It’s no coincidence that our Universe is naturally full of symmetry. The mirror symmetry of a stately home reflects the external form of many creatures, from butterflies to humans. At a deeper level, the very laws of the Universe are a consequence of its symmetries. An easy-to-state but profound example in the groundbreaking work of the German mathematician Emmy Noether is that the conservation laws that are ubiquitous in physics are in fact manifestations of the symmetries of the Universe. Energy is conserved, for instance, because the laws of physics are the same now as they were a millennium ago; momentum is conserved because they are the same here as they are on Pluto. Symmetry thus has the unusual distinction that it is fundamental both to the way the world works and to the extent to which we are capable of understanding it. [...]
If, by contrast, we want to represent or store new information, it follows that we need to find ways to break the symmetry in order to encode our data. If successive palings in the picket fence differed in some way – say, if each were painted either white or blue at random – then the symmetry (and your ability to draw the whole fence) would be lost. Replace white palings with zeroes and blue palings with ones, and we have a binary representation of a number, the basis of digital data storage and manipulation. [...]
Like materials design, the act of telling stories is about breaking patterns. In fairy tales, we’re likely to come across three bears, three pigs or three sons; in modern times, an enduring joke-pattern involves three protagonists (think ‘an Englishman, an Irishman and a Scotsman walk into a bar’) while comedians, improvisers and scriptwriters speak of the ‘rule of three’. Why this obsession with the number three? The answer is simple: the first time, something happens; the second time, something similar happens, establishing a pattern; but the third time, something different happens, breaking the pattern. The first two of the king’s sons come to a sticky end, while the third slays the dragon, marries the princess, and lives happily ever after. There is nothing magical about the number three, but since a pattern has to have at least two elements, a series of three is the most efficient way of establishing a kind of symmetry in order to disrupt it.
No comments:
Post a Comment