rhodoraonline

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!

About these ads

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

%d bloggers like this: