How do cranes get so high?

Tower cranes flock to money. During the economic boom years,
high-rise construction cranes migrated from Beijing to Shanghai
to Dubai, where it was estimated in 2006 that there was one
tower crane for every 44 residents of the desert boom-opolis.
Tower cranes are feats of structural engineering that often outshine
their creations. They are designed to stand 80 metres tall and reach 80
metres out supported only by a narrow steel-frame mast, a concrete
foundation and several counterweights.
The engineering principle that keeps the twiggy tower crane from
tipping over is something called a ‘moment’. If you hang a weight
from the crane’s jib arm, it exerts a rotational force or torque where
the arm connects to the top of the mast. The magnitude and
direction of this force (clockwise or anti-clockwise) is called the
moment. If the weight is hung close to the mast, the magnitude of
the moment is lower than if the weight is hung far out on the jib. To
keep the crane upright, counterweights are used to create a moment
of equal magnitude in the opposite direction, balancing out the
rotational forces.
Once a tower crane meets its maximum unsupported height, it
can be tethered to the building itself and continue to grow with the
rising skyscraper. The tower cranes that rose with the construction of
the record-breaking Burj Khalifa skyscraper in Dubai reached a truly
dizzying height of 750 metres