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What is Non-Linearity?

April 8, 1997

What is non-linearity?
Survey of non-linear materials
Non-linearity and Communication
Non-Linearity and Post-Modernity
Problems and Predictions for Non-linearity
**** Non-linear exploration of Non-linearity


Channel surfing, web surfing, multimedia. All of these have been called "non-linear." But what does that really mean? On a purely literal level, non-linear means not "having or resembling a graph that is a line and especially a straight line" (Merriam Webster Dictionary 429). That means my hair and shoes are non-linear but nobody seems to be getting excited about that. So, why the hoopla? Why does it seem as if everything today must be non-linear?

This report seeks to answer the following questions. What is non-linearity? What are examples of non-linear communication? How does non-linearity affect communication and learning? And finally, what is the relationship between non-linearity and Post-Modernity?

What is non-linearity?

To begin, let's rewind back to 1945 in the final days of World War II. A computer scientist who had been responsible for the development of military technology looked ahead to the post-war era. His name was Vannevar Bush and he wrote the essay, "As We May Think." In it, he bemoaned the fact that despite increases in knowledge, access to that knowledge was still quite primitive. He wrote:

The summation of human experience is being expanded at a prodigious rate, and the means we use for threading through the consequent maze to the momentarily important item is the same as was used in the days of square-rigged ships.

Important information was lost in a sea of data and even if you knew what you were looking for, you would still be long in finding it.

He suggested the creation of a machine called a "memex." This machine would look like a desk but would include a keyboard as well as several screens and levers. Part of the machine would consist of a microfilm recording and storage compartment. The bulk of the machinery would be employed in displaying the text and images stored on the microfilm. The memex would hold more microfilm and therefore more information than any human being could examine in three lifetimes. The user could instantly bring up any article or the index of any book simply by typing its code. The memex would also allow the user to record and playback information in the sequence in which it was viewed.

In this way, it would mimic the human mind which " operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts, in accordance with some intricate web of trails carried by the cells of the brain." (Bush).

The memex, sounding suspiciously like a modern computer, would be the platform for something we now call "hypertext." Although Bush was the first to mention the concept in print, twenty years would pass before theoretician, Ted Nelson, would name it (Deemer). Today, for anybody who has been on the World Wide Web, hypertext is nothing new. Through "links", the user can jump from one page to another, reading about a series of related topics as his fancy takes him.

Most people would jump on hypertext as being the most non-linear thing they know. A Web page or computer program employing hypertext is non-linear in that it allows the user to control the direction and flow of the narrative. It allows the user to carve their own custom path through the information. Power over the text shifts from the author to the reader.

But is non-linearity a new development? When people speak of it, they usually refer to technology-mediated experiences, principally using computers. But what about a simple conversation between two people? Beyond information gathering exchanges, we do not know in which direction a dialogue will turn yet we help to shape its outcome. Like Web pages, which require a creator and a user, conversations require at least two people. Non-linearity implies interaction and control. The Web designer creates the context and links while the user chooses which links to follow. Similarly, the two conversationalists interact to create the dialogue.

Therefore, a conversation can be described as non-linear. But are hypertext and conversation equally non-linear? No. Where the former is limited by a finite number of links, the latter can move in infinitely many directions. The possibility to turn the dialogue to any other topic is always present. So we need to expand the definition of non-linearity. Not only does it allow the user to choose a direction and thereby shape the narrative, but non-linearity is also a measure of degrees of freedom. The more degrees of freedom, the more non-linear an interaction. Non-linearity, then, spans a continuum ranging from the strictly linear to the totally non-linear.

As an example of this continuum, consider a train, a car, and a submarine. Usually, a train can travel forwards or backwards on the tracks; it can not move sideways off the tracks nor can it travel where there are no tracks. It has only a few degrees of freedom. A car, by contrast, needs no tracks and can move in any direction on fairly flat ground. It has more degrees of freedom than the train. A submarine, which can move forwards, backwards, sideways, and up and down, has the most degrees of freedom. Therefore, in reference to potential motion, the train is the most linear while the submarine is the most non-linear. The car falls somewhere in between.

However, although it appears to have infinite degrees of freedom, the submarine is not entirely non-linear. To be entirely non-linear would imply that the submarine could, at any moment, move in any direction. The submarine can not do this. For example, at any instant, it can not move directly sideways. It must make a gentle turn and come around to that same place. Similarly, in hypertext, the user can only move to other pages to which he has links. Even in conversation, it is considered impolite to cut off the other person or to switch topics without reason or warning. In short, there are rules. The submarine must obey the rules of physics. Hypertext must obey the rules of its design (i.e. every page can not link to every other page). And in conversation, we usually obey the rules of etiquette.

