This is chapter 1 of the book "Heuristic Enquires" edited by Professor Welby Ings and Professor Keith Tudor

https://www.taylorfrancis.com/books/edit/10.4324/9781003507758/heuristic-enquiries-welby-ings-keith-tudor

Written by: Hossein Najafi, Keith Tudor, and Welby Ings

Introduction

This chapter considers the evolution of heuristic inquiry as a research method and methodology and its application across two key forms of scholarly engagement, quantitative and qualitative research. As a quantitative approach, heuristics is applied in a range of fields including computer sciences, biology, finance, geography, mathematics, psychology, statistics, and physical sciences. As a qualitative approach, it is employed in diverse disciplines from art and design, through education, to nursing, psychology, psychotherapy, social geography, and sociology. The chapter discusses the concept of heuris- tics and clarifies some distinctions. This is followed by a discussion of the evolution and development of heuristic inquiry in both quantitative and qual- itative research.

The concept

The English word heuristics comes from the Ancient Greek word εὑρίσκω, meaning ‘to discover’, and is related to the word eureka, which comes from another Greek verb heúrek̄a meaning ‘I have found it’ (a word popularised by Archimedes’ discovery regarding volume and density through the displace- ment of water). Through this connection, the word has been associated with discovery (Douglass & Moustakas, 1985; Hjeij & Vilks, 2023). The etymolog- ical roots of heuristic tie it closely to investigative procedures (Pinheiro & McNeill, 2014); similarly, Smith (2022) draws an association between Aristotle’s discussion of epagôgê, by which one seeks to find but not neces- sarily prove a general truth, and the nature of heuristic inquiry.

As a noun, heuristics is used to describe an evolutionary mental phenom- enon in humans that results in faster and sometimes more optimal decision- making (Hjeij & Vilks, 2023), as well as reflective process of self-discovery. The word is also used to describe how artificial intelligence might replicate or reconstruct similar mental procedures in computer science (Nutakki & Mandava, 2023). Kahneman defines heuristics as a ‘procedure that helps find adequate, though often imprecise answers to difficult questions’ (2011, p. 97). As an adjective, heuristic is most associated with nouns such as inquiry, framework, method, methodology, and research. We suggest that heuristic inquiry describes a process of exploration and discovery that is used to navi- gate and make meaning of complex, unpredictable, and/or unknown realms. Given these two forms and uses of the word, we may understand heuristic inquiry as an approach to research that adopts and utilises heuristic mental processes to discover experience and/or to solve problems.

To understand the concept of heuristics better, one may juxtapose it with its antithesis, algorithmic problem-solving. Algorithmic thinking was devel- oped by the Persian mathematician, Al-Khawarizmi (from whose name the term is derived). Seen as a counterpoint to heuristic inquiry, algorithmic pro- cedures for solving a problem (or performing computations) follow an exact set of instructions that involve specified step-by-step actions. Thus, while a heuristic approach involves rules of thumb or educated guesses, an algorith- mic approach follows a set of rules or procedures to arrive at a solution. This means that an algorithmic process is more systematic and less prone to human bias than a heuristic approach (Grossman & Frieder, 2004), while a heuristic approach, especially in qualitative research, acknowledges, embraces, and makes meaning of the bias. Knuth defines an algorithm as ‘a set of rules that precisely defines a sequence of operations such that each rule is effective and definite and such that the sequence terminates in a finite time’ (1997, p. 4). Algorithms are based on logical or mathematical principles, and they ensure accurate and consistent results. Hjeij and Vilks (2023) note that inquiries based on pure logical decision-making, such as rational decision-making in economics (Savage, 1972), or the Aristotelian framework of syllogistic deduc- tive logic (Priest, 2008) are also not considered heuristic. However, Boyer and Merzbach (2011) argue that a reciprocal relationship can exist between heu- ristics and algorithmic problem-solving.

Hjeij and Vilks suggest that the spectrum of heuristics is very broad, observing that the application of a heuristic ‘may require intuition, guessing, exploration, or experience; some heuristics are rather elaborate, others are truly shortcuts, some are described in somewhat loose terms, and others are well-defined’ (2023, p. 2). The same authors observe that the broader application of heuristics in research has grown considerably, noting that, while in 1970 the Scopus data- base located only 20 published articles with the word ‘heuristic’ in their title, by 2021 this number had increased to 3,783 (Hjeij & Vilks, 2023). In contemporary research, heuristics and heuristic inquiry are used across diverse fields including artificial intelligence (AI) (Kaveh & Mesgari, 2023), artistic research (Ardern & Mortensen Steagall, 2023), computer science (Abdulsaheb & Kadhim, 2023), education (Isroilova, 2023), mathematics (Aghsami et al., 2023), nursing studies (Whybrow & Milligan, 2023), and psychotherapy (Tudor, 2023).

