Line - Tree - Network
Line - Tree - Network

A line, Euclid wrote, is length without breadth. It is a thing of one dimension, a series of sequential points along which one may move backward or forward, but never sideways. Trees, as I discuss them here, are branching hierarchies, mathematical forms that are only occasionally connected to their arboreal namesake. A tree begins with a narrow root and branches outward into complexity. A network is a seemingly disordered mesh of lines; unlike with trees, traversing a network may lead one down endless paths, taking a different route each time.

Lines, trees, and networks are here arranged by increasing complexity, not increasing importance or chronological order. Each has and continues to be used as a dominant metaphor for some aspect of the human condition. Movies and books progress in a storyline; you arrange your ancestors in a family tree; we interact with each other through social networks. Each ontological structure is ubiquitous in its own right.

In this story, however, lines and linear thinking are precedent (though not confined to prologue). They represent some early attempts by Western Europeans to order the world around them. In the first century BCE, for example, Marcus Agrippa created an expansive Roman road map that likely stretched from Britain to Sri Lanka, nearly 5,500 miles end-to-end, or more than a fifth of the earth's circumference. The only surviving copy of the map, the 13th century CE Peutinger Map,1 is twenty times wider than it is tall, with Rome near its center and paths stretching out in either direction. Its form is similar to modern straight-line diagrams (subway maps that contort geography into a straight line to make them easier to navigate) or the 19th century Ammassalik wooden maps (straight-line coastal maps of Greenland carved into driftwood by Inuit).2

Time, as well, has until recently been overwhelmingly linear.3 Whether they consider its passage progressive, regressive, or cyclical, people assume time to be unidirectional and one-dimensional, with no branching or intersecting paths. Its linearity is entrenched in our language, as when we speak of time as "long", "short", or in "intervals."4 This is not to say that lines were the only form in which maps and chronologies were found, nor that the Western European tradition was indicative of all traditions. Early maps came in all shapes and sizes, often circular, and neither the timeline nor the number line became standard visual arrangements until the last few centuries.5 Many non-Western cultures have a rich tradition of complex non-linear representations of space and time.6 But for the Greco-Roman philosophers and early Christian theologians, temporal and spatial linearity provided order, in which could be seen the traces of divine providence.7

The concept of a transcendent linearity drew its roots from Plato and Aristotle. Aristotle's "ladder of life" gave every organism a proper hierarchical place, with mankind at the very top and vegetation near the bottom rung. As the idea passed between theologians and natural philosophers over the next millennium and a half, this "great chain of being" became inextricably bound to cosmology, extending upward to God and downward to earth. The great chain was not merely metaphorical, but the essence of the cosmos (κόσμος, 'order'), the structure that ordered all.

The great chain contained many microcosms of the macrocosm, little self-reflections of the larger whole. As God sat above mankind, kings sat above their subjects. The same spatial ordering appeared in family lineages (notice the word's root?) dating back to ancient Rome. Ancient and early medieval European genealogical diagrams placed the oldest ancestor on top, and proceeded fairly directly and patrilineally to the descendant of note, with few if any branches to either side. Prestige or even divinity flowed like heaven's light from top to bottom, lessening a bit with every subsequent generation until reaching the lowliest bottom of the chain.8 The spatial linear relationship between divinity, order, and time was tightly-bound.

Linear hierarchy described space, time, divinity, and family for a millennium. Even when cosmic ontologies included branches, as in Porphyry's incredibly influential 3rd century tree which divided "being" into genera and species, they formed a direct hierarchical line, top-to-bottom. While the Porphyrian tree did not place God in the topmost position, that discrepancy would be remedied by many subsequent thinkers. The 13th century Matfre Ermengaud, for example, recreated the Porphyrian tree in his Albre d'Amor, this time placing God at the top.9 Porphyry's tree, like Aristotle's ladder, would be amended and added to for over a thousand years. Those amendments added complexity. Ramon Llull, in the 13th century, changed and added many branches to the tree, linking the order of being to the order of knowledge. Four hundred years later, Athanasius Kircher did the same, adding an even more complex set of overlapping branches.

In this fashion, as tree metaphors spread through the medieval and modern world, they did not replace lines so much as augment them. Genealogical diagrams eventually flipped upside-down and became known as "trees",10 while traditionally linear ontologies like Porphyry's tree changed and grew until the direct linearity was no longer clear. The hierarchy, however, remained. Trees, with their continuously branching paths, allow the encoding of a hierarchy with a single root but many equally-ordered offshoots. Thus God could remain the original font from which all lineage flowed, but it was no longer necessary to place the entirety of the cosmos on a single, direct ladder stretching out beneath. Kings and popes, fire and water, philosophy and history, could occupy their own branches in the great cosmic tree.

