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Beauty is the quality of being especially appealing and pleasing. Though the word will likely invoke association with traditional art, in technology, engineering, mathematics and other science beauty is, despite its relative vagueness and subjectivity, an important aspect of design, and in fact this "mathematical" kind of beauty has lots of times some clearly defined shapes -- for example simplicity is mostly considered beautiful. Beauty is similar to and many times synonymous with elegance.
Beauty can perhaps be seen as a heuristic, a touch of intuition that guides the expert in exploration of previously unvisited abstract land, as we have come to learn that the greatest discoveries tend to be very beautiful and so the path of beauty often leads to valuable discoveries. Indeed, beginners and noobs are mostly concerned with memorizing hard facts, learning standards and getting familiar with already known ways of solving known problems, they're often unable to recognize what's beautiful and what's ugly. But as one gets more and more experienced and finds himself near the borders of current knowledge, there is suddenly no guidance but intuition, beauty, to suggest ways forward, and here one starts to develop the feel for beauty. At this point the field, even if highly exact and rigorous, has become an art.
One groundbreaking discovery after another have come to show that the complex behavior and patterns surrounding us in life emerge from a very simple set of rules, like fractals born from a simple recursive formula, all of electromagnetism and optics following from Maxwell's equations or complex planetary motion being derived from a simple law of gravitation, it's like when a myriad or great meandering rivers, when followed upstream, are found to join one another and eventually originate in a single small spring. This is why simplicity is perceived as beautiful: we have learned that things complex, difficult to understand in such state, are understood EXACTLY by being reduced to something simple, easy to comprehend, and when we do so, there comes satisfaction from understanding, and that we call beauty. It's fair to note that this "obsession with beauty", or maybe better said undue reliance on the heuristic of beauty, has its critics too, for example Sabine Hossenfelder criticizes the search of beauty in modern quantum physics, claiming it has led to fruitless stagnation, but this is a rather unique and very controversial case, in general it still holds that pursuit of beauty and simplicity is the rock solid, most universal approach of a scientist.
What is beautiful then? As stated, a lot of subjectivity is at play, but generally the following attributes are correlated with beauty:
if-then branches).Examples of beautiful things include:
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