ART & ORGANISM
Elements of Art and Aesthetic Experience
ATTRIBUTES of ART
The investment of energy in DEFINING ART pays off as its connections are harvested. And connecting it to biological functions and needs that likely energize motivational systems are especially potent. But as we work from the perspective of art as it manifests in the traditional culture into which we were born, what are some of the key elements?
There are places in the infinite darkness where the great galaxies intersect. There are a few inevitable collisions but a final merging. I imagine these points of light clustered in the infinite darkness and then I feel something that brings this majestically glacial magisterial process to mind when great clusters of ideas come together.[i] When the constellations of sapience and sentience detect each other as their respective outliers come into each other’s gravitational fields … when the cascades of levels of organization intersect with cognition and its search for repose—the mitigation of dissonance—that accompanies your sense of proximity to the best story you can tell with the best facts you have. Unpacking these ideas, tinkering with them, exploring new assemblages. Relentlessly, necessarily, approximating and progressively improving real or perceived validity implied by a more confident equilibrium. How is it we can contain multitudes and still aspire to a stillpoint? Walt Whitman understood, TS Eliot understood, Freud understood—at least for a second. And how much time do any of us need?
ARTISTIC and SCIENTIFIC approaches to understanding the production of a representation of a phenomenon of interest as well as its reception share at least the deep need to pursue insight into its nature: “All men by nature desire to know. An indication of this is the delight we take in our senses; for even apart from their usefulness they are loved for themselves; and above all others the sense of sight. For not only with a view to action, but even when we are not going to do anything, we prefer sight to almost everything else. The reason is that this, most of all the senses, makes us know and brings to light many differences between things.”(Aristotle, Metaphysics, Book I, 980a.21).
Organisms need a sense of causes and consequences to maximize biological fitness, and most ferociously in the species with the huge prefrontal cortex.
[We appear to have a powerful intuitive disposition to minimize friction, so a working sense of how the organism processes information would affect how we present it. We try to “go with the flow” of the evolutionary and ecological terrain in which we find ourselves—like our WEIRD culture, a kind of silo from which we reach out tentatively to different cultures]
All phenomena exist within a complex network of connections and are known best by virtue of how they are represented by the signs that are themselves composed of multiple perspectives, each involving a chain of circumstances involving sensation, perception, and conception. And the more perspectives that can be intentionally brought to bear, the more fully we might be able to describe and eventually accommodate our need for estimating the causes and consequences of the phenomenon, a prerequisite for acting in accordance with the outcomes of actions. About descriptions, the richer they are, the greater the likelihood of developing effective explanatory hypotheses. More easily said than done, of course since we must carefully navigate the narrow path “between a pseudoexplanatory reductionist atomism and stultifying nonexplanatory holism” (E. Mayr 1983:329)]
Of course the processes of descriptive will eventually exhaust our resources and competence. In metaphoric accord with vision or hearing, what can be directly known is a very narrow range of what is knowable. ARTISTIC or SCIENTIFIC motives seen amongst us reflect slight differences in the balance of congenital as well as acquired interests, sensitivities, perceptual and expressive skills –but all these traits, albeit in varying proportions, are needed in all the disciplines through which an individual pursues arete. [I like the old Greek word to represent the maximizing of our individual potential] In lockstep with achieving arete is SELF-KNOWLEDGE (“know thyself”).
[i] The idea of these movements reminds me of seeing the Queen Mary dock on the West Side in the early 1960’s … cousin Zel was coming or going or meeting someone … https://www.queenmary.com/history/timeline/final-years-at-sea/ (arriving); Also, I can’t resist comparing the enormity of the numbers involved in the brain—speaking of the detectable activity of neurons 1015 (ref))—and of the cosmos (300 billion in our galaxy; 7X1022; 70 billion trillion in the universe (ref))—speaking of the detectable stars—both accessible only through complex technological protheses. And both complemented by strongly inferred other phenomena, such as dark matter.
In ART & ORGANISM I understand ART as an ensemble of related traits that are expressed or experienced as both processes and products of cognition. Typically the experience of creating art (“expressive”) and of perceiving art (“receptive”) is co-constituted by the processes of SENTIENCE and of SAPIENCE.
- These function in ways unlike those used in most moment-to-moment, day-to-day processes of identifying and dealing with biologically relevant needs. (Our consideration of NEEDS begins with Maslow’s hierarchy: see these now.) In other words, ART appears to “go beyond” immediate needs by exercising skills and combinations of skills (of perception, integration, and expression). In practice this results in “making special” (Dissanyake). That is the stimulus “stands out” and recruits more attention than it would routinely.
