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Elegance is often invoked as a characteristic of good design, but it cannot be pursued as a design objective because of the absence of actionable definitions that can be translated into design strategies and metrics. In this work, we analyze elegance in the context of systems engineering using a perspective that integrates visual art, Gestalt psychology, neuroscience, and complexity theory. In particular, we measure elegance as effective complexity and theorize that it can be achieved by a process of complexity resolution based on the adoption of eight visual heuristics. We present an empirical study in which a sample of systems engineers were asked to assess alternative representations of a same system and show that effective complexity is strongly correlated to perceived elegance and systems effectiveness. Our results are consistent with independent findings obtained in other fields including design and psychology of perception showing that good design must embed an effective level of complexity achievable through a mix of familiarity and novelty.

Research in neuroscience has made substantial progress in the last decade in improving our understanding about how our brain produces knowledge by extracting meaningful patterns from the flow of data that hit our senses. The complexity of the brain has evolved in time integrating the older subconscious and emotional strata with the more recent conscious and rational layers [

Drawing from Gestalt psychology [

Building on this perspective and findings, we argue that if evolution has hardwired the human brain with cognitive abilities for the appreciation of beauty, the aesthetic value of a representation must also matter for other practical purposes. In the engineering realm, systems engineering has been found valuable in dealing with complex system because of its inherent capability to reduce complexity [

In order to explore this idea further, based on findings and theories developed in design [

Artistic strategies for reducing complexity.

Noise-killing strategies | Add-meaning strategies |
---|---|

( |
( |

( |
( |

( |
( |

( |

Gell-Mann and Lloyd [

Interestingly, we found out that there is an overlap between the competences that artists and system architects need to master to design artifacts whose internal complexity matches the external complexity of the task they are designed to address [

In this paper, we test this hypothesis further. In particular, we present an empirical study in which we surveyed a sample of systems engineers about the perceived effectiveness and elegance of alternative architectures of a same system. Our results show that systems architecture elegance can be measured as effective complexity [

The remainder of the paper is organized as follows. Section

This research was designed to test the following hypotheses:

Perceived implementation effectiveness is correlated to the structural complexity of the architecture.

Perceived elegance is correlated with the effective complexity of the architecture.

Effective complexity is higher when both noise-killing and add-meaning strategies are used more intensively.

A sample of 54 systems engineering experts was presented with various candidate architectures of an automated teller machine (ATM); specifically, functional architectures have been used. Subjects were asked to rank the architectures based either on their perceived implementation effectiveness or on their perceived elegance (no definition of elegance was however given to the participants). Each participant was randomly presented with only one of the evaluations in order to avoid temporal precedence biases. Eight architectures were developed using different strength levels of the strategies reported in Table

Response data, together with demographic information, were collected via an online survey over a period of two weeks; each participant completed his or her task within 15 minutes in a single individual session. Participants worked autonomously, and there was no interaction between the participants and the researchers.

The ATM was selected to guarantee that the respondents were familiar with the operation and objectives of the system of interest. Besides, our subjects were experienced systems engineers that were familiar with systems engineering representation and notation; finally, the ATM system description we used in the empirical materials describes a traditional ATM service. These measures help in reducing the risk of biased evaluations that are obtained in single-shot assessments (assessments with just one evaluation phase without prior familiarization, see Section

The independent variable in this investigation is the set of artistic strategies that were used to develop the various ATM architectures. The strength or presence of the eight strategies in each architecture was assessed by an expert on a seven-point scale (1 corresponded to the “lowest level” and 7 corresponded to the “highest level”). Each level of the scale was anchored to descriptors determined through the construction of an evaluation rubric (see Supplementary

Two dependent variables were measured: perceived implementation effectiveness and perceived elegance. Participants were required to rank the alternative designs in terms of both variables using a 1 to 8 ordinal scale, where 1 indicates the most preferred and 8 indicates the least preferred.

In the survey, we did not provide any specific objective or requirement for the architectures because the goal was to measure structural perception as opposed to a more rational/technical analysis of the system. To compensate in part for this constraint, we considered a system of interest (i.e., the ATM) whose overall purpose and user’s needs are known by most adults. The time to complete the survey was limited to 15 minutes, much less than what would be necessary in a real-life assessment of a system’s architecture. Again, this limitation was enforced to capture perception and to prevent subjects from engaging in a more in-depth technical analysis.

The survey was divided into two parts (Supplementary

Examples of two architectures.

The diagrams were represented as box and arrows workflow and did not contain formal notations because the use of a more formal description could have affected the ranking depending on the level of expertise or familiarity of the participants with the specific modeling language. Every diagram was identified through a letter from A to H.

The diagrams were attached to the survey in a downloadable MS PowerPoint file and randomly displayed in a single slide as in Figure

Alternative systems representations of an ATM used in the survey.

The survey consisted of a single question asking participants to rank the eight diagrams in terms of either perceived implementation effectiveness or perceived elegance. Both surveys were administered online via Qualtrics and could be accessed via a web link provided to the subjects.

The architectures were designed by one of the authors of this paper to deliberately incorporate the strategies

Strength levels of the artistic strategies in the eight ATM architectures.

