Book Review on Per Bak
By Erin Tomlinson
& Maree Vincent
Overview of Per Bak’s:
How Nature Works
• Per Bak puts forth the theory of how
complex systems work by describing many
complexity and criticality formations such
as fractal geometry, power laws,
equilibrium models, and general laws of
nature.
Continued:
• He discusses self-organization and its
criticality. This concept can be related to
the process of evolution and complex
systems. For example, how one’s nervous
system works in their own body. It can also
be related to the relationship in the
fluctuation of world economics.
Continued:
• Throughout this presentations, we will
discuss the many questions Per Bak
proposes to his readers.
Chapter one: Questions
Proposed
• Could a rock slide be a
complex system?
• Could this motion be
understood in terms of
their individual,
physical properties?
• One rock could, one
day, slip and fall or
even dislodge another
rock causing them to
slide. This rock slide
shows how nature
works in its selforganized state by
action and reaction.
Chapter One: Questions
• Is a complex system
man-made like the
sandpile analogy or
are they laws or
equations of physics?
• In terms of a manmade sandpile, a hand
drops grains of sand to
create a pile, which
results in an avalache
effect. The properties
of the entire pile that
came from the hand,
can be understood as a
holistic description.
Holistic Description:
• This describes that each individual grain
conforms to the rest of the grains in the pile,
resulting in the pile becoming one. Thus,
moving as one, hence the sandpile creates
an avalache.
The Laws and
Equations of Physics:
As Newton’s and Maxwell’s equations describe, the
laws of physics are, in fact, simple but nature, as a
whole, is complex.
Newton’s law, f=ma, according to the book, it simply
tells us that an object that is subjected to a force
responds by accelerating at a rate proportional to
that force. (I.e. an apple falling to the ground, a
planet orbiting the sun, and how galaxies are
attracted to one another by the force of gravity
Continued: The laws
and equations of physics:
Maxwell’s equations, according to the book,
describe the interactions between electrical
currents and magnetic fields. (I.e. how an
electric motor or dynamo works)
• Both of these laws deal with simple
mathematical equations but can be complex
within themselves resulting in complex
systems.
CHAPTER 3: The Sandpile
Paradigm
• What exactly does the
sandpile represent in
nature?
• The sandpile can be
related to the swinging
of a pendulum; the
pendulum, as Bak
explains, is an analogy
to how grains of sand
can pile up after time
and, at some point,
create an anvalache.
Chapter 3: Continued
• Sandpiles are a part of our everyday life
giving us many degrees of freedom. One
grain of sand landing on the pile represents
potential energy. When the grain topples,
this energy is transformed into kinetic
energy. When the grain comes to a rest, the
kinetic energy is transformed into heat in
the pile.
Continued:
• As the slope of the sandpile increases, the
steepness of the pile can help determine
when the avalache may occur. Like one
would expect, the steeper the slope, the
more likely the grain will topple over.
• The Stationary State is when the average
amount of sand and the average slope are
constant or equal to each other in time.
Continued:
When there are avalaches that span the whole
pile, it is called the self-organized Critical
State. There must always be
communication throughout the entire
system.
Continued:
• The sandpile mataphor has reach well beyond the
world of physicists thinking about complex
phenomena; it contains EVERYTHING
• According to Al Gore in Bak’s book, he states that
“the sandpile theory---self-organized criticality--is irresponsible as a metaphor; one can begin by
applying it to the developmental stages of human
life.” It is his new way of viewing the world.
Hope you enjoyed it!!!
The End