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<div style="background:#fff;border:#bbb dashed 1px;padding:5px"><a href="http://en.citatepedia.ro/comments.php?id=477531" style="color:#000;text-decoration:none"><div style="margin:10px 0"><strong>Voyage around the Square Root of Minus One</strong></div><div style="margin:10px 0">I often heard <br>that while the sciences concern themselves<br>with objective truths<br>the arts deal with subjective phenomena. </div><div style="margin:10px 0">Many years ago I held the same view, <br>but later came to the conclusion<br>that this is just a well-combed popular myth.</div><div style="margin:10px 0">It is an untenable credo<br>because the sharp separation<br>of the arts and sciences is a rigid <br>and arbitrary mandate, full of holes.</div><div style="margin:10px 0">Although all subjects have their specificities, <br>at the same time they also share <br>many common traits with each other.</div><div style="margin:10px 0">There is art in science and science in art.</div><div style="margin:10px 0">Artists, for example, <br>apply geometry to represent<br>a three dimensional scene in a painting, <br>which is a two dimensional surface.</div><div style="margin:10px 0">By using ‘objective' geometrical perspective, <br>Renaissance artists, among them Alberti, <br>Brunelleschi, Uccello, Leonardo and Dürer, <br>developed in Europe the ‘subjective' illusion <br>of perceptual realism.</div><div style="margin:10px 0">Later, in the Dutch Republic of the 17th century, <br>Johannes Vermeer applied expensive pigments<br>to the canvas and conducted <br>pioneering research in optics that enhanced<br>the supreme quality of his work, <br>imbuing his paintings with sublime, <br>otherworldly light.</div><div style="margin:10px 0">In the 19th century<br>the Romantic painter John Constable<br>prepared detailed studies<br>of the landscape and weather conditions<br>of England, before transcribing them<br>into images of stunning accuracy and grace.</div><div style="margin:10px 0">Following the closing of the Weimar Bauhaus<br>by the Nazis in 1933, the artist Josef Albers<br>moved to the USA, where he worked at<br>Black Mountain College and at Yale University. </div><div style="margin:10px 0">Albers is credited with the discovery of<br>the gravitational laws of color interaction, <br>which he expressed in his minimalist paintings <br>of "Homage to the Square".</div><div style="margin:10px 0">Yet painters are not the only artists<br>who use science in their work.<br>Writers and poets often incorporate<br>scientific themes into their novels and verse, <br>making more than once<br>important contributions <br>to the development of science.</div><div style="margin:10px 0">A giant of German literature, <br>the poet, novelist and artist<br>Johann Wolfgang von Goethe was also<br>a pioneer of scientific phenomenology.<br>His myriad accomplishments encompassed<br>explorations in the metamorphosis of plants<br>and insects. Besides, his research interests<br>extended to geology and meteorology.</div><div style="margin:10px 0">Moreover, in 1810 Goethe published<br>his "Theory of Colors", an influential opus<br>that inspired the painter J.M.W. Turner, <br>the philosopher Ludwig Wittgenstein, <br>as well as many others. <br>In many ways Goethe's color theory <br>remains valid even in the 21st century.</div><div style="margin:10px 0">Shakespeare's work, too, may serve <br>to illustrate the links between art and science.<br>His plays are sprinkled with profound insights<br>regarding the psychodynamic processes<br>of the human mind and soul.<br>In the role of an early neuroscientist, <br>the bard can teach modern day physicians<br>a great deal about the mind-body connection, <br>about physical symptoms originating <br>in emotional disturbances.</div><div style="margin:10px 0">Or take William Wordsworth.<br>This great Romantic English poet wrote <br>about nature and nurture, <br>"The child is father of the Man", he said, <br>a century before Freud formulated <br>his psychoanalytic theories.</div><div style="margin:10px 0">And then, in a long prose poem, <br>titled "Eureka" and published in New York<br>in 1848, Edgar Allan Poe's gave expression <br>to his intuitive vision of the universe.