Evolution and application of heuristics in quantitative research

Kleining & Witt (2001) note that the German mathematician Joachim Jungius (1587–1657) was among the first researchers in the Common Era to use the term ‘heuretica’ formally. Jungius, whose work emphasised the importance of developing methods to solve unsolved problems and find new theorems, cat- egorised learning into empirical, epistemic, and heuristic, with the heuristic category representing the pinnacle of problem-solving and knowledge acquisition.

In 1637, the French philosopher René Descartes published his Discourse on Method (2012) in which he advocated mathematical reasoning as a means for advancing knowledge. Descartes outlined a problem-solving approach involving four steps: accepting only true axioms, breaking down problems, organising thoughts from simple to complex, and ensuring thoroughness (Lorenzini, 2023). Descartes also worked on transforming problems into alge- braic equations to create a universal science (mathesis universalis). However, towards the end of his life he began working on Rules for the Direction of the Mind (1701/2022), proposing heuristic rules for scientific inquiry that focused on simplification, geometric representation, and identifying knowns and unknowns. Despite criticism from other philosophers (such as Leibniz) for being overly general, Descartes’ methods laid a foundation for addressing the discovery and investigation of complex problems across diverse disciplines.

In 1837, the Czech mathematician and philosopher Bernard Bolzano pub- lished his multi-volume work on a Theory of Science (Bolzano 1837/2014), in the fourth volume of which he offered a structured approach to invention, with general and specific rules for discovering truths. In this work he empha- sised the use of heuristics which talented individuals often unconsciously apply to solve complex tasks.

In his paper on Truth and Probability, Ramsey (1926/1931) explored induc- tive logic as a heuristic habit of the mind. He provided a pragmatic justifica- tion for induction, suggesting that mental habits, such as inductive inference, are ecologically rational when they lead to generally true beliefs.

Nine years later, in 1935, Duncker, a pioneer in the experimental study of problem-solving, explored both facilitators and limitations to answering a question. His work on functional fixedness highlighted the challenges of thinking creatively and using objects in unconventional ways. One example of this was the Duncker Candle Problem which was a puzzle whereby one must attach a candle to a wall using only a box of thumbtacks and matches, without dripping wax, a task which was used to test creativity by using objects in unusual ways. Dunker’s work was significant because he emphasised the interplay between the internal mind and the external problem structure in successful problem-solving.

In 1945, George Polya, often referred to as the father of modern problem- solving in mathematics, sought to revive the study of heuristics in his book How to Solve It. His principles of problem-solving involved understanding the problem, planning, executing, and reflecting on improvement. His work focused on methods like inductive reasoning and analogy (Hertwig & Pachur, 2015) and influenced the development of artificial intelligence (AI).

In 1955, Herbert Simon (renowned for his theory of bounded rationality), suggested in his book A Behavioural Model of Rational Choice that decision- making is constrained by limited information, time, and cognitive capacity, arguing that these factors can lead to satisficing, that is, looking for satisfac- tory rather than optimal decision-making. His collaboration with Allen Newell produced the Logic Theorist and the General Problem Solver (GPS), which described early AI processes that employ heuristic approaches in decision-making (Newell et al., 1959; Simon & Newell, 1958). However, while the GPS was efficient with sufficiently well-structured problems like the Towers of Hanoi (a puzzle with three rods and moveable, different- sized disks), it was not capable of solving complex real-life problems. Consequently, Simon dedicated most of the remainder of his career to the advancement of machine intelligence. The results of his experiments showed that, like humans, certain computer programs can make decisions using trial-and-error and shortcut methods (Estevadeordal et al., 2003). Significantly, Simon and Newell argue that heuristics is used by both humans and intelligent machines. They note that ‘Digital computers can perform certain heuristic problem-solving tasks for which no algorithms are available… [and] In doing so, they use processes that are closely parallel to human problem-solving processes’ (1958, p. 7). Simon and Newell’s approach later evolved into meta-heuristics (a search within the space of solutions for a specific problem) and hyper-heuristics (searching within a heuristic space), underscoring the role of heuristics in complex problem- solving (Mart et al., 2018).

