As early as 1981, about 1 year before Shechtman’s discovery of an actual quasicrystal, Alan L. Mackay discussed, in a seminal paper, the first steps for the expansion of crystallography toward its modern phase. In this phase, new possibilities of structures and order, such as the structures of five-fold symmetry, for crystals have been discovered. Medieval Islamic decorators as well as Albrecht Dürer, Johannes Kepler, Roger Penrose, Mackay himself, and other pioneer crystallographers raised important contributions to the theoretical discovery of (...) crystalline possibilities long before or independently of the discovery of their actual existence. In this paper, I discuss further the philosophical significance of Mackay’s theoretical discovery and his contribution to the expansion of pure geometrical crystallography, biological crystallography, and generalized crystallography. (shrink)

From Mendeleev’s time on, the Periodic Table has been an attempt to exhaust all the chemical possibilities of the elements and their interactions, whether these elements are known as actual or are not known yet as such. These latter elements are called “eka-elements” and there are still some of them in the current state of the Table. There is no guarantee that they will be eventually discovered, synthesized, or isolated as actual. As long as the actual existence of eka-elements is (...) predicted, they cannot be considered as actual but only as purely possible. Given that eka-elements are chemical pure possibilities, a possibilist approach, entitled “panenmentalism,” can gain support as well as an important implication. (shrink)

Panenmentalist possibilities are individual pure possibilities existing independently of any mind, actual reality, and possible-world conception. These possibilities are a priori accessible to our intellect and imagination. In this paper, I attempt to shed some panenmentalist light on the discovery of chemical branched chain reactions and its implications on biology and cancer research. I also examine the case of the Belousov–Zhabotinsky reaction which, at first, was believed to be impossible. Finally, I proceed to examine through a panenmentalist lens Szilard’s discovery (...) of the possibility of physical chain reactions and Mullis’s discovery of a polymerase chain reaction. All these major actual discoveries clearly depend on the discovery of the relevant panenmentalist possibilities and the ways in which they relate to one another. (shrink)

In this paper, we review the history of quasicrystals from their sensational discovery in 1982, initially “forbidden” by the rules of classical crystallography, to 2011 when Dan Shechtman was awarded the Nobel Prize in Chemistry. We then discuss the discovery of quasicrystals in philosophical terms of anomalies behavior that led to a paradigm shift as offered by philosopher and historian of science Thomas Kuhn in ‘The Structure of Scientific Revolutions’. This discovery, which found expression in the redefinition of the concept (...) crystal from being periodically arranged to producing sharp peaks in the Bragg diffraction pattern, is analyzed according to the Kuhn Cycle. We relate the quasicrystal revolution to the non-Euclidean geometry revolution and argues that since “great minds think alike” there is a diffusion of ideas between scientific revolutions, or a resonance between different disciplines at different times. The story behind quasicrystals is an excellent example of a paradigm shift, demonstrating the nature of scientific discoveries and breakthroughs. (shrink)