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Concepts and terminology
A central issue of digitally based analysis of data is the linearity vs. non-linearity of an argument. The very fact that a proper term is missing to refer to non-linearity suggests that the field remains wide open for a clarification of the issue. As a contribution in that direction, we should reflect on some key concepts, distinguishing between the form and the substance of the argument.
While I suggest alternative positive terms (multi-linear, polyhedral) in lieu of the negative term “non-linear,” I do nevertheless retain the term “non-linear” simply because, by virtue of its oppositional value to “linear” and on account of its popularity, it provides a more immediate understanding of what is meant – as long as one attempts, as I do here, to explain what this meaning is.
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Multi-layering
In most cases, an argument includes multiple layers or registers, interlocked with each other. In this respect an argument is not only linear, but multi-linear, with the various threads running parallel, and yet calling at the same time for cross-overs from one linear path to the other. Thus, in the schematic rendering below, A is the main register, which runs linearly from beginning to end, and B and C are secondary registers which overlap either wholly (C) or partly (only the central portion of B being relevant to A). The argument still flows sequentially, but with data and inferences drawn from multiple planes.
Schematic representation of a multi-layered argument
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Reflection
The mechanism described here helps to understand what is the nature of reflection. To read in the sense of studying means more than being led passively along the sequential line proposed by the author. Rather, the reader is expected to develop parallel lines of inquiry and to draw on parallel data sets while following the argument presented by the author. There is, in other words, a parallel set of layers that the reader juxtaposes to those already offered by the author.
This multi-linear function can be greatly enhanced when articulated digitally – which is precisely the great promise of the medium. Access to these multiple layers is dramatically facilitated by the medium, because of the way in which they are structured: there are unlimited lines of inquiry that are built on equally unlimited bodies of data. The task of a digitally minded scholar is to capitalize on these possibilities of a non-linear approach understood as multi-linear, but developing a newly constructed digital text.
The non-linear, or multi-linear, perspective is interesting in that it shows both the positive and the negative aspects of the medium.
The positive side is that
- the bracketing of layers is practically unlimited;
- a suggestion to explore a parallel layer can be elicited by explicit or implicit associative mechanisms (hyperlinks, search functions, etc.);
- within each layer one can pursue an independent autonmous argument.
The negative side of things is that the ease with which one can dart from one topic to the next, and even more frequently from one detail to another, leads to distraction – the very opposite of reflection
Contextualized hyperlink path ("reflection")
Non-contextualized hyperlink path ("distraction")
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Linear and poly-segmental
It is further worth noting that, strictly speaking, even the linkage represented under 3 remains linear, since the linkage is indeed a line. To reflect properly the situation, the terms “poly-segmental” and “mono-segmental” are equivalent to “linear” and “non-linear.” The argument’s process represented under 2 is linear, but consists of many segments. The argument’s process represented under 3, on the other hand, is also linear, but, as it cuts across the polyhedron in the most direct way, it consists of a single segment, and is therefore more effective. Obviously, the degree of effectiveness increases in proportion to the complexity of the structure.
The Urkesh Global Record is built in such a way as to allow precisely an extensive use of polyhedral arguments. In practice, this relies on systematic use of hyper-links, which are generated automatically and therefore in unlimited quantities. The arrow represented under 3 in Fig. 10-1 stands for such a hyperlink.
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Intuition
It is worth noting that the situation represented under 4 describes properly the nature of intuition. A connection between A and B may well be perceived through a sort of logical short-circuit, one that bypasses the argument and cannot therefore be demonstrated – at least, not on the basis of the original intuition. But we all know that in most cases it is precisely such an intuition that initiates the process of discovery. A proper polyhedral argument is one that, building on such an intuition, shows how the linkage is possible, and therefore arguable.
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Pre-digital non-linearity
tablet
The term “non-linear” has achieved nearly cultic status in contemporary parlance. It evokes a sense of mystery, which gains in awe and power the less we try to explain it. It is, however, no different than the case of Molière’s bourgeois who felt he had reached a pinnacle at the discovery that he was able to speak in prose…
We have been conceptualizing our world in a non-linear fashion at least ever since writing was first invented, some 5000 years ago. The earliest ledgers, the earliest maps are based as much as today’s ledgers and maps on linkages that are not linear.
Consider this cuneiform tablet, from about 2000 B.C. It lists individual animals given to certain individuals (single circle), then it gives subtotals by types of animal (double circle), and finally gives the grand total (triple circle). It is so simple, anyone can “read” the numbers. Thus the grand total is 5 times 60 (the large vertical wedge), plus 10 (the oblique wedge head), plus 4 (the smaller vertical wedges). The connection is clear among all the various steps. It is non-linear, because it presupposes conceptual jumps, evinced by the sequence and general arrangement.
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