The Radical Philosophy Of Allan Kurzberg And His Fundamental Postulates, Part 1.

June 25, 2017 Leave a comment

I first became acquainted with Allan Kurzberg when I was a freshman at USC.  It was a time of immense turmoil and change, but also a time of great excitement and discovery.  Many college students were seeking alternative lifestyles other than those propounded by “The Establishment.”  The reason for this was simple:  the lifestyle emanating from “The Establishment” was producing a plethora of lies, bodies of prejudice, and the Vietnam War, resulting in countless injuries and deaths.  Many students thought of alternative lifestyles that encompassed communes, the Hippies of San Francisco, philosophies from the Far East, especially meditation as practiced by famous Maharishis.  Youths were also reading about the links between science and psychology, mathematics and computers.  To cope with the rigid mindset of “The Establishment”, young people smoked marijuana, took PCP and LSD to reach other mental states than were condoned by the AMA.  Families were not only torn by war, but by “the generation gap”, which led to a total breakdown in the family structure, the shock waves of which are still affecting the present.  It was a time when one person could change the world and each was encouraged to  “do your own thing”.  People used profanity as a rebellion against the norm and as a strike for human freedom.  Sex became far more casual and explicit.  The notion of premarital sex as a taboo was tossed out the window.  The Living Theater performed on streets and in parks.  And there were “sit-downs” and riots across college campuses as the emotions of anger engulfed the U.S.  The authoritarian approach that had for so long defined the hierarchy of professor and student broke apart, and closer, more meaningful relationships were developed and encouraged.  Especially, there was much talk of peace, while paradoxically, different factions were building.  It was during this epochal time that my then girlfriend, Janet, suggested that I look at Allan Kurzberg’s essays on the Theory of Us.  I told her that I already had a full course load and had numerous books I wanted to read.  Why should I read Kurzberg?  She told me that in her opinion he was the only true radical, because he opposed both “The Establishment” and the youth.  She thus led me into a hitherto unknown world:  the mind of Allan Kurzberg.

His first essay was entitled:  The Fundamental Postulates.  I started reading and found myself absorbed by a writer that was a curious mixture of strict reason and digressions.  “In this essay I have attempted to establish the cornerstone to the Theory of Us.  In my writing I use some principles of mathematical reasoning when applicable…  Different branches of psychology remind me of lonely subsets in search of a universal set.  Each is merely a limited, restricted set of elements…    The Main Postulate, 1. reads:  There is no species on earth that lies, prevaricates or dissembles more than the human species.  Since to lie is to speak falsely and no other species can “speak” in the way that we define it;  as an assemblage of sounds so sequenced  and intoned as to give expression so broad it allows not only for denotation, but connotation as well, our case is proved.  We might also accept the postulate, since no counter example can be proffered.  We do know that camouflage is widespread in the animal and insect kingdom, but this is only for survival.  Humans can use camouflage on, say, Halloween, and the object is sheer play, not survival…”

I must say that I found Kurzberg’s essays the most difficult of any essays I had ever read.  It was not on account of their intelligibility, but rather that I found myself being challenged, so I retaliated by writing NOs on many of the pages, and, in some cases, actually writing rebuttals.  Now, after almost fifty years have passed, I’m not sure I was altogether correct in my objections…

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The Liebers And The Anti-SAMites

June 12, 2017 Leave a comment

The Liebers, Lillian Rosanoff(Rosenberg) Lieber and her husband, Hugh Gray Lieber, were pioneers in conceiving of mathematics in terms of human values.  They also sought to link the disciplines of science, mathematics and art through informal and often entertaining writing accompanied by creative drawings.  Lillian Lieber was the mathematician, and her husband Hugh was the artist.

Mathematician and Educator, Lillian R. Lieber, Courtesy of Robert Jantzen.

Lillian Lieber was born in Nikolaev, Russia, on July 26, 1886 and died less than a month from her 100th birthday on July 11, 1986.  She did not marry until 1926, quite unusual for a woman at that time.  Her husband, Hugh Gray Lieber, was about ten years younger and died in his mid-sixties in 1961.  Together, they wrote some innovative books mostly about mathematics with insightful social commentary.  Lillian often linked the development of modern mathematics with ethics, politics and humanity.  The Liebers encompassed non-Euclidean geometry, lattice theory, the theory of the infinite and Einstein’s theory of relativity.  They also wrote an entire volume on the nature of logic.  However, their most popular volume was The Education of T. C. MITS, (The Celebrated Man In The Street), which begins with problems intended to show that things are not always what they seem!  Lillian’s language ranges from the informal to the formal and then to a downright questioning manner intended for the reader:  “But what are “Truth”, “Justice”,”Freedom”, “Reason”?  Do these words really mean anything?  And how can we be loyal to them if their meaning is not clear?  Are they not just “fakes” invented so that some people can make slaves of others by fooling them with such meaningless abstractions?…”  To explore and investigate such terms is a major part of her and Hugh’s educational purpose.

