Sherlock vs doctor who

I have always liked programmes where someone has a higher level of IQ than the average person. Both sherlock and the doctor has the highest IQ which makes it easier for them to solve problems and to storge large amount of information. They are from different backgrounds, one is a time and space traveling alien and the both a private detective working with the police and the government to help solve crimes. Most people don't understand them both but they just lack the mental capacity to solve the mysteries, such as the one where sherlock jumped too his dead,  to later it was seem alive. I thought about the different ways they could do that. My first thoughts were that it was a double that fell and sherlock hid on the roof. Then it came to me that he jumped on some form of pillow but an enlarged pillow then a cover but was done to make Dr waston believe he was dead. The doctor is smart from thousands of years of knowledge and experience....