Using the Tools of Structure
By: Charles L. Owen, Distinguished Professor Emeritus, Institute of Design, Illinois Institute of Technology
Monday June 16, 2008
Problems worthy of innovation range across the map from
seemingly simple ones like the design of low-function objects
(think tableware) to complex systems so multifunctional it's hard even
to know where to start. For complex problems, as you might expect,
we usually insist on some kind of structure to work from; but for the
"simple" ones, we almost never feel the need. Somehow it seems right
to innovate within structure for a big problem, but its OK to treat
lesser problems as one-shot idea generation exercises.
The reality is that structure is the tried and true friend of
innovation. For big problems, it can show not only where to begin,
but how aspects of the problem fit together, how the context of the
problem is organized, how solutions can be best communicated, how
systems can be modeled for evaluation and comparison, and much, much
more, as they say. The interesting thing is that, from the
planner/designer/innovator's point of view, the same constructs that
help us to bring order to big problems work to expand our thinking
for the seemingly simple ones. The tools of structure are tools
of innovation.
Graphs and Hierarchies
What I mean by "structure" is (1) an organization that abstracts
the real world to a chosen set of things we wish to think about, and
(2) one or more ways to think about those things that creates the
organization. There are more ways than one to represent structure.
Two that I think make great sense for concept building are graphs and
hierarchies. By graphs, I don't mean the x/y plots, bar charts and pie
charts familiar to everyone, but the network-like models that show how
elements in a set are linked to each other. Hierarchies are probably
more familiar - they should be; they exist all around us - but, like
graphs, the information they convey is dependent on what they organize
and what relationships they use to do the organization.
Both graphs and hierarchies have been subjects of mathematical
appreciation since Leonhard Euler invented graph theory in 1736. Euler
put together the first principles while explaining to the burghers of
Königsberg, Prussia why they couldn't find a way to walk from their
homes around the city and back again while crossing all seven bridges
spanning the River Pregel only once each, The challenge had been
a traditional Sunday after-church exercise for many years (try it―
Figure 1 is a diagram of the river and bridges in Euler's time).
 Figure 1 - click image to view PDF
In November 1968, under the auspices of the McDonald Douglas Corporation
and the University of California Irvine, the first scientific gathering
on hierarchy was held in California, "bringing together scientists,
engineers, designers and others interested in the function of hierarchical
structure in nature, concept and design" (Hierarchical Structure.
Whyte, Wilson and Wilson. eds. NY: American Elsevier, 1969). Some 47
speakers presented papers from nearly as many disciplines, all exploring
hierarchy as seen in their domains of study. Whether it exists in an
identifiably real sense or is a conceptual overlay to bring order to
complexity, structure is fundamental to human comprehension.
Mental Manipulation
Two interesting numbers relate to this. First is George Miller's famous
"magic number 7 plus or minus 2". In his well-known 1956 paper,
Miller discussed human capabilities for dealing with amounts of
information. From a number of studies, he concluded that our capacity
is limited (perhaps to 7 items plus or minus 2), but that we can
increase our ability by coding information into chunks that can be
remembered and manipulated as individual information elements and
then decoded (an example of superimposing hierarchy). Among many uses
of this information is the general admonition to executives to organize
with no more than 7 (plus or minus 2) individuals reporting to a single
superior.
A second number of interest is 3. This one came forcibly to my attention
at a cybernetics conference some years ago. After watching a
government researcher illustrate his entire talk categorically with
each category containing three sub-categories - at every level of
every topic - I asked (not too innocently) if there was any significance
in that. I got what I deserved when he told me it was just an example of
"Peirciadic triadomania". A little private research later revealed
that Charles Sanders Peirce, the eminent logician, philosopher and
founder of semiotics and pragmatism, was fond of three-part categorization
in his writings…
From a psychological point of view, though, the use of 3 makes sense
(Figure 2). When we have to choose sub-categories for a category, we
look for word descriptions that "feel right" in balancing the choices
with each other; parallelism, consistency, coherence and other principles
for comparison come into play. Two sub-categories is too easy - only
one comparison to consider. Three requires three evaluations, not
at all difficult and much more satisfying. Four, on the other hand,
requires six comparisons to be considered, twice what were
required for three - up around Miller's magic number and not too easy
to do. Five requires ten comparisons, and we begin to lose control.
With sub-categorization of more than three, the list is increasingly less
likely to be well-balanced. The four graphs of Figure 2 visually
demonstrate the rapidly rising complexity of the task.
 Figure 2 - click image to view PDF
So what does this have to do with structure and innovation? First,
it explains again why it is hard to deal unaided with complexity;
second, it suggests a tool that can help. Graphs give us a way to
visualize complexity with a precision brought about through abstraction.
