Some Thoughts About Mathematics And Life

The one thing that comes to mind when I think about mathematics and life is:  You can’t solve any mathematical problem with a confused or unfocused mind.  So, to do a math problem your mind needs to be clear and directed to the problem at hand.  The same could be said about any problem that arises in a life situation.  We are more likely to achieve a better solution if our mind is tranquil and rational.  In other words,  unsettling, spoiling emotions must be kept at bay.  For, a great disturbance in many life events is the spilling over of emotions that cause us to act in an irrational manner and to reach sometimes distorted and even absurd “solutions”

In the realm of life problem solving, mathematical problems form only a tiny subset of all the problems we must deal with.  Mathematicians have established clearly defined rules for solving mathematical problems.  In their special province they serve as architects, beginning with the simple counting numbers or natural numbers, and then including 0 and the rational numbers and stretching out to the irrational numbers to form the set of real numbers.  The real number line is created where all these numerical sets have their home.  And mathematicians begin with axioms and postulates(assumed truths) and from them derive theorems and corollaries to theorems.  Theorems and their corollaries must be subjected to the rigor of mathematical proof before they can be accepted as truths.  What can we use to prove a particular theorem?  Any definition(a definition is an agreement to use words, phrases or symbols as substitutes for other words, phrases, or symbols.), postulate or axiom, or previously proved theorem may be used in a proof.  The use of precedent is also essential to legal, medical and some forms of scientific problem solving.  And mathematics teaches us that to disprove a theorem it is sufficient to find only one example where the statement does not hold.  This latter statement applies to all life problems as well.  For, when we toss around generalizations, it is important to realize that it takes only one counterexample to destroy our generalization.

Mathematics also teaches us to think twice; to be careful before reaching a conclusion.  When graphing functions on the Cartesian plane, it’s not uncommon to have restricted domains, meaning the functions are defined on a certain interval.  And sometimes separate cases must be considered, for example, what does the graph look like when x is greater than zero and how does the graph change when x is less than zero.  Arguments in life may also have restricted domains and statements that may be true for an adult are utter nonsense when applied to a child.  So, we must be cognizant of our audience and know where to apply our argument.  Thus, the study of mathematics can and does help us to cope better and to grasp better the multitude of problems we encounter in life.

“And You’ll Gonna Pay!”: Oh, Those Memories!

When my ex-wife and I lived in South Pasadena from 1986-1991, we encountered an eccentric French couple who became our landlords.  The woman was in her 60s, of a highly suspicious nature, and was always going through other people’s trash to find evidence of their misdoings, which she never found.  She also liked to place a quarter near one of the laundry machines to see who would take it, but nobody ever did.  Whenever she got angry at a tenant, she would exclaim, “And you’ll gonna pay!”  She used to scream at her husband, yelling out that he was the son of satan and a monster.  However, her spouse merely shrugged his shoulders and turned his back to her.  Unlike the woman, he was quite cordial and agreeable and loved to fix things.  “I fix. I fix.”, he would proclaim whenever we had a plumbing problem.  But he used scotch tape methods rather than any bonafide plumbing tool, so the problem always recurred.

The Case of the Water Men:

When we moved into this apartment complex, two men from the water company occupied the apartment opposite us on the second floor(We lived on the first floor).  Not long after our arrival, the water men left and the space was to remain unrented for the rest of our stay.  Now many people went up the stairs to visit the apartment,  but nobody took it.  We began to wonder what was so terrible about that apartment that kept prospective tenants away.  We thought about what the water men could have done to have made the space so repulsive.  These thoughts kept us busy on dreary days and were the source of much amusement.  However, this was a case that had no solution.

Roach motel:  Reservations Recommended!

When I first told my ex about a roach motel, she envisioned several rooms with furniture, a dining table and several accessories for comfort.  She was truly disappointed when she saw a bleak rectangular box with glue-like material inside, which would be the last object a roach would see before heading into eternal silence.

