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ART & ORGANISM

OVERVIEW of RESOURCES

& test-pages for A&O web

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INTRODUCTION to ART & ORGANISM

 

EACH TOPIC is connected to a collection of RESOURCES.  These do not represent the entirety of CONTENT TO BE MASTERED. 

THESE TOPICS TRANSFORM REGUARLY AS NEW CONTENT IN CONSTUTUENT FIELDS EMERGES. 

Below, are collections of notes on topics and ideas that have emerged in recent years.  

sitemap for resources

ART and SCIENCE [i]   ART and SCIENCE are catchphrases for distinctive but overlapping configurations of cognitive functions. (localized and distributed coordinated processes in the brain and body that have more-or-less privileged connections with each other that make specific aspects of INPUT « INTEGRATION « OUTPUT more-or-less likely) ARTISTS and SCIENTISTS (and we are all more-or-less both) are highly motivated to make the contents of mind understandable (both to themselves and to others).  (“All art is autobiographical; the pearl is the oyster’s autobiography.”–Federico Fellini, Italian film director. (1920-1993)

 

  Our evolutionary biology has prioritized functions that support MEETING BIOLOGICAL NEEDS (including “to know and to be known.”)  At the right time specific COGNITIVE FUNCTIONS are highly ADAPTIVE and contribute to direct and inclusive FITNESS.

 

INTRODUCTION  (“The professor’s problem: “So, we have generations of teachers who can speak eloquently to concepts and their connections with each other, but are not particularly compelling in speaking to the connections between concepts and people.  This not the process for which teachers are trained.  Of course, people have to make these connections for themselves (and the best a professor can do is create an environment that encourages this), but that requires that people know themselves better, and that was not why they are taking this class. It is a challenge.”) 

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Perspective on A&O:  Read: Art and Science of Teaching 

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A&O (like life itself)  consists of nested collections of related fragments — see the uses of Aphorism

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CONNECTIONS CREATE “MEANING”

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  •  
    • Understanding each other:  “language is integrated with, and in constant interplay with, an incredibly broad range of neural processes.” It structures and is structured by the brain (see Boroditsky’s brief editorial on  Language and the Brain )

 

  • KNOWLEDGE is generally validated by REASON–coherence and correspondence –but SAPIENCE is balanced with SENTIENCE:  sensual delights that go beyond the necessity of mere reason are perceived as ART (and if you can communicate the experience well enough (know what I mean?) you are an ARTIST. 
    • ADAPTIVE REFERS TO COPING WITH NEEDS:
    • ADAPTATION—copes with change.   An adaptation is a trait that contributes to fitness, BUT the term also refers to the process by which that trait has come about. “The processes by which organisms or groups of organisms maintain homeostasis in and among themselves in the face of both short-term environmental fluctuations and long-term changes in the composition and structure of their environments.” (Rappaport, 1971) Its several definitions are all unified by the idea of compensation for change, either short-term (such as a stimulus or life experience) or long term adaptations (such as Other (complementary) definitions are: “an adaptation is an anatomical, physiological, or behavioral trait that contributes to an individual’s ability to survive and reproduce (“fitness”) in competition with conspecifics in the environment in which it evolved” (Williams, G. 1966. Adaptation and Natural Selection Princeton). and “a regulatory or advantageous change in response to an environmental stress by an individual or by a species in the course of evolution”
    • Coping strategies, of course, depend on context: what is the stressor, selection pressure, with which we must cope.   In a given context we must ask WHAT IS NORMAL?
    • when coping is inadequate, we can speak of DYSFUNCTION
    • associated with changes indicated by differences from the NEUROTYPICAL brain BUT “NEUROATYPICAL” (and “NEURODIVERSE”) brains are not necessarily maladaptive other than conformity to conventions or social norms.  
    •  Reading: Witty Ticcy Ray by Oliver Sacks 

 

 

EXPERIENCE 

REPRESENTING your EXPERIENCE: (this is what art and science are all about)  perceptions, conceptions — ideas and states of mind in the concentric rings of their respective contexts [inviting the idea of recursion]. 

