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1 Introduction: The Nature of Biophysics
of conceptual models through careful observation; and the simple realization that
we are capable of successfully expressing natural behavior in logical form.
Amazingly, our minds have proven of sufficient intellect to unravel some logic
behind Nature, at least on her surface. This includes models describing the structure
of the whole Universe as well as being able to predict observations at particle
separations down to much smaller than a proton diameter.
In observing the natural world, we find it possible to diminish external influences
onto certain ‘localizable systems’. Natural processes appear isolatable in space
and reproducible in time. It therefore becomes possible to study systems under
controlled conditions. If the behavior of such systems depends predominantly on
only changes in a few observables, those systems are said to be simple. The
motion of two or three point-like masses under gravity is relatively simple, but
so is the macroscopic behavior of 10 23 particles in an ideal gas if that gas is near
thermodynamic equilibrium, for then the intrinsic macroscopic properties of the gas
depend simply on its density, specific heat, temperature, and pressure.
Of the exact sciences, ‘classical mechanics’ was successful over 300 years ago
because it could be applied to simple isolatable systems, such as planetary systems.
The theory of mechanics given to us by Isaac Newton in 1687 is still used by NASA
to plot the motion of spacecraft. The phenomenal success of classical mechanics is
still a source of wonder, and a stimulant to the development of other sciences. Its
descendant, quantum mechanics, is capable at once of accurately tracking planets,
baseballs, molecules, and electrons within a theory built on just a few logical
statements. (NASA does not use quantum theory to plot spacecraft motion because
Newton’s theory is a very good approximation for objects much more massive than
molecules, and moving much slower than light speed, and because Newton’s theory
is much simpler to handle than quantum theory.)
A distinction must be made between the number of independent observables
within a system and the complexity of its ramifications. As Henri Poincaré
recognized in the nineteenth century, simple mechanical systems can show chaotic
behavior, manifest in how small differences in the initial conditions can evolve
exponentially into large differences in the resultant paths of motion. Given the
finite resolution of our instruments, we are incapable of determining the longterm evolution of certain systems with the same precision as our knowledge of
their present state. Even so, definitive statements often can be made about the
probabilities of a class of future paths, and about their possible confinement.
A collection of interacting fundamental elements will be a simple system if
its dynamics can be followed by using only a few relationships between selected
system observables. If a large system (containing many elements, also called a
macrosystem) requires a large amount of information to specify its dynamics, it
is called a ‘disordered system’. Those systems whose long-time behavior becomes
intractable exponentially with time because of inevitable information loss are called
‘chaotic systems’. Those systems whose behavior depends on the development of
transformable substructures with evolved relationships between those substructures,
are said to be ‘complex systems’.
1 Introduction: The Nature of Biophysics
of conceptual models through careful observation; and the simple realization that
we are capable of successfully expressing natural behavior in logical form.
Amazingly, our minds have proven of sufficient intellect to unravel some logic
behind Nature, at least on her surface. This includes models describing the structure
of the whole Universe as well as being able to predict observations at particle
separations down to much smaller than a proton diameter.
In observing the natural world, we find it possible to diminish external influences
onto certain ‘localizable systems’. Natural processes appear isolatable in space
and reproducible in time. It therefore becomes possible to study systems under
controlled conditions. If the behavior of such systems depends predominantly on
only changes in a few observables, those systems are said to be simple. The
motion of two or three point-like masses under gravity is relatively simple, but
so is the macroscopic behavior of 10 23 particles in an ideal gas if that gas is near
thermodynamic equilibrium, for then the intrinsic macroscopic properties of the gas
depend simply on its density, specific heat, temperature, and pressure.
Of the exact sciences, ‘classical mechanics’ was successful over 300 years ago
because it could be applied to simple isolatable systems, such as planetary systems.
The theory of mechanics given to us by Isaac Newton in 1687 is still used by NASA
to plot the motion of spacecraft. The phenomenal success of classical mechanics is
still a source of wonder, and a stimulant to the development of other sciences. Its
descendant, quantum mechanics, is capable at once of accurately tracking planets,
baseballs, molecules, and electrons within a theory built on just a few logical
statements. (NASA does not use quantum theory to plot spacecraft motion because
Newton’s theory is a very good approximation for objects much more massive than
molecules, and moving much slower than light speed, and because Newton’s theory
is much simpler to handle than quantum theory.)
A distinction must be made between the number of independent observables
within a system and the complexity of its ramifications. As Henri Poincaré
recognized in the nineteenth century, simple mechanical systems can show chaotic
behavior, manifest in how small differences in the initial conditions can evolve
exponentially into large differences in the resultant paths of motion. Given the
finite resolution of our instruments, we are incapable of determining the longterm evolution of certain systems with the same precision as our knowledge of
their present state. Even so, definitive statements often can be made about the
probabilities of a class of future paths, and about their possible confinement.
A collection of interacting fundamental elements will be a simple system if
its dynamics can be followed by using only a few relationships between selected
system observables. If a large system (containing many elements, also called a
macrosystem) requires a large amount of information to specify its dynamics, it
is called a ‘disordered system’. Those systems whose long-time behavior becomes
intractable exponentially with time because of inevitable information loss are called
‘chaotic systems’. Those systems whose behavior depends on the development of
transformable substructures with evolved relationships between those substructures,
are said to be ‘complex systems’.