NOTES for Gen 18:12
In the antiquity of all the peoples, children were considered as blessing from the gods. Many children meant a big blessing; the infertility was a punishment and a curse, above all for the woman, but not only: if the continuation of the family broke off, it (what is not surprising) was considered as a sign of anger from above, which fell on all.
And what, if God promises children when there are no more hope for a long time, just because all the possible deadlines of their birth already passed? What means in such situation the laugh of a woman without children, whose husband had been promised that his descendants will grow into a nation, and when will come his time, he will create his nation on the land, where he went? The laugh of the one, who was promised to have a successor? What do we have here: joy or sorrow? Or neither one, nor the other? Probably, going through all which is described in a few decades (and maybe, a few years) earlier, Sarah's reaction would have been anger, indignation, or joy, depending on whether she would have had enough strength to believe what was said. But, apparently, Sarah laughed the laugh, people laugh, when there is already no strength for whatever, the laugh, that becomes now the only reaction to all which takes place in the life of man, and on life itself.
When there is already no strength either to cry, or to be delighted, life becomes ridiculous, quite as is ridiculous to man any nonsense, any absurd, if it becomes the only reality, to which all the neighbors are absolutely seriously. Well then comes the moment of God's intervention in the situation. It is He who ends the absurd. And this end is perceived, as a miracle. Because the miracle always supposes the rupture of a genuine reality in our world, which after the fall is not really genuine. And the history of God’s people could begin only in a real world. Begin with a miracle. Miracle, far of being the last in this history.