Design problem analysis and process. A case of technology - augmented problem decomposition in analysis and understanding of public space

: Values of a society surrounding civic health are reified in the ideal of public space as space capable of receiving behaviours which have creative provenance, are evolutionary, are even unstructured. These inventive and spontaneous actions, however, present obstinate design challenges. They are hard to anticipate precisely through reading environmental factors. They are innumerable. They broaden the problem space outstandingly. | Design for next addresses reframing design investigation, approaches, processes and tools. | One of the problem-solver’s strategies is mobilization of technology as a tool of production/process. Another is decomposition of the problem. We decomposed that alternative behaviours are functions of reinforcement. We explored the reinforcement-behaviour relationship through agency of two computational models. For data, students on campus completed surveys. Each respondent listed activities she/he would freely perform in a depicted space. In the current paper, we enquire into reading, dancing, skateboarding/skating and working-out in public space. Each converged on a hyperbolic solution.


An assumption
The city is a vastly elaborate system, networked and entangled in diverse ways. We aver that the city is a complex system. (See section 1.2.) We observe that, within the complex system of which the city is constituted are subsystems, some of which are, themselves, complex (e.g. street and alley networks and their evolution).
Within extant subsystems, there are varied impulses, including ostensibly random provocations and their attendant responses. Such, for instance, is the case of some of the behaviour of the inhabitant of the city in the latter's public spaces. Humans in the city exploit its spaces in inventive ways.

The matter of complexity
Vast entanglement is not tantamount to complexity. Zuchowski (2012) has urged a distinction between complexity and other states, such as chaos or randomness, which might be mistaken for it. She has proposed that complexity in systems could be described in terms of two dynamical properties. First, complex systems are many-component systems. There are multiple components in action. The second criterion for complexity, according to Zuchowski, is that complex systems "feature directed interactions" (p. 186). In other words, each component of the system has specific other components with which it interacts in particular ways. In her final definition, Zuchowski noted that these directed interactions yield "locally distinct patterns" evident in, at least, one representation of the evolution of the system (p. 200).
The city is constituted of myriad components, so the first of Zuchowski's criteria is met easily. The second criterion could be approached in different ways. We offer the following instance. People watching a sport activity are involved in a directed intervention--between players and audience. There are localized evolutionary patterns: audience members cheer players at particular points in time and there is concomitant increase in effort by players. These forms of directed interaction can be seen across life in the city: people-coupling-shopping centers; limestone facades-coupling air and vehicle exhaust/pollution; humans-coupling-navigation-coupling-landmarks; etc. Chen and Crilly (2016) suggested that an aspect of complex systems could be a "multi-structural function realisation," where a function maps onto "more than one architecture" (p. 20). Behaviour, as we have employed it in the current paper, is mapped with multiple elements (forms of reinforcement) and identifiable patterns are evident--both in the short term (activated response) and long term (deceleration towards a behavioural ceiling with increasing interval of reinforcement).
In summary, we are making the observation that our system (the city and its existence as an organic unit) possesses the dynamical properties of multi-element constitution and directed interaction. Representational patterns may also be detected in cases of the directed interactions. The city is a complex system.

Scourge of complexity
In a way, the challenge of designing some modern-day systems may be described, tongue-in-cheek, as a self-inflicted scourge. Humans have acquired greater knowledge and developed more sophisticated tools. The complication is, the problems themselves have become more intricate as we have improved our capacity for penetrating them. Our more advanced knowledge and tools are able to uncover more of the structure of things and the configurations have gradually taken on a greater appearance of complicatedness.
In terms of Zuchowski's (2012) dynamical properties of complex systems, it has become increasingly difficult for the unaided human mind to keep track of all the components in a many-component system and chart all their directed interactions. Unearthing new problems and their components have placed exertion on the unaided human mind in its attempt to keep pace.

