Friday, July 16, 2004


This blog page summarizes my personal information. Born to Rea and Pansy Gardner on 1370 Richins Avenue, Gridley, CA in 1938 (the house, canals, and town are viewable on google street maps). I am 11th child of a 7 boy 4 girl family. One girl, a twin of Colin, Coleen, died at birth. My growing up years were economically easier than depression era siblings. Rea and Pansy were high school grads. Rea, born in 1891, attended some college, but poor financing killed his dream of graduating, the same situation that happened to his father, Sy, 30 years earlier. In his free time Rea was a sports enthusiast, checkers champion, geographical historian, and religious philosopher, considering astronomy and cosmology. Rea followed several of his father's life interests, i.e. county checkers champs, political geography, loving the medieval era, the Silk Road, Charlemagne, and economic links that empowered the European Enlightenment. Pansy was the musician (piano), an interest passed down to one son (Jack, clarinet), and all three daughters through singing and piano. Rea and Pansy's youngest three sons graduated with degrees in Agriculture, Physics and Mathematics, respectively. All seven sons may have graduated from college except for War War II. Three daughters attended two years of college, a high level for the early 1950's.

Reading came early for myself, enjoying Prince Valiant and the comics before the first grade. School added westerns, and local facts (i.e., Wilkes Expedition and Shinn's "Mining Camps"_) of pre-Gold Rush and scholarly documented Gold Rush people and events. Reviews of native Americans and Wild West people and myths also included Ishi. who walked into nearby Oroville in 1911, Wild Bill Hickok, and Kit Carson type books. From our backyard we dug up Indian grinding bowls and baskets, and in the evenings read books of the period.

As a farm boy, serious work was not required until age ten. From that point on I dreamed of another life, not enjoying dairy, custom hay cutting, drying, chopping, and blowing into barns, at 50% the cost of baled hay. My father also grew row crops and rice on his 90 acres, and 200 acres of rented land. Revenue and segmented costs per acre dominated discussions. Many hours were spent driving tractors, plowing, and discing, sometimes all night, to avoid the heat of the day.

My social conscience developed early in labor and interpersonal areas. Gridley was the home of a migrant labor camp. Weekly new "Okies" came to school, often with chips on their shoulders. To make friends playground/recess fights of some sort would take place. Winning the majority of those fights, I made many friends, almost never fighting with that person again. School administrators allowed the fighting, as well as allowing many of its insensitive teachers to discriminate against the poorly dressed kids in ways that made my heart and conscience cry.

Sports were an early passion. Grammar school championships in flag football, basketball and softball, were great fun. I once broke a leg at half-time of a high school football game, playing tackle football in the back of the end zone. My cheerleader sister was surprised to see an ambulance carrying off her 8th grade brother. I missed the championship flag football game, which we won anyway. High school was sports filled. I improved on my 880 and 1320 times (though no where near one of my brother (Vere)'s times, who once held a national class B record in the 1320). High school basketball was played on D, C, B, and A teams, as was the case in the weight/height/age based teams of that era, winning D and C championships. Baseball, and track were played two years, and football one year, winning a couple of southern league 880 championships. During all times of the year pick up games were played on local sports fields, especially basketball and baseball at the outdoor facilities.

Movie going was enjoyed frequently, often twice a week. Friday nights and Saturday matinees opened my eyes to fantasy, as well as the wider news of the world, and US sports. Given that my hometown had one theater, it was the main source of entertainment. I was often first in line. Once an older brother shook me hard when I emulated Gentleman Jim Corbett's boxing skills (at age 5 or 6). This brotherly act showed his lack of appreciation of fantasy as a motivating aspect of life that many, like myself, consider when setting high standards and goals in life.

During the summer swimming was big. Behind my home was an irrigation canal. The kids from south end of Gridley swam there seven days a week. There were two other canal swimming holes in our area, places that the kids from all over town reached on bicycles. The town also had a swimming pool, and tennis courts.

Math became a special high school interest, as well as Spanish, chess and the science side of life. History was fun, but my school offered only US history. Taking college entrance exams, achieving only a 50 percentile score, and being under financed, I decided to work a couple of years before going to college.

