Homework 1 due Feb. 22 at beginning of class
Space & Time, Prof. Dowden     
          
     
1. Describe the arguments that have been given throughout history for believing in the
absolute theory of space, rather than the relational theory of space.

2. (a) It's important to distinguish accuracy from precision.  If you use a bow to shoot
arrows at a target, then the shooting is precise if all the arrows cluster near a point,
even if that point is far from the bull's-eye.  For your shooting to be accurate you need
to hit the bull's-eye.  What does it mean for Prof. Dowden's K-Mart wristwatch to be
accurate?   (b) In the Northern Hemisphere, winter daylight doesn't last as long as
summer daylight; winter days are shorter.  But in another sense of the word "day"--the
one in which a day is 24 hours long the winter days are not shorter because one day is
as long as any other, or so most people assume (ignoring leap seconds).  Yet it is
difficult to check on this by comparing the duration of Tuesdays with the duration of
Thursdays.  According to Leibniz in his book New Essays on Human Understanding,
our measurement of time would be more accurate if we could keep a past day for
comparison with days to come.  Because we can't, it's difficult to ensure accuracy.  How
then do we ensure the accuracy of our civilization's best clock?  

3. According to Le Poidevin, how is time related to our clocks and to our minds?  Do
you agree with him?

4. One of the most philosophically shocking implications of Einstein's special theory of
relativity in 1905 is the relativity of simultaneity.  Explain what the relativity of
simultaneity is.

5. In the 1830s, the world's most famous mathematician Carl F. Gauss invented
hyperbolic non-Euclidean geometry.  This had a huge impact upon philosophy,
especially after the results of Beltrami and Klein in 1870.  Explain.