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.

Something To Think About

Below are two quotes from two mathematicians.  Robert Brooks is speaking about mathematics, but could his statement refer to something else?  Charles Kalme mentions education and not mathematics, but is there a connection between the two quotes?  What do these two quotes suggest in our everyday lives?

“…it dawned on me that all the numbers we had been given to add up until that time had been kind of “cooked up”, so you didn’t have to carry…;  and I said to myself,  “I wonder what else they’re holding back?”–Robert Brooks, Assistant Professor of Mathematics, University of Southern California

“Education courses are where you learn not to rock the boat.”–Charles Kalme, Assistant Professor of Mathematics, University of Southern California

Some Early Morning Thoughts About Life

It is early in the morning and my brain is pondering on the nature of life.  It occurs to me, that from a physical point of view, life is fundamentally an agitation, a disturbance.  Many nonorganic physical systems tend towards equilibrium; sugar dissolving in water is such a system.  Eventually, the rate of dissolving equals the rate of absorption.  But life resists any attempt towards equilibrium, because such a state would reduce life to water and a pile of chemical ashes.  The way life avoids such a catastrophe is to introduce order(water and food), which agitate and disturb the system, triggering a whole series of responses.  Life must resist equilibrium in what is a noble, but losing battle.  At some point, the oxygen, which helped put the living system in order, reverses its role and contributes to life’s dissolution.  The physical approach has implications in other areas such as philosophy and religion.  Heraclitus recognized the importance of dynamic change, but didn’t have the knowledge or scientific precision to prove some of his philosophical postulates.  Religious thinkers and monks that aim to bring life’s passions under control, and often employ the most stringent diets to achieve their aims, still must drink some water and eat some food to avoid death.  As soon as they do so, the same reactions are triggered in their bodies as would be by a gourmand’s enjoyment of a sumptuous meal.  Fundamentally, there is no difference;  life is a dynamic system that feeds on order.

Life is an extremely complex system as recent science has shown through the magical structure of the double helix and the ever intriguing mysteries of cell division, which may hold the secrets to many disorders.  Can life be reduced to a series of mathematical equations?  D’Arcy Thompson asserts that what is essential to a living system is that it resists all attempts to mathematical reduction.  There is also J.T.Fraser’s notion of the biological clock, which has neither been proved nor disproved, and Henri Bergson’s “experiencing” of life, recreated in the impressionistic novels of Marcel Proust.  Is there such a thing as time’s arrow?  Western civilization affirms it, Hindu civilization denies it.  An example of the dynamic conflicts implicit in human life forms?  And so the questions continue as I enter the final phase of my life, trying to make sense of what has gone before….  Early morning thoughts about life.

My 100th Post: Just for Fun

Today I celebrate my 100th post!  I am so grateful to the visitors that have come from 62 different countries for their support and interest in my posts.  Health willing, I plan to offer more posts in the future.

I thought I would offer a glimpse into some items that have meant a lot to me over the years.  I hope you appreciate them.

Dorothy riding the Cowardly Lion, and the Wizard of Oz riding the Hungry Tiger

Dorothy riding the Cowardly Lion, and the Wizard of Oz riding the Hungry Tiger. Part of The Wonderful Wizard of Oz map by Dick Martin

  The Tin Woodman rowing the Scarecrow on the Blue Moon.
The Tin Woodman rowing the Scarecrow on the Blue Moon.

Russian nesting doll

Russian nesting doll

My totem pole, which Grandma brought me from her trip to Alaska in the early 1960s.

My totem pole, which Grandma brought me from her trip to Alaska in the early 1960s.

My silver unicorn to fight for me in times of danger.

My silver unicorn to fight for me in times of danger.

This lion bank(which is empty) was given to me by Grandma for my junior high performance as Androcles in George Bernard Shaw's Androcles and the Lion.

This lion bank(which is empty) was given to me by Grandma for my junior high performance as Androcles in George Bernard Shaw’s Androcles and the Lion.

A Kein Bottle, which was given to me by Dad.  A Mobius strip is a two-dimensional surface with one edge.  Technically, a Klein Bottle is a three-dimensional surface with one edge.(It is impossible to realize in practice.)

A Kein Bottle, which was given to me by Dad. A Mobius Strip is a two-dimensional surface with one edge.  Felix Klein tried to imagine what would happen if you sewed two Mobius Strips together to create a bottle with one side and no edge.  Since its outside is its inside, it has no volume!  But it requires four dimensions for the surface to pass through itself without a hole.

Thanks again for your ideas and support.  Hope to see you soon!

Mathematics Pays Court To Literature

Sarah Seff Rolfe was my poetry mentor.  I recall spending many evenings listening to her helpful criticisms.  She had a musical voice, which I still hear when I read her poetry.  Her book of poems, Heart and Mouth are One, was published by Terebinth Press in 1983 just before her death in 1984.  She never read the following poem of mine, but I’d like to think she would have enjoyed it.

Mathematics Pays Court to Literature

Literature appeared, leaving a castle of words, trailing silver metaphors.

Moonlight touched her face, luring her into a poetic garden.

She paused to think, then rested beside a river of flowing ideas.

Suddenly, a steady footstep echoed through the flowering shrubs.

Fearful, lest the person see her beauty rare, she enveloped herself in a cloak of ambiguities.

The sound grew nearer.  It was Mathematics-tall, slender, and with an exactness that made her tremble, he spoke:

“Oh, Mistress of Language, why must you hide your elegant beauty?  I beseech you to glance at me.”

Literature coyly smiled, and seemed to laugh beneath the protective cloak.

“I have many suitors.  I am courted by Linguistics.  What can you offer me?”

“I have manifolds, singular points, vector fields of thriving grain, coordinate rings of ruby and diamond.  All these I offer thee.”

Mathematics kissed her cheek.  Literature blushed and turned away.

“You are too bold , Sir.”

“It is my way to come to a swift conclusion.”

Then the two embraced in a shadowy corner of infinite space.

And the galaxies winked to see the pair linked

as they rode a nebula of possibilities…