Perceptual Organization Research Articles

Facilitation of students’ disembedding in an online visual arts and mathematics education program

BackgroundDisembedding is a crucial spatial thinking skill in visual arts and mathematics education. It is important in creating and analyzing artworks by separating a figure from its background, as well as for solving geometric problems where shapes must be viewed from new perspectives. Drawing upon research in psychology, arts, and mathematics education, the present study aimed to facilitate students’ disembedding in an online educational program employing the teaching experiment methodology. This program utilized concrete movement artworks, particularly those by Max Bill. Seven sixth-grade students participated remotely in this program, utilizing GeoGebra Classroom.Main findingsThe analysis of video data (talks and drawings) and written notes over three sessions revealed that this online educational program, which was designed for the specific context of visual arts and mathematics, offered students opportunities for the individual and group observation of diverse artworks, the tracing of shape contours, and guided attention to new perceptual organizations of shapes through prompting questions. Overall, this had the potential to facilitate students’ disembedding. This overall process challenged students’ initial simplistic shape organizations based on Gestalt principles, leading to the identification of primary and secondary structures, as well as reversible figures.Conclusions/potential implicationsThis research sheds light on the concept of disembedding skills rooted in Gestalt psychology, and its connection to the figure-ground phenomenon observed in both artistic and mathematical contexts. This research offers theoretical and practical contributions. First, it suggests an emerging trajectory of disembedding and proposes methods for nurturing students’ disembedding skills. Second, this study serves as an example for art and mathematics educators in schools and informal learning environments (e.g., art museums) to support students’ spatial thinking. This study contributes to the development of educational programs that facilitate students’ spatial thinking in the context of STEAM (Science, Technology, Engineering, Arts, and Mathematics) education.

Higher testosterone level is associated with improved cognitive functions in Klinefelter syndrome

AbstractKlinefelter syndrome (KS) is a common sex chromosome aneuploidy affecting one to two per 1000 live male births. Testosterone therapy and neuropsychological support can enhance the quality of life in affected individuals. While cognitive deficits have been documented in Klinefelter syndrome, the influence of hormonal variability on cognitive profiles remains underexplored. This study aimed to determine whether testosterone levels correlate with neurocognitive functions in Klinefelter syndrome individuals. This cross‐sectional study involved a heterogeneous clinical sample from a single tertiary referral hospital. Participants: Thirty Klinefelter syndrome individuals were enrolled, being 21 with 47, XXY without neurological comorbidities, aged 17–65 years. Participants underwent blood tests for total testosterone, free testosterone, estradiol, sex‐hormone‐binding globulin, follicle‐stimulating hormone, luteinizing hormone, and anti‐Müllerian hormone. A comprehensive neuropsychological assessment was also conducted, covering intellectual quotient (Wechsler Scale) and higher‐order cognitive functions (attention, executive functions, language, memory, and visuoconstructional abilities). Neuropsychological performance was notably better in Klinefelter syndrome individuals with higher levels of testosterone. Spearman's test revealed significant correlations between total testosterone, free testosterone, and gonadal status measured by free testosterone/luteinizing hormone and free testosterone/estradiol ratios and cognitive flexibility tasks. The mean age of participants was 33.1 years (SD = 14.0), and free testosterone/luteinizing hormone and free testosterone/estradiol measures were correlated with set‐shifting, verbal memory, visual functions, and adaptive behavior domains, including communication, daily living, and motor skills. The free testosterone:estradiol ratio was also consistently associated with total intellectual quotient, verbal comprehension, perceptual organization, and processing speed indexes. The study highlights the positive correlation between testosterone levels and cognitive functions in Klinefelter syndrome males. These insights reinforce the role of testosterone in neurocognitive development, suggesting the potential benefits of testosterone therapy in managing cognitive deficits in Klinefelter syndrome. More extensive confirmatory studies are necessary to substantiate these findings and to explore the mechanisms involved.

Effect of epileptiform discharges and hippocampal volume on cognitive dysfunction following clipping of ruptured aneurysms in the anterior circulation.

