January 4, 2018, by Philip Moriarty

## The Art of Physics — Guest Post by Noah Harwicke

*The following is a post from Noah Hardwicke that I really, really should have uploaded long before now. (Sorry, Noah). The Christmas and New Year holiday, combined with the traditional (at least for me) start-of-year illness, slowed me down. Noah highlights the key importance of creativity in physics, and describes how mathematics and physics can be exploited in art, and vice versa. *

*Over to you, Noah….*

The idea that creativity belongs to the arts and that its application in science is unnecessary and rare is unequivocally false. Any field would stagnate in the absence of creativity, a statement as true of physics, as it is of fine art, as it is of business. The collaborative nature of science creates an environment in which shared ideas cumulatively develop into progress, with creativity from different people folded through at every stage of the process, and where advancement relies on viewing a problem in a new way that is different to current thinking. Perhaps the pinnacle of creativity in physics is when two apparently separate entities are unified. I think the most incredible example of this to date is Einstein’s unification of space and time in his theory of Relativity. To realise that space and time are two manifestations of the same thing, where one man’s space is another man’s time, is a feat of spectacular creativity and confidence, as it questions what seem like such obvious and immutable properties of nature and elegantly describes gravity as the warps and curves of this unified spacetime.

An area of equivalent elegance is that of complex number theory, where an entire area of mathematics was built around a purely imaginary entity that cannot exist, has no physical meaning and is found nowhere in nature. Some of the consequences of complex numbers are truly astonishing and immediately challenge your ability to link the pure mathematics of a proof with an intuitive interpretation of what’s going on. Due to one of these such consequences, namely Euler’s identity, complex numbers present a convenient way of performing geometrical transformations in two dimensional space, which means complex number algebra can simplify the generation of fractals.

In a recent Computerphile video, a Christmas card that I designed based on this type of application of complex number analysis was featured…

The use of complex numbers in my Christmas card is almost entirely for geometrical transformations that could also be performed with matrices and vectors in real, two dimensional space. In other words, other than the sextic Mandelbrot set “star” atop the Christmas tree, these fractals are not related to Juila or Mandelbrot sets (the fractals usually associated with complex numbers), which are examples of escape time fractals. The card represents a rather literal interpretation of creativity in science. In science, elegance is found in reducing complexity to its basic elements, while beauty is found in the complex manifestations of the simplest laws. For me, fractals (specifically escape time fractals like the Mandelbrot set) are a wonderful example of this, where a few simple lines of code can create something infinitely detailed and visually beautiful.

The code is written in Mathematica, a language perfect for this sort of mathematical problem. In its original form, the code generated a unique scene each time it was run, within which each snowflake and each fern was unique, as is the case in nature. Subsequently I have rewritten it as a Wolfram Demonstration with customisability of the scene elements and the ability to export your creation for use elsewhere. The code employs maths as a tool to make something creative for creativity’s sake. Science, however, is a field in which creativity abounds because it is vital to the progression of ideas and theories.

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