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Autobiographical details

Motto: I'm not a wimp, I'm a wamp (wary ass medial positioner). Think about it. Goldilocks was a wamp in The House of The Three Bears.

Born Niangua, MO, 7/8/20, to a Southern Methodist minister who, in a Ford "flivver", was a "circuit rider", serving 7 churches, sometimes intimidated by the KKK, which took control of many churches. For support, Dad received the Parsonage in which I was born, and (as with Atticus Finch in the book and film, To Kill a Mocking Bird) received salary in goods and services from his congregations. (My religious beliefs are ONLINE in the hyperlink "Religion" on the Frontpage of the Website, http://.../scimathrelpage.htm , a complaint about presentations of science and mathematics as revealed. A similar complaint, http://.../platpage.htm , partially blames Platonism in "Math Establishment" for this.)

Later Dad ministered in the parks of Tulsa (OK) and Springfield (MO), to business executives, politicians, ball players, widows and widowers, etc., who found therapy in the loving care Dad gave to his gardening. (Wherever trees congregate in petitive pose, and flowers raise hosanna to the skies, there my father is.) Dad displayed genius by resusitating the botched home gardens of petitioners.

Mother, a dressmaker, when brought a photograph or drawing of a Paris design or Hollywood creation, could duplicate it. Back of a every great deisigner is a greqat cutter, who can cut the material so that it drapes well and uses minimal material. Mom could do that, a great talent in the "Great Depression". Mom also showed genius in resuscitating botched dresses of petitioners. But Mom couldn't manage well. In 1927, "Miss Tulsa" Norma Smallwood became the second "Miss America", and Mom sewed her wardrope for her world tour, but was cheated out of everythng by an absconding partner.

Having few craft skills, myself, my father and mother inspired in me great awe of and admiration for artisans.

I was born when Dad was 46. His father, John Hays, was said have been a captain in Union Army during Civil War, and his wife, Emily Davis Hays, was said to have been a cousin of Jefferson Davis, President of the Confederacy. All in the family.

Started school in Tulsa, where I was also part of children's theater, in plays and minstrel shows (I didn't know any better); reciting on Saturday morning children's radio shows. Later, while going to school in Springfield. I played trumpet in a Boy Scout Band, which could put 3 bands of 100 boys each into parades and concerts throughout Southwestern Missouri. In my callow career, during the 1920's and 30's I was a segregated 1st Grader ( ), "Standardized Tests" Lab Rat (http://.../testing.htm ), 6th Grade student teacher (htt;://.../kidteacher.htm ), "white trash" in JHS (http://.../trash.htm ), high school dropout http://.../dropout.htm ), making me critical of The "Testing Establishment" -- http://.../psycho.htm , http://.../metricab.htm , http://.../tyranny.htm, http://.../me.htm .

Served in Army Air Force, 1/27/41 to 12/21/45, mostly as Weather Observer and Forecaster. Last post, Muroc Flight Test Base (CA), now Edwards Air Force Base, where I built the Weather Station. (The 1983 film, "The Right Stuff" has shots of a large hangar, across from our Wx Station, from which I checked out tools for building plotting tables, display panels, etc.) On Overseas Orders 3 times in 5 years. In spring, 1941, volunteered to go to Phillipines. But had only 2 months experience, so man back from furlough went. He was killed 2nd day of War when Wx Station was bombed. In Feb., 1943, became Wx Station Chief at Garden City (KS)Intermediate Base, but Wx Officer immediately shipped out leaving me to pull 24-hr-7-day duty for 3 1/2 months until another forecaster came. (Planes flying any distance must have clearances signed by forecaster.) Meanwhile, put on Overseas Orders, which Commanding Officer delayed. When ready, outfit had already shipped to Italy. In August 1945, Overseas Orders from Muroc to Kearns, Utah. When arrived, Japanese forces had signed Armistice, so I was sent to Goldsboron (NC) for discharge. In between 2nd & 3rd "calls", weather officers from Weather Cadet programs in universities were sent overseas, since had more officers than forecasting sergeants.

