Dear LO,
"...the practice of Zen is not the true practice so long as it has an end
in view, and when it has no view in end it is awakening - the aimless,
self-sufficient life of the 'eternal now'". The Way of Zen
...He realizes, in his work as in his life, that he will always venture
into uncertainty (the place for imagination) as he creates. He revises his
creations constantly. He focuses on expressing his authenticity and lets
the invisible become visible, living out what Samuel Becket said, "I have
never in my life been on my way anywhere, but simply on my way." We live
and lead in a context of chaos, uncertainty, and multiple transitions and
we will be in this place for a long time. It's a perfect place for
artistry, creativity, and imagination. This is a state where artists can
convert anxiety to inspiration. Today's great leaders are artists at
heart.
Those who aspire to lead must face themselves honestly and must understand
that few know how to lead in this unique context of accelerated global
change. To be a leader requires a willingness to be a novice in learning
new leadership beliefs, skills, and actions. Self-examination and feedback
are required. This process is threatening and, at times, humiliating. It
cannot be avoided if people are to do the hard work of development
necessary to lead in today's leadership context. Artists are also
adventurers who take a personal journey with every creation. As they lead
change, they too are changed. To lead into the unknown requires a strong
and constant core identity. The industrial era was about external
journeys. The era we are moving into is mostly an inner journey of
conscious evolution. People weather the storms of internal and external
chaos by being clear about their purpose in life, their values, and their
vision for themselves and the organizations they lead. The leader's core
purpose and values remain constant and give the adventurer the courage and
commitment to go forward into uncertainty, learning along the way. Vision
can change as people proceed, as their horizons broaden, and as new
discoveries are made. People and organizations lacking a clear and
conscious core identity place themselves and their organizations at risk
in today's leadership context.
Artist leaders proceed into uncertainty with limited information and with
faith in their ability to learn and adjust as they proceed. - snip -You
can only proceed with faith and courage and learn as you travel. Mihaly
Csikszentmihalyi wrote of research into creativity. Art students who
approached the canvas without a clearly worked out image of the finished
product were significantly more successful (by the standards of the art
community) 18 years later than their peers who worked out the details of
the finished product beforehand. Great organizations, like great art,
emerge from a complex interplay of variables and choices influenced and
guided by the artist's wise and firm hand...
Bateson wrote, "It is to the Riddle of the Sphinx that I have devoted
fifty years of professional life as an anthropologist. It is of
first-class importance that our answer to the Riddle of the Sphinx should
be in step with how we conduct our civilisation, and this should in turn
be in step with the actual workings of living systems. A major difficulty
is that the answer to the Riddle of the Sphinx is partly a product of the
answers that we already have given to the riddle in its various forms.
Kurt Vonnegut gives us wary advice - that we should be careful what we
pretend because we become what we pretend. And something like that, some
sort of self-fulfilment occurs in all organisations and human cultures.
What people presume to be 'human' is what they will build in as premises
of their social arrangements, and what they build in is sure to be
learned, is sure to become a part of the character of those who
participate. And along with this self-validation of our answers, there
goes something still more serious - namely, that any answer which we
promote, as it becomes partly true through our promoting of it, becomes
partly irreversible. There is a lag in these affairs."
- Innocence & Experience. 1987 - p.178
The Nash Equilibrium
The theory constructs a notion of "equilibrium," to which the complex
chain of thinking about thinking could converge. Then the strategies of
all players would be mutually consistent in the sense that each would be
choosing his or her best response to the choices of the others. For such a
theory to be useful, the equilibrium it posits should exist.
Graphical Lineages of the Renaissance
Durer's Rhino
Albrecht Durer (1471-1528) is one of the giants of world art. Like
Leonardo da Vinci, he was an intensely curious man. Where Leonardo
invented, Durer observed. Although he became wealthy and famous for his
engravings, his interest in biology was quite literally the death of him;
journeying far from his native Nuremberg to see a stranded whale, he came
down with a fever from which he never fully recovered.
In 1515, he drew a rhinoceros. Unable to see the beast himself, he based
his drawing on a sketch and a verbal description. It is remarkably
accurate for a drawing-not-from-life. However, it does contain an error: a
small second horn set on the shoulder. His drawing was the archetype for a
long graphical lineage. Indeed, Clarke (1986) has an entire volume of over
200 pages devoted to cataloguing all the plagiarisms of Durer's image. The
copies of Durer are easily recognized because they repeat his mistake of
the phantom second horn. The science essayist David Quammen in
Boilerplate Rhino has partially rehabilitated Durer: it is now thought
that rhino observed by the artist's friend was an un-usual species, and
Durer's drawing is actually more accurate than had been previously
thought.
