Nonlinear Writing
Structuring information beyond the paragraph and table of contents
This is the introduction. Composed of sentences, the introduction must create a hook and hint at connections or provide a narrative that will tie together various concepts, which its reader may not have been exposed to. With so many topics to cover, the writer faces a great challenge: how should the information be ordered to convey the information in the way they want?
Ordering a set of things is a combinatorial problem. When lining up N elements there are N! permutations to choose from: N! = N(N-1)(N-2)…(1). An essay with 5 main topics has 5!=120 potential orderings. If you look instead at the number of sentences the numbers get gigantic. Most reshuffles of this post’s sentences wouldn’t turn out well.
What’s the big deal, though?
The structure of every thing we interact with shapes our understanding of that thing. Creating linear news stories implies a simple straight line explanation cutting through the events. Independent concepts (scientific, political, personal) can come to be seen as causes and effects if they are presented in a linear format.
While permutations have a completely defined order, combinations radically expand the number of possibilities and allow for groups of topics to sit at the same conceptual level.
The structure of our writing is by default linear, and this implicit structural framework poses a series of limitations that are not immediately obvious because the format is so familiar. In reality, the world is hierarchical, networked, branched, multivariate:
Cyclic
Multivariate
Networked
Hierarchical
Branched
Tangled
Why Linear?
Chronology
While a story is chronological, meaning each particular line (ie. a character's experience) is linear, the entire story is really the combination of all of these linear pathways. The pathways overlap and connect in various ways and it is the job of the author to create the story and weave these lines in an interesting way.
At a level even before writing, sequences of pictures were used to convey meaning. Hieroglyphics and cave paintings are interpreted for sequence even when it's hard to be certain of the order. In modern days, sequential pictographic stories are called comics. These have been studied in detail for their visual narrative structure by cognitive scientist Neil Cohn. Even having a sequence of pictures is not enough to resolve the structure precisely because history or even a single story is not a single narrative thread but many. Cohn elucidates the role of the filmmaker as parsing a linear time in his 2013 paper Visual Narrative Structure:
Narratives also appear in the visual modality through film. In film, cameras capture events as they unfold in time — just as in perception. This ongoing temporal progression records a single unbounded stream of events from one camera’s viewpoint. Filmmakers then break up this recording into “shots” in the editing process, which combine with other shots to create a novel sequence in which a new temporality emerges (sec. 7.1, paragraph 4)
Cohn goes further to explain that even a single narrative thread can be ambiguous in sequential frames because of the combinatorial possibilities of combining pictures in series or parallel. The serial-parallel dichotomy is the most basic element that makes linearity underpowered for explaining even simple chronological stories without more structure- even before arriving at the problem of limiting the number of “shots” out of practicality.
Of course, in explicit symbolic writing, it’s possible to denote parallel and serial structures with much greater clarity, but in nearly all writing writers proceed to collapse this structure into a series of paragraphs of sentences. In this format, a segment of a story loses the ability to have structural parallelism because paragraphs of sentences always have just one word following another. This collapse of structure into a crumpled line, a paragraph, is simply a larger linear interrupt than switching to a new sentence with a period. Functional improvements in writing structure have improved more, but the basic technique of paragraph breaks wasn’t really invented until around 900 AD (Johnson, 2015, p. 110)! Poetry has continued to evolve and more recently hypertext has emerged, but most writing is still structured only by a table of contents, paragraph breaks, and periods. Today, writers and readers can choose to break the overly chronological linear paradigm with the help of modern technology.
Alternate Narrative Timelines
There are many different ways to weave story lines together that aren’t just a close following of one character or chain of events. For instance some authors will write following the perspective of just one character or switch which character to follow in different chapters. However, the bottom line commonality is the fact that the book as presented to readers structures the entire story in a single line. The extreme opposite case is that of a Choose Your Own Adventure book. In this format the actions undertaken by characters depend on the path the reader takes. This is a branching structure and is representative of how events might unfold in reality. Another alternative is a book where chapters that take place at the same time in the story are not necessarily ordered for the reader. That is, the perspectives of different characters could be read within the context of a single storyline as chosen by the author as opposed to a set of many options in the case of a Choose Your Own Adventure book.
