Does "playing by ear" mean "playing by memorizing"? I haven't heard a good definition of playing by "ear".
Let me ask you this: Is there not a rather simple song, a song you really like, and can hear it in your head, parts or the whole thing?
I'm sure the answer to that question is yes. Can you take parts of the melody and find the keys to make it sound as such. Probably yes again. Then, when you get good, the chords as well?
When you listen to a song can you not hear harmonic changes? At this point it doesn't matter really whether you know the chords but rather just having the ability to say, yea, it changed, I can hear that. If you can, you are hearing the chord progression or chord changes like a simple song with C F and G. That's a progression and is also 3 of the 7 chords in a diatonic system which most songs are built from.
In the beginning, playing by ear is about "LISTENING" and finding those notes and chords on the keyboard and recognizing them as sounding right compared to what you hear in your head or from a radio, etc.
The memory of doing this is in your head first. Remembering how to play what you figured takes repetition just like anything else. First, the sound of the music must be in your head first regardless of whether you understand it or not.
THEORY:
What "Theory" gives you is this: The understanding of "Structure", of a chord progression and much more of course. You will begin to recognize structure just from listening and it makes playing by ear a whole lot easier. All music has structure and you will become surprised just how common structure can be with most music.
Remember on thing: Music is relative. Many songs are built on the same progression. Here is an example of what I'm talking about:
40 songs using the SAME 4 chords. You tell me what the chords are. I already know.
https://www.youtube.com/watch?v=5pidokakU4I
