If you're a big fan of Isaac Asimov and sentient robots like Johnny Five and Sonny, you might not be happy to hear that computer science researchers have used mathematical theory to prove that robots capable of feelings and emotions will never exist.

Using a variation of Giulio Tononi's influential mathematical framework for consciousness, a team of researchers from the National University of Ireland have proved mathematically that computers are unable to completely integrate information.

Tononi's 2008 framework argued that integrated information cannot be reduced into smaller components, so for example, if a human were to perceive a red triangle, the human brain would not be able to break down the triangle as a colourless outline of a triangle and a shapeless patch of red at the same time.

Computers cannot fully integrate information

"Conscious systems are ones that take in lots of information, integrate it and bind it together. In people's brains, the information is integrated with all your previous memories so it can't easily be separated, for example, the way that we react to a thing that we perceive," Dr Phil Maguire, who led the research, told IBTimes UK.

"We agree with Tononi's approach but we feel his quantification of integrated information didn't work. The cost of integrating something was that you would lose a lot of your memories at the same time, so we decided to provide a new type of quantification."

Maguire and his team have used algorithmic information theory instead to define integration by "edit distance", i.e. how hard it is to edit a memory on its own.

The researchers use the example of a digital camera – it's easy to delete a photo on the memory card of a camera as each image on the camera is a separate file. On the other hand, human memories are integrated together so it would be impossible to remove just one memory.

Deleting memories is also impossible

Eternal Sunshine of the Spotless Mind
Eternal Sunshine of the Spotless Mind Focus Features

"There's no computer you could build that could integrate information so that it cannot be edited. Computers can still be useful and intelligent without complete integration, but we will never trust it as we trust a person, as the computer is just following certain algorithms," said Maguire.

"You can't break down human behaviour easily, so we call that consciousness."

The researchers are exploring the significance of the human brain and the role it plays in human concepts of objectivity and reality, and what they have proved establishes a clear distinction between the human brain and computers.

Their research also proves that the concept of being able to remove memories from your brain, like in the Jim Carrey film Eternal Sunshine of the Spotless Mind, is also impossible.

"Any artificial system can be decomposed, but if a neurosurgeon were to try to remove a memory, it would just cause severe brain damage. If people's brains could be edited like that, then you wouldn't even trust your own memories anymore, so this un-editability is a key thing."