Tjyylli

If you shine light on a wall, what will be seen is a "patch" with constant intensity. However, if light is viewed as a wave, then it is oscillations of the electromagnetic field changing from 0 to the amplitude and back really fast. So my question is, if I were able to look at the world at extreme slow motion, a quadrillion times slower or so, and I shined a beam of light at a wall, will I see a "patch" with oscillating intensity, with maximum brightness at the peaks of the wave and minimum when the field is 0? If so, is the constant brightness seen normally just our puny mortal eyes capturing only the average of this oscillating brightness?

You would need a coherent beam, because in waves it is not only intensity but also phase that makes a difference. In an incoherent beam, as sunlight, you would not get any changes in this thought experiment, because the average intensity would hold even at wavelength distances.

In a coherent laser beam you should see in your thought experiment what is shown towards the end of this youtube video,(at 2' 09") the sinusoidal in time pattern of impinging intensity . The video draws the oscillating electric field E, and the intensity left on the screen will be $=E^2$, which will also be oscillating in time.

After all, mathematics allows us to materialize thought experiments as this one.

All depends how you "look" at the light.

For example, in a linearly polarized EMW the electric and the magnetic fields oscillate like $sin(omega t)$ or $cos(omega t)$ at a given point of space. Then the question is: what device do you use for "detecting" the EMF?

For EMF there are two notions expressed via fields: it is the energy density $ propto E^2+B^2$ and the energy-momentum flux $ propto vec{E}timesvec{B}$ which may oscillate or not at a given point, depending on their phase shifts.

Some devices deal with a light "spot", where there are many points of the space involved, so you must average (sum up, integrate) local things. Some devices have inertial response and effectively average over time the incident wave too.

However, some devices are much more sensitive to the electric field than to the magnetic one (photo effect, for example), so they clearly "feel" oscillations.

There are also some devices (magnetic antennas, for example) that are more sensitive to the magnetic field (some radio-receivers).

In other words, the incident fields get into the equation of motion of the detector charges and currents, and the detector features determine what you get in reality.

The EM field strength in a linearly polarized, coherent light wave does indeed cross through zero in between + and - peaks, just like the surface of a pond goes through its natural rest height in between going up and down as ripples go by. If you slowed the wave down, you'd change its frequency, which is the same as changing its color. You could change from blue, to red, to infrared, and all the way through radio waves and other invisible colors. So no, you could not see the EM field changing as a flashing light for a slow wave (the slow changes couldn't simulate your vision receptors) , but you could set up an electric field meter and measure the change in field as the (no longer visible) wave went by. What does it really mean for the field to cross through zero? Not much; just like having the surface of a pond cross through its equilibrium height doesn't mean the ripples are gone, neither does a moment of 0 electric field mean the light wave is gone.

"Light intensity" in my opinion means the number of optical photons absorbed by a light detector. Such detectors resonate with the electric field and absorb the photons with a characteristic time of many periods of oscillation. So you can say that the oscillation is observed by the detector, but is not translated into a rapid oscillation of the detected intensity. The latter varies with the number of photons absorbed instead, which is at a generally much longer timescale. However, extremely short laser pulses can approach the timescale of the light oscillation period.