Topology of creativity

1. Topology of creativity A. Bogojevic Scientific Computing Laboratory Institute of Physics, Belgrade May 22, 2004

2. Spatial and temporal distribution of creativity The end of the 15th and beginning of the 16th century mark what is probably the most creative period in painting the world has ever seen. The multitude of great painters of that time were concentrated in Italy and of them three stand out as larger than life: Leonardo da Vinci, Raphael and Michelangelo – arguably the three greatest painters of all time. Statistically it is quite improbable that the three should all appear at almost the same time and place – improbable that is unless they are in some sense correlated. What is the connection between the three? What was specific to that time and that place? Why isn’t creativity spread out? Is it enough to look at the greatest of the greatest – how deep do we have to dig to reach the roots of creativity?Do other endeavors such as music and science display such similar creative hot spots?Can something be done to create future hot spots? For works of genius one certainly needs men of genius, but in what way were Florence of the 1450s and 1470s and Urbino (100km east of Florence) of the 1480s different from the same places a century or two later, or earlier – did genius peter out of the gene pool? Why wasn’t the focus of the arts at the time in Delft or Leiden, and why did the “creative genes” migrate there two centuries later with the likes of Vermeer and Rembrandt? There are many different answers to these important questions: historic arguments, economic arguments, explanations having to do with religious freedom or lack of it… We will not seek to answer these questions but rather to give an impressionistic look at (some of) the data and to try to see what that data is telling us. We begin with Italian Renaissance painters.

3. Painters of the Italian Renaissance (15th and 16th centuries) Timoteo Viti Antonio del Pollaiuolo (1431-1498) Sandro Botticelli (1445-1510) Giulio Romano (1499-1546) Leonardo da Vinci (1452-1519) Raphael (1483-1520) Fillppo Lippi (1406-1469) Petro Perugino (1450-1523) Domenico Ghirlandajo (1449-1494) Andrea del Verrocchio (1435-1488) Michelangelo (1475-1564) Alesso Baldovinetti (1425-1499) Bertoldo di Giovanni Donatello (1386-1466) Formal master/apprentice relationship Desiderio de Settignano Strongly influenced by

4. The artists of the Italian Renaissance honed their skills as did all other craftsmen – by serving for several years as apprentices to well known Masters. The apprenticeship system was used extensively by the craft guilds from the Middle Ages till the Industrial Revolution in the 18th century. At a given time a typical Master’s workshop had a dozen apprentices helping the Master and his senior students, learning through doing and emulating. Through practical training apprentices acquired the necessary skills and tricks of the trade. In the process (in the best workshops) the most talented apprentices were allowed to slowly build up their own individuality and style and, ultimately, were encouraged to leave and become independent artists and craftsmen. This kind of an education system, when it worked, made possible the flowering of creativity, craftsmanship and dynamism. The Master workshops set up a strong personal connection between artists – a network that makes it easier to understand the correlations between (say) Michelangelo and Raphael. The two knew of each others work, they had met, there certainly was a mutual influence, yet this is not enough of a tie – it does not give us any causal connection that would explain how the two appeared as full grown geniuses at the same time and almost the same place. The previous diagram widens the field a bit in time and in the number of artists that are viewed. In the diagram, individual artists are points to which are added arrows indicating master/apprentice relationships or links of strong personal influence. This new structure makes the diagram into an ordered graph or network. The network gives us a new insight into the correlation between Leonardo, Michelangeo and Rapahael. We are looking at a kind of topology of creativity. We next jump 200km northwest and just a bit into the future and look not at painters but at musical instrument makers of Cremona.

5. Violin makers of Cremona (16th to 18th century) Pietro Giovanni Guarneri (1655-1728) Andrea Guarneri (1626-1698) Pietro Guarneri (1695-1762) Antonio Amati (1550-1638) Giuseppe Giovanni Battista Guarneri (1666-1739) Andrea Amati (?-1578) Nicolo Amati (1596-1684) Giuseppe Antonio Guarneri (del Gesu) (1687-1745) Francesco Stradivari Girolamo Amati (1556-1630) Antonio Stradivari (1644-1737) Omobono Stradivari Girolamo Amati (1649-1740) Formal master/apprentice relationship, most often also a father/son relationship.

