leonardo
da vinci and chaos theory? : : ian
clothier
fluid
in motion
A
late afternoon soft breeze directly through an unpaned window does little to relieve
the perplexing problem Leonardo da Vinci has on his hands. The year is 1513; da
Vinci is now 61, close to the culmination of forty years of research. All through
his life, he had been studying water; such studies are the backbone of his research.
By the time he
had arrived in Rome with the aim of working for the new Pope Leo X, Leonardo had
made many detailed studies of fluid in motion, analysed the destructive power
of vortexes created by water breaks on the river Arno, and provided plans for
the diversion of the same river, along the route the modern highway goes today.
In 1510 he completed
the dissection of 'the centenarian', considerably advancing his knowledge of anatomy.
He was yet to produce the Deluge Drawings, which bear awesome testament to his
understanding of turbulence and the terrifying consequences for humanity.
Ever pursuing the
unraveling of universal forces as expressed in humans and nature, we find him,
in studies of the vortex motion of the blood in the heart posing a question
he cannot answer: when blood hits a wall, how are the resultant waves formed?
"It is doubtful if the percussion made by the impetus… divides the impetus into
two parts, one of which rolls upwards and the other turns backwards. Such doubts
are subtle and difficult to prove and clarify," he wrote in the notes accompanying
the study. When fluid goes from stable flow in a straight line to being turbulent,
what exactly happens?
the
onset of turbulence
464 years later, Albert Libchaber, working at the
Ecole Normale Superieure in Paris, sat hunched over a computer read out, wondering
what the seismic-like spikes on the graph paper he was examining, really meant.
Initially, the full consequences of his experiment were not apparent.
Libchaber was a unique combination
of 20th century physicist and hands on, nuts and bolts experimenter. He enlisted
the help of an engineer, Maureer. Together they would tie down turbulence, encasing
it in an experiment so elegant, some would say Libchaber cheated nature, by freezing
a vortex into just one then two rolls at a time.
To
solve the question of the onset of turbulence, Libchaber and Maureer created a
box about the size of a lemon pip. As if bearing a magic talisman, the scientist
would sometimes carry the whole apparatus around with him in his pocket, encased
in a matchbox. The elegant thing about this pip-sized box was the scale of it's
insides, in particular the relationship between size and material, and their relation
to temperature. In liquid helium a temperature difference of a thousandth of a
degree is created, between a copper bottom and a sapphire top plate.
The Frenchmen's tiny box
was perfectly machined to register the onset of turbulence. Micro machining was
needed to solve da Vinci's question, and no calming breeze could ever provide
respite. "Was anything ever done?" the lamentation of the frustrated researcher,
is echoed time and again in the margins of Leonardo's drawing books.
Although Libchaber was probably
unaware of da Vinci's questioning, he confirmed that at the onset of turbulence,
fluid does indeed split in two - 'the impetus is divided in two'- in Leonardo's
words. From there, it splits in two again, a process cascading in smaller and
smaller scales the longer the experiment is run.
universality
Libchaber certainly didn't know it at the time, but he had provided direct experimental
evidence for what previously was theory. Theoretical physicist Mitchell Feigenbaum
predicted a precise pattern of splitting in two or bifurcating (branching). Predictive
and precise was the theory: repetitive scaling bifurcations converging around
a particular number - 4.6692016090.
In
this way, live experimental conditions confirmed theoretical physics. The connection
point is maps (the specialist's all inclusive term for a wide range of images
- diagrams, graphs, computer plots, computer model print outs, photographs, actual
maps). In some imagery the scaling bifurcations can be shown to converge - and
these same patterns could be attained whether the starting point was reality or
just numbers. Universality. The patterns are deeply nested within the associated
maps, but they are there nonetheless.
No
doubt this universality was different to the one held by da Vinci. After all,
his assumptions were clearly different. But just as it took science until 1977
to answer da Vinci's question, so too has it taken science that long to come full
circle and again see the basis for the connection between all things.
