In Book Four, The Alchemist, the notion of the Philosopher's Stone is brought up by Nadir Divanbegi. Nadir, the khan 's right hand man, questions Iwang's belief with regards to the Philosopher's Stone. Nadir wonders if it actually truly exists and questions Iwang on its existence. Iwang is not sure himself whether the Philosopher's Stone actually exists. Despite the legend of the philosopher's stone, the rejection of alchemy later on in the story and the rejection of certain legends such as the Philosopher's Stone results in the revolution of science and the discovery of a plethora of scientific innovations. Such scientific innovations include the speed of light, the speed of gravity, prisms, gravity, etc. The information below explains the legend of the Philosopher's Stone. (Page originally posted by Carlos Urtecho)

According to Wikipedia:

The philosopher's stone, in Latin lapis philosophorum, is a legendary substance that supposedly could turn inexpensive metals such as lead into gold and/or create an elixir that would make humans younger, thus delaying death. It was a longtime holy grail of Western alchemy. In the view of spiritual alchemy, making the philosopher's stone would bring enlightenment upon the maker and conclude the Great Work. It is also known by several other names, such as the Golden Wedding Garment, the Soul body, the Astral Body, and the Living Stone, spoken of in some of the ancient philosophies as the Diamond Soul.

Alchemy itself is mostly an original concept and science practiced by the ancient Egyptians and Middle East. However the concepts of more easily transmutating one metal into a more precious one (silver or gold) and ensuring youthful health apparently originated in China and from the theories of the 8th century Arab alchemist, Jabir ibn Hayyan, latinized as `Geber'. He analyzed each Aristotelian element in terms of the four basic qualities of hotness, coldness, dryness, and moistness. Fire was both hot and dry, earth cold and dry, water cold and moist, and air hot and moist. He further theorized that every metal was a combination of these four principles, two of them interior and two exterior. From this premise, it was reasoned that the transmutation of one metal into another could be effected by the rearrangement of its basic qualities. This change would presumably be mediated by a substance, which came to be called al-iksir in Arabic (from which comes the Western term "elixir"). It is often considered to exist as a dry red powder made from a legendary stone — the "philosopher's stone". 16th-century Swiss alchemist Philippus Paracelsus believed in the existence of alkahest which he believed to be a undiscovered element from which all other elements (earth, fire, water, air) were simply derivative forms. He believed that this element alkahest was, in fact, the philosopher's stone. Jabir's theory and the concept of the philosopher's stone may have been inspired by the knowledge that metals like gold and silver could be hidden in alloys and ores, from which they could be recovered by the appropriate chemical treatment. Jabir himself is believed to be the inventor of aqua regia, a mixture of muriatic (hydrochloric) and nitric acids, one of the few substances that can dissolve gold (and which is still often used for gold recovery and purification). Gold was particularly valued as a metal that would not rust, tarnish, corrode or otherwise grow corrupt. Since the philosopher's stone would turn a corruptible base metal to incorruptible gold, naturally it would similarly transform human beings from mortal (corruptible) to immortal (incorruptible). Essentially one of the many theories was that gold was a superior form of metal, and that the philosopher's stone was even purer and superior to gold, so much so that if combined with lesser metals would turn them into superior gold.
(Wikipedia contributors, "Philosopher's Stone," accessed 02/13/07)