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When a man writes to the world, he summons up all his reasons and deliberations to assist him; he searches, meditates, is industrious, and likely consults with his judicious friends; after all which done he takes himself to be informed in what he writes as well as any that writ before him.|[[John Milton]] (1644)|[[Areopagitica]]}}

My great-grandparents lived in the land of [[Herman Boerhaave]] and [[Abel Tasman]], most of my grandparents were born there. When I was a boy I took an interest in [[coin collecting]], like the [[Lincoln cent]] and the [[Canadian penny]] that circulated in [[Michigan]]. In a local library I read about [[meteorology]], a perpetual spur to understanding. A schoolmate showed me how [[chess]] was played; it captured my attention. As an [[adolescent]] I read [[Hans Kmoch]]'s ''Pawn Power in Chess''. The [[YMCA]] offered [[swimming lessons]] in its [[swimming pool|pool]], a [[summer camp]],  and a room for weekly meetings of the city [[chess club]].

I was amazed that my [[crystal radio]] worked without batteries -- the power to drive the earphone was "in the air". At that time there was no [[internet]], but [[shortwave]] communications offered a window on the world. I studied [[Morse code]], took up [[amateur radio]] practice. [[ARRL#Publications|Radio Amateur's Handbook]] served as a [[textbook]]. The League magazine [[QST]] discussed [[impedance matching]] a transmitter to an antenna, opening up the [[frequency domain]]. Though I was fascinated with [[electronics]], reading ''[[Mathematics and the Imagination]]'' gave abstraction and ''[[One Two Three...Infinity]]'' opened the cosmos.

I put some of my physical energy into learning to ride a [[unicycle]]. In the final year of [[junior high school]] there was a [[science fair]] in which I competed with a problem in [[combinatorics]]. The creative experience of innovative mathematics was rewarding enough without award. (Originality is expected in [[Wikibooks]] but not allowed in Wikipedia. See for example [[b:Geometry/Unified Angles]], [[b:Abstract Algebra/3x3 real matrices]] or works that have been archived by [[Wayback Machine]]:  
[https://web.archive.org/web/20160528215405/http://imechanica.org/node/12369 Complementary numerals], and 
[https://web.archive.org/web/20171229191730/http://imechanica.org/node/10543 Corner flow and Common ground].

After junior high school I started studying through the summers, taking a courses in [[speech (public address)|speech]] and [[typewrite]]ing the first summer. I participated in [[policy debate]]s as a [[high school]] student, and learned to use the [[Readers' Guide to Periodical Literature]] to find articles on topic. The textbook by [[Mary P. Dolciani]] on algebra and trigonometry taught that a function is a type of [[binary relation]]. It described [[matrix multiplication]] and included an [[exercise (mathematics)|exercise]] to verify an [[involutory matrix]]. The [[National Science Foundation|NSF]] sponsored science and mathematics programs for high school juniors. Students learned a little [[calculus]] and a bit of [[physics]]. I wrote a report on [[electroluminescence]] based on readings at the [[Carnegie library]] downtown. We also spent a few weeks on [[college campus]]es with classes presented by [[professor]]s. Each of my parents had a cousin in [[academia]], so that was my career goal. Advisors told me to get three [[academic degree]]s and to learn to read French, German and Russian [[mathematics]].

==University==
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First year sciences were [[physics]] and [[psychology]]. Later there were courses in [[economics]] and [[astronomy]]. Another course introduced programming in [[Fortran]] and [[SNOBOL]] using [[punched card]]s. The [[University of Michigan]] had some professors teaching out of their own texts: [[Raymond Wilder]] on [[foundations of mathematics]] and [[Irving Copi]] on [[logic]]. Studying through the summmers, soon I graduated with a degree. On the basis of a very good [[grade point average]] and faculty recommendations [[University of California at Berkeley]] admitted me for graduate study in mathematics. [[Alfred Tarski]] was my advisor and courses included [[measure theory]] with [[John L. Kelley]]. But graduate students were not deferred from the [[Vietnam War]] so I applied for recognition as a [[conscientious objector]] but was turned down. It seemed that all the learning was going for nought while the [[Selective Service System]] provided young men for induction into the Army. 
In [[California]] I saw for the first time that regular consumption of animal parts ([[carnivorism]])
was unnecessary for human vitality. On [[Sproul Plaza]] many groups promoting [[civil rights]] had set up [[card table]]s. Some of them explained the process of "refusing induction" available for young men standing their ground against conscription. After the usual [[physical examination]], at the moment for entrance into the army, one simply stayed back while willing recruits stepped forward. Neither the Army nor the SSS enforced conscription; that was left to the [[Department of Justice (United States)|Department of Justice]]. I refused induction in [[Oakland, California]]. When [[Eugene McCarthy]] started his [[Eugene McCarthy presidential campaign, 1968|campaign to stop the war]] I participated in getting out the vote in that [[California primary]]; the tragic outcome on election day was a real blow and has discouraged me from politics since.