So, we have a continuum of non-linearity but do we have anything at the extreme ends of that continuum? Can anything be described as totally linear or totally non-linear? Books have often been described as linear when compared to hypertext. Read traditionally, books are quite linear because one word follows after another and the reader must go from one page to the next with little choice. However, even books have the potential to be non-linear. The reader can jump from any page to any other (consider an Encyclopedia) and fashion her own meaning. Because of the nature of human consciousness, any object can be treated in a non-linear fashion or in a linear fashion. The user could read a Web page from top to bottom without activating any of the links. Hypertext would then become linear.

Therefore, only things that can not be manipulated could fit on the ends of the non-linearity continuum. And these are time and space. Time follows second after second. Time can not move sideways nor can it move backwards. Our perception of time may change but that does not change time itself. For that reason, time, being totally linear, fits on one end of the continuum. Empty space, with the potential of movement within in it in any direction, is totally non-linear and fits on the other end. Now comes a paradox. When a Web page is unexplored then it is non-linear (to a degree). However, once the user activates the links and navigates the hypertext then it becomes linear. First, he visited this piece, then this, and finally this bit. The experience becomes tied to time; the user created a linear narrative. For other users, the page remains non-linear. The page has become both non-linear and linear.

Non-linearity, then, relates to both interactivity and degrees of freedom. For something to be considered non-linear, the user must be able to control the narrative path. The degree of non-linearity is determined by the number of choices the user has at any one time; the more choice, the more non-linear the work.

Survey of non-linear materials

When most people consider non-linear materials, they think immediately of computers. However, as we have seen with the example of conversations, this is not an essential ingredient. Some classic non-linear activities include reading Choose Your Own Adventure books, channel surfing, and playing Dungeons and Dragons.

The Choose Your Own Adventure series of books present young readers with two or three choices at the bottom of every page. Depending on which path the reader chooses, he will be directed to a different section of the book and the narrative proceeds down a different path. Similarly, by rapidly changing television channels, the viewer can construct a unique narrative composed of segments from various programs. These experiences are non-linear since the user controls the direction of the 'story.' Despite that, they remain fairly linear in that the user has few choices. Even in a 500 channel universe, the viewer can only choose whether to keep watching or to switch channels.

In the Dungeons and Dragons family of games, players role-play in order to reach an objective. These games are quite non-linear since there is a very high degree of interaction. The players' decisions directly shape what happens next. At any given time, the players also have very many options (i.e. many degrees of freedom).

However, the bulk of modern non-linear materials exist on computers. They fall into three major categories: Web pages, multimedia applications, and games.

By far the most hypertext can be found on the Internet. The number of Web pages has expanded prodigiously. Four years ago, there were only twelve Web sites and few people knew about the World Wide Web. Today, there are over one million sites and twenty million people surfing regularly (Calcote). This implies a phenomenal amount of hypertext content.

Along with regular web pages, several types of more non-linear works have been published on the Internet: hyperfiction and interactive story writing. In the former, the reader navigates through a narrative. The simplest of these are like the Choose Your Own Adventure books, where the reader is only given two or three choices after reading a few paragraphs. An example of this type of work is Shawn Aeria's "Where am I?" Generally, these are substandard versions of the physical books with less content and inferior writing.

Hyperfictions that take advantage of the opportunities offered by HTML (Hypertext Markup Language) are much more non-linear and exciting. Words throughout the text are linked to other pages. Again, by expanding the number of choices, these stories become less linear. For example, in Mike Benedetti's "Mercury", almost all the text is linked. It is the unlinked words that jump out at the user.

Interactive stories are an even more non-linear Web-based form. On these sites, readers can add to stories in progress or read finished tales. Each visitor to the site can write what happens next in any unfinished story. Example sites include "Tales from the Vault", "Round Robin Storybook", and "Gav and Peloso's Interactive Story."

Multimedia programs that run on personal computers also employ hypertext to create non-linear interactions. Some hyperfiction stories have been published on compact disc for Windows and Macintosh by Eastgate Systems in Massachusetts. The first of these was "Afternoon, a story" written by Michael Joyce and published in 1987. Others include "Twilight, a symphony" also by Michael Joyce and "It's Name was Penelope" by Judy Malloy. Music too has been transformed in non-linear multimedia applications like Todd Rundgren's "No World Order" (Electronic Arts). The user can manipulate the mood, tempo, form, and even direction of the music.

Researchers at the Massachusetts Institute of Technology (MIT) Media Lab have experimented with non-linear narrative. Members of the Interactive Cinema Group have developed "Multivariant Movies" in which the user can determine how much visual detail they want to see in the key scenes of the film. Even more non-linear are "Thinkies," created by Lee Morgenroth, which allow the user to explore different scenes and information to uncover a mystery. Examples of these include "The Files of Dr. Bern" and "Lurker." (FRAMES Number 29 and 43).

