Q:

Can the brain detect the passage of a neutrino?

On a few occasions either in bed or sitting around a fire, with my eyes closed, I rarely but sometimes see a very quick fast flash of white and then, with my eyes still closed, the flash disappears immediately. It happens so fast that I sit up and rethink if it was even real. But I know it is real because I have had it happen to me many times in my life. I have also asked other people if it happens to them and 4/5 replied back saying that they had experienced the flash before.
Is it possible for a neutrino to pass the brain and in response produce the white flash? After all the brain is made of 73% water and neutrino detectors are predominantly water. 
I tried submitting this question on biology.stackexchange and I was told that questions like these belonged on the physics.stackexhange site.

A:

The cross-section for neutrino interactions is energy dependent.
For solar neutrinos at $\sim 0.4$ MeV, which would likely dominate any neutrinos likely to interact (the cosmic background neutrinos have way low energies) , the cross-sections are $\sigma \sim 10^{-48}$ m$^2$, for both leptonic processes (elastic scattering from electrons) and neutrino-nucleon interactions.
The mean free path of a neutrino will be given by $l \sim (n\sigma)^{-1}$, where $n$ is number of interacting target particles per cubic metre and $\sigma$ is the cross-section.
If your head is basically water with a density of 1000 kg/m$^3$, then there are $n_e = 3.3\times10^{29}\ m^{-3}$ of electrons  and about $6 \times 10^{29} m^{-3}$ of nuclei.
Including both nucleonic and leptonic processes, the mean free path is $\sim 10^{18}\ m$.
So unless your head is 100 light years wide, there is little chance of any individual neutrino interacting with it.
This is only one part of the calculation though - we need to know how many neutrinos are passing through your head per second. The neutrino flux from the Sun is about $7\times 10^{14}$ m$^{-2}$ s$^{-1}$. If your head has an area of about 400 cm$^2$, then there are $3\times 10^{13}$ neutrinos zipping through your brain every second.
Thus is we take $x=20$ cm as the path length through your head, there is a chance $\sim x/l$ of any neutrino interacting, where $l$ was the mean free path calculated earlier.
This probability multiplied by the neutrino flux through your head indicates there are  $6\times 10^{-6}$ s$^{-1}$ neutrino interactions in your head, or roughly one every two days. 
Whether that would produce any perceptible effect in your brain needs to be shunted back to Biology SE. If we require it (or rather scattered electrons) to produce Cherenkov radiation in the eyeball, then this needs $>5$ MeV neutrinos and so the rate would reduce to 1 per 100 days or even lower due to the smaller number of neutrinos at these energies and the smaller volume of water in the eyeball.
EDIT:
In fact my original answer may be over-optimistic by an order of magnitude since water only acts as a good detector (via Cherenkov radiation) for neutrinos above energies of 5 MeV. Solar neutrinos are predominantly lower energy than this. My calculation ignored atmospheric neutrinos which are produced in far fewer numbers (but at higher energies $\sim 0.1-10$ GeV). The cross-section for these is 4-6 orders of magnitude higher, but I think they are produced in so much lower numbers that they don't contribute.   
Conclusion It doesn't have anything to do with neutrinos. The rate would be too low, even if they could be perceived.

A:

If you are that fast in detecting light, you are seeing cosmic ray muons. They are charged and leave an ionizing track in anything they cross and  Cerenkov light. in liquid, and the eye is mainly liquid. 

They are the most numerous energetic particles arriving at sea level, with a flux of about 1 muon per square centimeter per minute. This can be compared to a solar neutrino flux of about 5 x 10^6 per square centimeter per second. 

Even though there are a lot more neutrinos they do not generate photons to first order so as to be detectable in bubble and spark etc chambers, and therefore not even to the eye.
The easy creation of cloud chambers showing muon tracks is recorded on several YouTube videos .
With such a chamber, you could have your eye under the cup and have a friend check for coincidence with one of the tracks coming in, to verify the sharpness of your light detection. :)
Edit after googling:

It is proposed that the primary cosmic radiation is responsible for the light flashes observed by astronauts in translunar flight. Cherenkov radiation may be an important or even the dominant mechanism. An alternative mechanism is the direct excitation of the retina by cosmic ray particles.

And then I remembered a story told me by an oldtimer physicist at those early times of high energy physics experiments where physicists controlled the beams: he would center the beam to his detector by the cerenkov light in his eye. Possibly no connection was made with radiation and cancer at those times, and the beam fluxes were not as strong  as the beams  we currently have. (just recalled that I asked about it and he did the centering with a very weak beam.)
The retina excitation part cannot hold for one off cosmic muons.  One would not see a flash, just a point would be excited by the ionization which only travels microns.

