rhodoraonline

Archive for the ‘cognition’ Category

THE QURAN CYCLE: Illuminating Metaphors – III

In Admiring Literature, cognition, excerpts and quotes, language and communication, literature, perception, philosophy, poetry, psychology, sources of knowledge, The Method on December 8, 2011 at 12:09 am

Linked to Part I and Part II

The irreplacability of a metaphor

The potential meaningfulness of metaphor does not yield to simple paraphrase, its meaning cannot be reduced to a nonmetaphorical, propositional format without loss. This is the reason for the enormous creativity that metaphor displays not only in poetic discourse: In ordinary everyday life it can restructure ingrained patterns of thinking. And in scientific contexts it can have a heuristic* function.

*heuristic= “serving to indicate or point out; stimulating interest as a means of furthering investigation.” (dictionary.com)

The above ‘creativity hypothesis’ of the cognitive theory of metaphor (as summarized by Jakel↓1) mentions one of the reasons why metaphor is an irrerplacable part of any effective verbal message: it is has no simple substitute for meaning. Its meaning can only be elaborated, explored, interpreted, speculated upon to an extent; but it cannot be specified exactly and absolutely.

We need the metaphor in just the cases when there can be no question as yet of the precision of scientific statement.*

*see the last post for source

As the above quote from the previous post reminds us, we depend upon metaphor to express abstract or obscure phenomenon in terms of familiar, concrete and imaginable terms. As Andrew Ortony (↓2)  puts it, “somethings are by their nature not describable.” (p. 14), and it falls upon the metaphor to express the inexpressible.

My references so far may relegate the ‘irreplacibility’ of a metaphor to the way things are: we simply use the metaphor when we have no way around it, when we lack more straightforward ways of describing something. But that view is certainly wrong. Through a literary example, see how metaphor creates new worlds of meaning to whom no other effective entry might be possible other than through the metaphor itself:

 

Fursat mein sun shaguftgi-e-ghuncha ki sada

ye wo sukhan nahi jo kisi ne keha bhi ho

 

When free, listen to the sound of the roses’ glee.

This is not speech that has been uttered.

The above is a Nasir Kazmi couplet, both in the original and in translation by me, from a previous blogpost. ‘Roses’ glee’ is a metaphor in itself (to be considered later here as an example), but right now i’m concerned with the ‘sound of’ part. The reader is forced to stop and try imagine what the sound of roses’ glee must be like. Upon analysis (which the readers of that pertinent post linked above may recall), the sound of roses’ glee most likely refers to the many messages of metaphysical nature the poet discerns in the sights and sounds of nature. Yet the interpretation is still open beyond the meaning already considered. And in terms of imagination, the metaphor forges new ground by inviting us to imagine an event that has never been experienced before. Philosopher Mark Johnson↓3 explains well what happens in such cases:

… one experiences the insight that two entire systems of implications… belong together in some fundamental way. The cognitive activity at this level… consists of the alteration of certain experiential structures (e.g. categorizations, concepts), such that one discovers a formal unity between previously unassociated things. 

We automatically associate sound with animate beings; that is the way we experience the world. When presented with Nasir’s couplet, however, we have to re-conceptualize sound as ‘a channel of communication’ or more precisely, as ‘a general aura of meaningfulness that emanates from all beings that have a purpose in their existence’ to get to the meaning of the verse. We similarly recast the flower as ‘an object created with a purpose’ from its foremost conception as ‘a part of the natural world’ or as ‘an object of beauty’.

This is not a rare phenomenon in the rarified arena of literature; more everyday examples abound. For instance, ‘my boss is a shark’ creates a new concept of ‘sharkness in humans’ that is different from both the literal shark and from the usual concept of brutality (for an elaboration of this example and the theory behind it follow the reference in Note 4. below).

 

The intensity of a metaphor

There is a sense of shock about a metaphor… which results from the clash of juxtaposed literal sense.

__ Paul Henle↓5

One puzzling aspect of the expressive capaciousness of metaphor takes the form of an image’s potential for focusing both thought and emotion in a particularly intense, economical way.  

__ Robert Rogers↓6

…by circumventing discretization [metaphors] enable the communication of ideas with a richness of detail much less likely to come about in the normal course of events.

and

… the emotive as well as the sensory and cognitive aspects [of the subject of metaphor] are more available [in mind], for they have been left intact in the transferred chunk [of meaning].

__ Andrew Ortony↓7

As Ortony explains so well in his essay, metaphor “lies much closer to perceived experience” in a significant way that makes it a particularly vivid phenomenon. We experience the world in a continuous and holistic fashion. Our stream of consciousness is a flow of sensations of all kind coming in simultaneously, whether at that time we are interacting with the outside world or going through our own ideas, emotions, or memories. We don’t experience things in a discrete, fragmented, one-by-one fashion as when we see concepts graphically displayed in a presentaion, or dissected frog parts laid out on a science lab table. Metaphor does the same by not spelling out the new grounds of meaning: it just poses an image before us and our attempt to apprehend it (holisticall, continuously) does the job. 

The following short poem by Emily Dickinson (found at bartleby) illustrates the point well:

It dropped so low in my regard

I heard it hit the ground,

And go to pieces on the stones

At bottom of my mind;

 

Yet blamed the fate that fractured, less

Than I reviled myself

For entertaining plated wares

Upon my silver shelf.

 

Without spelling out what ‘it’ was and why and how it came to be discarded from its high place in the author’s mind, the intensity of the mental event, the vivacity with which the poet experienced it, the emotions associated with the whole episode, and the strong sentiments with which the poet seems to regard in general the contents of her mental life, are all immensely clear from just one reading of the poem.

There is another reason for the vividness of a metaphor, and that is its compactness (Ortony, see notes for source): By juxtaposing two apparently unrelated objects in the readers’ minds (human emotion and a flower in one of Nasir’s examples) and forcing them to envisage a new kind of relationship between them, metaphors posit endless shades of meaning for the reader’s appreciation. For instance roses’ glee could be a reference to their beauty (smiling happy faces have been often likened to flowers), to the emotion that a beautiful sight such flowers create in us (a thing of beauty is a joy forever), to the purity associated with sights of nature, to the freshness of flowers, to their swaying on their stalks like children swinging gaily, to the pleasant sensation generated through their smell, etc. All these shades of meaning and more have been packed into a single two-word phrase, what Ortony calls the ‘compactness thesis’ of his theory.