My roommate and I lived in a relatively clean, well-furnished apartment for several years until a couple of girls moved in downstairs(This time we were upstairs).  For amusement and extra money these girls sold their services on the top of the roof, so their clients could get an aerial view of Westwood as a bonus.  Alas, the girls had a habit of leaving garbage bags outside their room for days.

Word spreads quickly in a college town, and soon every UCLA roach dropped its studies to head for our apartment building.  Unfortunately, these roaches were not like our current garden roaches, large and orange-brown and quite choosy about their mates, but small German roaches that mated with every female roach no matter how unattractive she might be.  Soon our apartment was full of roaches that liked the dark, so we bought a roach motel.  The next day it was filled with roaches and a few other curious insects.  And every day it would be the same story.  Finally, we resorted to other methods.

Retribution!

Our owner’s in-laws came over when repairs were needed.  The man was quite the gentleman, but the woman we called “The Wicked Witch of the West”, because she needled us and said that the repairs were our fault.  We honored her by intoning the evil witch’s theme from the 1939 MGM movie.  One day she was showing our apartment to to possible renters.  She yelled at us:  “What is all this white powder on the floor?!”  I replied, “That’s to kill off all the roaches.”  My roommate and I laughed and laughed, but I will draw a curtain of silence over this scene and this post.

 

Another Brief Note

Because of health issues, family problems and sudden changes in lifestyle, I have decided to suspend my posts until I’m able to establish some equilibrium in my life.  I am grateful to the 101 followers that have taken the time to read my posts.  I am also grateful for the many comments I have received.  I wish all my followers lives of joy and fulfillment.

“Where’s The Moon? I Don’t See The Moon!” Or, Mathematics To The Rescue

I was dragging myself up the stairs of Founders Hall.  The cement steps and barren walls reflected the darkness of the time ahead.  For, my next class was Speech Communication with Professor B.  I was not doing well in the course.  As my current lady would say:  “You’re going down, down, down!”  And so I was.  But perhaps, I should tell you something about Miss B and how I got into trouble.

Miss B was a tall, wiry lady with sharp, unforgiving eyes and a total lack of manners.  We didn’t get along from the start.  I remember her saying with a sarcastic tone:  “Look at that!  A little boy wearing his tennies!”  She was frank, if nothing else.  And when I tried to act out a favorite childhood verse, she would yell out:  “Where’s the moon?  I don’t see the moon!”  At the time, that comment stunned and hurt me, because I was quite fond of the verse I was interpreting.  Later, Professor B told me that the only thing that could save me was the final, which was a monologue of at least ten minutes.  I thought and thought about possible selections.  I knew if I picked something well-known I could be compared with the greatest and I’d come up way short.  Fortunately, at that time, I was reading some wonderful mathematical stories from Clifton Fadiman’s Fantasia Mathematica.  Bruce Elliot’s story, “The Last Magician” really appealed to me.  The main character was an old man who was fond of a magician’s helper and commits murder because of the cruel way the magician treats her when a futurist society has condemned her to death for misceganation(She was Martian and became pregnant by the magician from Earth).  So, the story had intrigue, action build-up and the main character was an old man.  And, growing up next door to my Dad’s parents, I knew my Grandpa Johnny quite well, so I thought I could act out the part with some accuracy.  Also, the story dealt with the magician trying to escape from a supposedly real Klein bottle

Attempt to picture a Klein bottle, a three dimensional surface that has only one side, which is impossible.

An attempt at constructing a Klein bottle, a three dimensional surface that has only one side, which is impossible.

and was mathematical in nature, so probably few, if any, people had seen it performed.  When I thought about all the advantages, I thought it would be an excellent choice for a monologue.  I would need to trim some parts, though.

