There are two things I would definitely highlight. The first is very general, but I think extremely important. The second is more specific and its great importance lies more within science than outside.
Greatest invention: ‘experiment and theory interplay in gaining knowledge.’ This is the so-called scientific method, where mathematical models made in an abstract way are then tested in nature. Surprisingly, it took until the renaissance before this method of obtaining knowledge got firmly established. The idea escaped even the ancient Greeks and the ancient Eastern cultures.
Subsequently it has lead to a series of major discoveries and technological developments, which transformed, through the industrial revolution, first the Western world and then the whole world beyond any recognition. The scientific method also seems to have intimate links with liberal democratic traditions in the society that have kept one part of the world (relatively) stable and prosperous for an exceedingly and unusually long amount of time. If the Earth was to disappear in a gigantic cataclysm and we were allowed to preserve only one message from our culture in order to aid posterity, I think it should be: ‘Thou shalt test thy beliefs against experiments and discard those that do not match experimental evidence.’
2. Greatest discovery in physics: S=k logW. This formula, which represents the epitaph for Boltzmann’s grave in the central cemetery in Vienna, provides the link between our microscopic and macroscopic understandings of the world. ‘S’ is the entropy of a system and it signifies how disordered the system is. This is a macroscopic property and it can be related to other macroscopic properties such as pressure, temperature, volume and energy. ‘W’ is the number of possible microscopic states that the system can find itself in and k is Boltzmann’s constant.
For example, when we are talking about a gas of atoms, their velocities and positions would constitute their microscopic state. It is Boltzmann’s formula that shows us that it is, at least in principle, possible to reduce all or knowledge so far to some basic microscopic physical laws, an attitude and philosophy that is frequently labelled as ‘reductionistic’. The same formula was also instrumental in the discoveries of both quantum mechanics and information theory, and it is it is at the crossroads of the two that my research work lies. S=klogW has all the hallmarks of a great physical law: it is aesthetically beautiful, conceptually profound and surprisingly simple.
Professor Vlatko Vedral is Centenary Professor of quantum information and head of the Quantum Information Science Group at Leeds University.