JANUSIAN THINKING 

ART  (expressive and receptive) 

ART can be the great facilitator of MEANING:  Mark Johnson, whose writing is a great resource for understanding how our mind and body co-constitute understanding and meaning  is…   “following in the footsteps of John Dewey, who argued in Art as Experience (1934) that art matters because it provides heightened, intensified, and highly integrated experiences of meaning, using all of our ordinary resources of meaning-making.  To discover how meaning works, we should turn first to gesture, social interaction, ritual, ritual, and art, and only later to linguistic communication.…”  Johnson pursues “…Dewey’s insight that the arts are a primary means by which we grasp, criticize, and transform meanings. … [he ends up] with the idea that philosophy will matter to people only to the extent that it is built on a visceral connection to our world.” (Johnson 2007).  [from A&O webnotes on CONNECTIONS]

For examples I tend to emphasize:

  • ABSTRACT ART (selective emphases of elements  of particular relevance to the artist or the viewer … distillations, unrecognizable unless they are linked by steps, consciously (or not) perceptible and more-or-less recognizable … and 
  • BIOMORPHIC ART is exemplary of the mutual influences of art and biology and their influence on generations of visual culture from art and architecture to design, fashion, jewelry, that continues today.  
        •  ART and SCIENCE quotes from Constable and Zola  and the great Claude Bernard: “ART is I, SCIENCE is WE” (quoted in Bulletin of New York Academy of Medicine, Vol. IV 1928) 

ART DEFINED: 

 

The cultural and social context of art

 

    • ETHOLOGY of ART (art can be considered as a process, the product of which is an artifact.  It is  a behavioral pattern which  –like all behavioral patterns– is manifest by an organism (or population) because it is to their advantage to do so. And like all behavioral patterns, art is more fully understood when reviewed in terms of the DEEP perspectives of ethology, thus considering simultaneously its origins and future possibilities.)  (from A&O web notes on ART and ARTIFACT
    • PATTERNS –their creation and recognition are significant elements in aesthetic experience

READING Dissanayake on “ART” meaning “making special” (“selective attention”)

    • REAL versus IDEAL
  •  
    • To EXPERIENCE ART is to go beyond the immediate needs of biology: to take something which has become (or been made) “special” (Dissanyake).
      • The cognitive implications are huge: to the extent we appreciate a specific work of art we have found a sort of communion with an artist (“The antennae of our race”—Ezra Pound called artists) and likely to see things beyond the bounds of mere habit.  In this sense, an artist is also the canary in the coal mine: early warning systems for movements into potentially dangerous territory. (Danger and Beauty together can evoke the “sublime“.) It also implies possessing the  resources, such as leisure, to explore and can thus be seen as a potentially attractive trait in sexual selection.   This MAY be an element in the many species that work to manifest their value as a reproductive partner: bower birds to peacocks. Observations that tend to validate the evolutionary argument for the emergence of art are at the A&O Page: NEEDS MET BY ART.  (arguably, needs when met ultimately serve inclusive fitness, most conspicuously when they are therapeutic) 
    • QUALITIES of  the EXPERIENCE of ART (=
    • SCHOOLS of ART?

 CONSCIOUSNESS

PARABLE- Two Monks Saw Some Goldfish “how do I know?” …

  • READING: “In the River  of Consciousness” by Oliver Sacks (2004). ( William James and Henri Bergson may have intuited correctly that “the brain mechanisms that give coherence to perception and consciousness somehow analogous to motion picture cameras and projectors? Does the eye/brain actually “take” perceptual stills and somehow fuse them to give a sense of continuity and motion? No clear answer was forthcoming during their lifetimes.”)
  • What the brain diseased can reveal about the normal brain: https://neilgreenberg.com/ao-reading-fractures-and-bindings-of-consciousness-holmes-tucker-2011/ 

 

  • STIMULI, Perception, Conception, Expression
  • A&O-ABSTRACTION
  • ART is also an EXPERIENCE and “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…”–Aristotle (Metaphysics, Book 1)[ii] –these are distinct kinds of things: Aristotle distinguishes “things that are good in themselves” from “useful things.” (Nicomachean Ethics 1:6) 

[…”The relation, then, between epistêmê and technê in ancient philosophy offers an interesting contrast with our own notions about theory (pure knowledge) and (experience-based) practice. (Stanford Encyclopedia Philosophy)]

COMMUNICATION (as, for example from artist to audience) can utilize any medium  we have the sensory capacity to detect.