Frustrated in my course of study, a broader perspective was sought in reading ''[[Understanding Media]]'', the novel ''[[Siddhartha (novel)|Siddhartha]]'', and [[Herb Caen]]'s column in the ''[[San Francisco Chronicle]]''. Deeper considerations arose in [[List of hexagrams of the I Ching|hexagrams]] of the ''[[I Ching]]''. Travelling to [[Alaska]], I took up study at [[University of Alaska Fairbanks]] which provided a course of study including [[differential geometry]] and [[integral geometry]] (after [[Luis Santaló]]) leading to M.Sc. degree. Coursework at university included [[ring theory]] courses that provided enough abstraction for wide application. When the book ''[[Diet for a Small Planet]]'' appeared, it offered a glimpse of [[sustainable living]] for [[Earth]]. In [[Anchorage]] I refused a induction Army second time, and when threatened with prosecution left the country. Some years later President [[Jimmy Carter]] granted amnesty for refusal of induction.

[[Pierre Trudeau]] was [[Prime minister]] when I landed in [[Canada]], which was then a major contributor to [[United Nations]] operations in [[peacekeeping]]. For [[science policy]], reference is made to [[Francis Bacon]] in Canada rather than to [[Benjamin Franklin]]. 

It was my good fortune to hear F.A. Kaempffer, author of ''Concepts in Quantum Mechanics'' (1965) and ''Elements of Physics'' (1967), speak in [[Halifax (former city)|Halifax]] to a conference on differential geometry and relativity. He reviewed the symmetry of the [[electromagnetic field]] that is expressed by [[spherical wave transformation]]s that form a [[conformal group]] on spacetime. [[Paul Cohn]]'s book on [[Lie group]]s was recommended, and [[Wolfgang Rindler]]'s textbook ''Essential Relativity'' was acquired. Investigation of conformal mapping proceeded at one of [[Nova Scotia]]'s leading universities. In a university program, I was a [[teaching assistant]] and studied [[functional analysis]] including [[topological group]]s and [[Haar measure]], and attended the functional analysis [[seminar]]. Going for the third degree, research was aided by [[Science Citation Index]]. My approach to the conformal symmetry was expressed on the projective line over [[biquaternion]]s. I wrote a report on the [[projective line over a ring]] and made some deductions for [https://en.wikibooks.org/wiki/Associative_Composition_Algebra associative composition algebras], using the title ''Geometry of Electromagnetism''. As [[J. Arthur Seebach]] wrote in his telegraphic review for [[American Mathematical Monthly]] (volume 85, foot of page 778), "The geometry is that of a homography transformation on the category of projective spaces with two homogeneous coordinates taken from an arbitrary associative ring with 1. The development of these geometries is shown to be relevant to the study of Maxwell's equations." As a "Recent book", it was noted by [[IEEE Spectrum]] (page 74, February 1979).

==BC==
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<blockquote>δὤς μοὶ πα στῶ και ταν γαν κινασω</blockquote>
There were some classroom teaching opportunities in [[elementary algebra]], introductory [[physics]] and [[computer science]], particularly after [[microcomputer]]s and [[personal computer]]s became a [[retail|retail products]]. So for a few years [[binary arithmetic]] and [[Boolean algebra]] were in my [[curriculum]]. In 1987 I wrote a letter to [[American Journal of Physics]] (56:296) : "An Also Known As List for Perplex Numbers", which listed some references for [[split-complex number]]s.

At last I became a [[vegetarian]], relying on [[whole grains]] (particularly [[brown rice]]) along with [[legumes]]. Of the animal [[protein (nutrient)|protein]] sources, [[egg (food)|egg]]s, [[milk]], and [[meat]], I choose only the middle one, like [[Elmer McCollum]].

