Counter example: The universal icon for "play", as in to play a movie, is a right facing arrow. It is not a visual analog of anything, since playing a movie is an entirely abstract concept.
The same is true of rewind, pause, and most other controls on a VCR.
Having two icons next to each other, one that looks like a "+" and the other that looks like a "-" indicates a set of controls for increasing and decreasing. Again, these are icons that are not visual analogs of anything; they're entirely abstract.
The fact that a lot of icons are visual analogs is merely for convenience sake. Having a button that looks like an open door helps communicate to people, who've never been taught what that icon means, that this is probably a button that opens a door. That's more convenient than having to educate all users that a completely arbitrary symbol means "open a door".
But, as I mentioned with the VCR control examples, if the thing you're trying to represent doesn't have a visual analog at all, then you just have to design something arbitrary and explain it to people until it becomes common language. Much like a heart symbol.
Of course it is.
The very reason it's called an "arrow" is because it is fundamentally a visual analog of a physical arrow, which moves linearly through space.
Note that the icon to go backward is an arrow pointing the other way.
Now, the stop button is more of an abstraction, to be sure.
"one that looks like a "+" and the other that looks like a "-"
+ and - are text, not icons. Written mathematics is a form of text.
Yeah no abstraction there. Moron.
"Moron", indeed.
Nope. Icons are direct visual analogs of the things represented. There's just one layer of abstraction: thing -> picture of thing. An icon, at least in principle, looks like the thing represented (or at least like some important property of it).
That's feasible for "save" or "center the text", but starts to get pretty damned hard when it's something like "Earl Warren's opinion in Brown v. Board of Education".
Western text, by contrast, is a visual representation of the phonemes in the verbal representation of the thing.
Thing -> audio of word representing thing -> phonemes making up that word -> text.
There are at least two more layers of abstraction involved, with all the additional power that implies. The word "horse" has virtually nothing in common with a physical horse.
Another important difference: a literate person can immediately write down any word that can be spoken, and any other literate person (who has learned that same character set) can immediately reproduce the original spoken word.
(I'm assuming, arguendo, that we're using the IPA alphabet or some other character set that tries to cover all the world's phonemes in an unambiguous manner).
Icons, by contrast, have to be designed. Good ones take a lot of thought and artistic skill to create, and even then they are notoriously prone to misinterpretation or outright user bafflement.
'Text can be just as bad. Imagine reading "subtract b from a and divide that result by q" versus "(a - b) / q". The latter is a more efficient language which most everyone will understand. Better to use the latter.'
The latter is still text. It's just using a different written language. It is a compact representation of "subtract the second thing from the first thing and divide the result by the third thing". How on earth could you represent that using icons? It seems like it would be quite a challenge.