The mythical thinkers approach the world through intuitive means, while logical thinkers explain the world using experiments and observable facts. The logical thinkers do not involve divine actions when explaining the reality and they disregard as illogical all the stories that describe the natural phenomena based on non-scientific arguments such that: divinity punishments or blessings.
At the time when Greek culture had a mythic explanation for the solar eclipse, the great philosopher Thales has introduced, for the first time, the analytical thinking, in contrast with the mythical thinking, explaining that the solar eclipse occurs when the Moon passes across the Sun in direct line. For the first time, the divine anger was not the cause of solar eclipse, but the a scientific principles such as the superposition of the Sun and the Moon, as well as the "earthy" composition of a celestial body, the Moon. This scientific explanation can be regarded as the beginning of the analytical thinking, using means as observations and deductive proofs to explain the cause of natural phenomena.
Another story that may be very well considered, because it stresses out the huge differences between the both ways the mythological and scientific thinkers' visions about life, is the turtle shell story. While analytical thinkers try to explain the turtle shell as an outgrowth of turtle skeleton, the mythical thinkers offers an explanation, through Aesop's fable, such that the turtle shell is a punishment applied to the turtle by Zeus, because the turtle did no want to leave its house to participate to Zeus' wedding. Yet again, you can see the big difference between these ways of thinking, one way involving the physical laws and the other way involving the Gods' laws.