Homo neanderthalensis has changed dramatically. Initially, Neanderthals were seen as primitive brutes. Increasingly, however, Neanderthals are regarded as basically human. New discoveries and technologies have led to an avalanche of data, and as a result of that it becomes increasingly difficult to pinpoint what the difference between modern humans and Neanderthals really is. And yet, the persistent quest for a minimal difference which separates them from us is still noticeable in Neanderthal research. Neanderthal discourse is a vantage point from which the logic of ‘us’ versus ‘other’ is critically reconsidered. Studying contemporary academic literature and science autobiographies from an oblique perspective, focusing not on Neanderthals as objects, but on the dynamics of interaction between Neanderthal researchers and their finds, basic convictions at work in this type of research are retrieved. What is at issue is not the actual distinction between modern humans and Neanderthals (which is continuously being redefined), but rather the dualistic construction of human and nonhuman. Neanderthal understanding is affected by the desire to safeguard human uniqueness. The overall trend is to identify the human mark or spark, which defines us as favoured ‘winners’. The paradoxes emerging in contemporary Neanderthal discourse are symptomatic of the fact that a dualistic style of thinking is no longer tenable.During the past decades, our image of  The New York Times Magazine, featuring an article on the ways scientific perceptions of Neanderthals have changed over time, attempting to show how ‘we’ denied for so long that ‘they’ were people too . Recent research, however, yielded perforated and ochre marine shells and colorants attributed to Neanderthals, suggesting once again that they were cognitively indistinguishable from modern humans , and yet ‘not-us’ (as Homo sapiens) at the same time, Neanderthals are especially fascinating. The genus Homo is a messy, contested category that is closely tied to the concept of being human, and the boundaries of both the species and the genus remain fuzzy (Collard and Wood Homo with the words nosce te ipsum (know thyself). After the discovery of the partial skeleton in Neander Valley in 1856, William King introduced the species name Homo neanderthalensis, for the first time expanding our genus beyond Homo sapiens  and ancient proteins , for example. This allowed researchers to generate and assess an avalanche of data, shedding more light on Neanderthal life, changing how we see them, but also challenging the way we see ourselves. And this happens at a crucial moment when we are already questioning in a very fundamental manner a number of basic concepts such as nature, technology and the human, due to the fact that, at present, during the AnthropoceneRecent genetic evidence and archaeological data show that Neanderthals and their modern humans contemporaries were very similar in biological and cultural capacities  human beings Stuurman . In the Building on the work of Plumwood as a conceptual framework, we will argue that merely expanding the scope of what counts as human means redefining the boundaries along slightly different lines of inclusion and exclusion, while the yardstick of inclusion (namely: similarity to those deemed to be fully human) remains unchallenged. Numerous anatomical and behavioural features have been used as markers of humanness, such as upright bipedalism, manual dexterity, certain facial or cranial angles, cranial capacity, language, the extent of rational control over emotional impulse, conceptual thinking, art, self-recognition and tool making. Much scientific effort and ingenuity has gone into redefining these criteria as soon as nonhumans seemed to qualify as well, re-establishing the alleged human uniqueness Cartmill . What isFeminism and the Mastery of Nature . Binarizing is a necessary constituent of the process of dualizing, but not the only one. Dualizing also involves polarization and polarization and hierarchy: introducing distance and opposition between elements which are constructed as higher and lower, superior and inferior, as ruler and ruled. Thus, entities are regarded not merely as different, but as belonging to radically different orders or kinds, and hence as not open to change. This is what Plumwood terms ‘hyperseparation’: the radical exclusion of the other, seeing differences not as relative, but as differences in kind. While ‘backgrounding’ the other, this strategy denies dependency, continuity and relationship between the self and the other. Another important characteristic of dualism is ‘relational definition’, meaning that one side defines the other. Whatever is essential to defining the one side serves to define the other side as well, for hyperseparation is always a matter of presence or absence, of privilege or lack. The other is objectified and stereotyped. In this way, the other’s independent identity is denied, for the other is primarily seen as not-us or not-quite-us. The domination/subordination relationship determines the identity of both opposites.This hyperseparated conception of the human expresses a ‘master perspective’ and sees the essentially human as part of a radically separate and higher order of reason, mind or consciousness, set apart from the lower order of naturalness, where agency and intelligence are lacking and which comprises the body, the woman, the animal and the pre-human. It is a hierarchical conceptual system for sorting, organizing and understanding the world around us, an effective way to position ourselves and orient our research practices, providing a symbolical order, but also an intellectual basis for human-centeredness and domination, making it seem inevitable, self-evident and natural. Difference, in this perspective, is not a neutral equation, but convey polarity and hierarchy. According to Plumwood, however, this dualistic perspective can no longer be taken for granted as ‘the’ human model, since this way of thinking has resulted in a massive destruction of the biosphere. It is an egoistic model, a master story of western culture which sees history in terms of conquest and control, appropriation and exploitation, destruction and incorporation.One area in which the question of what is human is very prominent, is in the relation of humans to animals. Animals present complex interplays of similarity and difference. On the basis of dualistic assumptions, a recognition of others as ‘alike yet different’ seems impossible. They are either valued in human terms (so that their otherness is lost) or constructed as different . The more similar to humans an animal is, the more apparent the tension becomes. When genetic similarity between humans and primates is emphasized, for example, separation is safeguarded by producing yet another uniquely human trait, or by constructing difference in terms of the function of these shared genes Holmberg .When it comes to determining the relationship between modern humans to other species of humans, dualistic thinking becomes even more problematic. While we regard them as basically human, we still try to distinguish ourselves as human beings and use these proximate others to define and redefine our own self-image. Neanderthals are praised or disqualified in terms of their conformity to a concept of the ‘fully human’, but affirming full humanity can never go without redefining the model, that is grounded in the exclusion of a vast number of beings, deemed nonhuman or not fully human. The positions of ‘being the same as’ or ‘different from’ mark asymmetrical power relations, signifying differences that are organized according to a hierarchical scale. ‘To be different’ therefore implies ‘to be less than’  are actually envisioned. How are dualisms mobilized to construct differences in terms of inferior and alien?We will therefore study contemporary  Neanderthal discourse from an oblique perspective Zwart , which fNA Pääbo , but a sPaleogenomics plays an important  role in this. Improved methods for the extraction of ancient DNA from fossils and paleontological sites and advances in genome sequencing technologies have revolutionized the research on ancient organisms, extinct species, and past environments. At present, whole genomes have been sequenced from numerous ancient individuals and extinct species .The work of the Swedish geneticist Svante Pääbo and his team provides a remarkable case history in this respect. In his book Homo sapiens divide. As Pääbo phrases it:‘Studying how we differ genetically from our closest relatives would potentially allow us to find out what changes set apart the ancestors of present-day humans from all other organisms on the planet. In essence, we would be studying perhaps the most fundamental part of human history – the biological origin of fully modern humans, the direct ancestors of all people alive today (p. 72).The research explicitly started from the supposition that Neanderthals are ‘profoundly different from us’ (p. 14) and that Neanderthal DNA is ‘very different from the DNA of modern humans’. The expectation was that powerful DNA sequencing machines and PCR technology would now provide a high-resolution window into the past (p. 42), so that the difference between them and us could now be fleshed out in terms of a limited set of decisive genes that exemplify the Neanderthal–Science) was expected ‘to give us a picture of ourselves’ so that we can see ‘the essential genetic changes that make us human—the things that made our emergence as a global species possible’ (p. 220). Yet, interestingly, while Pääbo’s descriptions become increasingly technical, it becomes increasingly difficult to link the project’s findings with concrete and allegedly unique aspects of human behaviour, experience or culture. Unintentionally perhaps, rather than enabling us ‘to directly identify the genetic underpinnings of the differences between Neanderthals and modern humans’, the research outcomes rather increasingly convey the message of how similar we are. Neanderthals shared, for example, the FOXP2 language gene with modern humans. Symptomatic perhaps is Pääbo’s persistent fear of ‘contamination’ already mentioned above: the possibility that, instead of Neanderthal DNA, researchers are actually sequencing modern human DNA (perhaps even their own DNA) which somehow contaminated ancient Neanderthal bones, for instance via dust particles in the lab where living human researchers work. Pääbo describes how a significant number of Neanderthal publications are indeed ‘contaminated’ by human genetic material: the claimed results are tainted as the isolation between living human bodies and Neanderthal bones proves difficult to maintain, so that DNA passes from the one to the other and blurs the difference. And this not only applies to Neanderthal research. Most of the DNA allegedly retrieved from iceman Ötzi likewise came from the several contemporary humans who handled his remains. In Pääbo’s own terms: fear of contamination (DNA traffic) between ‘us’ and ‘them’ inside laboratories became more than just a concern, it evolved into ‘paranoia’ , it became a real ‘obsession’ (Pääbo p. 9). But even clean results increasingly suggest continuity rather than discontinuity (similarity rather than dissimilarity) between them and us. Indeed, the most important and tangible result of Pääbo’s research so far, perhaps, is that Neanderthals genetically contributed to modern human DNA via interbreeding. Eventually, Pääbo contends that even a complete catalogue of all the genetic differences between Neanderthals and modern humans would not by itself tell us what the difference between Neanderthals and modern humans would be (p. 226). Thus, the end result of Neanderthal genomics seems to be that, after exposure to the data deluge of next-generation sequencing technologies, the portrait of Neanderthal humans becomes increasingly—human.His research consistently revolves around the question of ‘what makes humans unique … what had set humans on an evolutionary track so different?’ (p. 83). The published version of the Neanderthal genome  special? Pääbo . Althougbecause ‘we’ survived and ‘they’ became extinct, our ancestors must have been superior to them somehow.Although paleogenomics was expected to have the potential to settle the debate and provide us with answers to the question who we are and what made us special, it increasingly revealed continuity and similarity between them and us. And yet, most Neanderthal researchers still seem bent on discovering minimal differences, based on the assumption that National Geographic under the telling headline ‘Gap between Neanderthals and us narrows, but does not close’  in  Shreeve  or a res Shreeve .Homo sapiens is often explained by brain differences. Wynn and Coolidge, for example, argued that a ‘relatively simple’ genetic mutation about 100,000 years ago led to enhanced working memory capacity. This was allegedly the final evolutionary development that modernized the human mind  went extinct.Pearce et al.  argue thmust be a difference between them and us, some genetic or neurological cause which explains our remarkable success, and this conviction is explicitly guiding the research. Overall, whereas the actual differences are become increasingly minimal and technical, it is clear that the difference between them and us is what these researchers are persistently after: a particular signature feature which may offer an explanation of why they became extinct while we  survived.Geneticist Alysson Muotri and his team take this even one step further. Unlike skulls, brains do not fossilize, and therefore they are now trying to literally ‘recreate Neanderthal minds’, using the genome-editing technique CRISPR-Cas9. Human stem cells are engineered so as to include Neanderthal genes and grown into cortical ‘minibrains’ that should reflect the influence of ancient DNA. Compared with modern human minibrains, the Neanderthal organoids make fewer synaptic connections, these researchers argue, which may have influenced their ability to socialize, again a minimal but allegedly decisive difference which may explain their demise Cohen . Muotri must have had some advantage over the former, it was now argued that modern humans were able to free themselves from environmental constraints, probably with the aid of superior technology, so that a more efficient and flexible exploitation of dietary resources might have given modern humans an advantage over Neanderthals  because during the Pleistocene their use of stone tools and hunting methods hardly seemed to change, so that their ‘conservatism’ is considered ‘very strong’ (p. 97). Although experts now consider Neanderthals as far more advanced than previous generations of researchers did, their ability to innovate is still generally seen as limited (p. 99). And this seems linked to another advantage modern humans were beginning to develop around 50,000 years ago, namely the use of ornamentation, notably in the form of body paint (red ochre) and in the form of jewellery , thereby perhaps exploring new forms of symbolic expression. Was this the key to their (to ‘our’) success: new forms of symbolism as a decisive milestone (p. 120)? However, this seems to suggest that the divergence between modern humans and Neanderthals was a cultural event rather than something in their genes. The general idea is that, whereas Neanderthals were living in the here and now, new symbolical codes may have opened up a much more extended ambiance of culture for modern humans, but on closer inspection the evidence again seems indecisive. According to some researchers, Neanderthals also used red ochre, albeit sporadically, perhaps even as a form of symbolism. It seems indisputable by now that they used eagle talons for ornamentation (p. 120). And indeed, the Neanderthal cross-hatch (‘hashtag’) pattern in Gorham’s Cave, Gibraltar, may also point to incipient symbolic thinking, although Papagianni and Morse hasten to add that Neanderthal symbolism ‘was not nearly as extensive as the modern human use of shell jewellery’ (p. 120).In search of Neanderthals, solving the puzzle of human origins, Stringer and Gamble . They communicated about the here and now. Absence of innovation meant that they could rely on tried and tested methods so that their language was holistic, consisting of fixed utterances. Homo sapiens utterances, Mithen argues, were different, namely compositional and referential, which means that phrases could be broken into separate units of meaning which could be recombined to broaden the communicative repertoire. Because of their ‘immense cultural stability’, Mithen argues, Neanderthals did not have much to say, which explains the absence  of symbolical objects. This is exemplified by their ochre use. While black ochre was used by Neanderthals, probably to protect their skin (p. 252), the use of red ochre counts as an early Homo sapiens innovation , basically because the colour red  is associated with symbolic activity . Red ochre may be regarded as the first symbol to be used by humans (p. 253). Although some of Mithen’s descriptions are quite enticing, the problem is that he persistently clings to a dichotomous or binary way of thinking . The logic of hyperseparation is still at work, albeit now focusing on cultural rather than genetic differences. Instead of starting from the Neanderthals = holistic and modern humans = compositional dichotomy, why not see the shift from holistic to compositional as a gradual pattern of evolution of language as such, which may have affected both Neanderthals and modern humans, and which is still ongoing by the way (because remnants of holistic language are still in vogue in human language even today)? If this perspective is taken, the tension between holistic versus compositional becomes a matter of circumstances and socio-cultural ambiance, rather than reflecting the absence or presence of certain (gene-based) properties, associated with certain  ‘survival’ genes.Similar discussions can be encountered in the book n Mithen , who looThe humans who went extinct: Why Neanderthals died out and we survived, Clive Finlayson  began to process information in an entirely revolutionary and unprecedented way. At the same time, Tattersall agrees that it is unclear how this difference can be explained. For him, it is not a question of better genes or better brains, but of a cultural event: humankind’s symbolic awakening.Ian Tattersall starts from the opposite position, considering modern humans uniquely gifted creatures, distinctly different, unprecedented, extraordinary, and overwhelming all competition whilst taking over the world. In his book The Invader, how humans and their dogs drove Neanderthals to extinction  characteristic which singles us out as different. As a rule, characteristics that are seen as essential to defining the upper side are used to define the other (inferior) side as well, but now in the sense that they lack these characteristics. Innovation, for instance, may be used to define Neanderthals, but in a negative manner, as something which they allegedly missed. With the help of characteristics such as ‘being innovative’, the familiarity and closeness of Neanderthals is negated. The other is relegated to a position of oppositional subordination and is not considered as an independent other, with their own needs, identity and aspirations. The qualities of the other are either negative features (deficiencies), or the result of failings, while qualities that do not fit into the scheme tend to be ignored or explained away.Building on Plumwood’s conceptual framework, we have argued that this focus on difference, on discontinuity rather than continuity, is connected with the dualist, hyperseparated conception of the human. Our concept of the human is based on a tenacious set of assumptions about the inferior status of the nonhuman world. What is taken to be authentically and characteristically human is not to be found in the nonhuman, so that we see ourselves as separate and distinct. A dualistically construed dichotomy typically polarizes difference and minimizes shared characteristics. Moreover, it construes difference along the lines of superiority/inferiority, and views the inferior side not as an end in itself, but as instrumental to the higher or superior side Plumwood . By emphboth alike and different. It obfuscates the continuity and ‘familiarity’ between them and us. Neanderthals, familiar and strange at the same time, incite in us an uncanny feeling. While we regard them as basically human, we still try to keep a distance and use them to define our own self-image, often based on series of oppositions such as sluggish versus agile, brutish versus smart, conservative versus innovative, etc. Thus, the Neanderthal story emerges as a tale about insiders and outsiders, exploring innovators and conservative savages, reflecting the desire to see ourselves as different somehow, not only from other mammals, but from pre-modern humans as well  allegedly had a complex and syntactical symbolical language, while Neanderthals did not. Moreover, while AMH were innovators, the capacity of Neanderthals for innovation was much more limited. AMH used projective technology, while Neanderthals did not. Modern humans had a diverse diet, but Neanderthals a restricted one. AMH used traps and snares, while Neanderthals did not. AMH had extensive social networks, while Neanderthals did not. Last but not least: while AMH hafting techniques entailed complex procedures requiring abstract reasoning and ‘modern cognition’, hafting of tools by Neanderthals was a simple procedure, only using naturally available glues. Yet, Villa and Roebroeks systematically show that for all these contentions the evidence is inconclusive. They conclude that the available data do not convincingly support the supposed technological, social and cognitive inferiority of Neanderthals compared to their AMH contemporaries. Characterizations of Neanderthals as cognitively inferior to modern humans, they argue, relies on a framing which overemphasizes the significance of subtle differences.Not all Neanderthal experts, however, fall into this trap. The pervasive use of double standards—considering the in-group, or upper side, capable until proven incapable, while the out-group is incapable until proven capable—in the assessment of Neanderthals has been pointed out and questioned by a number of Neanderthal researchers themselves  differences is symptomatic for it reveals the desire to impose clear demarcations when it comes to upholding our identity. In the light of scientific evidence, continuity rather than discontinuity appears to be the rule, and it has become increasingly difficult to explain how our uniqueness can be upheld. When