Cognitive dysfunction after aneurysmal subarachnoid hemorrhage (aSAH) remains unclear due to various neurological impairments. This study aimed to evaluate the changes in hippocampal volume, cognitive function, and interictal epileptiform discharges after clipping in patients with aSAH of anterior circulation. Patients with modified Rankin Scale scores of 0-3 points who underwent clipping were evaluated. Aneurysmal locations were classified as middle cerebral artery (MCA), internal carotid artery (ICA), and anterior cerebral artery (ACA). Surgery was performed using the transsylvian approach or interhemispheric approach. Hippocampal volume measurement, neuropsychological assessments, and interictal electroencephalogram evaluations were performed postoperatively at the subacute phase. Epileptiform discharges were assessed using the spike index (SI). We included 60 patients (23 men, 37 women; median age, 57.4 years). Aneurysmal locations were found in the MCA, ICA, and ACA in 23, 19, and 18 patients, respectively. The postoperative hippocampal volume was significantly reduced on the clipping approach side in the MCA and ICA groups (MCA, p < .001; ICA, p < .001). There was no correlation between hippocampal volume and cognitive function. A significant difference was noted in elevated SI on the approach side of the MCA (p < .001), ICA (p < .001), and ACA (p < .001) in the transsylvian approach group. The elevated SI on the left approach side showed significant differences in some neuropsychological assessments (performance intellectual quotient, p = .028; perceptual organization, p = .045; working memory, p = .003). Cognitive dysfunction in the subacute phase after clipping for aSAH was not correlated with hippocampal volume reduction but was correlated with interictal epileptiform discharges.

The shift of attention: Salience modulates the local vs global processing of auditory scenes in musicians and non-musicians.

This study addresses how salience shapes the perceptual organization of an auditory scene. A psychophysical task that was introduced previously by Susini, Jiaouan, Brunet, Houix, and Ponsot [(2020). Sci. Rep. 10(1), 16390] was adapted to assess how the ability of non-musicians and expert musicians to detect local/global contour changes in simple hierarchically-organized tone sequences is affected by the relative salience of local information in the timbre dimension. Overall, results show that salience enhanced local processing capacities, at the cost of global processing, suggesting a bottom-up reallocation of attention. Interestingly, for non-musicians, salience caused a reversal of the basic global-over-local processing prioritization as it is typically observed in expert musicians.

A taxonomy for human social perception: Data-driven modeling with cinematic stimuli.

Every day, humans encounter complex social situations that need to be encoded effectively to allow interaction with others. Yet, principles for organizing the perception of social features from the external world remain poorly characterized. In this large-scale study, we investigated the principles of social perception in dynamic scenes. In the primary data set, we presented 234 movie clips (41 min) containing various social situations to 1,140 participants and asked them to evaluate the presence of 138 social features in each clip. Analyses of the social feature ratings revealed that some features are perceived categorically (present or absent) and others continuously (intensity) and simple social features requiring immediate response are perceived most consistently across participants. To establish the low-dimensional perceptual organization for social features based on movies, we used principal coordinate analysis and consensus clustering for the feature ratings. These dimension reduction analyses revealed that the social perceptual structure can be modeled with eight main dimensions and that behaviorally relevant perceptual categories emerge from these main dimensions. This social perceptual structure generalized from the perception of unrelated Hollywood movie clips to the perception of a full Finnish movie (70 min) and to the perception of static images (n = 468) and across three independent sets of participants (n = 2,254). Based on the results, we propose eight basic dimensions of social perception as a model for rapid social perception where social situations are perceived along eight orthogonal perceptual dimensions (most importantly emotional valence, empathy vs. dominance, and cognitive vs. physical behavior). (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Divergent pattern of functional connectivity within the dorsal attention network differentiates schizophrenia and bipolar disorder patients.

Schizophrenia (SZ) and bipolar disorder (BD) share common clinical features, symptoms, and neurocognitive deficits, which results in common misdiagnosis. Recently, it has been suggested that alterations within brain networks associated with perceptual organization yield potential to distinguish SZ and BD individuals. The aim of our study was to evaluate whether functional connectivity (FC) of the dorsal attention network (DAN) may differentiate both conditions. The study involved 90 participants: 30 remitted SZ patients, 30 euthymic BD patients, and 30 healthy controls (HC). Resting state functional magnetic resonance imaging was used to compare the groups in terms of the FC within the core nodes of the DAN involving frontal eye fields (FEF) and intraparietal sulcus (IPS). BD patients presented weaker inter-hemispheric FC between right and left FEF than HC. While SZ did not differ from HC in terms of inter-FEF connectivity, they presented increased inter- and intra-hemispheric FC between FEF and IPS. When compared with BD, SZ patients showed increased FC between right FEF and other nodes of the network (bilateral IPS and left FEF). We have shown that altered resting state FC within DAN differentiates BD, SZ, and HC groups. Divergent pattern of FC within DAN, consisting of hypoconnectivity in BD and hyperconnectivity in SZ, might yield a candidate biomarker for differential diagnosis between both conditions. More highly powered studies are needed to confirm these possibilities.

