Nizar and the Beauty of Chance
What is the information content of a poetic message? With what probability can a work of art emerge from chance? A literary journey between Combinatorics and Information Theory.
by Alessandro Chessa
[IT — Nizar e la Bellezza del caso]
Have you ever heard of ‘liquid sculpture’? It took the tragedy of an entire people for it to be born from the amazing imagination of a Syrian sculptor, Nizar Ali Badr. His works are made of stone, but not sculpted as a normal sculptor would; instead, they are compositions of pebbles, small and large, of various shapes and colors, which he arranges on a flat surface to give life to bodies, plants, animals, stars, and entire landscapes, almost as if water, with its motion on the shore, had magically arranged them in a form of natural beauty. The liquidity is in the creation process, which creates similar figures with the same basic components: heads, legs, arms, trunks, and leaves, but never identical, as if chance always intervened from the depths to undermine the perfection of the world.
In Figure 1, for example, a work composed of only ten stones is represented, excluding the two at the bottom right, which are his signature. How could he have better represented human desperation with such a limited number of elements?
Since the elements are so few, we might be tempted to try it ourselves, to take these stones and quickly arrange them in some more or less random configuration to see if a similar effect can be achieved. So a more intriguing question might be: on average, how many times do I have to toss a small pile of Nizar’s stones for the result to evoke an emotion, like the one transmitted by one of his suggestive works? With what probability can a work of art emerge from chance?
Nizar, obviously, does not need to challenge chance. Sometimes, a few stones of the right size and color, placed well, are enough for him, from which the mere idea of one of his bodies, huddled on the path to salvation, can emerge, as in the work in Figure 2.
Nizar boasts Ugaritic origins, the people who around the 14th century B.C. developed one of the first alphabetic scripts in the Near East. He proudly cites these origins and feels inspired by this tradition as a source of primordial creativity. Indeed, he uses his multi-formed stones like letters to generate stone codes, codes that emanate beauty, that are not sculptures but assemblages of free elements that can slide next to each other — liquid, precisely — to be composed according to the inspiration of the moment.
What, then, is the real difference between a work of art, a text that has meaning for us in that particular sequence of letters, and the order that can emerge from the void of chance, which has no soul — at least not yet for our time, for our history, and for our tastes? What lies behind the combinatorial aspect of the elements that make up a painting or a piece of music? What is the information content of a poetic message, and how does it relate to our way of perceiving a work?
Let’s set aside Nizar’s work for a moment and try to introduce some mathematical concepts that can outline our reasoning and give us useful elements for a broader understanding of these phenomena, which in any case transcend the scientific aspect.
First of all, Combinatorics, the branch of mathematics that studies finite sets of simple objects (integers, strings, nodes and links, points and lines, discrete configurations, finite sets, …) that satisfy well-defined and generally simple properties. Examples include the arrangement of pieces in a game of chess or the drawing of colored balls from an urn. When you have a finite number of distinct elements, Combinatorics is like a tool that allows you to multiply the possibilities immensely, to amplify their power and at the same time govern their order with precise rules. If we want to draw a literary parallel right away, it is the principle of the story The Library of Babel where Jorge Luis Borges imagines a library that contains all possible books from the start, even those that are completely meaningless, at least for our current understanding, or versions of known works with some small error or variation.
But there is much more than Combinatorics in the creation of a literary work, because once the sequence has been generated from all possible ones, it is important to ask what information it contains. The reference theory in this case is Shannon’s Information Theory, the mathematician who laid the foundations of modern computer science. It consists of two theorems, the first is the ‘Source Coding’ theorem and the second is the ‘Channel Coding’ theorem. These theorems may seem obscure in their mathematical formulation, but once unfolded in natural language, they reveal connections with familiar ideas like the information of a message and how it can be transmitted.
The second theorem, which is the fundamental one, says something quite intuitive: however much a communication channel is affected by noise, it is possible to transmit data (information) with an arbitrarily small probability of error up to a maximum rate through the channel itself. It’s as if during a party, in a noisy and crowded room, we wanted to communicate with a friend at a distance. To counteract the noise, we must raise the tone of our voice, so that the vocal signal overcomes it. The more we raise it, the more our interlocutor will have the possibility of understanding the message, even if some words might be missed. The higher the tone, the smaller the error in comprehension will be. This is not a rigorous comparison, but it serves to give the idea.
But what interests us more closely is Shannon’s first theorem, which is directly related to the limits of encoding a message and its information content. Let’s first try to offer a rigorous definition, and then translate it into more understandable language. Shannon’s first theorem, or the ‘Source Coding’ theorem, states that it is not possible to compress data into a message shorter than the total Entropy without loss of information. Conversely, compressions arbitrarily close to the Entropy value are possible, with an arbitrarily small probability of information loss.
