We Share Science

Video abstract for the article 'Hearing random matrices and random waves' by M V Berry and Pragya Shukla (M V Berry and Pragya Shukla 2013 New J. Phys. 15 013026). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/15/1/013026/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. Scientific papers written a century ago differ from modern ones in at least one immediately obvious way: the modern ones contain many more pictures. This is because it is now widely understood that illustrations can enable scientific and mathematical concepts to be quickly assimilated, and also because modern software enables images to be produced easily and effectively. By contrast, exploitation of our perception of sound has been almost nonexistent. Here we present a step in this direction, by rendering as sounds two classes of mathematical function that have been extensively studied in other ways. The sounds are included as mp3 files. Main results. The first class of functions comes from random-matrix theory. This generates series of numbers (eigenvalues) with many applications (e.g. models for energy levels of quantum systems that are classically chaotic). The numbers are the zeros of the functions, distributed quasi-randomly, with fluctuations that depend on underlying symmetries (time-reversal, etc). When rendered acoustically as phase modulations of a carrier wave, the different fluctuations can be heard. The second class of functions represents random waves (e.g. laser speckle) in one, two or three dimensions; again differences can be heard when these are rendered as sounds. Wider implications. The sounds are strange (we hesitate to call them music). We are not sure if they can aid our understanding of conceptually subtle ideas, or whether they are mere curiosities. We offer them to stimulate further exploration, of different classes of function and with other renderings, perhaps involving harmony and rhythm.