Associations of polygenic risk scores differentiating attention-deficit hyperactivity disorder from autism spectrum disorder with cognitive and cortical alterations in Schizophrenia patients.

Schizophrenia (SCZ) is a clinically and genetically heterogeneous disorder that shares genetic factors with autism spectrum disorder (ASD) and attention-deficit hyperactivity disorder (ADHD). A genome-wide association study (GWAS) differentiating ADHD from ASD was performed recently. In this study, we investigated whether polygenic risk scores (PRSs) differentiating ASD from ADHD are associated with cognitive impairments and alterations in cortical structures in SCZ patients. Based on the GWAS data (9,315 ASD and 11,964 ADHD patients), PRSs differentiating ADHD from ASD (indicating a greater risk of ADHD and a lower risk of ASD) were calculated for SCZ patients (n = 168). Cognitive performance, including verbal comprehension (VC), perceptual organization (PO), working memory (WM), and processing speed (PS), was assessed using the WAIS-III (n = 145). The surface areas and cortical thicknesses of 34 bilateral brain regions were extracted using FreeSurfer (n = 126). We examined the associations of these PRSs with cognitive performance and cortical structures in SCZ patients. Among the four cognitive domains, a higher PRS, indicating a greater risk of ADHD, was associated with impaired WM in SCZ patients (beta=-0.21, p = 0.012). A lower PRS, indicating a greater risk of ASD, was associated with decreased surface areas of the left medial orbitofrontal (beta = 0.21, p = 8.29 × 10- 4), left entorhinal (beta = 0.21, p = 0.025), left postcentral (beta = 0.18, p = 7.52 × 10- 3), right fusiform (beta = 0.17, p = 6.64 × 10- 3), and left fusiform cortices (beta = 0.17, p = 7.77 × 10- 3) in SCZ patients. A higher PRS, indicating a greater risk of ADHD, was associated with decreased cortical thickness in the bilateral transverse temporal regions (left, beta=-0.17, p = 0.039; right, beta=-0.17, p = 0.045). Our study revealed a relationship between genetic factors that differentiate ADHD patients from ASD patients and both cortical structure and cognitive performance in SCZ patients. These findings suggest that the heterogeneity of SCZ might be partly derived from genetic factors related to neurodevelopmental and psychiatric disorders other than SCZ.

The role of task on the human brain's responses to, and representation of, visual regularity defined by reflection and rotation

Identifying and segmenting objects in an image is generally achieved effortlessly and is facilitated by the presence of symmetry: a principle of perceptual organisation used to interpret sensory inputs from the retina into meaningful representations. However, while imaging studies show evidence of symmetry selective responses across extrastriate visual areas in the human brain, whether symmetry is processed automatically is still under debate. We used functional Magnetic Resonance Imaging (fMRI) to study the response to and representation of two types of symmetry: reflection and rotation. Dot pattern stimuli were presented to 15 human participants (10 female) under stimulus-relevant (symmetry) and stimulus-irrelevant (luminance) task conditions. Our results show that symmetry-selective responses emerge from area V3 and extend throughout extrastriate visual areas. This response is largely maintained when participants engage in the stimulus irrelevant task, suggesting an automaticity to processing visual symmetry. Our multi-voxel pattern analysis (MVPA) results extend these findings by suggesting that not only spatial organisation of responses to symmetrical patterns can be distinguished from that of non-symmetrical (random) patterns, but also that representation of reflection and rotation symmetry can be differentiated in extrastriate and object-selective visual areas. Moreover, task demands did not affect the neural representation of the symmetry information. Intriguingly, our MVPA results show an interesting dissociation: representation of luminance (stimulus irrelevant feature) is maintained in visual cortex only when task relevant, while information of the spatial configuration of the stimuli is available across task conditions. This speaks in favour of the automaticity for processing perceptual organisation: extrastriate visual areas compute and represent global, spatial properties irrespective of the task at hand.