In “going beyond,” ART has much in common with PLAY. Both ART and PLAY were once considered “autotelic” in that they were done for their own sake and not to meet some other external need. We are now aware that they meet important biological needs and are important parts of development that enables the fullest expression of a human’s potential–self-actualization.
- All of this is in light of the belief that we are motivated to “know and be known” –that is, closely integrated into a society in which we develop and must meet our needs. [this is discussed at the context of the perpetual tension between “individuation and socialization”–two process in dynamic relationship to each other.
Ethology—the study of behavior in developmental, evolutionary, ecological, and physiological context (“DEEP ETHOLOGY”)—integrates these disciplinary perspectives at every accessible level of organization from the cellular to the social in order to cultivate a holistic sense of art that will not neglect the fine-grain details on which it is built while simultaneously allowing the emergence of unique possibilities of one’s self and of humanity. The tools of traditional empirical science paradoxically reveal mystery that seems to go beyond the simply “undiscovered” and evoke a deep spiritual sensitivity. There is a dynamic dialectical relationship between what we feel is known and unknown, real and ideal, that manifests in thought processes and feelings, often manifest in art.
Both the expression and perception of ART are often found to be enlightening—a part of our growth, our continuing development as individuals—but like most traits these aspects of art exist along a continuum, a spectrum of more-or-less power at different ages and according to our intellectual and emotional needs.
A&O ELEMENTS of ART. These few elements roughly are enacted with varying amounts of energy and in different combinations to meet some basic biological needs (including the needs “to know and be known”). They correspond roughly to sender, medium, and receiver as they might be represented in ethologically viewed communications theory. They directly or indirectly serve essential biological needs by consciously or unconsciously representing your self to yourself (self-knowledge), representing yourself to others (communication), and representation of others to you.
1. PRODUCTIVE/EXPRESSIVE (“creating art” … acting on one’s self or environment; meeting the artist’s needs to create … involves actions (or their suppression) and projecting or representing the state of the artist)
2. INTERACTIVE (organisms require feedback—most fundamentally to know the outcomes of upon one’s self of actions—intentional or otherwise.)
3. PERCEPTIVE/RECEPTIVE (“appreciating art”…attending to one’s self or environment; meeting the “recipient’s” needs) is interpretive in that SELECTIVE ATTENTION is involved (involves what the recipient perceives)
REPRESENTATION necessarily involves perceptual and conceptual processes that reflect AROUSAL of ATTENTION, and SELECTIVE ATTENTION–foregrounding of specific elements of stimuli, Ellen Dissanayake has emphasized a ubiquitous element of art she terms “making special.” read her chapter. ) What is perceived as “special” is also related to the selective evolution of sensitivities to specific stimuli that are (or have been) important to survival—our competencies guide us in a relative predictable environment and with a relatively normal development. (read about “sensory bias and exploitation” –taking advantage of evolved selective responsiveness.)
- An example of going deeper: into the CNS: Habitual versus goal-driven attention : “The visual world is complex; not all input can be perceived or acted upon at once. Spatial attention allows one to prioritize locations that are most relevant or significant. Extensive research has examined factors that drive spatial attention, leading to the theoretical development of an attentional “priority map”” (Read on: Jiang 2018)
SELECTIVE ATTENTION “By the artist’s seizing any one object from nature, that object no longer is part of nature. One can go so far as to say that the artist creates the object in that very moment by emphasizing its significant, characteristic, and interesting aspects or, rather, by adding the higher values.” – (Johann Wolfgang Von Goethe, Propylaea, introduction, 1798), This sounds like “selective attention” and perhaps it is selected because it is, like beauty (as Pascal says) “… a harmonious relation between something in our nature and the quality of the object which delights us.”(Pascal)
BELOW are listed a few of the many schemes that outline what various scholars have—based on disposition or experience—found to characterize “good” (effective, adaptive…) ART.
IN terms of RAW Geometrical and structural STIMULI read Wikipedia on elements of art, some parts of which are annotated below.
REPRESENTATION: recalling always the epigraph of A&O-2014: “Cesi n’est pas une pipe” (the words Rene Magritte placed beneath the pipe in his painting “La Trahison des images” (1929) forcing us to appreciate the distance between things and representations of things such as pictures or words). see the painting
I think we seek to represent our explicit and implicit –manifest or latent– thoughts and feelings. There are assorted reasons and any expression of art is some combination of them: to help us remember, to share with other people, to better understand our our selves as more-or-less sapient and sentient beings. At one level, I think our efforts represent our desire to be one with the truth of what we seek, and the intimacy of our immersion in what we perceive and the production of a representation is a good first step.
