Physics plays a role in answering your question and that information is out there. The basics from that linked discussion are that the index of refraction of the lens material will affect the maximum aperture you can achieve, so for pure glass that has an index of refraction of 1.5, the maximum aperture would be f/0.5 or thereabouts. Better substances, such as diamonds, with an index of refraction of 2.417 can give you an aperture of f/0.235 with a corresponding insane cost of ownership (consider just how much a lens of pure diamond might cost). The lensmaker's equation is the basis for the numbers.

As for minimum aperture, you could basically get down to what amounts to an atomic size hole, large enough for one photon to pass through, but that's useless for, well, anything. For a lot of lenses, getting to some place around f/11 or higher results in loss of sharpness as a function of diffraction, so f/32 is about the top out point for 35mm lenses though they can get smaller for larger formats and do so. Pinhole lenses are often in the smaller range, as much as f/177 (Lensbaby has one like this). Still, even if the optics were perfectly able to handle something like this, consider what the ISO and shutter speeds would need to be to get an image, so at some point, the value of this is pretty much zero unless you're into blurry abstracts.