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Design problem analysis and process. A case of technology-augmented problem decomposition in analysis and understanding of public space 1.4 Elusive complex: The divergent problem of inventive action and the implicitly veiled problem of spontaneous behaviour Uncounted instances of alternative consumption, colonization or inhabitation of public space exist and they do at different levels of sophistication. Instances include an eight-foot metal pig planted on a sidewalk (Seattle); installation of benches in empty spaces ["Guerilla benching"] (London); dancing in streets (Beijing); skating atop the structural arch which partially suspends a pedestrian bridge (Melbourne); leapfrogging over bollards lining a promenade (Melbourne) (Chen, 2010;Hou, 2010;Stevens, 2007).
These occurrences of informal behaviour and activity, of the spontaneous event and unintended occupation, generate, Hou (2010) has noted, new uses and forms of public space which "defy or escape existing rules and regulations" (p. 10). The behaviours "transform urban spaces into [sites of] potentiality, difference, and [even] delightful encounters" (Watson, quoted in Hou, 2010, p. 10).
Uncharted usage of space by the urban dweller demonstrates, said Stevens (2007) an "integration of desire into [otherwise] rational everyday practices" (p. 75). The result is a kind of "urban informality" (Laguerre, in Hou, 2010, p. 12).
Within the metropolis, it is possible to observe inventive uses of space for ends for which the space was not principally designed. It is also possible to witness public acts that could be described as spontaneous, impetuous, unconstrained or with any such term characterizing some degree of impulsivity. Inventive use expands range of use by extending functional definition of components/constituents of a space. Spontaneous use does the same, but it is conceptually somewhat more intractable because of an obscure, inherent capriciousness. We will take a loose definition of spontaneous or inventive to be "not inhibited or constrained by manifest environment." We employ the term, alternative behaviour, to capture all such forms of behaviour.
There are certain obstinate challenges with alternative actions. One is that they are hard to anticipate precisely through reading environmental factors. A second challenge is that there likely exists an uncountable number of possibilities of action and that makes the task of assigning definite chances to them more confounding. Generally, for the designer of space, matters of spontaneity and inventiveness complicate designing.
All of the foregoing cast greater light on the deficit embodied by the designer when dealing with complex problems and problems with either vast or indeterminate boundaries. The fact of it adds to the general wisdom of taking advantage of technology to reduce the burden of problem solving for the designer--or, at least, prepare a softer landing for consequences (Meng, 2015). As humans, our ignorance of certain things is sustained by the fact that our rationality is bounded (Meng [Simon], 2015). One way forward is to design (or use) systems that "outsmart" us (Meng, 2015). In that, we have the technologies of mathematics and the computer, among other things. Following, we present a case.

Problem decomposition
One of the problem-solver's strategies is to carry out decomposition of the problem of interest. The problem of alternative behaviour is, as argued, vastly intricate and there are bound to be numerous ways of decomposing it. There is time in this paper to address just one reframing of the problem. We suggest that spontaneous behaviour in public space might be "predisposed" by reinforcement,

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AWONIYI STEPHEN that people are instigated to act in particular ways when forms of reinforcement attend those types of behaviour.
Elsewhere (Stephen, 2015), we have proposed different forms of reinforcement that might attend behaviour in public space. (See table 1.) Apprehension of the presence of such stimuli is an early step in sketching a generative description of behaviour in public space and speculation on some behavioural possibilities, to the extent that the latter is possible. These stimuli could be considered as values. It is likely cumbersome for a designer to attempt to work with all of the values in concert, besides the fact that the idea of reinforcement itself could not always be directly embedded into a design-as-tangible-artifact. It is here that the tools of mathematics and the computer come to be of effectiveness for the designer. These tools are able to take such values, regulate them conjointly, iterate on them and, with outcomes interpreted by the researcher, offer the designer a pathway to a more informed problem analysis--and, ultimately, design solution. In the current paper, we attempt to explore the conjugate pair, human behaviour and reinforcement, using said tools as facilitators.

Matching law and MPR
Herrnstein proposed the matching law as a system for describing the relationship between reinforcement and associated behaviour (Herrnstein, 1961;Poling, Edwards & Weeden, 2011;Reed & Kaplan, 2011). The matching law has its expression in the following equation: (1) where B represents observed response, R is known reinforcement, Re is an estimate of sum of all other forms of reinforcement associated with off-task responses not captured by measurement system used and k is an "estimate of the sum of all on-and off-task behaviours" (Reed & Kaplan, 2011, p. 20).
Design problem analysis and process. A case of technology-augmented problem decomposition in analysis and understanding of public space An analogous model was offered by Killeen (1994) in the mathematical principles of reinforcement (MPR). In MPR, three core principles (specific activation, temporal constraint and coupling) are used to model the relationship between behaviour and reinforcement. MPR is articulated as follows: ( 2) where B represents behaviour, R represents reinforcement, a is specific activation, δ is temporal constraint and C• is coupling coefficient. 1 We have attempted to describe behaviour in public space using the MPR model in particular (Stephen, 2015).

