The activist and academic recalled the experience his wife had in the 1970s in a hospital in England when she gave birth to their first child.
Sir Geoff said: “The medical people came up to her after the birth and told her they were a ‘little concerned’ in terms of the colour.
"They thought something was medically wrong with my child.
"They thought they would have to incubate, that there was respiration issues.
"My wife clicked and told them that her husband was Jamaican.
"They just smiled with great embarrassment after that.”
Sir Geoff has done work with Edinburgh City Council, the University of Edinburgh and the University of Glasgow to help deal with the legacy of racism within the country.
He explained: “There is still this idea that white skin is superior and black skin is inferior.
"Where does this come from?
"David Hume back in 1753 said this, that black people were inferior to white people.
"This is the statement that killed George Floyd.
"This is the statement that lead to the incident that Meghan and Harry talk about.”
In an interview with Oprah Winfrey, Meghan Markle and her husband, Prince Harry spoke of an incident where a member of the Royal Family asked what colour their child would be.
Sir Geoff, who lives in Penicuik, explains that racism like this is pervasive throughout all society, and says that it is crucial to change education, as racism starts at home.
He recalls: “Sometime ago, I was walking down the street, there were these two little boys.
"One was maybe around ten to 11 years old, and the other was around seven or eight.
"The younger one pointed and said ‘look, there’s an n-word man’.
"The older boy nudged him in the back and said ‘it’s rude to point.’
"They were taught at home that it was rude to point at an adult, and I was afforded that respect as I was an adult.
"But they weren’t told not to use that word.
"This is the power of education.
"Influence at a young age will last a life time.
"These ideas are formed in childhood.
"If is can persist to the position of the Royal Family, then it is everywhere, throughout society.”
Sir Geoff has also advocated for more diverse representation across politics, and those who manage society.
He added that this deeply entrenched racism, and subconscious idea’s about superiority have : “destroyed the lives of black people for centuries.
"We still judge black people on all of these old prejudices.
"It starts at home, in schools and in the streets.
"It is through education, that is the way out.
"We cannot change the past, but we can change the consequences of the past.”
Sir Geoff is Professor Emeritus in the School of Life Sciences at Heriot-Watt University and a prominent human rights activist. He was Scotland’s first black university professor.