My background is in cosmology and the mathematical aspects of gravitational theory, so I admit my knowledge of fluid dynamics is pretty sketchy. However, condiments are of vital importance to all of us, so I passed her question along to Scott Waitukaitus, the lead author of the original non-Newtonian fluids paper. Unfortunately, Waitukaitus had to answer in the negative: you won’t be able to run on ketchup like you can run on quicksand.
While there is one basic behavior for Newtonian fluids—their viscosity (resistance to flow) is independent of external stimuli—non-Newtonian fluids split into two groups. The first group, which includes quicksand, cornflour suspensions, and so forth, is known as shear-thickening: stirring, which creates shears between the deeper and shallower parts of a fluid, will increase its viscosity. This is why stirring a pudding is necessary to make it “set,” and it is related to the “solid plug” phenomenon described in Waitukaitus’ paper.
Ketchup, however, belongs to the shear-thinning group: perturbations make it easier for the fluid to flow. These fluids become thinner and less viscous when struck, so we won’t see videos of Adam Savage running across the surface of a wading pool filled with ketchup. Such is the disappointment we scientists must face from time to time, but it’s worth it to learn something new.