What does this mean? Let’s try to explain it in simpler terms. No matter how much you try to shorten an alphabet to write certain words and express concepts in a certain language, you will need a certain number of letters. What is the minimum number of these letters? Well, it is possible to calculate it with a mathematical function called Entropy (Shannon’s entropy in information theory), which has a deep connection with Combinatorics because it is mathematically related to all the possible combinations/words that can be generated with that alphabet. In the end, Entropy roughly (in the particular case of uniform probability distributions) corresponds to the minimum number of bits (0s and 1s) to encode that channel.
Let’s take a very simple practical example. If the letters I need are A and B, and the words I want to compose have a maximum of two characters, it is immediate to verify that I don’t need more than 2 bits (see Figure 3, panel (a)).
If, instead, the letters are A, B, C, and D and the words are a maximum of 3 letters long, the necessary bits become 6 (Figure 3, panel (c)). I could also use the so-called ASCII encoding, the standard one we use in PCs, which uses 8 bits per character (Figure 3, panel (b)), but in the cases mentioned, I would have redundant information.
The reasoning holds if the words have the same frequency. But if the language provides for different frequencies for words and letters, as is the case in reality, then I can have smarter encodings, like Huffman coding, which use fewer bits for more frequent words and more bits for less frequent ones. In any case, it is always Entropy that determines the information content. In the particular case of uniform distributions for which I can express the combinations as powers of 2, the Entropy is precisely the exponent that in some way represents the combinatorial power of the sequence of letters (Figure 3, panel (d)).
But besides the compression of the alphabet encoding, like Huffman’s, there are other ways to compress information. We do it daily when we ‘zip’ a file or an image on our computer’s disk. If, for example, a sequence like ‘ababababababab’ appears in a file, it is intuitive that we can condense it into ‘7ab’, seven times the pair ‘ab’. The same thing happens with image compression. In that case, there may be large areas of the same color, like the background of a blue sky or the black of a shadow, which can be compressed in a similar way to the previous sequence, by repeating the relative color code an appropriate number of times.
But not all of it is necessarily useful information. An example of this is genetics. We know that in a human genome, a full 98% of the DNA is ‘non-coding’, meaning it is not used for transcription into RNA. Its function is unknown; it’s as if it’s in the background, but it’s not certain that it doesn’t play a role, however indirect. Sometimes order can arise from disorder, and we recognize it by difference, by the fact that it is surrounded by a kind of background noise.
Even in the new frontier of Big Data, we find ourselves in a similar situation. This great mass of data contains traces of all kinds: GPS tracks, physiological information, expressions of feelings on Social Media, even simple ‘likes’. Here the challenge is similar but different. In this case, besides distinguishing the signal from the noise, a further step is needed: it is necessary to map the data into understandable structures in order to analyze them and extract the relevant information.
But what happens with emotional content? What is the relationship between the two? Returning to the analogy with the works of Nizar Ali Badr, what is the minimum number of stones necessary to move us, instill fear, or make us feel happy? With his technique, he has stripped it down to the bare essentials. Compared to orthodox painters and sculptors, he has compressed the informational part to the maximum without sacrificing the emotional part. He uses the same stones in different combinations, but always in very limited numbers. So what’s the point?
We could argue that the emotional part of the work is not primarily in the work, but in the person looking at it. It is the combination of the two that ultimately creates the sentimental connection. The observer has a baggage of already accumulated images and experiences, including from the same artist, and it is from the comparison with this experience that the spark is ignited, as soon as the represented configuration fits with sufficient precision the images stored in our brain.
If we were to stick to purely scientific aspects, we would not get very far in our reasoning. It is the poetic aspects that can allow us to make a qualitative leap in artistic understanding. The basic elements are similar: the combination of symbols, the definition of information, data compression, coding and non-coding information (therefore significant/non-significant), the signal and the noise, and finally the extraction of meanings with automated processing algorithms.
But how much emotion can a certain sequence of letters or colors give us? Perhaps, even if it is not compressed, the repetitive and redundant rhythm of a verse, although not optimized for Information Theory, can resonate with the beat of our heart, or even a very simple haiku could contain a whole universe of feelings. Therefore, pure information content is not a good measure of the emotional content of a work.
Scientific themes fascinate us when we compare them with the unfathomable world of our inner dynamics, and in the case of Nizar Ali Badr’s art, the connection between Combinatorics and Information Theory is more evident than in many other cases. Beauty arises from the combination of simple granular elements, which are skillfully juxtaposed to create a visual effect that touches the soul. We have other examples in art such as mosaics, to stick to material/sculptural compositions, but also Tibetan mandalas or the ‘pointillisme’ technique of the Impressionists follow similar rules, as does the combination of geometric elements in Cubist works.
