Consideration by Carlo Beenakker, Chair of the jury for the 2006 Lorentz Medal. Amsterdam, 27 November 2006. "It's an experience like no other experience I can describe, the best thing that can happen to a scientist, realizing that something that's happened in your mind exactly corresponds to something that happens in nature. It's startling every time it occurs. One is surprised that a construct of one's own mind can actually be realized in the honest-to-goodness world out there. A great shock, and a great, great joy." These are the words of professor Leo Kadanoff, whom we honor today with the Lorentz medal. They express the essence of theoretical physics, where deep intuition can reveal a law of nature that explains in a unified way many, apparently unrelated, observations. Kadanoff's research has revolutionized the way in which we describe phase transitions, such as the sudden appearance of a magnetic field in a piece of metal, or the transition from a gas to a liquid phase. Phase transitions are characterized by a critical point, at which the two phases are indistinguishable. Kadanoff discovered that the behavior of a material near a critical point is subject to laws which are universal, meaning independent of which transition one is investigating. The explanation for the universality lies in the concept of scale invariance, which relates quantities at very different length scales. It doesn't matter whether your are studying the magnetic field in a metal or the density in a gas --- close to the critical point the relationships with temperature or pressure become the same. This original idea of Leo Kadanoff has turned out be unusually fertile, bearing fruits far beyond the field of phase transitions, where it started. By applying the concepts of universality and scale invariance to phenomena in hydrodynamics (such as turbulence) and in granular media (such as avalanches), Kadanoff developed a systematic approach to the understanding of what we call "complex media". These are systems that develop the same intricate structures on a range of length scales or time scales. Scale invariance has also been applied by Kadanoff and his school to bring order into chaotic phenomena outside of physics proper, such as the fluctuations in the stock market, irregularities in the rithm of the heart, and the random appearance of traffic jams. The laws of scale invariance make it possible, as Kadanoff explains, "to distinguish between the things that are predictable and not predictable; in the ones that are predictable to try to pick out the universal features, and then to do something to characterize the unpredictable parts." Professor Kadanoff: by awarding you the Lorentz medal we honor one of the architects of the edifice of theoretical physics. You built a new floor and for a relatively short period were its only inhabitant. You described this period "as something that happens from time to time in the history of science. And then this new floor becomes occupied by the rest of science, by the rest of the world, but there's this wonderful period in which the new floor is yours alone." Hendrik Lorentz must have felt something similar when he discovered his theory of the electron. His "floor" is several levels below yours in the edifice of theoretical physics, but he too, was its only inhabitant for a brief period in time. The memory of Lorentz is special in this country, because he was the founding father of the Dutch school of theoretical physics. The two of you share this commitment to research and education. The field of soft condensed matter physics, which has many followers also in this country, has you as its founding father. We are proud to honor you as the 20th recipient of the Lorentz medal.