<br>His work anticipated <br>cosmological discoveries <br>of the twentieth century. </div><div style="margin:10px 0">Packed with bold conjectures, <br>the poet describes in "Eureka"<br>the concept that astronomers today call<br>Cosmological Black Hole. <br>Poe envisions here a pulsating universe, <br>evolving in an endless series<br>of Big Bangs and Big Crunches.</div><div style="margin:10px 0">Now, let's bear in mind that<br>while science promises to provide us <br>thoroughly objective research products, <br>in the end it fails to deliver them.</div><div style="margin:10px 0">Consider, for instance, the Queen of Sciences, <br>our most exact subject: Mathematics. <br>This powerful and noble discipline serves<br>as an indispensible tool for every branch <br>of science, as well as for common errands<br>that we carry out in all walks of life.</div><div style="margin:10px 0">However, the astonishing success <br>of mathematics remains a baffling enigma. <br>For, how we can accomplish so much with it, <br>despite its inherent inconsistencies<br>and its uncertain relation to nature, <br>defies rational explanation.<br>Mathematical equations are embedded <br>with mysterious forces <br>and their uncanny power transcends <br>the cognitive faculties of the human mind. </div><div style="margin:10px 0">A case in point concerns<br>a highly effective but bizarre <br>mathematical concept, the imaginary number <br>of the square root of minus one, <br>marked with the humble symbol, "i".</div><div style="margin:10px 0">This number is a precise mathematical idea, <br>and at the same time a poetic celebration <br>of absurdity, because it hails from<br>a genderless state of an outlandish kingdom.<br>"i" is neither positive nor negative. <br>It exists in spite of itself, <br>percolating through the faulty filters <br>of remote stars of another galaxy. </div><div style="margin:10px 0">And then there is the bizarre case of zero.<br>A central pillar of arithmetic, the naught<br>is a stringent figment of the imagination, <br>a number used as a symbol <br>of both nothing and infinity, <br>by which you can multiply, <br>however, never allowed to divide.</div><div style="margin:10px 0">Now, a careful examination<br>of the pivotal hard core sciences<br>of physics and chemistry reveals<br>that their cardinal notions, such as: <br>space, time and matter, numbers, <br>molecules, atoms and particles, <br>with their quantum probabilities, <br>are actually elusive figures of speech, <br>sophisticated abstract metaphors.</div><div style="margin:10px 0">Consequently, physicists and chemists <br>don't really understand their subject matter, <br>although many of them pretend<br>that they do.</div><div style="margin:10px 0">Mind you, <br>the sciences are not superior<br>to music, poetry or painting.<br>Their epistemological status is equal.</div><div style="margin:10px 0">For, the creative genius of Archimedes <br>does not surpass that of Homer; <br>nor do the swings of Galileo's pendulum <br>controvert the rhythm of iambic pentameters<br>on Dante's keyboard. </div><div style="margin:10px 0">Similarly, the shining jewels of<br>Euler's magnificent mathematical equations<br>are not more brilliant, or more meaningful<br>than the triumphant melodies<br>of Vivaldi's masterpiece, "The Four Seasons".</div><div style="margin:10px 0">Nor does the aesthetic splendor<br>of Cantor's transfinite sets<br>eclipse the majestic beauty<br>of Mozart's symphonies.</div><div style="margin:10px 0">The earth revolves around the sun<br>surrounded by inexhaustible mysteries. <br>Still, Newton's infinite abstract space<br>is no closer to reality<br>than the adjacent concrete sky of Rembrandt.</div><div style="margin:10px 0">And thus, in the final analysis, <br>Einstein's glorious Theory of Relativity <br>does not reveal more ultimate truths<br>about the transcendental cosmos<br>than the paintings of Picasso's universe.</div><div style="margin:10px 0"><br /></a><br />poem by <a href="http://en.citatepedia.ro/by.php?a=Paul+Hartal">Paul Hartal</a><div class=q> <img src="https://www.citatepedia.ro/g/32share.png" style="float:left" alt="Share"> <script type="text/javascript" src="//s7.addthis.com/js/300/addthis_widget.js#pubid=citatepedia" async="async"></script><div style="display:inline-block" class="addthis_sharing_toolbox" data-url="http://en.citatepedia.ro/comments.php?id=477531" data-title="Voyage around the Square Root of Minus One de Paul Hartal" data-description="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 ..."></div> </div> </div>
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