MEDIA:  Potential media for artistic expression are indexed by Wikipedia; beyond the traditional media of familiar art forms (painting, music, dance, language), consider AIR, EARTH, FIRE, and WATER (ATYPICAL MEDIA)

SELF as a medium of art (performance)

Nature and Earthworks

 

COLLABORATIONS with LIVING NATURE:  Nature is always a raw material for inspiration and execution, but some artists develop a deep understanding of natural processes (e.g., Earthworks or Land art, above).  Understanding the lives and behavior of other species, however, goes further …. 

 

 

AURAL – AUDITORY stimuli —

MUSIC

 

RESONANCE notes – the evocative power of stimuli can exp;oit unexpected connections and take us far beyond the mere workings of sound and music work — it is also a powerful metaphor for things that must be connected but it is not clear how. 

VISUAL stimuli

 

“ENTOPIC STIMULI”

LANGUAGE  

see Language and the Brain  

 

  AMBIGUITY. (Apophenia, pareidolia)

SIMPLICITY – realizing seems easier than knowing … hallmark of validity?? 

 

 

BIOLOGY

Facts and theories[iv], now and then

    • The best story you can tell with the best facts you have
    • SCIENCE is an engine of MYSTERY
    • The aesthetics of hypotheses
        • “Beautiful” math
      • Experiments, Natural and artificial

 

    • NEEDS and MOTIVATION  considering needs, evolutionary and physiological thinkings is particularly relevant.
    • Physiology, the proximate need –in the aggregate regarded as HEALTH.  
      • At the “base” of a hierarchy of needs is PHYSIOLOGY:  The core need for any organism is its machinery for extracting energy from the environment and channeling it in ways that serve its life–  
      • Dynamic balance, homeostasis. Needs that are or may be compromised can evoke a stress response
      • POST on health-enhancing effects of art 
    • Physiology,  
      • STRESS   … involving the real or perceived possibility of not being able to meet a real or perceived need.  Stress energizes the processes that might act to mitigate it.
    • Self-actualization, the ultimate need — is this connected to WISDOM? 
    • Transcendence and art
      • How NEEDS and STRESS are related [A real-or-perceived challenge to meeting a real-or-perceived NEED evokes more-or-less of stress response (which “energizes” organism’s resources (motivational systems) to cope with challenge and restore homeostasis]  (Exemplified in the health  consequences  of LONELINESS)
      • NEED to KNOW; Aristotle, infovory
        • But in our pusuit of NEEDS, we must know ourselves and do nothing in excess.  
        • “Knowledge is Power.”  “All of us have felt the pleasure of acquiring information—a view of a dramatic landscape, a conversation with a friend, or even a good magazine article, can all be profoundly gratifying. But why is this so? What makes these experiences so pleasurable? // We believe that the enjoyment of such experiences is deeply connected to an innate hunger for information: Human beings are designed to be “infovores.” It’s a craving that begins with a simple preference for certain types of stimuli, then proceeds to more sophisticated levels of perception and cognition that draw on associations the brain makes with previous experiences. When the hunger becomes even moderately starved, boredom sets in.”  (Biederman, Irving & Vessel, Edward A. 2006)  Key Word: INFOVORE
      • NEED for ART: including Maslow

  

DEEP ETHOLOGY  The INTEGRATIVE BIOLOGY of BEHAVIOR involves the coordinated activities of four broad areas (as biologists study them): DEVELOPMENT, ECOLOGY, EVOLUTION, and PHYSIOLOGY and how they are brought to bear on BEHAVIOR (“DEEP ETHOLOGY”) 

    • Development.
    • Ecology
    • Evolution
    • Physiology
    • NATURE-NURTURE – Excerpts from Barlow and Pinker  The questions about the relative importance of nature and nurture–congenital and acquired biases, tendencies, traits–in the determination of manifest behavior illuminate every aspect of the continuous processes of evolutionary and developmental change– phenomena that virtually define life itself.  