Readers' space
In a given case, we collected written survey data. In two separate public open spaces on a university campus, students voluntarily completed one of several types of form handed out to them. Each form had a photograph of a public space. There were different images, but they were repeated across forms.
In one form, respondents were asked to list activities they would freely perform in the given space.
Respondents included how long they would perform each activity. They also indicated on a rating scale how much their free behaviour would be motivated by another's approbation.
Simulation through use of images has been documented as an effective protocol. Stamps (1999) indicated that correlation of ratings received from color slides with those obtained on-site was at r = .83. (See also, Stamps, 1993.) In a later meta-analysis involving 84 empirical findings and 967 environments, Stamps (2010) found the correlation between on-site subjective responses and those obtained using static color simulations to be a slightly higher, but comparable, r = .86.
In a paper (Stephen, 2015), we have presented an MPR-driven model of one of the activities respondents included: reading. Following, we summarize actions involved. Space will not permit full elaboration. The reader interested in more detail will be able to find them in the cited document above.
We employed the variable interval (VI) model. The VI schedule is one where the first response "following varying intervals of time with a specified mean value is reinforced" (Bancroft & Bourret, 2008, p. 227). We created schedule levels which we termed an episodic set due to the fact that they are conspicuous in human experience. We generated members for our schedule set using a derivational system presented by Catania and Reynolds (1968).
We specified values for the three MPR principles--specific activation (a), temporal constraint (δ) and coupling (C•)--through a combination of extant data, prior modelling values (Killeen's) and simple calculations. We constructed and optimized an equation for behaviour (B) and derived plots which, as hoped, returned as hyperbolic. In terms of activation, a, we ran our final model on reading data twice: once using "a" drawn directly as median value from our observed data and a second time as derived from another portion of the observed data which we interpreted as arousal. 2.3 Readers' space revisited + dancers + skateboarders + workout aficionados 2 In the current paper, we revisit the reading model outcomes. Already introduced in the earlier paper (Stephen, 2015), we take up the use of an arousal indicator (A) from our data (mean Aread = 5.82 on a 0 to 10 scale; n = 65) for calculating activation (a). Operationally, for future purposes, we believe that using a decompositional approach as this will provide us with an additional analytical facility in the capacity to regulate the parameter during iterative investigations. Consistently, in this paper, we maintain the arousal-derived form of activation.
One of the matters addressed in Stephen (2015) was respecification of δ. A value of 0.20 was signalled. Pragmatically, δ as reciprocal of k yields the same value (Killeen, 1994). In the current paper, we employ that latter standard.
In the current paper, in place of calculating coupling coefficients with δ acquired from extant secondary data, we derive particular values of δ from our observed data and substitute those values into calculation of coupling coefficients. In addition, we use our data-specific δ (as opposed to δ extracted from secondary data) in calculating response values in every schedule.
Moreover, in the current exploration, we create a new set of VI schedules, delimiting our time space to the period of one day. Members are derived for each schedule. Employing the MPR model (equation 2 above), we calculate response values (B), perform optimizations and generate a plot ( fig.  2).
Furthermore, in the current paper, we import B values into Wilkinson's model (McDowell, 1981) for estimation of k (total amount of behaviour) and re (aggregate of extraneous reinforcement) values. Following, we generate another, different set of across-one-day VI schedules, derive members, and calculate B values, this time, using the matching law equation (equation 1 above). We perform optimizations, and generate a second plot ( fig. 2).
Comparison of the two plots in figure 2 shows that both parallel schedules interrogated, articulated with the two separate models, are convergent in form--which suggests viability of a reinforcementbehaviour description model. Careful observation by the reader will indicate different ordinate values between the two plots. In the MPR plot, we held the previous conjectured, ideational ceiling 2 Caveat: ns will be small for robust estimation. Models are descriptive, not predictive.

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Design problem analysis and process. A case of technology-augmented problem decomposition in analysis and understanding of public space of response across 336 days at 5 hrs. 3 In the matching law plot, we have set the 5-hr. ceiling across 1 day. Consider this a stress test to see if the formal model would hold under such adverseness. As clearly illustrated, it does. (Figure 3 shows a comparative MPR-matching-law plot at the ceiling of 5hrs. across 1 day. Difference in response at 1-hr-reinforcement is marked.) We carried out the foregoing series of steps of model exploration with three other public space activities observed through our data. (We are able to discuss only a few.) Below, we present model plots for dancing-in-public-space (n = 21; Adance = 5.38), skateboarding/skating-in-public-space (n = 18; Askate = 6.17) and working-out-in-public-space (n = 27; Aworkout = 5.52).

