How does the cathedral reflect the Gothic culture and the interest in creating a place of worship that was “flooded with heavenly light”?
By the end of the Western Roman Empire in 485 BCE at the hands of a loosely-confederated group of Goths under Alaric, Goths were generally feared throughout what is now western Europe, in part because many Goth tribes were still largely pagan. As Gothic tribes began to assimilate into other, often Christian, groups, Goths adopted Christianity and thereby became less threatening.
Some architecture historians believe that what we now call the Gothic Cathedral was based on the typical Gothic main hall, which was made of wood, but usually had a large and high central space for celebrations. We date the beginning of Gothic Cathedral construction in France at about the 12thC. to the 15thC, and most of the cathedrals in France, for example, were under construction during this period.
The typical Gothic Cathedral is shaped like a cross, which was meant to remind people of the central tenet of Christianity--Christ's sacrifice for man's sins. More important than the form, however, was the space created by vaulted ceilings--rather than a sense of enclosure, one gets a sense of openness and light. The cathedral's structure is designed to draw one's eyes upward, just as one's spirit should be drawn upward by faith. But perhaps the most important feature of the cathedral is its light.
Medieval people were generally illiterate and depended on paintings or illustrations to understand the basic tenets of Christianity, and they lived in low, dark structures. The cathedral supplied those illustrations in the form of stained-glass windows, whose purpose was both to dazzle the eyes and instruct the viewer. Most of the powerful examples of stained glass took as their subjects saints' lives, Christian history, moral subjects, and the joys and torments of the afterlife. Medieval people "read" stained glass windows and sculpture the way we read books--each window and sculpture reminded them of a central aspect of Christian faith and history, and, of course, brightened their eyes and lives in the process.
The principles of design of the Gothic Cathedral, as pioneered by St. Denys, were based on Christianized versions of Platonic-Pythagorean numerology, in which the distances between pillars and proportions of various section followed theories of number symbolism and harmony. Many aspects of the decorative features of the cathedral were based on the notion of anagogy, i.e. that the outward beauty of the cathedral should lead the soul of the worshipper to a vision of the immaterial beauty of God.
Light is especially important as a symbol of the emanation of God's grace and goodness that illuminates the word as "uncreated" light. In a practical sense, the development of new technologies such as ribbed vaulting, pointed arches, clerestories, and flying buttresses allowed architects to include much bigger windows than were found in Romanesque cathedrals, and thus the interiors of many Gothic cathedrals, such as the York Minister or Ely Cathedral, give the impression of being filled with light from their many stained glass windows.