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

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 one of my girlfriends, 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 Pestulates.  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…  I will use the term pestulate instead of postulate, because these fundamental principles by which humankind is denoted are rather like pests in the lives of humans…  The Main Pestulate, 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 pestulate, 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…

The Liebers And The Anti-SAMites

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.



Gokusen: The Japanese Morality Tale

Gokusen was a Japanese manga series(2000-2007) by Kozueko Morimoto that was later converted to a three season TV program(2002, 2004, 2008.)   Gokusen(“gangster teacher”) concerns the adventures of orphan, Kumiko Yamaguchi, who has been brought up by her gangster grandfather in the Oedo Clan.  She is in line to take over as the fourth head of the Clan, but chooses instead a life teaching estranged, would-be delinquent boys in all-male private high schools as a homeroom teacher.  Because of Kumiko’s training in the Oedo Clan, she has become an expert in all forms of martial arts and can defeat most opponents easily, even groups of opponents.  The role of Kumiko in the TV series was played by former Japanese model, Yukie Nakama.  Throughout the series, other Japanese models appear as well, usually as school colleagues.

3D at each school contains the worst students, future delinquents, kids with no apparent future, troublemakers in general.(The one exception is Sawada, Shirokin High School’s top student, who gives a stirring and insightful valedictory speech at graduation.)  Thus, Kumiko or Yankumi(her students name for her) has her hands full right from the start.  Her specialty is mathematics and the first day we see her writing equations on the blackboard that require complex numbers as solutions.  However, her mathematics skills are never appreciated by her students.  And this is important.  Formal education with a small e:  mathematics, languages, history, science, music, art, physical education, etc. is minimized throughout the series.  Indeed, excellent students are often shown to be arrogant, domineering, and even engaging in criminal activity just for sport.  The emphasis here will be on universal moral Education(education with a capital E) and that is where Kumiko demonstrates her strength.  The main reason for the particular emphasis is that formal education does not apply to everyone;  not everybody is skillful in the above-mentioned disciplines.  However, universal moral Education is just that:  It is universal, so it applies to everyone.  That is the point Yankumi will try to make with her troubled students.

Kumiko’s first step is to observe her students carefully to find out which one of them is the leader.  Then, she tries to gain that student’s confidence and support.  This is often a difficult task, but essential,  because that student will convey her principles to the group.  Her goal is to show that school is more than formal education, but that there are experiences that school provides that impact all their lives.  Above all, there are friendships that are made in school which will last a lifetime.  This principle is repeated emphatically whenever any student separates himself from his schoolmates.  Friendship means you are never alone and Yankumi emphasizes that there is nothing she wouldn’t do to save her precious students.  Her students begin to see through her actions that she means what she says and often fights off opponents to help them and is unwavering in her support of them at school.  She teaches her students about other experiences that can be shared by them regardless of society’s condescension.  Fighting is meaningless, she says, unless it is to defend another person or is carried out to achieve a noble goal.  When Kumai, the worst student in his class, fights to protect a girl, he is rewarded by gaining a girlfriend and eventual wife.  Later, other students from Akadou Academy share Kumai’s profound feelings for the awesome birth of his daughter.  Students learn to appreciate the great sacrifices their parents have made and not to take their parents for granted.  The parents, though, are sometimes overindulgent, or sometimes overly strict and unwilling to listen to their children.  In each case, the student learns to appreciate a moral lesson from life.  And, Kumiko reminds her students that they have a choice to make something of their lives and that there are beautiful human experiences which can be shared by all.

A River Idyll And A Voice Dialogue

Along the banks of the river crawled a lizard.  It was olive green with a long tail.  Its eyes moved back and forth as if looking for something…

The river itself was an imposing force that demanded attention.  Its swift currents and mischievous eddies showed the stream was not to be taken lightly.

A keen eye could discern a scrap of raft near the beach, which was hanging on a willow.  The beach displayed an array of shiny pebbles, glittering in the sun.

Sometimes reeds would sway in a light breeze and blackberry bushes protruded from the quiet grass.

The ripples moved in expanding circles and a trout glided along the beckoning water.


A voice dialogue is a way to connect with the different parts of self, some of which are often ignored.  By revealing these voices, one can sometimes sense which ones are out of alignment, thus locating possible causes of emotional stress.  In the dialogue that follows, only one voice is identified.  What parts might the other four represent?

I.  “Well, here we are again.  Although it’s cool this morning, the weather is becoming splendid.”

V.  “A nice day to put your feet up and do nothing.”

III.  “You would say that.  With that attitude nothing would get accomplished.”

I.  “But a great deal was accomplished.  We read another twenty or so pages of the novel.”

V.  “Pretty boring if you ask me.”

III.  “But we didn’t ask you.  Perhaps, you should go to sleep, Sluggish, and let us do the work.”

V.  “I have as much right to be here as you do.  It was my suggestion that we listen to music when we took that ride last night.”