Neanderthals are regarded more and more like us, it abolishes their ‘otherness’. And to the extent that binary separations evaporate, the question of who we are, the question of humanity, becomes increasingly uncertain. Although researchers develop technological windows that provide access to the lost world of Pleistocene existence, Neanderthals continue to serve as mirrors reflecting how ’ Corbey . NeanderMoreover, although views and theories about Neanderthal existence are informed by quickly expanding collections of findings, they remain sensitive to the broader socio-cultural environment. One could argue, for instance, that the current focus in Neanderthal research on innovation as a typical human feature (so that ‘we’ are ‘innovative’ while ‘they’ are ‘conservative’) basically reflects the current neo-liberal zeitgeist, rather than being an objective paleoanthropological statement of fact. We define ourselves as innovative because in contemporary dominant culture, innovation is considered something positive. The innovation theorem should raise suspicion precisely because it is in accordance with the syllogism: We were better at something; traditionalism is ‘bad’ and innovation ‘good’; ergo, we were more innovative.Human-centeredness is not serving us, nor others, well. The way to proceed, we argue, is to dismantle the deep dualism that underpins our superiority complex. This would be beneficial not only for Neanderthal research, but also for contemporary human culture on a more general plane. What if we stop trying to fit every new piece of evidence into this rating system that essentially presupposes that we were more competitive, and therefore superior? What keeps us from reading the Neanderthal evidence in a different manner? The alternative is not pure homogeneity, equality without any diversity, however. Neanderthal existence may have been different, but also similar, and it is intriguing to use technoscientific tools to try to enter their world . The problem is perceiving diversity in terms of dichotomy and hierarchy, rather than in terms of diversity. Dismantling dualism does not imply erasing all differences, nor reversing the value of the poles . Instead, it requires recognition of a complex interacting pattern of both continuity and difference. It involves recognizing the relationship and continuity between self and other, but also affirming the independence of others, with their own ends and needs, alike and different at the same time Plumwood . A non-hAlthough Neanderthals are now generally regarded as basically human, it is often not that obvious what the starting point, the null hypothesis in Neanderthal research is. When studying animals, the null hypothesis usually is to assume that they are different and if we discern similarities, we opt for the simplest possible explanation to avoid anthropomorphism. In anthropological studies of humans, the opposite applies, namely the assumption is that others are people like us, and we take care not to interpret diversity in terms of difference. What applies to Neanderthals? Do we consider them fully human, or rather as somewhere on the way towards becoming human For nearly a century, archaeologists had argued about whether Neanderthals recognized mortality, understood death, or buried remains of their dead. Neanderthals were fundamentally human, with a brain size and evidence for complex culture that rivalled those of modern humans. With The discovery of the partial skeleton in 1856 in the Neander Valley marked the beginning of palaeoanthropology as a distinct field of study. From the start, it has evolved around concepts of identity and inequality. Neanderthals are the longest known and best-known hominin species, but we now know that we have shared our world with many different human species during the last two million years or so. In 2015, a previously-unknown species of extinct hominin was discovered in South Africa (Berger et al. Homo naledi; ‘almost human’ and ‘clearly not human’ at the same time. The Neanderthal controversy is only the beginning.It took a century for Neanderthals to be included as ‘fundamentally human’. Before them, around 1900, the Cro-Magnons of the Upper Palaeolithic, earlier interpreted as a kind of animal, crossed the threshold to humanness and were considered to be ‘people like us’, anatomically, behaviourally and cognitively Corbey . There i


To this day, the study of the substratum of thought and its implied mechanisms is rarely directly addressed. Nowadays, systemic approaches based on introspective methodologies are no longer fashionable and are often overlooked or ignored. Most frequently, reductionist approaches are followed for deciphering the neuronal circuits functionally associated with cognitive processes. However, we argue that systemic studies of individual thought may still contribute to a useful and complementary description of the multimodal nature of perception, because they can take into account individual diversity while still identifying the common features of perceptual processes. We propose to address this question by looking at one possible task for recognition of a “signifying sound”, as an example of conceptual grasping of a perceptual response. By adopting a mixed approach combining qualitative analyses of interviews based on introspection with quantitative statistical analyses carried out on the resulting categorization, this study describes a variety of mental strategies used by musicians to identify notes’ pitch. Sixty-seven musicians  were interviewed, revealing that musicians utilize intermediate steps during note identification by selecting or activating cognitive bricks that help construct and reach the correct decision. We named these elements “mental anchorpoints” (MA). Although the anchorpoints are not universal, and differ between individuals, they can be grouped into categories related to three main sensory modalities – auditory, visual and kinesthetic. Such categorization enabled us to characterize the mental representations (MR) that allow musicians to name notes in relationship to eleven basic typologies of anchorpoints. We propose a conceptual framework which summarizes the process of note identification in five steps, starting from sensory detection and ending with the verbalization of the note pitch, passing through the pivotal role of MAs and MRs. We found that musicians use multiple strategies and select individual combinations of MAs belonging to these three different sensory modalities, both in isolation and in combination. But in the majority of cases, these studies are still far from being able to concretely grasp the essence of the matter of thought. We note that this follows from methodological difficulties in developing reliable tools likely to validate such direct experience.Scientific studies on human cognition reveal that the brain, including its sensory inputs involved in cognitive functioning, has a highly complex structural and functional architecture. The objective of deciphering such a functional architecture is therefore extremely ambitious. The modern period of this search was in fact initiated in the second part of 19th century, with the founders of the experimental psychology, W. Wundt in Germany and W. James in the United States . Since, Hence, with the aim of tackling directly the study of the matter of thought, we opted for a holistic method. We followed a phenomenological approach based on introspection, i.e., we started from the mental point of view rather than from the neuronal substrate material, following an exploratory interview method. After a first series of interviews, we gradually refined and stabilized our protocol. We narrowed our observations as much as possible to a very specific task in the field of auditory cognition, ending up with the identification of the pitch of one or a few musical notes by students or professional musicians.top–down experimental approach, presents in return a major drawback: it is solely based on subjective therefore potentially misleading pieces of evidence  of sounds: as we hear a mixture of complex sounds, we may, on the one hand, switch between apperception of many, even all, of their constituents; on the other hand, complex sounds may be perceived as a highly integrated whole , and 39 Conservatory students  . Profess1). One participant (P165), who played the violin, complained that identification of notes at the piano was too difficult; as requested, the notes were then played at the violin. When required, a reference note  was provided.One or a small number of notes of various pitches were provided to each subject. In the case of several notes, they were presented in sequence (melodies) or in superposition (chords). Representative examples are presented in All interviews were performed by AL, a teacher and professional musician, as a contribution to his Ph.D. research. Interviews took place at Conservatories. They lasted between 30 min and two and a half hours. For two minor students only, a parent was present during the interview. On a whole, 80 interviews were performed, most of them during a 3-year period (2005–2007). Fifteen interviews were performed before 2000 and served to refine the procedure (see below); seven interviews were performed later (2015–2016). One participant declined to participate in the study and another dropped out after completion of the interview; both argued that the questionnaire was intrusive and potentially damaging for their image. All documents relative to these interviews have been deleted. At the beginning of the interviews, participants were asked to answer simple questions about their musical background . All the interviews were recorded in audio format and faithfully transcribed into text files. Participants were not asked to read, comment or correct the texts. In some cases, a few comments were added during interviews and identified as such in the written transcription. For four musicians , several sessions took place. In one case (P107), the interview was summarized a posteriori.Interviews were conducted following an approach based on introspection. The study started with a quite long exploratory stage during which the method was progressively stabilized, being also influenced by interview methods proposed in the nineties . HoweverThe main task of each interview was to identify individual notes. The interviews systematically started with identification of individual notes, isolated from any context . MAs are associated, one way or the other, with the mental representations (MR) of the note’s names, i.e., the inner elements which come to the mind to explain the external signal and ascribe it a meaning. Second, we carried on systematic quantitative analyses of interviews, by extracting and classifying the text elements corresponding to MAs. We started with a pilot study on ten interviews, where annotations for MA and MR were independently carried on by two of us – AL and PL (who are both French native speakers), by means of the QDA Miner 5 software It’s an E flat”), the question “How do you know this?” was systematically asked. A few musicians were spontaneously able to describe their strategies, for example: “Because I “heard” – or “saw,” etc. – something in my head.” Most musicians found themselves unable to provide such an explanation and just answered “It’s obvious”. In such cases, the interviewer insisted by inducing introspection on the process of note recognition: “Can you try to describe what happened in your mind during identification?”