6. There is a stamp of individual talent that marks the great painter. Quite rarely does more than one individual in a family show such talent. For this reason the painting craft was not handed down from father to son. As we see from the example of the three great violin making families of Cremona the opposite is true for the makers of musical instruments. Master/apprentice networks again help to explain what brought about such a concentration of talent (the Amati, Guarneri and Stradivari families lived and worked just several streets apart). This time, however, these networks of creativity are almost identical to geneological charts of the three families – identical, that is, except for the pivotal figure of Master Nicolo Amati. Still, one might wonder why the talent for instrument building, unlike the talent for painting, is easily passed on from father to son? A quick explanation would be to say that there is much more art (individual creativity) than craft (learned skills) in painting and that the opposite holds in instrument building. Whatever the case may be the Renaissance artists would certainly not agree with this – they would see our distinction between art and craft as an entirely artificial one. It is we who have lifted “pure” art on a higher pedestal than craft, just as we have made a similar distinctions between “pure” and “applied” science or between various disciplines. We believe that the reason for this is the great growth of knowledge which has made “renaissance men” like Leonardo, Michelangelo and Galileo a thing of the past. We believe this, not necessarily because it is true, but because that is what our education systems teach us. Luckily, a large percentage of the most creative people of all ages have not listened too intently to untested adages. Another indication that the above explanation (that hinges on the difference between art and craft) is too simplistic comes from looking at the greatest musical composers. Here we find several examples of the passing down of “music genes” from one generation to the next. There is no better example of this than the Bach family. Even before its greatest proponent (Johann Sebastian Bach) was bornin their part of the world the word “bach” was synonymous with the word “musician”.

7. Classical music (Germany and Austria 18th and 19th centuries) Friedrich Wilhelm Zachow Leopold Mozart George Frideric Handel (1685-1759) Wolfgang Amadeus Mozart (1756-1791) Dietrich Buxtehude Johann Christian Bach 1735-1782) Richard Wagner (1770-1827) Johann Sebastian Bach (1685-1750) Ludwig van Bethoven (1770-1827) Friedrich Wieck Johannes Brahms (1833-1897) Joseph Haydn (1732-1809) Robert Schumann (1810-1856) Carl Philip Emanuel Bach (1714-1788) Felix Mendelssohn (1809-1847) Nicola Porpora Carl Zelter Formal teacher/student relationship or strong personal influence Ignaz Moscheles Influenced by style of music

8. Both of the examples of networks of creativity from Renaissance Italy were characterized by the existence of thriving Master workshops that brought about a strong clustering of young talent around great artists and craftsmen. The stamp of individuality is surely not more pronounced in music composers than in painters, still the biographies of the former do not show them being nurtured in Master workshops. In most, though not in all cases, the greatest composers seem to spring up where they do without obvious rhyme or reason. The ties between great composers are also not family ties - there are examples of families that have contributed several generations of noted musicians, but these are exceptions rather than the rule. Still, the distribution of musical genius is far from uniform – the greatest period in music (classical period) was to a large extent brought forth by German and Austrian composers of the 18th and 19th centuries. Again one finds important inter-personal influences – relationships that result from similarities in musical styles, temperament and approaches. Many of these influences are even posthumous. The ties being less personal – one would expect a reduction in clustering as compared to Renaissance painters, for example. One should not however underestimate the strong clustering effect of the patrons of the arts. In Renaissance Italy the most famous were the Medici’s and the Borgias, in 18th century Europe the patrons were the German nobility – foremost among them King Frederic the Great of Prussia and Catherine the Great, Empress of Russia (also Prussian by birth). In order to have clustering of creativity we need to have a critical number of great masters that the young talents can look up to as well as a critical activity of patrons and financiers willing to foot the bill. We next jump to the 20th century and to two sciences: Physics and Molecular Biology.