B.S., 1952, Columbia U., in Physics (equivalent of major in Math, Minor in Chemistry). (At nearby Watson Laboratory, operated by IBM and Columbia U. I took computer courses prior to internal programming, inputting data by punch cards, with external programming by plugging in switchboards.) ONLINE file, http://.../murder.htm , explains how a murder turned me into a mathematician.

M.S., New York U., in Mathematics; ABD (NYU) 1961. (My late wife, Esther -- "a smart sassy woman" -- was afflicted by polio in infancy; broke legs 12 times, twice while working for my doctorate. Caring for her and two small sons, ... I mention this only to say I know something of what many women have had to surmount. http://.../abd.htm )

Instructor, Ass. Prof. Math, Inter American University of Puerto Rico, San German, P.R., 1955-58. (My ONLINE poem, http://.../myschool.htm describes what this school once was.) In 1957, I received a grant from the National Science Foundation to conduct the first NSF Institute held in P. R. -- this one for High School Teachers of Mathematics. Among the offerings, I gave a series of lectures on The Foundations of Mathematics. But some of my criticisms of the Bourbaki set-theoretic foundations of mathematics unwittingly became "an attack" on "The New Mathematics" which NSF launched next year (1958). So I was persona non grata to NSF.

While on doctoral studies in the States, I was Ass. Prof. Math, Fairleigh-Dickinson U., Florham-Madison Campus, NJ, 1958-61.

Returning to IAU in P.R., I was Assoc. Prof. and Head of Math. Dept., Inter American U., 1961-6, where bilingual Esther taught English, Spanish, French and Latin at Campus School. (She specialized in teaching reterning Nuyoricans to read and write the language they learned to speak at home.) Assoc. Prof. Math., U. of Maine at Orono (ME) 1967-1971.

Computer programmer, mathematician, National Wildlife Federation, Reston, VA, 1971-7. Computer programmer (UNIX-C-AWK), Naval Research Laboratory, Washington (DC) 1979 to retirement, 1/15/90, building scientific datebases, using a beta-version of relational databasing (a type of system which made ORACLE oracular).

On home computer, since 1995, I've establised 42 Websites, as listed http://.../webring.htm , see http//.../fable.htm and http://.../momma.htm, inspired great German-American mathematician Emmy Noether (1882-1935), and explaining why history is not herstory; also http://.../toteenmathpaj.htm. Three websites are memorials to Esther: http://.../memorial about "First Modern Woman"; http://.../dragonpage.htm , about adult literacy; http://.../christinapage.htm about disability. (I designed a memorial shirt, with fotos and tributes transferred to front aand back, in tee-shirt form for mild and warm wx, in sweat-shirt form for cool and cold wx, which I wear going out to mourn and honor her.)

Widower, living alone; stroke rehab; wife of 52 years died of cancer, 12/22/00. More about me at http://.../prototype.htm , discovering I am The Reluctant Rooster, Cousin of The Little Red Hen, and Penpal of The Reluctant Dragon, as well as The Beggar of Serendip. Translation: I'm only reluctantly doing what some one else should be doing, and (as noted in Webring) others may dig or redig. Be my guest!

As a veteran who spent 2 months living on streets of NYC after WWII, I grieve at newstories in The Washington Post that 3 millions or more veterans now live on streets of this country. I note that U.S. has not been in a declared war since 1945, and ONLINE, http://.../scofwarpage , wonder if this "illegitimacy"has worsened the plight of veterans.

My ONLINE website, http:/.../blakpage.htm , details concern that, in a republic and market society ("Meritocracy"?), the math (18th cent. Combinatorics) of decision-making, choice-making, role-playing are not taught to our students in pre-college classes or in general college classes. This website describes a combinatoric mathtivity I've shown to 3rd Grade children: "How to Build a Googol World in a Shoebox", more extensively developed at http://.../toteenpaj.htm .

