Properties of complex adaptive systems

Complexity in science, music and literature

Merging and splitting are natural operations for increasing complexity in complex systems, which consist of a large number of mutually interacting and interwoven parts.

Examples :
Merging and Splitting of
Code and Data -> Programming Languages
Firms, Companies -> Economy
Neural Assemblies -> Learning, Adaptation
Countries -> Politics, War
Elements -> Astrobiology (Fusion in stars, supernovae)

Every operation which increases complexity in systems which many parts must involve more than one part. Different Parts can be merged, linked and melted together, or a single component can be splitted, divided and separated into several distinct parts.

  • Merging alone leads to huge, solid components without structure
  • Connecting alone leads to a dense, incomprehensible network
  • Splitting alone leads to a chaotic explosion or proliferation of parts.
  • Separating alone leads to many small, isolated pieces

To increase complexity, you need the right balance between merging and splitting. In the case of networks, you need the right repeated combination of connecting and separating.

Finding this balance is not easy, and sometimes an art, for example persons who create great works of science, poetry or music are rare and often admired. They usually have the unique ability of interweaving and interlocking differnt

  • Threads of Knowledge (Science)
  • Muscial Voices, Motives and Themes (Classical Music)
  • Verse lines, Styles, Story Threads (Classical Literatue)
    in a new, interesting and fascinating way.
Let us take a closer look at the emergence of complexity in science, music and literature. A overview what science is can for example be found in this NAS article : (*) On Being A Scientist: Responsible Conduct In Research National Academy of Sciences, National Academy Press, 1995

Science: Merging and Splitting of Ideas and Publications

A scientist usually takes several publications, which he names in the bibliography, and merges them to a new publication. He splits each publication into relevant and irrelevant parts, and recombines the different fragments to a new work. By interweaving and interlocking the different threads of knowledge, the scientist creates a new thread of insight and information. It may become a part of common knowledge, if it is accepted by the scientifc community. Science is a "shared knowledge based on a common understanding" (*).

A good publication tries to illuminate the nature of a certain problem from a new angle. Scientific papers are the short-term memory of science, books the long-term memory. If the results of a paper are correct and the community pays attention to it and does not reject it, the territory of knowledge can be extended : "Once results are published, they can be freely used by other researchers to extend knowledge" (*).

Science is to gain new territoy of knowledge from the sea of ignorance, to cut clearings of known facts in the forest of the unknown : "The object of research is to extend human knowledge of the physical, biological, or social world beyond what is already known" (*).

You start with collecting and reviewing information and ideas, and if you are lucky you discover a really new idea. In the best case, you "observe or understand something that no one has ever observed or understood before" (*). If everything has been said and you have not found anything new, you try to hide your ignorance behind complicated phrases and formulas, write nothing, or write a review. In a review, you cite all relevant scientific papers of a certain field, not only the most relevant and essential as usual.

Books are long, extented reviews. A good book tries to illuminate the nature of a certain problem or topic by examining it from every angle imaginable. For example, Steven Pinker's Book "Words and Rules" tries to illuminate the nature of language and mind by choosing the phenomenon of regular and irregular verbs, or Stephen Wolfram's thousand page NKS book, which focusses itself on cellular automata.

New branches of science are created either by splitting or by merging existing branches of science. If two scientists of the same subject specialize themselves so much that they are not able to understand or cite each other, they split the subject into two new subjects. If a scientist applies the methods of a science to describe a new object or merges and combines the methods of distinct sciences, he eventually creates a new science. Computer science emerged as a daugher of electrical engineering and mathematics. Astrobiology is an interdisciplinary combination of Astronomy and Biology. The new science of complexity, the study of complex adaptive systems, is the prototype of an interdisciplinary science in general, which combines the natural sciences as computer science, physics and biology with the social sciences as psychology, sociology, politics.

Music: Merging and Splitting of Voices/Motives/Themes/Styles

In his fugues and contrapuntal works, Bach used the merging and splitting of different voices to create complex, dense, polyphonic music. The splitting into different musical voices by the main theme ("Dux") marks the exposition, the beginning of a fugue. During the development, merging and splitting of voices and motives are used among other techniques (modulation, augmentation, diminution,..) to create complex and dense harmonies. A fugue "creates the impression of organized complexity" (

Bach wrote in a dispute during the years 1737-1739: "The true amenity of music consists in the connection and alternation of consonances and dissonances without hurt to the harmony." Complexity in music arises from consonance in dissonance and vice versa. In baroque music and especially fugues, the structure was governed by the rules of counterpoint, which lead to complex and dense compositions.

This high complexity was the driving force behind the transition to the classical music of Haydn and Mozart. Fugues were not completey abandoned in the music of Mozart, Mozart admired J.S.Bach and his son C.P.E. Bach, and the finale of his last 41st "Jupiter" symphony is a large, complex fugue. But they are difficult to write, and the music was too complex.

