turon, the first town to the south. I rode my horse to these sessions, a distance of about 8 miles each way. In Stafford high school I played the French horn, the Piano Accordion and sometimes the organ for the city’s local funeral home. Classical music was my great love. On one occasion when the community’s artistic society--The Lyceum--met at Possum Trot grade school (near Neola), I was asked to play, and did so, choosing to play something by J. S. Bach. My presentation was wildly unpopular. Thus I learned at a fairly early age to give an audience some consideration.
Eager to be in school, I started, aged 5, in the first grade at Fairview School. It was a good building, 2 miles south and one-half mile west of Zenith, Kansas—a town that one of my grandfathers, Samuel McComb, had helped found. The school stood alone on the prairie except for a small barn to shelter the horses that the older kids rode to school. If you were too young to ride a horse, you walked, and that’s what I did the first year. The school had a coal bin and a coat room, and one big room for all eight grades. What an opportunity for learning! If you did not know, say, 4th grade geography by the time you were in the 4th grade, something was seriously wrong. It was a splendid place and every day was a pleasure.
Well, there was an occasional bad day. I was instructed at the beginning that if I were spanked at school, I would be spanked at home, no matter what explanation I might have, or what story could be invented. I had no doubts of the truth of that warning as spankings happened. I recall that the coal bin was off limits, but in a flat world with only a school building and a barn for the horses, it was a very attractive place when we were playing hide and seek. It took me a little bit of time to figure out how the teacher knew I had been in the coal bin, but the potential cost was sometimes worth not being found.
One game we played was stick hockey with a crushed tin can. I’m not sure where the sticks came from as there were no trees anywhere. Really they were clubs, and we had bruises to prove it.
At Fairview School we had a ciphering match each Friday afternoon, when everybody went to the slate blackboards and competed on arithmetic problems. After practice rounds, there would be a problem for the record, and the last person to get the correct answer, or an incorrect one, would sit down. Eventually there would be a lone survivor. By the time I was in the second grade, I was reasonably good at math for a 6 year old, but thanks to my Dad (I think) I had learned that for certain multiplications I could just write the answers down. For example, for 78 x 82, I could write down the answer, 6396, without any chalk work. It was a trick, of course, derived from simple algebra which I came to learn about only years later. Remember that (a+b) x (a-b) = (a2-b2). Therefore, (80+2) times (80-2) was very easy to see as 80 times 80 minus 2 times 2. So I could write down 63 (8 squared minus 1 as the first two digits, and 96, or 100 minus 4 as the last two. Thus I could do 73 x 57, or 65 x 55, etc., knowing only the squares of the numbers 1 to 9--and the trick. When the teacher discovered that I could do this type of problem quickly, she was evidently impressed, but I have no idea that she herself knew it was simple algebra, or the way I did it. But that set the scene for one Friday afternoon, when she fed us a whole series of this particular kind of multiplication problem, and I was the only one left standing at the blackboard! Of course I later came to the realization that I had won the ciphering match at the teacher's whim, and she probably only wished to embarrass an exceedingly confident 7th grader. And it was not a particularly good event in my young life from one aspect, for while my math reputation was probably enhanced, it gave me certain delusions of grandeur, and made recesses pure torment until the older kids evened the score. But this experience may have been what motivated me to look for mathematical shortcuts at an early age, and this paid off handsomely in high school, college, and graduate school. I was nearly always looking for ways to save time at homework, and if I should happen to find a way to do arithmetic quickly, there was much to be gained.
For instance, I once had a graduate course in infinite series. Professor Smith, head of the mathematics department at the University of Kansas, delighted in giving us much more homework than it was possible to do, and on one occasion we were given the tedious task of working out coefficients for many terms of an infinite series, for many problems. I diligently sought and discovered a way to find the coefficients by a fairly simple, but novel, gimmick, and turned in all homework problems at the next class. Knowing the task assigned was "impossible", Prof Smith's suspicions were obvious. He knew that I had somehow found the answers, and had copied them. So after the class he asked me to come to his office, having caught me cheating. After I showed him how I had done it, he was much surprised, spent a lot of time trying to prove that scheme wouldn't always work, and finally said he would work on it. However, I had my A for the semester! Subsequently he submitted a note to a mathematical journal, and offered to make me a joint author, which I declined as underserved. I had proved nothing. But I was given credit.
I'm confident that the encouragement I had in the second grade, by being allowed to win the ciphering match, paid off for me throughout my whole life.
By the time I got to the fourth grade, Fairview had closed, and school was now in Zenith. That was a fine brick building, with two rooms and two teachers. We were across the street from an abandoned building that had once been a high school. High school kids now went to Stafford, seven long miles away, and that would be my destination as well.