(Both models set at 5-hrs-across-day ceiling).
3 While the episodic reaches beyond data range, we hold it tenable for the time being because it reflects the model kept strictly within the 1-day data range (Fig. 4).

Discussion
The presented models represent a work in progress. It is obvious that our investigations portray early stages of a potentially expansive undertaking. There are several issues to consider. Currently, our n's are relatively small. The population examined is delimited. The behavioural range is vast. Some data could be otherwise (e.g. ceiling for skateboarding/skating could be higher than the observed 2 hrs.). Not unexpectedly, errors could be further minimized. There needs to be continued optimization and/or re-estimation of parameters.
The above suggest considerations for future work, but there are also favourable outcomes. Models have expressed hoped-for form. The accelerating arm of the graphic model is less steep than in some prior explorations (see Stephen, 2015). That signals a rich environment (McDowell, 1988;Reed & Kaplan, 2011)--which is reflective of public space. We have been able to identify or derive some sense of critical points and operational dynamics of a model of behaviour--e.g. descriptively, the multi-facetedness of behaviour; a potential ceiling in some cases (e.g. with reading, k across populations will likely not be that different from that currently observed); potential for decomposability (particularly using MPR). As already said, there is suggestion of model integrity; as plots in this paper indicate, models maintain viability across activity types.
There are a few other future exploration possibilities with favourable potential. The media (computer + mathematics) allow us to introduce elucidative parameters which might refine observations or discriminate among lines of activities or conditions (e.g. aversiveness indicators introduced into activity). We are also able to invest parameters and values in modelling agents and generate large numbers of runs of the model. In that last regard, parameters derived from the current model play a mediating role, as they are progressed into an agent-modelling role and the latter is used to explore properties (parameters) and [human] behaviour dynamically. Dynamic data result from interaction between static data (e.g. density) and human action/behaviour. Bernard Tschumi (1994) has described city space as a stage where events are witnessed in a complex spaceuse relationship. Experience of the city, he observed, can be deconstructed into a model: objects + events + movement. All are linked within sequence.

Values of presented model for design
Considering reinforcement as an instigator of behaviour is useful for designers. Whyte (1980) illustrated this multiple times: people stopping to talk in the street and on street corners (autonomy granted) or passers-by who seem to generate spontaneous interest in a photo-shoot and who stop/congregate in order to watch. A designer's awareness of spontaneous behaviour is important and should be an explorative variable of the design process.
Anthropologists, sociologists and ethnographers, generally, talk about the particularistic nature of ethnographic description. That makes it possible for one to tailor solutions to particular situations. Parameters derived from/for particular situations are instrumental for the designer when the problem calls for a solution tailored to fit the instance.
An understanding of behaviour of people in social and public contexts is of interest to more than just designers. Disciplines, practices and persons interested in crowd management, for instance, might find something of interest in these discourses. Some policy makers might take interest in dynamics of public behaviour. For the designer and interested others, prediction of behaviour will certainly be of interest. That, however, is not the only end that drives exploration of the current sort.
Description is a potent, pre-eminent property of science. A model such as ours provides a lens through which behaviour might be contemplated. The ability to enrich description of behaviour (e.g. describe potential patterns; decrypt logics of behaviour; describe effects of behavioural complementary or adjunctive factors such as aversiveness, solitariness, skill [future model targets]; describe points of conflict) could be of direct utility to, not just designers, but critically as well, other students of the metropolis who are regarding the city through their own specialized lenses (e.g. ethnographers, essayists--see e.g. Benjamin, 1999;de Certeau, 1984;Low, 2000;Low, Taplin, Scheld, 2005;Ocejo, 2013;Perec, 1997Perec, , 2000. There is also critical and viable indirect utility--by way of the designer using new information to diversify space design, that, leading to enrichment of space experience and, consequently, provocation of alternative narratives for other critical observers as those mentioned above. In the latter case, the designer is ensconced in the role of a bridge which [who], through the act of recreating the metropolis, has strategically created a platform for other students of the city--sages, scholars, observers, researchers, etc.--to re-engage the city. The agency of ethnographers, sociologists, archaeologists, anthropologists, human geographers, psychogeographers, historians, essayists, fiction writers--these eminent chroniclers of human society, civilization or culture--is facilitated through a designer's shaping of space in a way which takes into account materiality and phenomenology of the space to inform or redefine time-space parameters of inhabitation-dimensions of spaces, layered usage, "temporary rewriting of the urban space," etc. (La Varra, 2000, p, 428; see also Chen, 2010;Haydn & Temel, 2006;Whyte, 1980).
In the end, our goal is not to do designing for the designer. That agency still remains the designer's.
Our hope is that we are able to provide counsel which might inform the designer crucially about decisions being made.

