I'm not embarrassed to admit I just tried this. I will walk around with thumbnail oriented thusly and make my observations. Perhaps the origin of the thumbs up? If anyone asks I will casually explain that I'm reducing my thumbail cross section to minimise the unknown effects of solar neutrinos.
Good question! I can't find a truly authoritative source, but a few calculations on the web put photon flux at the earth's surface at 10^21/m^2/s, give or take. Assuming your thumbnail is one square centimeter, that would be 10^17 photons per second, or 100,000,000,000,000,000, but only during the day :)
One follow up question. When reading about low-light cameras, the number of photons per pixel seem much smaller. I guess the following factors are involved:
Several orders of magnitude reduction under low light.
The same problem is faced by optical communication during the day with the sensors exposed to sunlight. SNR can be increased a fair bit with even slight directionality. If sensitivity of detection is one day high enough, I think it would be theoretically possible to obtain directional information about neutrinos, by building a whole network of sensors and synthesizing an aperture.
For conventional electronic and optical purposes this isn't a huge deal. You "just" modulate the signal to be transmitted onto a fixed-frequency carrier, and have the receiver ignore everything that's not a sideband of that particular carrier frequency.
It's one of those cases where "just" really does apply. IR remote controls work this way, using a slow bitstream to key a 40 kHz carrier that drives the IR LED. Scientific applications that need even greater sensitivity can take advantage of the fact that the expected phase of the carrier is known as well as its frequency. Devices called lock-in amplifiers are used to run a wide variety of experiments and processes using that principle.
Doing this stuff with neutrinos rather than photons, however, is one of those * * * * * exercises that the textbook authors put in as a joke.
"If the sensitivity gets high enough" is the big if to my conjecture. We may never be able to detect enough neutrinos to be reliably detect multiple coming from the same source passing through multiple detectors.