On Beauty
Beauty in physics and mathematics is something that is talked about very often, but rarely ever explained. This is for good reason as people who talk about it have a good eye for it, but have a hard time describing it. People look for beauty in their equations and logic, often letting it lead the way in their research, thinking that if their equations are beautiful, they must be correct.
We call a myriad of different things beautiful. We humans usually find things, like faces, which are symmetric extremely beautiful (with the obvious exception of things like symmetric cockroaches and the like) and appreciate patterns, just think of music, dance, art ,and theatre. These criteria for beauty are also reflected in physics, however, as you surely have guessed, beauty in physics is much more objective than it is anywhere else. Equations that are symmetric hint at deep conservation laws (if this excites you, google Noether’s Theorem), and seeing patterns in physical phenomena lies at the heart of science. As beautiful as symmetry and patterns are, these are generally not what people mean when they talk about beauty in physics, what they usually mean is more akin to simplicity and elegance. Now before you misunderstand, by simplicity I do not mean simple maths, Einstein’s General Theory of Relativity is an extremely beautiful theory that, according to me, should be in an art museum, but it involves some fiendishly complicated maths. By simplicity what I mean is the least possible number of special cases(ideally zero) that it takes to explain everything in the theory.
We call a myriad of different things beautiful. We humans usually find things, like faces, which are symmetric extremely beautiful (with the obvious exception of things like symmetric cockroaches and the like) and appreciate patterns, just think of music, dance, art ,and theater. These criteria for beauty are also reflected in physics, however, as you surely have guessed, beauty in physics is much more objective than it is anywhere else. Equations that are symmetric hint at deep conservation laws (if this excites you, google Noether’s Theorem), and seeing patterns in physical phenomena lies at the heart of science. As beautiful as symmetry and patterns are, these are generally not what people mean when they talk about beauty in physics, what they usually mean is more akin to simplicity and elegance. Now before you misunderstand, by simplicity I do not mean simple maths, Einstein’s General Theory of Relativity is an extremely beautiful theory that, according to me, should be in an art museum, but it involves some fiendishly complicated maths. By simplicity what I mean is the least possible number of special cases(ideally zero) that it takes to explain everything in the theory.
Newton’s Law of Universal Gravitation is a deceptively simple equation, explaining away the motion of the planets around the Sun, the Sun around the Milky Way, and something as simple as an apple falling to the ground, all in one simple equation. For the longest time, people believed that this equation was all there was to be known about gravitation (mathematically speaking), due to its elegance and simplicity. It handled all different types of problems, requiring no special cases. That was until a peculiarity in the orbit of Mercury was observed, at which point people realised that the universal law of gravitation was not so universal after all. Special cases were born, and the equation was stripped of all its beauty and elegance. Einstein had to come and fix this; as a solution, he provided yet another ‘single’ equation which absorbed all the special cases and helped usher in a new era of modern physics.
Something akin to this sort of simplicity and elegance is also seen in programming. The best programs are those that are able to solve their targeted problems with the fewest possible (zero is what you should be aiming for) special cases. A single algorithm is much more elegant than seven algorithms separated by if-elseif statements tackling different parts of the same problem . This, however, describes very well the position that modern physics is in. We have two separate ‘algorithms’, them being Quantum Mechanics and General Relativity, that work beautifully in separate cases (blissfully ignoring the limitations of the standard model like one does) but mix like oil and water. There’s a big if-else statement in physics and theoretical physicists are giving it their all to remove it. A promising candidate is String Theory, which has already seduced many physicists despite its problems because of its simplicity, and how the equations of General Relativity pop out (excuse my language) like magic.
Something akin to this sort of simplicity and elegance is also seen in programming. The best programs are those that are able to solve their targeted problems with the fewest possible (zero is what you should be aiming for) special cases. A single algorithm is much more elegant than seven algorithms separated by if-elseif statements tackling different parts of the same problem . This, however, describes very well the position that modern physics is in. We have two separate ‘algorithms’, them being Quantum Mechanics and General Relativity, that work beautifully in separate cases (blissfully ignoring the limitations of the standard model like one does) but mix like oil and water. There’s a big if-else statement in physics and theoretical physicists are giving it their all to remove it. A promising candidate is String Theory, which has already seduced many physicists despite its problems because of its simplicity, and how the equations of General Relativity pop out (excuse my language) like magic.
Up till now, the progress in physics has been led by unification, combining concepts that seem totally distinct at first, and after closer inspection seem inseparable. Unification of the physics of falling apples and orbiting planets, electricity and magnetism are a few notable examples. Unification of theories is seen as another elegant aspect of nature, and a great achievement by man. There really is no good explanation for why this should be the case, why should nature be beautiful and elegant at all? Maybe it’s not and we’ve been fooled all this time. It’s certainly possible that the unification of General Relativity and Quantum Mechanics will result in a theory that’ll be considered by many to be ugly, but for no good reason, I think that that’s unlikely.
Hermann Weyl (a great mathematician and physicist whose work inspired string theory) once said, “If I have to choose between beauty and truth, I choose beauty.”
Many people enjoy physics, not due to its practical applications, but because of how satisfying, elegant ,and awe-inspiring it can be. If at the end of something the truth doesn’t turn out to be beautiful, would the journey really have been worth it?
Originally published at http://shortdotcircuit.wordpress.com on October 6, 2020.
