Reading Roger Penrose

After our first get together we've agreed to treat "The Road to Reality" as having three different sections "(1) Mathematical Preliminaries (Chs. 1 to 16); (2) Theoretical Physics (Chs. 17 to 26); and (3) Cosmology and Beyond (Ch.27 onwards). We will dip into each section for a fortnight at a time during the Autumn:

26th October - Chapter 2

2nd November - Chapter 3 and 4.1

9th November - Chapter 17

16th November - Chapter 18

23rd November - Chapter 27

30th November - Chapter 27/8

7th December - Review and plan ahead

26th October: So now on to Chapter 2 "An Ancient Theorem and a Modern Question"

Some issues:

(1) What does "proving Pythagoras' Theorem" assume ?

(2) What is the significance of Euclid's "parallel postulate"?

(3) How are "non-Euclidean geometries" possible?

(4) What does it mean to say a geometry is "true"?

(5) How could we tell if physical geometry were "elliptical" or "hyperbolic"?