Root Privileges

Unto the canopy termini

In the middle of a conversation this morning, my friend wondered aloud as to whether there were any advantages to teaching history forward in time (i.e. with causality) instead of backward. Neither of us being historians… rather, both of us being far too quantitative in our thinking to be able to reason like historians at a moment’s notice, there was some back and forth for a few minutes during which we dwelled mostly on the awareness of presentist biases, anchoring, etc.

The debate was eventually settled when I likened my principal contention – of being able to cognise and record dominant and non-dominant narratives alike – to the parsing of non-linear data structures in computer science. I was quite pleased with myself for having realised this metaphor so quickly. However, I describe it in some more detail below to invite my readers to point out any flaws in my argument and/or, more importantly, provide other arguments in favour my contention against my friend.

Linearly ordered data can be indexed as a straightforward series of values. But when it is ordered in non-linear fashion, there is more than one way to read the values. The simplest example of such a structure is the tree, and the process of indexing the values therein is called tree-traversal.

In other words, tree-traversal refers to the way you move through a tree, top-bottom or bottom-top, from branch to branch such that you traverse all branches sans jumping and in as few steps as possible. For example, in the tree shown below, you can move in the following ways:

• 1 2 3 4 7 5 6 8 9 10 11
• 1 2 4 5 6 7 8 3 9 10 11
• 1 2 3 4 7 9 5 6 8 10 11

… etc.

In these three instances, I’m imagining myself to be an algorithm switching through nodes from the bottom (roots) to the top (canopy), equating this orientation to the direction of time*. If I were to represent the algorithm as an ant moving along the tree, then the first sequence could be delineated thus: 1-2 2-1 1-3 3-1 1-2 2-4 4-2 2-7 7-2 2-4 4-5 5-4 4-6 6-4 4-2 2-7 7-8 8-7 7-2 2-1 1-3 3-9 9-10 10-9 9-11. In turn, it would comprise the following sequence of orientations (f for backward, b for backward): f b f b f f b f b f f b f b b f f b b b f f f b f.

Now, instead of an algorithm, if I were commanding a group of historians, would I be able to traverse all branches of this 1-11 tree by forcing them to either always move forward or always move backward (without jumping)? It’s obviously possible to do this if you started at the root with as many historians as the number of terminal nodes and always moved forward. At each fork, two historians would walk down the two branches. If one of them reached a terminus, she would call back and no other historian would walk down that branch. If one of them reached another fork, should would call back and another historian would come forward.

But if you tried to do this backwards – from canopy to roots – with as many historians as the number of canopy termini, then all of them will miss the unnumbered terminus off of node #3. The only way to get there would be, after recognising the presence of a fork, to send one historian forward along that branch, which act in turn will break the rule about always going backward.

The canopy termini, in my metaphor, stand for contemporary events tethered to historical narratives – the branches in the tree – that have survived intact or modified but nonetheless unbroken from a predecessor event. The unnumbered terminus is a narrative that has no present-day representation and therefore cannot be discovered or elucidated as such if one were to only work backwards in time from today.

In fact, the only ways such narratives would get unearthed were if historians (or get taught if teachers), including in the form of palaeontologists and archaeologists, came upon (or introduced) material or immaterial fragments of information that didn’t fit into any prevailing paradigms of the time. However, this means one has to rely on accidents or, worse, the beneficence of those tasked with interpreting (or unpacking) such information – which is always a bad proposition.

*And assuming that divergence increases with time.