Busy night on this thread!
Chris:
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My comments meant no offense, nor are they "educated". But just my personal view and reaction about photographs and paintings.
Here are some observations:
1. Each medium has its own attributes that the other cannot match.
2. There are creators of one medium striving to emphasize or make use of such attributes so that their work are distinct from the other medium.
3. There are creators of one medium attempting to emulate the other medium.
Thanks very much for elaborating. In my case, I believe I'm mainly in category 2, but now & then I'm tempted by category 3 for particular images that I believe would be made more interesting by it (which is what prompted this thread to begin with). Unlike most established photographers, I don't have a "personal style"; I prefer to be constantly experimenting with various different styles (and I don't mean emulating other photographers, I mean trying for different effects in my own photography). I don't sell my photos, so I have no need to cater to the market, only to my own entertainment.
Ray:
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It doesn't have to be like the other in all respects. There just has to be something about it which is unphotographic (in the case of the photograph looking like a painting) or 'photographic' (in the case of the painting looking like a photo).
Generally, any painting that pays special attention to accurate perspective, fine detail and realistic proportions and color, will be considered photographic.
Any photograph that blurs or distorts definition, exaggerates color and 'looks' a bit of a mess , will generally take on a painterly effect.
Right on. I think this is the best summary of an answer to the original question so far, though I would replace the "and" in your last sentence with "or".
BTW, I love your waterfall photo. Gorgeous! (Though in the small web image, I don't particularly see the painterly effect. However, it may come through in a large print; my image #3 does that too, I realized after I included it here. The surface texture on the farther buildings looks "smeared", with less detail than expected.)
Dale:
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We know as photographers that we are all too often in a race against the motion of a cloud or the setting or rising of the sun, etc. to set up and get in one or more shots. Imagine, then, how that is for a painter. If the magic that caught your eye depends on a passing cloud, a painter can often hardly sketch in a few lines before the scene has radically changed. Painting is in its natural element when exploring an inner landscape of the imagination; to the degree that the painter wants to record an outer landscape she is swimming against the current. For the photographer it's pretty much the reverse.
Interesting observations from the standpoint of a painter. I would think, though, that even if the moment is fleeting, the painter would still have the scene in his/her mind's eye (perhaps even with some optional improvements), so that it could be reproduced at leisure, a luxury that photographers don't have. Or doesn't it work well that way in practice? Or is that what you're sort of implying later in the paragraph? It wasn't clear to me.
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Painters have quite a few options too, and if a painter opts to work in a representational style she has the option of projecting a slide onto the canvas, sketching the outlines, then using the slide as a colour reference.
I have to laugh.

That's exactly what I did in high school art class, since, as previously mentioned, I can't draw (though I did take great artistic liberty with the colors). Thank goodness for technology!
Lisa