Some Mathematical Healing

Mathematics is not often thought of in regards to healing.  Instead, we think of meditation, absorbing the wonders of nature, relaxation, living in the moment, letting go, listening to soothing music.  However, lately mathematics has been a source of healing.  The following example will show you how.

Recently, my Dad’s 93 year-old brain has been on the on and off mode.  Sometimes he cannot distinguish between dream and reality and acts with extreme apprehension concerning the circumstances of his dreams.  The more practical side of his mind is obsessed with financial transactions, often spending hours trying to solve problems that seem impossible, but are really quite doable.  It dawned on me that a simple algebra problem might gather Dad’s thoughts in a tighter and more purposeful direction.  I might say that mathematics seems to me like a demanding yet supportive parent.  Like a parent, there are rules that must be obeyed and an order to be preserved.  However, there is also something truly soothing about logical boundaries, and a clear set of rules, which, if followed to the letter, lead to future paths of discovery.  Parts of the mind are held in check,  but others are ever expanding, testing, and exploring.  So too, an effective parent guides the child through progressive steps toward exploration.  With these thoughts in mind, I gave Dad the following problem:  Solve for x:  (x)(x)-7=9.  Dad simplified the equation to (x)(x)=16.  Then he began to test numbers such as 2, 4, 6, 8, to see which ones might work.  He also talked about square roots.  After about ten minutes, he came up with the answer 4.  When I told him that was only half the solution, he was nonplussed.  It took him awhile(with some prodding from me) to realize that negative numbers also exist.  When he resisted the idea, I told him that during our lifetimes we had encountered many negative numbers, and a smile crossed his wizened, unshaven face.  He allowed for the possibility of negative numbers.  He then gave -4 as the other solution.  Suddenly, he said that any two negatives squared would result in a positive, so there would always be two numbers as possible solutions  to the type of problem I was asking in which the x’s squared are equal to a positive number.  It amazed me to see how his mind was able to move to such a generalization, so I cried out,  “Bravo!”  Later that evening he was able to solve a financial problem that he couldn’t solve earlier.  Temporarily at least, my Dad’s mind had climbed to a new level of thinking.  I thought this was as an excellent example of mathematical healing and that is why I decided to share it with you.

Something to think about: “Would you pay the price? What would you do?”

The above lines come from the 1966 American musical Cabaret based on writings of Christopher Isherwood and John Van Druten.  The musical focuses on the lives of a few people and their reactions to the growing Nazi threat in 1930s Berlin.  The musical was unusual in that it did not have a happy ending, and Americans are used to happy endings.  Thomas Hischak offers his own description of Cabaret in his The Oxford Companion to the American Musical:  “Arguably the most innovative, hard-hitting, and uncompromising musical of the 1960s,…”  What makes this musical so innovative?  It introduces us to decadent Berlin through an MC of the Kit Kat Club, himself a mixture of playfulness, immorality, and darkness.  As the show progresses, the political overtones become ever more ominous and threatening.  The title, which also serves as one of the main songs in the musical, is a celebration of irresponsibility and seediness.  Sally Bowles, one of the chief entertainers at the Kit Kat Club and the girlfriend of Clifford Bradshaw, an American writer, sings the song as a tribute to her late girlfriend Elsie.  Sally’s friend was a prostitute, drug addict and alcoholic who died from too much of the latter.  Sally sings of Elsie’s death, “… But when I saw her laid out like a queen, she was the happiest corpse I’d ever seen.”  Elsie’s memory motivates Sally to return to the cabaret where she will probably end up like Elsie.

A sub-plot concerns the romance between Cliff’s landlady, Fraulein Schneider and the Jewish fruit seller, Herr Schultz.  After she accepts Herr Schultz’s proposal of marriage, pressure is put on her by Nazi smuggler, Ernst Ludwig, who had introduced Cliff to Fraulein Schneider’s boarding house, to break off the marriage to avoid the repercussions of marrying a Jew.  She decides to comply with Ernst’s demand.  Cliff and Sally are shocked to learn of her decision, so she asks them, “What would you do?”  Although, she emphasizes her status as an old woman, the song that follows could be sung by anyone who is confronted with a despicable regime and the consequences of doing what is ethically right.

In London in 1993, Sara Kestelman gave an intense, harrowing interpretation of the role of Fraulein Schneider for which she won the Laurence Olivier Award for Best Performance in a  Supporting Role in a Musical.  What follows is her version of the song, What Would You Do? My thanks to lluluss for posting this song on youtube.