[shall we live in the landscape and reproduce it from memory (as in Sung Dynasty art) or try to dupicate what we pay selective attention to at the site (as in photograph or plein air)]
Arguably, the qualities of representation –the attributes of art– serve the process of “MAKING SPECIAL”, a term used by Ellen Dissanayake for the distillation or convergence of evolved processes on making specific stimuli stand apart from the merely mundane. That is, to draw selective attention to objects or their attributes that may be of particular relevance to meeting needs that contribute to fitness. ART is thus an indispensable quality recognized or imposed upon objects and actions that allow the artist to transmit their view of a transcendent meaning that may serve individual and societal needs. Transcendence as always means going beyond, for example in the way learning theorists urge instructors to guide students from areas in which they can learn on their own into a surrounding “zone of proximal development” in which the students personal “boundaries” are transcended and the circle of understanding in enlarged. A form of social construction of shared knowledge. The “guide” can be a peer but is most often a “more knowledgeable other” person — a teacher … or an artist. Effective teaching recognize the limits and potential of the student, acquired by interaction and responsiveness to positive or negative feedback processes.
The QUALITIES OF REPRESENTATION, whether to explore our own knowledge, to communicate our knowledge to others (to extend or test or corroborate our own senses), or to teach, are often identified in art as a discipline. The scholar of art and organism examines first the hypothesis that these qualities are more or less congenital (in-born, genetic, an evolutionary question) or acquired (learned intentionally or not, a developmental question)
- ABSTRACTION and SIMPLICITY. Representations reflect selective emphasis on components of a mental model that are most relevant to the artist (A&O notes on abstraction and simplicity). They reflect the artist’s understanding of the concept or the artist’s judgement about how it can be most effectively communicated to his audience.
- HARMONY. The concord that derives from the manner in which elements “fit together” in ways that provides mutual support. In music, one discordant note can destroy otherwise carefully crafted composition. In cerebral functions, “harmony” may be a necessary condition for higher levels of consciousness (see A&O notes on consciousness) — In parts of the brain rich in mu-opioid receptors a harmonious convergence of multiple streams of information is intrinsically pleasurable (Biederman & Vessel 2006)
- MOVEMENT. The mind attends to available stimuli in FRAGMENTS. Perception is necessarily fragmentary and phenomena are “assembled” from a flow of perceptual attention, typically so fast that we are unaware of the process. The order in which the fragments are attended can be important in the feeling about the entire experience. An artist is by intuition or intention likely to guide the viewer’s senses –leading them down a path to converge on the phenomenon being represented by means of arranging the elements that will catch and guide the eye or ear (or touch or scent, or taste).
- “Techniques such as scale and proportion can be used to create an effect of movement in a visual artwork. For instance, an element that is further into the background is smaller in scale and lighter in value. The same element repeated in different places within the same image can also demonstrate the passing of time or movement.”)
- Visual hierarchy ‘is the order in which the human eye perceives what it sees.” (Wikipedia on Visual Hierarchy) The most prominent visual characteristics are color (hue, saturation, value), texture, size, alignment, and character (rectilinearity and curvilinearity of forms).
- UNITY. The connectedness of the elements of the work; often presumed to work together because of an underlying concept. Consider the gesamtkunstwerk, an ideal of all senses integrated in the cause of the artwork)
- [but consider the tensions in apparently conflicting attrbutes: INDIVIDUATION versus SOCIALIZATION or COMPETITION versus COOPERATION). Great pleasure derives from the detection of UNITY from disparate fragments or threads (the bias towards the Theory of Everything? And seen Biederman and Vessel (2006) about a neurological bias toward the pleasure of the convergences that serve problem solving)
- VARIETY. Diversity of elements which may act to keep sensory processes alert but nevertheless (hopefully) maintain the underlying unity. (sensory satiation). When a new element is perceived it may be immediately categorized as a member of a population of similar percepts and easily assimilated. IF the new element is sufficiently different from predecessors that it resembles, that is may be a significant variation on the theme, it may require consolidation into one’s mental model and the resolution of incongruity can be highly pleasurable. (see A&O notes on “getting it”)
- Theme and Variation (“unity in variety”): the balance between unity and diversity is crucial … relates to Creative and Mundane: too creative and it won’t be recognized (Stent, Prematurity and Uniqueness) … the “baby steps” when pointed out, contextualize it (allow it to be accommodated with minimal change) How are things the same and different: “compare and contrast” [look into the sonata]
- BALANCE. The symmetrical, asymmetrical, or radial patterns of presentation of the elements of the work (symmetry as an attribute of a prospective reproductive partner in important in sexual selection –see Møller and Thornhill (1998) in The American Naturalist.151(2):174-192)
- CONTRAST. “conflicting” elements emphasize other qualities of representation and maintain attention
- PROPORTION. The relative size and density of elements with respect to each other (the “Golden ratio”); can support the illusion of relative distance or importance.