Finally, the long-awaited day arrived.  Everyone was busy rehearsing their lines and trying to get into character.  Wouldn’t you know it?  I was the first person Miss B called on.  I knew if I wanted to do well, I was going to have to become an old man in every way.  I tried hard to imagine my Grandpa Johnny and become him.  I tried to walk with difficulty, struggle to get some of my words out and look confused.  And as I reached the podium, the words did come out.  “The harder he worked the worse he treated Aydah…  It seemed as if every time I turned around I’d find her hiding in some corner, crying… I knew she would have to die.  That was why I had pressed the button that switched the bottles the first time, before she ever did…  I guess I must be getting old;  lately I’ve taken to wondering about King Solomon.  He knew so much, I wonder if he knew about Klein bottles…”  Then, a loud applause.

“Well, Bob just disappeared!  A feeble old man replaced him!”  Professor B’s eyes sparkled with admiration and respect.   Mathematics had come to the rescue.

 

 

Something To Think About: A Filipina Secret: “Tossing The Dog”

The Philippines are a series of small islands dotting the Pacific Ocean.  Its people are predominantly Roman Catholic, except for the Muslim population of the southern-most island, Mindanao.  Therefore, divorce is not recognized and annulment is prohibitively expensive.  A Filipina’s main weapon in an unhappy and troubled relationship is “tampo”(“the silent treatment”), which can last for hours and even days.  During “tampo”, the Filipina’s soft facial features turn to stone and her eyes stare out with a cold ferocity.  But there are times when even “tampo” does not work, and if a Filipina does not have sufficient funds for an annulment, and since divorce is not accepted, it would appear that she is stuck in a miserable relationship for life.  But Filipinas are known for their tenaciousness in solving problems, so they came up with “tossing the dog” as a permanent solution to this disturbing problem.

Filipinos are known for their close, extended family relationships.  Thus, there are always a lot of relatives to assist a Filipina in a time of despair.  Making use of this fact, the Filipina always has other Filipinas to rely on when she needs to “toss the dog”.  “Tossing the dog”  is certainly a last resort, but is used more often than one might expect.  Briefly, it consists of this:  Late at night when the unsuspecting offender is in a deep sleep, a group of the Filipina’s female relatives creep up to the offender’s room.  By applying a cloth with a knock-out chemical to his nose, the Filipinas ensure that he continues to live in the land of dreams.  They then bind him with strong coiled rope and put him in a vehicle, parked conveniently near his home.  Then, they drive the unfortunate man to Pangitka Bay.  There, like looming shadows of the night, using their combined strength, they carry the offender up a rocky cliff.  When they reach the top, they give out tribal screeches and curses and “toss the dog” into the shark-infested waters of Pangitka Bay.  The offender is never seen again and his disappearance is called an unfortunate accident.  Thus, the ingenuity of the Filipina overcomes a persistent obstacle and she is at last free to breathe the air of joy and freedom.

 

Some Miscellaneous Thoughts On Turning 200

It’s hard for me to believe that this is my 200th post.  Frankly, I never thought I could come up with enough ideas to furnish so many posts.  There was also a question of existence;  I never thought I’d live to be 62.  But, here I am and I still have ideas for further posts.  I’m so grateful for my 100 followers, who continue to read my posts and offer helpful comments.  That I have forged strong links with people from Australia, Canada, the Philippines, Russia and the Ukraine, makes me very proud.

Our world is a tempestuous one, and now that the U.S. has broken open the magic bottle of the Middle East, not so nice genii have spread their wickedness throughout the region.  While the Cold War had well-defined enemies, the current wars often have shadowy figures that lurch between good and evil, making them hard to pin down.  The concept of “freedom fighter” has often appealed to gullible Americans, who often give aid to “fighters” of dubious character.  Throw “religious motivation” into the mix and you have a real mess.  The malignancy of misguided hate has spread throughout the world, and only time will show if we have experienced and intelligent enough “doctors” to cure it.

