Mind: the Fourth Circle

Mind, the fourth circle of practice, tries to answer these questions:

  1. What am I interested in, or curious about?  What holds my attention?
  2. What is good, or true?  How can I increase my knowledge and understanding of the world?
  3. How can I appreciate or create what is beautiful?

Once we begin to find our answers to the questions of the spiritual domain, we naturally begin to raise these questions of the mind.  We want to spend our time, and find purpose and meaning in, those things that interest us, that pique our curiosity, and that fully engage our attention.

We want to pursue those things we perceive to be good, and believe those things we know to be true.  It brings pleasure to the mind to grow in knowledge and understanding.  It also gives opportunity to apply that knowledge and understanding in the world around us, from which come reputation, compensation, and power.

Beauty arrests our attention, whether by symmetry, or rhythm, harmony, or melody; whether visually, aurally, tactilely, or fragrantly.  In some respects it is subjective; in others objective.  We know it when we experience it.  It fills us with awe, with longing, with desire.  To appreciate it is to grow, like a plant toward the sun.  To create it is to bear fruit that blesses the world, like an apple that falls ripe from the tree.

When we can answer these questions with clarity and confidence, then we have marked out an intellectual path before us as plain as the yellow brick road.  To read about and apply those ideas which fully engage us, to grow in knowledge and understanding, to appreciate and create beauty, is to walk the Elysian Fields crowned with laurel.

The Siren Song of Mathematics

Treat yourself to a book or two of Euclid.  You might discover an aesthetic you never knew existed, a beauty bare, austere, and elegant.

Forget about utility.  Forget about any fear you might have of math, or some childhood humiliation you may have experienced.  Expect a pleasant surprise.  Just enjoy the geometrical progression of your rule and compass across the page, as they make visual music out of a geometrical problem.

The book begins with definitions, common notions, and postulates.  These are the assumptions, the building blocks out of which everything else in the books of Euclid are made.

Take each proposition as a puzzle to solve, or a dilemma to resolve.  The thing I love about geometry is how the visual and rational aspects come together there before you on a sheet of paper.  Each construction seems to me to be a thing of beauty.

And I love Euclid’s proofs, his economy of expression, his rhythmic flow of thought, and his inexorable downhill run of reason.

I discovered Emily Dickenson while I was in college.  I loved the compressed language of her poems.  Math is like that.

At some point math captured me with its symbols and proofs.  The symbols were an innovation made to compress an oft repeated, complicated verbal expression into a single visual expression.  I can remember being drawn to “The World of Mathematics” by James Newman by the summation symbols that ran along its spine.  And I felt that when I’d come to the end of a proof that I’d finally understood the concept expressed in the proposition.

That power of a name Ursula Le Guin describes in her Earthsea trilogy realizes its full force in mathematics, e.g., e=mc2.  That formula precisely names the relationship that exists between energy and matter.

Math is a wonderful ocean, deep and wide, and brimming over with ideas.  Dive in.  Euclid is a great place to start.