- Is the Golden Ratio a significant biologically grounded proportion? Not always: see more about the Golden Ratio: http://www.youtube.com/watch?v=4oyyXC5IzEE ; http://www.youtube.com/watch?v=fmaVqkR0ZXg
- does MATHEMATICS describe the quantitative and relative significance of the elements of art? see: notes on art & mathematics/ Probability about the validity of beliefs derives from an apparently inborn ability.
- PATTERN. The way the elements are organized with respect to each other. (Science is organized knowledge. –Herbert Spencer (1861:ch. 2)
- ANALOGY. Things may resemble each other and invite cognitive efforts to confirm or deny their common ground. Not just what a perceptual element of “ART” summons to mind, but arguably the CORE – the “fuel and fire”– of human thinking. (see review of Hofstadter & Sander book — “long distance” analogies reach beyond familiar boundaries and even into other modalities and domains — but does art have poetic license to reach further? … As with “theme and variation”, reaching too far may break the thread for some people, disabling connections that otherwise be illuminating.
- How do artistic representations promote INFERENCE. Much (possibly all) of what we understand is “inference” (“deriving logical conclusions from premises known or assumed to be true.”) Conclusion derived from “circumstantial evidence.”
- To mix metaphors, “Standing on the shoulders of giants” we can “extrapolate” from the more-or-less solid ground on which we stand to the adjacent unknown ground…
Filling in gaps is the business of “interpolation” … Coherence often assumes the existence of intermediaries that can in principle maintain an unbroken chain of causation.
“Filling in” is an important concept in neuroscience where in vision, the phenomenon is prominent in vision, particularly by providing probable “information across the physiological blind spot, and across natural and artificial scotomata.”
ANY attribute of the mind-web of memory: a detail amidst the flood of stimuli in which we are immersed, in which we swim through—color, sound, smell—a fragment or juxtaposition of fragments emergent from the integration of percepts, or a thread of the output of mind into action. Resemblances, connections, processes… things seen from a perspective a hair’s breadth differently [Thoreau It is only necessary to behold the least fact or phenomenon, however familiar, from a point a hair’s breadth aside from our habitual path or routine, to be overcome, enchanted by its beauty and significance … To perceive freshly, with fresh senses is to be inspired. (Thoreau, Journal Dec 11 1855 8:44), Whitman “Do I contradict myself? / Very well then I contradict myself, /(I am large, I contain multitudes.) (Whitman, Song of Myself) ]
In anthropomorphism, we indicate our disposition to understand the little-known in terms of the slightly-better known. — we reason about areas of ignorance by reference to areas of less-ignorance. We—our experiences—become the measure of the unknown, we may even validate ourselves by projecting into that void, seeking the peace of corroboration …
The “Six principles of Chinese painting” were established by Xie He, a writer, art historian and critic in 5th century China, in “Six points to consider when judging a painting” (繪畫六法, Pinyin: Huìhuà Liùfǎ), taken from the preface to his book “The Record of the Classification of Old Painters” (古畫品錄; Pinyin: Gǔhuà Pǐnlù). Keep in mind that this was written circa 550 CE and refers to “old” and “ancient” practices. The six elements that define a painting are:
- “Spirit Resonance”, or vitality, which refers to the flow of energy that encompasses theme, work, and artist. Xie He said that without Spirit Resonance, there was no need to look further.
- “Bone Method”, or the way of using the brush, refers not only to texture and brush stroke, but to the close link between handwriting and personality. In his day, the art of calligraphy was inseparable from painting.
- “Correspondence to the Object”, or the depicting of form, which would include shape and line.
- “Suitability to Type”, or the application of color, including layers, value, and tone.
- “Division and Planning”, or placing and arrangement, corresponding to composition, space, and depth.