The investigation of dysregulated visual perceptual organization in adults with autism spectrum disorders with phase-amplitude coupling and directed connectivity

The investigation of dysregulated visual perceptual organization in adults with autism spectrum disorders with phase-amplitude coupling and directed connectivity

The psychology of Mona Lisa’s smile

Mona Lisa’s ambiguous expression, oscillating between melancholy and contentment, has captivated viewers for centuries, prompting diverse explanations. This article proposes a novel interpretation grounded in the psychological theory of perceptual organisation. Central to the investigation is the “Ambiguity-Nuance”, a subtly shaded, blended region framing the upper part of the lips, hypothesised to influence perceived expression due to perceptual organization. Through carefully crafted artwork and systematic manipulations of Mona Lisa reproductions, experiments reveal how alterations in the perceptual relationships of the Ambiguity-Nuance yield significant shifts in perceived expression, explaining why Mona Lisa’s appearance changes and under which conditions she looks content versus melancholic based on perceptual organization. These findings underscore the pivotal role of psychological principles in shaping ambiguous expressions in the Mona Lisa, and extend to other Leonardo’s portraits, namely La Bella Principessa and Scapigliata. This study sheds light on the intersection of psychology and art, offering new perspectives on timeless masterpieces.

The phonological store of working memory: A critique and an alternative, perceptual-motor, approach to verbal short-term memory.

A key quality of a good theory is its fruitfulness, one measure of which might be the degree to which it compels researchers to test it, refine it, or offer alternative explanations of the same empirical data. Perhaps the most fruitful element of Baddeley and Hitch's (1974) Working Memory framework has been the concept of a short-term phonological store, a discrete cognitive module dedicated to the passive storage of verbal material that is architecturally fractionated from perceptual, language, and articulatory systems. This review discusses how the phonological store construct has served as the main theoretical springboard for an alternative perceptual-motor approach in which serial-recall performance reflects the opportunistic co-opting of the articulatory-planning system and, when auditory material is involved, the products of obligatory auditory perceptual organisation. It is argued that this approach, which rejects the need to posit a distinct short-term store, provides a better account of the two putative empirical hallmarks of the phonological store-the phonological similarity effect and the irrelevant speech effect-and that it shows promise too in being able to account for nonword repetition and word-form learning, the supposed evolved function of the phonological store. The neuropsychological literature cited as strong additional support for the phonological store concept is also scrutinised through the lens of the perceptual-motor approach for the first time and a tentative articulatory-planning deficit hypothesis for the "short-term memory" patient profile is advanced. Finally, the relation of the perceptual-motor approach to other "emergent-property" accounts of short-term memory is briefly considered.

Editorial: Perceptual organization in computer and biological vision

Editorial: Perceptual organization in computer and biological vision

A Psycho-Pragmatic Study of Superstition in Literary Texts

The present study investigates the concept of superstition in some literary texts from a psycho-pragmatic view. It aims to present the conceptualization of the superstition in literary texts by employing psycho-pragmatic tools as implicatures, specch acts, items of relevance theory, perceptual organizations and types of deictic expressions. It comes up with two types of superstition which are causal and coincidental in which pledges, condemnation, request, states, description speech act have been used; scopal, epistemic, existential, partitive, and privatalization are utilized as relevance items to avoid ambiguity in the representation of superstition; and perceptual organization as similarity, focus, elaboration are played psychological role to reflects inner feeling and belief of the character in the chosen texts.

The hidden structure of consciousness.

According to Loorits, if we want consciousness to be explained in terms of natural sciences, we should be able to analyze its seemingly non-structural aspects, like qualia, in structural terms. However, the studies conducted over the last three decades do not seem to be able to bridge the explanatory gap between physical phenomena and phenomenal experience. One possible way to bridge the explanatory gap is to seek the structure of consciousness within consciousness itself, through a phenomenal analysis of the qualitative aspects of experience. First, this analysis leads us to identify the explanandum concerning the simplest forms of experience not in qualia but in the unitary set of qualities found in early vision. Second, it leads us to hypothesize that consciousness is also made up of non-apparent parts, and that there exists a hidden structure of consciousness. This structure, corresponding to a simple early visual experience, is constituted by a Hierarchy of Spatial Belongings nested within each other. Each individual Spatial Belonging is formed by a primary content and a primary space. The primary content can be traced in the perceptibility of the contents we can distinguish in the phenomenal field. The primary space is responsible for the perceptibility of the content and is not perceptible in itself. However, the phenomenon I refer to as subtraction of visibility allows us to characterize it as phenomenally negative. The hierarchical relationships between Spatial Belongings can ensure the qualitative nature of components of perceptual organization, such as object, background, and detail. The hidden structure of consciousness presents aspects that are decidedly counterintuitive compared to our idea of phenomenal experience. However, on the one hand, the Hierarchy of Spatial Belongings can explain the qualities of early vision and their appearance as a unitary whole, while on the other hand, it might be more easily explicable in terms of brain organization. In other words, the hidden structure of consciousness can be considered a bridge structure which, placing itself at an intermediate level between experience and physical properties, can contribute to bridging the explanatory gap.

