The philosophical significance of Alan Mackay’s theoretical discovery of quasicrystals

Dan Shechtman was the first to discover an actual quasicrystal (on April 8, 1982). He was, however, not the first to discover the pure possibility of this novel structure (the theoretical discovery), which had been excluded from the range of the possibilities of crystals (as it had been fixed by both theoretical and empirical means in the beginning of the twentieth century). Penrose and Mackay, in particular, had contributed to the discovery of the pure possibilities of quasicrystals quite some time before their actual discovery. These pure possibilities are mathematical–structural, and like purely mathematical entities, they do not exist spatiotemporally and causally, whereas actual quasicrystals exist only spatiotemporally and causally. The pure possibilities of quasicrystals do not depend on their actualities, and without them, these actualities would have been theoretically groundless, meaningless, and could not be correctly identified if at all. Hence, Mackay’s contribution to the meaning and theoretical basis of the discovery of actual quasicrystals is indispensable.