Treasure Island

Paul Hartal


Voyage around the Square Root of Minus One


I often heard
that while the sciences concern themselves
with objective truths
the arts deal with subjective phenomena.

Many years ago I held the same view,
but later came to the conclusion
that this is just a well-combed popular myth.

It is an untenable credo
because the sharp separation
of the arts and sciences is a rigid
and arbitrary mandate, full of holes.

Although all subjects have their specificities,
at the same time they also share
many common traits with each other.

There is art in science and science in art.

Artists, for example,
apply geometry to represent
a three dimensional scene in a painting,
which is a two dimensional surface.

By using ‘objective' geometrical perspective,
Renaissance artists, among them Alberti,
Brunelleschi, Uccello, Leonardo and Dürer,
developed in Europe the ‘subjective' illusion
of perceptual realism.

Later, in the Dutch Republic of the 17th century,
Johannes Vermeer applied expensive pigments
to the canvas and conducted
pioneering research in optics that enhanced
the supreme quality of his work,
imbuing his paintings with sublime,
otherworldly light.

In the 19th century
the Romantic painter John Constable
prepared detailed studies
of the landscape and weather conditions
of England, before transcribing them
into images of stunning accuracy and grace.

Following the closing of the Weimar Bauhaus
by the Nazis in 1933, the artist Josef Albers
moved to the USA, where he worked at
Black Mountain College and at Yale University.

Albers is credited with the discovery of
the gravitational laws of color interaction,
which he expressed in his minimalist paintings
of "Homage to the Square".

Yet painters are not the only artists
who use science in their work.
Writers and poets often incorporate
scientific themes into their novels and verse,
making more than once
important contributions
to the development of science.

A giant of German literature,
the poet, novelist and artist
Johann Wolfgang von Goethe was also
a pioneer of scientific phenomenology.
His myriad accomplishments encompassed
explorations in the metamorphosis of plants
and insects. Besides, his research interests
extended to geology and meteorology.

Moreover, in 1810 Goethe published
his "Theory of Colors", an influential opus
that inspired the painter J.M.W. Turner,
the philosopher Ludwig Wittgenstein,
as well as many others.
In many ways Goethe's color theory
remains valid even in the 21st century.

Shakespeare's work, too, may serve
to illustrate the links between art and science.
His plays are sprinkled with profound insights
regarding the psychodynamic processes
of the human mind and soul.
In the role of an early neuroscientist,
the bard can teach modern day physicians
a great deal about the mind-body connection,
about physical symptoms originating
in emotional disturbances.

Or take William Wordsworth.
This great Romantic English poet wrote
about nature and nurture,
"The child is father of the Man", he said,
a century before Freud formulated
his psychoanalytic theories.

And then, in a long prose poem,
titled "Eureka" and published in New York
in 1848, Edgar Allan Poe's gave expression
to his intuitive vision of the universe.
His work anticipated
cosmological discoveries
of the twentieth century.

Packed with bold conjectures,
the poet describes in "Eureka"
the concept that astronomers today call
Cosmological Black Hole.
Poe envisions here a pulsating universe,
evolving in an endless series
of Big Bangs and Big Crunches.

Now, let's bear in mind that
while science promises to provide us
thoroughly objective research products,
in the end it fails to deliver them.

Consider, for instance, the Queen of Sciences,
our most exact subject: Mathematics.
This powerful and noble discipline serves
as an indispensible tool for every branch
of science, as well as for common errands
that we carry out in all walks of life.

However, the astonishing success
of mathematics remains a baffling enigma.
For, how we can accomplish so much with it,
despite its inherent inconsistencies
and its uncertain relation to nature,
defies rational explanation.
Mathematical equations are embedded
with mysterious forces
and their uncanny power transcends
the cognitive faculties of the human mind.

A case in point concerns
a highly effective but bizarre
mathematical concept, the imaginary number
of the square root of minus one,
marked with the humble symbol, "i".

This number is a precise mathematical idea,
and at the same time a poetic celebration
of absurdity, because it hails from
a genderless state of an outlandish kingdom.
"i" is neither positive nor negative.
It exists in spite of itself,
percolating through the faulty filters
of remote stars of another galaxy.

And then there is the bizarre case of zero.
A central pillar of arithmetic, the naught
is a stringent figment of the imagination,
a number used as a symbol
of both nothing and infinity,
by which you can multiply,
however, never allowed to divide.

Now, a careful examination
of the pivotal hard core sciences
of physics and chemistry reveals
that their cardinal notions, such as:
space, time and matter, numbers,
molecules, atoms and particles,
with their quantum probabilities,
are actually elusive figures of speech,
sophisticated abstract metaphors.

Consequently, physicists and chemists
don't really understand their subject matter,
although many of them pretend
that they do.

Mind you,
the sciences are not superior
to music, poetry or painting.
Their epistemological status is equal.

For, the creative genius of Archimedes
does not surpass that of Homer;
nor do the swings of Galileo's pendulum
controvert the rhythm of iambic pentameters
on Dante's keyboard.

Similarly, the shining jewels of
Euler's magnificent mathematical equations
are not more brilliant, or more meaningful
than the triumphant melodies
of Vivaldi's masterpiece, "The Four Seasons".

Nor does the aesthetic splendor
of Cantor's transfinite sets
eclipse the majestic beauty
of Mozart's symphonies.

The earth revolves around the sun
surrounded by inexhaustible mysteries.
Still, Newton's infinite abstract space
is no closer to reality
than the adjacent concrete sky of Rembrandt.

And thus, in the final analysis,
Einstein's glorious Theory of Relativity
does not reveal more ultimate truths
about the transcendental cosmos
than the paintings of Picasso's universe.

Submitted: Monday, June 18, 2012

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