Experimentation: natural and artificial; Ethologically Informed Design

 

  • DESCRIBE Before we interpret or analyze our experience of behavior (our own or that of others) we must DESCRIBE it … using your “scaffolding” of art and science to describe has the extraordinary–and sometimes surprising effect of conveying insight and understanding,

WE tend to apply the DEEP perspective  at the level of manifest behavioral patterns, but it applies at ALL LEVELS of ORGANIZATION: proximate causes and consequences, (mainly physiology) ultimate causes and consequences (mainly evolutionary biology), always manifest in more-or-less intimate internal and external environments (mainly ecology) and in constant flux (mainly development) 

THE TRANSFORMATIVE LEARNING EXPERIENCE

  • PHYSIOLOGY  
    • the BRAIN is at the center of our interests–it seems like a single organ, but it is more a MOBILE of many carefully balanced  functional units that are integrated with each other at several different levels of organization:  A very broad and compelling sense of the interaction of multiple units working together comes from considering the two hemispheres of the brain, understood after they are separated from each other:  Read Wolman’s news article from the journal NATURE (it includes a good account of split brain research that provided these insights)… (including comments by a split brain patient and an old (1970’s) short video of early research nicely explained–and not much has changed)
    • COGNITIVE NEUROSCIENCE: collection of excerpts that focus on how this is understood
    • Brain development involves both highly programmed (“closed genetic program”) change and flexibility: neuroplasticity, generally in response to situational and environmental influences
    • CIRCUITS and CENTERS that orchestrate specific behavioral patterns are a primary target of the physiological ethologist–indeed, anyone seeking to understand the proximate causes and consequences of behavior (the physiology part)?  Any behavioral patterns sufficiently well described (the ethology emphasis) becomes the basis for  search for its causes and consequences.  AS AN EXAMPLE, PARENTAL BEHAVIOR. (in the DEEP ETHOLOGY – BRAIN notes) 

 

NEUROSCIENCE, ART, AESTHETICS  

§  neurofiction essay (Gary Marcus recent essay,  “Neuroscience Fiction,”  in the New Yorker (Dec 2, 2012) 
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DEEP COGNITION

  • INPUT—INTEGRATION—OUTPUT
    • nervous system& endocrine & somatic connectivity and coordination: Feedback, feedforward, error-detection.  Arousal, Attention, Action. 

Language itself creates bias: read Language and the Brain: Lera Boroditsky’s brief editorial for SCIENCE (2019)

  • BELIEF—TRUTH | KNOWLEDGE—REALIZING (why we may believe in things we cannot personally experience; extrapolation, interpolation, coherence and correspondence)
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  • MEMORY (MEMORY is the essence of INTELLIGENCE (but can you have memory (or be intelligent) without a brain?)
  • MEMORY and IMAGINATION      
      • CNS: A Surprising Connection Between Memory and Imagination.  
      • “USELESS ATTRACTOR” is a nickname for a focus which in itself has no particular meaning and with no previously obvious connections that suddenly triggers a redintegrative cascade of otherwise apparently unconnected and otherwise useless snips of knowledge. The cascade (and we can here apply the metaphor “angle of repose“–particularly as it applies to an avalanche) may have had a coherent outcome suddenly glimpsed or intuited. 
      • (Attractor [xv] is a convenient but not precise metaphor).  The coherence may only be apparent OR TOT (“tip of the tongue phenomenon”) OR FOK (“feeling of knowing phenomenon”). I often feel that a very important solution to a problem is (as Franz Wright put it once, a “Radiantly obvious thing I need to say, though quite what that might be escapes me at the moment, as it always has, and always will.”)
      • Synecdoche and redintegration—trigger experience, the attractor of hidden dreams, infusing previous experience with new meaning and putting it in the service of coherence, validating a new realization[xii]—all things are connected—
      • “not quite memory(?):  tip-of-tongue—Feeling of Knowing–  INTUITION    Intuition presentation
  • GOOD STORIES:
      • FILLING IN: extrapolation[xiii] and interpolation
    • Excerpt on brain processes of filling in

