By digging around there seems to have quite a numerous views on the subject of ‘counter-intuition’ alone but in terms of the meaning of the word itself, one possible way we could look at is a form/method of deviating the brain’s perception from our natural tendencies. Whether it be done through an unorthodox fashion or in an unruly manner, a more straightforward interpretation to the phrase ‘counter-intuition’ involves factors never based on logic and common sense. Further to that what might seem intuitive to one might be viewed differently by another in a counter-intuitive fashion, due through scientific rationing and observation,when emotion and other thought process interprets such judgment incorrectly. However, common sense is something what people in common would agree on.

Hope that made sense.

Science and mathematics deals a lot with the concept of ‘counter-intuition’. Here are some interesting examples:

double slit experiment -

Monty Hall problem -

“Counterintuitive universe: The failures of human perception”

‘Human perception is remarkably fallible. As tiny creatures on a comparably tiny planet in a vast universe, there is much about our surroundings that would go unnoticed or misunderstood if we relied on personal perceptions alone to make conclusions about the universe.

The bottom line is, when it comes to the ground truth, our personal perception frequently fails us…

It follows that we always have to leave the door open that we could be wrong. But the difference between science and non-science (nonsense) is that science strives to remove the fallibility of humanity from the equation as much as possible. Science admits that our intuition, what we see when we look only down the ends of our noses, could be wrong, and is willing to consider counterintuitive ideas – ideas that run contrary to our personal experiences. Non-science, on the other hand, ignores that fallibility – and often embraces it. It argues from a position of not what is most likely true based on evidence, but what seems to be true based on a glance down the end of its nose.’

An interesting article by Tim Nordstrom. Worthy read.

For the full article.

These three examples alone leaves behind quite a load to think about in regard to this topic.

But lastly, not exactly scientific nor mathematics related, fairy tales in general are quite counterintuitive (morals) depending on how it’s being viewed upon. Particularly Grimm’s fairy tales and Marie-Louise von Franz’s Shadow and Evil in Fairy Tales work. On top of that, Jean-Luc Jucker wrote several interesting entries on counterintuitiveness in everyday life with various examples used ranging from :

1) Recipe to creating successful religious and supernatural concepts.
2) Boyer’s discovery towards human culture.
3) Art.
4) Photography.
5) Comedy.
6) Fairy tales.