Pineal gland cyst and ADHD in a juvenile patient: a case report

IntroductionThe role of the pineal gland in psychiatric disorders is poorly investigated. There are studies, primarily on adult patients, that indicate a higher presence of pineal gland abnormalities in patients suffering from depression, schizophrenia and attention-deficit/hyperactivity disorder (ADHD). When it comes to ADHD, there is speculation about the role of melatonin and the influence of the pineal gland on the dopaminergic system. Data on the association between pineal gland cysts and ADHD in juvenile patients are particularly scarce.ObjectivesDue to all of the above, our goal is to present the case of a nine-year-old male patient who has a confirmed cyst of the pineal gland and is being treated for ADHD. MethodsThe patient was examined by a neuropediatrician, EEG and brain MRI were performed. He was also examined by a psychologist and by a psychiatrist. Endocrinological, hematological, rheumatological, pulmonological treatment and karyotyping were performed.ResultsMRI of the brain revealed a cyst of the pineal gland with an anteroposterior diameter of 1 cm without significant compression. The EEG was mildly slowed and paroxysmally dysrhythmic for the age, ie. paroxysms of high-voltage delta waves were described. The EEG findings after sleep deprivation were paroxysmally altered with rare focal changes in the right temporoparietal region. Through psychological analysis, it was determined that specific deficits persist in the area of verbal understanding, perceptual organization and visual processing, information processing speed, numerical reasoning, attention and short-term memory. On the level of visuomotor perception and coordination, deviations are observed by organic type. He is motorically more active, impulsive, emotionally immature, easily distractible.ConclusionsThe etiology of ADHD is poorly researched, and so is the role of the pineal gland, its cyst and melatonin. There is scant knowledge for other psychiatric disorders, but primarily from researches on adult psychiatric patients. Additional researches are definitely needed on this topic, especially in the field of child and adolescent psychiatry.Disclosure of InterestNone Declared

Approaching the nature of consciousness through a phenomenal analysis of early vision. What is the explanandum?

Loorits (2014) identifies the solution to the hard problem of consciousness in the possibility of fully analyzing seemingly non-structural aspects of consciousness in structural terms. However, research on consciousness conducted in recent decades has failed to bridge the explanatory gap between the brain and conscious mind. One reason why the explanatory gap cannot be filled, and consequently the problem remains hard, is that experience and neural structure are too different or "distant" to be directly compatible. Conversely, structural aspects of consciousness can be found in phenomenal experience. One possible alternative, therefore, is to seek the structure of seemingly non-structural aspects of consciousness not in the neural substrate, but within consciousness itself, through a phenomenal analysis of the qualitative aspects of experience, starting from its simplest forms. An essential premise is to reformulate the explanandum of consciousness, which is usually attributed to qualia and what it is like to be in a certain state. However, these properties do not allow us to identify the fundamental aspects of phenomenal experience. Sensations such as the redness of red or the painfulness of pain are inseparable from the context of the experience to which they belong, making qualia appear as phenomenal artifacts. Furthermore, the simplest qualitative aspects can be found in early vision. They are involved in perceptual organization and necessarily have relational significance. The unitary set of qualities found in early vision-such as those related to being an object, background or detail-constitutes the explanandum of the simplest forms of consciousness and seems to imply a justifying structure. Although early vision is characterized by interdependent qualitative components that form a unitary whole, we cannot find in it the structure of seemingly non-structural aspects of consciousness. Phenomenal appearance alone does not seem sufficient to identify a unitary structure of consciousness. However, the closeness of these characteristics to a unitary structure prompts us to delve into less explored territory, using the components of experience also as possible explanans.

Intra-V1 functional networks and classification of observed stimuli.