 

The memorability of a metaphor

Compactness, vividness, and irreplacibility make for a memorable image: well-suited for educational purposes. In class-room, it were always the skillful lecturers who made the often remote-from-routine-life concepts of __ math, physics, medicine, psychology __ alive in our imagination so that we could picture them easily (and even enjoy the lecture!) that were more successful. Not possible without good metaphors:

The educational power of metaphors is thus twofold. The vivid imagery arising from metaphorical comprehension encourages memorability and generates of necessity a better, more insightful, personal understanding. But also, it is a very effective device for moving from well-known to the less well-known, from vehicle to topic.  

__ Ortony, (p. 17)

Humanliness of the literary metaphor 

Literature’s world is a concrete human world of immediate experience. The poet uses images and objects and sensations much more than he uses abstract ideas … The world of literature is human in shape, … where the primary realities are not atoms or electrons but bodies, and the primary forces are not energy or gravitation but love and death and passion and joy.

__ Northrop Frye↓8

Human beings become human through the acquisition of language, and the acquisition alienates humans from all those things language names. The name is a substitute for the thing, it displaces the thing in the very act of naming it, so that language finally stands even between one human being and another. Much of our poetry has been written to undo this situation, to remove the veil of language that covers everything with a false familiarity… 

__ Robert Scholes↓9

… literary metaphor depicts the themes that occasion it, communicating meaning imagistically by rendering it presentational.

__ Phillip Stambovsky↓10

The success of the  metaphor thus lies in recreating for us the lively vivid life in our reading experience which is so close to us. Thus it most effectively performs its fundamental function in literature: giving it the human shape we need to connect with it; and, as Stambovsky reminds us, performs it in the very manner so essentially familiar to us. This latter feature of the metaphor may be called intimation through a metaphor and is psychologically enticing and influential for the reader…

 

Intimation through metaphor

There is a unique way in which the maker and appreciator of metaphor are drawn closer to one another. Three aspects are involved: (1) the speaker issues a kind of concealed invitation; (2) the hearer expends a special effort to accept the invitation; and (3) this transaction constitutes the acknowledgment of a community.

__ Ted Cohen↓11

Perhaps the reason why so many metaphors have a peculiarly poignant beauty is because each of them kindles in us momentarily a dim memory of the time when we lost the outer world–when we first realized the outer world is outside, and we are unbridgeably apart from it, and alone. Furthermore, the mutual sharing of such metaphorical experience would seem, thus, to be about as intimate a psychological contact as adult human beings can have with one another.

__ Harold Searle↓12

Some authors even believe that the force of a metaphor’s image can lead to an exchange of material from the unconscious to conscious mind in the reader (in Rogers, p. 11). We must now consider what exactly constitutes this force; what is it in a metaphor that leads to such influence. Let us see.

 

The metaphor can be disclosive in the sense of being an eye-opener, helping us to understand hidden relations between the [target and source].

and  

Poetic devices and imaginative literature do not necessarily provide us with new information. What they do best is to give us insight into the (tacit) knowledge we already possess.

__ Snaevarr↓13

Both Snaevarr and Stambovsky associate certain terms with metaphorical comprehension that help us realize how metaphor induces an intimate connection with the author, the subject-matter, and, potentially, the world at large. Snaevarr argues how, when we understand a metaphor, we go through the same process of ‘seeing something as something’ involved in many instances of purely sense-based perception. For instance, when an object (such as a cat) is before us, typically, we merely notice what it is. Here our knowledge/concept of the object helps us quickly recognize it: perception nearly depends here on pre-existing knowledge. But when an ambiguous oil painting is presented before us and, while appreciating it, it suddenly ‘dawns’ on us that it depicts a beautiful cat: that is what Wittgenstein↓14 called ‘seeing as’.

from wikipedia 

An easy-to-relate example would be of the famous Necker cube which can be seen either as a cube projecting away from us on its northeast side or as a cube projecting on its southwest side. This kind of seeing-as is internal and spontaneous: external descriptions do not necessarily lead us to see the two different possible cubes in our mind, it has to come from within. There is also a kind of filtering and ‘foregrounding’ involved. When our mental image switches from one possible cube to the other, the first one seems to disappear and certain features of the new cube seem to ‘lighten up’ in the image. The same happens when the meaning intended by the metaphor dawns on us. The metaphor foregrounds a part and when we appreciate it a new meaning dawns on us, or an old obscure or forgotten meaning lightens up with new significance, or a subtly familiar one is brought into explicit focus.

When applied to less visual material, such a seeing-as is better termed ‘insight’: understanding the inner nature of things. The process of insight is both intuitive (that is, it does not involve conscious reasoning) and spontaneous. It also has the quality of an ‘enlightment’ and is often (specially in problem solving) sudden. It gives a feeling of familiarity with the subject in question by suddenly casting it for us in a new light (in the above stated ‘seeing as’ fashion) that we were not able to appreciate before (see famous cognitive psychologist Herbert Simon‘s paper for good descriptions of both intuition and insight). The kind of effective lectures I mentioned before created this in us: a feeling that now we really knew the topic, we knew how things really worked, how it really feels. Good metaphors achieve the same effect. Perhaps that is why:

Metaphors which provide insight into an unknown, transcendent, or mysterious subject thus can have an extremely powerful effect on those who accept them.

__ Stallman↓15 

As Snaevarr clarifies, what metaphor really does is to lighten up a piece of tacit knowledge we already possessed. The most comprehensive definition of tacit knowledge that I could find online is that it is:

Unwritten, unspoken, and hidden vast storehouse of knowledge held by practically every normal human being, based on his or her emotions, experiences, insights, intuitions, observations and internalized information. 

Indeed the feeling of intimacy and closeness will not be produced if we did not realize that the metaphor focused us on a thought or feeling we were familiar with but had never been consciously aware of. For instance consider the following verses by Nasir Kazmi, in translation by me along with the original Urdu in Roman script:

 

On the town’s vacant station

A passenger must have alighted

[shehr ke khali station per

koi musafir utra hoga]

_

 Hear it immersed in the depths of heart

No song is indeed a song of glee…

[dil ki gehrayion mein doob ke dekh

koi naghma khushi ka naghma nahin]

_

Shivering, the long nights put to us a haunting question

Their laden sound-like silence hisses answers…

[ye thitri hue lambi raaten kuch poochti hein

ye khamushi-e avaaz numa kuch kehti he]

_

In your lane all day

I pick the pebbles of grief

[teri gali mein sara din

dukh ke kankar chunta hoon]

_

From the nameless reaches of the islands of memory

The waves of your voice still reach

 [yad ke benishan jazeeron se

teri avaaz arehi he abhi]

 

These verses conjure up in us strange unspeakable feelings (and certainly many more shades of the atmosphere related to) respectively, lonely change or movement through life; the sombre sadness associated with awareness of existential realities that give rise to creative expression; introspection on the nature of our existence that typically transpires in the dark and silent moments of night before we fall asleep; the rambling recall of the many pleasures of a friendship after it has terminated; and the persisting subconscious connection with a long lost love… experiences we have all encountered in life, directlyor indirectly. That is why we relate to them and their author, and feel affected by them.

