Crossings - Volume 1, Issue 2 - Mac an Airchinnigh

Dynamic Poetry – Dynamic Haiku

Mícheál Mac an Airchinnigh
Department of Computer Science
Trinity College, Dublin
Ireland

Abstract. Poetry is like mathematics. The poem encapsulates thought and perspective in much the same way that a mathematical account does. Both, like music, are imbued with harmony in all its manifestations. Both result in static and frozen forms of expression, misunderstood by subsequent generations of readers, often lacking enlightenment and means of renewing interpretation. The poet as artist, like the mathematician, utilizes technology as it becomes available and accessible. Today, in our times, the dominant technological form is not only enabling but dynamic. The computing system enables all that could ever be desired in the static form of writing, printing, archiving. The computing system is dynamic (ever changing) and multi-faceted in its distributed nature. This paper explores the possibility of the dynamic, overtaking though not supplanting, the static poetic form. Moreover it proposes to exhibit more profoundly the mathematical structure, of which number and meter are both a small part, which is an essential characteristic of all artistic forms. In order to clarify the nature of the discourse on the dynamic in poetry the Japanese poetic form of haiku is chosen for experiment and analysis after synthesis.

Prologue

One of the greatest problems in the writing of poetry is to stop the rewriting. There comes a time when the poem must be left alone forever, when it takes on its final form never again to be altered. It is precisely at this time of the release of the poem that it can be said to be finished, to be complete. It is also the time of the release of the poet from the poem.

But the poet remembers the earlier drafts and may have kept notes as well as the drafts. Here can be seen what has been changed in the process of the development of the poem. That word was replaced by this one. An entire line may have been reordered to achieve a more pleasing harmony of sound while keeping the sense invariant. Even entire verses may have been cut out from the final version.

Why should the writing of the poem end with the single final version? Are there not other nascent possibilities? Might not the poem have siblings? Might not a poem have a twin?

Why should the finished poem be static? Is there not room for the idea of the dynamic poem, of the poem that is always in a state of becoming?*

The popular Japanese form haiku seems particularly suitable for exploring the possibilities of poetry in process. David McMurray outlines the basic formula for the Japanese poetic form haiku thus:

3-short lines
1-season word
1-cutting word
no rhyme or metaphor
(17 syllables, 5-7-5) [12].

It seems to me that haiku affords an admirable opportunity to experiment with the idea of the dynamic poem for two reasons. Firstly, the haiku is compact, seventeen syllables in three lines of five, seven and five syllables respectively. Due to its small size it is clear that experiments might be considered to be well-bounded. I should note, however, that the experiments I want to perform have nothing to do with the random generation of haiku such as that developed by Selendy Communications. Secondly, due to the very nature of the terseness, I find it very difficult to accept that the final version is all there ever could be to capture that elusive inspiring thought or image. For example, to capture this essential ‘limiting’ characteristic of haiku, I composed the following haiku on haiku:

To limit oneself;
Self expressing in Haiku
Is Soul threatening [9].

According to the ‘strict’ rules of haiku above, this haiku is fatally flawed. This poem apparently does not contain a ‘season word,’ which is a word that clearly indicates, or points to, or is characteristic of, one of the four seasons: spring, summer, autumn, and winter [19]. Senryu is another poetic form that adheres to the syllabic rules but not the thematic principles of haiku. Senryu focuses on human nature and emotions rather than the natural world, and it is frequently satirical or humourous in tone [13]. However, I do not consider the above to be senryu. Unlike most senryu, the above haiku on haiku is intended to be serious, non-humorous and non-satirical. How then shall one describe it? Initially, I was uneasy about using the word haiku to describe both haiku and senryu. I am not fluent in Japanese, and the subtleties of exact definition are necessarily lost in the transfer of a poetic form into a radically different linguistic and cultural context. A decision had to be made. For the purposes of this paper, any poetic form (in whatever language) of three lines of five, seven and five syllables, shall be called haiku.

In this short note I propose to sketch out my thoughts for a series of artistic, technological experiments in the writing and reading of what I call dynamic poetry, by which I mean poetry that is always in the state of becoming, always in the state of making. I use the word experiment in the classical scientific sense. One must have a theory. One must be able to measure.