Previous studies suggest that co-fluctuations in neural activity within V1 (measured with fMRI) carry information about observed stimuli, potentially reflecting various cognitive mechanisms. This study explores the neural sources shaping this information by using different fMRI preprocessing methods. The common response to stimuli shared by all individuals can be emphasized by using inter-subject correlations or de-emphasized by deconvolving the fMRI with hemodynamic response functions (HRFs) before calculating the correlations. The latter approach shifts the balance towards participant-idiosyncratic activity. Here, we used multivariate pattern analysis of intra-V1 correlation matrices to predict the Level or Shape of observed Navon letters employing the types of correlations described above. We assessed accuracy in inter-subject prediction of specific conjunctions of properties, and attempted intra-subject cross-classification of stimulus properties (i.e., prediction of one feature despite changes in the other). Weight maps from successful classifiers were projected onto the visual field. A control experiment investigated eye-movement patterns during stimuli presentation. All inter-subject classifiers accurately predicted the Level and Shape of specific observed stimuli. However, successful intra-subject cross-classification was achieved only for stimulus Level, but not Shape, regardless of preprocessing scheme. Weight maps for successful Level classification differed between inter-subject correlations and deconvolved correlations. The latter revealed asymmetries in visual field link strength that corresponded to known perceptual asymmetries. Post-hoc measurement of eyeball fMRI signals did not find differences in gaze between stimulus conditions, and a control experiment (with derived simulations) also suggested that eye movements do not explain the stimulus-related changes in V1 topology. Our findings indicate that both inter-subject common responses and participant-specific activity contribute to the information in intra-V1 co-fluctuations, albeit through distinct sub-networks. Deconvolution, that enhances subject-specific activity, highlighted interhemispheric links for Global stimuli. Further exploration of intra-V1 networks promises insights into the neural basis of attention and perceptual organization.

Perceptual organization and task demands jointly shape auditory working memory capacity.

Listeners performed two different tasks in which they remembered short sequences comprising either complex tones (generally heard as one melody) or everyday sounds (generally heard as separate objects). In one, listeners judged whether a probe item had been present in the preceding sequence. In the other, they judged whether a second sequence of the same items was identical in order to the preceding sequence. Performance on the first task was higher for everyday sounds; performance on the second was higher for complex tones. Perceptual organization strongly shapes listeners' memory for sounds, with implications for real-world communication.

Neurophysiological correlates of the perceptual magnet effect in speech perception

This study investigated the Perceptual Magnet Effect (PME) in speech perception using behavioral and Event-Related Potentials (ERP) measures. There were two primary research questions: (1) whether category goodness rating influences speech discrimination with reduced sensitivity near the prototype and increased sensitivity in the vicinity of a poor exemplar, (2) whether the PME is domain-specific to speech sounds. Twenty adult native English speakers participated in identification, goodness rating, and discrimination tasks. The stimuli were synthesized vowels for /a/ and their nonspeech analogs by systematically varying the first two formants. ERP oddball conditions included four conditions presented in a counter-balanced order with the prototypical /a/ as the standard stimuli and its variants as deviants, and a non-prototypical /a/ as the standard and its variants as deviants, as well as the nonspeech matches. Results indicated that participants rated vowel category goodness based on the F2/F1 ratio for the /a/ sounds. Mismatch negativity amplitudes in the two speech conditions aligned with PME predictions, but similar patterns were also observed in the nonspeech conditions. The findings collectively demonstrated neurophysiological evidence for the perceptual organization of within-category variations in line with PME, which may transfer to auditory processing of similar acoustic patterns in nonspeech.

The psychological scaffolding of arithmetic.

Where does arithmetic come from, and why are addition and multiplication its fundamental operations? Although we know that arithmetic is true, no explanation that meets standards of scientific rigor is available from philosophy, mathematical logic, or the cognitive sciences. We propose a new approach based on the assumption that arithmetic has a biological origin: Many examples of adaptive behavior such as spatial navigation suggest that organisms can perform arithmetic-like operations on represented magnitudes. If so, these operations-nonsymbolic precursors of addition and multiplication-might be optimal due to evolution and thus identifiable according to an appropriate criterion. We frame this as a metamathematical question, and using an order-theoretic criterion, prove that four qualitative conditions-monotonicity, convexity, continuity, and isomorphism-are sufficient to identify addition and multiplication over the real numbers uniquely from the uncountably infinite class of possible operations. Our results show that numbers and algebraic structure emerge from purely qualitative conditions, and as a construction of arithmetic, provide a rigorous explanation for why addition and multiplication are its fundamental operations. We argue that these conditions are preverbal psychological intuitions or principles of perceptual organization that are biologically based and shape how humans and nonhumans alike perceive the world. This is a Kantian view and suggests that arithmetic need not be regarded as an immutable truth of the universe but rather as a natural consequence of our perception. Algebraic structure may be inherent in the representations of the world formed by our perceptual system. (PsycInfo Database Record (c) 2023 APA, all rights reserved).