In literature, the combinatorial aspect is even more marked given the discrete nature of alphabets and the words that can be composed with them. Borges again observes in one of his American lectures, the Harvard Norton Lectures, the same ones that Italo Calvino would hold 20 years later, that in the end, there are not that many metaphors conceived by man in all of literature. Therefore, a good computer program that could juxtapose the right ones, in relation to the context of the story we are developing, would suffice, like one of those smartphone keyboard suggesters that intuits the correct completion of the word we are typing.
Borges had addressed a similar theme in the aforementioned story The Library of Babel, but in the case of the American Lecture on metaphor, the emphasis is on the generative/selective aspect, on the genesis of creativity, rather than on blind Combinatorics. This hypothetical mechanized guardian angel could provide the writer with the poetic layer as a sort of spiritual guide in literary composition.
In the same American lectures, Borges goes further, saying that in poetry, especially rhyming poetry, certain combinations are limited by the assonances of the verses, and therefore dictated almost by fixed combinatorial rules, which in his opinion makes them more natural and simple, almost fundamental expressions of the human soul, archetypes of the myth within us, more so than free verse or prose.
Calvino had already spoken of this idea of obligatory concatenations of actions and objects of tribal people at the dawn of language in his notable essay ‘Cybernetics and Ghosts’, a transcript of a series of conferences held from Turin to Bari in 1967: “…The storyteller explored the possibilities implicit in his own language by combining and permuting the figures and actions and the objects on which these actions could be exercised; stories came out of it… The development of the stories allowed certain relationships between the various elements and not others, certain successions and not others: the prohibition had to come before the transgression, the punishment after the transgression, the gift of magical objects before overcoming the trials. …; every animal, every object, every relationship acquired beneficial and malevolent powers, those that will be called magical powers and that could instead be called narrative powers, potentialities that the word holds, the faculty of connecting with other words on the plane of discourse.”
So, combinatorial power serves to tell stories, to find the right path among all possible ones, that is, the sequence of events that simulates the paths of our past, present, and future lives. In the same essay, Calvino had imagined an automatic generator of literary content produced by a calculating machine, which is very similar to Borges’s idea and the web project mentioned above. Here, however, the Italian writer goes further and also develops a theory of the reader, as the main architect of the poetic discourse: “The literary machine can perform all possible permutations on a given material; but the poetic result will be the particular effect of one of these permutations on a man endowed with a consciousness and an unconscious, that is, the empirical and historical man. It will be the shock that occurs only because around the writing machine there exist the hidden ghosts of the individual and of society.”
This suggests that the constraints of a finite number of elements being combined can give rise to an order not necessarily designed a priori. This observation is not at all unfounded if one thinks of Ramsey Theory, which postulates the inevitability of order even when trying to disorder a finite number of elements. As if to say, order is mathematically inherent in disorder, and therefore it is only a matter of recognizing it.
On this path, Calvino proceeds in his essay: “The procedure of poetry and art — says Gombrich — is analogous to that of a play on words; it is the childish pleasure of the combinatorial game that pushes the painter to experiment with arrangements of lines and colors and the poet to experiment with juxtapositions of words; at a certain point, the device is triggered whereby one of the combinations obtained by following their autonomous mechanism, independent of any search for meaning or effect on another plane, is charged with an unexpected meaning or an unforeseen effect, which consciousness would not have arrived at intentionally: an unconscious meaning, or at least the premonition of an unconscious meaning.”
It is clear that our experience plays a decisive role. We recognize certain figures because they are already inside us. Literature as a means of re-evoking myth, as Calvino says in this essay. So, producing literature and art could mean engaging in combinatorics with the artistic constraints and fashions of the time, with readers in the role of selectors, of ‘fixers’ of the images and rhymes that best adapt to the collective feeling sedimented over centuries of experiences and fruition of the human cultural heritage.
Therefore, there is a perfect expressive complementarity between order and disorder; there is a functional connection as Calvino still observes: “The true literary machine will be the one that itself feels the need to produce disorder but as a reaction to its previous production of order, the machine that will produce the avant-garde to unblock its circuits clogged by too long a production of classicism.”
Nizar also offers us his version of primordial disorder, of the formless mass of data: a set of his stones arranged in the shape of a circle (Figure 4). They would seem to be placed randomly. They are the same stones he has used for his other works. But are we sure they are really so disordered? Here Nizar challenges us. The first time I saw this work, after my memory had absorbed all his previous ones, I felt vertigo. From this circle, images began to emerge, like ghosts from a nightmare. The stones began to tremble, to come to life, to tell stories. I began to see pieces of bodies, blood, broken branches… Then this sea of possibilities calmed down. The stones returned to their place, and only the emotion remained, in its purest state.
The mystery will remain of how the boundary between published art and the magmatic world of combinatorial possibilities moves in the meanders of chance, as time, our experiences, and our common human feeling change.