Diagram | Strategies | ||||||
---|---|---|---|---|---|---|---|

Subtract details |
Symmetry |
Grouping |
Split |
Emphasize |
Power of center |
Contrast/balance | |

A | 6 | 7 | 5 | 4 | 4 | 7 | 7 |

B | 6 | 6 | 5 | 4 | 7 | 7 | 7 |

C | 4 | 3 | 2 | 2 | 2 | 4 | 4 |

D | 3 | 2 | 2 | 2 | 2 | 3 | 3 |

E | 2 | 6 | 1 | 1 | 1 | 1 | 1 |

F | 6.67 | 7 | 6 | 6 | 5 | 7 | 7 |

G | 6.67 | 7 | 6 | 6 | 7 | 7 | 7 |

H | 2.67 | 6 | 4 | 3 | 1 | 1 | 1 |

Fifty-four complete and usable surveys were collected. Participants did not receive any compensation. Participation was anonymous. Only the answers provided by participants belonging to one or more of the following categories have been eventually included in the analysis:

Self-identified systems engineers with at least 5 years of professional experience: a practicing systems engineer is defined as an individual who executes some or all of the activities described in [

Systems engineering faculty

Doctoral students in systems engineering

No definition for elegance was provided to the participants. A simple and shared definition of elegance is notoriously difficult to find, so we relied on the subjective interpretation that participants had of the concept, typically interpreted in terms of a mix of ingenuity and simplicity. Implementation effectiveness was defined as the quality of each architecture to be conducive to easy implementation.

Structural complexity was computed using two different metrics: cyclomatic complexity [

The

This metric counts the number of linearly independent cycles present in the network. Fewer cycles within the network should result in easier implementability.

Graph energy reveals the complexity of the structural dependency among the components. Topological complexity metric

A conceptual example of how topological complexity relates to architectural patterns is shown in Figure

Architectural patterns defined in terms of topological complexity (source: Sinha [

The questionnaire was submitted to experts belonging to online groups of systems engineering and by individual email invitation. Eventually, we collected 54 usable surveys. The average ranking of elegance and perceived implementation effectiveness is reported in Table

Average ranking of perceived implementation effectiveness and perceived elegance (

System diagram | Perceived implementation effectiveness ( |
Perceived elegance ( |
---|---|---|

A | 4.2 | 3.9 |

B | 3.8 | 3.5 |

C | 5.5 | 5.2 |

D | 5.9 | 6.4 |

E | 6.5 | 7.1 |

F | 3.1 | 3.0 |

G | 2.6 | 2.7 |

H | 4.3 | 4.2 |

The two rankings are perfectly correlated (Spearman rank correlation is equal to 1), which means that independent experts considered the most elegant diagrams as the ones that turned out to be also easier to implement.

The first experimental hypothesis predicts the presence of correlation between preference judgments on implementation effectiveness and structural complexity measures (most preferred diagrams are the least structurally complex).

First,

Data for Spearman correlation coefficient calculation.

Diagram | Cyclomatic complexity (CC) | Perceive implementation effectiveness ( |
Rank CC | Rank |
---|---|---|---|---|

A | 14 | 4.2 | 3.5 | 4 |

B | 14 | 3.8 | 3.5 | 3 |

C | 15 | 5.5 | 5.5 | 6 |

D | 23 | 5.9 | 7 | 7 |

E | 34 | 6.5 | 8 | 8 |

F | 11 | 3.1 | 1 | 2 |

G | 12 | 2.6 | 2 | 1 |

H | 15 | 4.3 | 5.5 | 5 |

We retested the hypothesis using topological complexity. Table

Data for Spearman correlation coefficient calculation.

Diagram | Topological complexity ( |
Perceived implementation effectiveness ( |
Rank |
Rank |
---|---|---|---|---|

A | 0.74 | 4.2 | 1 | 4 |

B | 0.86 | 3.8 | 2 | 3 |

C | 0.998 | 5.5 | 5 | 6 |

D | 1.14 | 5.9 | 6 | 7 |

E | 1.26 | 6.5 | 8 | 8 |

F | 0.92 | 3.1 | 3.5 | 2 |

G | 0.92 | 2.6 | 3.5 | 1 |

H | 1.15 | 4.3 | 7 | 5 |

Hypothesis 2 states that perceived elegance is correlated with effective complexity. Effective complexity for each diagram was calculated using the

Table

Entropy calculation for each diagram.

Diagram | |||||
---|---|---|---|---|---|

A | 14 | 27 | 182 | 0.148 | 110.237 |

B | 13 | 26 | 156 | 0.1667 | 101.403 |

C | 14 | 29 | 182 | 0.159 | 115.157 |

D | 14 | 36 | 182 | 0.198 | 130.587 |

E | 14 | 47 | 182 | 0.258 | 149.983 |

F | 11 | 21 | 110 | 0.191 | 77.371 |

G | 11 | 22 | 110 | 0.200 | 79.412 |

H | 11 | 26 | 110 | 0.236 | 86.783 |

Using these data, we constructed the effective complexity curve (Figure

Effective complexity curve.

