Intro

Engineering and Beauty
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This issue is dedicated to the intersection of arts and STEM — science, technology, engineering and mathematics. Or, as some further usefully call it, STEAM, which adds the arts. Is there an intrinsic beauty in STEM? And how can art enrich it?

The concept of truth is invariably and intrinsically connected to art and beauty. “Beauty is truth, truth beauty, — that is all / Ye know on earth, and all ye need to know” is the message celebrated in “Ode on a Grecian Urn,” by the Romantic poet John Keats. It connects the right- and left-brain processes, logic and creativity. Truth is, of course, intrinsically connected to STEM. There is a moment in all science and engineering endeavors, whether basic or applied research, when you know you have found the truth, the answer you are seeking. It is an exhilarating moment, because the result you have discovered is as elegant, as minimal, as rare and as complete as it can be — but no more than that. Indeed, Einstein has said: “Make it as simple as possible, but not simpler than that.” In a similar way, beauty shares the same properties: elegance, minimalism, rarity, completeness. And so do science, mathematics and engineering.

In the past, the beauty of mathematics was mostly reflected in geometry, where true elegance required the geometer to use only a ruler and a compass: the Pythagorean theorem, the elegant properties of triangles and its elements, the purity of circles (limit of a polygon of infinitely many sides), the concept of parallel lines never intersecting. This was the world of symmetries, order and classical beauty, the world of Newton.

With the advent of computers and computational power, the beauty of mathematics has been transformed into the beauty of algorithms, which still follow the same principles: elegance, minimalism, rarity and completeness. I can’t resist mentioning fractal geometry, the towering figure of Benoit Mandelbrot, and even a number of books on “The Beauty of Fractals.” And I will definitely mention the Viterbi algorithm, whose 50th anniversary we celebrate this year! More significant, this has brought to the fore the new geometric elements of self-similarity and of multiple scales (and of nested hierarchies), impossible to capture before the exponential increase in computational power. These allow us to describe and visualize disorder, chaos, phase transitions and turbulence (and, in the Viterbi case, a way to remove signal noise) — a bit more real world, but within the same beautiful concepts of elegance, minimalism, rarity and completeness.

The connection of art with innovation is, of course, essential. Indeed, innovation happens at the intersections of feasibility (technical), viability (economic) and desirability (art). Art ensures that the innovative technology has the elements we quoted — elegance, minimalism, rarity and completeness — and that it is true in the above sense and in the particular time and space. That function and form intertwine, commingle and converge. Technology and engineering have allowed us to seek this harmony not only in the physical world, but also in the virtual one.

Visualization, computer vision, and virtual, augmented and mixed reality now present amazing opportunities for the creation of technologies that will use the commingling of art and computer science to trigger emotional, learning and behavioral responses that will help advance various forms of self-actualization and other stages in Maslow’s hierarchy of needs. And, hopefully, to help us advance our humanity. In fact, Advancing Virtual Reality is one of the 14 Grand Challenges of the National Academy of Engineering.

Whether it is the establishment of a theorem, the discovery of a new phenomenon, the solution to a puzzle or the development of an innovative technology — often expressed with the powerful and beautiful elegance of a2+b2= c2 or of E=mc2 — the moment of discovery is a moment of exhilaration because it is the moment we reach the associated truth.