- “Transmission by Copying”, or the copying of models, not from life only but also from the works of antiquity. [NOTE: but beginning in the Tang Dynasty (c. 600) emphasis shifted from nature (en plein air) to the emotion associated with the scene in the mind of the painter & memory & feeling became more important than accurate rendition) and then after 900, & especially associated with the Song Dynasty (c. 960), philosophical principles of Tao (humans were only fragments of the greater cosmos) and Confucianism (the same themes recurred at different levels of organization)]
Six General Principles of Aesthetic Experience and Presentation (Morris. 1962:158; THE ETHOLOGIST, Desmond Morris studied the biological principles of picture making and confirmed that several points apply from Leonardo da Vinci to his research chimpanzee, Congo):
- “Autotelic” (“Self Rewarding”) Activation (painting can be a rewarding activity) (does this serve the goals “to know and to be known:” BUT adaptive functions CAN be postulated
- “Calligraphic Differentiation” (advancement from scribbles to circles to representation [and see Howard Gardner’s “Artful Scribbles” and “Reflections on Artful Scribbles” published several decades later)
- “Thematic Variation” (vastly important in the theories of aesthetics) (See VARIETY/Theme and Variation)
- “Optimum Heterogeneity” (– when is a composition completed? Does it depend on individual’s mood, culture? (might include relative degrees of abstraction: ambiguity)
- “Universal Imagery” – intrinsic elements (… externalized projections of some factor of biology (such as phosphenes?) … gratification in certain movements, optically pleasing (golden mean), psychological factors.)
Desmond Morris also cites Nicholas Humphrey who had investigated visual preferences of primates. (He defines “preference” as a “combination of aesthetic pleasure and curiosity (or novelty)”. Ideas that emerged;
1.Curiosity (interest) trumps pleasure [is this a conflict of NEEDS?) (“we are infovores”) the curiosity implicit in making art making has no obvious survival value (therefore it is considered “autotelic”—“self-reinforcing,” not connected to meeting “needs”). Alternatively, it may be a collateral expression of clearly adaptive behavioral pattern that reflects selection pressures that were adaptive in ancestry—in an unknown “environment of evolutionary adaptedness.” Although closely associated with non-conscious processes, could it be a kind of “mental model making” that is more effective for being externalized (“the Corporealization of the Psyche”) … does giving pure idea a sensuous form aid in understanding or integrating the idea?
2. Some examples of innate dispositions that may be expressed in art:
- preference for blue/green colours [jump to safety],
- bright light [desire to see things],
3. The ability to compose pictures [represents a capacity to handle notions about complex spatial relationships; monkeys showed remarkably little individual variation in their preferences]
Neuroaesthetics. “I’ve always loved art, but now I’m in awe of it,” said neuroscientist V.S. Ramachandran, quoted by Jonah Leher in a short essay, ”Unlocking the Secrets of the Artistic Mind,” 2009. “…All I’m trying to do,” Ramachandran said, “is figure out what artists figured out a long time ago.” Leher (2009) outlined “10 Perceptual Principles of Great Art,” corresponding & enlarging upon “eight laws of artistic experience” described by Ramachandran & Hirstein (1999):
- Peak Shift: exaggerated responses to exaggerated stimuli: supernormal, caricature, selectively emphasized key elements of stimulus.
- Grouping: the law of “grouping” discovered by the Gestalt psychologists around the turn of the century….after several seconds you start grouping elements together, and if successful in evoking a specific meaning, an “internal “Aha!” sensation as if you have just solved a problem. In short, the grouping feels good.” A signal extracted from the noise.
- Balance: Successful art makes use of its entire representational space, and spreads its information across the entire canvas.
- Contrast: because of how the visual cortex works, it’s particularly pleasing for the brain to gaze at images rich in contrast, like thick black outlines or sharp angles—or, as in the geometric art of Mondrian, both at once. “… the extraction of features prior to grouping — which involves discarding redundant information and extracting contrast—is also ‘reinforcing’. Cells in the retina, lateral geniculate body (a relay station in the brain) and in the visual cortex respond mainly to edges (step changes in luminance) but not to homogeneous surface colours; so a line drawing or cartoon stimulates these cells as effectively as a ‘half tone’ photograph. What is frequently overlooked though is that such contrast extractions — as with grouping — may be intrinsically pleasing to the eye (hence the efficacy of line drawings). Again, though, if contrast is extracted autonomously by cells in the very earliest stages of processing, why should the process be rewarding in itself? We suggest that the answer once again has to do with the allocation of attention. Information (in the Shannon sense) exists mainly in regions of change—e.g. edges—and it makes sense that such regions would, therefore, be more attention grabbing — more ‘interesting’ — than homogeneous areas. So it may not be coincidental that what the cells find interesting is also what the organism as a whole finds interesting and perhaps in some circumstances ‘interesting’ translates into ‘pleasing’.”
- Isolation: Sometimes less is more. By reducing reality to its most essential features—think a Matisse that’s all bright color and sharp silhouettes—artists amplify the sensory signals we normally have to search for.