On a more technical note:  We humans tend to be rather bad at long-term reasoning.  Our history confirms this fact over and over.  One reason that this is so is because we cannot predict all possible outcomes of a given event.  Hence, it follows that we cannot predict the collection of events that form what we call future.  Is this an inevitably fatal flaw in our mental structure?  Again, time will tell.

“Man’s a kind of missing link.  Fondly thinking he can think.”–Piet Hein

One of the most disturbing books I’ve read in the last twenty years is Dale Peterson’s stupendous and highly insightful biography of Jane Goodall.  Disturbing, because it reveals often surprising connections between the lives of chimpanzees and the lives of humans.  At times, it’s hard to differentiate the two worlds.

I know that French naturalist, Francois Buffon, tried to show that there is an unbridgeable gap between animals and humans. He thought that man was the reasoning being, while all animals were irrational beings.  Alas, scientific research has shown that this gap is not as large as Buffon suspected.  We now know that the rational aspect of the human brain developed late in our development.  Those primal desires that we inherited from our cave ancestors dominate our lives.  We have only to look around us to see the proof.  Most of our TV programs thrive on greed, vanity, cruelty and other basic human instincts.  How many programs deal with the nature of mathematics, forms of problem solving, or what we can learn from peoples other than ourselves?

“Who is to say that we’re born and we die, and what’s in between doesn’t matter?”–Charles Kalme, Assistant Professor of Mathematics, University of Southern California, 1970.

What is my philosophy of life?  I think it’s a mixture of Samuel Beckett, Thornton Wilder and Walter Kaufmann.  From Beckett I take the tenuous quality of life;  from Wilder the belief that some moments are special and Kaufmann’s belief that reason is our best defense against chaos and madness in the political realm.  As to free will and determinism, I see life as a boat ride in Disneyland;  you think you’re doing the steering, but you don’t realize that your boat is being guided by unseen underwater tracks.  Let us hope that we are guided by tracks that will take us to greater understanding and the light of unbounded human potential.  In the end, nobody knows what is really at stake on this tiny planet.  That is the great mystery.

 

Some Thoughts On Fly Fishing And The Rogue River

Fly fishing was de rigueur for my Dad.  In Oregon, he would fish from after breakfast until shortly before dinner.  After dinner, he would usually put on his heavy waders and come trudging back as darkness fell.  He would do this virtually every day of our one month summer vacation from the end of July until right after Labor Day.

His preparations, though, would begin toward the beginning of July.  Then, he would take out his fly tying equipment and begin making flies for the trip.  I remember seeing flies shining in his den with many different colors.  He was quite an expert at creating flies, and usually had an abundance of them ready to be dropped into the water for trout, and, most importantly, summer steelhead, which he loved to barbecue or put into the freezer for future eating.

Dad learned about the art of fly fishing from the chauffeur at Rogue’s Roost, Joseph Chevigny and river guides Glen Wooldridge and Bob Pritchett.  The latter initiated him into the art of boating, and locating steelhead holes on the Rogue River.  From an early age, Dad could find steelhead water and navigate a navy surplus raft.

Dad always enjoyed fishing the Upper Rogue.  He tried to teach me how to fish, but trout was all I could manage, and, besides, I didn’t want to pull fish hooks out of my ear, which happened almost every summer with Dad!  But I did learn to appreciate and love the river and all its natural habitat as well as do some inner tubing and rafting.  Swimming across the river was never one of my talents!

In the early years, the Rogue River was a pristine mountain river, its color a pristine blue and so clear that you could see trout swimming or salmon spawning.  All that changed when the Lost Creek Dam was built in the late 1070s.  Because it was an earthenware dam, it increased the amount of silt that floated downstream and the river’s clear beauty disappeared with it.  In the years that followed, more and more people used the river, though without the respect early residents had shown.  At one point, the river was declared unfit for swimming and a major effort was made to bring it back to its natural state.

I’m grateful that I saw the Rogue River in all its splendor.  The short videos that follow show my Dad fly fishing on a truly magnificent river.  I hope you enjoy them!