9. Physics and Molecular Biology (20th century) Goetingen and Munich physics Robert Oppenheimer (1904-1967) Peter Debye (1884-1966) Wolfgang Pauli (1900-1958) Julian Schwinger (1918-1994) Werner Heisenberg (1901-1976) Arnold Sommerfeld (1868-1951) Linus Pauling (1901-1994) Molecular Biology Max Born (1882-1970) Max Delbruck (1906-1981) Enrico Fermi (1901-1954) Francis Crick (1916-) Lev Landau (1908-1968) James Watson (1928-) Aage Bohr (1922-) Niels Bohr (1885-1962) Erwin Schroedinger (1887-1961) William Lawrence Bragg (1890-1971) Ernest Rutherford (1871-1937) J. J. Thomson (1856-1940) William Henry Bragg (1862-1942) Cambridge physics

10. By the 20th century the Master/apprentice type of education had become a thing of the past. Still, a kind of Master workshop could be found in some of the Universities. The revolutions that rocked physics at the beginning of the last century were in no small measure brought forth by researchers from such centers as Cambridge, Goetingen, Munich and Copenhagen that traditionally nurtured laboratories that had much in common with old Master workshops. The clustering was strongest around individuals who, along with being excellent practitioners of their science, were at the same time great teachers that attracted talented young people. The best examples at the start of the century were Sommerfeld in Munich, Bohr in Copenhagen. In the 20th century the world was already becoming a much smaller place – hence, the networks of creativity were becoming wider, covering several countries. Still, a major part of the key research was being done at a small number of institutions. The ties between different laboratories and different countries were made by small number of individuals. Niels Bohr, for example, personally epitomized the migration of the principle setting of the physics revolution from England to Germany (start of the century), while his students like Oppenheimer, Landau, Pauling and Delbruck epitomize the further shift of focus. On the one hand a geographical shift in physics to America and Russia. On the other hand an out migration of the physics method into new territories and the birth of such new fields as molecular biology (middle of the century). At the same time that the networks were widening their topology (i.e. interconnectedness) did not change, nor did the number of individuals in them that one needs to look at in order to understand the clustering of creativity.

11. Topology of creativity Throughout the period we have looked at, cultural advances were focused and localized in small areas of the world. The most important reasons for this are economic – great artists and craftsmen needed their patrons, as today’s scientist need their government and private funding agencies. Within those focal areas the distributions are still far from uniform – rather they are severely clustered around a small number of key individuals. The communication revolution that is enfolding is slowly but surely broadening the field where important cultural advances are being made to include the whole world. Much more slowly, but economic differences between countries are also diminishing, and this also acts to broaden the field. As the field widens we should not expect to see a change in what we might term as the topology of creativity – the links between creative individuals. Technology already makes it possible for these links to span the globe (and the centuries), but the links will need to be just as individual, just as personal as ever before. We live in a society that is defined by and exists because of a continuous cultural and technological revolution. Such a society needs to rethink its education paradigms. The economy of mass production is quickly becoming less important in the global economy – much slower to change are our education systems which still have more than one foot planted in the industrial revolution that brought about the last great change in education.

12. New schools and new Master workshops Mass production in education has lead to a huge broadening of education outreach. We codify our wishes to continue this process in such resolutions as UNESCO’s global program Education for All. We even seek to get rid of some of the less appetizing aspects of educational mass production by insisting on increasing educational quality, relevance, equity and diversity. This process is slowly transforming our education landscape. Still, in addition to these new schools and universities, we need to start to nurture totally different kinds of educational settings – environments for learning and doing that have much in common with the Master workshops of the past. Not elitists settings (the Master workshops were never that) but places that nurture creativity, places where “masters” and “apprentices” work in small groups, places where both “masters” and “apprentices” learn as a result of this work. Much can be done by setting up new types of schools – yet we need to take heed of the needs of the most talented and creative among us. For a long time the talents have come out not because of but, rather, despite the prevailing education systems. We can no longer afford to be so cavalier with our talents. The young people in today’s Florence have among them the same concentration of Leonardo’s and Michelangelo’s – the fact that they are not appearing is a serious condemnation of our education. If we want more Leonardo’s we need to expose them, as early as possible, to the Verrochio’s of our time – however we improve our schools their teachers will never be of this caliber. The new research and learning incubators won’t be a substitution for our universities and other educational institutions (or we run the risk of stopping creativity through overspecialization). Instead they will need to be additional educational layers complementary to existing institutions. In a time of true lifelong education a person would then continuously meander from one layer to another.