Let us begin then in the second section, ‘Haiku and Numbers,’ by examining some of the numbers that one might associate with haiku. Then in the third section, ‘Experiments,’ I will set down some of the parameters that we will use in the planning of the experiments. The paper concludes with an ‘Epilogue.’

Haiku and Numbers

Haiku is syllabic and thus distinguished from most Western poetic forms, which are largely based upon the devices of stress-based metre and rhyme [15, p.74]. In the first instance, as a mathematician, I note that there is an essential relationship between poetry and numbers. In fact ‘versification, like music, is at base a sort of mathematics of sound’ [15, p.10]. Before proceeding to further observations on poetry and numbers, it is important to remember that poetry is a matter of sound, and that reading is really voicing or sounding, recalling that to read is to speak internally or mentally.

It is interesting to note that the numbers associated with haiku are all prime numbers. There are three lines, and 3 is the smallest odd prime. The numbers of syllables are 5 and 7. Both are prime numbers. So far haiku uses the first three odd primes: 3, 5 and 7. The total number of syllables in a haiku is 17, also a prime number. Given an arbitrary whole number n, one wonders whether it is prime or not and, if not, then what the prime factors are. The prevalence of prime numbers in the structure of haiku contributes to the sense of elemental simplicity the form affords.

Now, there are two basic ways in which a mathematician will look at a whole number, the multiplicative view and the additive view. In multiplicative terms, every number has a unique prime factorisation which is a very precise way to state that every number can be broken up into a unique product of primes each of which is raised to some power. For example, the number 60 may be broken up (i.e., factored) uniquely into 60 = 2^2 × 3^1 × 5^1. This is the multiplicative view. But there is a second way to look at whole numbers, the additive view. Here one talks about partitions of a number instead of the prime factors of a number. For example the number 5 has seven partitions. Isn't that a curious fact considering the structure of haiku? The number 5 itself is a partition. So is 4+1, then 3+2, etc. However the number of partitions of 7 is only fifteen (not seventeen, as this analogy would lead one to expect). The looked-for pattern does not materialise. On the other hand, 5+7+5 is one of the partitions of 17. We will note below that additive number theory is especially useful in experimenting with haiku. The mathematical processes of factoring and partitioning to make sense of a given number are not unlike the strategies of breaking poems into lines, syllables and sound patterns, or sentences, phrases and words, in order to make the poem meaningful.

Mathematics is as much about structure, shape and symmetry as it is about numbers. The haiku has the property of symmetry about the middle line of seven syllables. This is clearly an essential feature. How, then, might the symmetry be broken in order that the haiku poem be interesting? It appears from the rules of haiku listed above that in Japanese the first five syllables may be accentuated by the use of a cutting syllable (or word) at the end of the line [12]. In my haiku above, the semicolon is intended to mark that the syllable ‘self’ in ‘oneself’ is a cutting word. I associate the partition 5+12 with this particular feature of haiku.

Frances Stillman remarks that the ‘stark progression of syllables up to an image [...] implies far more than it says [and especially] there is a concluding concept in the third line which gains in suggestiveness by its brevity’ [15, p.75]. One might be persuaded that the last line stands out in some special way. The partition 12+5 would indicate such a strong third line. Mathematically, 5+12 and 12+5 would normally be regarded as the same partition of 17. In a poem, however, the shifting of perspective involved in seeing the poem as groups of 5+12 syllables vs. 12+5 syllables is likely to have a profound effect on the reading process. That both partitions (and many more possible ways of grouping the elements of the poem) can exist simultaneously and independently is a fundamental aspect of the mental pleasure of the reading process.

Experiments

The Parameters

The most important thing at the outset is to declare the exact parameters of the experiments to be performed. The question of how strictly to adhere to the traditional formal rules of haiku is primary. One might choose to define haiku poetry in other ways besides the syllabic formula, as Jack Kerouac does in describing the transformation of haiku in the American cultural context:

The American Haiku is not exactly the Japanese Haiku. The Japanese Haiku is strictly disciplined to seventeen syllables but since the language structure is different I don't think American Haikus (short three-line poems intended to be completely packed with Void of Whole) should worry about syllables because American speech is something again . . . bursting to pop.