3.2/3.3 Values of technology for design and design research
The theme of this track is the future of technology in design and design research. Questions include, among others, appraisal of how "technology scenarios will change design research and practice" and examination of "how tools, methods and the purposes of design" are evolving. In that thematic light, we shall discourse here on our presented model in terms of its technological benefits.
In the toil to manage the increasing sophistication of our problems, a solution presents itself in technology turned upon itself. Technology reshapes or transforms some of the human world into its own modality, but the human mind also possesses ingenuity, a capacity which enables it to re-cast its own world in the language of technology and then use technology to solve some of the design problems the latter has, elle-même, been a collaborator in generating or structuring.

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Design problem analysis and process. A case of technology-augmented problem decomposition in analysis and understanding of public space We discuss several assertions made by technology in argument for itself as a vital player in designing for next. 4

Manifold computations
Modelling involves numerous calculations. For instance, in just one run over our data on reading, we counted about 15 distinct calculation brackets. When schedules we used were included, there came about 65 calculations. Adding some confirmatory checks increased the number to about 92. This last figure does not include revising errors, re-confirming again, etc. It does not, also, include working with other data presented (dancing, skateboarding/skating, working-out). Some of the computations involved sophistications such as exponents. The human mind would grow weary if it were to do all these by itself.

Networked variables and interactional webbing
A survey of the presented model showed numerous instances of tracking interactions between multiple variables (and performing calculations on them). Efficiency of mathematical representation and computerized control facilitate management of the processes involved. The unaided human mind might feel oppressed under such labour.

Large number of iterations
While iterations in the cases presented have not been extensive, many more will be present in continuing explorations. These iterations will number in hundreds and thousands. The human mind, working alone, holds a monumental deficit when such tasks are called upon.

Representation
Iterations, through brute force, serve another purpose. They yield a desired by-product of problem "normalization." One could look at it this way: As iterations grow larger and larger, potential for capturing more and more possible conformations of the problem increases. Thus chances for a more adequate representation of a phenomenon in its different guises are improved.
The facilitation lent by technology in its capacity to make the above practicable--i.e. computation, interaction, iteration, inclusion--engenders another rank of benefits. It is as if brute force, in the process of saturating the possibilities above were able to reshape a different world in which a different class of investigative operations became feasible. Facilitation, brought about by sheer technological force/power, shapes a platform.

Solution refinement
Capacity of a computer to manoeuvre multiple variables simultaneously, iteratively or dynamically provides a powerful tool for convergence on a solution to a problem. "Brute force" begets an outcome which is, comparatively, refined. We were able to draw on this facilitation.

Decomposition and resource engineering
Isolation of components of phenomena can be managed during the process of analysis. Opportunity is afforded for some components to be integrated in new ways. For instance, we were able to "splice" our observational data described as arousal into matching law procedures through facilitation of MPR. If one were estimating k and re by fitting a curve to observational data directly about reinforcement and behaviour, arousal would not be explicitly articulated. Due to the fact that this latter was a basis for expressing our MPR data and those MPR data, by order, preceded our matching law estimations, we are cognizant of the express presence of the arousal factor in the latter.

Reverse exploration
Secular time moves deterministically forwards. When certain things are needed to beget others, there is an imposed order. With adequate computational functionality, one could preempt and project forwards. Following MPR, we were able to hypothesize values and fit a curve for generating re. Computational models can be used to transcend the rationality of time.

Predictability or thick understanding? A final note
In summary, a designer could benefit in one of two ways, given the form of exploration in which we are engaged. She might become able to predict (e.g. behaviour). On the other hand, she might benefit from a richer understanding of the phenomenon on hand. Regarding the former, whether one subscribes to an epistemic character of indeterminacy (we do not know enough or measure well enough) or an ontic character (there are intrinsically random possibilities of things) (Kuś, 2015; also see Ciprut, 2008), the challenges of predicting human behaviour perfectly, especially with alternative behaviours, could be significant. Having a rich understanding of phenomena (the latter benefit), at least, might provide insight into how one might reduce degrees of freedom--besides the fact that it facilitates eruptions of rich histories and narratives.