John W. Pinkerton

Mathematics is an area of interest for me.  It’s not that I have any skills in this field; it’s just something that I’ve always respected.  I got through algebra and plane geometry and trigonometry in high school.  “I got through them” means I ended up with a passing grade, not that I understood them.  I took a couple of algebra courses in college still not understanding.  I even worked as a paper grader for one of the college math teachers still not understanding.  My interest in mathematics can be compared to a dog baying at the moon having no concept of what it is or why he’s baying at it. 

One of the best teachers I had in school was my eighth grade math teacher.  He was new to the school and suspected that we were lacking in basics.  He drilled us daily on the multiplication tables.  We recited them aloud in unison: 2x2 is four, 2x3 is six, etc.  If you’ve gone through that, you’ll never forget.  By the time he was finished with us that year, we could add, subtract, multiply, and divide which, by the way, is enough for most of us.

In high school I learned to derive square roots, something I understood.  I also learned and understood and have used since then simple equations like 2 is to 12 as x is to 30.  I’ve actually used this in my art.

A few years ago I looked over a practice state math test which students must pass in order to graduate from high school.  Holy crap, I only noted about 50% of which I felt that I could probably successfully arrive at the answers.

Why we insist that all high school students take four years of math--Algebra I, Algebra II, Trigonometry, Geometry, and Calculus--is beyond my comprehension.  Who are we?  The Japanese?  There is, to say the least, a lot of nonsense in education.  Some students are not capable; the vast majority simply have little need for the higher math courses.  Yet we act as though we’ll lose our place, wherever that is, in the world if we don’t hammer everyone with mathematics.  A more sensible course of action would be to make certain that all students can add, subtract, multiply, divide, derive square roots (perhaps), and be capable of doing universally useful algebraic problems.  For those who intend to major in mathematics, the sciences, or technical occupations should volunteer  to take the higher math courses.

One of the best books on mathematics is The Education of T. C. Mitts written by Lillian R. Lieber and illustrated by her husband Hugh.  It was first copyrighted in 1942.  I came into possession of a really rough looking copy which was discarded by a library.  I recently checked Amazon and they only have a couple of used copies.  I did find a company in India which produces the book at the present time.  The hero of the volume, T. C. Mitts, is actually an acronym for “the common man in the street.” The purpose of the book is to emphasize that mathematics can be understood by anyone.  Well, I’m anyone, and I’m pretty common.  It not only explains math but relates it to many subjects: democracy, freedom and license, pride and prejudice, success, isolationism, preparedness, tradition,  progress,  idealism, common sense, human nature, war, self-reliance, humility, tolerance, provincialism, anarchy, loyalty, abstract art, etc.  In summary, the book is a delight.

Although I seem to have an innate fondness for math, I was an absolutely dismal math student.  I suspect my problem was that it was seldom related to real world problems.  It was pretty much presented in an abstract fashion.  If I had had a greater grasp of math, I suspect that I would be an architect today instead of an old retired English teacher writing essays.  When I find someone who truly understands mathematics, I am in awe of them.  I have a nephew who seems to have this ability, and it serves him well.  I’ve had several friends who are or were math teachers.  I’ve thought well of them in spite of their obvious superiority. 

I suspect people who are capable of interpreting the world in mathematical terms see the world differently from me.  A good example of this occurred when I met a fellow in front of Buckingham Palace who happened to be a triple doctorate at Oxford.  He asked if there was anything in London I really wanted to see: yes, I did: the Tate Gallery.  He accompanied me via one of those red double-decker buses to the Tate Gallery to view the art.  As we strolled past a shiny metal spiraling sculpture, my new friend abruptly stopped and muttered under his breath, “Pi.”  What for me was a spirally metal thing, represented Pi to him.  I have to confess that math is everywhere, even in art.

Speaking of math and art, have you ever heard of the golden ratio?  The golden ratio is the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

                                                                      a+b      a    

                                                                      -------  =  ----  =   Phi       

                                                                        a        b  


In Texan: it occurs when the little part is in the same ratio to the big part as the big part is to the big and little parts together. 

                                                            Big Part                   Little Part


                                                                   Big Part + Little Part

It’s a mysterious math formula that goes by many names: golden section, golden mean extreme, mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, and mean of Phidias (From Phidias we have derived the Greek letter Phi which represents the golden ratio--probably more than you wanted to know.).  I think I’ll stick with the golden ratio.  It has captured the imagination of artists, architects, scientists, mystics, and even me since the Renaissance.  When I use the golden ratio in my paintings, there is a natural settling of the proportions.  It does not jar.  Hell, I can’t explain it, but it works.

Although I began this essay by saying that I respected mathematics, I should have said that I have a crush on mathematics; I’m afraid it’s an unrequited emotion, but if I had a chance to go back in time, I think I would try much harder to learn all I could about mathematics so that it might love me back.


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