In 1968, at the Chemnitz University of Technology, Johannes Müller intro- duced systematic heuristics to improve efficiency in scientific and technolog- ical problem-solving. His approach employed a library of proven solutions for recurring problems and was used to streamline the process of problem-solving from planning to evaluation. Despite the program’s early termination (due to ideological conflicts), Müller’s methods found success in diverse industrial applications (Banse & Friedrich, 2000).

In Methodology of Scientific Research Programmes, Imre Lakatos (1978) presents the concepts of ‘negative’ and ‘positive’ heuristics, where a ‘negative heuristic’ represents the unchallengeable foundation of a research program, while a ‘positive heuristic’ steers its progress and the forecast of new discover- ies. Lakatos’ thinking highlighted the significance of concentrating on achiev- able solutions to intricate problems, by excluding what was less pertinent.

In their influential 1974 publication Judgement under Uncertainty: Heuristics and Biases, Tversky and Kahneman introduce three fundamental cognitive heu- ristics: availability, representativeness, and anchoring and adjustment. These became cornerstones to understanding human judgment in uncertain contexts (Kahneman, 2011; Tversky & Kahneman, 1974). Their study became a funda- mental framework for designing AI procedures (Martínez et al., 2022). Kahneman and Tversky’s availability heuristic describes a situation where the ease of recalling an event skews our perception of its likelihood, leading to overestimations of risks (such as those from terrorist attacks as highlighted in the media, or misjudgements in business contexts where success stories over- shadow numerous failures). Their representativeness heuristic is used to assess the likelihood of an object belonging to a certain category based on its similar- ity to a prototype where statistical reality is overlooked (which often results in errors such as the base rate fallacy; Bar-Hillel, 1980). Anchoring and adjustment describe how initial information (or an anchor) can heavily influence subse- quent judgments and decisions, even when the anchor is irrelevant, as illus- trated in experiments where starting points in a multiplication task significantly affect the outcomes. However, while simplifying decision-making, Kahneman and Tversky’s heuristics often lead to systematic biases and errors and demon- strate the complex nature of human cognition and decision-making.

Another quantitative researcher whose work on heuristics has contributed to the field of decision-making is the German psychologist Gerd Gigerenzer. His theory opposes Kahneman and Tversky’s heuristics and biases approach. Gigerenzer argues that heuristics are neither irrational nor inferior to the opti- misation or probability calculations. Instead, he emphasises the ecological rationality of heuristics, especially in uncertain and complex environments, and introduces the concept of the adaptive toolbox: a collection of mental shortcuts tailored for specific problems (Gigerenzer, 1996; Gigerenzer et al., 2015; Gigerenzer & Gaissmaier, 2011). His research included the recognition heuristic, which can lead to more accurate decisions in situations with limited information, and the take-the-best heuristic which focuses on the most impor- tant cues in decision-making (Gigerenzer & Todd, 1999). In a similar vein, Slovic and his colleagues write about the ‘affect heuristic’ which proposes that emotion is important in guiding judgements and/or decisions, and, thereby, acts as a ‘mental shortcut’ in making and acting on such decisions quickly (Slovic et al., 2002, 2004, 2007).

Heuristic inquiry in qualitative research

Although heuristics describes a broad approach to research that adopts and utilises heuristic mental processes to solve problems, when employed in qualitative research, heuristics appears somewhat different. Nevertheless, in both quantitative and qualitative approaches, in a heuristic inquiry the researcher moves away from the application of pre-established formulae and emphasis is placed on heightened levels of flexibility, trial and error, astute questioning, and acceptance that there will be an optimal solution that is discovered rather than guaranteed.

Clark Moustakas, an American psychologist who was a prominent figure in the humanistic psychology movement of the 1960s, began to develop a systematic qualitative approach for heuristic studies in the fields of clinical and educational psychology (Moustakas, 1967). In the 1950s, Moustakas’ academic career was disrupted by his daughter’s serious illness. While he accompanied his daughter throughout this difficult journey (and subse- quent recovery), the experience had a profound impact on Moustakas, which then led him to investigate the phenomenon of loneliness in three books: Loneliness (1961), Loneliness and Love (1972), and The Touch of Loneliness (1975). This journey of personal exploration and understanding led to his seminal book, Heuristic Research: Design, Methodology, and Applications (1990), in which he elaborated the heuristic method, provid- ing a comprehensive framework and diverse examples for conducting such research. According to Moustakas, reflecting on his own experience, the process of heuristic research has six phases: initial engagement, immersion, incubation, illumination, explication, and creative synthesis (Douglass & Moustakas, 1985; Moustakas, 1990). However, it is worth noting that Moustakas came to these phases a posteriori, i.e., after the research; they may not be applicable to all such heuristic projects. We make this point as some heuristic researchers assume that they have to follow these phases (for discussion of which, see also Chapter 8).