. In the end, the mental processes leading to the identification of notes were reported by participants through a wide variety of mental descriptors that were interpreted by the participants themselves as dynamic supports in the act of identifying the note. In some cases, participants illustrated their anchorpoints by means of drawings, as reported in Most of the interviews revealed that musicians were not aware of the strategy or method they used to identify the pitch of a note. Once the note name was provided . Such descriptors emerged as the smallest mental elements that could be detected by means of introspection. We formulated the concept of “mental anchorpoints” as the minimal structures detectable by a subject by introspection, in association with a perceptual recognition process. Such MAs were described by participants in several ways. For example, participant P125 indicated that the “sounding” nature of his MA consisted of a fusion between two timbres: “Mental anchorpoints, as a support for recognizing a low-complexity perceptual object, appeared then to work as key elements of an effective cognitive strategy: sometimes as immediate grasps, that might even be ignored so far by the musicians themselves, or as a micro-reasoning requiring several seconds. The idea that MAs play a strategic role is also reflected by the fact that it was possible to establish a strong correspondence between their use and different ways of ascribing a meaning to perceptual features. To provide an example, we observed a significant consistency between the specific adopted strategy and the type of musical hearing (relative or absolute pitch). Musicians with relative pitch failed to identify an isolated note, and asked to hear a reference note first. These musicians said that they were to mentally compare the gap between the two notes with an interval stored in their memory. This revealed a relationship between the employed strategy and relative pitch, since the procedure for identification indicated a sort of measurement of the distance between two references. Those having absolute pitch identified the note without any prior reference. They said for example that they mentally felt the gesture that should be performed with their instrument or phonatory system to produce that pitch. This strategy is compatible with direct pitch recognition without any comparison between two sounds. But this was not always the case. Here is a concrete example: participant P164 never requested a reference note to identify a note in isolation. However, in some situations, he mentally imagined a reference note A4 and compared it with the external sound he was physically perceiving. He then had a kind of “absolute” approach, typical of perfect pitch, consisting in not-need of any external reference but proceeding nevertheless by “relative” comparison of two elements: recognizing a first  note before identifying the second  one. It should be noted that, as a first approximation, this approach did not seem to require more time than direct identification. Many musicians with absolute pitch showed different abilities to stock internal references in their memory over time. Participant P123 specified, for example, that he might stay for several days, even weeks, without listening to music, still maintaining his capability to identify the notes in an absolute way. Differently, participant P139 said that he needed to “reactivate” this skill one or more times a day.All these descriptions suggested a direct relationship, connecting the MAs with the response(s) in the process of identification. Here are two additional examples:(a)In fact, for this note, I did not see a keyboard, but an interval, a distance between two sounds (…). A kind of black background, with the interval between the notes on the keyboard like a [space] distance on a neutral background (…) I felt the mental distance of five keys.”Participant P164 did a comparison between two sounds. When he described his MA, he evoked the distance between the sounds and said that it was the relative position of the second “luminous point” that allowed him to identify the note in question : “In fac(b)As for participant P163, she often heard internally pronounced syllables such as C (“Do” in French) or E (“Mi” in French), which put her on the track of naming the note.The note said to me “mi” [E in French]); (2) the specificity with which the ending vowel of the note name was pronounced (the ending i was pronounced with a rather dark color: “It was a bit like a “mu””), which put on the trail of detecting an alteration , and finally (3) the blurred vision of a piano: “… and I superimposed the overall view of the piano to detect which E it was about.”From participants’ reports, many situations emerged where the MAs interacted with each other, spreading out or merging together. Processes in which the identification occurred through combination of several MAs were regularly described. In this situation, each MA provided only one piece of information, and it was therefore from the combination of several complementary elements that pitch recognition was achieved. Thus, for example, participant P163 needed to focus on three aspects: (1) internally heard vowels, which provided information on the name of the note  “I identify a chord first as a whole.” Some musicians might use either strategies, for example P123. These examples suggest that, depending on what attention was focused on, strategies could differ, still using the same MA. Another illustration of the role of intentional aims during note identification is: most musicians mentally identified enharmonic pitches by naming the notes regardless of the harmonic context , mentioning, later on if applicable, the odd naming they came up with.The obtained results suggested that this diversity of strategies was far from being concerned with only the distinction between the two main types of musical ear, i.e., absolute versus relative pitch. Indeed, participants mentioned explicitly the contribution of their intentional aim during note recognition especially for complex sounds , the so formed MRs were always related to a single primary sensory modality – according to what all the participants declared: “I” mentally “see”, “hear” or “feel”.This first qualitative analysis provided evidence that musicians didn’t used the same strategies or MAs to identify pitch. However, it also suggested that – while a wide range of descriptions was provided – the underlying mental processes were not so numerous. Consequently, we conducted a second, more focused, qualitative analysis on all available interviews in order to relate participants’ MAs to a limited number of categories and to identify a minimal repertoire of anchorpoints.The 11 resulting categories of MAs are listed in internally pronounced (being an entire word or part of it). It was the focus on the last vowel, for example, that made it possible to define the role of this MA. Some musicians, like P148 and P162, mentally “heard” only the final vowel of the note’s name. Both admitted to be confused between the notes mi and si (E and B in English), as well between fa and la (F and A), since their names ended with the same sound – a quite surprising confusion for an expert musician. The same didn’t happen, for example, to participant P139, who was able to “hear” the names of the notes in their entirety. Intriguingly, for some participants the sound location  was a very prominent mental strategy. For example, P123 “heard” the names of notes; in case of doubt, for example in the presence of alterations, he could distinguish between different possibilities as, he said, the sound sources “generating different names” were “located in different positions.” P123 used sound location for MA1 very frequently. Besides him, we found trace of such usage also in other interviews, for example in the case of P126. For P161, some notes might “pronounce their names” stronger than others depending on the pitch from the “very loud” Fa (F) to the “almost inaudible” Si (B) along an ascending circle of fifths, as drawn by the participant himself . Musicians had various uses of this anchorpoint: indeed, descriptions focused on different aspects such as the specific location of the sound or the timbre with which the words were  himself .The intervals, (…) I recognize them in any case, for all instruments.” In the second case, MA2 corresponded to direct recognition of conventional chords such as the major triad, the minor triad, the dominant seventh, etc. This kind of instantaneous grasp is typical of harmonic pattern recognition  and in superposition (chords). It essentially corresponded to a strategy associated with relative pitch. For example, participant P136 said: “ognition , and migI rose from C to B; I climbed C, D, E, F, G, A, B.”The identification of a note started from a well-known reference pitch: the musician mentally sang or heard sounds with the purpose of counting the steps needed to reach the pitch under identification. As an example, student P102 said: “For me, the note itself has a particular timbre, a particular color, an E does not sound like a D, and if you play a note on the piano, it’s above all the timbre of that note that will provide me its name”. For some musicians, pitch identification from the human voice (P163) or from a computer sound (P131) was impossible. Such individual diversity suggested a cognitive signal processing of the sound, whose complexity went far beyond the simple recognition of the fundamental pitch. This reminds to experimental studies comparing humans and macaques on the different functional organization of the auditory cortex for the treatment of the musical stimuli , associated to each note or chord. For most musicians, this anchorpoint seemed to be related to the wavelength of the fundamental, perceived as a unique signature; for some of them (we detected five participants), its usage was closely associated to the timbre of the sound, i.e., sounds containing a minimal number of higher harmonic frequencies and produced by well specific instruments . Participant P131 stated: “ stimuli . Some muNote that although the boundaries between MA2 and MA4, as well as between MA2 and MA3, are quite clearly defined, musicians demonstrated that they were able to use these anchorpoints also in combination, which makes their distinction less prominent. Note also that the distinction between MA2 and MA4 is particularly delicate, since the “color” of a chord – a feature expressing its timbral signature depending on the balance between the harmonics – can be either memorized as such or associated with previously learned music concepts.