Introduction to Probability: Second Revised Edition by Charles M. Grinstead
My rating: 5 of 5 stars

"One may summarize these results by stating that one should not get drunk in more than two dimensions."

The above is the most extraordinary sentence one can find in a university textbook on advanced mathematics! Charles M. Grinstead's and J. Laurie Snell's Introduction to Probability (Second Edition, 1997) is indeed a most remarkable textbook, by far the best text that I have ever used in my almost 40 years of teaching undergraduate mathematics and computer science. Probability was my favorite field of mathematics during my own studies in the early 1970s, but I somehow avoided teaching it, most likely because I had not found a textbook that I really liked. Until Grinstead and Snell.

Standard textbooks heavily focus on the combinatorial aspects of probability, which do not interest me too much. When I teach the upper-division probability course I love to emphasize the calculus-based approach, particularly when it involves multidimensional calculus and its applications to joint probability distributions. Grinstead and Snell's approach is virtually tailor-made for my probability course.

The second factor that makes me love the textbook is the emphasis on random numbers and pseudo-random variables generation. Having worked in the field of mathematical modeling and simulation for over 40 years I believe this is a natural approach to ground the probability course in. Grinstead and Snell's geometry-based problems that use the cumulative distribution functions to find the densities are a wonderful teaching tool: the students can also appreciate the applications of calculus: many of my students seemed to like discovering the connections.

Yet another great feature of the textbook is its emphasis on the moment generating function. Naturally, it is used to prove the Central Limit Theorem, the fundamental theorem of probability and the foundation of statistics. I follow the mathematical argument in class every time I teach the course so that math majors can appreciate a little more elaborate proof than the usual toy ones.

I also love the inclusion of a chapter of random walks (from which the epigraph is taken). When teaching partial differential equations (another of my favorite fields in math) I often discuss the Tour du Wino method of numerically solving the Laplace equation, which uses the random walks approach. The authors provide the famous proof by Pólya, which shows that a random walk must eventually return to the origin in one or two dimensions, but not necessarily for higher dimensions.

Of many other nice features of the textbook I should mention the authors' clear treatment of the Bayes' Theorem and the fascinating Historical Remarks that accompany many chapters. A truly wonderful book! The best textbook I have ever used!

Five stars.


View all my reviews

The Sea by John Banville
My rating: 5 of 5 stars

"What a little vessel of sadness we are, sailing in this muffled silence through the autumn dark."

"The past beats inside me like a second heart."

John Banville's The Sea (2005) offered me one of the most remarkable literary experiences of my life. After just a few pages I knew I was reading a magnificent novel. By mid-book I was absolutely certain this was one of the very best books I had ever read. And I kept reading, very slowly, savoring the masterful prose. And then... Then the ending came, the last few pages where the author suddenly decided to explain things, and some of the extraordinary charm of the novel instantaneously dissipated. Real life turned into a story; human truth turned into a plot. What a disappointing moment!

The Sea is a masterpiece fully deserving its Man Booker Prize; I will naturally round the rating up to five stars, but - to me - it is no longer a novel unique in its greatness, which it had been until the ending. In this inept but heartfelt review I am trying to convey my early feelings about the novel before the very ending broke the spell.

There is no linearity in life; life is not a story. Things in life occur for no reason and for no reason they do not occur either. Life is a jumbled collage of events that had once happened. The present is the accumulation of the past, but they also exist concurrently and one flows through the cracks of the other:

"[...] it all has begun to run together, past and possible future and impossible present."

Max Morden, a retired art historian, is an 11-year-old boy, playing on the beach with the Grace family, his wife Anna is dead, the boy falls in love with Mrs. Grace while Anna is dying "leaning sideways from the hospital bed, vomiting on to the floor," and the boy falls out of love with Mrs. Grace during an erotic experience at the beach, Anna is getting the death sentence from the doctor and the magical moment with Mrs. Grace - the culmination of the boy's love - begins to happen

"[...] in that Edenic moment at what was suddenly the centre of the world [...] and blonde Mrs. Grace offering me an apple [...]"

But the magic of the moment is broken by a hurricane of events. And it all begins and ends with the sea, the great infinity that created us and then absorbs us.

So deeply human the novel is that - although nothing even remotely similar ever happened to me - I feel all these events belong to me as they belong to all people. I feel that my past and everybody else's past merge with Max Morden's past in the universal human past. The truth of the elderly art historian, a grieving widower who is the 11-year-old boy in love with a mature woman is my truth and the truth of all people.