 

  • INPUT—INTEGRATION—OUTPUT      
    •  [OUTPUT/ to memory or action]

 

 

A&O ANECDOTES

 

A&O QUOTES

A&O VIGNETTES

Position not yet determined:

·        RULES
·        USELESS KNOWLEDGE. All the consequences of a specific trait may never be known, but the prodigal diversity of consequences is revealed and open to further thought with the support of systems such as DEEP ethology. For example,  The Usefulness of Useless Knowledge [xiv]   Not only have extraordinary breakthroughs emerged from what seemed like idle curiosity but there are multiple CONNECTIONS.
·        Both the PROCESS and the PRODUCT of CURIOSITY move the human race forward [hopefully the urge to CONTROL and EXPLOIT will be better coordinated with the urge to PROTECT and RESPECT or we will be swept away in the failed trophic cascade.]   Just as paranoia might be adaptive at a battle front and devastating other places, our adversarial urges towards nature were adaptive for the small populations of ancestors in hostile environments, but not in contemporary environments.
·        DYSFUNCTION; PATHOLOGY – informed by Aristotle’s Golden Mean: the nearer the endpoints along a continuum of a trait, the more likelihood its expression would be dysfunctional.  A trait such as curiosity may be populated by individuals who perform different functions in society and may be valued to the extent that is appreciated.  Occasionally—depending on the stresses of a given environment—populations may seem to need protection: “pure” (as opposed to applied) artists and scientists.
Example.  compare to the tension between INDIVIDUATION and SOCIALIZATION—in that each is vital at one level of the NEED HIERARCHY and devastating at others. (see Listening Angels and A&O notes on Uniqueness) then read about the difference between loneliness and solitude (then look in on  loneliness and longing)(reading on the History of Loneliness)
·        Perception and hallucination: “Instead of relaying every detail up the chain,  the brain combines the noisy signals coming in with prior experiences to generate a prediction of what’s happening. If you hear the opening notes of a familiar tune, you expect the rest of the song to follow. That prediction passes back to lower regions, where it is compared to the actual input, and to the frontal lobes, which perform a kind of reality check, before it pops up into our consciousness. Only if a prediction is wrong does a signal get passed back to higher areas, which adjust subsequent predictions.” Read https://www.newscientist.com/article/mg23230980-400-you-are-hallucinating-right-now-to-make-sense-of-the-world/ And http://www.nybooks.com/articles/2013/04/04/hallucinators-among-us/

HALLUCINATIONS essay in CEREBRUM with readable history of research into hallucinations: https://neilgreenberg.com/ao-reading-hallucinations-and-vision-essay-in-cerebrum-jan-2002/ 

[i] Art is I: Science is We. 

[i] “scientific abstraction liberates us from the slavery of facts” (Walter Kaufmann. 1958:93.  Critique of Religion and Philosophy.  Harper & Brothers Chapter 32 (Common Sense)

[ii] Aristotle, Metaphysics, Book I, 980a.21. 350 BC  http://www.classicallibrary.org/aristotle/metaphysics/index.htm

[iii] Science consists of facts and theories. Facts and theories are born in different ways and are judged by different standards. Facts are supposed to be true or false. They are discovered by observers or experimenters. A scientist who claims to have discovered a fact that turns out to be wrong is judged harshly. One wrong fact is enough to ruin a career.