“Yes, I saw the written word…, since when I think to the note, I don’t know why, in a solfeggio lesson, sometimes, I [mentally] write it… sometimes I think about it…”. In the first case, the key could also appear, and the ambitus was also somehow taken into account . In this regard, P105 said: “I imagine how the notes could be positioned (…) I see a stave with a key of Sol, an A, and then I see the notes going down…”In this case, the notes were placed inside the stave, or their names “appeared” in full letters. For example, the young student P153 said: Depending on the instrumental practice of the musician, a musical instrument appeared – a keyboard, a guitar fretboard, the clarinet keys, etc. – with the position of the fingers properly associated with the note. In some cases, participants provided a drawing of such mental images  steps, where each step corresponds to a note. And then, when I move downward, my eyes follow the steps in my head”. Some musicians drew diagrams to explain their visual anchorpoints , to identify a note in association with a reference note , or to recognize a relationship between two notes to be identified. P140 specified: “orpoints : P132 saorpoints . She saiI see the E reddish, while the E flat would be more brown… anyway, darker”. Others saw matter’s effects or deformations. Thereby, P132 described, “A form (…) which shrinks if the intervals are small and distends when [they] widen. But from a purely visual point of view, a kind of matter (…), like modeling clay.”This MA was used for example to identify single notes, or to refine identification of a note in the presence of an alteration. Some participants referred to colored visions, such as P112 who said: ““mental muscular gesture” that allowed these musicians to identify the perceived note, similarly to what one would have to actually do to sing it. For example, P132 said: “I do not think that my phonatory apparatus really positions itself, however, I have the feeling that it does so (…). It’s the same when I imagine a tennis gesture: I have this feeling but my arm does not move.” This MA was used by musicians who evoked a frequent use of internal mental singing in their musical practice, as for example P144: “When I hear a very high pitch, for example, then I do retract here [she showed her throat], as if I were going to sing it.”Some participants mentally positioned their phonatory apparatus in accordance with the production of the note. It was the act of provoking a I feel the gesture, I feel this specific shifting movement to go from A to F sharp, oh yes, I feel it”), the gap between the fingers on a piano keyboard , etc.Some participants mentally positioned themselves in accordance with the instrumental production of the note: the hand on the violin neck ; chills or tension ; mental feelings related to thermoception ; a nociception .This category includes the MAs that were described as any other mental sensations associated to the body: a feeling of openness . During the process of note’s recognition, we hypothesize that MAs are utilized and manipulated in order to create efficient MRs of notes, i.e., a mental image which come to the mind at the stage of recognizing a note or chord and providing an explanation for the perceived external signal. Indeed, the mental processes described by the participants explicitly referred to one of these modalities by means of words  that may be related to each case: I hear, I see, I feel; an inner voice, a drawing, a chill; etc. Eventually, it was through MRs that musicians fulfilled the task by communicating the name of the note.The qualitative analysis outlined so far allowed us to highlight that musicians tap into many different MAs, which can be grouped into eleven categories. All these categories may be used in a mental approach by which a musical note is identified. Such categories can be classified according to the involved sensory modality: auditory, visual or kinesthetic , the same signal can trigger the selection of different anchorpoints. In our formulation, MAs correspond to entities which store memories of previous perceptions or actions which can arise from multiple sensory modalities. Step 3 – Mental integration is the process of connecting one or more MAs in order to select, endorse and/or support a (possibly conscious) MR of the perceived signal. This corresponds to the stage of aggregation and/or validation of MAs. Many different operations are here performed, such as superposition or blending of anchorpoints, with different degrees of proximity and precision. This represents a complex cognitive task, which requires combining several levels of intervention and different intentional aims. What happens here is a sort of forging an amalgam, in order to get a meaningful conclusion. Depending on the difficulty of the task and the background/expertise of the participant, one could observe different levels of access to consciousness. Such integration is illustrated in “i”, which put on the track of a probable E ; (b) identification of the consonant “m” preceding the vowel “i” (a specific process described by P126 himself: “The consonant comes to me”); (c) instantaneous recognition of the triton : as a reference A was provided by the experimenter, P126 almost instantly refined his previous answer, consisting of the syllable “mi” (steps a and b), and inferred that the note was actually an E flat; (d) final confirmation by association of the previous three steps with the mental gestures related to “the physical sensation of [my own] phonatory apparatus” and “the gap between the fingers.” The interweaving of MAs, echoes of previous perceptual experiences, and building blocks of emotional or aesthetic valence appeared to be an important expression of the mental strategies implemented during notes’ identification. However, the role of such building blocks, alongside MAs and MRs, remains to be clarified. Step 4 – Validation of mental representations is the stage of ascribing a meaning to the perceived stimulus, i.e., a mental image  comes to the mind during conceptual grasping, more or less consciously, to provide an explanation for the perceived external signal. As mentioned above, we called these inner images “mental representations.” MRs are personal and may differ from one individual to another. They are not usually communicated as such, except during introspection. Step 5 – Verbalization is the final stage indicating successful identification of the stimulus by verbalization through standard terminology. Neither the nature of the underlying MR nor the associated MA(s) are hereby communicated; however, the recognition of the perceived object is completely established.The mental processes described by the participants seemed to be organized sequentially, making it possible to propose a conceptual framework consisting of several stages, beginning with the detection of the stimulus by the inner ear and ending with a verbal output corresponding to the name of the note(s) . The staIn order to assess this conceptual framework, i.e., to specifically precise the relationship between MAs and MRs, we undertook a more systematic approach consisting in a quantitative analysis of the content of all interviews. First, in a pilot experiment with ten musicians, we extracted and quantified any reference to MAs, MRs, and different manipulations of the former and the latter. After validation of this procedure, we extended our quantitative analysis to all interviews  to (i) quantify the usage of single categories of MAs, (ii) classify the usage of MAs according to gender and expertise, (iii) search and discuss simultaneous and sequential usage of MAs, (iv) look for possible grouping of participants based on sensory modalities, and (v) investigate the possible relationships between different anchorpoints. These analyses are presented in the next subsection.First, we selected a sample of 10 musicians based on the diversity of their profiles and the richness of their interviews see . We systOur analysis returned nearly 1000 occurrences for MAs and more than 450 occurrences for MRs . The quaEach MA mainly relates to a specific sensory modality: namely, MA1 to MA4 relate to the auditory modality, MA5 to MA8 to the visual modality and MA9 to MA11 to the kinesthetic modality. This resulted in three main groups of anchorpoints. For each musician, it was therefore possible to identify the sensory modality related to each group of anchorpoints and to compare it with the number of occurrences of the mental representations of the same modality. This comparison is shown in The correlation between the typology of MAs and the sensory modality related to MRs suggested a functional relationship such as a mental integration or fusion of MAs for building up MRs (step3). We extracted the text elements corresponding to this step. The vocabulary was extremely diversified from one musician to another (results not shown). We detected associations, fusions, comparisons and other manipulations of MAs. This could both reflect the diversity in the usage of MAs and be a consequence of different degrees of awareness in the process of introspection. To investigate this aspect would require a detailed separate study, and it has not been further examined hereby.In a next step, we counted the occurrences of MAs for each of the 11 categories in the remaining interviews. In 11 of them, it was not possible to properly extract the anchorpoints, so those participants were excluded from further analyses. The first case was a student, too young to satisfactorily complete the recognition task . Other four students, all guitarists, could identify the notes only by referring to the position on the guitar neck and were not able to name them . For three professional musicians , the interviews were conducted without any auditory test, so their mental descriptions were too generic and limited to discourses on how they heard the notes. Note that one of these musicians (P147), who played an African instrument, the balafon, was not used to practice pitch recognition on his instrument; he was rather used to capture, according to the musical context, a semantic meaning. This is an example of one of the limitations of our study, being confined to the context of Western classical music. Finally, for three professional musicians , the number of occurrences of anchorpoints identified in the text was too low  to be taken into account.The identification of MAs was thus carried out for 46 additional participants. For this group, assignments of occurrences for each category were jointly provided by two of the authors (AL and PL). A Kolmogorov–Smirnov (KS) test was performed, in order to check whether the results were consistent with those obtained for the pilot group . For tenThe range for such entries is quite broad (between 0 and 115). In some cases an entry might be overrepresented just because the interview focused more deeply on a given MA, without this necessarily meaning that such anchorpoint was more important than the others . To standardize these results, only the entries with at least 10% of the total number of occurrences for a given participant were counted. For the interviews with a low number of occurrences (less than 30), only the entries with at least three occurrences were taken into account. Conversely, for very rich interviews (more than 100 occurrences), we retained all the entries with at least ten occurrences. Such an analysis returned, for each musician, a signature for the usage of her/his preferred MAs, with the exclusion of those less used. This allowed us to convert the rough set of occurrences displayed in Following this procedure, we found that six categories were more widely used by at least sixteen musicians: MA1 to MA6. Two of these were most represented: MA1, “Hearing” the name or part of the name of a note, 31 musicians; and MA4, note recognition by association of pitch with specific auditory hues, or the notion of “timbre-pitch,” 32 musicians. Three categories were seldom selected  