I am very much impressed by three theories, in radically different domains (anthropology and cognition). I am ready to bet that these theories will be remembered in a far future.
His theory is one of the rare successful attempts to solve the many apparent contradictions between anthropological universals and what we expect from evolution through natural selection. Knight expands Turke’s explanation of sexual specialisation (with men leaving women alone when hunting). Woman synchronicity becomes central in explaining various universals like food restrictions, taboos, costly rituals, and myths.
Knight is aware of many constraints (esp. evolutionary and ethological constraints) that are merely ignored by most scholars in anthropology. His great achievement is to put logic in what, otherwise, looks like a vast mess of anecdotal anthropological facts.
Knight’s logic is impressive! Just read his Blood relations – Menstruations and the origin of culture (Yale University Press, 1991). Read the New Scientist’s review by Kate Douglas.
Leyton’s model is a remarkable synthesis of many previous theoretical advances like Gestalt theory. Leyton’s basic idea is that perception works through structure transfer. Mathematically, transfer results from elements of a group acting on another group. You perceived your tiled floor, not as a set of disconnected tiles, but as one repeated tile. This is why you find structure in the floor. One tile is transferred through the group of 2D-integer translations. The world appears to us as a nested construction in which each step consists of a maximal transfer of structure.
Leyton construction captures a fundamental property of human cognition. Our brain is not any universal Turing machine. We are bound to see the world through nested group operations.
Leyton’s work, though mathematically intricate, is insightful. I am impressed by its explanation power. Just read his Symmetry, Causality and Mind (MIT Press, 1992) and A generative theory of shape (Springer Verlag 2001).
Peter is well-known for his book Conceptual Spaces (2000), in which he explained for the first time in a clear way (1) that meanings are similar in nature to perceptions and (2) that they have certain geometrical properties like convexity. His account, once stated so clearly, seems evident, as it solves many problems and paradoxes in which traditional semantic theories get tangled up (especially all theories that postulate a ‘language of thought’, including many theories in cognitive linguistics).
Peter’s rencent book, The geometry of meaning, is a fantastic follow-up. The Publisher asked me how I liked the book and printed by appraisal on the back cover:
"Peter Gärdenfors is creating a new science of meaning. The recent ideas, expressed so clearly in The Geometry of Meaning,
make his achievements even more impressive. The book leaves us with the impression that semantics may be a tractable problem after all."