Network thinking arose similarly, with a slow accrual of branches resulting in more weight than any tree could bear. As encyclopedists and librarians grappled with classifying ever-increasing collections, as biologists began noticing inadequacies with Darwin's tree in describing evolution, and as Western culture shifted away from a theological geocentric cosmos towards a decentered postmodern universe, tree-thinking fell out of vogue. The predominant cultural metaphors no longer fit so cleanly into ever-dividing hierarchical branches. But splitting cleanly from ones roots is difficult. Classification theorist S.R. Ranganathan mused that, perhaps instead, knowledge is like a Banyan tree, with multiple trunks growing up and down.11 Deleuze and Guattari suggested a good cosmic metaphor to be the rhizome—that interconnected ball of roots from which grass grows.12 Hierarchical trees are still used to visualize, classify, and structure all sorts of phenomena, but their proponents seem decreasingly willing to admit them as the best and most natural ordering.

As the closest ontological metaphor to trees which requires neither hierarchy nor root, networks are rapidly taking their place. Ted Nelson, an early pioneer of the internet, wrote that "everything is deeply intertwingled" and hierarchies are no longer adequate.13 The replacement, of course, is a World Wide Web, or a set of networks that describe the structure of knowledge.14 Action in the cosmos, once attributed to a "prime mover" who sat atop a great chain or at the root of a hierarchy, is now often attributed to a diffuse network of people and things.15 Evolutionary biologists are rapidly replacing phylogenetic trees with phylogenetic networks (though biological networks predate Darwin's trees),16 and with genealogical websites like MyHeritage,, and Geni, family trees are rapidly merging with and using the language of social networks. Building on sociology,17 businesses have reorganized themselves to break traditional hierarchies and work more like overlapping networks [citation].

Network-thinking is neither the only nor the inevitable successor to the vacuum left by the contemporary inadequacy of trees. While Deleuze and Guattari's rhizome maintains the tree's arboreal roots, and Nelson's intertwingularity is invoked to justify node-and-link networks,18 the two easily conform to another paradigm: emergent holism. Emergent holism, a term I coin here, is a formal ontological layer at the intersection of machine learning, classification theory, and post-structuralism. If the world has no inherent structure, and as Dirk Gently claims there is a "fundamental interconnectedness of all things",19 then the only way to represent the world is in its messy entirety. There are no genres. There are no historical periods. There are no true races or species. There is, simply, everything.

Emergent holism offers a formal ontological replacement for network-thinking in that, through machine learning, it accommodates a structure that can emerge from the questions or categories being brought to bear. A cataloging librarian need not pre-determine a books place in an ontology; they merely need to know what subjects a patron is interested in, and the library will reorganize itself around the patron accordingly. The idea that structure is socially contingent is not new, nor is the idea that machine learning can act as a replacement,20 but the ontological form they together create is yet unnamed [check if this is true]. Hence emergent holism.

Why, then, is this not a chronology of ontologies, from lines to trees to networks to emergent holism? Because that chronology cannot exist. We still invoke linear metaphors every day, and the tenets of emergent holism may be found from Comte to Copernicus. Other common structural frameworks exist as well, like circles and sine waves, not to mention the great stew of metaphors with no geometric or visual component. The cultural trend from tree-thinking to network-thinking, however, is an interesting one with unexplored repercussions. Linear-thinking and emergent holism frame this trend well, and are worth mention, but cannot offer a neat prologue and epilogue to this narrative. They are, if anything, usefully intertwingled.

"Lineage" – family chronology

(Many indigenous peoples represented things much more complexly – see Ingold)

(Other old maps were circular, or T-shaped; number lines didn't come into existence until 17th century)

Lines are prologue.

Linear narratives! They still exist! Number lines were invented by John Wallis in 17th century!

Linearity – Hierarchy – Consilience(??)

River – Tree – Banyan Tree – Spider's Web

History of the number line

Ingold Chapter 321

Great chain of being

Klapisch-Zuber, Darwin

Map of roman world (long)

Linearity of time pre sci-rev (everything is in decay) (but also circularity of time!)

Reticulate meshwork

  1. Talbert, Richard J.A. “Peutinger Map Seamless Whole, in Color, with Overlaid Layers.” Pleiades. ://, 2010.

  2. Holm, Gustav. “Eskimoiske ,,Kaart’ Af Træ.” Geografisk Tidsskrift 8 (January 1886): 103–5.

  3. Lakoff, George, and Mark Johnson. Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought. Basic Books, 1999.Grafton, Anthony, and Daniel Rosenberg. Cartographies of Time: A History of the Timeline. Princeton Architectural Press, 2010.

  4. Mitchell, W. J. T. “Spatial Form in Literature: Toward a General Theory.” Critical Inquiry 6, no. 3 (1980): 539–67.

  5. Núñez, Rafael E. “No Innate Number Line in the Human Brain.” Journal of Cross-Cultural Psychology 42, no. 4 (January 2011): 651–68. doi:10.1177/0022022111406097.Grafton, Anthony, and Daniel Rosenberg. Cartographies of Time: A History of the Timeline. Princeton Architectural Press, 2010.