- Perceptual Problem Solving: Just as we love solving crossword puzzles, we love to “solve” abstract paintings such as cubist still lifes or Cézanne landscapes.
- Symmetry: Symmetrical things, from human faces to Roman arches, are more attractive than asymmetrical ones.
- Repetition, Rhythm, Orderliness: Beauty is inseparable from the appearance of order. Consider the garden paintings of Monet. Pictures filled with patterns, be it subtle color repetitions or formal rhythms, appear more elegant and composed.
- Generic Perspective: We prefer things that can be observed from multiple viewpoints, such as still lifes and pastoral landscapes, to the fragmentary perspective of a single person. They contain more information, making it easier for the brain to deduce what’s going on.
- Metaphor: Metaphor encourages us to see the world in a new way: Two unrelated objects are directly compared, giving birth to a new idea. Picasso did this all the time—he portrayed the bombing of Guernica, for example, with the imagery of a bull, a horse, and a lightbulb.
http://www.lehman.cuny.edu/courses/arh141/links.html Glossary of terms in A&O
[note] “The different extrastriate visual areas may have evolved specifically to extract correlations in different domains (e.g. form, depth, colour), and discovering and linking multiple features (‘grouping’) into unitary clusters — objects — is facilitated and reinforced by direct connections from these areas to limbic structures. In general, when object-like entities are partially discerned at any stage in the visual hierarchy, messages are sent back to earlier stages to alert them to certain locations or features in order to look for additional evidence for the object (and these processes may be facilitated by direct limbic activation).”
Last updated Monday, October 08, 2018
 ANALOGY. Science 3 May 2013: Vol. 340 no. 6132 pp. 550-551 DOI: 10.1126/science.1236643 BOOKS ET AL. and see: “Thinking, Broad and Deep,” Keith J. Holyoak’s review of “Surfaces and Essences Analogy as the Fuel and Fire of Thinking” by Douglas Hofstadter and Emmanuel Sander (Basic Books, New York, 2013. 592 pp. $35, C$38. ISBN 9780465018475. The reviewer is at the Department of Psychology, University of California, Los Angeles…)
What makes human thinking special? Addressing the American Psychological Association a half century ago, physicist Robert Oppenheimer made the case for the centrality of analogy: “Whether or not we talk of discovery or of invention, analogy is inevitable in human thought, because we come to new things in science with what equipment we have, which is how we have learned to think, and above all how we have learned to think about the relatedness of things” (1). In Surfaces and Essences, Douglas Hofstadter (Indiana University) and Emmanuel Sander [University of Paris (Saint-Denis)] build the case that the ability to see analogies indeed forms the core of human thinking—the way we “think about the relatedness of things.”
No one is better equipped to make the case for analogy than the senior author. Hofstadter, analogist extraordinaire, burst onto the stage of cognitive science in 1979 with his Pulitzer Prize–winning Gödel, Escher, Bach, in which he created playful analogies and allegorical dialogues to illuminate such mathematical abstractions as recursion and undecidability (2). His intellectual breadth—trained in mathematics and physics, professor of computer science and psychology, artist, translator of Russian poetry and French novels—brings with it the capacity to see long-distance connections between situations and ideas, abstract their essences, and ground these abstractions in illuminating analogies. Surfaces and Essences, though not a sequel to Gödel, Escher, Bach, inherits a good deal of its intellectual focus and playful spirit. Like a strong marriage, the collaboration between Hofstadter and Sander, a French psychologist, is sufficiently seamless that the book reads as a single voice. Sander deserves credit for bringing in a salutary dose of psychological research, particularly on mathematical problem-solving and education, where goals and causal understanding are critical in distinguishing essence from surface. The mathematician soars among pure patterns; the psychologist stays rooted in human concerns. Their Anglo-Francophone collaboration reifies the art of translation, one of the most complex types of analogy-making. Rather than producing a conventional translation from source to target language, the authors worked in parallel on English and French versions. The book includes an illuminating self-referential sketch of its bilingual origin.
Hofstadter and Sander’s thesis—analogy is the core of cognition—is less (or more) radical than it might sound, as they extend analogy to include “categorization through analogy-making.” One situation is compared to another—two faces, two dogs, a heart and a pump—yielding a proto-category, to be refined by additional examples. Categories are not fixed and final products but are endlessly extensible by analogy. Waves on water come to embrace sound waves, then light waves, then spin waves, and then probability waves, as the concept wave becomes increasingly abstract. The authors convincingly refute those enthusiasts of embodied cognition who assume that because concepts are typically grounded in human perception and action, abstraction has been explained away. No: “abstraction is key, and to leave it out of one’s theory of thinking is to miss the boat by a wide margin.”
