1. Spatial Hypertext Evolution
In early hypertext programs such as Intermedia and Note Cards, a visual display showed the items linked to the current node. Each item appeared as a box linked to other boxes. The items were not independently movable, though selecting one might re-center the display and show more linked nodes.
Fig. 1: A screen from Note Cards showing both a global and a local link map.
A new kind of spatial representation appeared in Storyspace, where the boxes representing text nodes could be moved about independently, forming spatial groupings that might or might not correspond to the link structure shown by lines connecting the boxes.
Fig. 2: A Storyspace map showing movable boxes connected by link arrows.
A further step was made by Aquanet and its descendants (VIKI, VKB). Aquanet facilitated spatial manipulations and visually indicated links, but tests showed that users were not using the links when working with the program. So Aquanet's successors, VIKI and VKB, dispensed with visible link structure and made spatial manipulation and grouping the central action provided to the user. Working in the background, an algorithmic spatial parser highlighted incipient groupings.
Fig. 3: A VKB screen showing spatial groupings highlighted by the spatial parser.
Spatial manipulation had come into its own as a way of organizing that could avoid premature definitions and allow "incremental formalization". In terms of spatial manipulation, VKB remains the purest spatial hypertext system currently available.
The Visual Knowledge Builder (VKB) is a hypertext information collection system. This means that it allows you to collect and sort information in a very natural, visual environment. The goal is to allow users to input, organize, and access large amounts of information without having to commit to any particular convention of organization or structure. . . . What is VKB for? To organize, and interpret information from a variety of sources. Examples of uses include: Writing a related work section of a thesis, dissertation, paper, etc. Making decisions that involve grouping or categorizing items. Scheduling or organizing tasks. What to do. . . Start by dragging and dropping items from the desktop, web pages, and images into your personal or group information space. Then move the visual symbols into clusters, lists, or other structures. Categorize symbols by changing visual attributes like color, border color, border width, font, etc. As your information space enlarges, put symbols into a hierarchy of collections. (VKB Primer)
2. Space and Spaces
The parts of an automobile engine, the houses in a suburb, the people in a crowd stand outside and alongside one another. Space surrounds them and lets them be both separate and related. Non-spatial things, such as a set of ideas or mathematical theorems, are not outside one another in the same way. The metaphors and the rhythm of a poem are not spatially separated. The words stating the steps of an argument may be spatially separated on a page but as ideas the argumentative steps have complex internal connections that form a whole which is not spatial. Meanings provide internal non-spatial relations.
Spatial hypertext lives in the interplay of spatial and non-spatial relations. Spatial relations can be used to suggest internal connections, likenesses, separations, and so on; these relations can be ambivalent and vague and tentative in ways that a definite hypertext link cannot express. Either a link is there or it is not, but a spatial hypertext can use adjacency and separation to suggest possible or tentative connections. Spatial hypertexts thus can support vague and incrementally discerned structures and categories that provide very flexible tools for information triage and idea organization.
On the display screen, blank space opens a field of external relations for where-is and next-to and over-there and near-here relations among items that may represent all sorts of complex inner relations, or none at all. The space on the screen spreads out open and receptive. It offers dimensions for movement and location. It is serenely indifferent to what orderings and classifyings we make within it. It behaves as a a blank, geometrical, receptive passivity, flat and open. Is that the only kind of space that might be useful for spatial hypertext? In science and in philosophy there have been many kinds of space, and modeling some of them might enrich the abilities of spatial hypertext.
3. Newtonian and Leibnizian Spaces
As modern science was beginning, two of its giants -- Gottfried Wilhelm Leibniz (1646-1716) and Isaac Newton (1643-1727), who both invented the calculus -- clashed over their rival theories of the nature of space. That conflict can be read in a famous set of letters between Leibniz and Newton's friend Samuel Clarke. It is likely that Newton either wrote or advised Clarke's letters (see Alexander 1956). The differences between the two scientist-philosophers ran deep, and many issues converged on the nature of space. Put in current terms, the disagreement was between an absolute and a relational conception of space.