Metaphors are closer to emotional reality for the same reasons that they are closer to perceptual experience. To say of an unexpexted event that it was a miracle is to say far more than that it was inexplicable: it is to express joy, admiration , wonder, awe and a host of other things without mentioning any of them.

__ Andrew Ortony↓16

Remember that tacit knowledge encompasses a great number of sources such as bits and pieces picked up incidentally, subconsciuosly or by implication; by engaging in non-verbal skills; through general observations and readings; and knowledge of internal states personally experienced or understood through empathy. That is why, metaphor is a powerful and often the sole means of expressing our internal states. And “the particular ability of imaginative literature to disclose the unique, not least the uniquely personal” (Snaevarr, p. 361) most probably depends on metaphor.

 

The psychological power of metaphor

If a new metaphor enters the conceptual system that we base our actions on, it will alter the conceptual system and the perceptions and actions that the system gives rise to.

__ Lakoff and Johnson, 1980, p. 111

In their book Metaphors We Live By (1980), Lakoff and Johnson make the case of how metaphors do not just represent our perception of common realities, they have the power to create realities themselves. For instance, the prevalence and conventionality of the metaphor “argument is war” not only represents but also reinforces in turn a culture of argumentation where it is viewed as competitive rather than as a cooperative social exercise; whereby it is supposed to be won or lost rather than as taken to be a means of forwarding consensual decisions.

Consider the example of a fresh metaphor: ‘problems are solutions’, where solution is used in the chemical sense of the word. Actually, the authors took the metaphor from a real example of their Iranian student who thought that the expression ‘the solution of my problems’ was metaphorical. The student visualized “a large volume of liquid, bubbling and smoking, containing all of your problems, either dissolved or in the form of precipitates, with catalysts constantly dissolving some problems (for the time being) and precipitating out others”. The metaphor is not actually in use anywhere, but, as Lakoff and Johnson demonstrate how this metaphor creates a new, more profitable view of ‘problems’ than is currently prevalent. In this new view, derived from the new meaning constructed by the metaphorical comparison of real-life problems with a chemical solution, problems are accepted as a more or less recurring part of life. We use certain catalysts which temporarily solve some problems but the same process, or the disturbance in the combinations of catalysts created by a single-instance usage may lead to the precipitation of some other problem. “Rather than direct your energies toward solving your problems once and for all, you would direct your energies toward finding out what catalysts will dissolve your most pressing problems for the longest time without precipitating out worse ones. The reappearance of a problem is viewed as a natural occurence rather than as a failure on your part to find “the right way to solve it”.”

In contrast the more current view of problems as puzzles reinforces the expectation that there is one solution to each problem, that once applied, it will make the problem go forever. Recurrence of the problem implies a failure on the part of our ability to solve it. While the problem lasts, a state of confusion and frantic attempts to solve it and resolve it continue. Etc, etc.

Similarly, James Geary mentions research to the effect that when finance journalists use ‘agent metaphors’ to describe stock market behavior (such as ‘prices climbed higher’, or ‘the market fought back’) “an enduring internal goal or disposition” is inferred with the implication that the trend “is likely to continue tomorrow” (p. 31). In fact, it is in this sense of metaphor’s effects that scholars such as Lakoff and Johnson have highlighted the political, or let’s say, ideological power of metaphor…

 

The ideological power of metaphor

  

The people who get to impose their metaphors on the culture get to define what we consider to be true.

__ Lakoff and Johnson↓17  

What therefore is truth? A mobile army of metaphors, metonymies, anthropomorphisms: in short a sum of human relations which became poetically and rhetorically intensified, metamorphosed, adorned, and after long usage seem to a nation fixed, canonic and binding;

 __ Friedrich Nietzsche↓18 (in James Geary, p. 116)

Indeed we are familiar with presidential candidates, regimes, or factions in society popularizing and reinforcing ‘pet metaphors’ in their followers’ minds to ingrain their preferred sets of attitudes — their ideology. Similar examples can be given from the domain of religion. The budhist’s wheel of life and the muslim’s Straight Path are presented metaphorically, binding important aspects of their faith, creating their spiritual reality for them, defining the meaning and purpose of life to them, and motivating important attitudes and behaviors in each.

[This is not the place to argue, however, on the absolute relativity (or not) of truth (a topic with which this blog though is very much concerned and is yet to present a full-fledged treatment of the problem; though the topic has been touched upon in various posts).]

After having explored the concept of metaphor, establishing its power and significance from the point of view of both the sender and receiver of a communication, we are now set to see how the topic relates to the Quranic corpus. It’s easy to find all kinds of metaphors in Qur’an; important systems of extended conceptual metaphors that present, educate, and penetrate to the heart and mind of it’s readers; beautiful, visualizable, and novel, original metaphors that capture the sentient nature of its target audience and leave lasting and powerful impressions; metaphors so original and absolute as they must be for depicting realities beyond the periphery of ordinary human perception.

I feel excited at this point of my journey in the realm of the Metaphor. For these past few months, having thought about familiar metaphors from the Quran against all my developing understanding of metaphors in general now makes me feel as if I am approaching the great universe of the Qur’an with fresh eyes.

Till then, fi aman-i Allah

Notes

1. Olaf Jakel (2002). Hypotheses revisited: The cognitive theory of metaphor applied to religious texts, metaphoric.de, vol. 2, pp. 20-42. Found at http://www.metaphorik.de/02/jaekel.pdf

2. Ortony, A. (1975). Why metaphors are necessary and not just nice. Reprinted in Cultural Metaphors: Readings, research translations, and commentary, Ed. M. J. Gannon, 2001, Sage Publications. Found at http://books.google.co.in/books?id=Ih0BUezsl6kC&printsec=frontcover

3. Johnson (1980), taken from Bob Stallman (1999), Divine hospitality in the Pentateuch: A metaphorical perspective on God as host. PhD Dissertation, Westminster Theological Seminary, Philadelphia, pp. 40-41. Found at http://eagle.northwestu.edu/faculty/bob-stallman/files/2011/03/2.pdf

4. Sam Gluckseburg (2008). How metaphors create categories — quickly. In Metaphor and Thought, 2nd ed., Ed. Raymond W. Gibbs. Cambridge University Press. Found at ftp://ftp.turingbirds.com/ai/The%20Cambridge%20Handbook%20of%20Metaphor%20and%20Thought.pdf

5. Paul Henle, (1958), Metaphor. Reprinted in Philosphical Perspectives on Metaphor, Ed. Mark Johnson, 1980, University of Minnesota Press, p. 102

6. Rogers, R. (1978). Metaphor: A psychoanalytical perspective. University of California Press, p. 7. Found at http://books.google.com/books?id=zxH3W27COqgC&printsec=frontcover

7. (1975), from Cultural metaphors, pp. 16-17

8. N. Frye (1964) found in Phillip Stambovsky’s (1988), The depictive image: Metaphor and literary experience, University of Massachusetts Press, p. 50.

