When J.S. Bach was challenged by King Frederick to compose on a subject of the King’s devising, he rose to the occasion with a spectacular Offering, applying his inventiveness in 2 fugues, 10 canons, and a four-movement sonata for flute and violin.
One of the pieces he offered is a single line of music (beginning with a variation on the King’s theme) that is to be played both forward and backward simultaneously, engineered so cleverly that it harmonizes with itself along the way and both begins and ends convincingly.
As we marvel at the mathematical/musical mind that could have created such an invention, consider a virus, whose complete DNA is a perfect palindrome, so that it can be read either forward or backward. “Reading” DNA means translating each triplet of letters (A,T,G,C) into an amino acid and linking them together to make a big, complicated protein molecule that does a particular job. In this virus, the three-letter codes are reversed, and their order is reversed , and the protein is the same, and the protein is not only functional, but adaptive and competitive enough to create a niche for the virus. Article in Quanta Magazine