Above all, a Haiku must be very simple and free of all poetic trickery and make a little picture and yet be as airy and graceful as a Vivaldi Pastorella [4].

Since experiment and theory ** are strictly autopoietic, that is to say, one makes the other, I have chosen to stick strictly within the syllabic rules of Japanese haiku irrespective of the (natural) language to be used.

Secondly, results must be measurable. By measurable, I mean that there must be a definite way in which numbers can be assigned to various outcomes of the experiments.

Thirdly, experiments must be repeatable in some general sense. Given the artistic nature of the work in hand, it is reasonable to suppose that the outcomes will differ considerably by subjective consideration and yet can be pinned down within an agreed objective framework.

Fourthly, the entire point of having a theory is to be able to ask questions and, therefore, to be able to perform experiments in order to obtain answers. Naturally, the theory determines the kind of questions that may be asked. On the other hand, a theory may be developed by asking questions.

Finally, and perhaps most importantly of all, I will need to assemble a variety of (computing) technologies to assist in the experimental development work of the composition of dynamic haiku. It will be taken for granted that the World Wide Web will provide the technological foundation. In terms of content, there are online anthologies of haiku from which to draw material for examination [14]. One does not have to write one's own haiku for every experiment.

Consensual Poetry

Certain haiku seem to be extraordinarily evocative to the extent that a reader becomes strongly involved with them, engaged in the thoughts or images evoked. I originally hypothesised that a haiku in formation might attract a following of authors, each of whom might contribute towards the final acceptable version. I call this a consensual haiku. I subsequently discovered that the experiment of multiply authored poetry was already very well established in Japan. What I envisioned as consensual haiku is remarkably similar to renku (‘linked poetry’), the classical Japanese collaborative poetic form from which haiku actually derives [16, 3].

Conceptual Context

I have already mentioned that Stillman remarked upon the ‘third line-big bang’ idea [15, p.75]. One might consider leading in with the concept on line one. I tried out this idea with a haiku celebrating the concept of autopoiesis, developed by Humberto Maturana and Francisco Varela [17]:

Autopoiesis –
Frog with fly in pond at one.
Both in becoming [10].

The word autopoiesis is newly coined by Maturana and Varela [17; 11] to capture an idea in natural language that did not permit its expression:

Curiously, but not surprisingly, the introduction of this word proved of great value. It simplified enormously the task of talking about the organization of the living without falling into the always gaping trap of not saying anything new because the language does not permit it. We could not escape being immersed in a tradition, but with an adequate language we could orient ourselves differently, and, perhaps, from the new perspective generate a new tradition [18, pp.38-53].

It is customary to carry out the constructions of new words using root words from a different language. In the ‘Western culture’ recourse is often made to Greek or Latin. In this case, autopoiesis is constructed from two Greek roots. The prefix auto (αυτο) means ‘self.’ It is commonly found in words such as automobile, automaton, autocrat, etc. The root poiesis (ποιησισ) is from poieo (ποιεω), ‘to do,’ ‘to make’ or ‘to create.’ Happily, for this paper, poiesis means ‘making,’ ‘creating,’ ‘poetry’ and ‘poem.’ The word autopoiesis is associated with the interlocking of life. In particular, it is argued that a frog does not have a concept of fly, even of fly as food. Instead the frog and fly co-evolve. In particular, the frog has evolved (is evolving?) to ‘see’ the fly as ‘food.’ Since frogs are associated with ponds then I have placed them all together in a single haiku. In addition there is a very famous haiku from the master poet Matsuo Basho (1644-1694) concerning an old pond and a frog:

An old pond
a frog jumps in
Sound of water [12].

It seemed fitting to link the old with the new through this image in my poem.

Experiment: The Seven-Syllable Permutation

Consider again the haiku on autopoiesis:

Autopoiesis –
Frog with fly in pond at one.
Both in becoming.

To what extent is it possible to rearrange the underlined words and still retain a sensible haiku? One immediately notices the reasonableness with which the words ‘frog’ and ‘fly’ may be interchanged to give:

Autopoiesis –
Fly with frog in pond at one.
Both in becoming.

Similarly, one sees that ‘in pond’ and ‘at one’ may be interchanged to give:

Autopoiesis –
Frog with fly at one in pond.
Both in becoming.