9. Scholes (1985) in Stambovsky, 1988, p. 89.

10. Stambovsky, 1988, p. 3

11. T. Cohen (1978) from Stallman (1999), p. 44

12. Harold Searle, Collected Papers on Schizophrenia. Quoted in Rogers, 1978, p. xi

13. Stefan Snaevarr (2010). Metaphors, narratives, emotions: Their interplay and impact, Rodopi, Amsterdam, p. 83 and p. 360 respectively.

14. Austrian philosopher Ludwig Wittgenstein is credited with this conceptamong many others he theorized upon in his now classic Philosophical investigations. For a simple explanation of his concept read point 1 of this lecture presentation: http://www.phil.cam.ac.uk/teaching_staff/ahmed/WittgensteinPhilosophicalInvestigationsLecture15.pdf

15. Stallman (1999), p. 41

16. in Cultural metaphors, p. 17

17. George Lakoff and Mark Johnson (1980). Metaphors we live by. Originally published by University of Chicago Press. Found online at: http://www.pineforge.com/upm-data/6031_Chapter_10_O’Brien_I_Proof_5.pdf

18. in James Geary, (2011), I is an Other: The secret life of metaphor and how it shapes the way we see the world, Harper Collins, p. 116.

 

 

Advertisements

THE QURAN CYCLE: Illuminating Metaphors – II

In cognition, language and communication, Literature|Religion, The Method on October 18, 2011 at 6:21 pm

 

Continued from Part I

The significance of Metaphor

The word metaphor consists of two Latin roots: ‘meta’ which means over, and ‘pherein’ meaning ‘to carry, to bear’; thus literally meaning ‘to carry over’. Thus the essence of a metaphor lies in the carry over of meaning, and as we consider the true purport of this ‘transfer of meaning’ concept we realize that the significance of metaphor underlies much broader areas of life than mere literary effectiveness.

Indeed, historically, metaphor was considered only a rhetorical device: a way of embelleshing (or adorning) the language to make the presentation of an idea more beautiful, effective, and vivid. However, scholars have come to acknowledge the almost universal presence of metaphor in all our speech and even thought, coming to much broader conclusions about the nature, function, and power of metaphor in human culture. Detailed analysis of the current theory of metaphor reveales that metaphor is a part and parcel of our thought processes. It’s neither unique nor restricted to any ‘special usages’ in literature.

As Lakoff and Turner claimed in their seminal paper titled Metaphors We Live By (1980) studying metaphors may be “one of the more fruitful ways of approaching fundamental logic, epistemological and ontological issues central to any philosophical understanding of human experience.”

We, unfamiliar readers, cannot fully appreciate the significance of metaphor unless we first consider the theoretical underpinnings of the concept and what current scholars in philosophy, psychology, and cognitive scientists have to say about it. Apart from that, and as a pretext, overviewing the omnipresence of metaphors in our life will help us realize just how broad the topic is, rather than being restricted, as traditionally thought, to the area of effective language skills.

 

The ubiquity of metaphors

We don’t realize when we speak but we are using metaphors all the time. Most of our speech is made of idiomatic expressions of some sort or another. A majority of those involve metaphor. To fall in love, to burn in anger, apple of the eye, hand in hand with, flying colors, sunny smiles, radiant beauty, snail mail, black death, dove as a symbol for peace, heart as a symbol for love, color red as a symbol for danger, all of these are specific examples of metaphor in various means of communication.

Apart from idiomatic expression, the very roots of words are pictorial, transfering meaning from something concrete and picturable to some other situation which may or may not go on to become so abstract that the combination loses it’s metaphoric significance (see dead metaphor in the last post). Examples of such words in which metaphorical origins are still obvious are: coinage, leggings, leap-frog, to moonlight, yardstick, heading, etc. For examples in which the meaning has become more abstract and conceptual we have to look into their etymology to reach their pictorial origins. For instance the word diverge comes from the latin di for two and vergere for ‘to incline’. Thus the literal meaning of ‘diverge‘ is to incline in two different directions. Similarly, the word delineate, meaning to outline and to portray, consists of de: completely, and lineare: to draw lines. The word confront consists of com-: together, and frontem: forehead; leading to the originally prevalent meaning of ‘to stand in front of’. Further metaphorical application lead to the current meaning of: to present with, to oppose, to find in one’s way, etc.

Traditionally, metaphor has been associated with literature. However, in his book, I is an Other: The Secret Life of Metaphor and How it Shapes the Way we See the World, James Geary presents examples of use of metaphor in common cultural enterprises such as advertising, finance, politics, entertainment, science and innovation. Stock exchange, the great depression, dead cat bounce, ‘fringe’ benefits, are some examples of metaphorical description of things related to finance, economics, and business. In advertising, personification of products is metaphorical since the intention is to imbue the product with some valued or desirable characteristics of humans/animals. Thus Explorer, Warrior, Mustang, Cougar, Jaguar are all metaphorical names of cars. In politics, slogans in times of war and conflicts, floursihing desrcriptors used to describe world or national affairs, and the metaphors used in politicians’ addresses all exude and cast certain meaning on the subject situation through the associations and implications of the metaphor.

Fields of science and innovation are again rife with metaphors. Talk of “first line of defense”, engulfing microphages, cells, transportation and carriage in the blood, assimilation, genetic transmission, inheritance, transcriptions, genetic code, neuronal triggers and wiring, killer T-cells, imprinting, the food web, lock-and-key position, chemistry, half life, (chemical) affinity, catalysts, electric current and flow of heat, black holes, dark energy, the big bang, space-time curve, dwarf and supergiant stars, spectrum, and many more↓1.

 

Metaphors enhance understanding and organize knowledge

We need the metaphor in just the cases when there can be no question as yet of the precision of scientific statement.

