I have not taken any course in civil engineering. What I was taught was that a broad base would prevent something from toppling. So it makes me wondering instead of nailing the foundation of a building vertically deep down into the ground, if it would make sense to make multiple buildings share a horizontal foundation.
Things topple when their center of mass moves past their supports.
Think of a square box: if you push it over slightly and let go, it'll fall back onto its original position. But if you push it past 45 degrees (when the center of the box would be exactly over the supporting edge), it'll topple onto one of its other sides.
Therefore, obviously, the wider the base, the harder it is for something to topple.
Unfortunately, that's not how earthquakes cause buildings to collapse. It's not that the earth moves the foundation so far that the building's center of gravity moves past it.
Earthquakes damage buildings by moving the base very quickly. The law of inertia (an object at rest wants to stay at rest) means that though the base moves, the rest of the building doesn't want to. And once the rest starts moving one way, the earthquake is then pulling the foundation the other way. In the worst case, this leads to a positive feedback loop, with each earthquake movement feeding the rest of the building's movement (the so-called "resonant frequency"). This causes significant stresses in the structure, which can damage or even destroy the building if it's improperly designed.
(For an example of how a low-energy earthquake at the resonant frequency is worth than a high-energy earthquake, see this video)
The foundation pylons (caissons) are commonly used for penetrating deep through incompetent strata of soil to reach and embed into hard layers, or in retaining walls, not specifically for resisting earthquakes.
seismic design of foundations are performed according to a geotechnical report of the site prepared by a soils engineer after he thoroughly investigates the site and nearby known fault lines, in collaboration with the geologist, structural engineer, city's grading department, state engineering department.
Because of the grave consequences of catastrophic failure of the large structures, many building departments require dynamic modeling and stress analysis of the foundation and structure exposed to the siesmic spectra of the 50 year anticipated earth quake.