and two categories were very rarely used . It can be noted that the four auditory categories, MA1–MA4, were the most selected. On average, participants selected three categories; some of them mentioned only one category, whereas others mentioned up to five categories.The note B is weak, fragile, it becomes a bit endearing and one feels it small,” while P161 stated: “G major reminded me of a [musical] piece of prime importance, which is the great Fantasy for organ by [Johann Sebastian] Bach (…) I was sent back to the womb.” These observations would require further investigation.In addition, quite surprisingly for a task of note identification, some professional musicians  ascribed different kinds of emotional or aesthetic valence to the note; this noticeably impacted the process of recognition and should be considered as a complementary feature. For example, P112 said: “p-values < 0.005 and equal to 0.029, 0.011 and 0.061 for MA3, MA5, MA2, and MA10, respectively). The low number of female musicians (4) in the professional group (22) did not allow us to analyze the effect of gender. By contrast, comparison between male and female students made it possible to highlight that categories MA5 and MA9  were primarily used by female students . Moreover, in the male group, MA3 was mainly selected by students , whereas MA2 was mainly used by professional musicians . The seeming preferred usage of MA10 by male professional musicians , was not statistically significant .The very varied use of MAs prompted us to take a closer look at the participant’s status  I go up an interval, (…) as if I were singing.” These finding positioned him close to the auditory-visual group.Inspired by the strong correlation between MAs and MRs on the pilot group cf. , we clusThe analysis by groups of distinct sensory modality led us to several observations: first, with the exception of the two students discussed above, all participants used auditory mental supports for note’s identification. Second, the majority of participants  used visual modality in association with auditory modality for their multimodal representations of notes. Seven out of 11 categories of MAs (MA5–MA11) implied a non-auditory sensory mental modality. MA1, which corresponds to mentally hearing the name of the note, also provides an example of a sensory transmodal strategy, in this case relating sound and language – something that might be interpreted as a kind of synesthesia . More spn = 15) who declared to have absolute pitch, except two, were able to identify a specific auditory signature (or hue) for each note (MA4). Similarly, all the participants (n = 12) who declared to have relative pitch, except two, were able to identify the note pitch from a typical interval signature (MA2). Indeed, it can be noted that participants, whether they had absolute or relative pitch, belonged to any of the groups related to different sensory modalities . It was not possible to substantially reduce the number of variables to explain the overall variance, as explaining the 74% of the total variance would require at least six new variables, that is more than 50% of the initial number of variables  but using different MAs, and compare their profiles during different tasks for pitch identification - such as recognition of single notes or identification of notes within chords or melodic sequences.All datasets generated for this study are included in the article.Ethical review and formal approval by a committee was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent to participate in this study was provided by the participants or the participants’ legal guardian/next of kin.AL and PL contributed to the conception of the project, carried out the annotations, and wrote the first draft of the manuscript. AL performed all the interviews. AL, EB, and PL designed and performed the quantitative study. EB performed the statistical analysis, revised the manuscript, and wrote the new sections. All the authors contributed to the initial manuscript and its revision, approving the submitted versions.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


In a social dilemma, cooperation is collectively optimal, yet individually each group member prefers to defect. A class of successful strategies of direct reciprocity were recently found for the iterated prisoner’s dilemma and for the iterated three-person public-goods game: By a successful strategy, we mean that it constitutes a cooperative Nash equilibrium under implementation error, with assuring that the long-term payoff never becomes less than the co-players’ regardless of their strategies, when the error rate is small. Although we have a list of actions prescribed by each successful strategy, the rationale behind them has not been fully understood for the iterated public-goods game because the list has hundreds of entries to deal with every relevant history of previous interactions. In this paper, we propose a method to convert such history-based representation into an automaton with a minimal number of states. Our main finding is that a successful strategy for the iterated three-person public-goods game can be represented as a 10-state automaton by this method. In this automaton, each state can be interpreted as the player’s internal judgement of the situation, such as trustworthiness of the co-players and the need to redeem oneself after defection. This result thus suggests a comprehensible way to choose an appropriate action at each step towards cooperation based on a situational judgement, which is mapped from the history of interactions. Reciprocity is one way to establish cooperation between rational individuals under this shadow of future5. Tit-for-tat (TFT) is one of the most popular reciprocal strategies in the iterated prisoner’s dilemma (PD) game6. Just by replicating the co-player’s previous action, it embodies several, intuitively appealing properties, that is, being clear, nice, provokable, and forgiving. However, if the prescribed actions are misimplemented, two TFT players easily run into TFT retaliation8, so the long-run average payoff becomes as low as those between two RANDOM players, where a RANDOM strategy means choosing cooperation with probability 1/2. Moreover, a TFT population is invaded by unconditional cooperators because a TFT player cannot distinguish an unconditional cooperator from another TFT player. Generous TFT has been suggested to avoid the TFT retaliation12, but it is outperformed by Win-Stay-Lose-Shift (WSLS)14. WSLS also solves the problem of distinguishability in the sense that it earns a strictly higher average payoff against an unconditional cooperator. However, it is vulnerable against unconditional defectors.George Berkeley says that a man who believes in no future state has no reason to postpone his own private interest or pleasure to doing his duty15. Each of them is a memory-one strategy, generally stochastic, and it can enforce a certain linear relationship between its own payoff and co-players’ payoffs irrespective of the co-player’s strategy17. This is true even when the co-player has a longer memory or when the strategy is known to the others. When both the players attempt to extort each other using an extortionate ZD strategy, they end up with mutual defection, so an extortionate strategy is hard to evolve as a group21. TFT is a special case of the ZD strategies, equalizing the players’ payoffs in the long run. The ZD strategies have been studied not only in a well-mixed population but also in structured ones23 because of the importance of spatiotemporal dynamics from a statistical-physical viewpoint24.A notable progress in the iterated PD game is the discovery of the zero-determinant (ZD) strategies25. It has been devised to remedy the problems of TFT by satisfying the following three criteria: Efficiency If all the players in the game have adopted this strategy in common, they will reach mutual cooperation with probability one as the implementation error rate e approaches zero.Defensibility If the focal player uses this strategy, her expected payoff is greater than or equal to any of her co-players’ regardless of their strategies.Distinguishability If all the co-players are unconditional cooperators, the expected payoff from this strategy is strictly higher than theirs.Here, an implementation error  refers to an event that a player erroneously takes the opposite action to the prescription of the strategy. Unlike the perception error, it is assumed that all the players, including the one who committed an error, correctly perceive which actions are actually taken. The class of strategies satisfying these three criteria are called successful hereafter. The first two criteria are especially important because a cooperative Nash equilibrium is formed when efficiency and defensibility criteria are simultaneously satisfied25. Moreover, it is guaranteed that the focal player’s long-term payoff will never be less than those of the others against any kind of strategies. Just as is the case for the ZD strategies, this relation is assured even when the co-players have a longer memory length or when they know the focal player’s deterministic strategy. TFT-ATFT is a memory-two strategy, namely, it prescribes its next action depending on the history profile for previous two rounds. The definition of TFT-ATFT is given in Table 25.To explore an even stronger class of strategies, researchers have proposed a strategy called TFT-anti-TFT (TFT-ATFT), which can be understood as a modification of TFT26. The payoff matrix of the three-person PG game is given as follows:27 and that no such strategy exists if the memory length is less than three. This fact immediately poses a problem on its understandability: Recall that a memory-three strategy is defined by an action table having 512 entries because the number of possible history profiles is Successful strategies exist not only for the iterated PD game but also for an iterated public-goods (PG) gamem rounds. However, a strategy may also be defined as an automaton28, i.e., in a way that a player has a finite number of internal states. A player’s internal state determines her next action, and it changes according to the actions taken by the players of the game. We will show that the decision mechanism behind the actions prescribed by the strategy can be understood more clearly in this ‘state-based’ representation.The purpose of this paper is to interpret the successful strategies by representing them as automata. In the previous works, we have represented successful strategies in a ‘history-based’ manner so that the next action is given as a function of the history profile for the last The paper is organized as follows: In the next section, we present an algorithm to convert a history-based representation to a state-based one. Then, its applications to some successful strategies will be demonstrated. We discuss possible interpretations for the resulting internal states and summarize this work in the last section.m rounds as an internal state. In this naive reinterpretation, the number of states  would amount to n is the number of players. Let us consider a directed graph with In this section, we show how a history-based strategy can be converted to a state-based representation. In general, history-based strategies may be regarded as a subset of state-based ones because one may also regard the history profile over