Abstracted by analogy. Waves on water are mapped to sound waves, then light waves, and then probability waves. Credit: Airom Bleicher
The book grounds its abstractions in a garden of delightful examples: analogies based on words, phrases, metaphors, and proverbs; “me, too” stories where one person’s anecdote elicits an analogical reminding in a listener; slips of action and of the tongue. Lofty scientific analogies are foreshadowed by the “banalogies” of everyday cognition. An elderly father driving by a cemetery baffles his adult son with the remark, “This is where all four of your grandkids were born”—the intended “all four of your grandparents are buried” fell victim to analogical slippage. As a child analogizes a toy truck to a real one, so Galileo analogized from Earth’s one-of-a-kind Moon to hypothesize the moons of Jupiter (exemplifying “meta-analogy”). In the final chapter, Hofstadter the mathematician-physicist provides a compelling exposition of the analogical origins of number concepts and Einstein’s relativity theory. Over a page of the book’s index is devoted to the entry “lists” (e.g., “of abstract uses of ‘mother,’” “of sour grapes situations,” “of computer concepts used in daily life”). Extensive endnotes and references provide an excellent overview of scholarly sources.
The authors provide a cornucopia of analogical examples and qualitative insights but largely bypass computational and neural constraints on analogy (e.g., the critical concept of “binding” is not discussed). The influence of prior experience on cognition is indeed ubiquitous, but is it always “analogy”? People (and other animals) also learn by conditioning, passive accumulation of statistical associations, and other implicit mechanisms [e.g., (3)]. The authors appear to be of two minds on the question of whether analogy is unique to humans. Like Darwin before them (4), they are avowed dog fanciers and similarly apply the most naïve of analogies—anthropomorphism—to their canine friends: “categorization for a dog is clearly the creation of analogical bridges to prior knowledge.” But a later section titled “What Makes Homo Sapiens Sapiens Sapiens?” reads like a retraction. The uniquely human core of analogy—the ability to encode and flexibly re-represent “the relatedness of things”—accounts for the fact that to date, scientists have emerged in only one species.
Surfaces and Essences warrants a place alongside Gödel, Escher, Bach and major recent treatments of human cognition (5). Analogy is not the endpoint of understanding, but its indispensable beginning. As Oppenheimer observed, “We cannot learn that we have made a mistake unless we can make a mistake; and our mistake is almost always in the form of an analogy to some other piece of experience” (1).
- ↵ B. J. Knowlton, J. A. Mangels, L. R. Squire, Science 273, 1399 (1996). Abstract
- ↵ D. C. Penn, K. J. Holyoak, D. J. Povinelli, Behav. Brain Sci. 31, 109, discussion 130 (2008). MedlineSearch Google Scholar
 “It is only necessary to behold the least fact or phenomenon, however familiar, from a point a hair’s breadth aside from our habitual path or routine, to be overcome, enchanted by its beauty and significance … To perceive freshly, with fresh senses is to be inspired.” (Thoreau, Journal Dec 11 1855 8:44).
 “Do I contradict myself? / Very well then I contradict myself, /(I am large, I contain multitudes.)” (Whitman, Song of Myself)
 “Circumstantial evidence is evidence that relies on an inference to connect it to a conclusion of fact—like a fingerprint at the scene of a crime. By contrast, direct evidence supports the truth of an assertion directly—i.e., without need for any additional evidence or inference. … On its own, it is the nature of circumstantial evidence for more than one explanation to still be possible. Inference from one piece of circumstantial evidence may not guarantee accuracy. Circumstantial evidence usually accumulates into a collection, so that the pieces then become corroborating evidence. Together, they may more strongly support one particular inference over another. An explanation involving circumstantial evidence becomes more valid as proof of a fact when the alternative explanations have been ruled out. … Circumstantial evidence is especially important in civil and criminal cases where direct evidence is lacking.” (http://en.wikipedia.org/wiki/Circumstantial_evidence)
 “In mathematics, extrapolation is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable …. Extrapolation may also apply to human experience to project, extend, or expand known experience into an area not known or previously experienced so as to arrive at a (usually conjectural) knowledge of the unknown…” (http://en.wikipedia.org/wiki/Extrapolation )
 “… interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e. estimate) the value of that function for an intermediate value of the independent variable. … A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function.” ( http://en.wikipedia.org/wiki/Interpolation)
 Humans have innate grasp of probability. Study of indigenous Maya people finds probabilistic reasoning does not depend on formal education. Ewen Callaway 03 November 2014
People overrate the chances of dying in a plane crash and guess incorrectly at the odds that a coin toss will yield ‘heads’ after a string of several ‘tails’. Yet humans have an innate sense of chance, a study of indigenous Maya people suggests. Adults in Guatemala who have never learned a formal number system or a written language did as well as formally educated adults and children at estimating the probability of chance events1, the researchers found.
