Nested parentheticals

Sometimes it’s hard to get back on track. People tell stories and construct arguments with subplots and digressions. It’s fine for stories to wander. But for coherence we expect the story-teller to return to the main point, to rewind the string they just unravelled back into a neat ball.

One of Trump’s improvised speeches illustrates this unravelling. Vox reporter Tara Golshan recounts a key paragraph in a Trump speech explaining why the so-called Iran nuclear deal was bad for the United States. Here’s my (faltering) paraphrase.

The development of the nuclear industry in Iran is a challenge for the world. My uncle was a physicist at MIT. Our family has good genes. If I was a Democrat, people would say I’m one of the smartest people in the world. I have to tell people my academic credentials as Republicans are at a disadvantage. …

The narrative of each clause is so far open ended. (…(…(…(…(…

We require the narrator (Trump) to close the brackets on each nested digression, and in reverse order, i.e. the relevance of being a Republican to claiming academic credentials, why the claim here to being smart is needed, the relevance of his uncle, and how this all justifies why the Iran deal is bad for the United States and the world.

Nested stories like this may be suspenseful, but are unsatisfying until closed off: (…(…(…(…(…)…)…)…)…).

If the nested parentheticals go too deep then it’s hard for both the speaker and the listener to recover, to return to the top or outer level bracket. (See an attempt to diagram the Iran speech by Lucy Ferriss.)

Conversations may also show nested parentheticals. In a friendly conversation, consultation or interview the interlocutors may help one another get back on topic by attempting to close off each other’s various trailing brackets, or of the arc of the entire conversation. It gets complicated.

Stacks

In their 1979 book Gödel, Escher, Bach: An Eternal Golden Braid, Hofstadter and Dennett talk about stories in this way. It’s another example of recursion: nested stories bracketed within stories. Hofstadter and Dennett understand such stories as stacks.

“the terms ‘push’, ‘pop’, and ‘stack’ all come from the visual image of cafeteria trays in a stack. There is usually some sort of spring underneath which tends to keep the topmost tray at a constant height, more or less. So when you push a tray onto the stack, it sinks a little-and when you remove a tray from the stack, the stack pops up a little” (136).

The customer can only ever take the top tray. Stacks are not unique to cafeterias. My browser software maintains a stack of interlinked websites I’ve visited. Hitting the return arrow button takes me back down the stack. The undo function on most text and image processing apps does something similar. A stack is a way for the software to keep track of a series of nested (recursive) computer events.

City stacks

The stack is also a useful metaphor for understanding the spatial organisation of cities. Builders stack elements on top of one another, e.g. bricks stored on a construction site. You can’t get to the bricks at the bottom of the stack until the bricks above are removed. Though less mobile, urban layers are stacked and accreted on top of one another over time, even down to archaeological strata.

Such strata are not as neat as cafeteria trays. It’s easy to undercut the order of a stack of bricks, or tunnel through the layers of a city — as it is to circumvent the bracketed elements of a narrative, and leave them dangling (to mix metaphors).

Precise, algorithmic stacks are the way that computer programs manage navigation through recursive algorithms. A stack is a data table that keeps track of the stages in a recursive process.

Many programming platforms, such as Prolog and Lisp, use stack-like data structures to accommodate recursion, and hence provide the means of searching a problem space, such as the best route through the city, i.e. exploring a tree of decision points. See post: Recursive cities.

Recursive cities, again

They don’t mention stacks, but in their 2007 book chapter “Imagining the recursive city” Michael Batty and Andrew Hudson-Smith explained how we can think of the city in terms of recursive structures. 

“In cities for example, evidence of recursion might be seen in the physical patterns of its development where certain modules repeat themselves in different places, at different times, evidence enough of similar processes at work. But recursion may not show itself physically. The way populations in cities behave in space and time, the way individuals, groups, institutions organize their activities, the way economic and social functions determine modes of living and work can all show evidence of such patterning” (39).

In so far as cities exhibit recursion, they also display characteristics of the stack. Stories are an essential part of our experience of the city, which takes me back to the start of this post — the stories people tell.

Excursion and return

Each nested plot event provides a context for the one nested within it, which in turn informs the events outside the brackets. That accords with the leitmotif of excursion and return popular in theories about play, tourism and interpretation.

“Essential to play is the freedom of movement to and fro, back and forth, up and down the field — the repeated circular movement of excursion and return that is under control of neither the individual players nor referees but belongs to the playing of the game” (104).

That’s another link with the city: the city is recursive, meaning it’s a place that invites return — through travel, narration, recollection and imagination. But the return is never a simple algorithmic return, as in a recursive algorithm. The traveller is transformed in the process, and the city is transformed, like the meanings accrued by nested parentheticals in an interesting story or coherent speech. See post: Oblivion.

References

• Batty, Michael, and Andrew Hudson-Smith. 2007. Imagining the recursive city: Explorations in urban simulacra. In Harvey Miller, J. (ed.), Societies and Cities in the Age of Instant Access. Dordrecht, The Netherlands: Springer, p.39.
• Ferriss, Lucy. 2015. Diagramming Trump. The Chronicle of Higher Education, 7 August. Available online: https://www.chronicle.com/blogs/linguafranca/2015/08/07/diagramming-trump-2/ (accessed 9 November 2019).
• Golshan, Tara. 2017. Donald Trump’s unique speaking style, explained by linguists. Vox, 11 January. Available online: https://www.vox.com/policy-and-politics/2017/1/11/14238274/trumps-speaking-style-press-conference-linguists-explain (accessed 9 November 2019).
• Hofstadter, Douglas R., and Daniel C. Dennett. 1979. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books.
• Weinsheimer, Joel C. 1985. Gadamer’s Hermeneutics: A Reading of Truth and Method. New Haven and London: Yale University Press

Note

• On stacks, also see post Romancing the blockchain.