White Water Relaxation
Just north of where I live is a small village called Wakefield. Although Wakefield is largely occupied by artists, it also has a system which solves very large sets of highly complex and linked partial differential equations in real time.The problems it solves are ones of fluid mechanics, including highly turbulent flow. Whenever I’m visiting Wakefield I always try to find time to go to stand and watch it at work, marvelling at its sophistication, simplicity, accuracy and method of displaying its results.
Equations associated with turbulent flow are known to be computationally intensive and readers who have grown up since digital computers started to dominate the desktop might be puzzled at having so powerful a machine in so remote a community. The answer is, of course, that it’s not a digital computer. It’s an analogue computer. And it’s not the type of analogue computer we all used to use (here for example, is a desktop—I don’t remember many laptops).
It’s a river. I stand on the bridge and watch the water flowing down over the rocks marvelling at how the water knows ahead of time that a rock is coming and moves to one side to avoid it. The world may be all that is the case but all that is the case is all that can be expressed as differential equations. If the world is the totality of the equations then my river is solving those equations in real-time and displaying the answer to me in a graphical form.
So two of our most difficult mathematical problems are being solved by an inanimate river with no program other than the initialisation of the equations. I was reminded of the graphical display of complex functions, something with which the river seems to have no problem, the other day when reading Don and Walker’s paper Time-Frequency Analysis of Music. This paper compares the spectrograms of the last 60 seconds of the Firebird Suite with the song Buenos Aires, a warbler’s “song” and a piece of fractal music. For each of these, it is necessary to display the essentially three-dimensional spectrogram (time, frequency, intensity) on a two-dimensional page—with limited success.
So, my river acting as an analogue computer, of which more in a later blog, correctly solves the complex set of differential equations which represent its part of the universe and elegantly and accurately displays the results.