“The Flowers that Bloom in the Spring”, part 1: Southern California

Despite a lengthy drought, flowers appeared in their many enticing colors.  Our front entrance was covered with azaleas and outlined by roses.  The back saw the emergence of freesias and camellias.  Unfortunately, the hyacinths didn’t do well due to the arid soil and warm April temperatures.  However, we were pleased with the flowers that did bloom in the spring.  Below are some photos of the Spring flowers around our Southern California home:IMG_6317IMG_6322IMG_6325IMG_6326FW 32FW 34FW 35FW 7FW 15FW 18FW 19FW 22FW 29FW 30

The map that Ray drew

Fishing map drawn by Ray Minehan.

Fishing map drawn by Ray Minehan.

Rogue’s Roost and many other spots on the Rogue River were known for excellent steelhead and salmon, so to provide their guests with a fishing map, Nion and Phyllis Tucker hired sketch artist, Ray Minehan.  He drew a limited amount of sketches that are all numbered.  This is #22.  It is supposed that the maps were drawn in the late 30s or early 40s. The Roost had been purchased by the Tuckers as a picnic site from Walter and Alice Bowne in the 1930s.  At that time, there was only a small cabin, and nothing to suggest what would become the magnificent Rogue’s Roost.  The Tuckers then bought other parcels from different landowners to complete the finished residence. Joseph Chevigny was the chauffeur and fisherman in residence.  He and my Dad used to go fishing together.  It was Joe who taught my Dad about the art of fly fishing.  The area near the Roost boasted a huge spawning bed and great steelhead fishing.  Joe created his own fly that he called the Chevigny fly.  My Dad copied it, and made numerous flies that he gave to friends.  He renamed the fly, The Rogue River Special, and the name stuck.  It is still used by fishermen today. The upper left of Ray’s map shows the elegant Roost with its spacious lawn.  The main building in the center opened out to a deck over the river.  It was not unusual to see Jack salmon or steelhead jumping in the sparkling water.The lower left of the map shows the end of a fisherman’s efforts: a large, tasty fish ready to be eaten. A few comments regarding some of the places mentioned on the map: 1.  The town of McLeod no longer exists.  It was subsumed by the U.S. Army Corps of Engineers as a visitors’ information center for Lost Creek Dam.  2.  Casey’s Camp was an extention of the original Casey’s Auto Park.  Today it is called Casey State Park. 3.  Round House(a stone house) was built by Emmett(Sno-Cat) Tucker(no relation to the Tuckers of Rogues Roost), and eventually became the famous Obstinate J Ranch until it was sold and the name changed.  4.   Beagle was a pioneer community that began in 1885 and ended in 1941 when the U.S. Army took it over to establish Camp White. 5.  Sunset on the Rogue included a gas station, store for food and fishing, and cabins.  It still exists today!  6.  California on the Rogue offered a gas station and cabins. The name has been changed, but the buildings remain.  I knew the owner during the 60s, Mr. Sullivan.  I brought a geode to him from the North Umpqua region and asked him if there could any crystals.  He said, “Nah!”  When I got to the Obstinate J Ranch, I split the geode and found it full of reddish-brown quartz crystals!  7. Captain Black’s refers to what became Black Oaks.  The place currently belongs to the Donald L. Donegan family and encompasses some of the best steelhead water between Dodge Bridge and TouVelle State Park.      8.  Dowden and Hardy’s should be reversed.  Hardy Rapid Class 2+ contains an enormous hole in the middle of the river that must be avoided.  Dowden refers to Dowden Falls, today known as Gold Nugget Falls Class 3+.  Every summer rafters and kayakers float the left channel of the falls that includes two large drops, especially the last one!  The campground provides a beach with great views of the lower drop.  A great place to relax and reflect on nature’s wonders.

The Removal of a Dam and a Tragedy

Gold Ray Dam had been a fixture for about one hundred years.  But, under pressure from the Oregon Fish and Game Commission, a decision was made to remove it.  The reason being that it provided a major obstacle for salmon swimming upstream and impeded their growth.  The dam itself was not really doing anything.  Above it, a slough had formed, creating a water sanctuary for hundreds of riparian creatures.  These life forms had thrived for over a century, but disaster was about to overtake them…

A long battle for the removal of Savage Rapids Dam ended several years ago when it was finally taken out.  The people involved in the job were cautious as to how much water they would let out at any given time, and no major incidents occurred.  Above it, a placid lake had formed, but there was nothing like the teeming slough in back of Gold Ray.  The river at first created a mean rapid, then settled into a more mild Class 2 with just a few rocks to dodge.  The river cut a wide swathe where there had once been a more narrow and treacherous drop.  It reminded folks of the effects of the 1964 flood, which did precisely the same thing.

