The Radical Philosophy Of Allan Kurzberg And His Fundamental Pestulates, Part 2.

What follows are Allan’s  thoughts on the implications of the First Pestulate:  “…  Since mathematical reasoning is the highest form of reasoning that we humans have developed, and since, according to P1, we distort the truth more than any other species, we have the main reason for a universal study of mathematics:  to undo false reasoning through careful mathematical reasoning.  Indeed, I would go so far as to say that the more mathematical reasoning is applied to every facet of our lives, especially to our personal, the less contradictions will occur in our lives.  The reader might wonder why.  The answer lies in the kind of language that mathematics represents:  It is an objective language that seeks to prove statements through a series of conditional statements using precise definitions or previously proved theorems.  Mathematics does have synonyms and does use symbols that have different contextual meanings, but never foregoes consistency and brevity whenever possible.  In addition, mathematics involves a kind of generalizing that often leads to universals.  Most importantly, no mathematical system allows for contradiction, which is definitely not the case with other human-contrived systems such as political or social…  In my Theory of Us, I try to locate universals which will subsume all possible human interactive behaviors…  Thus, I feel that the primary reason for studying mathematics is the universal need to apply mathematical reasoning to disprove false statements, whatever field they arise from.  Such a universal need should be the first thing listed in any preface about mathematics.  Perhaps, some of the resistance many feel and fear about mathematics is due to the intrinsic awareness that mathematics is hostile and unmerciful towards human falsehoods and negative states of mind that so often engulf us.  I will call such overwhelming negative states OE-(negative overwhelming energy), which I will expand on later.  One thing I will say is that to attain world peace we must learn to detect, define and minimize OE-.  Our very survival may depend on our ability to do so…  People might say that not every one is capable of mathematics and on a certain level this is true.  Humans may vary enormously in their capacity for abstract reasoning and not everyone can prove limit theorems so essential for understanding calculus.  However, if we state simply that calculus enables us to delve into the infinite, helping us to study instantaneous motion, quantum mechanics, and the theory of relativity, the reader would at least gain some understanding of the enormous scope mathematics has.  I would add the above facts to our mathematical preface in a purely descriptive way so that many would understand the implication of mathematical reasoning.  I would also include some of the magic of the Cartesian graph, which enables us to view the behavior of simple and complex equations, in our preface.  However, no such preface has ever been written…  Mathematics is a series of carefully defined and proven steps that lead to further growth in its carefully built structure.    Postulates and theorems have led to many branches of mathematics, which it would be ludicrous to ignore in any preface that purports to describe the purpose of mathematical thought.  But it is just as ludicrous not to describe mathematics as being reason’s most essential tool for dislodging falsehood, deception and misrepresentation…”

In the next post, Allan Kurzberg reveals his 2nd Pestulate and what he calls the Corollary of Human Existence.

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.

 

 

Time In Thomas Mann’s The Magic Mountain, Part 2.

Time is unreal, because the whole of any picture cannot be perceived at once.  Although the hands of a watch tick away, they cannot be said to be measuring minutes.  No one can know what the hands in truth are measuring for they are unaware of the divisions they pass over.  Grass grows so unobservably that it seems not to be growing.  However, at some minute grass appears from the seed.  This reflects the Greek paradox of being coming from non-being and furthers the mysterious notion of time as motion.  According to Mann, time has moved to bring changes according to a “succession of dimensionless points”, but at any one point the momentary effect on the grass is imperceptible.  As Piet Hein said in one of his Grooks, “We glibly speak of nature’s laws, but do things have a natural cause?  Black earth turned into yellow crocus is undiluted hocus pocus.”  Furthermore, the unreality of time rests on the premise that the immediacy of now varies with each person, with each event and with each thing.  According to the way it is interpreted, the same interval can be exciting, monotonous, capable, wasteful or productive.  Time is there in the feeling of the beholder, which Marcel Proust explored in depth in A la recherche du temps perdu.  As an entity, as a circular function that cannot go anywhere, time is a “hastening while” that “streams silently and ceaselessly on.”  So Thomas Mann develops the magic quality of time as a background against which seven years in the life of Hans Castorp takes place.