Newton's conception of absolute space is the more familiar. For Newton, space (and time) is an entity on its own, with its own properties, independent of whatever it might contain. It extends neutrally and without limits, offering an open field within which atoms, Newton's basic physical entities, move and rearrange themselves under the influence of gravity. It is at least conceivable that there could be a perfectly empty space, since space is a separate entity unaffected by what moves within it.
Newton's absolute space resembles the expectant window of spatial hypertext, flat and ready to receive, neutral and passive, offering empty extension for the arrangements created within it.
Leibniz's relational conception of space is almost the exact reverse. For him, space has no independent reality. Spatial relations are a derived perceptual effect brought about by the prior relations of the entities that make up the world. What primarily exists are what Leibniz calls "monads". These are not in their deepest nature spatial. They are centers of force and perception. They have complex relations to one another, relations of influence and clarity of perception. These mutual influences and relations are qualitative and causal, and they define an ordering of the monads in terms of closeness of influence and clarity of perception. Space and spatial ordering are consequent phenomena that summarize and present the deeper relations of objects by spreading them out in spatial connections and distances, near and far and next-to. When space is conceived this way, a perfectly empty space is inconceivable, since space is only an expression of the relations among what fills it.
Despite the strangeness of his notion of monadic entities, Leibniz's relational space has become quite familiar to us. It behaves like a pure node-and-link hypertext. It is the spatiality of web pages relating to one another. The spatiality of the web is created by the prior relations between the items that fill it. The web's link structure is not located in any other space. There is no prior space locating web pages externally; their relations are created by their links. They generate a spatiality of near and far, with perspectives from a given node toward other nodes. No web page is close or far from another except as the link structure dictates. The "distance" between web pages depends on the number of link jumps required to get from the first to the second. This is the space shown in the early Intermedia maps and other diagrams of link structure.
The vagaries of linking make the web's connectivity more contorted than Leibniz had in mind. Author-created links can reach in many directions. Search engines can make any web page at most two jumps away from any other: one to the search engine, and one from it to the new page. Algorithmic links after the fashion of Google's ads can make a page one jump away from what the computer thinks might be related. The complex network of author-created links is short-circuited, giving the connectivity of the web odd topological features.
Leibnizian relational space is the nearness and distance created by link structures and visualized in the Note Cards tree diagram above that showed links radiating out from a given center. This can be mixed with Newtonian space in hybrid presentations that map link structure onto spatially mobile objects. The maps in Storyspace and its cousin Tinderbox allow Newtonian spatial manipulations of their nodes but also show and can follow links that jump across distances, creating a Leibnizian set of relations. The link structure defines next-to and far-from differently than the visual closeness of the map view, while the map offers nearness and association that work independent of linkage.
Fig. 4: A Storyspace showing a Newtonian open space for spatial manipulations
overlaid with Leibnizian link relations.
In a Leibnizian relational space nothing is near anything else unless it is linked to it. There are no unexpected adjacencies. In Newtonian space and everyday physical space, there are unintended effects from adjacent but otherwise unrelated items. My restaurant's trade can be affected by your opening an separate noxious business down the block. A book may be read ironically in the light of the book shelved next to it. Such adjacency becomes a powerful tool in spatial hypertext, allowing the creation of half-way relations, tentative connections, and all manner and degrees of overlap and separation.
So it would seem that in spatial hypertext Newton wins over Leibniz. At most Leibnizian relational space can provide a useful add-on, but spatial hypertext needs Newtonian absolute open receptivity and freedom of movement.
4. Spaces with Different Topologies
However, these are other spaces. Newtonian space, flat and extending, has been replaced in science by Einsteinian space, which can be curved on its own and is shaped by the masses within it. Gravitational movement follows the shape of the space, and the space-time can possess intrinsic structure and odd topologies. Would Einsteinian space be useful for spatial hypertext?
We might envision a spatial hypertext that possessed intrinsic curvature and topological twists. There's not much to be done about the flatness of display screens, but they do not have to represent flat spaces. What if the spatial hypertext items resided on a curved surface? This could happen in two ways. One would be to curve the surface visually around a three-dimensional object pictured on the screen, perhaps a sphere or saddle-surface or a wave. This would, though, weaken the appeal of spatial hypertext that depends on immediate visibility and intuitive manipulation. Such complex surfaces would require a good deal of training and would diminish the usefulness of spatial hypertext for tentative and flexible classification.
