Sunday, March 27, 2005

Last night I dreamt of trees...

of data, trees of reality.

To begin, yesterday I spent a good part of the day working on my latest project which combines learning Python and brushing up on some basic data structures, such as Binary Trees. Maybe "brushing up" isn't a good way to describe my intentions. I am not satisfied with knowing that I can code up a Binary Tree whenever I care to. What I am looking for is a visceral, deep, intuitive understanding.
I coded up an AVL Tree which is a balanced Binary Tree. In order to test the tree, I had to come up with some specific values to insert and then determine the resulting tree. This work was done, not on a computer, but with pen and paper. After several hours of sketching trees, I was suddenly struck with the limitation of the Binary Tree. As the tree is traversed from root to leaf, branches of the tree are eliminated from consideration. All that matters are the options that lay ahead. This is what makes Binary Trees so powerful for searching, but not so great for modeling activities. In real life, branches that connect nodes of existence come and go, seemingly at random. Nodes are connected and removed due to past-events and probablities. We seem to have the ability to skip around the tree of reality, to teleport amongst its various nodes.
But reality is a Binary Tree. Consider the effect of time on reality.
Time delimits and defines reality. Choices are made, paths are taken. We don't have to concern ourselves with options on paths we are not on. Reality is a Binary Tree, could you imagine otherwise? The choices we make resolve to a path, which in turn resolves to a line. The time-line.
I looked at the smallest of Binary Trees, three nodes, one of which was the parent with its two children, and saw infinite possibilities. I looked at a main branch of a large tree and, even with all of its sub-trees to consider, all that came to mind was the removal of possibility, the refinement of the real.
So I went to sleep last night and I dreamt of trees. Elements of life, connected by branches now seen.

1 comment:

David Smith said...

I didn't know how to send you an email, but I wanted you to know that your post on Don Box's blog was hilarious. =)