Syllogism
Note: This section was edited to remove my own rather confusing graphics. I’ll eventually return to this topic to try making some clearer visuals of how I imagine stacking syllogistic logic visually (and interactively) from a tabular presentation of a proof.
In scientific writing there's a sense that linearity is inherently connected with logic, however this is a limiting notion since most concepts are multifaceted and branching, requiring multiple premises and lines to converge to a single point. It is critical that there is a direct line from assumptions and axioms to conclusions. However, this is still not strictly linear as many arguments rely on multiple premises that stem from different origins and have a branching structure as well.
Syllogisms are a particular type of proofs and are often presented in a tabular format. Syllogisms are statements of the properties of items in a set and conditions of set membership.
Especially while going to higher depths of sub-statements in multi-syllogisms, the table needs more and more indenting. However, great visuals of set membership and conditional syllogistic logic are available in the hardcore cousins of Venn diagrams.
A proof may be directed at using just one subsection of these complex inheritance structures. It’s clear how quickly theory space expands as more premises are introduced. Each line of a tabular proof points just towards the final result without commenting on the complexity (necessarily!) left aside.
Technical Concept
Another technical writing area is the presentation of a scientific concept. While scientific concepts still have cause and effect, there are many other aspects to consider in explaining a topic. An equation for instance doesn't have an inherent chronology. Each of the terms stand on their own conceptually, and explaining one after another can imply structure that is not strictly part of the definition. Different terms in an equation may be at one level of a hierarchical structure while the components of those terms have their own meaning. Each subcomponent still has its own origin and derivation or story, and together they have a different total meaning. By writing a scientific paper or textbook or article to describe such a topic in a linear/narrative fashion inherently builds in some order.
In explaining a technical concept it is good to start from the beginning and the end. This is true from an engagement perspective and theory perspective where it is desirable to capture the fundamentals. This is part of the detailed argument made by David Montanges and his colleagues in a 2022 paper titled Finding your scientific story by writing backwards. A story sounds linear, but the authors give strong framing for how to work from a pile of unstructured data to a coherent argument. This is about producing the best overall linear path through idea space. The author motivates this as follows: “Writing backwards may seem like an odd concept, but it’s not. Think about telling a joke to your friends. Knowing the punchline is essential.” (Montagnes et al., sec. Writing Backward?). A hierarchical breakdown (which the authors promote mapping visually) is ultimately still in service of the global trajectory of the useful takeaways.
Providing Other Structures
Lectures must be delivered in a single order, but it's important to indicate the structure in the medium through which the information is conveyed as much as possible. This means going beyond the table of contents as the exclusive organizational tool.
Nonlinearity for Learners
An indicator that alternate formats of information are better for communication is the plethora of education research demonstrating different techniques used by students to break information down into smaller parts to reassemble. Most famous among these examples is the Cornell notes system developed by Pauk and Owens in the 1950s (Pauk & Owens, 2010). Cornell notes divide every page in two and encourage a hierarchical and dialectic style that connects the reader.
Linearity Recast as Cyclic
However it is also the case that writing that is attempting to be presented in an objective manner can become too sterile and categorical. According to Julie Davis, a professor of education at Queensland University of Technology, the view of research as an objective, categorical assessment instead of a linear narrative, weakens the understanding of the analysis provided: “After much anxiety and considerable experimentation, I resolved the problem of `fit' between action research and the traditional thesis format by creating an alternative architecture based on each of the action research cycles.” (Davis, 2007). Although Davis frames this as defecting from the traditional research format, she identifies a new version of linearity that gives new meaning: cycles. The cyclical process is a two-dimensional structure as each pass through the one-dimensional research progression overlaps with the previous cycle. This means that the beginnings of cycles can be mapped to each other, and the cumulative result provides a new collective understanding of a work. Davis also emphasized that this is increasingly enabled by the digital nature of the production of theses.
Network
Another information structure is the network. Our modern communication world is defined by the social media networks that exemplify this distributed archetype of information storage. It is not obvious how to extract meaning from a large group of posts based on their time reference and reactions, but the algorithms that recommend this content could actually be said to understand this. New AI models may be able to help sort, visualize, and explain the thinking process or thoughts of a distributed network. It may never be possible to summarize research in a presentable way like this, but utilizing this as data and presenting it in an analogous form instead of an over-compressed linear structure could be highly valuable.
