What is complexity?

From what seesms to be an informational POV, Richard Dawkins (famed evolutionary biologist, atheist, science educator) offers a simple, easy-to-understand, rule in re comparative complexity (how complex is A with respect to B?)

Dawkins' Rule in Comparative Complexity

1. Take two objects, A and B.

2. Take a horizontal slice of both at the same level of organization e.g. for A is a crab and B is a whale, if one is being studied at the cellular level, do the same for the other and if at the molecular level, the same for the other, you get the idea.

3. Now record the information content for both A and B. Suppose I(x) = information content of x.

4. Possibilities [conclusions]

i) I(A) = I(B) [same complexity]
ii) I(A) > I(B) [A is more complex than B]
iii) I(A) < I(B) [A is less complex than B]

In a loose sense, it boils down to how thick a book on A and B is.