There is so much more in the novel: there is Claire, Max's "ungainly, unpretty daughter," and there are unforgettable Miss Vavasour and the Colonel. The boy's disgust at the mingling of God and sex, and a fragment seemingly taken straight out of another of my favorite authors, Cees Nooteboom:

"We carry the dead with us only until we die too, and then it is we who are borne along for a little while [...]"

There also is the absolutely stunning passage about Max becoming aware of the dichotomy between himself and that what is not-himself:

"In her I had my first experience of the absolute otherness of other people. [...] the world was first manifest for me as an objective entity.

Luminous, breathtaking prose.

Four-and-three-quarter stars.

View all my reviews

Looking for Alaska by John Green
My rating: 5 of 5 stars

"She had the kind of eyes that predisposed you to support her every endeavor."

A beautiful sentence from a wonderful book. A few months ago I reviewed Uglies, a very good novel in the Young Adult genre, recommended by a student of mine. I was astonished by how much I liked the book and became quite embarrassed of my generally disdainful attitude towards the genre. So when the same student highly recommended another YA novel I could not wait to read it. John Green's Looking for Alaska (2005) is a terrific book; although it is addressed to young people, it treats them as they should be treated - as adults.

We meet Miles Halter as he leaves his "family and Florida and the rest of [his] minor life to go to boarding school in Alabama." He refers to François Rabelais' last words when he says

"That's why I am going. So I don't have to wait until I die to start seeking a Great Perhaps."

Miles' adventures at the Culver Creek Preparatory School provide the plot of the novel. His roommate, Chip, aka "the Colonel," introduces him not only to the school's social structure but also to Alaska, "the hottest girl in all of human history." The plot is riveting and amazingly plausible to the very end.

This is a wonderfully mature book in how it handles serious topics and would do well as mandatory reading for all teenagers. Had I known the book twenty-something years ago, when my daughter was in her early teens, I would have wanted her to read it. I haven't found anything naive, cheap, condescending, overly simplistic, or brazenly didactic in the novel. It is amazing how much good stuff, how much common sense it packs with regard to life advice. And how well it handles the topics of sex and sexual initiation for which - as I understand - it got into some trouble with the self-proclaimed guardians of morality who attempt to perpetuate their own sexual hangups in their children. No vulgarity, no titillation with the subject, no guilt; just the healthy way of treating Things That Need To be Dealt With.

Completely unexpectedly I found a passage that touched a theme which would naturally belong to the type of Books for Very Old People that I love to read but which I would never expect to find in a YA novel. Take the quote that seems to come straight from Cees Nooteboom, the greatest scholar of human impermanence:

"Someday no one will remember that she ever existed, I wrote in my notebook, and then, or that I did. Because memories fall apart too. And then you're left with nothing, left not even with a ghost but with its shadow.

The novel is imbued with the love of books. It mentions so many great authors: François Rabelais, Gabriel García Márquez (a quote from The General in His Labyrinth provides a sort of motif for the entire novel), Kurt Vonnegut (his Cat's Cradle is one of Alaska's favorite books), poetry of Auden. While the author provides a charming description of Alaska's physical beauty - from which I took the epigraph - it is her love of books that adds a more important dimension to her "hotness."

Many wonderful passages in the novel: let me just mention the touchingly sweet Thanksgiving scene at the Colonel's mom. Then, there is all the humor, which made me laugh out loud so many times. True, I like to laugh and I probably laugh much more than an average person but I do not remember ever in my life laughing as hard as when I was reading the scene of the Great Prank during the Speaker Day at Miles' school. When Lara, the Romanian student, tells the speaker to "subvert the patriarchal paradigm" and he proceeds accordingly I got a hysterical attack of laughter which lasted 10 minutes and almost ended in suffocation. Oh, how I wish I were a part of a prank like that!

A beautiful love story whose poetry will be understood by young people, yet a mature and wise story. I am not quite sure what's going on with me: while always so stingy with the rating stars I am going to round up my 4.5 rating, even though the novel has not been written by any of the usual suspects like Joyce, Coetzee, Nabokov, Vonnegut, García Márquez, White or Nooteboom. Thank you, EK!

Four-and-a-half stars.