The development of scientific information is a branching, networked structure as alluded to in the Syllogism and Technical Concept sections for problems with linearity. Certain papers create entire branches on the tree of knowledge, while others fill out small details. This was visually demonstrated by one of the premier scientific journals, Nature. For the journal's sesquicentennial, the publication released an amazing, interactive three-dimensional visualization of the graph (web) of citations that connect papers (Gates et al.). This isn’t just interesting to look at. It could be used to look for areas where the branches should reconnect by combining disparate fields.
Nature publications citation graph. Connections by citation, colored by topic. (Gates et al., 2019)
Enabling New Structures
Technical Limitations and Solutions
In order to facilitate changes in typical writing practices, some researchers advocate moving away from word processing technology that is limiting in this respect. It's easier to sketch alternate kinds of diagrams and information structures on paper with pencil than in a word processor. Although text boxes and columns are supported in word processors, these aren’t the default, are difficult to format and have clunky interfaces.
To take the perspective of an academic outside of linguistics and computer science, Joo Hee Huh, an academic in the field of design, provides an analysis of the technical limitation. Huh argues that word processors inherently stifle the scope of creative thinking because they assume the structure is just ready to be received. Expanding a web or brainstorming network in Word is difficult. Huh writes in her thesis The Dynamic Interplay between Spatialization of Written Units in Writing Activity and Functions of Tools on the Computer: “The structure is something that needs to be made, thus, it exists as indeterminate and needs to expand. But, it should have a logical order for the argument. I criticize that the space of Microsoft Word, with respect to all those needs, presents novice writers with one simple structure while spatial and mediated activities are essential.” (Huh, 2012, p. 9). I strongly agree with this point and find the freedom of writing anywhere on a paper to brainstorm and structurally separate points to be extremely freeing mentally.
Some new note-taking tools like Notion and Obsidian support an open canvas architecture where you can insert links, images, videos, tables, or sub-pages anywhere on the screen (Notion). Every paragraph is an entity, not just a particular subset of the linear text. This means that you can drag and drop or collapse a paragraph or link to it from other locations. The intrinsic understanding of informational units and support for building simple hierarchy makes the organization faster and clearer.
Beauty of Hyperlinks
The earliest great digital tool in enabling more nonlinear writing was the hyperlink. Hyperlinks provide active, recursive, unintrusive connections between concepts and allow for simple expansion of hierarchy all the way to representation of complex network spaces that map high dimensional connections between ideas. Citation of sources is really the key technique of course. Other related techniques include footnotes and endnotes, but bound books, let alone papyrus scrolls, aren’t the most convenient to use with these! Hyperlinks allow for a piece to be written normally/linearly while providing structure and references to external sources in place. These can link to others and inherently represent the branching and networked nature of information. Wikipedia exemplifies the power of this modality and even provides previews of links in-line while reading an article. This greatly amplifies the ability to understand more topics and the network of ideas that make up a complex topic. Other websites are limited in their ability to do this by copyright (while Wikipedia is composed entirely of openly available material). Additionally, most websites have a direct disincentive to providing useful hyperlinks. Specifically, websites are trying to retain you for viewership.
Beginning as early as the 90s hypertext systems were already evolving around the use cases of scholars and literary fields. Contributions to study in literary fields or Advanced by academics working primarily from hard technical fields. Stephen DeRose is one such computational linguist who advanced these systems, characterized different types of linking in great detail, and identified the applicability of the technology to study in highly text based classics fields in the 1989 ACM conference on Hypertext:
Research in the humanities, particularly in text-oriented fields such as Classics and Religious Studies, poses particular challenges to hypertext and hypermedia systems. The complex set of primary and secondary documents form an intricate, highly interconnected network, for the representation of which hypertext is ideal. (p. 1)
Now that computers have greatly advanced, the technological limitations identified by DeRose and others are no longer present. This finally will allow for hypertext to achieve its full potential in expanding text into the network that allows writing to carry meaning and why it is often complicated to tease apart.