the previous cc, cd, dc, and dd, respectively. Suppose that the current history profile is cc. For example, if the two players’ last actions are c and d, respectively, the next history profile becomes cd. In case of TFT, the action tuples such as cd, denoted as link attributes, happen to look similar to node labels, but this is not the case for general memory-m strategies if 5. In case of TFT, it is straightforward to construct the graph in Fig. An example of such a graph is shown in Fig. mentclass2pt{minimmentclass2pt{minimmentclass2pt{minim29. Specifically, we use the following algorithm: c and d.Define a partition Initialize k by one. For each set in i and j in it are not equivalent, divide the set into finer subsets to define a new partition i and j are equivalent if the outgoing links from these nodes go together in Increase entclass1pt{minimaRepeat step 3 until In short, we regard two states as identical when they lead to the same future. The algorithm always terminates after a finite number of steps, and the final result is uniquely determined irrespective of the order of choosing node pairs. If we apply this algorithm to Fig. 30 in the history-based representation31, whereas its state-based version needs only four states  minimization in automata theorymentclass2pt{minimmentclass2pt{minimmentclass2pt{minimHere, we note that the transitions in Fig. No human experiments were conducted in this study.t, respectively. This graph shows every possible transition among the history profiles in the absence of the implementation error when Alice is a TFT-ATFT player.Let us consider the iterated PD game between two players, say, Alice and Bob. We assume that Alice has adopted TFT-ATFT, and its history-based representation is shown in Fig. cccc to cdcc by this error, and then Alice should defect once again as an ATFT player. If both use TFT-ATFT, they quickly recover mutual cooperation without being exposed to the risk of exploitation via the following sequence of history profiles: Alice normally behaves as a TFT player, and this behaviour is described by the strongly connected component indicated by the green dashed rectangle in Fig. The DFA minimization algorithm simplifies the graph to a great extent as shown in Fig. O(e) when two players adopt TFT-ATFT. For the sake of completeness, Fig. Although this automaton representation is meant to ignore error as we have mentioned, we depict a dashed arrow in Fig. 27, which are memory-two strategies with defensibility, distinguishability, and partial efficiency. By partial efficiency, we mean that the players achieve mutual cooperation with nonzero probability Now, let us proceed to the iterated three-person PG game among Alice, Bob, and Charlie. It has been proved for this game that successful strategies are possible only when the memory length is greater than two. However, it is instructive to begin with partially successful strategies (PS2)By enumerating all the possible memory-two strategies, whose number is greater than one trillion, we have discovered 256 PS2’s. Figure c whereas the other two players punish him by d, whereby Alice’s internal state becomes ‘full trust’ again. Another state labelled ‘1’ can be interpreted in the same way, and the only difference is that this time it is Charlie who defects from full cooperation. Thus, states ‘1’ and ‘4’ are symmetric under the exchange of the co-players. If both Bob and Charlie defect from full cooperation, Alice’s internal state changes to ‘5’, which lies at the the bottom of Fig. We can interpret the nodes in Fig. c at this state, and she can go back to ‘0’ by accepting defection from Bob or Charlie. In plain words, therefore, we could say that Alice wants to make an apology at this state. Similarly to TFT-ATFT, this apology plays an important role in maintaining mutual cooperation in a noisy environment.So far, we have explained how we can interpret ‘0’, ‘1’, ‘4’, and ‘5’ in Fig. dcc. It is this state ‘18’ that makes it possible for Alice to provoke her co-players and test their naivety: The loop between ‘16’ and ‘18’ implies that Alice can exploit Bob and Charlie by alternating provocation (d) and apology (c) if they are unconditional cooperators. This loop thus provides distinguishability for her PS2.Alice can also visit ‘16’ from ‘18’ with a link of 27. Their key difference from PS2’s is that they achieve full cooperation with probability By modifying the 256 PS2’s, we have reported the same number of fully successful strategies in the memory-three strategy spaceObviously, some of its features are different from the above PS2: First, this FUSS makes Alice more careful in distrusting one of her co-players. Recall that we have interpreted state ‘4’ as expressing Alice’s distrustfulness of Bob. It is now split into ‘8’ and ‘76’. Due to this split, it takes one more step to despair when one of the co-players defects. It means that the following recovery path is possible even if Bob defects twice in a row:27. When Alice, Bob, and Charlie have adopted this FUSS in common, we can show that the players recover cooperation from every possible type of one- and two-bit error by enumerating all the possible cases: i’s internal state  by accepting punishment from Alice and Charlie. This recovers cooperation as every player goes back to full trust (‘0’).Suppose that one of the FUSS players, say, Bob, committed an error. If One player, say, Bob, commits error twice in a row.Bob commits an error, and so does Charlie at the next round.Two players, say, Bob and Charlie, commit error simultaneously.The FUSS can also correct two-bit error, which has three possibilities: Now, we will show that all these three types of two-bit error are corrected by the FUSS:We have already seen from Eq.  that thid at the next round, but he mistakenly chooses c instead. Up to this point, the players’ internal states have evolved as c, appears to Alice as an unconditional cooperator. After provoking Bob and Charlie by choosing d, Alice wants to make an apology, and Bob and Charlie want to punish her provocation. Their internal states thus correspond to . Understanding that Bob and Charlie are not unconditional cooperators, Alice accepts their punishment, whereby everyone returns to the full-trust state, i.e., In the second case, Bob first defects in error from full cooperation. Charlie is supposed to punish Bob by choosing c is prescribed by this FUSS at those newly added states, ‘72’ and ‘65’, it does not violate the defensibility criterion because the states are accessible only by its player’s error, not by the co-players’ intention.For the third case, we have already considered such simultaneous two-bit error in Eq. . Alice fIn fact, these additional four states are needed to make this strategy tolerant against two-bit error, i.e., error of To sum up, the FUSS in Fig. n-person social dilemmas. Although successful strategies for In summary, we have investigated the working mechanism of successful strategies for two- and three-person social dilemmas by converting them from history-based representation to state-based one through the DFA minimization. The state-based representation suggests how a player’s internal state should interact with observed actions to make the strategy successful. The DFA minimization is especially effective when the number of players or the memory length increases because the history profile expands exponentially with them. It could also be useful when we evaluate the complexity of a strategy according to the number of states in its automaton representation. We thus believe that the method and the results presented in this paper serve as a solid and indispensable step toward future explorations of successful strategies for general n-person social dilemma sheds light on how to systematically manage collective action among self-interested players by using the shadow of future. We may consider a number of social phenomena such as voting and tax payments in the context of a social dilemma, but the most prominent example is found in the fight against climate change: One of the difficulties consists in the fact that it involves so many players who individually favour defection from collective efforts to reduce greenhouse-gas emissions. Even if a general consensus on cooperation exists on a global scale, it might often be hard to deal with occasional defectors in practice because one cannot tell if they have defected by accident or design. Our finding nevertheless implies a possibility to devise a successful solution by sharpening our intuition about when to retaliate against defection, when to accept punishment by way of apology, and when to maintain cooperation.Such understanding of solving an iterated


The value of malaria eradication, the permanent reduction to zero of the worldwide incidence of malaria infection caused by human malaria parasites, would be enormous. However, the expected value of an investment in an intended, but uncertain, outcome hinges on the probability of, and time until, its fulfilment. Though the long-term benefits of global malaria eradication promise to be large, the upfront costs and uncertainty regarding feasibility and timeframe make it difficult for policymakers and researchers to forecast the return on investment.A large online survey of 844 peer-reviewed malaria researchers of different scientific backgrounds administered in order to estimate the probability and time frame of eradication. Adjustments were made for potential selection bias, and thematic analysis of free text comments was carried out.The average perceived likelihood of global eradication among malaria researchers approximates the number of years into the future: approximately 10% of researchers believe that eradication will occur in the next 10 years, 30% believe it will occur in the next 30 years, and half believe eradication will require 50 years or more. Researchers who gave free form comments highlighted systemic challenges and the need for innovation as chief among obstacles to achieving global malaria eradication.The findings highlight the difficulty and complexity of malaria eradication, and can be used in prospective cost–benefit analyses to inform stakeholders regarding the likely return on eradication-specific investments. Plasmodium falciparum accounts for many of the 200 million annual cases as well as most of the half million annual deaths worldwide , even if delivered optimally”; a parasitologist argued that eradication could not be achieved without a “game-changing innovation”, whereas multiple others referred to the need for “transformative” technologies:We can't achieve eradication with our current tools. We'd need new medicines, a better vaccine, and maybe other vector control tools.In regards to Many noted the need to “overcome the challenge of drug resistance”. More than 10% of commenters noted the need for an effective vaccine. Genetic engineering was mentioned by several commenters as a promising means to achieve eradication quickly. Most comments coded as “solutions” were prescriptive in nature, often suggesting the nature of the needed innovation, with a heavy slant towards pharmaceutical options and vaccination.Systemic challenges to malaria eradication were noted by the majority of commenters. Comments in this category can be divided into four sub-themes: (i) lack of coordination, (ii) lack of good surveillance and health services delivery, (iii) lack of