Saturday, June 30, 2012

The Nature of Mathematical Genius.

In the book, _The Poincare Conjecture:  In Search of the Shape of the Universe_ by Donal O'Shea the author describes the commonly understood notion of mathematical genius.  Here, the romantic notion of mathematical genius is of the solitary genius heroically wrestling understanding from an uncaring cosmos. While this may not apply to many modern mathematical discoveries which were made "upon the shoulders of giants", this "great man" view of history is the traditional perspective.  As is, it applies to Grigori Perelman who was able to prove the Poincare Conjecture.  This is the finest the human species has to offer for this era.

Saturday, June 2, 2012

The Relationship of String Theory to Medieval Theology.

Modern string theory has been related to medieval theology in that it poses the possibility of multiple universes.  We may see this as the rise of a new "ironic science".  Sheldon Glashow opposes string theory for this reason and claims that it is a tumor on the larger body of physics.  Other instances of ironic science may be seen in relativistic theories of worm holes and time travel and applications of Godel's results to scientific theories.  Stanley Jaki maintains that Godel's theorems show the futility of providing a universal self contained theory of everything or final theory.  Murray Gell-Mann echoed these claims but only after he had been shown this by Jaki which Jaki maintains he was later to deny.  Other instances of ironic science involve the understanding of consciousness by Roger Penrose, various applications of artificial intelligence, and in particular the theories of Ray Kurzweil regarding a singularity.  In particular, the "simulation theory" is in accordance with classical medieval metaphysics or the notion of a "brain in a vat".  Other instances include the many worlds interpretation of quantum mechanics, the transfinite numbers of Cantor, modal logic, and the possible worlds of David Lewis.

The Brave New World of Science and Religion.

In a strange twist of fate a new synthesis of science and religion has been made possible.  Schools such as Caltech and MIT once traditional bastions of scientific empiricism and materialism are now offering courses on Bible study and courses on robotics and God.  The relationship between religion and science has always been a conflicted one but now it appears that religion has broken through into these prestigious science institutions where it had been absent since the nineteenth century in this brave new world.
I question some of this account however because when I was at Caltech I remember a strong Christian presence on campus.  Many of the students and especially some of the Asians (among whom Christianity appears to be growing) were strong Christians.  Also, at the founding of Caltech prominent members like Robert Milikan were actually Christians.