One day I noticed that if the i, j, and k in the [[quaternion group]] were given +1 for their squares, then one obtains a [[quasi-group]] of order 8, and the real algebra over this quasi-group has many features of [[Minkowski space]]. When I asked [[Nathan Divinsky]], it appeared new to him. But later I found out that [http://www.webcitation.org/5kmWeo7j0 Alexander Macfarlane] had the same idea for his [[hyperbolic quaternion]]s in the 1890s! Deeper background appeared with the writings of [http://www.webcitation.org/5koCLyT1S James Cockle] who found [[tessarine]]s and [[coquaternion]]s in the 1853 [[biquaternion]]s that [[William Rowan Hamilton]] had developed.

The waters of the [[Strait of Georgia]], sheltered by [[Vancouver Island]], are ideal for [[sea kayak]] touring. Buoyed by a double kayak, islands appeared up and down the Strait. In the wake of [[Oskar Speck]], [[George Gamow]], and [[George Dyson (science historian)|George Dyson]], expeditions were made possible by a [[folding kayak]]: fit for a bus bay, the frame dismantles, and skin rolls up. [[Lago Nahuel Huapi]] and other lakes in the Andes were explored. In the Atlantic the [[caravel]] visited [[Isla Mujeres]], [[Florianopolis]] and canals in [[Tigre Partido]]. In the Pacific the shores of [[Chiloé Island]], [[Waiheke Island]], and the [[Marlborough Sounds]] were viewed and visited. Such explorations were also in the wake of [[Pytheas]], who sought amber, but before the new millennium.

Returning to the quest for my own amber, new tools had been laid out by the digital revolution. The article "Split-complex Numbers" was posted including a longer list of [[split-complex number#Synonyms|synonyms of ''perplex numbers'']]. Ring theory may be contrasted to theory of [[Lie group]]s: they both rely of [[linear algebra]] of [[square matrices]] for representation of the abstract study. The [[general linear group]] GL(''n,F'') over [[field (mathematics)|field]] ''F'' engenders Lie's theory and includes the [[special linear group]] SL(''n,F'') where the [[determinant]] is one. According to ring theory SL(''n,F'') is a sort of sphere in M(''n,F''), the ring of square matrices over ''F'', size ''n'' × ''n''. The sphere has center in M(n,F) and has radial lines to points on the sphere. Two sphere points are separated by an arc-distance. The Lie theory posits the arc-distance as a group parameter, while in the ring the radial lines to the points form an [[b:Geometry/Unified Angles|angle]] which may be elliptic (ordinary), hyperbolic, or parabolic (slope). The angles may be founded on the [[area]] bounded by the radii and arc. Indeed, the [[hyperbolic angle]] emerged 1647 to 1748 with the [[natural logarithm]] as [[quadrature (mathematics)|quadrature]] of hyperbola ''xy'' = 1. 

I continue to be a bibliophile, enjoying especially [[biography]] and [[history of science]]. Currently I use [[Google Book Search]] in addition to [[search engines]]. 
Scientists of age please note: In writing a biography for Wikipedia, the existence of autobiographical notes makes a significant difference. For examples, [[Allen G. Debus]] and [[Jerald Ericksen]] wrote about their work and movements. Taking notes when they traveled, [[Stephen Timoshenko]] and [[Willard Quine]] give an impression of perpetual movement. Too many scientists leave no trace but their academic output in books, articles, or media releases. Recollecting some of the turbulence encountered in academic life may be a meaningful experience.

[[Vancouver Public Library]] and the [[University of British Columbia Library]] have provided some materials for references. And [http://www.biodiversitylibrary.org Biodiversity Heritage Library], [https://archive.org/details/texts Internet Archive], [http://www.hathitrust.org/ HathiTrust],[https://www.gutenberg.org/ Project Gutenberg],[http://projecteuclid.org/ Project Euclid], [http://mathbooks.library.cornell.edu/ Cornell Historical Math Monographs], [http://quod.lib.umich.edu/u/umhistmath/ University of Michigan Historical Mathematics Collection] and [[Jstor]] (early content) have been found to be vast repositories of [[W:Reliable sources|reliable sources]] that may be linked for encyclopedia users to read online.

For students interested in tools, beyond real numbers ℝ and complex numbers ℂ, that can structure mathematical models, the text [https://en.wikibooks.org/wiki/Associative_Composition_Algebra Associative Composition Algebra] is now available at [[Wikibooks]].

[[Category:Wikipedians interested in mathematics]]
[[Category:Members of the Fifteen Year Society of Wikipedia editors]]