Ok! I think of linear and non-linear in terms of visual-spatial (non-linear) vs. auditory-sequential(linear). I think we tend towards the visual-spatial at this house, so I've done a bit of reading about visual-spatial learners and how to challenge and reach them best. I like this list of visual-spatial vs. auditory-sequential learner traits.
http://www.visualspatial.org/Articles/appendc.pdfI do think you can be a blend and nuture both sides.
And chess has been a great game for my son!
On the reading - my son went from not reading books (he would read signs, labels sometimes) to reading long stories in a matter of months (which is a very visual-spatial way to learn to read) he never memorized books because he never had the opportunity to do so. Well, he had some board books memorized before 3. But my DD3 does memorize books quickly. We never had early readers for DS until it was too late. I was under the impression preschoolers couldn't and shouldn't read (silly me). DD's not a super strong reader, but I suspect it will come all at once like with DS. Who is reading at jr. high level in 1st grade. DS is a pure sight reader, as is DD, who knows her phonics but doesn't use them except to maybe identify what letter something starts with.