Along with the World Wide Web and multimedia, games have provided some of the best non-linear work to date. Many of the early computer games were based on games like Dungeons and Dragons and Choose Your Own Adventure. Today, with increased processing power, computer games can simulate cities and their inhabitants such as in "Syndicate" (Electronic Arts) and "Sim Helicopter" (Maxis). Games can now offer the user more choices particularly in complex simulations of vehicles ("Microsoft Flight Simulator") or eras (Sierra's "Lords of the Realm II").

Non-linearity and Communication

What cognitive resources are required when navigating non-linear works? Because of the novelty of non-linear technologies, few people have tackled this question. However, researchers have studied hypertext. Again, investigation of the above question has been minimal; more interest has been directed at the technology rather than the human side of hypertext (Wenger, Feb. 1996). The following discussion focuses on hypertext rather than other non-linear forms because of this lack.

The research team of Michael Wenger and David Payne determined that reading hypertext does not require more cognitive resources than does reading linear text. This task, however, draws on more spatial and relational information processing skills than does reading traditional text. These skills deal with the manipulation and association of objects in two or three dimensional spaces. This is particularly true of the defining task of hypertext: navigation (Wenger, Mar. 1996).

Wenger and Payne also found that reading hypertext does not require more working memory than reading linear text (Wenger, Mar. 1996). This portion of memory, also called short-term memory, has a limited capacity and is used as a handling area for pieces of information while consciously thinking (Gagné 74).

The researchers discovered that subjects with superior spatial skills better remembered hypertext information (Wenger, Feb. 1996). With the ever increasing use of this form, training in spatial processing would translate into more profitable use of non-linear text.

Wenger and Payne concluded that the large body of research on traditional reading can be applied to the reading of hypertext. Therefore, hypertext design can be optimized in the same way as print design has been optimized (Wenger, Feb. 1996). Research from traditional reading indicates that increased speed of acquisition leads to increased retention (Champion 103). By improving spatial and relational processing skills, the user could move more rapidly through hypertext documents and thereby raise retention of information.

But, how far can we extrapolate from hypertext to other non-linear forms? How much can we draw from traditional narratives when dealing with non-linear forms in other media? The answers will be found through research which will occur in response to the mushrooming of non-linear forms. The rapid acceptance of non-linear materials, particularly the World Wide Web, seems to indicate that they are not so radically different from their predecessors and that much can be learned from already established research.

Non-Linearity and Post-Modernity

Non-linearity and Post-Modernity bear a very close relationship. In fact, today's non-linear technologies probably would not have evolved if we weren't in a Post-Modern age.

Post-Modernity attacks the idea of absolute truth. Extreme forms of Post-Modernism attack the idea that there can be any truth at all. This concept leads to a radical pluralism; where Modernism had previously accepted only a few absolutes, Post-Modernism welcomes all ideas and privileges none. It rejects the meta-narratives (such as those proposed by religion) and attacks the idea that stories can only be told one way, from one perspective, and in one direction (Smith). It also rejects the idea of closure (Roberts).

Now compare this with non-linear texts. Since these stories can move in many different directions, they reject the idea of one definitive narrative. No storyline is privileged over another in the non-linear text. And certainly, non-linear works have no closure and no ending, only more links. Just as Post-Modernism criticizes Modernism, so does non-linearity criticize linear forms (Roberts).

Another fundamental concept of Post-Modernism is that readers and not authors create the text. Every person brings their own background to the work and takes away their own interpretation. Similarly, non-linear forms empower the user; creativity and power over the narrative pass to the user in creating his own version of the work (Lim).

Problems and Predictions for Non-linearity

What the mechanism [hypertext] really creates is not multiple coexisting levels of connection but a series of forking paths all, alas, on a single undifferentiated plane, so that it is almost impossible, for example, to take short cuts -- you have to follow every twist in the path -- and it is all too easy to forget the way home (McGrath).

I find it difficult to know the score when Web surfing or reading a hyperfiction. How many of the pages have I visited? Have I read everything I was supposed to? Am I finished? One of the greatest problems with many non-linear works (particularly on the World Wide Web) is that the user has no map and no way to differentiate the different portions she has read.

Wenger and Payne experimented with graphical browsers. They provided some experimental subjects with an index or map of the hypertext they were to navigate. They discovered that the graphical browser did not improve the subjects' performance as compared to a control group. Neither the subjects' recall, comprehension, nor their retention of the material increased. However, their efficiency in moving through the hypertext improved. The number of repeat visits to nodes (sections of the text) decreased and the percentage of nodes read increased (Wenger, May 1996).

These types of maps are already included in many computer multimedia products and would definitely allow for more productive use of the Web. Another solution would be the organization of data into three-dimensional landscapes. Researchers at the MIT Media Lab have experimented with representing text information, spatial data, and numerical data in this way. This allows the user the opportunity to use more spatial processing skills in processing relationships between information. Spatial representation of data also expands the user's options in exploring the work thereby making it more non-linear (FRAMES Number 32).

