The aim of the presented article is to provide an in-depth analysis of the adequacy of designating Penrose as a complex Pythagorean in view of his much more common designation as a Platonist. Firstly, the original doctrine of the Pythagoreans will be briefly surveyed with the special emphasis on the relation between the doctrine of this school and the teachings of the late Platonic School as well as its further modifications. These modifications serve as the prototype of the contemporary claims (...) of the mathematicity of the Universe. Secondly, two lines of Penrose’s arguments in support of his unique position on the ontology of the mathematical structures will be presented: their existence independent of the physical world in the atemporal Platonic realm of pure mathematics and the mathematical structures as the patterns governing the workings of the physical Universe. In the third step, a separate line of arguments will be surveyed that Penrose advances in support of the thesis that the complex numbers seem to suit these patterns with exceptional adequacy. Finally, the appropriateness of designation Penrose as a complex Pythagorean will be assessed with the special emphasis on the suddle threshold between his unique position and that of the adherents of the mathematicity of the Universe. (shrink)

If our mind is just an algorithm running on a flesh hardware, then it seems that there is no place for the free-will. An algorithm decides everything based on deterministic computations, or on random inputs, but neither inevitability nor pure hazard is free choice. Hopefully, some day, Science will be able to understand, monitor and simulate all the mind processes. Even then, it will still be a possibility for the free-will to exist, based on the convergence of the initial data. (...) I propose a crucial experiment to test this hypothesis. (shrink)

Evolution creates structures of increasing order and power; in this process the stronger prevail over the weaker and carry the evolution further. Technology is an artificial creation that often threatens life and evolution conceived of as natural phenomena; but technology also supports life and it works together with evolution. However, there are claims that technology will do much more than that, and bring about an entirely new epoch of evolution. Technology will replace the fragile biological carriers of evolution by a (...) new kind of nonbiological carriers of immense intelligence and power. The present paper discusses the plausibility and weaknesses of such fascinating projections that some people proudly announce as the final liberation of the Mind, while others fear them as signs of the final self-annihilation of the Man. (shrink)

Albert Einstein once made the following remark about "the world of our sense experiences": "the fact that it is comprehensible is a miracle." (1936, p. 351) A few decades later, another physicist, Eugene Wigner, wondered about the unreasonable effectiveness of mathematics in the natural sciences, concluding his classic article thus: "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve" (1960, p. 14). (...) At least three factors are involved in Einstein's and Wigner's miracles: the physical world, mathematics, and human cognition. One way to relate these factors is to ask how the universe could possibly be structured in such a way that mathematics would be applicable to it, and we would be able to understand that application. This is roughly Wigner's question. Alternatively, the way of the mathematical naturalist is to argue that we abstract certain properties from the world, perhaps using our bodies and physical tools, thereby articulating basic mathematical concepts, which we continue building into the complex formal structures of mathematics. John Stuart Mill, Penelope Maddy, and Rafael Nuñez teach this strategy of cognitive abstraction, in very different manners. But what if the very concepts and basic principles of mathematics were built into our cognitive structure itself? Given such a cognitive a priori mathematical endowment, would the miracles of the link between world and cognition (Einstein) and mathematics and world (Wigner) not vanish, or at least significantly diminish? This is the stance of Stanislas Deheane and Elizabeth Brannon's 2011 anthology, following a venerable rationalist tradition including Plato and Immanuel Kant. (shrink)