The other way to change the space's topology would be to treat the edges of the screen differently. Spatial hypertext usually works with an unbounded flat space. If you approach the edge, more screen real estate is created beyond it, and a zooming interface can allow large-scale overviews. It is also possible to have absolute edges that keep spatial manipulations within a limited area. The alternative I am suggesting would connect the edges. In some early video games, when an enemy spaceship wandered off the left edge of the screen it reappeared on the right edge. The visible portion had been mapped onto a cylinder, though it was presented flattened out. If a similar connectivity were applied to the top and bottom of the screen, then the mapping would resemble a doughnut shape or torus. The connected space might be no larger than the screen, or it might be larger, perhaps with a hand or scroll bars that would move the screen window about in the larger space. Scrolling down or to the right would ultimately bring you back to where you had started from. The topology could also be wilder, with spatial hypertext mapped onto a Moebius strip or other strange manifolds.
Fig. 5: Topological diagrams: glue the opposite sides together, aligned as directed by the arrows.
The figure on the left becomes a torus:
items moved off the side or top of the screen will reappear at the other side or the bottom.
The figure on the right becomes a Moebius strip:
the top and bottom are not permeable but items moved off to one side appear reversed on the other side.
It is not clear whether such new topologies would provide any better affordances for spatial hypertext than does a large or indefinitely extensible flat space. But there is one kind of complex topology already included in many spatial hypertexts: the ability to assemble components into groupings that can be manipulated as single units. VKB keeps its hierarchical groupings, which it calls "collections", on the same level as other individual items, so they remain tentative. Storyspace and Tinderbox represents collections as sub-spaces "on a deeper level". This simplifies the display of the top level, though it interrupts the smoothness of manipulations and visually segregates some items from others, so those collections are less useful for representing tentative relations.
Fig. 6: A screen from the early Storyspace version of George Landow's Victorian Web,
showing one page together with a map indicating subordinate spaces below the map level.
5. Outlines in Complex Spaces
There are many programs dedicated to creating and manipulating outlines. As a hierarchical arrangement of text on a page, an outline has a spatial dimension when indentation shows subordination. Unlike spatial hypertext, an outline does not allow half-way or tentative relations, but the software makes it easy to move blocks of text around. (See the ongoing discussion of outline programs by Ted Goranson.) The tree structure created by an outline can be mapped into a Leibnizian linked spatiality (as in the chart view in Storyspace and Tinderbox). Outline subordination can be represented by nested spatial groupings, either on one level as in VKB collections or on multiple levels as in Storyspace and Tinderbox. When the linked items are then made independently movable, the outline adds the flexibility of spatial hypertext (as in Inspiration or the combination of OmniOutliner and OmniGraffle.) Similarly, some programs devoted to "mind mapping" or concept generation (for instance ConceptDraw or NovaMind) start out with a Newtonian space and create a flexible spatial representation of the outline tree.
Fig. 7: An outline showing spatial indentation of text blocks (OmniOutliner),
and an idea map with movable nodes radiating from a central concept (Nova Mind).
My investigation of alternate notions of space was stimulated by comparing Tinderbox with VKB. Tinderbox had learned from VKB to offer more visual attributes for each item, allowing variation in color, size, edges, and color gradients for increased spatial expressiveness. Unlike VKB, Tinderbox provides several spatial representations. One is a familiar outliner window with indentation. Another is a Newtonian spatial hypertext showing outline subordination as containment on a lower level. This map also includes arrows showing any user-created links that are independent of the outline relations. A third is a chart of the levels of the outline structure shown as a tree of boxes. Finally there is a view that compresses the outline structure into nested boxes all on one level. Interestingly, there is no way to represent only on the link structure that is independent of the outline.