The discovery of non-Euclidean geometry destroyed the notion that mathematical truths are eternal verities, for by changing one postulate(the parallel postulate), new geometries come into being such as a geometry based on a sphere, Riemannian geometry where the angles of a triangle are greater than 180 degrees and as much as 540 degrees!  But the Liebers stress that within the new freedom to create other geometries remains the recognition that such creations are systems with definite rules, which cannot allow for contradictions.  They then make a comparison between mathematical freedom and human freedom and warn that true human freedom does not imply unlimited license but careful responsibility.

The Anti-SAMite was a unique creation of the Liebers.  S/he was a person who opposed or was totally ignorant of the wonderful discoveries that had been made in science, art and mathematics.  They believed that these three subjects formed the building blocks of human culture and that all three were united through the passion of discovery, which encouraged further questioning and exploration.  As Joseph S. Alter states in his perceptive article on Lillian R. Lieber, “She called those intolerant of new ideas in these fields”anti-SAMites.”  Anti-SAMites were indifferent to “the good, the true, and the beautiful,” and there was a clear implication that anti-SAMites were responsible for prejudice and war.  To Lieber, war was the greatest danger facing humanity and SAM our greatest hope against its destructive forces.  Philosopher, Walter Kaufman, would have concurred. Allan Kurzberg, controversial thinker of the 1960s-1970s, would definitely not have.  In fact, he accused the Liebers of being just as intolerant as the anti-SAMites by using the latter as scapegoats.  Allan was not shy in including the Liebers as competent “Other” creators in his essay “Mathematics and World Peace.”  However, I will defer a more in-depth analysis of Kurzberg’s essay to another post.

On a personal note:  The Liebers influenced me greatly during my college days.  At that time I was reading Einstein’s theory of relativity, various studies in the philosophy of science and discussing all the above with Grandma Lillian.  It was an exciting time and people were considering all kinds of thought and alternate lifestyles.  I was caught in the brouhaha concerning the Vietnam War and voted for the Peace and Freedom party a few times.  The “establishment” and the “military industrial complex” were highly pejorative terms at that time.  Professors were open, and, with few exceptions, liked to be called by their first names.  I remember talking to my calculus professor, Charles Kalme, about the meaning of life and the importance of reason.  I remember him telling me with his Latvian accent:  “Who is to say that you’re born and you die, and what’s in-between doesn’t matter?”  Who indeed?  Compared to the dogmatic, but sometimes fun studies in high school, I felt an incredible freedom in college that I had never experienced before in an educational setting.  My freshman year was a blast and I enjoyed applying mathematics to linguistic structures and taking a course in semantics with an ex-judge at the Nuremberg trials, Wolf Helmut von-Rottkay. My comparative literature instructor, Al DiPippo gave stirring talks on Greek culture and Kierkegaard.  My young Russian professor, Edward Purcell, was one of the first to use computer exams.  Alas, the excitement of my freshman year would never be duplicated.

My last three posts bring a strong sense of deja vu.  Thomas Mann had a major impact on my concept of literature, especially though his knowledge and application of science, philosophy, music and time.  It was the art of literature that encompassed the whole human experience that engaged my curiosity.  Susanne K. Langer’s works on aesthetics and her pioneering study, Mind:  an Essay on Human Feeling in three volumes were close to my bed.  It is curious that in August Dover Publications has chosen to reissue Take a Number by the Liebers, a book written more than seventy years ago!  Also, they are reissuing The Development of Mathematics by E.T. Bell the same month.  This is an extensive volume, dealing with the history and evolution of mathematical thought.  The Liebers refer to Bell’s works on numerous occasions and Bell was effusive in his praise of the Liebers:  “I have been following the education adventures of T.C. Mits with absorbed interest, and in doing so have(I hope) acquired some education myself…”  For anyone interested in the growth of human though, I cannot recommend these two volumes too highly and I look forward to seeing them on my shelves.

 

 

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