Originally posted by zuikoholic ... the 'purpose' of photography - to document or draw how we see the world ...
That may be A purpose. It is not necessarily THE purpose. Other purposes include art-entertainment and persuasion-propaganda. But that's another can of worms.
But I digress. Ultrawide photography can be done carefully or carelessly. Carefully, if you want to frame an exact image. Carelessly, if you're just trying to grab a context for later cropping. IMHO fisheye lenses require more careful composition than rectilinears. I can (and do) walk down the street with the 10-24 set to 15mm, shoot from the hip, and get images that can be nicely cleaned up. A fisheye is much more problematic. All those converging lines...
And human vision is more complex than any single lens. Our visual systems do MUCH work to filter, stitch, shift FOV, auto-compensate for changing light, fit photons into patterns, etc. And psychologically, we may only see what we expect to see. Cf the gorilla-on-the-basketball-court experiment. So we can only roughly equate any lens to what we see. My mantra:
What we want to see, what we think we see, what the camera sees, and what is really there (if anything), are not the same.
Right now, I see it's time for dinner. Oh boy, more BBQ...