What Powers of 2 has to do with family photos

Yesterday, when Aaron was getting ready for bed, he asked me if he had 2048 great-great-great-....-great grandparents.  I lost track of the greats, but I recognized that 2048 was a power of 2, I just didn't know which one.  He told me he'd said 13 greats. I assumed his question was based on something Thom had told him.  So at lunch today, I got out a sheet of paper and created a chart like this to see if I could answer his question:

For each line, I wrote the left-hand side and then the power of 2.  But after I did the Grandparent line, Aaron told me the total.  We got to nine Greats Grandparents which was 2048 and he realized it was 9 greats, not 13 and it was 2 to the power of 11.  I think he miscounted and was thinking 2 to the power of 13 was 2048.  Since we still had room on the paper, I figured 10 greats was a good stopping point and he figured out what 2 to the power of 12 was after asking me and not waiting for an answer. 

I'm not sure, but I guess he was doubling the previous number.  He was doing it in his head, so that's pretty good, but I don't think he was calculating powers of 2.  He may have had them memorized from working on powers of 2 with Thom, but he did seem to think about it like he was doing some kind of mental calculation.

After lunch was quiet time for him.  He took the sheet of paper I had written this on at lunch.  He complained that my writing was too fancy and he couldn't read it very well.  I explained that it wasn't fancy, it was just messy.  But he took it to the couch with him for quiet time anyway.  Exactly when quiet time was over, he came to me with the sheet of paper and wanted to sit with me and look at it.  We talked about it again and he pointed to the 4 circles on line 3 and he said the ones under the circle designated as me were his grandma and grandpa.  And then he pointed to the circles under Thom and said those grandparents had died.  So I got pictures off of the shelf of Thom's parents.  And then he wanted to see my parents' wedding photo. 

And then he asked me if one of the circles was Alan.  We don't have any Alan's in my family so I was confused.  And then he clarified that he meant the one whose tummy Grandma had been in.  That would be my Grandma Helen.  I happened to have a picture of my grandparents on the shelf, too, so we looked at them and then I got out some wedding photos and showed Aaron pictures of his aunts and uncles on his dad's side as well as another picture of his Grandma Lillie.  There were also a couple of cousins from his dad's side that he hasn't met.  He was fascinated by all the pictures and wanted to refer back to our chart.  But I pointed out his aunts and uncles aren't on there, just parents and grandparents and great grandparents.

I'm frequently amazed with how his mind works.  And how a lesson on the powers of 2 turns into a family tree discussion.  I think I will try to make this chart for him with photos instead of circles next.  And maybe another family tree showing aunts and uncles, too.