View all my reviews

Ascension: John Coltrane And His Quest by Eric Nisenson
My rating: 5 of 5 stars

"[...] the more one listens to Transition the more one hears a diamond-hard beauty unlike anything else in music. That something so roiling can also have such beauty is one of the paradoxes of Coltrane's art. A lot of great twentieth-century art, since it reflects its time, seems to confront and challenge its audience: Guernica, Finnegans Wake, The Rite of Spring. Like those modern masterpieces, much of Coltrane's work [...] has a modern grandeur unlike anything that has come before it.

Just last month I reviewed here Bill Cole's John Coltrane - a pseudo-research book full of New Age mumbo-jumbo and Fela Sowande's gibberish - which escaped the minimum rating on the strength of possibly interesting musicological analysis. Since I love John Coltrane's music and unreservedly admire what he stood for and what he tried to achieve in his art, I had to erase the anger caused by Mr. Cole's painful failure of a biography. In the ultimate contrast Eric Nisenson's work, Ascension. John Coltrane and His Quest is a totally wonderful book - deep, balanced, thoughtful, and focused.

I vividly remember the day (in 1966, I believe) when I first heard John Coltrane's music: I can see the room in my mother's small apartment when suddenly manic saxophone shrieks and wails came on the radio, immediately followed by utterly beautiful music. I remember my total fascination with the sound and with the raw power and deep passion of the music. Eric Nisenson begins his wonderful biography with an account how he first saw and heard John Coltrane live with his classic quartet (McCoy Tyner, Elvin Jones, and Jimmy Garrison) at the Half Note:

"Coltrane [...] played roiling arpeggios alternating with ribbons of intense lyricism often accentuated by saxophone cries and wails. [...] He seemed to be not in this world, and I, as well as most of the audience, [...] felt we had long left it far behind, too. [...] My body felt exhilaration, transport, even as much as my mind and spirit."

The story of Coltrane's life and his music is told traditionally, in a chronological manner. The author focuses in more detail on transcendent and timeless masterpieces in Coltrane's opus, such as A Love Supreme or Transition. Mr. Nisenson has the courage to call out failures as well, such as the audacious yet unsuccessful attempt to enter the realm of free jazz, Ascension or the bizarre artifact of the Sixties, Om.

The passages about A Love Supreme are some of the most compelling writings about music:

"[...] the last section on A Love Supreme [...] creates the impression of perfect stillness, like a man on his knees with his head bowed. It is utterly radiant and transcendent, at times pleading, almost sobbing in its need to be with God. It is one of the few works of art that, like the Sistine Chapel or Chartres Cathedral or Bach's St. Matthew's Passion is itself a religious experience."

The subtitle of the biography refers to Coltrane's quest, which - as most music critics agree - was the "quest to reach and find God through seeking within." Yet the author is careful to explain that Coltrane was not worshipping any particular God but rather "a personal synthesis of [...] ideas basic to all religions," Christian, Muslim, Jewish, Hindu, and others. Mr. Nisenson also points out that Coltrane's quest was more of spiritual than religious nature and that it might have been a search for the universal truth.

Coltrane's personal statements about wanting to be a "force for good," his continual search for that perfect sound, and the fact that never in his career had he made any concession to popular taste or cared what the audiences wanted to listen to tell me that his quest was for the three Transcendentals: Goodness, Truth, and Beauty. Certainly not for things that we, mere mortals, crave: Money, Power, and Fame.

A great biography! I will round the rating up.

Four and half stars.


View all my reviews

Herzog by Saul Bellow
My rating: 5 of 5 stars

"[...] he wasn't stable enough, he could never keep his mind at it. His state was too strange, this mixture of clairvoyance and spleen, esprit de l'escalier, noble inspirations, poetry and nonsense, ideas, hyperesthesia - wandering about like this, hearing forceful but indefinite music within, seeing things, violet fringes about the clearest objects."

I have finally read Saul Bellow's Herzog (1961-1964), one of the most acclaimed novels written in this country in the 20th century. A very difficult book to read but fully worthwhile the effort. I would venture a guess that of all fiction books I have ever read in my life this one may have the highest amount of content per page. I had to focus almost as much as if I were reading a math textbook. It took me a whole week to read the mere 340 pages and - at the end - I was sad that it was over.

Herzog is thoroughly un-American: it is mainly about human failure. Failure as an academic, failure as a spouse, failure as a father. Failure and its consequences in the form of a near nervous breakdown and depression. Failure is the most interesting of all possible topics in literature: we all fail, constantly, continually, and inevitably as we tend to always want more than we can get. A mathematician/computer programmer in me would say: failure is the human default while success is a random event. Mr. Bellow puts it succinctly in one of the greatest sentences I have ever read:

"Looking for happiness - ought to be prepared for bad results."

