Rosenhouse’s book is objectively bad. It purports to be a critique of mathematics as used by ID proponents and of my mathematical work in particular.
Rosenhouse’s belief in the creative power of evolutionary processes is based not on hard data but on his faith in the philosophy of scientific materialism.
Not all patterns eliminate chance in the presence of improbability. Take an arrow shot at a target.
Is a sense of humor a byproduct, an accident, or was it installed on purpose? For better health? There definitely seems to be a purpose.
Briefly, the design inference (the method rather than the book) identifies two features as essential for eliminating chance: improbability and specification.