Auto-Linking, A Proposal
I would like to return briefly to what I consider the fundamentally strange thing about English (and most languages): the structural connections between words are not drawn out. Sentences follow a format that includes consistent elements like subject and predicate, nesting elements like objects, and a hierarchical structure. This structure is drawn out for instructional purposes at times, but never reappears in “real life.” I was unable to find academic studies regarding the benefits of including this highlighting/diagramming, but I have to imagine that it could be a help, perhaps for those with dyslexia. One answer for the absence is that it would be time consuming to produce. However, powerful software tools have been developed to parse language like the Stanford Parser from Stanford University (The Stanford NLP Group). Other tools built on top of this model allow for active highlighting of the parser’s breakdown. While this tool was methodically developed from English grammar rules, new systems like OpenAI’s GPT models have learned the English language by digitized osmosis (OpenAI, 2023).
To create a truly structural writing tool, I would build on top of the base of something like Notion/Obsidian for the construction of paragraphs as entities (Paragraphs remain an effectively-sized chunk/idea and would be the smallest unit of purely linear content). The key addition is a parser that highlights not the connections within a sentence, but the ideographic connections between paragraphs arranged in space (like the Nature citation graph or Stanford Parser output scaled up). This addresses the limitation of hyperlinks that is that they don’t show you where you are going in relation to where you are coming from. I call this technique Ideographic Auto-Parsing and would like to develop this as a technology after graduation.
There is a huge amount more to discuss in the matter of nonlinear writing in poetry, code, song, and more. Even in this essay I was limited to heading hierarchy as my primary nonlinear tool. I would also have liked to put the sub-headers on truly equal footing instead of choosing an order for them at all. I intend to keep developing this idea and plan to release a new incarnation of this blog in a way that uses all the techniques here more. For now, you can already go out and use the tools of nonlinear writing to report events more honestly, explain complex concepts more clearly, and understand the world more deeply.
Bibliography
Cohn, N. (2013). Visual Narrative Structure. Cognitive Science, 37(3), 413–452. https://doi.org/10.1111/cogs.12016
Davis, J. M. (2007). Rethinking the architecture: An action researcher’s resolution to writing and presenting their thesis. Action Research, 5(2), 181–198. https://doi.org/10.1177/1476750307077322
DeRose, S. (1989). Expanding the notion of links. Conference on Hypertext and Hypermedia: Proceedings of the Second Annual ACM Conference on Hypertext, 249–257. https://doi.org/10.1145/74224.74245
Gates, A. E., Ke, Q., Varol, O., & Barabási, A. (2019). Nature’s reach: narrow work has broad impact. Nature, 575(7781), 32–34. https://doi.org/10.1038/d41586-019-03308-7
Huh, J. H. (2012). The Dynamic Interplay between Spatialization of Written Units in Writing Activity and Functions of Tools on the Computer (Order No. 3520852). Available from ProQuest One Academic. (1034721600). https://www.proquest.com/dissertations-theses/dynamic-interplay-between-spatialization-written/docview/1034721600/se-2
Johnson, G. M. (2015). The Invention of Reading and the Evolution of Text. Journal of Literacy and Technology, Volume 16, Number 1: May 2015. http://www.literacyandtechnology.org/uploads/1/3/6/8/136889/jlt_v16_1_johnson.pdf
Montagnes, D.J.S., Montagnes, E.I. & Yang, Z. Finding your scientific story by writing backwards. Mar Life Sci Technol 4, 1–9 (2022). https://doi-org.ezproxy.lib.purdue.edu/10.1007/s42995-021-00120-z
Notion. (n.d.). What is Notion? Notion. https://www.notion.so/help/guides/what-is-notion
OpenAI. (2023). GPT-4. https://openai.com/product/gpt-4
Pauk, W., & Owens, R. J. (2010). How to Study in College. Cengage Learning.
The Stanford NLP Group. (n.d.). https://nlp.stanford.edu/software/stanford-dependencies.html
T. Piesk. Syllogism. (2023, August 1). Wikipedia. https://en.wikipedia.org/wiki/Syllogism#/media/File:Modus_Baroco.svg