political will and (iv) poverty. In direct contrast to the previous comments, many echoed the comments of an epidemiologist who stated that “we already have the tools to achieve eradication” and that the only piece lacking was “robust health systems”. Many commenters noted problems of coordination, as illustrated in the below quote from a biologist.It will be very difficult to eradicate malaria… not because we don't have the technologies, which we already have… the problem is politics. Malaria doesn't stop in (sic) borders of a country and it would take a joint effort of a lot of political leaders to get programs in place to fight malaria. Unfortunately I don't see this happening anytime soon.Eradication requires a full systems-wide approach, not a disease-specific approach. The eradication of smallpox was a triumph of management, not medicine or technology.Others echoed the sentiment, with many comments focusing on the need for strong surveillance and treatment delivery systems. Many commenters focused on other reasons for stagnating progress; for example, a public health specialist pointed out the importance of “weak or failing health systems…due to political unwillingness or conflict”. Many noted that malaria is a “disease of poverty”, with “social injustice” as the root cause. Some made the sequential argument that “eradication of poverty” must precede disease eradication. Along the same lines, one epidemiologist wrote:Another epidemiologist noted that the survey “left off the list the most important factor—economic development”. Many echoed the sentiment, stating that without economic development, eradication will be impossible, and that poverty is the “cause” of malaria. Comments coded as “systemic” tended to be descriptive and more pessimistic than others.Complexity was a relatively rare category , those whose comments were coded as the “complexity” category were more pessimistic than average in regards to the timeline and likelihood of eradication. Many commenters highlighted the inherent challenges in the epidemiology of malaria, such as the changing dynamics of malaria transmission, the resilience of the parasite and vector, climate change, and the inability to aim interventions accurately with an “ever-moving target”. The potential for adaptation was highlighted in reference both to the mosquito as well as the parasite itself. Several participants pointed out that the vast animal reservoirs for Plasmodium knowlesi made it "impossible to eradicate". Many comments addressed the fact that the conversation on eradication is largely taking place within the public health community, whereas the causes of malaria endemicity are largely orthogonal to public health interventions. Several commenters pointed out the multitude of prerequisite conditions for eradication to even be considered feasible; for example, an economist and statistician noted:To my mind, this question is highly dependent on background context, e.g. global political and economic dynamics, as well as international conflict. Complete global eradication is an extremely singular goal that requires a vast array of necessary conditions - if any of these fail, eradication will not be achieved.Eradication is a different objective than elimination. Elimination means that the disease is not endemic but could reappear even in a country like Norway if infrastructure breaks down. Elimination may be possible in poor endemic countries, following socioeconomic development. Eradication means that the parasite disappears from the planet, which is not realistic…Many commenters thought that the terms “eradication” and “malaria” were so complex and nebulous that public health practitioners should avoid them all together, so as to not repeat the mistakes of the WHO GMP in the 1950s. For example, some implied that there were—at least operationally—multiple "malarias", and talking about “malaria” as one disease misses the mark, since the different species of parasite and contexts in which they live make elimination in each area very distinct from other areas. One clinician wrote that eradication is a “postwar” idea that developed from the “abandonment of a broad sociopolitical understanding of the causes of disease, and the emphasis on technological solutions.” Many stated that global malaria eradication was simply not possible, and two argued that it may not be desirable or ethical. One epidemiologist stated that the concept was “absurd” and that “I’m not even sure why people talk about it”. A clinician questioned the utility of discussing “eradication” as a concept:Comments questioning the utility of eradication as a concept or goal tended to be skeptical of its feasibility. Largely, they were prescriptive, advocating for a re-framing of the conversation so that the focus was not on an “arbitrary” goal like eradication, but rather on scaling up control and making region-specific progress.This study has elicited researchers’ view, through an online survey, on likelihood and approximate time to malaria eradication. Roughly three-quarters of respondents believe that malaria will not be eradicated in the next half century. When adjusted for selection bias, the perceived likelihood of eradication in 50 years remains similarly low, but estimates for shorter-term eradication are even lower.Eradication of a disease is a “high stakes game”, exposed to multiple competing—and at times contradictory—incentives from multiple stakeholders . UnderstHowever, areas of high malaria endemicity are often also those with high competing health costs. When estimating the return on investment of malaria elimination initiatives, not only must one take into account the potential benefits (even in the case of failure), but also the opportunity costs (even in the case of success). After all, eradication and elimination are not binary success/failure propositions—an initiative should be judged both on its epidemiological circumstances  as well This paper has several limitations. Conceptually, academic researchers are specialists—their narrow, field-specific view of eradication’s feasibility is of arguable reliability, given that they may be unfamiliar with the operational, cultural and “real-world” challenges of malaria eradication. Though crowds have been found to be more “wise” than individuals in many cases, the application of an approach similar to the “wisdom of crowds” is not suitable to all classes of problems . Crowds Though sample size was large, response rates were low, calling for the need to address potential selection bias. In the case of gender, even though males responded at a significantly greater rate than females , selection bias was not of concern since there were not significant differences by gender in regards to pessimism/optimism . In the case of researcher impact , selection bias plays an important role: being highly-cited was associated both with eradication “pessimism” as well as likelihood of non-response. In other words, the pool of respondents was less highly-cited than the pool of invitees, and among respondents, those who were highly-cited tended to be more pessimistic. Though results were de-biased, selection bias on other (unobserved) variables may still exist.Three additional potential biases are worth mentioning specifically. (1) “Conjunction fallacy” suggests that the general goal of eradication may seem less likely than the aggregation of the goals of country-specific elimination. (2) A (reverse) variant of the “hot hand fallacy”, in which researchers may mistakenly base their assessment of current chances of eradication on previous failures. (3) Parkinson’s law of triviality suggests that researchers may disproportionately see the challenges of their own research  as larger or more relevant to the global eradication campaign than they really are.., regarding the feasibility of eradication of neglected tropical diseases, this study detected relatively high levels of eradication skepticism and did not delve into whether researchers had clinical or operational experience, nor did it assess opinions of program workers, nor did it explore complexities pertaining to different types of or forms of existence of malaria. Though this study’s sample size was over twice Keenan’s, this was largely due to having contacted more authors, as response rate was only one fourth as large [As with the survey of experts of Keenan et alas large .This study included the first authors of indexed journals. Though certainly a group with important knowledge related to malaria, this misses malaria control programme employees, health agency workers, and other stakeholders. Their experiences and viewpoints may be different from those of academics, and arguably more relevant. The de-biasing method accounts for different response rates of “senior” vs. “junior” researchers, but does not take into account the fact that first authors are generally more junior than senior authors . To the extent that the results suggest that those with less experience (as represented through publications) tended to be more “optimistic” regarding eradication, it is reasonable to assume that the restriction of first authors may have led to an overly optimistic sample, making the results of the survey even more striking. Given these issues, the extent to which the respondents are representative of malaria experts cannot be known with certainty.There are other important limitations which may also affect this study’s generalizability. The restriction of the source of data to only the PubMed platform meant not detecting researchers who publish in journals indexed elsewhere. Data was collected in late 2016 and early 2017, and the extent to which the opinions of participants have changed is unknown. Though the qualitative coding of free-text comments was reviewed by all authors, only one individual carried out the coding. This, along with the low response rate among invited participants, suggests that this study may have been subject to both selection and analysis bias; results should be understood within this context.The findings of this survey show researchers expressing hesitance about the likelihood of eradication and suggesting a long-time frame until it is achieved. The causes for skepticism are diverse, but common themes were the need for innovation, systemic challenges, and the complexity of the disease and its transmission.The implication of these results are twofold: (1) that those working or investing in eradication-specific campaigns, as well as those modeling these campaigns’ hypothetical cost–benefit, should factor in researchers’ perceived long time frame when calculating those campaigns’ expected value; (2) that champions of near-term eradication may need to make a more compelling case to malaria researchers of eradication’s feasibility, in order to better focus and inspire the latter.The “true” feasibility and timeframe of eradication is unknown, as only time will tell whether the collective “wisdom” of researchers was worth adhering to or not. The actual cost–benefit of eradication interventions is not only a function of eradication’s success, but also of a number of other factors which are only knowable retrospectively. This study’s primary contribution is the provision of a snapshot of perceptions of malaria researchers, whose opinions may be of value not only to other researchers, but also to the malaria and public health communities at large.