They afford us a tool for selectively examining the effects of specific
relationships in organizing elements of a problem. Figure 2 shows
forcefully how increasing the number of elements exponentially increases
the relationships to be considered among them.
Relationships can be virtually anything as long as they can be expressed
clearly enough to be tested against the elements. Insights gained usually
derive from seeing how groupings assemble for a specific relationship;
however, there is often insight to be gained in seeing which items are
not linked as well as seeing which ones are.
Using the Tools
Figure 3 shows a graph that organizes a set of fifteen elements.
A link between elements indicates that the organizing relationship is
satisfied. The set of elements might be fifteen controls,
gauges and warning lights on a piece of equipment under development,
and the relationship might be "in emergency, is used together with".
The tests are made by plugging in successive elements and asking,
is it true or false that: x “in emergency, is used together with” y ?
 Figure 3 - click image to view PDF
A graph often provides enough structure to reveal insights not otherwise
readily obvious. If the graph is large, however, Miller's magic number
comes back into play, and it is useful to bring in hierarchy to help.
Figure 4 shows the same graph with superimposed boundaries that "chunk"
the elements into six clusters of highly interrelated elements. In this
case, the graph is small enough that this single level of hierarchy is
probably enough structure to provide all the insight necessary (groupings
for the controls, gauges and warning lights, for example). If that isn't
enough, however, the clusters can themselves be clustered as shown
in Figure 5. In this case, the form generally shifts to one of the
familiar tree-like structures better suited to communicating complex
hierarchical information.
 Figure 4 - click image to view PDF
Hierarchies allow us to represent and look intelligently at very
complex collections of information. Since the 1960's when computers
became relatively capable and available, it has been possible to use
the tools of structure effectively for many purposes, including
innovation. The invention of numerical taxonomy in the '60's furthered
this considerably. Computer programs implementing numerical taxonomy
concepts (such as RELATN used in Structured Planning) enable us
to construct typologies organizing sets of elements according to almost
any characteristics we see as important. For example, if we were
contemplating the development of the next generation of cell phones (or
maybe better described as "personal communication devices"), we might
wish to see how existing kinds of informal communications organize
themselves against a series of characteristics possibly important for
potential users. These could include formality required, privacy
afforded, transmission fidelity, emotive capacity, simultaneity,
spatial reach and many more possibilities.
 Figure 5 - click image to view PDF
The study diagrammed in Figure 6 used 39 such characteristics.
The computer calculates the amount of similarity between message types
based on the characteristics scored and establishes a graph with links
where the similarity is strong. The important thing is that similarity
is what we say it is - we choose the characteristics that define
it, and we decide how important each is. When the graph is
complex enough to benefit from hierarchical structuring (usually),
the computer is called upon to build a hierarchy (the VTCON program
is used in Structured Planning). The final structure is tree-like, but not
necessarily a tree because elements (and clusters) can belong to more
than one higher level cluster. The name for this kind of hierarchy
is a "semi-lattice". It is a more general form of hierarchy than a
tree and is usually more appropriate for the kinds of typologies
created when exploring the subjects of human innovation.
 Figure 6 - click image to view PDF
The structure in Figure 6 is a semi-lattice organizing types of
communications from the previously mentioned 2001 study on media.
Labels on the far right summarize the first level media clusters
formed using the 39 characteristics. As an example of interpretation,
the shaded area suggests an emerging market for delivery of urgent,
confidential messages with high fidelity and reliability - an early
warning of the social communication revolution now overtaking youthful
cell phone users.
Similarity is useful for generating structure in many of the phases
of innovation. But one of the most powerful uses of structure for
innovation is in the organization of the synthesis phase when the
relationships among Functions are reconsidered. In Structured
Planning, a special measure has been developed to link elements that
should be considered together (the Functions discussed in "Covering
User Needs") not on the basis of similarity or categorical likeness,
but on the basis of whether there is a strong likelihood that they
would be affected by the same solution concepts. I will discuss this
in the next article.
 Figure 7 - click image to view PDF
For those still wondering about the burghers of Königsberg, Figure 7
abstracts the bridges and city neighborhoods to a graph such as Euler
used to show why it was impossible to make the "once each bridge"
journey and get back home. I don't think he told them, though, that if
they just built two more bridges - or took two away - they could.
Try it again.
Charles L. Owen is Distinguished Professor Emeritus at the Institute of Design,
one of the six academic units of the Illinois Institute of Technology (IIT) in Chicago.
There, Mr. Owen conducts research and teaches semiannually in the MDes, MDM
and PhD Design graduate programs.
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