The number of rearrangements, or permutations, of these seven syllables is factorial 7, written 7! = 7×6×5×4×3×2×1 = 5040. Therefore, at first glance, it would appear that based on this experiment of permutation of the middle 7 syllables, there are another 5039 (= 5040 - 1) alternative haiku to the one I wrote. (It may be worth noting that 5039 happens to be prime.) However, from the point of view of sounding, it is clear that ‘at one’ and ‘in pond’ are essentially atomic sounding units.*** Counting on the basis of five sounding units (Frog / with / fly / in pond / at one) gives 119 (= 5! - 1) alternatives. (119 = 7×17. Isn't that interesting?) This ought to suffice to illustrate the kind of simple experiment that one can perform on a given haiku.

The above analysis derives from multiplicative number theory. From the additive point of view, we know that there are 15 distinct partitions of 7. The given line has the type 1+1+1+1+1+1+1, which is usually denoted by [1^7], read as 1 to the power of 7.† Swapping monosyllabic words such as ‘frog’ and ‘fly’ does not change the partition type. On the other hand, reading ‘at one’ and ‘in pond’ as atomic bisyllabic sounding units suggests the partition type 1+1+1+2+2, denoted [1^3,2^2]. Finally, one might decide that ‘frog with fly’ was essentially trisyllabic. Hence, one might hypothesise that the poet ought to work with the partition type 3+2+2, denoted [2^2,3^1].

The use of the word type in this context is peculiar to the mathematics of permutations and partitions. A permutation is a one-to-one onto map (also known as a bijection or isomorphism). For example, if we partition the second line of the haiku above into five distinct units as above, we can permute the units, denoting the change thus:

Frog -> Fly / with -> with / fly -> frog / in pond -> at one / at one -> in pond

There are 5! = 5×4×3×2×1 = 120 such permutations, i.e., 120 lines on 5 distinct sounding units. For simplicity, mathematicians discuss such permutations in the most abstract way possible. This gives universality. There are 5! permutations on the five digits 1, 2, 3, 4, 5. The permutation of the line above can also be written:

Frog with fly in pond at one -> Fly with frog at one in pond.

The corresponding permutation of the 5 digits is 12345 -> 32154. Noticing that we always start with 12345, mathematicians might simply write 32154 to denote the permutation. In practice, we write (1 3)(2)(4 5) to denote that 1 maps to 3 and 3 maps to 1, 2 maps to itself, and 4 maps to 5 and 5 maps to 4. We classify this permutation by saying that its type is 2+1+2, corresponding to the way in which the digits are partitioned. The important thing to notice is that there is an intimate relation between the shape of a permutation, its type and the partitions of a number. In mathematics, 1+2+2, 2+1+2, and 2+2+1 all have the same type and are considered to be the same partition of 5.

It is not clear to me just now how I can assign numbers to the haiku in such a way as to support a theory. What is clear is that there is a number system to be explored in conjunction with haiku. I wondered whether there was ever any research undertaken in this particular field.

The mathematical/literary experiments of Oulipo, the current modern acronym for Ouvroir de Littérature, founded in 1960 by Raymond Queneau and François Le Lionnais, provide one useful example. The goals of the workshop are:

to offer writers a wide arsenal against the rampant fear of the white page; to overcome all historical and personal literary formulas [...], and to write that which has not been written; in short, to develop, elaborate, and rediscover all means of writing under self-imposed constraint, mathematical and otherwise [8].

Among Oulipo's current membership are Claude Berge, a well-known mathematician (graph theory) and Jacques Roubaud, mathematician and poet (among other things). It is absoutely clear from the 1962 Manifesto by Le Lionnais [7] that mathematics is at the heart of every oulipien(ne). The techniques that emerged from the movement include the use of combinatorics, bifurcation, ‘lipograms’ (texts which omit one or more letters) and a technique of producing poems from the rhyming words of existing poems that happens to be called ‘haikuisation.’

Results

This short note was originally intended only to set the scene for haiku experiments to be carried out at some stage over the next nine months. However, since I do have access to some good private technology (an Apple Macintosh iBook) then I thought that I might perform a simple experiment and record the results.