__ Black, (1962)↓2

In summarizing tenets of a cognitive theory of metaphor, Jakel Olaf (2002) wrote that metaphors commonly form “coherent cognitive models: complex gestalt structures of organized knowledge” that serve as “pragmatic simplifications of an even more complex reality.”  An example is the concept of ‘commucination’ whose metaphorical nature was illustrated by Reddy (1979)↓3. We conceive of communication as sending of ideas from one person to another through the use of language. This conceptualization entails equalizing ‘idea’ with an object, with ‘language’ as their container.

In Metaphors We Live By↓4, Lakoff and Johnson (1980) explain: “Metaphor is one of our most important tools for trying to comprehend partially what cannot be comprehended totally: our feelings, aesthetics, moral practices, and spiritual awareness.”

This fact holds not just for ordinary experience but also for the scientific endeavor to understand the world. According to one scientist, Eugene Garfield: “metaphor enters into the communication of scientific ideas and at times influences the formulation of scientific problems and the ways in which problems are conceptualized and approached.” For instance Frued’s ‘topography of the mind’ uses a submerged iceberg as a metaphor for the levels of consciousness in human thought. Current cognitive science deploys a model of human mind as a computer to understand it’s working. The heart has long been viewed as a pump and blood as a transportation mechanism. The interiors of an atom have long been conceptualized as a ‘planetary system’ with electrons floating and revolving in orbits around a nucleus. Patterns of food consumption across animal species have been conceptualized as a web. Immunse system has been conceptualized as an army lined for defense of the body and deploying attack when foreign agents infiltrate the body.

The reason for this dependence on metaphor is that a majority of the concepts we utilize in scientific endeavor and in philosophy are abstract, not concrete. As such they are not directly observable or accessible by the human senses. Their presence must be inferred through their discernable characteristics which serve as ‘indications’ pointing to the underlying ‘hypothetical construct’. Thus in defining an emotion such as an anger we refer to the visible effects of anger and describe them metaphorically: a red face, a warm skin, etc. In referring to something as anxiety we rely on the metaphorical expression of butterflies in the stomach.

Furthermore, applying metaphor to scientific theory guides further quest for knowledge; an example of how  is the theory of light waves. Scientists applied to light the metaphor of water waves and wondered about the medium in which light waves propogate, given the fact that water waves do not exist outside of its medium. Thus scientific models, essentially metaphorical in nature, not only help us think about abstract phenomenon beyond our sensorial grasp, they also help us organize our understandings into a visualizable and manipulable form, ultimately becoming vehicles of further generation of knowledge. I will explore this power of metaphorical constructions further in the next post, InshaAllah, as this current part is devoted to understanding the nature of metaphor.

 

Metaphors and the human conceptual system

Lakoff and Johnson (1980) in The Metaphorical Structure of the Human Conceptual System, have classified human concepts into metaphorical and non-metaphorical. Examples of the latter include spatial orientations (down, near, etc), ontological concepts (person, substance, etc), and structured experiences and activities (eating, moving, etc.). In contrast, the three type of metaphorical concepts described by the authors are:

i) Orientational metaphors: “These structure concepts linearly, orienting them with respect to nonmetaphorical linear orientations.” (p. 196). For instance in statements ‘higher no. of mistakes’, ‘at the height of power’, ‘feeling down’, ‘high intellectuality’, etc have the metaphorical structuring of ‘more’ in terms of the spatial orientation of up (and vice versa for ‘less’ and ‘down’).

ii) Ontological metaphors: “These involve the projection of entity or substance status on something that does not have that status inherently.” (p. 196). Examples include Reddy’s example of language as container of ideas which themselves are conceptualized as objects to be contained. Expressions such as ‘getting something out of one’s head’, ’empty-headedness’, ‘clear one’s head’, etc imply the metaphorical view of ‘mind’ as a container.

iii) Structural metaphors: “These involve structuring of one kind of experience or activity in terms of another kind of experience or activity.” (p. 196) Examples include understanding as seeing in ‘I see what you mean’, and life as gamble in “taking one’s chances’.

As such these metaphors have rationally derived entailments just like non-metaphorical ones. Thus given the metaphor of time as a resource, some of its entailments show in the following expressions: ‘spend time wisely’, ‘it will cost me too much time’, ‘investing one’s time’, ‘profitable use of time’, etc.

Thus some of our very basic semantic concepts are metaphorical. Thus categories are viewed as containers: we place items in and out of them. Linear scales are viewed as paths with quantites measured along the path.

 

Metaphors, symbols, isomorphisms, and structural mapping

Lakoff further elaborated the process underlying the metaphorical representation of concepts. They call this process structural mapping. Before I come to that, however, I would like to relate the nature of metaphor with concepts I have learned from Hofstadter’s iconic Godel, Escher, Bach regarding the construction of meaning in the human mind.

According to Hofstadter, patterns of neuronal activation (one neuron activating and leading to the activation of another and so on and so forth) become associated with chains of bits of information in the real world giving rise to symbols in our mind. Thus when we associate certain sounds with certain shapes (letters of alphabets) connected in our brains through neurons linking up one bit of inforation in the brain area for sounds, with the pertinent paired information in the brain area for shapes, these are ‘signals’. It is when these signals are chained to for a pattern of sound which refers to some object in the real world (such as the sound pattern ‘table’ referring to the actual table), that a symbol is formed. Meaning, Hofstadter stresses, is not contained in the symbol (call it the sound pattern or the underlying neuronal pattern); rather, it lies in the association with the real-life object.

The concept of metaphor is similar to this symbolization process. Indeed, Lakoff, in his 2008 article on the neural basis of metaphor↓5, relies on the same phenomenon of neural circuitry that Hofstadter relies (as explained in laymen terms above) for his own concepts. Again, the value of metaphor lies not in the target or source stimulus alone, it lies in the comparison (a kind of association) between the two. More importantly, it is the reading of one thing onto another that redefines metaphor as type of symbol, hence a central vehicle of thought. When we read ‘cat’ we recall the real life cat we are familiar with. When we read ‘the poem is a diamond’ we read features of diamonds__’pricelessness’, ‘value’, ‘brilliance’, ‘an object of beauty and admiration’__onto the poem. This phenomenon of carrying meaning from one level of data onto another was referred to as isomorphism by Hofstadter. Again the meaning lies in the ‘carriage’ or ‘transfer’ of attributes from one level onto another, an assertion that clearly reminds one of the definition of metaphor.