When the removal of the Gold Ray Dam went from paper to action, the dam removers felt a surge of confidence based on the successful removal of Savage Rapids.  But, alas! Hubris and carelessness overtook them.  Instead of moving cautiously with measured steps of removal(as had been the case with Savage Rapids), they took large chunks out of the dam, while underestimating the power of the river in back of it.  The result was an ecological catastrophe.  Suddenly, the river burst through with a violent roar, and moved away from the habitat that had depended on it for sustenance.  Thousands and thousands of water creatures perished.  Photos published showed fishes faces in shock.  These pictures brought a truly affecting quality to creatures that were just caught and eaten at will.  And, irony of ironies, the removal of Gold Ray, which was intended to preserve the salmon and other species,  ultimately contributed towards their destruction.

It must be said that many people from the Fish and Game tried to save as many species as they could.  But their efforts caused only a mild dent in the tragedy that had occurred.  Let us hope that in the future, dam removers will show the same consideration for habitat as dam builders.

A video showing Class 2 Gold Ray Rapid today:

Something to Think About: Mathematical Lunacy

The notion that mathematical reasoning is somehow linked with mental illness is not as far-fetched as it might first appear.  The late mathematician, Robert Brooks, provides an amusing analogy of his own in our discussion of mathematical shape;

RW:  Then it’s(the world of mathematical shapes) your world.  You’re immersed in this abstract universe that you’ve created.

RB:  That’s right.  My wife is a family physician, and she says that the patients that remind her of me the most are the schizophrenics, because they’re walking around in a world that’s very real to them, but invisible to anyone else….  I actually spend a lot of time just sitting with… paper models, playing with them, and asking myself what is the same about them, and what is different.

Mathematics and mental illness:  Something to think about.

Some Notes on Spanish for Reading

Unlike the other languages for reading in this series, the Spanish edition is relatively recent and quite affordable.  It is a delightful and effective way for learning to read Spanish, and is highly recommended.

The book’s introduction treats Spanish vowels and consonants with descriptions on how to pronounce them.  The first chapter is critical for it deals with cognates of which there are an abundance.  These should be studied assiduously, since they are indispensable for expanding vocabulary.  I must say that although I had three years of high school Spanish, and took a summer course in Mexican civilization and culture, the first reading about the Spanish language seemed completely foreign.  The next three chapters place a strong emphasis on the geography and history of Spain and Latin America.  After these chapters, the authors concentrate on legends, festivals, and other aspects of Hispanic culture.  The readings are quite interesting and build up the reader’s knowledge of Spanish grammar, which is much easier to grasp than French or German.  It is not until Chapter 10 that the reader gets his/her first taste of Spanish literature.  The excerpts provided come from Juan Ramon Jimenez’s highly poetic and personal masterpiece, Platero and I.  In this intriguing work, the author shares his thoughts and reflections with his beloved donkey, Platero as they travel together.  An excellent translation of the complete work is available through the University of Texas.  The idea of traveling through towns and surrounding country is a major theme in Spanish literature.  Beginning with the picaresque(which features a rogue as hero, and was a reaction to courtly romances), it finds its culmination in Miguel de Cervantes’s work, Don Quixote, in which Sancho Panza(picaresque tradition) and Don Quixote(courtly tradition) travel the countryside together, viewing events from the point of view of their respective traditions.  The 12th chapter has a long reading:  Women and the Labor Force in Latin America and the Caribbean”.  This is the type of writing you might find in a newspaper or scholarly article.  At first it’s a bit intimidating, but repeated readings will flush out the meaning and boost your confidence.  Chapter 14 has two scholarly articles:  “Latin America in Transition”, and “Drug Traffic:  Two Sides of the Coin”.  The latter is particularly difficult, because some of the grammatical constructions are quite complex.  I would study these two articles until you are comfortable with all the syntactical windings.  Some brief poems by Pablo Neruda complete this instructional volume.

The major shortcomings of this book are two:  there is no comprehensive grammar test at the end as is the case with German for Reading, and there is no vocabulary list, so you will need to purchase a Spanish dictionary.  But the shortcomings are minimal compared to the excellent preparation for reading Spanish that it provides.  After completion, I found I could read a number of literary texts without much difficulty.  I recommend the book to you without hesitation as a wonderful way of experiencing the many facets and colors of the Spanish cultural heritage.


Get every new post delivered to your Inbox.

Join 98 other followers