I've been away for a couple of weeks, and it's amusing to read the discussions now I'm back.
There's a "truth" in music - don't ask classical musicians/composers to talk about improvisation, let alone do it, because mostly they don't have any idea what it really is.
I suggest you all first admit that you're totally ignorant about it.
Then listen to some music where improv is a way of life rather than just something extra to do because you're bored with following the notes. Start with Jazz - Diana Krall, Art Tatum etc, etc ..... Then try some Blues - Bessie Smith, B. B. King, Eric Clapton ('Rock me Baby' on the album Deuces Wild), Ben Harper, etc, etc ...... Follow that with some Gospel - Mahalia Jackson, Aretha Franklin etc, etc.
Then talk to some good Jazz/Blues musicians about improv.
Then come back and have your discussion, based on knowledge rather than ignorance.