Rule-of-Thumb 5 (Aref's Rule) Never publish the same graph more than once.
Poincare's Pear
The shape of a rotating, self-gravitating mass of liquid has been the
subject of active research for a couple of centuries. Not only is this the
shape of stars, but also of solid bodies like the earth. Our planet is so
large that if its shape deviated more than a fraction of a percent from
that allowed to a same-sized mass of liquid, then gravity would crumble
the mountains and make the stone flow as a very viscous fluid until the
shape returned to the equilibrium shape.
One remarkable fact is that as the rotation rate increases, the obvious
shape, which is an ellipsoid of revolution, is no longer the only possible
shape or even the stable shape. Instead, there is a branching or
"bifurcation" in which a triaxial ellipsoidal with three unequal axes
becomes the stable shape. At higher rotation rates, still more complex
shapes are possible. One topic of intense interest: if the earth was born
as a rapidly spinning mass, it might have become unstable and fissioned
into the earth-moon system. The only way to test this hypothesis was to
trace the different branches of equilibrium shapes. Bernard Riemann, Henri
Poincare and Sir George Darwin (son of Charles Darwin) were among the
nineteenth century luminaries who pursued the 'figures-of-equilibrium'
problem.
One advantage that scientists enjoyed a century ago was that instruction
in drawing was an integral part of education. (In modern America, students
receive "art" instruction at all levels from kindergarden through junior
high school, but most receive no art instruction in high school.) For
Henri Poincare, the drawback was that to pass his school exams and
continue to college, he had to gain a passing score in drawing as well as
history, literature and mathematics.
A person who can write or draw with both hands is usually called
"ambidextrous", meaning loosely "both-like-right-hand". Poincare could
wield a pen with either hand, but it would perhaps be more accurate to
label him as "ambisinistral". He was totally incapable of producing a
recognizable drawing with either hand. His school instructors passed him
anyway, though he should have received a failing grade, because his other
work was so brilliant. In 1885, Poincare made one of his most influential
discoveries: at a certain non-dimensional rotation rate, the Jacobi
triaxial ellipsoids bifurcated to a branch of unsymmetrical figures.
Unfortunately, Poincare translated his formulas into a cross-sectional
drawing. His illustration bulged unsymmetrically like a pear, so his new
branch became known as "Poincare's pear-shaped figure of equilibrium".
This caught the astrophysical imagination so much that a new term was
coined for this family of shapes: "piriform", which means "pear-shaped" in
Latin. Poincare showed that more complicated shapes would bifurcate at
other parameter values. He conjectured, "that the bifurcation of the
pear-shaped body leads onward stably and continuously to a planet attended
by a satellite, the bifurcation into the fourth zonal harmonic probably
leads unstably to a planet with a satellite on each side, that into the
fifth harmonics to a planet with two satellites on one and one on the
other and so on". Sir George Darwin went on to conjecture himself that the
pear-shaped figure eventually fissioned into two at a sufficiently high
rotation rate, thus generating double stars and the Earth-Moon double
planet.
Chandrasekhar (1969) takes up the story: "The grand mental panorama that
was thus created was so intoxicating that those who followed Poincare were
not to recover from its pursuit. In any event, Darwin, Liapounoff, and
Jeans spent years of effort towards the substantiation of these
conjectures; and so single-minded was the pursuit that one did not even
linger to investigate the stability of the Maclaurin spheroids and the
Jacobi ellipsoids from a direct analysis of normal modes. Finally, in 1924
Cartan established that the Jacobi ellipsoid becomes unstable at its first
point of bifurcation ... And at this point the subject went quietly into a
coma."
One moral of this story: don't become intoxicated with your own
cleverness. Good graphics cannot redeem bad thinking. In this case,
however, bad graphics seem to have contributed to the intoxication.
Although Poincare's image was likely engraved by a professional artist,
the engraver worked from a preliminary sketch by Poincare, yes, the same
ambisinistral lad who nearly flunked out of school because he couldn't
draw.
Sir George Darwin redrew the piriform figures twenty years later (Fig.
17.7). As he dryly remarked, "Comparison with M. Poincare's sketch shows
that the figure is considerably longer than he supposed."
Why did the error matter? Poincare's crime of visualization greatly
exaggerated the bulge, and therefore implied that the piriform shape was
much closer to fission than it actually was.
End ;-)
Love,
Andrew
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