Another problem with non-linear works is the medium itself. Computer screens, the predominant carrier of non-linear materials, are hardly ideal for reading. The low resolution of the text, small amount of text on one screen, and the glare of the image can cause eye fatigue and generally make reading off a computer screen unpleasant. Joe Jacobson, at the Media Lab, has been experimenting with paper-like displays. He is attempting to create a computer output device that acts and looks like a book (FRAMES Number 60). Certainly, display technologies will continue improving to a point where resolution and glare will no longer be an issue for non-linear materials.

The greatest problem that remains is that of authorship. Currently, most non-linear works and their navigation are created by one person or group and then released to the public which explores them. No matter what the users do, they can only explore what was put there by the authors. "Tales from the Vault" and "Round Robin Storybook" address this issue by allowing the user to write the next paragraphs in the story.

A more exciting direction is that being taken by computer programmer Chris Crawford, who wrote the computer games "Eastern Front" and "Balance of Power". He is experimenting with artificial personality in a simulation called "Le Mort d'Arthur", in which computer characters can make 109 facial expressions and 900 behaviours based on individual variables such as pride, initiative, and lust (Sipchen). The direction for non-linear work is to meld content and software programming. Artists will write the code that reacts to the user and allows her to move in different directions. Instead of only presenting pre-made content, non-linear materials of the future will create their content as the user interacts with the work. In this way, the degrees of freedom and hence non-linearity of the material are expanded.

The close linkage between Post-Modernity and non-linearity might indicate that when the first falters so will the other. Charles Jencks, who helped establish the Post-Modern movement, now attacks it, claiming it has moved away from its ideals (Popham). But even when Post-Modernity dies, it will not take non-linearity with it. This new form of work is too exciting, creative, and lucrative to die alongside the movement that spawned it.

Take a Non-linear look at Non-linearity


The citations in the text containing only a name refer to articles found on the World Wide Web or Lexis Nexis which do not have page numbers.

NOTE: Non hyperlinked Internet addresses below are no longer active.

"Gav and Peloso's Interactive Story."

Aeria, Shawn. "Where am I?"

Benedetti, Mike. "Mercury."

Bush, Vannevar. "As We May Think."

Calcote, Steven. "Internet Insight." Kerrville Daily Times' Tech World. 12 Feb. 1996.

Champion, R. Learning and Activation. Toronto: John Wiley & Sons, 1969.

Deemer, Charles. "What is Hypertext?"

Gagné, Robert. The Conditions of Learning. (4th ed.) Toronto: Holt, Rinehart and Winston, 1985.

Grant, Richard. "Never the Same Text Twice." Washington Post. 11 July 1993: Book World Section, page X8.

Guyer, Carolyn. "Hyperfiction."

Houston, John. Fundamentals of Learning and Memory. (4th ed.) Toronto: Harcourt Brace Jovanovich, 1991.

Lim, Richard. "When VR replaces RL and F2F is a shock." Straits Times (Singapore). 13 Oct. 1996: Upfront, page 4.

Longley, Clifford. "SACRED AND PROFANE: The trouble with Post Modernism is that it is not true." The Daily Telegraph. 1 Sept. 1995: page 23.

McGrath, Charles. "The Internet's Arrested Development." New York Times. 8 Dec. 1996: Section 6, page 80.

Popham, Peter. "Britain's strangest secret garden." The Independent. 26 June 1995: page 8.

Roberts, Paul. "Virtual Grub Street: sorrows of a multimedia hack." Harper's Magazine. June 1996: page 71.

Sipchen, Bob. "The Future of the Story." Los Angeles Times. July 30 1996: Magazine Section page 12.

Smith, Ralph. "The Question of modernism and postmodernism." Arts Education Policy Review. July 1995: page 2.

Wenger, Michael.; Payne, David. "Comprehension and retention of nonlinear text: considerations of working memory and material-appropriate processing." American Journal of Psychology. Mar. 22 1996: page 93.

Wenger, Michael.; Payne, David. "Human information processing correlates of reading hypertext." Technical Communication. Feb. 1996: volume 43, page 51.

Wenger, Michael; Payne, David. "Effects of a graphical browser on readers' efficiency in reading hypertext." Technical Communication. May, 1994: volume 41, page 224.

"Designing an Information Landscape in Time and Space." FRAMES. May 1994. Number 32.

"Lights! Camera! Interaction!" FRAMES. April 1995. Number 43.

"Negotiating Narratives" FRAMES. Feb. 1994. Number 29.

"New Faculty- Jacobson." FRAMES. Nov. 1996. Number 60.

"Story Resources."

Eastgate homepage


Round Robin Storybook.

Tales from the Vault.