Clark Moustakas credited various humanistic psychologists with influenc- ing the development of his heuristic methodology, specifically: Paul Bridgman’s (1950) insights into subjective knowledge; Abraham Maslow’s (1956) work on self-actualisation; Carl Rogers’ (1963) theory of the structure of personality; Eugene Gendlin’s (1962) concept of focusing; Martin Buber’s (1965) concept of mutuality; Michael Polanyi’s (1966) ideas on tacit knowl- edge and intuition; Sydney Jourard’s (1968) work on self-disclosure; and Willard Frick’s (1982) theories on identity. Moustakas was also influenced by the writings of Søren Kierkegaard, Edmund Husserl, and Gordon Allport. From this, Moustakas identified a number of concepts that, in effect, provide the methodology underpinning the method, i.e., identifying with the focus of inquiry, self-dialogue, tacit knowing, intuition, indwelling, focusing, the inter- nal frame of reference (Douglass & Moustakas, 1985; Moustakas, 1990), and validation (Moustakas, 1990).

Moustakas’ heuristic research approach represents a deeply introspective journey, emphasising the researcher’s personal experience and self-discovery. As a process, it involves a conscious engagement with perceptions, intuitions, and knowledge, leading to a deeper understanding of both the subject and the self (Moustakas, 1990). Moustakas argues that questions about the subject of the research as well as methodology arise from inner search, thus requiring the researcher’s full commitment and immersion in, open to, and reflective exploration of the subject of inquiry. This process often involves venturing into unknown territories, the tacit dimension of knowledge, and relying on discovery through illumination (Moustakas, 1990), as well as exploring any resistance to the process (Sela-Smith, 2002). In this process a researcher cre- ates a depiction and/or a narrative that portrays the essence of their experi- ences, which requires full engagement of self-resources and autobiographical connections (Moustakas, 1990). Finally, Moustakas argues that such an approach demands total presence, honesty, and a commitment to personal transformation, making heuristic research a profound and transformative exploration of human experience.

In 2002 Sela-Smith critiqued Moustakas’ research, arguing that his focus had moved away ‘from the self’s experience of the experience to focusing on the idea of the experience’ (2002, p. 53). From her own heuristic self-inquiry and a re-evaluation of Moustakas’ work, she identified six key elements in heuristic research: self-experience, inward reach, surrender, self-dialogue, self-search, and transformation. More recently, Tudor (2022, 2023) offers a critique of what he considers to be Sela-Smith’s undue focus on the interior and the individual, represented in the phrase ‘I-who-feels’, and argues in favour of a more exterior and collective view of and focus for research repre- sented by the phrase ‘we-who-care – and act’.

Most recently in this tradition, and encompassing the disciplines of educa- tion, psychology, social work, and sociology, as well as therapy, Sultan (2018) published a book on Heuristic Inquiry in which she emphasises the holistic and embodied nature of this approach to research.

In a separate tradition from that of Moustakas, German sociologist Gerhard Kleining (1982) proposes a qualitative heuristic as a suitable method for social science research. His approach was founded on four principles: the research- er’s open-mindedness and willingness to revise preconceptions; the flexible and evolving definition of the research topic; the consideration of a wide variation in research perspectives; and the identification of similarities in data. His work and later writing with Harald Witt emphasises adaptability in quali- tative research (Kleining & Witt, 2001).

Heuristics has also been used in geography, in which Thompson under- stands a heuristic to be ‘a practical method that attempts the solution of the- oretical, empirical, or interpretative problems, while geographical metaphors are ways of seeing and of framing these problems’ (2017, p. 57).

In the last two decades, heuristic inquiry has also been employed as a method for heightening the potential for creative discovery in artistic, practice- led, and ethnocultural studies, notably in the visual arts, film, creative writing, music, and communication design. In examining studies from these fields, Welby Ings (2011, 2014, 2018, 2022) has considered the nature and supervi- sory implications of immersion, self-care, and critical, aesthetic refinement. His work has also focused on instances where heuristic inquiry is employed to artistically engage with semi-fictional storytelling.

