In "Half a Day," what is the concept of time and how does it connect with death?

Naguib Mahfouz's short story "Half a Day" is about a reluctant young man who goes off to his first day of school. The story is a metaphor for life and how short a life can be. No sooner has the boy gotten through his first day of school than he is pictured at the end of the story as an old man who has to be helped across the street. During the course of the story the first person narrator gives hints that this is no normal day and that time is passing. He talks of learning new things, of struggle, and of the entanglements of relationships, some involving love and some hatred. Just before this figurative day of school is over, the narrator seems to acknowledge that a great deal of time is passing and that the world is changing:

In addition, the time for changing one's mind was over and gone and there was no question of ever returning to the paradise of home. Nothing lay ahead of us but exertion, struggle, and perseverance. Those who were able took advantage of the opportunities for success and happiness that presented themselves amid the worries.

This paragraph, which in a short number of words, sums up a person's life, is quickly followed by a paragraph which transports the narrator to the day when school is out and he must return home. Instead of the calm, tranquil streets of his childhood, the city has become crowded and bustling, symbolic of the fact that many years have passed and that the city has greatly changed. For the narrator, only death awaits after only "half a day." Life is short and before the narrator knows it time has ebbed away, school is out and people are suddenly referring to him as "Grandpa."