Moses E. Herzog, a once promising assistant professor of history of literature, author of an outstanding PhD thesis and an unfinished book on the history of Romanticism, now teaches in an adult-education night school in New York. He is twice divorced and his second wife, Madeleine, an aspiring academician herself, cheated on him with his best friend. Mr. Herzog does not have much contact with his two young children. Struggling with his emotional and intellectual crisis he seeks help of a psychiatrist. He also seeks contact with women to satisfy his sexual needs but having been burned by two failed long-time relationships he is unable of emotional engagement.

Characters in the novel are superbly portrayed - those are real, full-bloodied people. Characterization of Madeleine, "a highbrow broad", is an absolute masterpiece. I am totally convinced I personally know her and I feel I have personally witnessed her predatory, manipulative, and egotistic behavior. By the way, it would be so cool to read a novel written from her point of view, all about Herzog's faults.

Herzog is technically a novel but there is really no plot to speak of until the ending of the book when a few events begin to happen. This is another reason of my sadness at the ending fragments of the book - I have found reading the ravings of a defeated intellectual much more interesting than his life story. Juxtaposing Hegel's or Kierkegaard's philosophical arguments with Madeleine's caprices and misdeeds is absolutely priceless. The narrator's letters to philosophers, scientists, writers, public officials, (some dead like Nietzsche, Schrodinger, or Teilhard deChardin, some contemporary like Eisenhower), his colleagues, friends and adversaries, constitute a substantial portion of the text. These are wonderful letters - Mr. Herzog is a wonderful writer, just a failed one. Having myself been an aspiring intellectual and having failed at it I can vouch to the truthfulness of the following quote:

"Somewhere in every intellectual is a dumb prick."

I love the literary device of mixing the first- and third-person narration, similar as in another masterpiece The Beastly Beatitudes of Balthazar B . This simple device yields wonderful effect: it makes the novel sound not like a story of one particular person but rather the story of the times.

Based on what I have written above one might think that Herzog is a relentlessly dark and grim read. Absolutely not! It is in fact (painfully) funny in many places. Observing a human being thrashing about searching for happiness has a strong comic component. We suffer, we struggle, we fail, and then we die. Yet there is good news, sort of. Mr. Bellow writes:

"Unexpected intrusions of beauty. This is what life is."

Wonderful! The emergence of a plot at the end of the novel prevents me from assigning the maximum numeric rating but I would have to be insane not to round it up.

Four-and-a-half stars.

View all my reviews

Ravelstein by Saul Bellow
My rating: 5 of 5 stars

"Often the dying become extremely severe. We will still be here when they're gone and it's not easy for them to forgive us."

Finally I have begun to fill a huge gap in my Great American Literature education: I have just read my first novel by Saul Bellow - Ravelstein (2000). What a great read it has been! True, the first 20 or so pages are highly intimidating: the author assumes the reader's erudition and complete focus, and the text almost overwhelms with hyper-intellectualism. But having survived the beginning pages many readers should get accustomed to the challenges of the prose, like I did. However, I need to offer a warning: this novel may be better understood by older people, and by 'older' I mean people for whom death is no longer an abstract concept but a conspicuous event on the horizon.

The narrator, known as Chick, a seventy-something writer, is obviously an alter ego of Mr. Bellow himself (the author was in fact 85 when the novel was published). Professor Ravelstein, for whom Chick is the closest friend, is "a major figure in the highest intellectual circles," an internationally renowned professor of philosophy, and the author of a best-selling book that expounds his conservative views about the decline of American culture. The book made millions for Prof. Ravelstein and now he can afford flying to Paris to buy Lanvin jackets and custom-made silk shirts. He also happens to be gay and suffers from AIDS complications. He wants Chick to write his memoirs.

In his writings Professor Ravelstein captures "modernity in its full complexity" and the human costs of modernity. He criticizes the mass-market aspect of cultural modernity and juxtaposes it with culture of the olden days, writing about people who read "Stendhal's novels or Thomas Hardy's poems", instead of sucking garbage flowing from TV, Facebook or Twitter. He recommends interest in Plato and Thucidides rather than current celebrities:

"I like to say when I am asked about Finnegan[s Wake], that I am saving him for the nursing home. Better to enter eternity with Anna Livia Plurabelle than with the Simpsons jittering on the TV screen."