(b)
(c)
(d)
Fig. 8: Different spatialities: (a) outline view with indentation,
(b) Newtonian map view with subordinate collections,
(c) Leibnizian map of outline structure,
(d) map of outline as nested boxes on one level. (All from Tinderbox)
Despite these many representations, Tinderbox (and Storyspace) demands priority for the relations of subordination created by outline manipulations. Subordinations in the outline are automatically reflected on the map, and vice versa. Spatial groupings on one level do not have to follow the outline order, but the subordination of levels does.
This limitation is partially offset in Tinderbox because it allows aliases, so that items can appear in multiple locations. Aliases can be created by hand for freeform use and be spatially arranged as the user wishes, though changes other than position affect the originals as well. So alternative spatial arrangements can be tried and compared. There are restrictions, however, since while manually created aliases can be moved about freely on the map and can be made children of substantive items, aliases cannot have children, whether substantive items or other aliases. Aliases can also be created by software agents according to user-chosen criteria. Automatically created aliases are gathered as children of their agent on outline and spatial sub-levels. The priority of outline order asserts itself again in that aliases collected by agents cannot be rearranged either spatially or in the outline. So while multiple spatial arrangements can be made and compared in Tinderbox, it is not easy to create multiple or alternative outlines except by creating duplicate items. These are copies, not aliases, so any additions or modifications to the contents need to be made separately to both the original and its copy.
(b)
Fig. 9: (a) Aliases collected by agents remain immobile within subordinate collections.
(b) The hand-created Tinderbox aliases at the top have been grouped differently than the originals below, while a color change applied to the aliases has affected the originals.
Collections in VKB can be copied and pasted to experiment with different arrangements, with the same restriction that internal changes would need to be made on both of the two copies of an item. VKB also includes a "history slider" that allows regress to earlier spatial arrangements; this can be used to compare alternatives, though not side by side. (The next version of VKB will allow aliases, thus facilitating side by side comparison of different spatial arrangements of the same materials.)
Fig. 10: VKB allows temporary reversion to previous states of the spatial array,
in the first hand image, by date, in the second image, by specific event.
Part way through the development of Tinderbox the dominance of the outline began to change when the program introduced what it calls "adornments". At first these did not seem to add much; they are rectangles that can be placed on the spatial background. They can be named and differentiated by color. They can overlap one another. Items can be put on them, or near them, or half on them. They can be moved independently, and later they acquired the ability to hold items placed on them so that the group moves as a whole. (However, they and their contents cannot be sent to a lower level.) The adornments that started out as simple labels have thus become a new kind of container that escapes the hierarchy set up by the ruling outline. Adornments keep their contents on the same spatial level as the surrounding items, as do collections in VKB. A single Tinderbox screen can now contain the outline hierarchy expressed visually by containers with sublevels, the spatial relations of near and far and grouping in flat Newtonian space, the Leibnizian node-and-link arrow connections, internal relations indicated by the color and shape of items, and now the new spatial containers outside the outline hierarchy. This can lead to visually quite complex screens.
Fig. 11: A complex Tinderbox screen showing spatial groupings, nodes and aliases collected on sublevels, adornments as collections, color differences, and link arrows.
6. Aristotelian Spaces
Thinking about this increasingly complex set of spatial tools, I began to wonder what would happen if instead of seeing adornments as a kind of container, they were seen as features of the background space. With their location, overlap and transparency, this would make the space seem Aristotelian. This suggested yet another kind of space for spatial hypertext.
There were two main conceptions of space in ancient Greek philosophy. The minority view was expressed by the Leucippus, Democritus, and later Epicurus: space was an infinite void in which little atoms moved and combined to make a multiplicity of worlds. The Greek conception of the atoms and their motions was not the same as Newton's, because all connections were due to the interlocking shape of the atoms; there were no long-distance forces. Still, the Atomist flat neutral void is very similar to Newtonian absolute space. This remained a minority view because of difficulties in the physics but also because ordinary perception seemed to favor the Aristotelian view. For Aristotle's space is not relational the way it is for Leibniz, but neither is it the neutral container favored by Newton and the Atomists. Taken on its own, Aristotelian space includes polarities, privileged locations, and absolute directions and gradients.