Synthetic Voice Experiment

When I write poetry, I write it to self-express; I write it to be read, at least internally. I suppose that everyone else does the same. The actual writing requires the use of certain syntactic conventions of writing. (One notes already that I have stepped outside the oral tradition which has its own syntactic conventions of voicing.) In the writing of the poem on a computer, a new technological possibility opens up. There is now the possibility of the ‘computer reading aloud’ the poem. I performed such an experiment with a haiku.

The experiment is a simple one. The equipment is standard for our technological age. The results are profound from the perspective of the voicing or sounding of dynamic poetry. First, let me describe the experiment itself, giving details of the equipment used and method employed.

Equipment: Apple Macintosh iBook 2001, Apple's SimpleText editor, Apple's voice synthesis program ‘Macintalk, English’ and a range of synthetic voices of which I chose ‘Victoria, high quality’ as the most pleasing. (Of course one might prefer a different synthetic voice to achieve another effect, and indeed one may need to take the synthetic voice into account in the construction of the dynamic haiku.)

Experiment: The haiku on haiku [9] was inserted into SimpleText, and Victoria was ‘asked’ to read it aloud.

Result: I discovered that Victoria read lines 2 and 3 as if they were a single line. In order that Victoria speak the poem properly, it is important that a pausing mark be inserted at the end of the middle line. In addition, a hyphen inserted into ‘threatening’ was necessary, since Victoria was inclined to read the word as the bisyllabic word ‘threat-ning.’ Here now is the amended version of my original haiku to be read by Victoria:

To limit oneself;
Self expressing in Haiku,
Is Soul threat-ening.

I must confess that I was surprised by the results of this simple experiment. Victoria recognised the semicolon as a cutting symbol. Therefore, the syllable ‘-self;’ in ‘oneself;’ is a cutting syllable, or if one prefers ‘oneself;’ is a cutting word. To have written ‘oneself –’ in place of ‘oneself;’ would also be perfectly acceptable for Victoria. The repetition of the sound ‘self’ turns out to be particularly pleasing (at least to me). The resulting haiku sounds well.††

The use of a ‘synthetic personal voicer,’ such as Victoria, suggests new research directions for the development of dynamic haiku. In particular, it is clear that cutting syllables can be provided for English in a ‘natural’ way. New sounding units can be developed and experimented with. For example, replacing ’;’ by ‘f’ in ‘oneself;’ to give ‘oneselff’ makes ‘oneself’ strangely trisyllabic and sounds like ‘on-es-elff.’ I would never have supposed that, as a poet, ‘small modifications in written syntax’ could have such a profound change in sounding structure had I not used the synthetic personal voicer. As a mathematician this does make very good sense, as for example in perturbation theory and chaos theory, small changes in initial conditions have profound consequences. A theory of haiku partitioning may emerge as a result of methodical voice synthesiser experiments. The synthetic personal voicer may also be used to classify and rank partitions. Looking ahead along the technology trajectory into the future of voice synthesis it is obvious to me at least that there may come a time when the synthetic personal voicer will surprise us by its sounding of a poem, a sounding of which we might never have dreamt. This opens up the possibility of a new kind of oral tradition or an enriching of an existing one. Consensus on the collaborative ‘becoming poem’ or ‘poem to be’ may be based on a synthetically voiced version to which the collaborating poets have agreed. I am sure other avenues of exploration and experiment will open up as a result of adding this extra dimension of synthetic personal voicer to the proposed use of mathematics in the synthesis of dynamic haiku.

Epilogue

Looking back over the ideas expressed above in this short paper I wonder to what extent I believe what I wrote. I ask myself whether this is good for poetry, whether it be in haiku form or otherwise. I wonder will there be readers who will be shocked. Then I remember that I am a computer scientist as much as a mathematician, and I have written poetry.

Putting on my liberal arts hat I recall prosody, the ‘theory and practise of versification; the laws of metre,’ [1] and metre means measure, and with measure we have number. I remember that ars (Latin) = techne (Greek). The supposed dichotomy of ‘art’ and ‘technology’ is truly modern. Let us return to the unity.

It is only when the skills and devices of the poetic art form are mastered that the master becomes free to be poet. I would expect the same to happen when the range of devices is extended (considerably) to include those of the computing technologies. Once these new skills and devices are used to enhance and augment what is now customary, then another new age of poetic forms will dawn. I hope and expect that these experiments with dynamic poetry and dynamic haiku will add to the potentiality of the oncoming new poetic forms.