Children are born with a sense of number, and the roots of our mathematical abilities seem to exist in monkeys, chickens and even salamanders. But evidence has suggested that the ability to assess the chances of a future event is not as innate.
In a 1972 study, Daniel Kahneman, a psychologist at Princeton University in New Jersey, and the late psychologist Amos Tversky found that educated adults incorrectly judged the sequence of coin tosses ‘heads-heads-heads-tails-tails-tails’ as less probable than ‘heads-tails-heads-tails-tails-heads’2. (Any such sequence has the same exact probability, 1/64, of occurring.) Other researchers have pointed to the fact that the mathematics of probability were not worked out until the seventeenth century to argue that probabilistic reasoning is not innate and relies on formal education.
More recent research has pointed to a primitive sense of probability. In a study published in December 2013 and titled “Apes are intuitive statisticians”, researchers found that chimpanzees, gorillas and other great apes made decisions on the basis of the chances of receiving a preferred treat such as a banana over a less-coveted carrot3.
Vittorio Girotto, a cognitive scientist at the University IUAV of Venice, Italy, and his colleagues have found in past work that young children have some grasp of probability, albeit with limits4. For instance, 12-month-old babies shown three yellow balls and one blue ball being put into a container expressed surprise when a blue ball emerged. Yet 3- and 4-year-olds answer at random when asked which colour will be pulled from the container, and older children who passed that task struggled at more complicated tests of probabilistic reasoning.
Running the numbers
To further probe humans’ innate sense of probability, Girotto’s IUAV colleague Laura Fontanari travelled to rural Guatemala to work with adults from the indigenous Kaqchikel and K’iche people who had not been formally educated in language or maths. In a series of tests of probabilistic reasoning, the adults performed just as well as Maya schoolchildren and Italian adults.
Related stories: Scientific method: Statistical errors … Dyscalculia: Number games … Animal Instincts … More related stories
The tests involved picking the colour of a chip drawn at random from a pool of several. If the pool contained three blue chips and one yellow chip, for example, most of participants guessed that the chip chosen at random would be blue.
The Maya adults also updated their predictions with new information. In a test in which a pot contained four square-shaped chips (all of them red) and four circular chips (one red, three green), they determined that a red chip of any shape was most likely to be drawn. But when the researchers told them that a circular chip would be drawn, the volunteers updated their decisions and picked green.
In a third test, participants were shown a collection of differently-coloured tokens and asked to bet on whether two tokens chosen at random would be the same colour. Schoolchildren under 6 tend struggle with such combinatorial probabilities. But Mayan adults and 9-year-olds and Italian adults all performed better than chance. The results were published on 3 November in Proceedings of the National Academy of Sciences1.
Girotto says that people’s problems estimating probabilities may have to do with how uncertainty is expressed. Tasks that people struggle with, such as those presented by Kahneman and Tversky, often involved reading about percentages, while Girotto’s tests were visual.
“Eventually we will have a map of boundaries between the tasks that untrained people or other animals can perform and those they fail,” says Kahneman. “The present study is very useful in allowing us to colour one segment of that large map — but we should not draw overly general conclusions from it.”
Girotto also distinguishes between innate ability and advanced understanding. “The fact that we discovered this intuition in infants and in preliterate adults does not mean that this form of reasoning is flawless,” he says.
- Fontanari, L., Gonzalez, M., Vallortigara, G. & Girotto, V. Proc. Natl Acad. Sci. USAhttp://dx.doi.org/10.1073/pnas.1410583111 (2014). Show context
- Kahneman, D. & Tversky, A. Cognitive Psychol. 3, 430–454 (1972). Article Show context
- Rakoczy, H. et al. Cognition 131, 60–68 (2014). Article PubMed ISI Show context
- Téglás, E., Girotto, V., Gonzalez, M. & Bonatti, L. L. Proc. Natl Acad. Sci. USA 104,19156–19159 (2007). Article PubMed Show context
Related stories and links From nature.com Scientific method: Statistical errors 12 February 2014
 V.S. Ramachandran, neuroscientist and director of the Center for Brain and Cognition at the University of California at San Diego.
 The Journal of Consciousness Studies 6, 1999: Art and the Brain, ed. J. Goguen.