Strictly speaking, Aristotle (1941) did not believe in space as a separate entity. In his cosmology there is no vacuum, only different kinds of extended substances touching and blending with one another, each with its natural motions and mixtures. Space is the name we give to the place created by the extension of objects and their locations and movements in and by one another. (Similarly, for Aristotle there is no separate entity called time, there are only objects and their changes. In some ways Einsteinian space-time is closer to Aristotle than to Newton.) But despite the lack of space as a separate entity, Aristotle talks about different regions of the cosmos as distinct goals for natural motion. Space, in this sense, possesses textures and gradients.
To understand Aristotelian space one needs his theory of natural motion. In the Aristotelian cosmos, things have an innate tendency to go to their natural locations. For instance, the weight we experience as gravity is not due to any pull from the earth but is due to the effort of our bodies and other items containing the earth element to get as close as possible to the center of the cosmos. There is no pull but rather a push downward by the earth element in rocks and in our bodies, meeting resistance from the earth element already there below us. (As the earth element struggles to get as close as possible to the center it produces a spherical shape for what we, but not Aristotle, would call our planet. In Greek planetos means wanderer; it names those objects that move among the stars.) Given its natural tendency, our earth does not move, though Aristotle suggested that if by some means you were able to push the Earth away from the center of the cosmos, it would move back, because that is where the stuff of which it is made wants to be.
Different kinds of matter (the four elements,earth, air, fire, water, plus a fifth celestial element) naturally want to move in different directions. The earth element tends to move toward the center of the cosmos. The other four elements naturally move away from the center toward their own regions. Springs flow up and over the earth, air escapes and hovers, fire rises, the fifth element moves circularly around the center. If unmixed and left to go their way undisturbed, the elements would form concentric spheres with earth at the center, surrounded consecutively by water, air, fire, and the fifth element. Even now the elements are more or less in those locations, but the four lower elements mix and move, through processes brought about by the rotation of the heavens and the inclined course of the sun. Aristotle also thinks that under causal influences the four elements may transform into one another, so there is no danger of stasis and total separation.
Fig. 12: The Aristotelian cosmos, with its "natural" areas for earth, water, air, fire, and the fifth element.
The four terrestrial elements are mostly in their natural places
but also get mixed with each other to create familiar objects.
The effect of this theory of natural motion is to distinguish the space of the cosmos into different regions. Aristotle has no notion of pure geometrical space. His regions and zones are not superimposed upon a flat Euclidean space. By observing the motions of the elements we can see that space is not neutral; it contains gradients and polarities. This could be incorporated into spatial hypertext.
Another feature is Aristotle's distinction between natural and forced ("violent") motions. Forced motion is a motion different from the natural motion of an element. Such motion always has an outside cause. Stones naturally move toward the center of the cosmos, but I can pick up a stone and throw it into the air. This motion is "unnatural" in the sense that it is not what the stone would do if left to itself, but the motion is still part of the "natural" course of the cosmos, as when plants raise up water or birds fly off with seeds or humans build stones up into walls and houses.
Current spatial hypertexts present a neutral Euclidean window onto flat Newtonian absolute space. In that space items are arranged in spatial orders of classifications and containments. An Aristotelian space would offer two additional features: a structuring of space itself and a distinction between natural and forced behaviors of items. These features would influence the motion and location of items within the space.
Much of the research that inspired spatial hypertext programs (Aquanet, VIKI, VKB) came from observing people dealing with piles of paper by separating items into different stacks put in place on real physical desktops. (See, for example, Marshall and Shipman 1997.) Performing information triage, people create spatial groupings that express vague and changing classifications and relations. But real physical desktops are Aristotelian spaces. They offer built in gradients and polarities due to the ratio of their size to people's reach, variations in lighting, zones of accessibility, and position relative to significant objects near the desk. These gradients influence what kinds of meaning can emerge in different zones of the desktop. It is not likely that a stack in a far dark corner of the desk will be as significant or as manipulable as a stack in a central well-lit location.
Fig. 13: A desk as an Aristotelian space with regions "natural" for different kinds of piles and actions.
