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.”

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.