I'm concerned about rampant cheating (http://.../cheater.htm) in our schools and colleges. Starting in 1956, I stopped this by giving a different test to each student: same problem with different numbers and postition on test paper; same question with different sentence forms and synonymous wordings. In 1970, at time of Apollo 13 Crisis, I gave a Statistics test to 125 students at U. of Maine (Orono), 125 different versions. But, if a colleague discovered my type of testing, it was taken as as criticism her or him.

In the medical profession (considered successful), the procedure is test, then treat. In the educational profession (subject to criticism), the procedure is treat, then test. Physicians do not try to treat all patients with the same therapy or dose with the same medicine. For differing needs, a doctor consults a Phamacopoeia. In 1960's, I sent several requests for a National Science Foundation grant to work with mathematicians at other universities to develop a "Methodocopoeia" (http://.../methodo.htm ), describing different ways of "treating" a "learning need". The NSF never once acknowledge my correspondence. Apparently, this "hole" has not been "filled".

The Bush "Leave No Child Behind" emphasizes English and Arithmetic, but these subjects are predominantly taught by opposing methods: English "bottom-up" generatively (letters, phonemes, prefixes, suffixes, etc.); Arithmetic "top-down" quasi-axiomatically in the style of Moses' Ten Commandments. But generatics (http://.../genny.htm) , going back to Pythagoras, for learnng Arithmetic, unites the ways of teaching these two critical subjects, so that learning in one helps in learning the other.

English teahcers have a "Handbook" providing that a given error or deficiency can quickly be indicated on a student's paper by a coding reference to the Handbook for understanding and correction. In the 60's, I sent several requests for a National Science Foundation grant to work with mathematicians at other universities to develop a "Mathematical Teachers Handbook" (http://.../handbook.htm ) for a similar purpose. The NSF never once acknowledge my correspondence. Apparently, this "hole" has not been "filled".

Teachers spend much time as "recorders", repeating definitions or procedures. In the 50's, while developing the FORTRAN programming language, John Backus developed "BNF: The Backus Normal Form" (later labeled "Backus-Naur Form") to bypass the tedium of repetitive teaching. BNF is a purely SYNTACTIC form wherein ONE LANGAGE FORM IS REPLACED BY ANOTHER LANGUAGE FORM -- syntactic because understanding is not necessary: the two forms could be in two languages unknown to the replacer. In the 60's, I sent several requests for a National Science Foundation grant to work with mathematicians at other universities to develop a "Syntactic Dictionary" (http://.../syntactic.htm ) using BNF to aid teachers. The NSF never once acknowledge my correspondence. Apparently, this "hole" has not been "filled".

As noted in my motto, I'm a wamp. (Think about it. Goldilocks was a wamp in The House of The Three Bears.) Being a wamp, I was sometimes forced to take a middle position between extreme positions in mathematics -- say, constructivism vs. nonconstructivism -- and got banged on from both sides. I regard only constructive math as first class math, since a constructive proof tells us more than a nonconstructive one. But I give provisional acceptance to a nooncsontrutive proof as second class math, since it sometimes motivates a constructive proof.

In P.R. high schools, science and math were taught from English text books, so any person with some collge credit who could read English could immediately start teaching science and math. To prepare my students, I instituted a Pass-Fail grading. In basic math course, each must individually perform correctly 100 "standard Tasks" to pass. If incorrect, no marking but do over in different formulation. (I can vary by the thousands.) I have examples of these ONLINE, http://.../stndtsk.htm . At U. of Maine, I found some Math Dept. colleagues who had never seen some of these problems (say, from 1900 private texts, such as Chrystal's Algebra), and could not solve them.

I'm concerned about the reported number of creative women (http://.../ ), with a hypothesis to provoke discussion, http://.../spartacuspage.htm , listing many women inventors, mathematicians, scientists.