A summer AT&SF railroad fireman job in hot Needles, Barstow CA, and Seligman, AZ, following my mother's family trade, further focused my attention to better working conditions. Work for work's sake was a bore, so I dreamed of going to Europe via the US Army.

Three years were spent in the US Army. Processed in at the Oakland Army Terminal, a meningitis outbreak at Fort Ord, ended a two week stay, riding the train to rainy Ft. Lewis, WA for basic training. We all worried about Quemoy, Matsu, and the revolt in Hungary, spots that we thought that a few of us would end up. Advanced training was spent in the Boston area, Ft. Devens, seeing professional sports for the first time, at Fenway (Ted Williams ) and the Boston Garden (Bill Russell, Bob Cousy). Finishing 3rd in my class, beaten by two college grads, I became a cryptanalyst. I had qualified for the Army Language School, in Monterey, an assignment that would have brought me home for Christmas. But code breaking was for me. It applied my chess, math, and language interests. Code breaking continues as a retirement hobby. Code breaking allows an outside-in view of life, providing enjoyable and productive perspectives to the common inside-out view of life. Several classes of unsolved problems have been 'broken', or nearly broken, by working in ad hoc teams put together on the internet.

Earning a desired European assignment two years were spent in Bavaria, between Munich and Salzburg, Austria. Three of us GI's owned a 1939 Opel. It was used to travel as far away as the French Riviera, Switzerland and Vienna. Our favorite spot was Salzburg, located 60 miles away in a neutral country where military uniforms were not allowed. We felt like civilians almost every weekend. Train trips were taken to Italy (Venice to Rome), France (its Riviera, and Paris), and Holland, during tulip time. A two month side trip to Lebanon, thanks to Pres. Eisenhower widened my interests to include Arabic, and several the cultures of the Middle East. Tent cities were set up in biblical olive orchards. Housing soon moved to the beach outside of Beirut. Daily swims were relaxing. But my time away from California soon ended.

Before going home, a couple words on my European sports activities might be of interest. Company level basketball and fast pitch softball were played. The softball brought two championships, beating nearby Special Forces and other nearby military units. We had a guy that threw in the 90 mph range, I was often his catcher. Three of us softballers tried out for an all-ASA (my Army unit) baseball team to play in the larger European military league. One made it. I soon choose to end my enlistment. After an Atlantic boat ride, seeing the Statue of Liberty, Ft. Dix, and throwing away my last 10 cent pack of cigarettes overboard, I never smoked again. A discharge at the Oakland Army Terminal was obtained in 1959, in time to start the fall semester of college.

College entrance tests obtained 90 percentile results, a level that motivated my college career. An undergrad math degree was earned. Ample electives allowed the history of economic thought, from the Ancient Near East uses of money, to European advances in trade, to the economic systems that preceded Capitalism, and final our modern economic systems were studied.

Post-college work began in aerospace, Vandenberg AFB and missile range issues, learning NASA definitions of mathematical astronomy. Bertha and I dated for four years. We were married in 1965. She is the second oldest of a 9 boy, 5 girl family. She was born in Durango, Mexico, moving to Gridley in 1955, the year of the big flood. Bertha and I enjoyed southern Cal for five years, especially beaches, Disneyland, Dodger and Angels baseball games. Three years were spent in LA, working for Rockwell in Anaheim, Downey and Fullerton. Three evenings/week were spent at Cal State Fullerton grad school.

Completing an MBA degree allowed a career change to take place. Bertha I and two children moved to northern California to be near our families. In northern California public health, the medical field and public service were enjoyed. After 10 years my wife's family restaurant business called. As the corporate CFO, a splitting of a seven brother chain of stores to a three brother operation was enjoyed.

Bertha and I are the parents of three children. Tommy and Michelle arrived in Downey, and Anaheim, respectively. Missy arrived in Yuba City. Raising the kids was great fun. Tommy loved baseball. Michelle loved softball and basketball. Missy loved softball, basketball and volleyball . Completive softball was enjoyed by attending three national tournaments finishing 2nd, 5th and 9th. Missy played center field at Cal Poly (SLO), making all tournament in the NCAA Western Regionals, her last completive softball day. Today, Missy is a registered civil engineer. Michelle is a corp. tax collector for the State of California.