Actual time in the novel is sometimes represented by the number seven.  The book has seven chapters and the plot interval covers the seven years from 1907-1914.  There are seven tables in the sanatorium dining room, each of which is occupied by Hans Castorp during his seven years there.  The room of Frau Chauchat, “the charmer” is numbered seven.  Of course, the number seven has symbolic Biblical meaning.  Mann may be implying that the “new” Hans Castorp emerges within the Biblically significant number of years.  The seven years do change Hans through his own efforts.  There is unmeasured time for self-education in depth.  Self-study in books opens widespread areas of learning in the structure and function of the body, in the structure of snowflakes, in the functions of government, in the beginnings of the world, in the preservation of food and in the efficiency of the x-ray.  Time permits Hans Castorp to acquire encyclopedic knowledge.  It is interesting to note that in our modern era, educator Howard Gardner has identified seven distinct intelligences and French topologist, Rene Thom writes about seven elementary geometric catastrophes, so central to his Catastrophe Theory.

Time also becomes a relative concept as Hans Castorp stays longer away from the flat-land, under the influence of the magic mountain.  And the magic of timelessness becomes operative.  The days go by and Hans Castorp’s stay is lengthened to a month, then to six months, then to a year, then to seven years.  Hans loses all sense of time and cannot remember how long he has been on the mountain.  He becomes so engrossed that he forgets the flat-land and becomes part of the timeless spirit of the mountain.

The circular quality of time affects Hans when he welcomes back his cousin, Joachim, from the army.  He completes the circle of his own arrival as he meets his cousin on the same train, at the same station, and at the same time of the year.  The plot development is also circular.  Hans Castorp finally returns to the very place from where he started;  the flat-land.  He disappears on the battlefield of World War I, having completed the circular journey up and down the mountain.  And the higher one goes on the mountain the more unreal a measured minute becomes.  In the snowy vastness there is only the magic of timelessness…

 

Time in Thomas Mann’s The Magic Mountain, Part 1.

“Can one tell-that is to say, narrate-time, time itself, as such, for its own sake?   That would surely be an absurd undertaking.”  So Thomas Mann asks and answers one of the fundamental questions of his novel.  It is the “magic” of the “magic mountain” that obscures definite flatland time and establishes the verities of timelessness and infinite space.  However, Mann qualifies this thought by stating that one can only tell a story of time by assuming that time is  something flowing, a succession where one event follows another.  Mann actually views time as something inordinately complex and puzzling.  Humans lack any time organ that could measure it precisely.  Also, watches and clocks have no “feeling for the limits, divisions, or measurements of time.”  A concept of time must embody its actual value, relative value, circular quality, its relation to change and its essential unreality.  Time is so central to his work that he includes two complete sections:  “Excursus on the Sense of Time” and “By the Ocean of Time”, which are philosophical interpretations of time.

He speaks about the scientific definition of time:  the measurement of motion in space.  However, time is extremely relative like the distance from one place to another.  A long train journey might take twenty hours, by foot it would be greatly longer and in the mind it might take but a second.  And the motion of the seasons is also relative.  The calendar might indicate a regular succession of months, but in appearance and in effect, spring might be a phase of winter and autumn might reflect pieces of summer.  The very equinoctial movements are only relative for they anticipate each subsequent season in the midst of a current season.  The seasons flow with time not with the “actual state of the calendar.” Relative time flows like a piece of music.  It is a succession that requires more than one sound, but needs others to form a pattern.  Mann speaks of relative time as a “line composed of a succession of dimensionless points…  that goes on bringing about changes.”

Time is also circular.  After eons or seconds, all is as it was in the beginning.  Time cannot be shortened by novelty.  At first, novelty may seem to pass quickly, but as one becomes accustomed to the novelty, one shifts back to the old life and it is if the novelty has never existed.  Even monotony cannot make time seem long; “great spaces” of monotonous time merely shrink together and make the longest life appear short.  Earth’s very movement and the motions of the planets return to the point they have set out from.  Time is so much of a circle that Mann says it is a “cessation of movement–for the there repeats itself constantly in the here, the past in the present.”  But, at the zero point, an acceleration begins that leads through subsequent changes until finally zero is reached again.  And time change in a cell can be compared to time change in the individual.  An individual is born only to die, but in death he has only “closed his eyes on time.”  In fact, the individual has an abundance of time and is “timeless.”  The dissolution process of death is caused by combination with oxygen in the process of oxidation.  Here the circular time is complete, because life also rests on oxidation.  Living consists in dying and the dead partake of life processes.

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.”