Mathematics of Information

Our world has been shaped by the outcome of the scientific revolution and its offspring, the industrial revolution. The essence of this scientific revolution, shaped by its pioneers – Newton, Gallileo, Descartes, Kepler, Huygens, Boyle, Leibnitz – was in the rigorous understanding of the physical world, the laws underlying matter, energy and their interaction. The word “rigorous ” is a hint to the fundamental role of mathematics in this endeavour but, one way or the other, the process has been driven by physics. Ultimately, physics led to applied physics (also known as engineering) and to the industrial revolution. Humanity has been changed forever. We are living in interesting times, arguably at a juncture of an equal impor-tance and impact to the original scientific revolution. The world around us is changing and it is clear that the future will be as unrecognisable to us as our world – the Internet, mobile telephony, medical imaging, satellite navigation, so-cial networks, the entire panoply of personal computers, laptops, tablets, smart phones so ubiquitous in our daily life of work and leisure... – would have been incomprehensible to previous generations. In as much as physics is fundamental to these developments, from quantum to solid state physics to nanotechnology, the common denominator underlying them is not physics but information. We are surrounded by technology that collects, transmits, manipulates and ultimately needs to understand reams of information, of an order of magnitude which is hard to comprehend: in 2012, in every single minute the Internet processed 2 × 108 emails, 2 × 106 Google search queries, 7 × 105 Facebook postings and 48 hours of youtube uploads [18]. At the same minute CERN computers would have generated up to 600 gigabytes of data: ostensibly a theoretical physics centre, its main tool of trade is information. Even such emblematic ‘physics machines ’ like cars are increasingly crammed with information systems, while avionics dominate the cost of modern jet fighters. 1 Mathematics has historically been the language of physical reality and it