Ghosts and Prof. Brian Cox

Professor Brian Cox has tweeted about believers of the paranormal, calling them 'utter nobbers'. His derogatory term suggests that he has closed his mind to the possibility of there being a science he cannot understand.
The Prof, now a celebrity after his hit series, 'Wonders of the Solar System' was talking of his disbelief in ghosts on a Radio 4 programme that was accused of being one-sided.

It is likely that ghosts have been around as long as Humans Beings have existed and wondered what happens to the human persona (souls) after death. Eventually, using much the same ignorance, a priest class emerged that took advantage of peoples fears and developed the earliest religions. As with many things that have been around since the beginning of Homo Sapiens, there may be an element of truth in what they say.
My son was playing in the basement of a friend's house in Watlington, when both boys saw a figure of a woman descending the steps. She was dressed in old fashioned clothes and on reaching the bottom of the steps she turned and vanished through a solid brick wall. Both boys witnessed the event and swore that it was true. My son, I know, is not given to imagining this sort of thing, so what happened?

Instead of poo-pooing this sort of thing, the good professor should try and envisage some truths that don't necessarily comply with his mathematically based science which states if you can't calculate it, it doesn't exist. Or can it?

Imagine a square with sides of one unit. It has an enclosed area of one square unit. (1x1=1) A handkerchief might be an example of such an object. You can see and touch it.
Now imagine a square with sides of minus one. You can't see it or touch it, but wait. It too has a positive area of one square unit. (-1x-1=1). Is this object, although we can't sense it, also real? This argument can be extended to three dimensional objects.

My point is that the universal truth of mathematics is flawed because the square root of one has TWO correct answers. Until scientists recognise this fundamental they will always be sceptical of the paranormal.
Could it be that ghosts are manifestations of negative dimensions!!