Now the kind of isomorphism that exists between the target and source stimuli of a metaphor was elaborated as ‘structural mapping’ by Lakoff (1993)↓6. According to Lakoff there is one ot one correspondence between features of the target and source domains. This idea is excellently elaborated by the example presented by Lakoff himself (p. 217):

 

Times are things.

The passing of time is motion.

Future times are in front of the observer; past times are behind the observer.

Along with his students, Lakoff identified a general mapping scheme which underlies our metaphorical understanding of several “states, changes, processes, actions, causes, purposes and means” (p. 220), which he called as ‘event structure’:

States are locations (bounded regions in space).

Changes are movements (into or out of bounded regions).

Causes are forces.

Actions are self-propelled movements.

Purposes are destinations.

Means are paths (to destinations).

Difficulties are impediments to motion.

Expected progress is a travel schedule….

Long-term purposeful activities are journeys.

 

Different parts of this mapping schemes are evident in expressions such as ‘leaving life’, ‘achieving milestones’, ‘overcoming obstacles in one’s way’, ‘reaching maturity’, ‘stagnant career’, ‘moving ahead in life’, etc.

 

More on metaphor and meaning

 

 I want a naturalized theory of meaning: a theory that articulates in nonsemantic and nonintentional terms, sufficient conditions for one bit of the world to be about (to express, represent, or be true of) another bit.

Fodor (1987)↓7

… every single sentence may give rise to an open array of interpretations which go well beyond the encoded senses. Some of the best examples of this are … creative metaphors.

Sperber and Wilson (2008)↓8

People are simply unwilling to be silent about what they cannot talk about — they use metaphor instead. [And] while [metaphor and literal comprehension] clearly differ in linguistic analysis, in terms of psychological processes their underlying continuity should be emphasized.

Kintsch (2008)↓9

The discussion using Hofstadter’s concepts and the quotes above make it clear that as far as cognition is concerned, the case of metaphor is neither special nor limited. Human thought can never be direct: we can never access reality directly in a pure sense__ a much discussed topic on this blog. What cognition does is approximately represent some part of the outer world internally, supported by the underlying physical base: the brain. Metaphor is one way how that happens. When metaphor is used explicitly in communication (as apart from it’s implicit presence in our conceptual system), it may be viewed as an endeavor to create the same cognitive scenario in the audience’ mind as in the communicator’s.

In the words of Sperber and Wilson (2008, p. 87): “[Paul] Grice characterized a speaker’s meaning as an overt intention to cause a certain cognitive effect in an audience … A speaker’s meaning is … [thus] a mental state. The mental states of others cannot be simply perceived or decoded, but must be inferred from their behaviour, together with background information. … speakers intend their audience to discover their meaning, and provide evidence to that effect, in the form of communicative behavior.”

 Thus what matters in communication is not the nature of the input, but it’s relevance in guaging the speaker’s intention or it’s relevance to the context of communication such that it succeeds in eliciting a cognitive effect in the audience’s mind. “The input may answer a question the individual had in mind, it may raise or settle a doubt, suggest a hypothesis or a course of action, confirm or disconfirm a suspicion, correct a mistake. … The greater the cognitive effects produced by processing an input, the greater its relevance… [Also] the smaller the processing effort required to achieve these effects, the greater the relevance. (p. 88)”

 Therefore, as Sperber and Wilson (2008) clarify, as far as construction of meaning in the audience’s mind is concerned, literal meanings go through the same process as non-literal ones. It is by referrence to the context and to non-verbal and non-literal cues in the communicating situation that the reader’s mind arrives on the right interpretation back and forth between literal and non-literal connotations. Indeed these two authors propose a continuum of verbal communications ranging from ‘literal’, as in ‘I have a diamond’, through ‘loose’, as in ‘I have some carbon’ (with ‘carbon’ applied to the same literal ‘diamond’), to metaphorical, as in ‘This poem is a diamond’ applications of the same verbal inputs.

 

Summary and Post-Script

In summary, metaphor is not merely a linguistic device for creating pretty images in literature. Merely considering the omnipresence of metaphor across human media and culture is enough to persuade us of this point. Metaphor is part and parcel of the human conceptual system. It is a necessary fall-back mechanism for understanding the world and for communicating that understanding to others, for the simple reason that we can neither access the outside world directly nor communicate our internal states to others directly. Indeed, the research on how parts and cells of the brain represent the world, and theories on meaning construction support this point. Moreover, metaphor is not even unique or special when compared with more literal ways of expressing throught: the same context- and association-based processes underly comprehension of both literal and nonliteral expressions.

There is much more on the nature and significance of metaphor. How it generates emotion, it’s relationship with beauty, it’s link with imagination and it’s powerful hold on human culture. Contrasting and comparing metaphor to similar devices such as similitude and analogies also sheds further light on the nature of metaphor and how it works. However, this post was devoted to a basic understanding of it and for reinforcing it’s deep and irrefutable link with human cognition, given the fact that Quran relies primarily on metaphor for its beautiful and heart-rending messages.

So, fare well until Part III. 

 

Notes

1. Those unfamiliar with any of these terms and wishing to know more, please find them on wikipedia. Two links other than that have been inserted in place.

2. Quoted in the online Chapter 2 of the PhD dissertation by Bob Stallman.

3. From Lakoff and Johnson (1980), Conceptual metaphor in everyday language. The Journal of Philosophy, 77 (8), pp. 453-486. Available online: http://www.cse.buffalo.edu/~rapaport/575/F01/lakoff.johnson80.pdf

4. Available for online study: http://www.pineforge.com/upm-data/6031_Chapter_10_O’Brien_I_Proof_5.pdf

5. Lakoff, G., (2008), The neural theory of metaphor, in The Cambridge Handbook of Metaphor and Thought, 3rd ed., edited by Raymond W. Gibbs, Jr., Cambridge University Press. The book is available online at: ftp://ftp.turingbirds.com/ai/The%20Cambridge%20Handbook%20of%20Metaphor%20and%20Thought.pdf#page=100

6. George Lakoff (1993), The contemporary theory of metaphor, in Metaphor and Thought, 2nd ed., edited by Andrew Ortony, printed by Cambridge University Press. Available online at: http://www.cogsci.ucsd.edu/~coulson/203/lakoff_ps.pdf

7. in Mark Johnson, 2008, Philosophy’s Debt to Metaphor, The Cambridge Handbook of Metaphor and Thought, p. 49

8. A deflationary account of metaphors, in The Cambridge Handbook of Metaphor and Thought, p. 87

9. How the mind computes the meaning of metaphor, in The Cambridge Handbook of Metaphor and Thought, p. 141

BOOKS: What I learned from “Godel, Escher, Bach” – Part II

In Books, cognition on May 3, 2009 at 11:59 am

geb-book-coverContinued from Part I.