There remains a pict
ure of the boys in the Zenith school revealing several poignant glimpses of those splendid days.
Back Row, from the left: Bob Brownlee, Lavonne Pruner, Lee McComb, Rex Paulsen,
Calvin Volker, Dick Nichol, Leo Groseclose. Front Row: Glenn Volker, Dale Paulsen,
Veryl Volker, Dwight Zonker, Lee Paulsen, Ralph Krey.
I’m the guy on the left. I first saw this picture more than sixty years after it was taken. I quickly identified each boy, but only after a minute or so did I notice the dogs and the guns. They were just things that accompanied boys, so appeared quite normal. When I shifted my brain into the 21st century and looked with those eyes, then the guns seemed quite extraordinary. Boys used guns to shoot rabbits when going to and from school. The dogs went along, waiting for the games at recess times. The guns were never any kind of problem that I can recall. But then, we did have school prayer!
Another picture that has survived shows Dad and our hired man, Lawrence Thorp, preparing for harvest. I am especially pleased that it shows the old Wallace tractor. I was allowed to ignore shoes if the month name did not have an “r” in it, so the picture was taken sometime between April and September.
I asked questions of my father all the time. One of them, asked when I was five, was “What makes the sun shine?” Dad’s response that nobody knew was a real surprise. He was able to explain why no one knew, so I vowed that someday I would find out. Surely someone, somewhere, would one day find the answer. But this answer also inspired me to try to find more questions for which there was no answer. I must have been a real pain. However, I could never have guessed how significant the answer would come to mean to me later in my life.
The first year in Stafford High School I stayed in Stafford during the week as I was too young to have a driver’s license that would permit me to drive on a state or national highway. My parents rented a room in the basement of a house near the junior high school for seventh, eighth and ninth graders. Home on weekends was very welcome, but I did have the opportunity to learn things that the city boys knew, and was smug when I noticed the additional and magnificent things that farm boys knew that city boys did not. I lived in Stafford until I could obtain my driving license, then I drove each day to high school in the pickup truck. I had been driving on the farm for quite a few years, for boys began driving when their feet reached the pedals, but I began to drive for real when I was a sophomore in high school, aged l4. My first dates came at age 15, and believe me, pickup trucks were essential for such activities.
High school went well. I enjoyed the music more than sports, so I was in the orchestra, the band, and the pep band, playing the French horn. The latter group was relatively small, and we played for the basketball games and special occasions. I also played the piano accordion, but did not play it in groups—I did that on my own, as needed or requested.
I liked the math courses, and particularly enjoyed chemistry and physics.
I had a very close friend, Jerry Baxter, a city boy (see Essay 1). His parents ran the drug store, and there was a magnificent soda fountain there that I tried to inhabit. I was best man at Jerry’s wedding in the fall of 1941.
Our class was poised perfectly for the war. We were well aware that much was ahead, but at this point in time imagined that the action would all be in Europe. We were in for some surprises.
IN THE BEGINNING
First memories should probably be family, but I confess first being aware of distances. It was a long way to the next place of interest. After one got there, the model T Ford was slow to somewhere else. My mother once told me that she would put me in the Model T when I needed sleep, for I was happy there. That makes sense.
The cattle across the creek actually looked small. Each vista, however, was filled with wonders of all sorts. There were cows, and milk, and potato patches, and wheat fields, and two barns, and the tall, tall silo. There were things to learn, but one memory better than almost any other is that of a sea horizon. Those Kansas prairies were magnificent. Here they are, though the picture was taken “recently” when trees surround every farm house.
Located 2.7 miles south and 0.7 miles east of Zenith, my “home town”, the farm house was the site of my birth and youth, the center of my world. But the world was a big one; see that wonderful horizon! In the upper right portion one can see the granaries of Stafford, Kansas—the location of my high school. Those are located 7 miles west of Zenith. The trees on the north side of the house--north is to the right in this picture--are “shelter belts” where trees were planted by the government in 1934 and shortly thereafter if the farmers would donate the land. Most of the remaining trees one sees were planted, though there are numerous volunteers. Once there was sufficient population to put out all prairie fires, trees could grow.
Kansas prairies are flat. Stafford County, where I was born, is reputed to be the flattest county in Kansas. There, rain water tends to pool--they are called “mud holes”--and if there is a lot of water, it can drain from the flatter fields in a direction depending on the wind. Flat land, with very few trees, permits one to anticipate views of an ocean.
Growing up with a “sea horizon” has some real merit. By standing in the same place, I noted that each star rises in the very same spot on the horizon, though at different times each night—about four minutes earlier. Now, why was that? And I soon learned that planets wandered around, seemingly in mystical ways. Because there was no electricity, nor near neighbors, the nights could really be dark, leaving bright skies to incite many new questions about the heavens. Dad supplied good explanations and I came to appreciate regularity, and precision. Astronomy became important to me.