In addition to these applications, heuristic, practice-led ethnocultural stud- ies have also begun to profile in artistic, doctoral, practice-led theses. These studies, emanating from indigenous and culturally specific knowledge sys- tems, transcend conventional research paradigms. Within them heuristic inquiry has been explored as a means of creating bridges between culturally shaped approaches to research and existing methodological writing.

Beginning in 2008, a number of theses associated with Persian and Middle Eastern storytelling and filmmaking began drawing connections between heu- ristic inquiry and the subjective journey of the artistic researcher who, through the process of artefact creation becomes integrated with their work – see El Noor (2008), Aziz (2009), and Najafi (2023).

Heuristic inquiry was also used by the Chinese film poet Chen Chen in her doctoral thesis, Bright on the Grey Sea (2018). Her study involved an explor- atory journey into the realms of Chinese poetic wisdom by anchoring itself in the philosophical and aesthetic principles of the Xiang system (a layered con- ceptual framework derived from Chinese poetry), and the concept of men- glong (akin to mystery or enigma, in Western thought).

Among Oceanic Indigenous scholars, four doctoral candidates have recently embedded heuristic inquiry inside existing culturally-shaped approaches to artistic research. Building on work he began developing in 2016 in 2020, Robert Pouwhare advanced a model he called Pur̄ak̄au which unpacked how Indigenous Maōri scholarship utilises tacit, explicit, and spiritual knowing in a process of creation and reflection. His heuristic framework was later adapted by the choreographer Tangaroa Paora (2023) and the documentary-maker Toiroa Williams (2024), both of whom progressed their research projects through heightened levels of sensitised immersion, customary practice, and the studied-self in the context of collective responsibility.

As these studies were emerging, in 2021, the Samoan composer Igelese Ete employed heuristic inquiry as a framework for developing a Koneseti (a form of Samoan narrative opera). His research design moved through processes of fesili (questioning), foafoa (taking action), mai toton̄u (inner reflection), and mai fafo (external reflection).

Conclusion

Despite divergent trajectories in quantitative and qualitative research, heu- ristic inquiry exhibits numerous commonalities that bridge these two realms. In both research approaches, heuristics fundamentally rely on instances of human experience as data, a basis which underscores its expe- riential nature (Russell & Norvig, 2010). Researchers utilising heuristics in either approach demonstrate a willingness to engage with the unknown, and to embrace complexity. This acceptance of, and navigation through, the unknown and the tacit dimension of knowledge is intrinsic to heuristic inquiry, regardless of whether it is quantitative or qualitative (Ings, 2014; LeCun et al., 2015). Central to this, again in both approaches, is the con- cept of intuition. Traditionally perceived as exclusive to qualitative method- ologies (Moustakas, 1990), intuition has also found its place in quantitative realms, manifesting in various heuristic procedures (Johnny et al., 2020; Simon, 1979). Its focus on and facilitation of the recognition of emerging patterns in human behaviour, experience, and society further illustrates the applicability of heuristics across research approaches (Flasinśki, 2016; Ventling, 2017). Heuristics requires researchers to prioritise efficient problem-solving and/or discovery over absolute certainty, an approach that is particularly pertinent given the extreme complexity of the questions, issues, subjects, and spaces explored and navigated by heuristic research- ers (Lash, 2007; Moustakas, 1961; Russell & Norvig, 2010). Given its emphasis on discovery, heuristic research also tends to reflect on – and in this sense to discover – things about itself, for instance as Sela-Smith (2002) did about Moustakas’ (1990) work. There are few frameworks of methodol- ogy and/or method that have proved so adaptable and mutable across diverse disciplines and approaches in research.

This chapter has offered a brief outline of the complex development of heuristics as a protean system of inquiry by tracing its presence in different traditions and across a number of disciplines. Initially grounded in philoso- phy and mathematics, heuristics has evolved and played a pivotal role in diverse fields of inquiry, including artificial intelligence, humanistic as well as cognitive psychology, education, geography, and art and design. Its evolution has been marked by significant milestones, including Herbert Simon’s theory of bounded rationality, Moustakas’ disciplined self-inquiry, and the ground- breaking work of Tversky and Kahneman on cognitive biases. These develop- ments have not only enhanced our understanding of knowledge inquiry but also underscored the importance of heuristics in human thought.

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