A dramatic new mathematical challenge?

This a rich one. The Hoover Institution at Stanford University is a center of scholarship and retirement for conservative intellectuals. It started as a place for retirement for former President Herbert Hoover, after the voters decided that his approach to coping with the Great Depression was not quite optimal (his replacement became a President of some note). In 1941 it erected(*) Hoover Tower, a startlingly visible landmark on the Stanford University campus. It has continued to associate itself with mostly conservative former politicians. Up until now, it has always cultivated an aura of respectability. Creationism was never its “thing”.

Now all that is changing. Some sharks seem to have been jumped. The Institution’s Peter Robinson, a former speechwriter and television host, has moderated a discussion between some of the intellectuals taken most seriously by the Discovery Institute, and presumably now by the Hoover Institution. They are Stephen Meyer, David Berlinski, and David Gelernter. The discussion is entitled “Mathematical Challenges To Darwin’s Theory Of Evolution, With David Berlinski, Stephen Meyer, And David Gelernter”. It is one hour long, and I have not yet been through it all. In case you end up hungry for more, there are longer videos expanding on the views of Meyer and Berlinski (here and here, and we very recently discussed an article by Gelernter here).

(sorry for the size – I can’t figure out how to resize this video preview)

I need you to help me understand this dramatic new development.

The assignment for you is to see if you can answer these study questions:

1. With all this emphasis on how mathematical the challenges are, are there any actual mathematical challenges noticeable here?
2. What new and sophisticated arguments, far more subtle than those put forward by ordinary creationists, will be found in this discussion?
3. Exactly what is it that these folks think is in principle impossible for natural selection to accomplish? New species? New genera? Not just really big changes but really-really-really big changes?
4. Do they understand that in evolution one does not have to go directly from a dog to a cat, but can change more gradually from their common ancestor?
5. What exactly do they say about common descent? How accepting of it are they?
6. It is interesting that the discussion was held in Fiesole, a town near Florence, Italy where Harvard University and Georgetown University have centers of Italian Renaissance Studies. Is this purely an excuse for a junket to a pleasant place with great food, or might these folks be in Italy hoping to find common ground with the loudmouthed reactionaries in the new Italian government and encourage them to include Intelligent Design in Italian school curricula?

As usual, I will pa-troll this discussion, eliminating off-topic trolling and off-topic troll-chasing.

* (The Tower has a famous and scurrilous nickname – if you can handle a little off-color humor, ask a knowledgeable friend about its nickname, or search on Google for “Hoover Tower interesting nickname”)