In Paulo Coelho's The Alchemist, how does the alchemist demonstrate his powers to Santiago with the philosopher's stone?

After the general of the warring tribe allows Santiago and the alchemist go free, the pair heads towards the Egyptian pyramids. The alchemist doesn't go all the way to pyramids with the boy, though. Instead, he stops with the boy at a Coptic monastery, and he asks a monk to use the kitchen. Once there, the alchemist demonstrates his skills in front of the boy and the monk, as follows:

"The alchemist lighted the fire, and the monk brought him some lead, which the alchemist placed in an iron pan. When the lead had become liquid, the alchemist took from his pouch the strange yellow egg. He scraped from it a sliver as thin as a hair, wrapped it in wax, and added it to the pan in which the lead had melted" (154).

The "yellow egg" is the philosopher's stone. It is an essential ingredient to the recipe for turning lead into gold. Once the mixture receives the thin piece of the philosopher's stone, it turns as red as blood. The alchemist then takes the pan off of the heat to cool for a while. After cooling, the monk and the boy are surprised as follows:

"When the pan had cooled, the monk and the boy looked at it, dazzled. The lead had dried into the shape of the pan, but it was no longer lead. It was gold" (154-155).

Santiago asks the alchemist if he will ever learn to turn lead into gold. The alchemist explains that the skill is his Personal Legend, not the boy's. He only shows the boy his skills because he wants him to know that the process is possible.