Particularly sharp is Ravelstein's critique of the modern education system and the fact that the "liberal education had shrunk to the vanishing point." The universities are excellent in sciences and engineering but a failure at liberal arts. At this point I realized that Mr. Bellow's Ravelstein is modeled on the real-life philosopher and classicist, Allan Bloom. And indeed I have found out that the author and Dr. Bloom were friends and colleagues at the University of Chicago. The life story of Ravelstein and that of Dr. Bloom are in fact parallel. Yet let us remember: this is a novel, not any kind of Dr. Bloom's biography. By it being beautifully written fiction I find the novel much more realistic than any non-fiction biography could be.

Scattered throughout the novel are wonderful morsels of truth about human life and especially death. We the geezers will appreciate the mention of one of the main problems of aging - "speeding up of time." We the geezers may also be able to understand the sentence I quoted in the epigraph above. It's a hard truth to swallow and very painful. Ravelstein is a great novel. My "to read" shelves will now gather other Bellow's works.

Four and three quarter stars.

View all my reviews

The Beastly Beatitudes of Balthazar B by J.P. Donleavy
My rating: 5 of 5 stars

"'Yes sir, I know that my redeemer liveth. I know it.'"

One of the most unforgettable books I have read in my life! J.P. Donleavy's The Beastly Beatitudes of Balthazar B (1968) combines breathtaking prose, lyricism, and biting humor with sobering reflections on the human condition. It also has the potential to offend many readers on many levels. Descriptions of pre-adolescent sexuality, numerous risqué scenes, and taboo topics make the novel perfect fuel for barbecues in fundamentalist communities. There have been documented cases of Slaughterhouse-Five burnings in this Land of Freedom of ours; Mr. Donleavy's work is a way more deserving book-burning material but - fortunately - not many people have heard about this wonderful novel.

In the grim days of Internet-generated uniformity of opinions, intimidation by political correctness, "safe zones" on campuses and the like, I found this novel a refreshing deviation from the safe-to-read-for-everybody, lukewarm, agreeable pap that dominates the so-called culture these days. We need more rather than less of controversial art to prevent the inbreeding of popular ideas - ideas that most everybody likes.

The novel recounts the first twenty-something years of Balthazar B's life beginning with his early childhood in Paris when he was raised by nannies in a very rich family. His father had died in the boy's early years and the mother was mainly focused on preserving the vestiges of youth. The boy attends exclusive public schools in England and the famous Trinity College in Dublin, and faces the tribulations of the early adulthood. Ostensibly the author focuses on the romantic and sexual aspects of Balthazar B's life: a boy's coming-of-age usual stuff - masturbation, school pranks, pubic lice, first love - but a discerning reader will notice that underneath the titillating facade of the novel the author tackles more important life issues.

The novel is exceptionally rich in humor in its entire range: subtle and understated funny phrases, sentences, and passages are intermixed with laugh-out-loud fragments. From the childhood memory of the Enema Anglaise, through the utterly hilarious scenes of public school housemaster excoriating smuttiness ("concerning things between the legs") and combating boys' masturbation, the live demonstration of dangers of pubic lice for medical students at the Sorbonne, to one of the funniest scenes I have ever read - the neighborhood vigilantes interrupting a carnal coupling:

"'Sir, gurgling and groaning and some cries have been heard out in the garden.'"

Yet underneath all this ribald humor there is so much understanding of human foibles, so much compassion that there is no doubt whatsoever about the author's intentions.

The portrayal of Balthazar B is subtle, nuanced, and realistic. A child, a boy, and a young man in search of love. "While others are cunning and deceitful," Balthazar "remains always [...] kind." B's best friend is Beefy, also an unforgettable, vivid character, always in search of "pleasurings." For reasons of public decency I can quote only one of the many beatitudes coined by Beefy:

"Remember, blessed are they who are willing victims of the whip for they will scream to high heaven."

It may seem that the novel is light-hearted and fun all around. Absolutely not! It is full of lyricism, melancholy, and even sadness. Miss Fitzdare thread is bittersweet and makes an old man want to cry. And I have left the best thing for last: the extraordinarily accomplished prose. When I read books I mostly care about the beauty of the prose and the author's mastery of the literary craft. This is what makes me round my rating up to the rare maximum, reserved only for masterpieces.

Four and a half stars.



View all my reviews