Effective complexity calculation and ranking for each diagram.

Chart | Disorder ( |
Effective complexity (LMC) |
---|---|---|

F | 0.425 | 0.244 |

G | 0.436 | 0.246 |

H | 0.477 | 0.249 |

B | 0.557 | 0.245 |

A | 0.606 | 0.239 |

C | 0.633 | 0.232 |

D | 0.717 | 0.203 |

E | 0.824 | 0.145 |

The value of Spearman’s correlation between EC and elegance ranking (Table

Data for Spearman correlation coefficient calculation.

Diagram | Elegance | Effective complexity | Elegance ranking | Effective complexity ranking |
---|---|---|---|---|

A | 3.9 | 0.239 | 4 | 5 |

B | 3.5 | 0.245 | 3 | 3 |

C | 5.2 | 0.232 | 6 | 6 |

D | 6.4 | 0.203 | 7 | 7 |

E | 7.1 | 0.145 | 8 | 8 |

F | 3.0 | 0.244 | 2 | 4 |

G | 2.7 | 0.246 | 1 | 2 |

H | 4.2 | 0.249 | 5 | 1 |

Hypothesis 3 states that higher level of effective complexity is achieved when both noise-killing and add-meaning strategies are used at higher level of intensity.

The diagrams that are perceived as the most elegant, such as G, F, A, and B, are the ones that in Table

Spearman correlation coefficient was calculated between the vector norms of the strategy assessments corresponding to the architectures (Table

Data for Spearman correlation coefficient calculation.

Diagram | Vector norms | Elegance | Vector norms ranking | Elegance ranking |
---|---|---|---|---|

A | 15.5 | 3.9 | 5 | 4 |

B | 16.1 | 3.5 | 6 | 3 |

C | 8.3 | 5.2 | 3 | 6 |

D | 6.6 | 6.4 | 1 | 7 |

E | 6.7 | 7.1 | 2 | 8 |

F | 17.0 | 3.0 | 7 | 2 |

G | 17.7 | 2.7 | 8 | 1 |

H | 8.4 | 4.2 | 4 | 5 |

However, in order to discount for potential correlation between the original strategy variables, we performed a principal component analysis. The loading factors over two principal components are reported in Table

Principal components analysis.

Diagrams | ||||||||
---|---|---|---|---|---|---|---|---|

A | B | C | D | E | F | G | H | |

1.5715 | 1.8962 | −1.5962 | −2.2354 | −3.0415 | 2489 | 2.7969 | −1.8805 | |

−0.1329 | 0.4977 | 1119 | 1.2275 | −0.8415 | −0.325 | −0.184 | −1.3609 |

Figure

Principal component graph.

The results presented in this paper suggest that elegance can be described in terms of effective complexity.

First, our results show a high degree of correlation between elegance and structural complexity, as well as between elegance and implementation effectiveness. In other words, the most elegant design is perceived both as structurally simple and as conducive to more effective and easy implementation.

Second, the correlation between perceived elegance and effective complexity shows that the level of elegance can be understood in terms of “desirable” complexity. While generally elegance is considered as a very subjective and vague concept, our results show that the effective complexity metric used in this study was highly predictive of the elegance ranking provided by the experts. The proposed metric assesses complexity as a balanced mix of familiar and discoverable order, with order measured in terms of entropy as defined in information theory.

Based on this result, we speculate that understanding and resolving complexity is a dynamic process in which individuals adopt noise-killing heuristics to simplify the problem representation. On the other hand, when the representation becomes too simple and potentially unable to deliver the expected performance, we resort to add-meaning heuristics that eventually make the representation more complex, but also more meaningful.

This process may proceed by trial and error through the adoption of the seven artistic strategies until a sweet spot is achieved in terms of ideal mix of order and disorder. Of course, additional empirical work is needed to test this hypothesis by focusing on how subjects actually design systems and not only on how experts assess already made system architectures, as it happens in this work.

Elegance in this perspective can be considered as complexity reduction, as a tension toward simplicity that is balanced by an opposite tension toward the achievement of some level of meaningful complexity.

The same idea has been surprisingly mentioned in different fields. In design, Norman stated that good design always needs

These works refer to previous research in psychology of perception. Berlyne [

Suggestively, semiologists and art critics of the caliber of Barthes extended this observation to art by arguing that art is a system without noise and that in great work of art, no unit of meaning gets wasted [

For instance, we expect that similar results could be obtained by replicating this study with different types of visual stimuli and subjects. In particular, the methodology proposed in this paper could be applied to the analysis and design of user interface, such as in control panels, information dashboard, data visualization devices, and app or web site design.

The selection of the ATM and the use of functional architectures yield two potential limitations, in addition to the obvious—the generalizability issues that we already discussed in Section

All authors declare that they do not bear any conflict of interest regarding the publication of this paper and that their professional judgment concerning the validity of research is not influenced by secondary interests including financial gain or other forms of personal advantage or constraint.

Strategies evaluation.

Elegance system architecture.

Alternative systems representations of an ATM used in the survey.