Theories have an entirely different status. They are free creations of the human mind, intended to connect facts and thereby provide an understanding of nature. Since our understanding is incomplete, theories are provisional. Theories are tools of understanding, and a tool does not need to be precisely true in order to be useful–they are more-or-less true, with plenty of room for disagreement. A scientist who invents a theory that turns out to be wrong is judged leniently. Mistakes are tolerated, so long as the culprit is willing to correct them when nature proves them wrong.  (Freeman Dyson’s review of   Brilliant Blunders: From Darwin to Einstein—Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe by Mario Livio.   NYRB  Mar 6 2014:4-8)

[iv] “Physicists have come to see that all their theories of natural phenomena, including the ‘laws’ they describe, are creations of the human mind; properties of our conceptual map of reality, rather than of reality itself.  This conceptual scheme is necessarily limited and approximate, as are all the scientific theories and ‘laws of nature’ it contains.  All natural phenomena are ultimately interconnected, and in order to explain any one of them we need to understand all the others, which is obviously impossible.  What makes science so successful is the discovery that approximations are possible. . . . This is the scientific method; all scientific theories and models are approximations of the true nature of things, but the error involved in the approximation is often small enough to make such an approach meaningful.” (Fritjof Capra 1975 in The Tao of Physics, p. 287).

[v] Biology occupies a position among the sciences at once marginal and central. Marginal because‑‑the living world constituting but a tiny and very “special” part of the universe‑‑it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man’s relationship to the universe, then biology must be accorded a central position.” (Jacques Monod Chance and Necessity Alfred A. Knopf, New York, 1971, p xi.)

[vi] Infovory.  Biederman, Irving & Vessel, Edward A. (2006) Perceptual Pleasure and the Brain. American Scientist. 94(3), 247-253. [PDF] http://www.americanscientist.org/issues/num2/2006/3/perceptual-pleasure-and-the-brain/1 A neurobehavioral elaboration of Aristotle: “All men by nature desire to know.” (Metaphysics, Book 1)

[vii] “Between the ages of twenty and forty we are engaged in the process of discovering who we are, which involves learning the difference between accidental limitations which it is our duty to outgrow and the necessary limitations of our nature beyond which we cannot trespass with impunity.”—W.H. Auden,1963)[vii]

[viii] “Nothing in Biology Makes Sense Except in the Light of Evolution” (Theodosius Dobzhansky, 1973, in the American Biology Teacher, volume 35, pages 125-129. (Dobzhansky first published the title statement in a 1964 article in American Zoologist, “Biology, Molecular and Organismic”, to assert the importance of organismic biology in response to the challenge of the rising field of molecular biology” – Wikepedia

[ix] ADAPTATION—copes with change.   An adaptation is a trait that contributes to fitness, BUT the term also refers to the process by which that trait has come about. “The processes by which organisms or groups of organisms maintain homeostasis in and among themselves in the face of both short-term environmental fluctuations and long-term changes in the composition and structure of their environments.” (Rappaport, 1971) Its several definitions are all unified by the idea of compensation for change, either short-term (such as a stimulus or life experience) or long term adaptations (such as Other (complementary) definitions are: “an adaptation is an anatomical, physiological, or behavioral trait that contributes to an individual’s ability to survive and reproduce (“fitness”) in competition with conspecifics in the environment in which it evolved” (Williams, G. 1966. Adaptation and Natural Selection Princeton). and “a regulatory or advantageous change in response to an environmental stress by an individual or by a species in the course of evolution”

[x] CONSCIOUSNESS

    • BIG QUESTION: as information trickles from our senses (or memories) through our brain, at what point is information transformed into consciousness? [I like comparing ice to water to mist and clouds]
  •  
    • Susan Greenfield speaks of the “collective activity of brain cells that expand or diminish from one moment to the next to accommodate varying depths of consciousness.” (quoted by Ananthaswamy – and in his terms, transient assemblies, size, and duration determined by external stimuli, levels of neurotransmitters and hormones in brain and body.)
  • (Bullock 1977) sensory adaptation is when receptors are less responsive to stimuli after long term exposure to them –e.g., the smell of food or the feel of clothes. and see exaptation (from A&O Glossary)  compare to habituation