In this post we will look more closely at “symbols”, “levels of meaning” and “isomorphism”.

Symbols – the carriers of meaning

Strange loops arise in systems that are powerful enough to capture meaning. Meaning is achieved when networks of signals stand for one particular concept in the world.  Thus each letter of the alphabet signals a particular sound. These signals in turn get arranged into a pattern – a word – that refers to one particular object or idea from the external world.

In a similar vein, the firing of a single neuron in response to a specific stimulus is a signal. For instance, studies on the visual cortex have shown that different specific neurons are stimulated upon presentation of and variation in very specific features of the visual stimuli such as length and orientation.

When we sense (see, hear, or touch) a new object, all the neurons responding to its various features are activated in the pertinent area of our brain are activated and form a neural circuit. Circuits in different regions of the brain are themselves interconnected: As you talk about an apple you are using i) the muscles of your respiratory system to create the right sounds, ii) the corresponding visual circuit to visualize the apple, and iii) circuits in the language areas representing the word apple as well as the corresponding phonetic pattern needed to pronounce the word correctly.

The above described network caters to one meaningful concept in the world. It is to such networks that Hofstadter applies the term symbol. The world is full of such information-preserving  symbols and below are some examples:

astronomical-symbolsarabic-sign-language-symbolsseismographhofstadter-butterfly

Meaning is not inherent in the symbol

By now it is clear that the power of a symbol does not reside in the signals that it is made up of; rather it is the correspondence with a specific concept from the outer world. Every word will be a meaningless pattern of sound if it was not associated with something we are familiar with. Words such as ‘mother’, ‘money’ and ‘love’ evoke strong personal reactions in most of us, not because there is something in the special arrangement of those particular sounds, but because of what each of these words refers to.

Thus the fact that each constituent of the symbol stands for a particular sound is explicit (i.e. apparent). On the other hand, the fact that the pattern as a whole stands for something else altogether is implicit (i.e. hidden) –  the meaning is not readily apparent to anybody who’s not  well-practiced in the use of these symbols (e.g. a child, a person not familiar with the English language).

Meaning is thus independent of any rules for combining signals to produce patterns. That is how, even though the formal system in Principia Mathematica was especially designed to shun explicit self-reference, it is by association with a different (a higher, and less readily apparent) level of meaning that self-reference is achieved.

Isomorphism – reading meaning into patterns of signals

The key is that the transition from the explicit to the implicit level is  information-preserving. In math, such a case wherein elements of two sets correspond with each other in an information-preserving fashion (math theorems and Godel numbers in the above example) is called an isomorphism.

Thus the word “table” is isomorphic to that piece of furniture on which my PC sits. So is the neural circuit that gets activated in my mind when I think of a table. The symbol ‘=’ is isomorphic to the concept of “is equal to”.  Genes are isomorphic to the protein synthesized from them. A code is isomorphic to the text of the message it hides. The camera film is isomorphic to the color photograph printed from it.

In short, human thinking and culture is fraught with isomorphisms of various kinds.

As far as we cannot detect and read the isomorphism, the structural similarity between two different sets of elements, we will be oblivious to the fact that one is a message encoded by the other. In Hofstadter’s terms, meaning is induced in the explicit lower level matter (or components of a pattern) by identifying its isomorphism with a real world concept at a more abstract level.

We recently have had an eerie reminder of this fact, when a scientist Craig Hogan realized that he may have hit upon some observations supporting the holographic principle. It seems that the totality of information on all the particles in our 3D universe may be contained on the 2D cosmic horizon…

Isomorphisms and mental life

The swirls of neuoronal activity back and forth across the brain are isomorphic to mental activity. In other words: consciousness of our inner life is attained because we can read off the explicit neurological processes at a much more higher and implicit level.

When you are looking at a TV screen, the data you are receiving is nothing but a fluctuating pattern of pixels. But you are not conscious of this ‘lower level’ of the message. You can simply read off the higher level meanings coded for by those pixels – feat we call as perception.

This shows how its totally unnecessary to be conscious of the lower level in order to read the implicit. Fluent readers are rarely conscious of the exact letter sequences making up the words they are reading. A practiced reader in a book describing highly visual scenes will simply see the scene by scene depiction of the story on the pages. The feel of reading is completely replaced by the sense of watching in such instances…

In sum, both intelligence and consciousness may be redefined as our capacity to perceive the meaningful isomorphisms in the world and within ourselves.

Tangled hierarchies and strange loops

Many a times a clear differentiation of ‘lower’ and ‘higher’ levels is possible when dealing with two isomorphic sets. A majority of the examples of such sets given above illustrate this differentiation. There are times however when such a clear differentiation is not possible, since levels keep leading back to each other.

It is the entangledness of our concepts that leads to recursion in human thinking. All our concepts are interrelated, are constantly activated by each other, and this constant exchange among themselves and with information from the outside leads either to modification or reinforcement of every concept.

We define our preferences and loves in relation to our own selves. We reflect upon the outer world and interacting with it obtain further information from ourselves thus re-affirming, enhancing or adjusting our self-concepts. All this modification is indeed not just at the abstract, conceptual changes. The changes are reflected in the underlying patterns of connections across networks of neurons. This is what happens in any level-crossing feedback loop. The system does not just mirrors meaning, it has the capacity to  change in response to changing information.

That is also why human intelligence is definitely superior to machine intelligence. Where a computer will get hanged, the human will leave the level on which it was working (for e.g. some office task) and work on other levels to solve the problem (for e.g. confronting the supervisor who didn’t explain the task fully, confronting and modifying one’s own level of knowledge and skill required to achieve the task, etc.).

The beauty of Hofstadter’s ideas is that they apply equally well to human intelligence and human consciousness. Fluid Concepts and Creative Analogies is the result of his research into the intricacies of human cognition, whereas I am a Strange Loop presents more fully Hofstadter’s ideas of the emergence of the human ‘I’.

An example of the all-tangled up semantic network underlying GEB (Click on the image to see in full size)

An example of the all-tangled up semantic network underlying GEB (Click on the image to see in full size)

After I have completed reading I am a Strange Loop, I’ll find some excuse to post about it as well, InshaAllah!

