Posts Tagged ‘isomorphism’

QUR’AN ANTHOLOGIES: Illuminating Metaphors – By Form VI

In Anthologies, philosophy, Quran, universe, Words of Gold: The Quran on April 10, 2013 at 11:01 am

Metaphors are utilised in the Qur’an in the even broader sense of ‘isomorphism’. As readers of this blog might recall↓, isomorphism is the mirroring of one set of information onto another. This might be examplified by the usage of symbols and literary metaphors or in the way brain processes information coming in from the world, or in the way on-screen pixels take the shape of live-action images in real world.

Thus, whereas in case of metaphors similarity lies in between one piece to another piece of information (source and target), isomorphism is more broad-scale with likenings (or, structural mappings, using Lakoff’s terms) between two series of information.

Evidence of isomorphism in the Qur’an


يَا أَيُّهَا النَّاسُ إِن كُنتُمْ فِي رَيْبٍ مِّنَ الْبَعْثِ

فَإِنَّا خَلَقْنَاكُم مِّن تُرَابٍ ثُمَّ مِن نُّطْفَةٍ ثُمَّ مِنْ عَلَقَةٍ ثُمَّ مِن مُّضْغَةٍ مُّخَلَّقَةٍ وَغَيْرِ مُخَلَّقَةٍ لِّنُبَيِّنَ لَكُمْ ۚ

وَنُقِرُّ فِي الْأَرْحَامِ مَا نَشَاءُ إِلَىٰ أَجَلٍ مُّسَمًّى ثُمَّ نُخْرِجُكُمْ طِفْلًا ثُمَّ لِتَبْلُغُوا أَشُدَّكُمْ ۖ

وَمِنكُم مَّن يُتَوَفَّىٰ وَمِنكُم مَّن يُرَدُّ إِلَىٰ أَرْذَلِ الْعُمُرِ لِكَيْلَا يَعْلَمَ مِن بَعْدِ عِلْمٍ شَيْئًا ۚ

وَتَرَى الْأَرْضَ هَامِدَةً فَإِذَا أَنزَلْنَا عَلَيْهَا الْمَاءَ اهْتَزَّتْ وَرَبَتْ وَأَنبَتَتْ مِن كُلِّ زَوْجٍ بَهِيجٍ 

O PEOPLE, if you should be in doubt about the Resurrection, then [consider that] indeed,
We created you from dust, then from a sperm-drop, then from a clinging clot,
and then from a lump of flesh, formed and unformed – that We may show you.
And We settle in the wombs whom We will for a specified term,
then We bring you out as a child, and then [We develop you] that you may reach your [time of] maturity.
And among you is he who is taken in [early] death,
and among you is he who is returned to the most decrepit [old] age so that he knows, after [once having] knowledge, nothing.
And you see the earth barren, but when We send down upon it rain,
it quivers and swells and grows [something] of every beautiful kind. [Al-Hajj 5]
 In the above ayah, three different types of growths have been likened to each other:
  1.  development of the embryo inside the mother’s womb,
  2. progression of the born human from birth till senile age, and,
  3. the blossoming of foliage from barren earth into beautiful grass.

The common thread between all three types of growths is the fruition from a non-existent or immature stage to the fully developed stage. The wilting of luscious grass into brown hay is not mentioned here but has been mentioned in similar vein otherwise. Each living thing’s cycle of growth infact shows similar progression with basically the same two end-points: a) beginning of life and b) reversal of prime followed by death. The ayah thus succintly points out that no matter which stage or whose growth one might look at they all mirror the same pattern. This isomorphism in turn strongly suggests the sameness of the penultimate source of this cycle, in contrast to ‘random mistakes’ as suggested by the evolutionists.


 وَلَقَدْ جِئْتُمُونَا فُرَادَىٰ كَمَا خَلَقْنَاكُمْ أَوَّلَ مَرَّةٍ وَتَرَكْتُم مَّا خَوَّلْنَاكُمْ وَرَاءَ ظُهُورِكُمْ 

“AND you have certainly come to Us alone as We created you the first time, and you have left whatever We bestowed upon you behind you.” [in Al-An’am 94]

As per the above ayah, the two end-points of the cycle of growth themselves mirror each other: a progression from nothing to nothing. We are born empty-handed. Whaterver we acquire during our lifetimes (money, property, skills) is a part of the process of growing up in the world. In the end we leave empty-handed again. This mirroring was also catptured in the second example of the above ayah: God reminded there that after our birth we progress until old age where we become ignorant and unaware just as we were when we were born. The special aspect of the particular ayah now referred is that the sameness of the two unobserved phases of human existence has been implied: the phase before our birth and the phase after our deaths. We came from nothing (nothing here means only in the ‘physical sense’) and we return to nothing: matter and material are a midway stage observed only in this finite world.


إِنَّ مَثَلَ عِيسَىٰ عِندَ اللَّـهِ كَمَثَلِ آدَمَ ۖ خَلَقَهُ مِن تُرَابٍ ثُمَّ قَالَ لَهُ كُن فَيَكُونُ

Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, “Be,” and he was. [Al-i-Imran 59]

On a theological subject, the Quran here points out the inherent sameness in the birth of Hazrats Adam and of Isa (alaihima-s-salaam). The Christian tendency is to regard Isa as (na-‘uzubi-Allah) Son of God on account of his fatherless birth to Bibi Maryam. Allah (subhanahu ta’ala) here gently points out how Hazrat Adam was created from scratch without a father or a mother. Birth to all sorts of creation in this world, of indeed the whole universe, and of the universe of heaven and hell that is invisible to us, is by virtue of God’s powers. It is after having descended Hazrat Adam onto earth with wife Hawwa that the familiar system of human reproduction was put in place. However, it goes without saying, that the Creator can re-create another sample of any being in whatever manner He wishes as a miraculous reminder of His Great Powers. Thus the birth of all human beings, indeed all living beings in this world are isomorphic to each other. This agains points to the unity of the Source of all this creation.


Usage of isomorphism in the Qur’an

The three examples we have considered are sufficient to illustrate how isomorphism differs from metaphors in their more narrowed, literary sense. Isomorphisms point out the correspondence and basic sameness of apparently different phenomenae. They seem to be more factual, used to point out big cosmic realities. On the other hand, literary metaphors might be used more often as examples and illustration.



All exposition regarding the ayahs relies on basic exegises as found in Maulana Maududi’s Tafheem-ul-Qur’an and Mir Taqi Uthmani’s Ma’ariful Qur’an.



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. 



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:


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!