IV.  “We probably should have gotten out and walked to the river.”

I.  “But Sluggish is right.  The rest was needed.”

IV.  “But we will take a walk today.”

I.  “That’s our intention.”

II.  “Then perhaps we can learn more about operetta from the book we were reading.”

V.  “Oh, you and your books.”

I.  “I don’t want any arguments now.  Let’s settle down and go for that walk.”

L.Frank Baum, Education And Aunt Jane’s Nieces

L.Frank Baum, the famous writer of many children’s books, had an undisguised distaste and wariness for formal education.  He satirized formal education in the character of the Highly Magnified Wogglebug, who, through a mix-up in a science experiment, became human size(“highly magnified”) with an air of superiority.  The Wogglebug thinks crude puns proof of a higher intelligence and mimics the attitudes of the professors whom he watched.  He establishes the Wogglebug College where “scholars” are given magic pills to swallow that are full of information for the next exam.  But the Wogglebug and his arrogance is out of place in Baum’s world where people usually don’t brag about their accomplishments but demonstrate them through action.  Baum is more concerned with the Latin root of education,”educare”, “to draw out”, rather than the formal curriculum that originated with the ancient Greeks.

Baum placed great emphasis on moral and social education as opposed to formal education.  It is significant that in Aunt Jane’s Nieces there is almost no mention of college or formal education.  To Baum, character development is the only meaningful kind of education.  He makes this clear through the personage of Uncle John in Aunt Jane’s Nieces on Vacation(The girls have proposed starting their own newspaper in Millville, which causes Arthur Weldon, Louise’s fiancee, to condemn the venture as madness.):  “I’m educating my girls to be energetic and self-reliant.  I want to bring out and develop every spark of latent ability there is in them.  Whether the Millville Tribune succeeds or fails is not important;  it will… tax their best resources of intellect and business ability…”  For Baum, intellect is sharpened through challenging experiences instead of studying books.  Baum was a doer and this spirit permeates all ten of the Aunt Jane’s Nieces volumes.

Baum believed that only through hard work, persistence and true friendship could an individual’s mental life unfold.   Using Uncle John as a kindly mentor, he subjects the nieces to difficult obstacles they need to overcome.  The nieces are exposed to violence, dissipation, rampant corruption, condescension and abduction, but they always persevere.  Despite being competitors for an estate, they learn to appreciate each others strengths and help each other to deal with their weaknesses.  The last volume in the series, Aunt Jane’s Nieces in the Red Cross, subject them to their toughest test:  the agonies of war.  This dark book, stark in its description of war casualties, shows the nieces as caring, active participants as they heal the wounded and deal with the psychological trauma of war.  But they have been well-trained by their teacher, Life, and are able to bring joy and comfort when needed, and so are educated in the highest sense of the term.   

Cello Player

                                                          CELLO PLAYER

A diffuse glow appears on the orchestra pit.

The music begins softly;  a faint, lilting melody rises…

Light slowly illuminates a tall girl playing the cello.


She plays the cello in total harmony.

Her body rhythm flows smoothly through brown hair and slim arms,

blending beautifully with the cello and escaping through the strings.


While she plays, my heart swings along her bow.

Sighing, the strings gently free the melody.


Hearing notes dance and leap,

tonal patterns bursting into stars,

her brown eyes ignite the music into a cosmic cry…


The chords slowly drift into empty space.

Her cello idles lazily at her shoulder.

She reduces the room to stillness.


So, too, I am reminded of my own rhythm.

In time, my strings will grow slack.

And I, too, must approach silence.




Some Thoughts About Scrapbooks, The New Year And Writing

My baby scrapbook, published by Richard G. Krueger, Inc. and designed by Ditzy in 1946. It was a gift from my godparents Aunt Jackie and Uncle Ralph.

My baby scrapbook, published by Richard G. Krueger, Inc. and designed by Ditzy in 1946. It was a gift from my godparents Aunt Jackie and Uncle Ralph.  At that time my name was “Rodger” Weiss, but was soon changed to Robert Weiss.

“Life may be a stage, but I wish I didn’t have a reserved seat!”–Uncle John from Aunt Jane’s Nieces by L. Frank Baum

Usually in the month of January I peruse my many scrapbooks.  I begin by looking at my baby scrapbook with its satin sheen cover and remarks about me by my mother, Twyla.  It takes me back to my childhood days of the 1950s, when people left their doors open, kids had vacant lots and piles of sand to play in, and lemonade stands were plentiful with lemonade one cent a cup.

However, time goes on and memories begin to fade as new memories take their place.  The almost unbearable slowness of  early childhood is exchanged for the almost unbearable speed of late adulthood.  And New Year follows New Year.  I think of lines by Robert Clairmont from Forever X:

When wrinkles cut your brow

And love goes gaily by,

Sing:  Young, old, tiny, tall,

Whatever happens, happens to all

When we leave this Odd Old Ball.

Indeed, this earth truly is an “odd old ball”.  Events follow events, triggering other events.

Like any mathematical curve, life has points that mark a change of direction.  Some of these points are obvious:  marriage, the birth of children, the loss of a beloved family member.  However, other points are not so obvious and I must admit that I envy Truman Burbank for he is able to “rewind” his life from the time he escaped his set up world to his birth.  Thus, he can see how certain events changed his thinking and further actions.  I am not so fortunate.  And when I look through old scrapbooks only pieces of experiences remain, so I have to reflect and guess at events that might have caused my life to shift dramatically.  Such critical points mark the essence of theater, novels and other writings where an author can juggle them and insert them where s/he wills.  Perhaps, that sense of power and completeness is what attracts us to literature.  The writer plays God just as Christoff does with Truman.  However, the individual must depend on his/her own wavering memories to try to understand the meaning of his/her life.