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Rationality is over priced. Some experiments indicate that people use rationality to explain things they did, for example under hypnosis they suggest you should open your umbrella at a party, then you do it and try to explain why.

In this case rationality is a false distortion of what is going on. Living and thinking is at a higher level that rationality. We can use computers, logic, maths and rules to improve our rational mind, but thinking is much more that rational thinking. Creativity and emotions play a vital role. Destroy emotions and you loose your memory (citation required), because memorizing is linked to attention and attention is linked to emotions and feeling.

As a mathematician I can prove a theorem and give a prove, but there is something creative in finding a proof. Sometimes our mind is a wonderful mind.

That’s rationalization which is not the same as rationality. If you were interested in being rational you would learn as much as you could about rationalization and try to detect or avoid it.

Rationality is also not the opposite of emotionality. You don’t have to be Spock to be rational.

Thanks for commenting the difference, but what would happen when people use rational thinking only to construct excuses, that is rationalization of what they do.

An example: I am a rational people, I will pick certain portion of reality that allow me to construct a good model of myself, with blind eyes for the part I don't want to see.

You can use "rational thinking" to construct rationalization of your behaviour.

Since there is no logical notion of justice, rational thinking and rationalization are not far away.

Non sequitur; you can't call your actions driven by being a rational person, yet choose to exclude data points because run counter to your desired conclusion.

If you're excluding data points because they lead you away from your desired conclusion, then you're not thinking rationally, you're rationalizing.