Acknowledgements

When I had begun to consider the possibility of using modern interactive computing technology to elaborate and develop the self-expressing art form called poetry, I had supposed that I was setting down some preliminary ideas, a sketch if you will, for the purpose of experimentation (by others). This short paper was the outcome.

Once it had been written it was reviewed. Now I have tried to incorporate all of the excellent recommendations made by the three anonymous reviewers to whom I am very grateful for the care and attention that they lavished on the original piece.

I owe a special debt of gratitude to Elizabeth Drew who, in conversation on a draft, drew my attention to the need to spell out Jack Kerouac as the author of the ‘American Haiku’ vision [4]. She also mentioned the interest that Samuel Beckett had in mathematical permutations [6, pp.564-5], an interest manifested in the short prose work Sans (in French), translated by Beckett himself into Lessness [2]. Other ideas and suggestions arising from our conversation will have to wait for the next edition.

Notes

*: I use the word becoming in the obvious(?) sense of ‘coming to be.’ I naturally associate it with the word autopoiesis, discussed later. In addition, it is also clear that this paper seems to be in a dynamic state just like the poetry under discussion. The initial review has already prompted significant addition and some re-thinking. Since this journal is furnished with dynamic feedback, via Loquacious there is every reason to hope that I and others may contribute to this paper's becoming. Indeed, this very notion of permitting the author to comment on the text released, in the context of that text, releases the text from the author. On the other hand, the initial formal and public release of the text is, and must be, dated if only for the purposes of the ‘historical record.’ Technological means must then be found to date the re-telling of the story in the paper, much in the same way that editions of books are done, at least in principle.
**: One anonymous reviewer considered the section on scientific experimentation to be ‘somewhat basic for the readership.’ I must confess that I would heartily agree. In this particular case, however, I am deliberately interlinking ‘experiment and theory’ with ‘becoming’ and ‘autopoiesis.’ Thus, one might conclude that frogs evolve by carrying out (mostly successful) experiments. The outcome is essentially a ‘lively’ representation of what it means to be a frog, a sort of ‘theory of frog-ness’ written largely in the DNA, etc. Moreover, it is not widely known (outside the circle of working mathematicians) that mathematics is also an experimental science, certainly made manifest in particular in number theory. I consider poetry, music and so on in a similar scientific light. Finally, the interlocking of experiment and theory with autopoiesis suggests a holistic philosophy of science rather than a traditional reductionist philosophy of science.
***: It seems obvious that poetry is about sound. However, one is inclined to forget that the constraints of modern written syntax belie that fact. In particular, in English one seems to be obliged to adhere to the syntactical conventions and write ‘in pond’ instead of ‘inpond,’ thus thinking that apparently two words are necessary for what is really atomic in this context. The sounding unit here is ‘inpond’ consisting of two syllables. One might then raise the objection that introducing this new form necessitates ‘inthepond,’ ‘inapond,’ ‘inthemurkypond,’ ‘inamurkypond,’ etc. In a poetic context, this might not be a bad thing at all. However, restricting ourselves to haiku written in English (or French, etc.), I hypothesise that it would be extremely rare in general to find the need for the definite or indefinite article since their use would needlessly consume valuable syllables. Exceptions exist I am sure.
†: It is a peculiarity of number theory that one uses a power notation to denote the partition. Consider a partition of 5, such as 1+2+2. Its type is denoted by [1^1, 2^2]. The partition 2+3 is denoted [2^1, 3^1]. (In a multiplicative context, [1^1, 2^2] would mean 1×2×2, and [2^1, 3^1] would mean 2×3.)
††: For those who have access to an Apple Macintosh I provide the SimpleText document ‘haiku.txt’ in order that they may listen to both Victoria and I myself reading aloud this new haiku. Work is in progress to convert it into mp3 format. Then all will have the pleasure equally.

References

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About the Author

Mícheál Mac an Airchinnigh (1950-to date) is a Senior Lecturer in Computer Science at the University of Dublin, Trinity College. His field is the Mathematics of Computing. Apart from Mathematics and dancing, his other major passion in life is self-expressing in rhetoric and poetry, among other things.