 

[xi] Sensory Bias:  (pitch to the most responsive system in your audience (or avoid the systems of your adversaries)  – in the sense of “know your demographic” …”know your sense organs” )  (The sensory bias hypothesis (in mate selection) states that the preference for a trait evolves in a non-mating context and is then exploited by one sex in order to obtain more mating opportunities. The competitive sex evolves traits that exploit a pre-existing bias that the choosy sex already possesses.)

[xii] “Redintegration” is “the process of reconstructing an entire complex memory after observing or remembering only a part of it.”  Sometimes, only a tiny fragment of new information will suffice: “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 …” (Thoreau, Journal 8:44)

[xiii] There is a universal tendency among mankind to conceive all beings like themselves and transfer to every object those qualities with which they are intimately acquainted and of which they are intimately conscious (David Hume, 1757) [When faced with ambiguity or ignorance, we extrapolate from the next nearest phenomenon . . . as with anthropomorphism] origin of ToM –they think like I do?

[xiv] http://www.nature.com/articles/s41570-016-0001 :  “Abraham Flexner, the founding Secretary General of the Institute for Advanced Study in Princeton, penned in November 1939 a most readable essay on fundamental research1. The Usefulness of Useless Knowledge described, in Flexner’s fluid prose, how apparently random experimentation eventually leads to the most important discoveries. He argued vehemently against the need for utility in the promotion of research and the allocation of funding. Instead, Flexner delivered a rousing plea for the “freeing of the human spirit”. His article is an eloquent discourse on the benefits and virtues of freedom in fundamental research. Flexner’s words are music to the ears of scientists who pursue science because they are curious and, in the venerable words of Friedrich Schiller, do not live off science but, above all, for science. Although Flexner’s essay appeared more than 75 years ago, it is still one of the most compelling pieces on the vital role of fundamental research — extolling not only its cultural value, but also its benefit to mankind in general.”

[xv] An attractor is defined as the smallest unit which cannot be itself decomposed into two or more attractors with distinct basins of attraction. This restriction is necessary since a dynamical system may have multiple attractors, each with its own basin of attraction.   Attractor — from Wolfram MathWorld   i.e., http://mathworld.wolfram.com/Attractor.html

An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically approach in the course of dynamic evolution. An attractor is defined as the smallest unit which cannot be itself decomposed into two or more attractors with distinct basins of attraction. This restriction is necessary since a dynamical system may have multiple attractors, each with its own basin of attraction.

Conservative systems do not have attractors, since the motion is periodic. For dissipative dynamical systems, however, volumes shrink exponentially so attractors have 0 volume in n-dimensional phase space.

A stable fixed point surrounded by a dissipative region is an attractor known as a map sink. Regular attractors (corresponding to 0 Lyapunov characteristic exponents) act as limit cycles, in which trajectories circle around a limiting trajectory which they asymptotically approach, but never reach. Strange attractors are bounded regions of phase space (corresponding to positiveLyapunov characteristic exponents) having zero measure in the embedding phase space and a fractal dimension. Trajectories within a strange attractor appear to skip around randomly.

Also, nicely stated at https://en.wikipedia.org/wiki/Attractor  And further developed in a way accommodating to mathophobes at http://schwitzsplintersunderblog.blogspot.com/2008/07/brief-introduction-to-dynamic-systems.html (“The simplest example of an attractor is an attractor point, such as the lowest point in the middle of a pendulum swing. The flow of this simple dynamic system is continually drawn to this central attractor point, and after a time period determined by a variety of factors (the force of the push, the length of the string, the friction of the air etc.) eventually settles there. A slightly more complex system would settle into not just an attractor point but an attractor basin. i.e. a set of points that describes a region of that space.”)  When many of these guys say evolution they just mean change.

 

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