Topology of creativity

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Topology of creativity
A. Bogojevic Scientific Computing
Laboratory Institute of Physics, Belgrade
May 22, 2004
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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
isnt 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 wasnt 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.
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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
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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 Masters
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.
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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.
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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 born in their part of
the world the word bach was synonymous with the
word musician.
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Classical music (Germany and Austria 18th and
19th centuries)
Leopold Mozart
Friedrich Wilhelm Zachow
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
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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 Medicis 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.
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Physics and Molecular Biology (20th century)
Robert Oppenheimer (1904-1967)
Goetingen and Munich physics
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-)
Niels Bohr (1885-1962)
Erwin Schroedinger (1887-1961)
Aage Bohr (1922-)
William Lawrence Bragg (1890-1971)
Ernest Rutherford (1871-1937)
J. J. Thomson (1856-1940)
William Henry Bragg (1862-1942)
Cambridge physics
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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.
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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 todays
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.
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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 UNESCOs 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 todays Florence have among
them the same concentration of Leonardos and
Michelangelos the fact that they are not
appearing is a serious condemnation of our
education. If we want more Leonardos we need to
expose them, as early as possible, to the
Verrochios of our time however we improve our
schools their teachers will never be of this
caliber. The new research and learning incubators
wont 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.