Barn sitting was a regular big time activity. From the top of the barn, the horizon was considerably more distant, and day dreaming was easy, and avoiding work was easier yet! How pleased I was to discover some years later that the distance to the horizon for a round world was, in nautical miles, about equal to the square root of the height of the eye, in feet! Higher was better, and I could now calculate it whenever I chose!
As a devotee of the comic strip BUCK ROGERS, with its subtitle of “Twenty-fifth Century”, I was always saddened by the knowledge that I was born 500 years too soon for space travel. That did not hinder me having visions of the world in space, or what marvels might be found there, or what it might be like to travel there.
Kansas was surveyed as settlers arrived, and for most of the state was laid off in square miles, or “sections”. The settlers were given a quarter-section or 160 acres when they homesteaded. Across the section to the north lived a bachelor, Wilmer Learned. I would walk to see him at regular intervals, and he had a piano, and played it, much to my delight. It was only natural that he would teach me to play it. He was of an age that he knew a lot about the civil war, as did my father, so he taught me to play “Marching through Georgia”. It was a delightful tune, and I gave it my all.
I began to play the piano when I was four. That year being 1928, it was 63 years after the end of the civil war. As I write this, in 2008, it will soon be 67 years since Pearl Harbor! Being so close to the civil war, it is no wonder that I heard so much about it from Wilmer and my father.
One day we went somewhere in the community where there was a piano, and I now had an opportunity to play my tune. My parents were astounded, and a year or so later, when they concluded I was serious about music, they borrowed a piano from a relative, and I was in business. Sometime later when I was in elementary school, I took some piano lessons from a wonderful lady in Turon, the first town to the south. I rode my horse to these sessions, a distance of about 8 miles each way. In Stafford high school I played the French horn, the Piano Accordion and sometimes the organ for the city’s local funeral home. Classical music was my great love. On one occasion when the community’s artistic society--The Lyceum--met at Possum Trot grade school (near Neola), I was asked to play, and did so, choosing to play something by J. S. Bach. My presentation was wildly unpopular. Thus I learned at a fairly early age to give an audience some consideration.
Eager to be in school, I started, aged 5, in the first grade at Fairview School. It was a good building, 2 miles south and one-half mile west of Zenith, Kansas—a town that one of my grandfathers, Samuel McComb, had helped found. The school stood alone on the prairie except for a small barn to shelter the horses that the older kids rode to school. If you were too young to ride a horse, you walked, and that’s what I did the first year. The school had a coal bin and a coat room, and one big room for all eight grades. What an opportunity for learning! If you did not know, say, 4th grade geography by the time you were in the 4th grade, something was seriously wrong. It was a splendid place and every day was a pleasure.
Well, there was an occasional bad day. I was instructed at the beginning that if I were spanked at school, I would be spanked at home, no matter what explanation I might have, or what story could be invented. I had no doubts of the truth of that warning as spankings happened. I recall that the coal bin was off limits, but in a flat world with only a school building and a barn for the horses, it was a very attractive place when we were playing hide and seek. It took me a little bit of time to figure out how the teacher knew I had been in the coal bin, but the potential cost was sometimes worth not being found.
One game we played was stick hockey with a crushed tin can. I’m not sure where the sticks came from as there were no trees anywhere. Really they were clubs, and we had bruises to prove it.
At Fairview School we had a ciphering match each Friday afternoon, when everybody went to the slate blackboards and competed on arithmetic problems. After practice rounds, there would be a problem for the record, and the last person to get the correct answer, or an incorrect one, would sit down. Eventually there would be a lone survivor. By the time I was in the second grade, I was reasonably good at math for a 6 year old, but thanks to my Dad (I think) I had learned that for certain multiplications I could just write the answers down. For example, for 78 x 82, I could write down the answer, 6396, without any chalk work. It was a trick, of course, derived from simple algebra which I came to learn about only years later. Remember that (a+b) x (a-b) = (a2-b2). Therefore, (80+2) times (80-2) was very easy to see as 80 times 80 minus 2 times 2. So I could write down 63 (8 squared minus 1 as the first two digits, and 96, or 100 minus 4 as the last two. Thus I could do 73 x 57, or 65 x 55, etc., knowing only the squares of the numbers 1 to 9--and the trick. When the teacher discovered that I could do this type of problem quickly, she was evidently impressed, but I have no idea that she herself knew it was simple algebra, or the way I did it. But that set the scene for one Friday afternoon, when she fed us a whole series of this particular kind of multiplication problem, and I was the only one left standing at the blackboard! Of course I later came to the realization that I had won the ciphering match at the teacher's whim, and she probably only wished to embarrass an exceedingly confident 7th grader. And it was not a particularly good event in my young life from one aspect, for while my math reputation was probably enhanced, it gave me certain delusions of grandeur, and made recesses pure torment until the older kids evened the score. But this experience may have been what motivated me to look for mathematical shortcuts at an early age, and this paid off handsomely in high school, college, and graduate school. I was nearly always looking for ways to save time at homework, and if I should happen to find a way to do arithmetic quickly, there was much to be gained.
