Oct. 5 – 2B03 05/10/2011 9:32:00 AM
Major mathematical questions about the universe:
Shape of the universe – fixed or evolving?
Size - finite or not.
o Evidence that it is expanding – at an ever-increasing speed.
o Does not answer if it is finite or not.
If the summation of angles is more than 180, even incredibly in a
small way, that means that there is some sort of curve.
Different size triangles add up to different 180s.
On flat spaces, 180 is accurate yes. But, on curved spaces, it is a
little more than 180, depending on size.
Realized small triangles wouldn’t give him anything significant.
o Measured a triangle on different mountains.
People use this method w/ stars.
What is a dimension:
All curves are one-dimensional
By combining horizontal and vertical directions, you can get anywhere in the
plane – 2 dimensions.
Hollow spheres for ex, nothing insides.
Power of scaling
use it as a definition of dimension
Life in 2 dimensions o Just like a flat plane – many limitations.
Our universe could be a cyclinder.
Radius – several billion light years.
Could also be donut shaped.
Learning properties of dimensions
Intuitive level and the mathematical level.
How are we going to think about 4 dimensions :