During the transition from baroque to classical music, the merging and splitting of muscial voices was restricted to the interplay of solo and tutti, of solist and orchestra in concertos. An exception is the music written for experts or connoisseurs - string quartets and quintets - which is characterized by a complex interplay of four or five voices. Goethe compared string quartets to "four intelligent friends holding witty conversation". But merging and splitting of motives and themes is still used in concertos and sonatas.

Whereas 'Cantata' was used to name a piece of music which is sung, 'Sonata' is the basic term for an instrumental piece of music which is played. The Sonata usually consists of three or four movements, written mostly in the Sonata (or Rondo) form, which consists of exposition, development and recapitulation. The exposition present the themes and motives. During the development, themes are splitted and parts of themes are recombined again. The function of the recapitulation is to restate the most important musical ideas.

Musicians often combine several different styles to create a new, unique style. For example, Bach used a combination of german, french and italian styles to create his famous "Brandenburg Concertos". In modern music, this is known as "crossover".

Literature/Poetry: Merging and Splitting of Verses/Styles/Stories


In his "Ulysses", James Joyce describes a whole life in a single day. He combines daily life with the stuff of myth and legend (Homer's Odyssey) and combines many different styles : sections narrated in a direct style, experimental sections, lush and intricate passages,... He used the methods of the french author Eduard Dujardins to create a new style, the description of the stream of thought/consciousness. Authors combine many different styles to create a new, unique style.

Goethe and Shakespeare use in their masterworks FAUST and Hamlet, respectively, monologues, dialogs and discussions between multiple persons. They apply many different rhymes, tones and styles, dramatic and lyrical, reflective and farcical, pathetic and coarse, colloquial and soaring.


If a verse-line corresponds to a musical voice, then the melting and splitting of verse lines through rhymes corresponds to the melting and splitting of voices in polyphonic music.

Similar to the baroque music of J.S. Bach, famous authors are able to combine this strict outer form with rich inner content. Although Goethe tells an interesting story in his masterwork 'Faust', nearly every sentence contains a rhyme. He uses rhyme pairs (Paarreim), alternate rhyms (Kreuzreim), and every other type of rhyme. Consider for example the following beautiful interlaced rhyme structure in Goethe's FAUST II. In this part he describes rainbows as sun in the rain, complexity as enduring lastingness (Dauer) in change (Wechsel) : "Wechseldauer".


FAUST II. 1. Akt. 
"So bleibe denn die Sonne mir im Ruecken.           A  (-uecken)  
Der Wassersturz, das Felsenriff durchbrausend,      | B (-ausend)
Ihn schau ich an mit wachsendem Entzuecken,         A |
Von Sturz zu Sturzen waelzt er jetzt in tausend,      B 
Dann abertausend Stroemen sich ergiessend,            | C (-iessend)
Hoch in die Luefte Schaum an Schaeume sausend,        B | 
Allein wie herrlich, diesem Sturm erspriessend,         C
Wölbt sich des bunten Bogens Wechseldauer,            D |
Bald rein gezeichnet, bald in Luft zerfliessend,      | C 
Umher verbreitend duftig kuehle Schauer.              D
Der spiegelt ab das menschliche Bestreben.          E | (-eben)  
Ihm sinne nach, und du begreifst genauer:           | D
Am farbigen Abglanz haben wir das Leben."           E  

FAUST I (Mephistopheles about science)
"Zwar ist's mit der Gedankenfabrik                A  
Wie mit einem Weber-Meisterstueck,                A  
Wo ein Tritt tausend Faeden regt,                  B
Die Schifflein herueber hinueber schiessen,         C
Die Faeden ungesehen fliessen,                      C
Ein Schlag tausend Verbindungen schlaegt.          B
Wer will was Lebendigs erkennen und beschreiben,  A
Sucht erst den Geist herauszutreiben,             A   
Dann hat er die Teile in der Hand -                B
Fehlt leider! Nur das geistige Band.               B 
Das sollt Ihr mir nicht zweimal sagen!            A
Ich denke mir, wie viel es nuetzt                  B
Denn, was man schwarz auf weiss besitzt,           B
Kann man getrost nach Hause tragen.               A
Was diese Wissenschaft betrifft,                  A
Es ist so schwer, den falschen Weg zu meiden,      B 
Es liegt in ihr so viel verborgnes Gift,          A
Und von der Arzenei ist's kaum zu unterscheiden.   B



Like scientists who combine and connect several different publications to make a new publication, authors combine several stories to write a new story.

Johann Wolfgang von Goethe used Christopher Marlowe's "Doctor Faustus" and plundered several of his own poems to write his masterwork "Faust". Shakespeare used the danish tale/legend of Amleth to produce his masterwork "Hamlet".

It is impossible, that the work of an author is not influenced by his experiences and his life. And in most cases, authors describes themselves in their main- or master-works. Goethe and Shakespeare for example described themselves with Faust and Hamlet. James Joyce described himself with Leopold Bloom, one of the main character of Ulysses, and the writer Joyce is personified in his writings as Stephen Dedalus.

Like James Joyce expands in his Ulysses one day to a lifetime, Goethe's Faust tries to search Eternity in a moment.