For instance, I once had a graduate course in infinite series. Professor Smith, head of the mathematics department at the University of Kansas, delighted in giving us much more homework than it was possible to do, and on one occasion we were given the tedious task of working out coefficients for many terms of an infinite series, for many problems. I diligently sought and discovered a way to find the coefficients by a fairly simple, but novel, gimmick, and turned in all homework problems at the next class. Knowing the task assigned was "impossible", Prof Smith's suspicions were obvious. He knew that I had somehow found the answers, and had copied them. So after the class he asked me to come to his office, having caught me cheating. After I showed him how I had done it, he was much surprised, spent a lot of time trying to prove that scheme wouldn't always work, and finally said he would work on it. However, I had my A for the semester! Subsequently he submitted a note to a mathematical journal, and offered to make me a joint author, which I declined as underserved. I had proved nothing. But I was given credit.
I'm confident that the encouragement I had in the second grade, by being allowed to win the ciphering match, paid off for me throughout my whole life.
By the time I got to the fourth grade, Fairview had closed, and school was now in Zenith. That was a fine brick building, with two rooms and two teachers. We were across the street from an abandoned building that had once been a high school. High school kids now went to Stafford, seven long miles away, and that would be my destination as well.
There remains a pict
ure of the boys in the Zenith school revealing several poignant glimpses of those splendid days.Back Row, from the left: Bob Brownlee, Lavonne Pruner, Lee McComb, Rex Paulsen,
Calvin Volker, Dick Nichol, Leo Groseclose. Front Row: Glenn Volker, Dale Paulsen,
Veryl Volker, Dwight Zonker, Lee Paulsen, Ralph Krey.
I’m the guy on the left. I first saw this picture more than sixty years after it was taken. I quickly identified each boy, but only after a minute or so did I notice the dogs and the guns. They were just things that accompanied boys, so appeared quite normal. When I shifted my brain into the 21st century and looked with those eyes, then the guns seemed quite extraordinary. Boys used guns to shoot rabbits when going to and from school. The dogs went along, waiting for the games at recess times. The guns were never any kind of problem that I can recall. But then, we did have school prayer!
Another picture that has survived shows Dad and our hired man, Lawrence Thorp, preparing for harvest. I am especially pleased that it shows the old Wallace tractor. I was allowed to ignore shoes if the month name did not have an “r” in it, so the picture was taken sometime between April and September.
I asked questions of my father all the time. One of them, asked when I was five, was “What makes the sun shine?” Dad’s response that nobody knew was a real surprise. He was able to explain why no one knew, so I vowed that someday I would find out. Surely someone, somewhere, would one day find the answer. But this answer also inspired me to try to find more questions for which there was no answer. I must have been a real pain. However, I could never have guessed how significant the answer would come to mean to me later in my life.
The first year in Stafford High School I stayed in Stafford during the week as I was too young to have a driver’s license that would permit me to drive on a state or national highway. My parents rented a room in the basement of a house near the junior high school for seventh, eighth and ninth graders. Home on weekends was very welcome, but I did have the opportunity to learn things that the city boys knew, and was smug when I noticed the additional and magnificent things that farm boys knew that city boys did not. I lived in Stafford until I could obtain my driving license, then I drove each day to high school in the pickup truck. I had been driving on the farm for quite a few years, for boys began driving when their feet reached the pedals, but I began to drive for real when I was a sophomore in high school, aged l4. My first dates came at age 15, and believe me, pickup trucks were essential for such activities.
High school went well. I enjoyed the music more than sports, so I was in the orchestra, the band, and the pep band, playing the French horn. The latter group was relatively small, and we played for the basketball games and special occasions. I also played the piano accordion, but did not play it in groups—I did that on my own, as needed or requested.
I liked the math courses, and particularly enjoyed chemistry and physics.
I had a very close friend, Jerry Baxter, a city boy (see Essay 1). His parents ran the drug store, and there was a magnificent soda fountain there that I tried to inhabit. I was best man at Jerry’s wedding in the fall of 1941.
Our class was poised perfectly for the war. We were well aware that much was ahead, but at this point in time imagined that the action would all be in Europe. We were in for some surprises.
