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Regarding the primary meaning of the term ayah, see note [2] above. In the present context, the expression ayatayn ("two symbols") refers - as the subsequent clause shows - to the symbols of spiritual darkness and light.
I.e., the message of the Qur’an, which is meant to lead man out of spiritual ignorance and error into the light of faith and reason.
Lit., "the count ('adad) of years". Since, as the Qamus points out, this phrase denotes also "the years of [a person's] life, which he counts", it obviously implies here a call to spiritual self-criticism in view of the ephemeral nature of one's worldly life.
I.e., everything that man may be in need of in the domain of ethics and religion.
If we were to cry when it is night, we shall look foolish when it is day; for the night is but a preparation for the day: perhaps, as the last verse says, we pray for the day when we want rest for the night. Both are Signs from Allah. Darkness and light stand for ignorance and knowledge. "Where ignorance is bliss, its folly to be wise." Darkness and light may also stand for shadow and sunshine, sorrow and joy: both may be for our development.
By the physical light we see physical facts. And this physical gift of Allah is good for us in two ways: (1) we can arrange for our livelihood, or we can attain the knowledge of the physical sciences and gain some control over the physical forces of nature; and (2) the daily rising and setting of the sun gives us the computation of days and years, for the physical natural year is the solar year.