I'm also concerned about the plight of American independent inventors. An 80's WashPost story said 95% of independent inventors or heirs lost patent rights to corporations in American courts; one trial lasted 99 years. Comparing lists of inventions of independents in World Almanac 2002 and 2003, since the end of WWII and comparable period before our entry into WWII, I found an apparent decrease of 400%. I've files ONLINE describing African-American Gardner Murphy, who invented the three-color traffic light; and for Margaret Knight (1838-1914), who built the machine (now in The Smithsonian Museum) that cut, folded, and glued paper to form the familiar box-bottom brown paper bag.

As a non-Islamic man, I'm concerned that few (even among young Islamic persons) know the great debt we owe to Islamic science and culture, particularly during the "Dark Ages" of Europe. Mathematician Morris Kline, in his 3-volume work, Mathematical Thought From Ancient to Modern Times, notes that the first science, astronomy, and elementary algebra both began with ancient Babylonian priests, over a ten-thousand-year period, vastly longer than that of Western Science. At a time when Platonists taught that geometry and arithmetic are incompatible, and that motion is geometry-set-to-time, so that arithmetic measures of motion are impossible -- Galileo was condemned by Church leaders as a "Pythagorean" for believing otherwise -- yet Islamic scientists developed measures to the contrary. As Elmer Bendiner writes in his book, The Rise and Fall of Paradise, When Arabs and Jews Built a Kingdom in Spain, several hundred years of creative peaceful cooperative work brought us many of our material and cultural endoments. My ONLINE Website, http://.../def.htm , "Diverting Islamic Fanaticism", appeals to young Islamic men and women to draw upon the great past of their culture and create for the future.

Concerned about ignorance of history on part of young people, the general public, and partially among historians, I've an ONLINE Website, http://.../cliopage.htm , presenting scenarios of smeinal events (mostly in science and math) for young people to write plays and enact to learn history.

One of my masters, Alfred North Whitehead, said, "Let us grant that the pursuit of mathematics is a divine madness of the spirit, a refuge from the goading urgency of contingent happenings."

I see that MATHEMATICAL ALGORITHMS can become STRATEGIES of Life and become PROSTHESES for HUMANS (http://.../aspage.htm , htp://.../stratpage.htm http://.../mathforlife.htm ), the most "handicapped" of all animals.

The French anthropologist, Claude Levi-Strauss (1908-?), said that, among the peoples he had encountered, "primitive" or sophisticated, there seemed to be a common desire: to feel that one's life has a meaning, that it fits a pattern. As an example of the human love of patterns, he describes a native hunter, tracking an animal across the Kalihari Desert, stopping to rest under the shade of a rock and taking from the belt of his loincloth an embroidery hoop with threading of red roses in progress -- something this fierce hunter had learned from missionary women.

I believe that love of patterns motivated humans to create prosthetic environments and to create Mathematics and Science and Art. Years ago I wrote some verse, "Prayer of a Feckless Fool", about this.

                 Before I go to that great Playground
                 To spend that last Recess,
                 Lord! Make my life a Pattern,
                 Instead of this mishamy! mashamy! Mess!!!


  • "Matrices for free lattice logics", Notices of The American Mathematical Society, Sept., 1972
  • "A generalization of the Hardy-Weinberg law of population genetics", Notices of The American Mathematical Society, July, 1976.
  • "o-switchng gates and o-logic gates for o-fuzzy logics", Notices of The American Mathematical Society, May, 1977
  • "Group properties of hilbert-skolem algebras", Notices of The American Mathematical Society, July, 1977
  • "A clusterng algorithm for medical diagnosis, taxonomy, and general systematics", Notices of The American Mathematical Society, Aug., 1977
  • "Panalgebras and spanalgebras", Address to 84th Annual Meeting of AMS, Augusta (GA), Jan. 5, 1978; abstract in Notices of The American Mathematical Society
  • "The Battle of the Frog and the Mouse (from The Fables of Aleph)", Mathematical Intelligencer, 6, 77-80 (1984), reprinted in Pi in the Sky, by John Barrow, Little Brown and Co., Boston, 1992, also
  • "Momma Geometry", Rustlings, 1977, also http://.../fable.htm