Exploring Chemical Space

Chemical space is definitely vast and sparse. There are many problems to be answered.
What is size of the space?
How to chart the space? Using shape descriptors, topology descriptors, property descriptors, similarity to representative molecules, or other measures? Is there something as pure and pretty as primes for the numbers? Is the PCA (principal component analysis) method the only tool to establish the coordinates the axes of the space? Are there fundamental theories from mathematics that can be applied into this area?
Can we learn the structure and the pattern of the chemical space, as clearly as we know about the space universe? What are the driving forces that lie beneath the distribution of the molecules (all available compounds, natural products molecules, drug molecules) in the chemical space?
Is indeed it that there are some collective differences that distinguish the drugs out the rest of the chemical space? If so, what are they? Can we use such knowledge to build the drug-molecules library? If not, what are the effective routes to explore each drug molecule in the chemical space?
It all seemed that we are still very limited to the knowledge of the chemical space, compared with our marvelous understanding about the galaxy and the rest of the space universe.