In 1987 Tommy passed on as a passenger in a tragic accident. Since the accident, half-time work has been spent in local libraries studying a range of under reported, and unsolved math history issues. The first topic, the history of zero, mostly a medieval topic reported in my college days. The actual history of zero reports its use in 2,000 BCE Egypt, 2,000BCE Babylon and 600 BCE Mesoamerica. Several projects have centered on analyzing, and decoding under reported texts, mostly from the ancient Near East. Military code breaking skills were brought in to analyze several fragmented Egyptian and Mesoamerican data bases. At times, projects have suggested upgrades to a data base by freshly linking to a closely related data base.

Three professional papers have been published. Two papers describe scribal methods used in the Egyptian Mathematical Leather Roll (EMLR), and the Akhmim Wooden Tablet, each written around 2,000 BCE. The papers were published in India in 2002, and 2006. A condensed version of the EMLR paper was published in the Germany by Springer: Encyclopedia of the Non Western History of Science, and Medicine, 2005.

The Akhmim Wooden Tablet was published by Ganita Bharati, Bulletin of the Indian Society for the History of Mathematics, V ol 28 (2006), Numbers 1-2. The topic, the two-part numbers used in the Akhmim Wooden Tablet and the RMP . The exact quotient and scaled Egyptian fraction remainder method solved an Old Kingdom binary round-off problem. MK scribes partitioned a volume hekat unity (64/64) by divisors 3, 7, 10, 11, and 13. For example, divisor 13 set Q = 4 and R = 12; 4/64 + (60/13)*(1/320); and 1/4 + (4 + 1/2 + 1/13 + 1/26)*1/320.

The AWT is the first text that reported the exact partitioning method, a method often used in the RMP and the medical texts.

Online publications consist of:

A. Egypt

1. Why Study Egyptian Mathematics?

2. Akhmim Woodent Tablet (blog) ; (Wikipedia); (Mathworld)

3. Ahmes 'bird-feeding rate problem (Planetmath)

4. Economic Context of Egyptian Fractions (Planetmath)

5. Egyptian Mathematical Leather Roll (blog); (Wikipedia); (Mathworld); (PlanetMath)

6. Egyptian fractions (Planetmath), History of Egyptian fractions (blog)

7. Egyptian Fractions, Hultsch-Bruins Method (Planetmath)

8. Heqanakh Papyri (Wikipedia)

9. Kahun Papyrus (Wikipedia)

10. Reisner Papyri (blog); (Wikipedia)

11. Red Auxiliary Numbers (Wikipedia), (Planetmath)

12. RMP 2/n table, (blog) Wikipedia

13. Remainder Arithmetic (Planetmath)

14. Remainder Arithmetic vs Egyptian Fractions (Planetmath)

B. Medieval

15. Arabic Numerals (Planetmath)

16. Liber Abaci (blog); (Planetmath)

C. Mesoamerica

17. Aztec Surveying (blog)

18. Mayan Math (Planetmath)

D. Other (Astronomy)

19. Acano Lunar Calendar Method (Planetmath)

Today, our family has grown to five grand children. Michelle has three boys, and Missy two girls. The oldest boy, Chris has earned a 2nd degree black belt in karate, and is a college student. Erik loves football, (middle linebacker, and fullback: gaining 191 yards in one game). Two years ago Erik's team won a section title in DIII football, nearly attaining a second section title last year. Rugby is Erik's first sport. Last year's team won 11 games in a row, winning a West Coast B tournament on Stanford U.'s field. This year Erik was a rugby all star, finishing 4th in a national 20 and under tournament in Colorado. He'll play football his senior year with rugby team mates.

My other three grandchildren are small, so their sports and other interests will be made known years from now. Adam (age 7) plays baseball, and is in a public Montessori school. Avery (age 6) plays soccer, improving greatly this year, scoring five goals in one-half of one game, while learning to read and write in kindergarten. Hannah (4) begins soccer (with Dad as coach). Family and sports fill my time, leaving plenty of time for hobbies, and family vacations.