In a different way, a piece of blank white paper offers an Aristotelian space when it interacts with habits of reading that suggest starting at the top left. Seldom do people making notes or diagrams on blank paper start two thirds of the way down and a bit in from the right margin. Not all regions of the paper are the same; some are more "natural" for writing than others. The same is true for a display screen presenting spatial hypertext, where spatial structures tend to be created either from the top left or from the center of the screen.
We could increase these Aristotelian tendencies by making the background space more evidently textured and polarized. Imagine, for instance, a gradient color that was used as a background to influence emergent structure.
Fig. 14: Gradients and textures in a space encouraging different kinds of "natural" classification.
Or a patterned spatial background that suggested directions and modes of classification.
Fig. 15: A patterned spatial background creating distinct regions
that will encourage some kinds of arrangement over others.
Or a set of poles or sinks putting directions into the space.
Fig. 16: Poles and sinks in an Aristotelian space suggesting movements.
Or imagine an image used to texture a whole space.
Fig. 17: An aerial view of Denmark, and a map of the San Antonio Riverwalk,
used as backgrounds to create regions in a spatial hypertext.
Or a photo background used as a memory palace, an architectural image in which items can be placed to store or recall their meaning or sequence. This was a device used by classical and Renaissance orators.
Fig. 18: The National Building Museum in Washington used as a memory palace.
An Aristotelian spatial hypertext could also include sub-spaces with different spatial textures. A container in one kind of space might open into a space with different spatial textures, zones, or gradients.
Fig. 19: An Aristotelian space with its own gradient,
opening into differently textured subordinate spaces.
If a hypertext space contained gradients and directions, then it would be possible, with the assistance of software agents, to give items "natural" tendencies to move or cluster in certain directions or regions. Analyzing semantic content, agents could make items could naturally move in certain ways. Also, as in Aristotle's world, items could be set in unnatural places while retaining a trace of their natural motion or tendencies -- as stones can be set on but walls but remain liable to fall off. Items might show some graphic effects of being moved in unnatural directions, or change in visible ways as they entered different zones.
Fig. 20: Items changing color when moved out of their "natural" area toward other semantic poles.
Or a compound object could, because it is made of different semantic elements, produce several aliases that move naturally along different gradients or toward different poles. This would go beyond Aristotle by allowing items to be in more than one place. The aliases could cluster in their natural locations while the items themselves were freely positioned elsewhere.
Fig. 21: An item being moved to a chosen location
while leaving behind aliases at its "natural" semantic poles.
The semantic parameters that determined what was "natural" could be variable, providing another tools for creativity and classification. People could work on the structure of the space, embellishing or altering it and what was natural there. In addition, algorithms could analyze user-created groupings and create spatial-semantic gradients and attractions. Incremental and emergent structurings could be algorithmically suggested while remaining open to flexible revision. (At one point during the development of VIKI there was a plan to have collections exert a "gravitational force" on newly imported information; the influence could have been overridden by the user with a joystick interface.)
7. Conclusion
We might ask whether Aristotelian spaces are really different or just the arrangement of landmarks and agents in a Newtonian space. On the screen there is no obvious difference between an Aristotelian space and a suitably furnished Newtonian space. It is true, too, that once the concept of a pure geometrical space has been developed, it cannot be forgotten and space read only as concrete Aristotelian zones. Aristotelian textures and gradients can be represented by the placement of selective attractors in a flat space. We should remember, though, that experientially the concept of purely geometrical space is an abstraction from a more primal experience of space as textured and zoned (Casey 1993). There is a psychological contrast between creating movable labels and attractors versus working in a space with textures and poles. Aristotelian spaces are easier to implement than the more radical Einsteinian curved and other odd topologies. They are also closer to our daily experience, so they bring more affordances to aid spatial information triage and structure building.
The sharpest contrast, however, remains the one between a continuous background space, whatever its nature, and a discontinuous Leibnizian network of links. Spatial hypertext systems need a continuous background for free motion, over which a link network may or may not be represented. Combining the two increases the useful possibilities available, and varying the nature of the background space may increase them yet again. Spatial hypertext could then benefit from the interaction of semantic and spatial parsers assisting users with large scale textures and structures.