BOOKS: What I Learned from ‘GODEL, ESCHER, BACH’ – Part I

In Books, cognition on April 24, 2009 at 9:41 am

world-book-day-2009In keeping with UNESCO’s World Book Day which came to pass yesterday, I would love to revise my concepts from Gödel, Escher, Bach: An Eternal Golden Braid. They book first published in 1979, won for its author, Douglas Hofstadter, the Pulitzer Prize (1980) in non-fiction.  GEB may give the appearance of being a fun book, about music, art, computers, riddles and puns, but it is not just that. Using observations  from the diverse fields of math, language, and genetics, the book actually introduces very innovative concepts in an attempt to explain the nature of human thinking and intelligence.  The art of Escher and the compositions of Bach are actually referred to as analogies to help illustrate the highly abstract ideas presented. The inventiveness and originality of the author makes  the book a joy and a treasure in many ways. It is surely a book one would repeatedly return to.

geb-book-cover

So as a tribute to i) the love of books, ii) Gödel, Escher, Bach: An Eternal Golden Braid, and iii) Douglas Hofstadter, here is my attempt at summarizing what I learned from GEB.

Here we go…

In order to understand intelligence the GEB way, we first need to get certain key concepts straight. These concepts are “self-reference”, “paradox”, “recursion”, “isomorphism”, and “symbol”. As we whirl between and across these concepts, the view of intelligence a la Hofstadter will gradually emerge.

Self-reference and paradox

selfreferenceSentences that talk about their own selves and people reflecting upon themselves are examples of self-reference. A typical example will be

This sentence is false.

Now if this sentence is really false, then it means the sentence’s claim is true. So it turns out that the sentence is actually true. But how can it be true when  it is false….?

Now here we are caught up in a looping paradox! If it’s false, it means it is true; but if its true it means it’s false!

Lesson? When a system that represents  meaning starts  referring to itself (and it can and it will) it will lock itself into a loop.  Each ‘level’ of  the loop is constantly leading up to the other and there’s no way out of it … an infinite regress! This is what Hofstadter calls a Strange Loop – a  concept he brings out more fully in his latest book I am a Strange Loop. (See Here for an interesting anthology of paradoxes.)

Paradoxical Mathematics…!

What!!#!@!!

Math…..paradoxical? Well… Kurt Gödel, a young Austrian mathematician, proved that. kurt-godel

Gödel used Bertrand Russell and Alfred Whitehead‘s system of formal mathematics (from their book called Principia Mathematica) to show that it contains irresolvable inconsistencies in the spirit of the paradox stated above.

Any formal system of mathematics attempts to show that i) all mathematical truths (or theorems) are derivable through strict rules of logic from previous truths (initial truths from where the derivations are build up are taken as true a priori and are called as axioms) [completeness] and that ii) no mutually contradicting statements are derivable in the system [consistency].

On the other hand, Gödel proved how sufficiently strong and expressive formal systems cannot prove their own consistency (provided that they are in fact consistent).

How did he do it?

First of all, he devised a system of numbers to represent statements in formalized mathematics. Next, he assigned these “Godel numbers” to steps in derivation of the theorems of the math system. He found that these strings of Gödel numbers can themselves be derived through the rules of math just like the actual derivations of theorems. For every logical rule applied in the derivation, a corresponding mathematical rule will yield the very Gödel number that represents the next step of the derivation. Thus Gödel discovered a heretofore undiscovered level of meaning in the formal system.

But where is the paradox?

Gödel showed how this process of “Gödelization” can be used to construct the following paradoxical statement in terms of the formal system.

This theorem cannot be proved in this system.

Now if the concerned system of formal math is REALLY complete (i.e. able to provide logical proofs to all its theorems) then a proof for the above statement will automatically prove the system’s inconsistency (as the system now proves a contradictory statement). On the other hand, the inability to prove the statement (indeed that is the case) is evidence  of the INCOMPLETENESS of mathematical logic!

Herein lurks another paradoxical self-reference – a Strange Loop!.

Essential incompleteness and Recursion

Paradoxical statements like these defy the neat categorization of ‘truth’ and ‘false’. In fact, truth and falsehood seem to be constantly leading to each other in a continuous fashion. This is the strangeness of the loop and it involves a process of recursion.

Recursion is a procedure which entails repeating its own steps indefinitely. The shampoo instructions

1. Lather; 2. Rinse; and, 3. Repeat.

are recursive. If acted upon literally, there will be a continuous repetition of the procedure making your stay in the washroom infinite! Hence, recursion is a self-reference with a potentially infinite continuity.

A common and visual example of recursion is when you are standing between two large mirrors….  “endless corridors” (a term used by Hofstadter in I am a Strange Loop) on both sides!

Some other visual examples of recursion are as follows:

A picture embedded inside itself inside itself inside itself...
A picture embedded inside itself inside itself inside itself…
sierpinski-triangle
Example of a fractal pattern made using a recursive math equation

Waterfall - Lithograph by Escher (1961)

Waterfall - Lithograph by Escher (1961)

Example of a video feedback loop on the cover of "I am a Strange Loop"
Example of a pattern resulting from a video feedback loop, from the cover of “I am a Strange Loop”

The last example most closely illustrates the concept of a Strange Loop. When successive iterations of the recursive process are designed to have a slight variation, novel and complicated patterns emerge from the  starting and much simpler ingredients. The  patterns could never be predicted by looking at the starting levels alone.

Hofstadter presents an illustration of recursive cognitive processes by referring to the chess situation. Before making the next move in a game of chess, you would like to see with your mind’s eye how will the opponent respond to the move you are now considering. You may also try to “look ahead” further into the game by trying to determine a possible move against the opponent’s response to your next move and then again reflect on how the opponent will respond to that…. This process of repeatedly generating solutions belonging to a particular class (in math, members of a particular set such as the Fibonacci numbers) is called as recursive enumeration.

Hofstadter seems to suggest that a recursively defined set of procedures entails an increasing level of complexity of behavior. Furthermore, where a machine (for e.g., a computerized chess program) must be given a decision procedure to settle on a solution rather than engage in an infinite “looking ahead”, humans have the capability to “jump out of the system” at their will. They can put a break on the recursion, observe the workings of their  own reasoning process, draw some conclusions, and look for alternatives. Hofstadter illustrates his point beautifully by engaging his readers in a task involving recursive enumeration in the first chapter of his book. (For a go at the task, check out this site.)

The human ability to stand back and observe the results of their own thinking guarantees an unpredictability of ideas and behavior that the machine lacks. Ultimately, it is these strange loops of thought that are also responsible for the general self-consciousness that defines the human condition. Akin to the beautiful, totally unpredictable and unique pattern that emerges out of a video feedback loop.

human-mind

There is so much more still left to delve into…

I’ll complete this summary of my GEB concepts in the next post InshaAllah.