  6. Ingold, Tim. Lines: A Brief History. 1st ed. Routledge, 2007.

  7. Grafton, Anthony, and Daniel Rosenberg. Cartographies of Time: A History of the Timeline. Princeton Architectural Press, 2010.

  8. Klapisch-Zuber, Christiane. “The Genesis of the Family Tree.” I Tatti Studies: Essays in the Renaissance 4 (January 1991): 105–29. doi:10.2307/4603672.

  9. Kay, Sarah. The Place of Thought: The Complexity of One in Late Medieval French Didactic Poetry. University of Pennsylvania Press, 2007.

  10. Klapisch-Zuber, Christiane. “The Tree.” In Finding Europe: Discourses on Margins, Communities, Images Ca. 13th - Ca. 18th Centuries, edited by Anthony Molho, 293–314. New York, NY: Berghahn Books, 2007.

  11. Ranganathan, S.R. “Colon Classification and Its Approach to Documentation.” In Bibliographic Organization. Papers Presented before the Fifteenth Annual Conference of the Graduate Library School, 94–105, July 24-29, 1950.

  12. Deleuze, Gilles, and Félix Guattari. A Thousand Plateaus: Capitalism and Schizophrenia. Minneapolis: University of Minnesota Press, 1987.

  13. Nelson, Ted. Dream Machines. 1. Ed. Chicago, IL, 1974.

  14. Börner, Katy. Atlas of Science: Visualizing What We Know. Cambridge, MA: The MIT Press, 2010.

  15. Latour, Bruno. Science in Action: How to Follow Scientists and Engineers through Society. 11. Print. Cambridge, Mass: Harvard Univ. Press, 2003.

  16. Ragan, Mark A., James O. McInerney, and James A. Lake. “The Network of Life: Genome Beginnings and Evolution.” Philosophical Transactions of the Royal Society of London B: Biological Sciences 364, no. 1527 (August 2009): 2169–75. doi:10.1098/rstb.2009.0046.Ragan, Mark A. “Trees and Networks before and after Darwin.” Biology Direct 4 (2009): 43. doi:10.1186/1745-6150-4-43.Bapteste, Eric, Leo van Iersel, Axel Janke, Scot Kelchner, Steven Kelk, James O. McInerney, David A. Morrison, et al. “Networks: Expanding Evolutionary Thinking.” Trends in Genetics 29, no. 8 (August 2013): 439–41. doi:10.1016/j.tig.2013.05.007.Kunin, Victor, Leon Goldovsky, Nikos Darzentas, and Christos A. Ouzounis. “The Net of Life: Reconstructing the Microbial Phylogenetic Network.” Genome Research 15, no. 7 (July 2005): 954–59. doi:10.1101/gr.3666505.

  17. Granovetter, Mark S. “The Strength of Weak Ties.” American Journal of Sociology 78, no. 6 (May 1973): 1360–80.Burt, Ronald S. “Structural Holes and Good Ideas.” American Journal of Sociology 110 (September 2004): 349–99. doi:10.1086/421787.

  18. Morville, Peter. Intertwingled: Information Changes Everything. Semantic Studios, 2014.

  19. Adams, Douglas. Dirk Gently’s Holistic Detective Agency. 5.2.1991 Edition. Pocket Books (1991), Edition: 5.2.1991, 306 pages, 1991.

  20. Anderson, Chris. “The End of Theory: The Data Deluge Makes the Scientific Method Obsolete.” WIRED 16, no. 7 (June 2008).Underwood, Ted. “The Literary Uses of High-Dimensional Space.” Big Data &Amp; Society 2, no. 2 (December 2015): 2053951715602494. doi:10.1177/2053951715602494.Underwood, Ted. Why Literary Periods Mattered: Historical Contrast and the Prestige of English Studies. Stanford University Press, 2013.DiMaggio, Paul. “Adapting Computational Text Analysis to Social Science (and Vice Versa).” Big Data &Amp; Society 2, no. 2 (December 2015): 2053951715602908. doi:10.1177/2053951715602908.Enderle, Scott. “A Random Entry.” The Frame of Lagado, 2015-04-02T02:02:05+00:00.Underwood, Ted. “The Life Cycles of Genre.” Journal of Cultural Analytics 1, no. 1 (May 2016).Ekbia, Hamid R., Michael Mattioli, Inna Kouper, G. Arave, Ali Ghazinejad, Timothy Bowman, Venkata Randeep Suri, Andrew Tsou, Scott B. Weingart, and Cassidy R. Sugimoto. “Big Data, Bigger Dilemmas: A Critical Review.” Journal of the American Society for Information Science and Technology, 2015.

  21. Ingold, Tim. Lines: A Brief History. 1st ed. Routledge, 2007.