A structural innovation to break the limitation of
the Roman arch was a new form of the arch based not on the circle,
but on the oval. This does not seem a great change, and yet its
effect on the articulation of buildings is spectacular. Of course,
a pointed arch is higher, and therefore opens more space and light.
But, much more radically, the thrust of the Gothic arch makes it
possible to hold the space in a new way, as at Rheims. The load is
taken off the walls, which can therefore be pierced with glass, and
the total effect is to hang the building like a cage from, the
arched roof. The inside of the building is open, because the
skeleton is outside. John Ruskin describes the effect of the Gothic
arch admirably.
Egyptian and Greek buildings stand,
for the most part, by their own weight and mass, one stone
passively incumbent on another; but in the Gothic vaults and
traceries there is a stiffness analogous to that of the bones of a
limb, or fibres of a tree; an elastic tension and communication of
force from part to part, and also a studious expression of this
throughout every visible line of the building.
Of all the monuments to human effrontery, there is
none to match these towers of tracery and glass that burst into the
light of Northern Europe before the year i 200. The construction of
these huge, defiant monsters is a stunning achievement of human
foresight - or rather, I ought to say, since they were built before
any mathematician knew how to compute the forces in them, of human
insight. Of course it did not happen without mistakes and some
sizeable failures. But what must strike the mathematician most
about the Gothic cathedrals is how sound the insight in them was,
how smoothly and rationally it progressed from the experience of
one structure to the next.
The cathedrals were built by the common consent of
townspeople, and for them by common masons. They bear almost no
relation to the everyday, useful architecture of the time, and yet
in them improvisation becomes invention at every moment. As a
matter of mechanics, the design had turned the semicircular Roman
arch into the high, pointed Gothic arch in such a way that the
stress flows through the arch to the outside of the
building.
